two-dimensional carrier profiling of semiconductor ...

KATHOLIEKE UNIVERSITEIT LEUVEN

FACULTEIT TOEGEPASTE WETENSCHAPPEN DEPARTEMENT ELEKTROTECHNIEK AFDELING ESAT - DIVISIE INSYS Kardinaal Mercierlaan 94 - B-3001 Leuven (Heverlee)

TWO-DIMENSIONAL CARRIER PROFILING OF SEMICONDUCTOR STRUCTURES WITH NANOMETER RESOLUTION

Promotoren: Prof. Dr. ir. W. VANDERVORST Prof. Dr. L. HELLEMANS

Proefschrift voorgedragen tot het behalen van het doctoraat in de Toegepaste Wetenschappen door

ir. Peter DE WOLF

Mei 1998

imec

In samenwerking met Interuniversitair Micro-Elektronica Centrum Kapeldreef 75 B-3001 Leuven (Heverlee)

KATHOLIEKE UNIVERSITEIT LEUVEN

FACULTEIT TOEGEPASTE WETENSCHAPPEN DEPARTEMENT ELEKTROTECHNIEK AFDELING ESAT - DIVISIE INSYS Kardinaal Mercierlaan 94 - B-3001 Leuven (Heverlee)

TWO-DIMENSIONAL CARRIER PROFILING OF SEMICONDUCTOR STRUCTURES WITH NANOMETER RESOLUTION Jury: Prof. Dr. ir. E. Aernoudt, voorzitter Prof. Dr. ir. W. Vandervorst, promotor Prof. Dr. L. Hellemans, promotor Prof. Dr. ir. K. De Meyer Prof C. Hill, Univ. of Manchester Prof. Dr. ir. H. Maes Prof. Dr. ir. R. Puers Lic. T. Clarysse

Proefschrift voorgedragen tot het behalen van het doctoraat in de Toegepaste Wetenschappen door

ir. Peter DE WOLF

Mei 1998 U.D.C. nummer: 6210.3.049.77 +538.9

imec

In samenwerking met Interuniversitair Micro-Elektronica Centrum Kapeldreef 75 B-3001 Leuven (Heverlee)

c Katholieke Universiteit Leuven - Faculteit Toegepaste Wetenschappen Arenbergkasteel, B-3001 Heverlee (Belgium)

Alle rechten voorbehouden. Niets uit deze uitgave mag worden vermenigvuldigd en/of openbaar gemaakt worden door middel van druk, fotocopie, micro lm, elektronisch of op welke andere wijze zonder voorafgaande schriftelijke toestemming van de uitgever. All rights reserved. No part of this publication may be reproduced in any form by print, photoprint, micro lm or any other means without written permission from the publisher. wettelijk depotnummer: D/1998/7515/25 ISBN: 90-5682-124-5

Acknowledgments The realization of this work would not have been possible without the help, encouragements and assistance of many people. In the rst place, I would like to thank my promoters Prof. Wilfried Vandervorst and Prof. Louis Hellemans. Numerous stimulating discussions and advice from them form a major contribution to this work. I am also grateful to Prof. Roger Van Overstraeten, president of IMEC, for the possibilities he has oered me in carrying out this work. I am deeply indebted to friends and co-workers at IMEC, without whose interest and support over the years this book would not have been written: Bert Brijs, Trudo Clarysse, Jeroen Deleu, Thomas Hantschel, Johan Snauwaert, Robert Stephenson, and Thomas Trenkler. A special word of thank to Johan Snauwaert, who introduced me to the fascinating eld of scanning probe microscopy and who was always prepared to help me with the speci c problems associated to this eld. Also a special word of thank to Trudo Clarysse, who is one of the happy few to know everything about the spreading resistance method, and whose help and critical discussions formed a major contribution to this work. I am grateful to the people who have provided me with additional data: Hugo Bender, Serge Biesemans, Ingrid De Wolf, Kristel Drijbooms, Luc Geenen, Je McMurray, Danielle Vanhaeren, Patricia Vanmarcke, and to the people who provided instrumentation or materials used in the experiments: Goncal Badenes, Ivan Callant, Matty Caymax, Ludo Deferm, Albert Debie, Andy Erickson, Michael Geva, Stephan Kubicek, Mike Kump, Philippe Niedermann, and Rita Rooyackers. I am indebted to the Flemish IWT for my fellowship from 1994 to 1997. Finally, I wish to thank my parents for supporting me all these years. Peter De Wolf Mei 1998

i

Beknopte samenvatting In dit werk wordt een nieuwe techniek voorgesteld en ontwikkeld voor kwantitatieve elektrische ladingsdragerpro lering met nanometer resolutie: scanning spreading resistance microscopy (SSRM). Deze techniek heeft de mogelijkheid om zowel een- als twee-dimensionale metingen uit te voeren op willekeurige halfgeleider structuren. Dit wordt bereikt door een atomaire krachten microscoop (AFM) uit te rusten met een geleidende probe die lokale spreidingsweerstandsmetingen uitvoert terwijl de probe over een dwarse doorsnede van het monster wordt bewogen. De gemeten weerstandswaarden kunnen getransformeerd worden in een kwantitatief ladingsdragerpro el met behulp van een set calibratie curven en een algoritme dat corrigeert voor stroomspreidings eecten. De extreem hoge ruimtelijke resolutie en de preciese krachtcontrole van de AFM worden gecombineerd met de eigenschappen van de standaard spreidingsweerstands techniek (SRP): groot dynamisch bereik (1014 , 1020 atomen/cm3 ), grote gevoeligheid, toepasbaar op willekeurige structuren, en eenvoudig kwanti ceerbaar. De SSRM techniek kan gebruikt worden voor twee-dimensionale, kwantitatieve ladingsdragerpro lering van halfgeleider structuren met 15{20 nm resolutie.

Abstract In this work a new method is presented and developed for quantitative two-dimensional carrier pro ling: scanning spreading resistance microscopy (SSRM). The technique can be applied for one and two-dimensional carrier pro ling of arbitrary semiconductor devices. An atomic force microscope (AFM) is equipped with a hard conductive probe which is used to measure local spreading resistance values as the probe is moved across a cross section made through the structure under study while in physical contact. The measured resistance values can be transformed into a quantitative carrier pro le using a set of calibration curves and a data conversion algorithm which corrects for current spreading eects. The extreme high resolution and the precise force control of the AFM is combined with the attractive features of the conventional spreading resistance pro ling (SRP) technique. The SSRM technique has a spatial resolution of 15{20 nm, a dynamic range of 1014 , 1020 atoms/cm2 , a high sensitivity, and is applicable to two-dimensional carrier pro ling of arbitrary semiconductor device structures.

Contents Abstract List of symbols List of abbreviations Summary in Dutch 1 General introduction

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Goal of the presented work . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Contents and outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 2D dopant pro ling: state of the art

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 1D-based 2D techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 2D-SIMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Imaging SIMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2D-SIMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tomography SIMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 2D-SRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Microwave surface impedance pro lometry . . . . . . . . . . . . . . . 2.3 Scanning-Probe Microscopy (SPM) techniques . . . . . . . . . . . . . . . . . 2.3.1 Scanning Tunneling Microscopy (STM) . . . . . . . . . . . . . . . . Dopant atom counting . . . . . . . . . . . . . . . . . . . . . . . . . . Scanning - and Current Imaging Tunneling Spectroscopy (STS/CITS) Scanning Tunneling Potentiometry (STP) . . . . . . . . . . . . . . . 2.3.2 Dopant selective etching, staining or oxidizing . . . . . . . . . . . . . Dopant selective etching or staining . . . . . . . . . . . . . . . . . . Oxidizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Scanning Capacitance Microscopy (SCM) . . . . . . . . . . . . . . . Direct-capacitance mode . . . . . . . . . . . . . . . . . . . . . . . . . Dierential-capacitance mode . . . . . . . . . . . . . . . . . . . . . . Closed-loop mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Kelvin Probe force Microscopy (KPM) . . . . . . . . . . . . . . . . iii

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CONTENTS

iv 2.3.5 Scanning Resistance Microscopy (SRM) . . . . . . . . . . 2.3.6 Scanning Surface Harmonic Microscopy (SSHM) . . . . . 2.3.7 Scanning force surface Photovoltage Microscopy (SPVM) 2.4 Electron Microscopy (EM) techniques . . . . . . . . . . . . . . . 2.4.1 Field-Emission SEM (FE-SEM) . . . . . . . . . . . . . . . 2.4.2 Combined TEM/FIB . . . . . . . . . . . . . . . . . . . . . 2.4.3 Electron holography . . . . . . . . . . . . . . . . . . . . . 2.4.4 Electron Beam Induced Current (EBIC) . . . . . . . . . . 2.5 Inverse modeling techniques . . . . . . . . . . . . . . . . . . . . . 2.6 Conclusions: comparison of 2D pro ling methods . . . . . . . . .

3 Instrumentation & measurement procedure

3.1 Introduction: the SSRM concept . . . . . . . . . . . . . . 3.2 The Atomic Force Microscope . . . . . . . . . . . . . . . 3.3 Resistance measurement unit . . . . . . . . . . . . . . . . 3.3.1 Linear voltage or current ampli er . . . . . . . . . 3.3.2 Logarithmic current ampli er . . . . . . . . . . . . 3.4 Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Standard AFM probes . . . . . . . . . . . . . . . . 3.4.2 Metal and metal-coated probes . . . . . . . . . . . Metal probes . . . . . . . . . . . . . . . . . . . . . Metal-coated probes . . . . . . . . . . . . . . . . . Full-metal probes . . . . . . . . . . . . . . . . . . . 3.4.3 Diamond and diamond-coated probes . . . . . . . Bulk diamond probes . . . . . . . . . . . . . . . . CVD diamond-coated probes . . . . . . . . . . . . Diamond cantilevers with integrated tip . . . . . . Conclusion: the ideal SSRM probe . . . . . . . . . 3.4.4 Dual probe . . . . . . . . . . . . . . . . . . . . . . 3.5 Sample preparation . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Cross section preparation . . . . . . . . . . . . . . Focused Ion Beam sample preparation . . . . . . . 3.5.2 Back contact . . . . . . . . . . . . . . . . . . . . . Quality control of the back contact . . . . . . . . . 3.5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . 3.6 Probe Movement . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 First contact & determination of the applied force First contact . . . . . . . . . . . . . . . . . . . . . What is a force curve ? . . . . . . . . . . . . . . . How is the applied force determined ? . . . . . . . 3.6.2 From one point to the next . . . . . . . . . . . . . Contact mode . . . . . . . . . . . . . . . . . . . . . Tapping mode . . . . . . . . . . . . . . . . . . . . Stepping mode . . . . . . . . . . . . . . . . . . . . 3.7 Imaging artefacts . . . . . . . . . . . . . . . . . . . . . . .

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CONTENTS 3.7.1 Piezo non-linearities . . . . . 3.7.2 Friction . . . . . . . . . . . . 3.7.3 Double tip & tip-convolution 3.7.4 Sample wear . . . . . . . . . 3.8 Conclusions . . . . . . . . . . . . . .

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4.1 Mechanical . . . . . . . . . . . . . . . . . . . 4.1.1 Elastic regime . . . . . . . . . . . . . . 4.1.2 Elasto-plastic and fully plastic regimes 4.1.3 Diamond on silicon . . . . . . . . . . 4.1.4 Mechanical side eects . . . . . . . . Sliding contact . . . . . . . . . . . . . Dopant eects . . . . . . . . . . . . . Environmental and surface eects . . Discussion . . . . . . . . . . . . . . . . 4.2 Electrical . . . . . . . . . . . . . . . . . . . . 4.2.1 Zero pressure . . . . . . . . . . . . . . 4.2.2 Under pressure . . . . . . . . . . . . . Force dependence . . . . . . . . . . . . Probe penetration . . . . . . . . . . . Resistivity dependence . . . . . . . . . Calibration curve . . . . . . . . . . . 4.3 Electro-mechanical contact model . . . . . . 4.4 Side eects . . . . . . . . . . . . . . . . . . . 4.4.1 Sample illumination . . . . . . . . . . 4.4.2 Time-dependence . . . . . . . . . . . . 4.4.3 Unexpected piezo behavior . . . . . . 4.4.4 Spreading Impedance Probe . . . . . . 4.5 Conclusions . . . . . . . . . . . . . . . . . . .

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4 Point contact characteristics

5 Pro ling characteristics

5.1 Dynamic range and sensitivity . . . . 5.2 Concentration resolution . . . . . . . . 5.3 Reproducibility and repeatability . . . 5.3.1 Repeatability . . . . . . . . . . 5.3.2 Reproducibility . . . . . . . . . 5.4 Spatial resolution and spatial accuracy 5.4.1 Buried SiO2 . . . . . . . . . . . 5.4.2 Abrupt doping steps . . . . . . 5.4.3 Spatial accuracy . . . . . . . . 5.5 Quanti cation procedure . . . . . . . 5.5.1 Introduction . . . . . . . . . . 5.5.2 Problem de nition . . . . . . . 5.5.3 One-dimensional . . . . . . . .

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CONTENTS

vi Current spreading simulation examples . forward problem . . . . . . . . . . . . . inverse problem . . . . . . . . . . . . . . 5.5.4 Two-dimensional . . . . . . . . . . . . . 5.5.5 The NSRP software package . . . . . . . 5.6 Junction-isolated pro les . . . . . . . . . . . . . 5.7 Conclusions . . . . . . . . . . . . . . . . . . . .

6 Applications and intercomparison 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8

Introduction . . . . . . . . . . . . . . . . . . . Case study I: 2D diusions and implantations Case study II: NMOS and PMOS transistors Case study III: round robin . . . . . . . . . . Case study IV: asymmetrical implantation . . Case study V: vertical DMOS transistor . . . Case study VI: InP laser structures . . . . . . Conclusions . . . . . . . . . . . . . . . . . . .

7 Related applications

7.1 On-bevel high-resolution measurements . . 7.1.1 Introduction . . . . . . . . . . . . . 7.1.2 One-dimensional . . . . . . . . . . . Measurement procedure . . . . . . . Data treatment . . . . . . . . . . . . Comparison with conventional SRP 7.1.3 Two-dimensional . . . . . . . . . . . 7.1.4 Conclusions . . . . . . . . . . . . . . 7.2 Nanopotentiometry . . . . . . . . . . . . . 7.2.1 Introduction . . . . . . . . . . . . . 7.2.2 Instrumentation . . . . . . . . . . . 7.2.3 Discussion . . . . . . . . . . . . . . . What is measured ? . . . . . . . . . 7.2.4 Sample preparation . . . . . . . . . 7.2.5 Force calibration . . . . . . . . . . . 7.2.6 Examples . . . . . . . . . . . . . . . 7.2.7 Conclusions . . . . . . . . . . . . . .

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8 General conclusions

199

Bibliography Scienti c contributions Curriculum vitae

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8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 8.2 Future work and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

List of symbols Below, a comprehensive list of the symbols used in this text along with their most appropriate unit is given. symbol

description

unit

a E F k l R R t tox T Y Va,b Vz w n p

contact radius Young's elasticity modulus normal force cantilever spring constant cantilever length tip radius resistance cantilever thickness oxide thickness temperature yield stress photo-detector output voltage piezo voltage cantilever width indentation depth friction coecient electron mobility hole mobility Poisson's ratio resistivity stress

nm GPa N N/m m nm

m nm K GPa V V m nm { cm2 /Vs cm2 /Vs {

cm GPa

vii

List of abbreviations The most important abbreviations used in this text are listed below. ADC AFM CCM CITS CMOS CVD C-V EBIC EFM EM FE FIB FPP IC I-V KPM MBE MIS MOS MS NDP nano-SRP RTA SCM SEM SIMS SMM SPM SPVM SRM SRP SSHM SSRM

Analog to Digital Convertor Atomic Force Microscopy Contact Current Microscopy Current Imaging Tunneling Spectroscopy Complementary Metal-Oxide-Semiconductor Chemical Vapor Deposition capacitance-voltage Electron Beam Induced Current Electric Force Microscopy Electron Microscopy Field Emission Focused Ion Beam Four Point Probe Integrated Circuit current-voltage Kelvin Probe Force Microscopy Molecular Beam Epitaxy Metal-Insulator-Semiconductor Metal-Oxide-Semiconductor Metal-Semiconductor Neutron Depth Pro ling nanometer Spreading Resistance Pro ling Rapid Thermal Anneal Scanning Capacitance Microscopy Scanning Electron Microscopy Secondary Ion Mass Spectrometry Scanning Maxwell-Stress Microscopy Scanning Probe Microscopy Surface Photovoltage Microscopy Scanning Resistance Microscopy Spreading Resistance Pro ling Scanning Surface Harmonic Microscopy Scanning Spreading Resistance Microscopy ix

x STM STP STS TCAD TEM UHV ULSI

Scanning Tunneling Microscopy Scanning Tunneling Potentiometry Scanning Tunneling Spectroscopy Technology Computer Aided Design Transmission Electron Microscopy Ultra High Vacuum Ultra Large Scale Integration

Chapter 1

General introduction The objective of this thesis is to develop a new electrical carrier pro ling tool with nanometer resolution (in two dimensions) with application to deep submicron process technologies. The basis of this tool is the high spatial resolution of the Atomic Force Microscope (AFM) expanded with additional features to sample carrier distributions in such devices.

1.1 Motivation The development of deep submicron CMOS process technologies and miniature device structures is a challenging task with exciting perspectives. The successful implementation of such a submicron process demands high precision processing steps in combination with good quality control. Therefore, characterization tools are needed which are able to provide quantitative information on the same small scale. The 1997 US Roadmap for Semiconductors from the Semiconductor Industry Association (SIA) [ROADMAP 97] de ned the needs for nanometer-scale measurements in the semiconductor industry for the next decade. These needs appear in three areas of the manufacturing process: critical dimension metrology, materials processing, and electrical characterization. When facing these requirements, it is clear that the ongoing down-scaling of the semiconductor device dimensions has not been accompanied by an equal progress in the measurement techniques used to characterize those devices. Focusing on electrical characteristics, no good technique is available which provides feedback on the processing steps used to implement the two-dimensional (2D) distribution of dopant atoms (or electrically active carriers) inside the semiconductor structures. The role of computer modeling and simulation of devices and processing steps also has increased the need for these measurements. As design rules head into the sub-micrometer regime, the trend towards using ultra-shallow, ultra-high dopant distributions in device structures has led to the integration of process and device simulation (or technology computeraided design (TCAD)) approaches into the manufacturing cycle. Processing demands for sub-0.25 m technologies are such that optimization of the chip design through TCAD simulations would be cheaper than actually making test device structures. These simulation packages must rst be calibrated and ne-tuned against reliable, well-understood test 1

2

CHAPTER 1. GENERAL INTRODUCTION

structures before they can be used with con dence. There are two approaches to veri cation and calibration of TCAD simulators. One is calibration based on electrical test data from pilot line fabrication studies using exactly the same process tools that will be used in full scale manufacturing [Bartelink 94]. This method allows direct modeling of processes using a tool-dependent simulation. Inverse modeling of the electrical data may provide 2D dopant pro les [Ouwerling 90]. A second approach is direct measurement of the 2D dopant pro le in a test structure or the actual structure. The calibration coecients of the simulator model are then tuned such that the simulated and measured two-dimensional pro les correspond. Based on these observations it is clear that the availability of adequate metrology for ULSI technology is an important issue and eorts should be directed towards making these available for routine applications. The rst step is to de ne the ultimate goal of the pro ling measurement. Present consensus indicates that the measurement method should be able to characterize actual transistor structures. This goal rules out use of methods that require large test structures or that require many extra processing steps. The applications mentioned above, simulator calibration for 2D dopant pro les and implant process control, impose requirements which are a projection of the device developments mentioned in the SIA roadmap [ROADMAP 97]. For example, Duane [Duane 95] indicated that a 10% change in channel dopant concentration of 0.25 m technology MOS transistor alters the transistor leakage current by a factor as large as 2 and reduces the threshold voltage by more than 30 mV. Based on these considerations, the resulting analysis requirements for dopant concentration accuracy and spatial resolution for 0.25 and 0.18 m device technology can be derived (table 1.1). Clearly, there is a need for sub-10 nm resolution, combined with sucient sensitivity (down to the 1015 atoms/cm3 level) and high quanti cation accuracy over a dynamic range from 1015 to 1021 atoms/cm3 . Table 1.1: Requirements for 2D dopant pro ling imposed by the needs in semiconductor device optimization and TCAD simulator calibration.

Design rule 0.25 m 0.18 m Accuracy of dopant concentration 10% 5% Measurement repeatability 5% 5% Spatial resolution 20 nm 10 nm 3 15 20 Dopant concentration range (atoms/cm ) 10 -10 1015 -1021

1.2 Goal of the presented work It is the overall objective of this work to develop a new carrier pro ling method with nanometer resolution in the vertical and lateral direction and which is directly applicable

1.2. GOAL OF THE PRESENTED WORK

3

to real device structures. The requirements for this technique are such that it should:

have nanometer spatial resolution in two dimensions be applicable to real device structures, not requiring special test structures be fully quantitative over a dynamic range of 1015 to 1021 atoms/cm3 It is evident that these goals can only be achieved when a nanometer sized probe is used on the cross section of a device. This work starts from the observation that the Spreading Resistance Pro ling (SRP) technique has a nearly unlimited dynamic range (1013 , 1021 atoms/cm3 ), a high sensitivity, and provides quantitative information due to the direct relation between the measured resistance values and the local sample resistivity (Rspread = 2a , where is the sample resistivity, and a the contact radius). However, the application of SRP is limited to one-dimensional pro les. This limitation is closely related to the need for beveling, caused by the large probes which are used (probe radius: 2{5 m). If the probe could be replaced by a much ner probe, the need for a bevel would disappear and a measurement on the cross section could be made. This is illustrated in gure 1.1. The obvious way to produce such a contact is to use a conducting Atomic Force Microscope (AFM) tip. In addition to the well de ned contact geometry, the use of an AFM has the inherent bene t that the applied load can be controlled very precisely through its feedback mechanism and that very small steps can be made using its piezo-system. Using this approach, the attractive features of SRP (i.e. dynamic range, sensitivity, and the capability to pro le complex structures) are kept, while allowing for high-resolution twodimensional measurements. Due to its similarity to conventional SRP and scanning probe microscopy this new method is entitled nano-SRP or Scanning Spreading Resistance Microscopy (SSRM). The depth and lateral resolution are equal, and will be determined by the probe size and the step control. An interesting feature is that in addition to using the AFM tip as a spreading resistance pro ler, it still provides topographical information through its normal way of operating. This implies that the position of the surface and the presence of mask material and its shape can be detected, identifying the registration of the carrier pro le with respect to the mask edge. The experimental development of this concept forms the rst main task. The use of this nano-tool is however so dierent with respect to the conventional SRP procedures that the normal data interpretation is no longer valid and a new algorithm and software must be developed for the data interpretation. Indeed, one has to go from a purely one-dimensional approach to a full 3D-calculation of the current distribution to establish the relation between measured resistance and carrier concentration. Therefore, the major goals of this work are:

The development of an SSRM technique, including the instrumentation and measure-

ment procedure. The characterization of SSRM on homogeneously doped samples and special test structures to get insight in the physical processes occuring during the measurements

CHAPTER 1. GENERAL INTRODUCTION

4 (a)

(b) x

bevel

original top surface y

original top surface

z

α bevel angle

cross section back contact

Figure 1.1: Schematic diagram of the conventional SRP (a) and SSRM (b) methods. In SRP the resistance is measured between two probes who step over a beveled surface. In SSRM the resistance is measured between a large contact and a probe which is moved across a cross-sectional surface.

and to be able to de ne the possibilities and limitations of the technique for twodimensional carrier pro ling.

The development of a data quanti cation procedure which includes a calibration procedure and a correction for current spreading eects.

The intercomparison of the SSRM technique with other one- and two-dimensional carrier pro ling methods.

1.3 Contents and outline This book is divided into eight chapters. In chapter 2 an overview of the state-of-the-art of two-dimensional carrier and dopant pro ling techniques is presented. For each technique, the main limitations and pro ling possibilities are listed. The techniques are compared in terms of resolution, dynamic range, sensitivity, repeatability, and quanti cation possibilities. The instrumentation needed for SSRM operation is presented in chapter 3. The modi cations which are needed to a standard AFM instrument and to the AFM probes are discussed. The complete measurement procedure is also presented. First, a detailed sample preparation scheme is discussed including the cross section preparation and formation of the back contact. Second, it is investigated how the probe can be moved over the sample and how the resistance measurement can be performed. Possible artefacts are listed. In chapter 4, the correlation between the resistance values and the substrate resistivity for homogeneous samples is studied. The in uence of the applied force and sample surface quality is studied using current-voltage measurements. An electro-mechanical contact model is presented which includes both electrical eects (bias voltage, sample resistivity, contact resistance) and mechanical eects (elastic and plastic deformation, friction). The model provides insight in the physical processes occuring during the SSRM measurements.

1.3. CONTENTS AND OUTLINE

5

The speci cations of the SSRM technique as a carrier pro ling tool, in particular its resolution, dynamic range, reproducibility and accuracy, are discussed in chapter 5. The quanti cation procedure to transform the measured resistance values into the corresponding carrier concentrations is also presented in this chapter. Two-dimensional examples of the technique are presented in chapter 6. Test samples are shallow implants, MBE-grown material, fully processed MOS devices, etc. An intercomparison with other one- and two-dimensional carrier pro ling techniques like SIMS, SRP, 2D-SRP, SCM and dopant selective etching is given. The junction position as well as the complete pro le determination is evaluated. In chapter 7, two other applications related to and based on SSRM are presented. In the rst application, the SSRM technique is applied on beveled surfaces to characterize one as well as two-dimensional carrier pro les with high resolution. The attention is focused on ultra-shallow implantation pro les. In the second application, quantitative imaging of the potential distribution inside working devices is performed. This technique is named nanopotentiometry. The principle of operation and some simple examples proving this concept are presented. Finally, the major results are summarized in chapter 8.

Chapter 2

2D dopant pro ling: state of the art 2.1 Introduction Until today, more than 20 dierent methods have been developed for two-dimensional carrier or dopant pro ling. Each of these techniques is brie y described in this chapter. The techniques can be divided into four categories: two-dimensional techniques which are based on a widely used one-dimensional technique, scanning-probe microscopy based techniques, electron microscopy based techniques, and inverse modeling techniques. Some of these methods provide the dopant concentration pro le (the chemical pro le) while other methods provide the charge carrier concentration pro le (the electrical pro le). In this chapter, the operation principle and the most important features and limitations of each technique are presented.

2.2 1D-based 2D techniques Standard one-dimensional techniques such as Secondary Ion Mass Spectrometry (SIMS), Spreading Resistance Pro ling (SRP), Microwave Impedance Pro ling, Neutron Depth Pro ling (NDP), C-V pro ling and Hall measurements have a limited spatial resolution. The measured information is limited to an average of the pro le in the probed region, which is usually large (> 1 m). Consequently, these techniques can not be applied for twodimensional pro ling on arbitrary devices and their application is limited to one-dimensional pro ling of large-area structures. SIMS and SRP, which are the most widely used onedimensional techniques, can also be used to some extent for two-dimensional pro ling of special structures.

2.2.1 2D-SIMS In SIMS an energetic primary ion strikes the sample top surface and releases secondary ions. These secondary ions are analyzed and detected. In terms of one-dimensional dopant pro ling SIMS has certainly been the most heavily used technique, primarily due to its 7

8

CHAPTER 2. 2D DOPANT PROFILING: STATE OF THE ART

good sensitivity (< ppm), high dynamic range (1014 , 1021 atoms/cm3 ) and good depth resolution (2{5 nm). Recently, several methods based on SIMS have been proposed for the measurement of two-dimensional dopant concentration pro les [Dowsett 97]. Hereby, the main problem is the limited spatial resolution and the small analyte volume combined with a limited ionization yield, resulting in very low signal intensities.

Imaging SIMS

By using a high-energy liquid metal ion source (LMIS) (typically Ga+ or In+ ), the lateral resolution may be better than 30 nm [Levisetti 85]. However, the combination of a small analyte volume and the low ionization degrees (10,5 , 10,3 ) leads to very low signal intensities. On the other hand, the lateral resolution attainable with conventional ion sources (such as O+2 and Cs, ) which have a higher ionization yield, is limited because of the large ion beam diameter (> 0:1 m). Full three-dimensional images with 500 nm lateral resolution and 30 nm depth resolution were obtained by Bryan et al. [Bryan 85] using direct imaging SIMS with a rastering beam (O+2 , 15 keV, 1:3 10,3 A/cm2 ). The sensitivity was not reported but will be limited by the small target volume given a certain spatial resolution.

2D-SIMS The constraints of a limited sample volume and a large ion beam diameter can be overcome using a 2D-SIMS technique which allows integration of the dopants from a number of similar volumes and which magni es the lateral distribution at the same time [Cooke 89, Dowsett 92, Cooke 95]. The technique comprises the following steps ( gure 2.1): First a series of parallel long stripes are implanted and the sample is processed in a similar way to that occuring in device fabrication to form the (unknown) dopant distribution. Second, a series of parallel trenches are anisotropically plasma etched at a small angle to the original stripes and to a depth greater than that of the implant so that the resulting structure is composed of a large number of similar mesas each containing a triangular implanted region. The trenches are then lled with poly-silicon or epitaxially grown silicon to control surface topography during analysis. Third, the sample is analyzed with SIMS in a mode with the primary ion beam incident parallel to the normal. The fast scan direction is perpendicular to the mesas, and the secondary ion signal of interest is recorded at the end of each line-scan. The large number of mesas analyzed in a single pass increases the sampled volume, thus enhancing the statistical precision without loss of spatial resolution. With the current instrument con gurations lateral resolutions of 30{50 nm are feasible with sensitivities around 1016 atoms/cm3 [Dowsett 92]. The main drawback of this method consists in the laborious sample preparation and the need for special samples, excluding the application on real semiconductor devices.

Tomography SIMS In a third mode, two-dimensional SIMS is performed based on computer tomography [Goodwin 89, Goodwin 92]. The 2D distribution of dopants is extracted from a series of

2.2. 1D-BASED 2D TECHNIQUES

9

(a)

(b) silicon fill ion beam

linescan

θ θ

trench

Figure 2.1: Schematic layout of the 2D-SIMS setup. (a) implanted dopant stripes with plasma-etched trenches at = 0:2{0.02 , lled with silicon. (b) Top-view: SIMS line-scan perpendicular to the stripes

1D SIMS measurements performed at various angles relative to the sample. A polysilicon capping layer covers the samples and is beveled at the required angle such that the incident ion beam is always perpendicular to the sample surface. A schematic layout is given in gure 2.2. Since the SIMS technique is destructive, a new sample is needed every time a dierent angle is selected (typically 4 to 10 dierent angles are being used). An iterative tomography algorithm based on a maximum likelihood technique is used for the reconstruction of the 2D pro le from the obtained set of 1D measurements [Goodwin 92]. The sensitivity was estimated to be comparable to that of 1D SIMS. However, the features to be determined are often so small with respect to the rest of the source/drain pro le that the collected signal will be dominated by those, and thus large errors on the lateral reconstruction will be observed. Again, the major drawback is formed by the need for special samples. (b) undoped polysilicon

SIMS beam

doped region

5

4

3

2

sputtered dopant

(a)

1 0

θ

1

2

3

4

5

sputter plane

Figure 2.2: Schematic layout of the SIMS-Tomography setup. (a) Sample covered with undoped poly-silicon and beveled at an angle . Successive planes of sputtered material are indicated. (b) Measured pro le. The measurement is repeated for dierent values of , after which a tomography algorithm is used for the reconstruction of the 2D dopant pro le.

Lateral SIMS A fourth method, named lateral SIMS, measures the lateral dose distri-

bution (in atoms/cm2 ) of the dopant in the vicinity of and underneath implantation (or diusion) mask lines of special test structures [VonCriegern 94, VonCriegern 98]. Hereby, the incident ion beam does not fall on the top surface, but on a cross section of the sample ( gure 2.3). The cross section is made perpendicular to the lateral pro le to be measured. Due to the insucient lateral resolution of SIMS, the in-depth distribution of the dopants

10


cannot be resolved at the same time. Hence each data point of the laterally measured pro le integrates over the entire 1D depth pro le, i.e. it provides the lateral dose distribution (in atoms/cm2 ) of the dopants and not the lateral dopant distribution at a particular depth. For arsenic in silicon a dynamic range of 1016 to below 5 1012 atoms/cm2 could be measured with a 5 to 10 nm resolution [VonCriegern 98]. In principle, the spatial resolution is equal to the one of standard SIMS depth pro ling (2{5 nm). At present, the method is limited by a number of eects. First, the method is limited to the high dose range and to high-ion-yield elements such as arsenic and boron in silicon. For the case of phosphorus, where high mass resolution is required, the sensitivity is insucient. Second, slight changes in the dimensions and shape of the mask lines can disturb the SIMS measurement. Third, the top surface of the structure must be covered with a thick capping layer (usually silicon with a thickness comparable to the nal sputter depth) to avoid the formation of a facet during the SIMS sputtering process due to changes in the sputter removal rate [VonCriegern 94]. capping layer (silicon)

mask doped region

SIMS beam

Figure 2.3: Schematic layout of the lateral SIMS setup. The lateral distribution of the dopant dose is measured using a SIMS beam incident on a cross section perpendicular to the lateral direction to be measured.

In conclusion, all SIMS-based 2D dopant pro ling methods require a special sample structure. The application to real structures is fundamentally limited by the small analyte volume in combination with a limited ionization yield. However, the quanti cation possibility is good.

2.2.2 2D-SRP

The Spreading Resistance Pro ling (SRP) method is basically very simple [Pawlik 92, Clarysse 98b]. Two sharp conducting probes are placed as close as possible side by side at about a distance of 15 to 50 m. The sample to be measured is beveled over a small angle, which may range from 50 up to several degrees, in this way enlarging the depth scale ( gure 2.4a). The probes are stepped over the beveled surface with a horizontal stepsize of 2.5 to 5 m and each time the probes are put down, at a load of 5 g, the resistance between the probes is measured at a bias of 5 mV. In this way, one obtains a resistance versus depth pro le. The attractive features of SRP are its very large sensitivity, nearly unlimited dynamic range (1013 , 1021 atoms/cm3 ) and ease of quanti cation because the measured resistance scales directly with the local carrier concentration. Although in principle nanometer resolution can be achieved with very small bevel angles (< 50 ), physical phenomena limit its applicability for future technologies as individual layers become

2.2. 1D-BASED 2D TECHNIQUES

11

shallower than 100 nm. These resolution limitations are related with carrier spilling (or diusion) eects which refer to the redistribution of the mobile carriers with respect to the xed dopant atoms [Hu 82]. In the vertical in-depth direction, the dierences between the carrier and dopant pro le can be calculated from a one-dimensional Poisson problem [Schumann 69]. However, the need for a bevel and the pressure applied with the probes complicate the carrier spilling problem in SRP, such that SRP and SIMS pro les can be considerably dierent. Several groups have developed deconvolution schemes for this phenomenon [Casel 87, Choo 93, Clarysse 92, Clarysse 94, Leong 92, Mathur 92, Mazur 92]. However, for certain structures (e.g. ultra-shallow pro les) the measurement is totally dominated by the carrier spilling problem and the schemes do not provide a good solution. An additional problem for one-dimensional carrier pro ling is that the minimum sample size is approximately 50 1000 m2 . The rst dimension arises from the minimum probe spacing whereas the latter dimension arises due to the magni cation by the beveling of the sample. β

(a)

(b) bevel

bevel original top surface

original top surface α

α

Figure 2.4: Schematic layout of the standard SRP (a) and the 2D-SRP (b) techniques. For the 2D-SRP method, a double-angle bevel provides a magni cation of the in-depth direction (bevel angle ) and the lateral direction (bevel angle ).

The concept of 2D-SRP originates from the observation that conventional SRP is limited for lateral pro ling because it has a large probe step, a large probe separation and a large imprint such that stepping the probes in the lateral direction will not lead to the required resolution. In 2D-SRP, a magni cation of the lateral and vertical direction can be obtained simultaneously through the application of a double bevel to a structure which consists of stripes of doped and undoped regions (as shown in gure 2.4b) [Privitera 93]. The lateral and vertical magni cation are determined by their bevel angle which can be quite small (< 100 ) leading to a large magni cation (100{200). One or two SRP probes are stepped in a direction parallel to the bevel edge whereby the spreading resistance is measured as a function of the lateral distance. This can be repeated at any particular depth from the bevel edge, in this way providing a series of lateral spreading resistance scans, each corresponding to a dierent depth, ultimately leading to a full 2D carrier pro le. Several (identical) parallel stripes are needed for the two-probe setup. If only one probe is used, it is sucient to have only one stripe (which should, however, be long enough such that small values for can be used). In this case, a current-collecting back-contact is also required. The qualitative interpretation of the resistance variation in such a lateral scan and its relation to the lateral carrier distribution has been treated in references [Privitera 93, Vandervorst 94].

12


The accuracy of the quanti cation procedure is limited by the nite size of the probe contacts which are in contact with regions of dierent resistivity [Privitera 93]. Also, the impact of the removal of material in a two-angle bevel on the carrier spilling is not completely understood. Indeed, the distribution of the carrier pro le in the lateral direction with respect to the lateral dopant pro le is in uenced by the appearance of the bevel angle in this direction. This phenomenon is similar to the carrier spilling encountered for one-dimensional SRP, but it has a three-dimensional nature whereas a one-dimensional approach could be used in standard SRP. Detailed three-dimensional calculations of the carrier pro les are required to study the importance of this eect and to set up an algorithm which corrects for this eect. Finally, the application of the 2D-SRP method is limited to special test structures excluding most (real) devices.

2.2.3 Microwave surface impedance pro lometry Another one-dimensional carrier pro ling tool is the Surface Resistance Analyzer (SRA) or Microwave Surface Impedance Pro ler [Martens 94]. In this technique, the sample is part of a millimeter-wave resonator whose impedance is measured as a function of the microwave frequency. From this measurement, the resonant frequency f0 and quality factor Q can easily be extracted. From these values, the sample resistivity can be determined by using equation 2.1, where A and B are two constants dependent on the shape and the material of the resonator. 2 (2.1) = A fQ0 + B

The resonator can be formed by a closed box cavity or by a two-sided quasi-optical cavity comprising a spherical mirror and a conducting plane (the sample under test). Since the mirror and the sample are separated, the measurement is contact-less and non-destructive. By sweeping the frequency, the skin depth of the electromagnetic wave changes, allowing to pro le the in-depth resistivity variation of the sample. The in-depth resolution is dependent on the local resistivity but can be near 10 nm. A resistivity range from 5 10,8 cm to 50 cm corresponding to carrier concentrations of 1015 atoms/cm3 and higher is presently possible [Martens 94, Ishida 95]. The quanti cation towards carrier pro les is straightforward when using equation 2.1 and the electron and hole mobilities equations. This technique is limited to one-dimensional pro ling, since the spatial resolution is limited by the Abbe limit [Abbe 73] to a few millimeters.

Using a near- eld method, the spatial resolution of the microwave impedance pro ler can be dramatically increased. In near- eld microscopy a probe of a sub-wavelength size is employed and the sample is mounted in the near- eld of the probe so that the spatial resolution is determined by the probe size rather than by the wavelength. Several designs of the microwave near- eld probe are reported, resulting in a spatial resolution of 1{5 m [Golosovsky 96a, Wei 96, Steinhauer 97]. The problem in extending this technique towards higher resolution is formed by the limited transmission of smaller aperture sizes resulting in a much lower signal-to-noise ratio. A possible solution to this problem, has been proposed by Gao et al, who used a phase-sensitive technique rather than a frequency-sweep method

2.3. SCANNING-PROBE MICROSCOPY (SPM) TECHNIQUES

13

to obtain a resolution of about 100 nm [Gao 97]. At present, the near- eld microwave impedance technique is still under development and no dopant pro ling results have been reported.

2.3 Scanning-Probe Microscopy (SPM) techniques Scanning-probe Microscopy (SPM) designates a range of novel techniques which use a small probe, most often a microscopic tip, which senses a minute portion of the surface of an object. The invention of the Scanning Tunneling Microscope (STM) [Binnig 82a, Binnig 82b] by G. Binnig and H. Rohrer at IBM in 1982, for which they received the Nobel Prize in 1986, was the start for scienti c activity in the general eld of SPM. Four years later, G. Binnig, C.F. Quate and Ch. Gerber invented the Atomic Force Microscope (AFM) [Binnig 86a, Binnig 86b], which has become one of the most versatile types of SPM, particularly for technical and industrial applications. All SPMs are based on the ability to position various types of probes in very close proximity with extremely high precision to the sample under investigation. These probes can detect electrical current, atomic and molecular forces, electrostatic forces, or other types of interactions with the sample. By scanning the probe laterally over the sample surface and performing measurements at dierent locations, detailed maps of surface topography, electronic properties, magnetic or electrostatic forces, optical characteristics, thermal properties, or other properties can be obtained. The lateral spatial resolution which can be obtained is only limited by the sharpness of the probe tip, the accuracy with which the probe can be positioned over the sample surface, the condition of the surface under study, and the nature of the force being detected, and can vary from a few angstroms to tens or hundreds of nanometers. This extremely high spatial resolution makes SPM the ideal candidate for 2D carrier pro ling. SPM-based two-dimensional dopant pro ling methods include various Scanning Tunneling Microscopy techniques (STM), dopant selective etching, Scanning Capacitance Microscopy (SCM), Kelvin Probe force Microscopy (KPM), Scanning Resistance Microscopy (SRM), Scanning Surface Harmonic Microscopy (SSHM) and Scanning force surface Photovoltage Microscopy (SPVM). All SPMs applied to carrier pro ling rely on similar principles, but dier in which signals are used to measure dopant concentration and control tip location. Generally speaking, all SPM-based 2D pro ling techniques have a high spatial resolution and are being applied on the cross section of the semiconductor structure under investigation. Reviews have been given by Hill in 1990 [Hill 90], Subrahmanyan in 1992 [Subrahmanyan 92], Vandervorst et al. [Vandervorst 95a] and Dagata et al. in 1995 [Dagata 95], Yu in 1996 [Yu 96b], and Vandervorst et al. in 1997 [Vandervorst 97].

2.3.1 Scanning Tunneling Microscopy (STM)

In Scanning Tunneling Microscopy (STM), a sharp metal probe tip is scanned over the surface of a conducting or semiconducting sample at a very small tip-sample separation (on the order of several angstroms). A voltage bias (typically a few volts) is applied between the sample and the tip, allowing a tunneling current to ow through the potential energy barrier separating sample and tip. The magnitude of this tunneling current varies exponentially with the tip-sample separation, and is a function of the electronic density of states in the

14


tip and in the sample. An electronic feedback loop is generally used to maintain a constant tunneling current by adjusting the tip height during scanning. The change in tip height is monitored and yields a pro le of the local electronic density of states on the sample surface. Two modes are generally used: constant-current imaging, in which the tunneling current is kept constant by adjusting the tip-sample separation, and spectroscopy imaging, in which the dependence of the tunneling current on tip-sample voltage and/or tip-sample separation is measured. The STM technique can be applied on planar samples, in which the surface { typically (001) or (111) { is studied directly, or on sample cross sections. In both modes, STM is a very surface sensitive SPM technique which requires however a conductive surface, such that STM measurements on silicon can normally not be operated in air due to the presence of the native oxide. A standard solution in surface science studies to this problem are UHV measurements whereby the native oxide is removed through sample heating to relative high temperatures (> 1000 C). It is clear that such a high temperature treatment will lead to further dopant distribution and is therefore unacceptable for standard carrier concentration pro ling. Therefore, one has to use in-situ cleavage to generate a fresh sample cross section, which is however only possible along certain crystal directions (generally (001) wafers are cleaved to expose a (110) or (110) plane) [Kim 96]. The structure of interest must thus be oriented exactly in that direction, limiting the exibility of the technique. Additionally, it is not always possible to determine the carrier pro le with respect to the mask edge and mask shape since the STM can not image the oxide position (due to the requirement of a conductive surface). Despite these basic limitations, cross-sectional STM oers several methods for high-resolution dopant pro ling.

Dopant atom counting The most direct STM-based dopant pro ling method is to simply count the number of dopant atoms appearing in (or near) the surface atomic plane. An example is given by Johnson et al. [Johnson 93a, Johnson 93b, Salemink 94, Chao 98], who clearly resolved individual Be (and Zn) dopant atoms in a cleaved (110) surface of Ga. In this work, the negatively charged dopant atoms are attractive to holes and appear in the STM image as protrusions. From the number and the height of the protrusions, it is concluded that dopant atoms in the top several atomic layers are being imaged. From the size and shape of the features, dopants at the surface and one atomic layer below the surface could be distinguished from each other and from dopants further below the surface. Using this method dopant concentration pro les in the range 1018 to 1:5 1019 atoms/cm3 have been determined with atomic resolution. So far, no results have been reported on silicon substrates since the capability of imaging individual dopant atoms is associated with the special properties of cleaved GaAs(110) surfaces where the intrinsic surface states are outside the bulk bandgap [Chao 98]. Although this method provides the ultimate (atomic) resolution, its sensitivity is rather poor. Since only the atoms in the top 2 atomic layers are revealed, a high dopant concentration is required to be able to determine the dopant concentration adequately. For example, when scanning a 100 100 nm2 area of a Si sample with a dopant concentration of 1018 atoms/cm3 , there are (on average) only 5 dopant atoms imaged. It is clear from statistics that such a technique requires the measurement of several images on dierent cross sections.


15

Scanning Tunneling Spectroscopy (STS) & Current Imaging Tunneling Spectroscopy (CITS) The work using STM as a dopant pro ler has primarily been focused on pn junction delineation by detecting dierences in tunneling current characteristics for n-type and p-type material. Feenstra et al. carried out the rst detailed imaging and spectroscopic studies of GaAs pn junctions, observing electronically induced topographic contrast in which the p-type regions appeared to be 2 A lower than the n-type layers [Feenstra 92]. Currentvoltage spectroscopy allowed the n-type, p-type and depleted regions to be identi ed unambiguously. Measurements consistent with these results were obtained in later studies of GaAs pn junctions [Gwo 94, Feenstra 94, Silver 95]. The STM current dependence on dopant type and concentration within semiconductors is due to tip-induced band bending at the surface [Feenstra 87]. Hosaka et al. [Hosaka 88] performed STM and STS on hydrogen-passivated (001) surfaces of Si pn junctions in UHV to prevent oxidation of the Si surface. Dierences in the current spectra from p-type and n-type regions were apparent, and current images taken at +2 V sample bias allowed the junctions to be delineated with spatial resolution on the order of 100 nm. Kordic et al. [Kordic 90, Kordic 91] performed the rst cross-sectional STM studies of Si pn junctions exposed by cleaving in air [Kordic 90] and UHV [Kordic 91]. The location of the junctions could be resolved to within 30 nm using a potentiometric technique in UHV: A forward or reverse bias was applied across the pn junction, and dierences in tunneling current measured in p-type, depleted and n-type regions for various bias voltages applied to the pn junctions then revealed the electronic structure of the biased junctions. Measurements consistent with these results were obtained in later studies of Si pn junctions [Johnson 92, Chao 98]. Yu et al. [Yu 92, Yu 96a] used Current Imaging Tunneling Spectroscopy (CITS). In this technique a constant-current topographic scan with the current stabilized at a xed value I0 for a speci c voltage V0 is performed over the sample surface and, at each point, a current-voltage spectrum is measured. Variations in electronic structure across the sample surface produce corresponding variations in the current-voltage spectra; these spatial variations can be revealed by plotting the current measured at speci c bias voltages other than V0 { so-called current images. CITS under UHV conditions on cleaved, hydrogen-passivated cross-sectioned Si MOS structures makes it possible to image the source and drain junction pro les with a spatial resolution on the order of 10 nm [Yu 96a]. Because the current-voltage spectra diered signi cantly for the p-type, n-type and depleted regions, current images generated from the spatially resolved tunneling spectra were able to reveal the pro les of the pn junctions. A problem to extend this work further to quantitative dopant pro le information, is the dependence of the tunneling current on the Fermi level rather than on the carrier concentration itself as shown in equation 2.2 which displays the forward current Jt as a function of the barrier height VB presented to the electrons in the metal by the semiconductor alone, and the band bending VBi which is a function of the applied voltage [Jahanmir 89].

, VBi ) , 1) Jt = J0 (exp q(VBkT

(2.2)

16


Since the Fermi level scales with the logarithm of the concentration, the sensitivity of the STM approach to subtle pro le variations is limited. Chapman et al. [Chapman 92] have modeled the tunneling current-voltage spectra for tunneling into silicon pn junctions on the (100) surface (i.e. on the wafer top surface). These calculations suggested that the apparent junction location in topographic and current images can shift by as much as hundreds of nanometers from the actual junction location because of tip-induced band bending near and within the depletion layer. Furthermore, Gwo et al. [Gwo 94] observed that the Fermi level on passivated GaAs cross-sectional surfaces appeared to be pinned, while Stroscio et al. [Stroscio 86] pointed out that pinning also dominates on a clean, un-passivated silicon surface. This Fermi level pinning would tend to minimize tip induced band-bending eects. Hence, the applicability of STM (or STS) as a dopant pro ling tool is limited. Finally, it has been observed that the very high electric eld from the tunneling tip distorts the carrier pro le such that a quantitative analysis of the local concentration becomes very complicated [Feenstra 94].

Scanning Tunneling Potentiometry (STP)

Scanning Tunneling Potentiometry (STP) is an extension of STM in which the local potential across the sample surface is measured [Muralt 86a]. In STP, an AC tunnel voltage is used to control the tip-to-sample distance while a DC bias is applied across the sample ( gure 2.5). The DC voltage on the tip is independently controlled in such a way that there is no DC tunneling current. The tip voltage is then a measure for the local sample potential. The measured potential image reveals the junction contour line but does not provide any quantitative information on the carrier concentrations. Muralt et al. performed the rst cross-sectional studies of GaAs pn junctions using the STP method [Muralt 86b, Muralt 87]. An alternative potentiometric method has been used by Weaver et al. [Weaver 91b] and Anders et al. [Anders 90] who used a non-contact AFM mode to map the potential distribution inside operating devices. Again, the results were limited to 2D junction delineation. -

+

STM probe sample DC AC

I

Figure 2.5: Principle of scanning tunneling potentiometry (STP). An AC tunnel voltage is used to control the tip-to-sample distance. A DC bias is applied across the sample and the DC voltage on the tip is controlled in such a way that there is no DC tunneling current.

In conclusion, the dierent STM-based cross-sectional dopant pro ling methods { dopant atom counting, scanning tunneling potentiometry, and scanning tunneling spectroscopy { have low performance on silicon. This diculty can be ascribed to the dicult cross section


17

preparation, combined with the fact that the STM is a very surface-sensitive technique. First, silicon (001) wafers are more dicult to cleave than III-V wafers; and second, the as-cleaved (110) cross-sectional surface is atomically disordered with its electronic structure dominated by dangling-bond states [Lutz 95]. Despite these complications, 2D junction delineation and qualitative 2D nanometer-scale dopant pro ling of cross-sectioned Si-based structures has been achieved by several research groups.

2.3.2 Dopant selective etching, staining or oxidizing Dopant selective etching or staining

The method of chemical staining or etching of doped silicon layers has been known since the early days of semiconductor processing [Wu 79]. Staining techniques use selective deposition of a metal such as Cu, Au, Ag, or Pt on one side of the junction by an electrochemical displacement reaction from a metal-ion based solution. Generally, the entire n-type regions are plated, such that junction delineation is possible. Etching techniques use mixtures of HF and an oxidizing agent to preferentially etch regions with a high carrier concentration. Selective etching solutions exhibit greater concentration dependence. The impurity-sensitive etching solutions typically consist of a mixture of HF, HNO3 , and either H2 O or CH3 COOH. The sample topography after the staining or etching step is a measure for the two-dimensional carrier pro le and can be imaged using TEM [Sheng 81, Roberts 85, Romano 91, Alvis 96b, Neogi 98], SEM [Gong 89, Gong 95, Curling 89], STM [Takigami 91] or AFM [Neubauer 92, Raineri 94, Barrett 95, Barrett 96, Alvis 96a, Trenkler 98b, McDonald 98]. In a nal step, the measured topography pro les have to be converted to electrical carrier distributions.

Selective etching and X-TEM One approach uses cross-sectional transmission electron

microscopy (X-TEM) where the cross sections are prepared in the standard way before they are etched using the selective etching solutions [Roberts 85, Yu 96a]. The dierences in remaining thickness are then detected by line extinctions in the TEM image. A conversion of the thickness fringes to concentration levels requires a careful calculation of the contrast mechanism in TEM, which is convoluted with eects due to the wedge shape of the initial cross section. Using this method it is possible to obtain a few iso-concentration contour lines with high spatial resolution and with respect to the mask edge and shape. However, a detailed carrier pro le determination is not straightforward, sample preparation is very cumbersome and the sensitivity is limited to concentrations above 5 1017 atoms/cm3 . However, the etched topography can be measured with a high spatial resolution (5{10 nm).

Selective etching and SEM Alternatively, SEM can be used, whereby a cross section of the sample (but not thinned as in TEM) is selectively etched [Gong 89, Gong 95, Curling 89]. The resulting topography again leads to the observation of iso-concentration contour lines. The SEM delineation suers from a poor contrast mechanism since large steps are required before any contour line can be seen. The spatial resolution is determined by this contrast mechanism and not by the spatial resolution of the SEM itself. As in the TEM approach, the sensitivity is good in the high concentration regime (> 1017 atoms/cm3 )

18


but very poor below that. The technique is commonly applied in production control for contrast enhancement, but not for quantitative carrier pro ling.

Selective etching and SPM The surface topography of dopant selective etched samples can also be measured using STM [Takigami 91, Tanimoto 92] or AFM [Neubauer 92, Raineri 94]. The high spatial and vertical resolution of both techniques allows to perform high spatial resolution measurements as well as to extract quantitative depth information. Among the advantages of using AFM compared with STM in performing topographic measurements on selectively etched cross sections is that AFM makes it possible to measure the surrounding structures (oxides, metals, etc.) since this is not possible with the STM which requires a conducting sample surface. Also, AFM is less sensitive to the detailed electronic structure of the etched surface and to possible contamination of the sample or tip surfaces. Both the STM and AFM method can suer from tip-sample convolution leading to an incorrect image of the etched region. The regions with a high carrier concentration gradient (resulting in a steep topography after etching) are particularly sensitive to this eect [Mahay 97]. Independently of the technique which is used to measure the sample topography, the accuracy of etching and staining techniques is always limited by the reproducibility of factors such as surface preparation, the concentration of the staining or etching solution, staining time, the volume and the agitation of the solution on the sample, temperature and light illumination [Wang 97]. The eects of these factors can be minimized by careful sample preparation and precise control of the etching factors. In this context, dierent approaches have been used by several groups. A promising method to obtain longer etching times and a better general control of the etching, makes use of an electrochemical etching procedure with potentiostatic control [Trenkler 98b]. An important drawback of the etching techniques until now is that analysis suers from a poor understanding of the etching process and relies on other methods like SIMS or SRP for the correlation between carrier concentration and the observed topography. Two approaches have been employed so far for this calibration. The rst calibration method uses a 1D doping pro le adjacent to the 2D area of interest. The 1D doping pro le may be measured by SIMS [McDonald 98, Mahay 97] or SRP [Neogi 98] or be numerically simulated. After etching, the 1D etched pro le is characterized and related to the known 1D dopant distribution. A 2D doping map is obtained by assuming that the dependence of etching rate on dopant concentration obtained for the 1D region is also correct for the complete 2D area. The second calibration method includes direct measurement of the etching rate as a function of dopant concentration using homogeneously doped bulk or epitaxially grown silicon samples [Raineri 94]. Again, it is assumed that under similar etching conditions (temperature, concentrations, light, time, etc.) the etching rate for a particular spot depends exclusively on the dopant concentration at this point. However, it has been found that the etching also depends on the dopant concentration gradient [Ukraintsev 98a].


19

Oxidizing An alternative method for dopant delineation, based on electrochemical principles, relies on the fact that the thickness of an electrochemically grown oxide depends on the dopant density and type [Bardwell 96]. The dierence in oxide thickness depending on doping is primarily due to the dierence in availability of holes, which are required in the anodic oxidation reaction. After growth, the oxide is etched o using dilute HF solution, and thus the silicon that was incorporated into the oxide is removed according to the doping density. Next, the change in height is measured using AFM. The oxidizing-etching-pro ling cycle is repeated several times. Since the amount of Si removed per cycle is well de ned, based on the dopant type and concentration, then in principle, a complete quantitative, 3D dopant characterization can be obtained. However, little is known about the dopant dependence of the oxidation and the sensitivity is expected to be very low (for example, for p-type silicon, a dopant concentration change from 1014 to 1019 atoms/cm3 results in an oxide thickness dierence which is less than 1 nm [Bardwell 96]). In a similar method, the cross section of a sample is thermally oxidized and the resulting topography is measured using TEM [Hill 85]. Since the oxidizing rate is determined by the surface concentration of the dopant atoms, the topography reveals the 2D dopant distribution. The technique has a good resolution (10 nm) but a very limited sensitivity (1019 atoms/cm3 ). In summary, the etching method has a higher sensitivity than the staining and oxidizing methods. However, the applicability of the selective etching method to 2D carrier pro ling is limited because of (i) poor understanding of the etching process, (ii) poor control of the etching conditions, and (iii) lack of a good general quanti cation procedure. Nevertheless, the method remains valuable for fast qualitative analysis.

2.3.3 Scanning Capacitance Microscopy (SCM) The Scanning Capacitance Microscope (SCM), originally developed for the measurement of the sample topography [Matey 85, Williams 89a], can also be used for two-dimensional mapping of the potential distribution [Martin 88] and for two-dimensional dopant pro ling [Williams 89b, Williams 90, Abraham 91] inside silicon device structures. Indeed, if the sample (or the metallic tip) is covered with a thin dielectric layer, the tip-sample contact forms a metal-insulator-semiconductor (MIS) capacitor, whose capacitance and capacitancevoltage (C-V) behavior is determined by the local carrier concentration of the semiconductor sample. The capacitance for a simple planar MIS structure is related to the dopant concentration n as shown by equation 2.3, where q is the electron charge, is the dielectric constant of silicon, A is the capacitor area, Cd is the depletion capacitance. Additionally, the depletion depth d is given by d = CAd . 3 n = C2ddCd qA dV

(2.3)

The total capacitance (C ) is formed by the depletion capacitance (Cd ) and the dielectric capacitance (Ci ): C = CCi +i CCdd . If no dielectric layer is used, the tip-sample contact forms a


20

metal-semiconductor (MS) structure whose capacitance equals Cd (if assumed planar). In this case, we have a so-called Schottky contact SCM [Morooka 96, Li 97]. By monitoring the capacitance as the probe scans across the sample surface, one can measure a two-dimensional carrier concentration pro le. Since the total tip-sample capacitance is large compared to the capacitance variations due to dierent dopant concentrations, one usually measures the capacitance variations and not the absolute capacitance values. Note that no signal is measured if the probe is positioned over a dielectric or metallic region since these regions can not be depleted. Initial implementations of the SCM were analogue to the STM in that they controlled tip height by maintaining a constant capacitance [Williams 89a, Lanyi 94]. More recent SCMs have been based on AFM with a conducting tip, and an essentially independent capacitance measurement in parallel [Huang 94]. A conventional AFM is usually operated in the contact-mode. The capacitance between the tip and sample is measured by using a capacitance sensor from an RCA or JVC video disc player [Palmer 82], which is electrically connected to the tip. The capacitance measurement is made independently of and simultaneously with the AFM topography measurement. The RCA sensor operation is based on a 915 MHz oscillator driving a resonance circuit which is tuned in part by the external capacitance to be measured. As the resonant frequency is moved o the oscillator frequency by a change in the external capacitance, the amplitude of the oscillation decreases. The peak oscillation of the resonant circuit is detected and recti ed into a DC voltage which forms the sensor output. The capacitance detection limit is as small as 10,19 F. The SCM can be operated in three dierent modes, displayed in gure 2.6. They will be brie y discussed in the following. open loop UHF capacitance sensor

conducting AFM probe

lock-in amplifier (ω)

dC/dV

C (VDC )

n

p

p+

back contact VDC

VAC (ω)

VCO

+ -

setpoint

closed loop

Figure 2.6: Schematic layout of the scanning capacitance microscope (SCM) with open loop and closed loop operation. The closed loop makes use of a voltage controlled oscillator (VCO) to keep dC=dV constant.

Direct-capacitance mode A direct-capacitance mode simply monitors the capacitance sensor output while the probe is scanned across the surface at constant force. A DC sample bias is used, while the tip is at ground. As the changes in capacitance are very small (10,18 , 10,20 F) while the probe


21

moves across dierently doped regions, the measured signal is almost entirely composed of stray capacitance (about 1 pF).

Dierential-capacitance mode In a second mode, the dierential-capacitance mode, an AC bias (typically 0.5{10 V, 10{ 100 kHz) is superimposed on a DC sample bias (0{2 V), while the tip is at DC ground [Neubauer 96]. The AC bias is chosen large enough to alternately deplete and accumulate the semiconductor surface region. The modulated surface capacitance changes C under the probe tip are registered using a lock-in technique, simultaneously with the topographical data, while the probe is scanned across the surface. When using large AC voltages (5{10 V), this setup measures C across the entire C{V curve and does not allow to extract information which would be available from full C{V curves. However, it is less dependent on shifts in the at band voltage caused by oxide or surface charges. When smaller AC bias dC is measured. voltages are used, the dierential capacitance dV

Closed-loop mode In a third mode, the closed-loop mode, the magnitude of the AC bias voltage applied to the sample is adjusted by a feedback loop { using a voltage controlled oscillator (VCO) { to maintain a constant capacitance change as the tip is scanned across the sample at constant force [Huang 95, Huang 96a]. The feedback-controlled magnitude of the AC bias voltage is recorded. The main advantage of the closed loop mode is the fact that the capacitance and consequently the depletion width is kept constant, whereas the depletion width might become very large (> 1 m) for lowly doped regions in the dierential capacitance mode, leading to a loss in spatial resolution. In the closed-loop mode, the spatial resolution is no longer a function of the dopant concentration but is constant and is determined only by the tip radius. Since the measured capacitance signal is proportional to the tip interaction area, shrinkage of the tip size will improve the spatial resolution, but also reduce the sensitivity of the capacitance measurement. A dynamic range of 1014 , 1020 has been demonstrated on a special calibration structure [Clarysse 98a]. The sensitivity is a function of the dopant concentration (as can be seen in equation 2.3) and can be increased by reducing the thickness of the oxide layer. Several groups have published qualitative 1D and 2D [Kopanski 98, McMurray 98, Harris 97] closed-loop SCM images, which were compared with TCAD simulations and conventional one-dimensional dopant pro ling results. The resolution of these images is on the order of 20 nm. Much of the work related to SCM is focused on the theoretical interpretation and quantitative conversion of the measured signals into carrier pro les. In a simple MOS capacitor, the dopant concentration n is extracted from the variation of capacitance with voltage as shown in equation 2.3. The situation is more complex for SCM since there are stray- elds between the probe shaft and the sample surface, the sample has a non-constant dopant concentration, and the quality of the surface is largely unknown (surface charges, contaminants, oxide quality, etc.). Several models were presented to set up a quanti cation procedure. In the most simple model, the quanti cation of the SCM images is achieved

22


using SIMS data in conjunction with contour mapping software [Harris 97]. Hereby, it is assumed that the dependence of the SCM signal on dopant concentration obtained for the 1D line is also correct for the complete 2D area In a quasi-1D analytical model, the tip is modeled as a metallic sphere placed in an insulating dielectric medium near a silicon surface with a sphere-silicon gap just equal to the experimental measured oxide thickness [Huang 96b]. The silicon surface is divided into annular regions. The insulator capacitance between the sphere and each annular region, and the silicon depletion capacitance for each annular region are calculated and summed to give the total tip-sample capacitance. This approximate analytical model provides a means to rapidly calculate the C-V relation as a function of tip radius, dielectric constant, gap distance, and dopant density. Note that a constant dopant density is assumed in these calculations, the eect of a dopant gradient (in the lateral direction) is not included. In an alternative model the capacitance-voltage relation is calculated using the solution of the three-dimensional Poisson equations for various tip-sample bias voltages, tip-sample gap distances, dopant concentrations, and oxide thicknesses [Kopanski 98, Marchiando 98]. The probe is modeled as a cone with a hemispherical tip end to include stray- eld eects. The quality of the sample surface, although known to be an important parameter, was not included in the calculations. A fast algorithm was developed, utilizing interpolation of the model output, to convert a measured SCM pro le into a quantitative dopant pro le. Hereby, each measured capacitance point is treated independently; i.e. the eect of dopant gradient is ignored. In order to include the eect of lateral variations of the dopant concentration or the eect of nearby isolating or conducting regions, additional three-dimensional calculations are required. In particular, the behavior of the SCM signal (in the open or closed loop mode) at pn junctions is not well understood and is observed to be in uenced strongly by such eects [Kopanski 98]. Recent calculations show that the tip-sample bias has a pronounced eect on the presence, position, and extent of extra contour lines in the vicinity of the junction, making precise junction delineation complicated [Kleiman 97, Kang 97]. At present, this eect has not been included in any of the presented models. In conclusion, the SCM is a promising tool for quantitative 2D carrier pro ling with nanometer resolution. The resolution (10{20 nm) and dynamic range (1015 ,1020 atoms/cm3 ) are good. Also, it does not require special test structures. Its recent development resulted in 1996 in the rst commercial qualitative 2D carrier pro ling instrument [DI]. In addition to carrier pro ling, the SCM can also be used to evaluate small thickness variations of dielectric layers with nanometer spatial resolution [Yamamoto 96, Mang 96]. The major challenges in SCM include: surface preparation including the dielectric oxide, and the quanti cation and calibration methodologies. At present, the technique is limited by a poor understanding of the signals measured at pn junctions, and a lack of a generally applicable quanti cation routine.

2.3.4 Kelvin Probe force Microscopy (KPM) Kelvin Probe force Microscopy (KPM), also known as Scanning Maxwell-stress Microscopy (SMM), was proposed as a high-resolution and highly sensitive potential imaging method [Nonnenmach 91]. A conductive AFM tip is scanned in the non-contact AFM mode. That


23

is, the cantilever is driven by a sinusoidal driving force with constant amplitude and frequency (slightly o the cantilever resonance), and the frequency shift is detected from its vibration amplitude variance. The electrostatic force acting between an axi-symmetrical tip and the sample is given by equation 2.4, where V is the potential dierence between the tip and the sample, C the capacitance and z the tip-sample distance.

F = 21 V 2 @C @z

(2.4)

2 + 1 V 2 ) @C + VDC VAC sin(!t) @C , 1 V 2 cos(2!t) @C F = 12 (VDC 2 AC @z @z 4 AC @z

(2.5)

@C = , C 2 @z iA

(2.6)

When a sinusoidal voltage is superimposed on the tip bias (V = VDC + VAC sin(!t)), equation 2.4 is replaced by equation 2.5. A cross-term electrostatic force with frequency ! is now acting between the tip and the sample. This force disappears when the DC potential dierence VDC is set to zero. Thus, by observing the amplitude of the cantilever oscillation at frequency ! by a lock-in technique, and nulling it by changing the DC bias voltage on the tip, the sample surface potential can be measured. The maximum sensitivity is obtained when the applied voltage frequency ! corresponds to one of the resonance frequencies of the cantilever. In order to separate the height-control signal and the voltage signal, the rst cantilever resonance peak is usually employed for the tip height control while ! is taken equal to the second resonance peak on a dual resonant probe [Nonnenmach 91]. This mode was used to measure the two-dimensional potential distribution inside GaAs [Chavez 95, Mizutani 96] and Si device structures [Kikukawa 95, Kikukawa 96, Tanimoto 96]. The measured electrochemical-potential dierence between the probe tip and sample surface, is dependent on the carrier concentration related work-function dierence, and can thus be used as a measure for the local carrier concentration, although the sensitivity is limited. This mode of KPM has been applied successfully for qualitative two-dimensional carrier pro ling of cross-sectioned Si structures [Tanimoto 96, Henning 95]. The technique is presently sensitive to changes in dopant concentration from 1015 to 1020 atoms/cm3 with a spatial resolution of 100 nm. However, the sensitivity to small concentration changes and the application towards quantitative pro ling are limited by surface charges on the sample and calibration of the KPM technique against absolute dopant concentration standards remains to be demonstrated. Additionally, the amplitude of the electrostatic force term in equation 2.5 with frequency 2! can be used to obtain an estimate for the spatial variation in @C @z [Martin 88]. If an ideal, planar MIS structure is assumed, this term can be calculated to ful ll equation 2.6, and can thus be used to measure the local carrier concentration through the tip-sample capacitance C as is also done for scanning capacitance microscopy. For this purpose, VDC is kept constant and no longer varied to null out the electric eld between the tip and sample.

In this mode, the sensitivity is comparable to the one for standard SCM, but the spatial resolution is limited by the height at which the probe is scanned above the sample surface.

24

CHAPTER 2. 2D DOPANT PROFILING: STATE OF THE ART LIA(ωr ) LIA (ω) LIA(2ω)

height feedback topography to z-piezo dC/dz

Vr (ωr ) conducting AFM probe

sample with 2 electrodes

VAC (ω) VDC

V feedback Vsample

Figure 2.7: Schematic layout of the Kelvin probe force microscope (KPM) (LIA = lock in ampli er).

2.3.5 Scanning Resistance Microscopy (SRM) The principle behind the Scanning Resistance Microscope (SRM), also known as the Contact Current Microscope (CCM), is simple. The SRM uses localized contact resistance measurements, performed by a conducting probe to delineate between regions of dierent doping on a cross-sectional sample surface [Nxumalo 96, Nxumalo 97a, Nxumalo 97b] or sample top surface [Shafai 94, Maywald 94, Maywald 95]. The force used is chosen such that the measured resistance is dominated by the contact resistance and not by the spreading resistance of the tip-semiconductor point contact. Two modes are used: In the constantvoltage mode the contact resistance is measured at a xed bias voltage (typically 0.3-3 V) [Shafai 94, Maywald 94]. In the constant-current mode the probe bias potential is modulated in order to maintain a constant tip-sample current. The latter mode provides a high measurement dynamic range [Nxumalo 96]. Both metal probes [Shafai 94, Nxumalo 96] and diamond probes [Nxumalo 97a, Nxumalo 97b] yielded high resolution images on silicon test structures (30 nm). The technique is capable of pn junction delineation but could not yet be used for quantitative carrier pro ling. The main limitations are its strong dependence on the surface quality (surface contaminants and oxide, trapped charge at the interface) and the limited dependence of the contact resistance on the carrier concentration, resulting in a poor sensitivity.

2.3.6 Scanning Surface Harmonic Microscopy (SSHM) The Scanning Surface Harmonic Microscope (SSHM) consists of an STM with a microwave cavity, in which a microwave signal is applied across the tip-sample tunneling gap [Michel 92]. The non-linear tip-sample MIS capacitance C results in higher order harmonics in the tunneling current. The second harmonic and third harmonic signals are proportional to the rst and second derivatives of C . The driving frequency is chosen such that the second or third order harmonic frequency corresponds to the resonance frequency of the cavity (typically 2.7 GHz), making it detectable [Bourgoin 94, Bordoni 95]. The capacitance C is


25

a measure for the local active carrier concentration in the semiconductor and the insulator quality in the same way as in the SCM technique. Bourgoin et al. have applied the SSHM technique to delineate the qualitative carrier pro le of Si pn junctions with 5 nm resolution [Bourgoin 94]. Quanti cation of the data is faced with similar problems as the SCM technique. spectrum analyzer (2.7 GHz)

amplifier & bandpass filter

Vref

signal generator (900 MHz)

STM probe

-

+

resonant cavity aperture current

sample to z-piezo

3rd harmonic

height feedback

Figure 2.8: Schematic layout of the scanning surface harmonic microscope (SSHM) setup.

2.3.7 Scanning force surface Photovoltage Microscopy (SPVM) Surface photovoltage permits one to measure a wide range of features in semiconductors including doping concentrations. The basic principle is as follows: On illuminating the sample with light of suciently short wavelength, electron-hole pairs are generated in the bulk semiconductor. The carriers of the appropriate sign will be attracted to the surface, neutralizing the surface charge and eliminating the band bending (which is caused by the large density of states at energies in the bandgap). This process results in a detectable voltage at the surface, the surface photovoltage, whose magnitude depends on the proportion of the surface charge neutralized by photo-carriers and on the initial degree of band bending and thus on the doping concentration. Thus, the sign of the surface photovoltage indicates the local carrier type, while the magnitude is related to the carrier concentration. Using potentiometry on the AFM or Kelvin probe force microscopy (see 2.3.4) the surface potential can be measured simultaneously with sample topography [Weaver 91a]. The technique has been illustrated by measurements on a pn silicon structure, showing a high contrast in the surface voltage image arising from the dierent sign of the band bending in p-type and n-type material. Quantitative measurements of surface dopant concentration, however, are made dicult by variations in surface state density which are uncontrolled in measurements made on cross-sections in air.

26


2.4 Electron Microscopy (EM) techniques

2.4.1 Field-Emission SEM (FE-SEM)

Compositional and doping dierences in semiconductor structures have been studied both in the secondary electron (SE) and backscattered electron (BSE) imaging modes at high resolutions [Turan 96, Perovic 95, Venables 98]. Perovic et al. [Perovic 95] have shown that similar dopant types (i.e. n-type versus p-type) always exhibit similar contrast behavior in SE images for both GaAs and Si-based heterostructures. The contrast dierences between n-type and p-type materials originates from the electrically active dopant species and can be explained by an electronic band structure model which accounts for the enhanced or retarded SE emission from a semiconductor surface within p-type versus n-type doped regions, respectively. The samples are usually cleaved in air, clipped to a conducting specimen stage and then immediately loaded into the SEM chamber in order to minimize the thickness of the native oxide layer. The SE image quality is degraded because of the increased eective SE work function in the presence of an oxide lm. Cross sections through actual devices are prepared by polishing and etching in diluted HF just before analysis, so that the surface to be imaged is in a controlled condition. Tilting of the sample under a small degree (5 o the normal axis) slightly increases contrast [Perovic 95]. The sensitivity threshold for n-type [Venables 98] and p-type [Turan 96] silicon was observed to be around 4 1016 atoms/cm3 . An approximate logarithmic relationship between contrast and carrier concentration level has been observed, limiting the best attainable sensitivity and concentration resolution [Venables 98]. Furthermore, a large scatter in the data is consistently observed and is believed to arise from sample micro-topography (sample roughness) and macro-topography (sample tilt and device structure). In the absence of a complete theoretical understanding, an empirical correlation to one-dimensional SIMS data is performed in an attempt to convert the two-dimensional contrast images into a quantitative carrier concentration distribution [Venables 98]. However, such an approach is not completely right because it assumes that the contours are representative of the atomic dopant concentration and are not representative for some other characteristic (such as carrier concentration, internal potential or electrical eld distribution). The spatial resolution was found to be around 20 nm.

2.4.2 Combined TEM/FIB

The combined use of the Transmission Electron Microscope (TEM) and Ga+ Focused Ion Beam (FIB) has widespread application to microstructural analysis of semiconductor structures. Additionally, TEM imaging of thin membranes prepared by the FIB show strong dierential contrast between regions with dierent doping [Hull 95, Hull 97]. Typical contrast levels on the order of 10-50% between n-type and p-type material have been observed [Hull 97] with a 20-40 nm resolution. The polarity of the images is always such that n-type regions are lighter and p-type regions are darker. Such high contrast levels from such low doping levels (about 1 atom in 104 , 105 ) are unexpected from conventional TEM contrast mechanisms. The exact contrast mechanism operating is unknown, but appears to be associated with a combination of the highly perfect sample geometry generated by the FIB fabrication, anomalous absorption mechanisms operating in the dierently doped layers and

2.4. ELECTRON MICROSCOPY (EM) TECHNIQUES

27

point defects created by the FIB irradiation. In this context it is interesting to note that contrast is only observed in samples which are prepared for TEM by FIB sputtering. The contrast is observed to increase even more when electron beam irradiation is used in the TEM [Hull 95]. So far, only InP-based structures could be pro led. Other semiconductor materials such as Si and GaAs do not show this contrast behavior when using the same experimental conditions which reveal strong contrast in InP. A better understanding of the underlying physical mechanisms is needed for extending this technique to other semiconductor materials and to arrive at a quantitative dopant pro ling method.

2.4.3 Electron holography Electron holographic measurement of potential contours due to dopant distribution is reported by McCartney et al. [McCartney 94]. The method is known as o-axis electron holography and it requires a TEM equipped with a coherent electron ( eld emission) source. The sample covers half of the eld of view of the TEM, and the wave that does not pass through the sample is used as a reference and to create interference by overlapping it with the wave that passes through the sample. The Fermi-level potential distribution inside the sample results in a (interference) phase image which is collected for digital processing using a CCD camera. The precision of the absolute voltage measurement is about 0.5 V over 10 nm, but can be made more precise by averaging over larger areas. Artefacts in the sample thickness image are the main source of error. It remains an open question whether the potential distribution information can be translated into a two-dimensional carrier or dopant pro le.

2.4.4 Electron Beam Induced Current (EBIC) SEM can be used to locate junctions within devices via EBIC. In this technique, electronhole pairs are created within the depletion region of the junction by the relatively high voltage electrons from the SEM source. Both diusion of these point charges and drift promoted by the built-in potential bias of the junction create a current which can be measured with an electrometer. This method has been used for locating point defects (traps) within depletion areas and for nding structural faults within devices. Generally a plan-view geometry is used, with the beam normal to the device surface, having an energy sucient to penetrate to the junction depths. The EBIC current, which is monitored as a function of beam voltage, will rise as the junction depth is rst penetrated ( gure 2.9a) [Fitzgerald 94]. This plan-view geometry cannot be used for two-dimensional junction delineation. An alternative approach is to probe a cross sectioned surface with the beam. In principle, as the probe scans from the top of the device toward the substrate, the EBIC signal would peak at the junction depth. A limiting factor for the spatial resolution corresponds to the width of the excitation volume of the electron beam. This is largely sensitive to beam energy, with a 10 keV beam producing excitation in a volume of width greater than 1 m. To attain reasonable beam current at energies near 1 keV, for which the excitation diameter is on the order of 10 nm, would require the use of a eld emission electron source. The SEM can also be replaced with a STM, whose microscope tip is used as an electron source for primary electrons in the energy range of some ten electron volts, leading to EBIC


28

measurement results with an improved spatial resolution [Koschinski 94, Koschinski 96] (see gure 2.9b). The voltage applied to the STM tip must be taken high enough to emit electrons with a kinetic energy suciently high for the formation of electron-hole pairs in the semiconductor sample. However, with higher voltages strong band bending will occur and eld ionization of the ambient gas molecules will take place, hence requiring a vacuum environment. Using the STM-EBIC setup, Koschinski et al. could perform 100 nm resolution EBIC measurements on doped silicon samples [Koschinski 96]. The application of the EBIC-STM setup is limited to junction delineation and cannot be used for measuring dierences in dopant concentrations. (a)

e -beam

(b) STM probe to ADC

p n

Vemission current amplifier

to ADC p

n current amplifier

VDC VDC

Figure 2.9: Two geometries for junction delineation with EBIC: (a) plan-view surface; (b) EBIC-STM on a cross-sectional surface.

2.5 Inverse modeling techniques Inverse modeling techniques deal with the determination of the 2D carrier pro le from experimental measurements, along with the physical laws and theories (Poisson's equation and the current continuity equations) which are known to be valid [Ouwerling 90]. A possible approach for 2D-dopant pro ling of MOS transistors was presented by Khalil et al. [Khalil 96] and consists of the following steps. First, input parameters such as the gate oxide thickness, polysilicon gate length and polysilicon gate concentration are determined from capacitance measurements. Next, an initial 2D carrier pro le is constructed using the SIMS results obtained for the in-depth source/drain implantation and the channel pro le obtained from capacitance measurements. Finally, the 2D pro le is adjusted to achieve a good t between the experimental and simulated capacitance measurements using a least squares optimization procedure. To simplify the procedure, the 2D carrier pro le is formulated using two tensor product splines. This method is nondestructive, does not require any dicult sample preparation and uses measurements easily performed during process characterization. TEM imaging can be used to get the precise structural information, which has a direct eect on the extracted pro le. The main drawbacks of this method are: (i) A quantitative study of the resolution and accuracy of the method is still needed, (ii) the extent of the device region where the pro le can be determined depends on the range of measurement voltage, the doping level, and the device characteristics, (iii) modeling assumptions in solving Poisson's equations are a source of uncertainty, and (iv) large calculation times are required. Further development of the technique is needed to make it a reliable tool for 2D carrier pro ling.

2.6. CONCLUSIONS: COMPARISON OF 2D PROFILING METHODS

29

2.6 Conclusions: comparison of 2D pro ling methods Various features of the methods described above are summarized in Table 2.1. The most important features are: spatial resolution (in nanometers), dynamic range (in atoms/cm3 ), sensitivity (de ned here as the ratio of the change in the instrument response to a corresponding change in carrier concentration), quanti cation ability, and applicability to real devices (without needing special test structures). The listed resolution and dynamic range correspond to the best speci cations found in literature. Note that dierent de nitions for spatial resolution and sensitivity (or dynamic range) are used by dierent groups, complicating this intercomparison. If no value is found in the literature, the speci cation is labeled as 'not available' (NA). The ability to transform the measured raw data values into a fully quantitative 2D dopant or carrier pro le is labeled as 'yes', 'no' or 'limited'. The concentration resolution is labeled as 'linear' if the instrument response is proportional to the carrier concentration, 'logarithmic' if the instrument response is proportional to the logarithm of the carrier concentration, 'power' if there is a power-law relation between the carrier concentration and the instrument response, or 'limited'. Based on this intercomparison, it is clear that none of the available techniques ful lls all the requirements formulated in table 1.1 and can at the same time be applied on any arbitrary semiconductor structure. Most techniques are limited to junction delineation or provide a qualitative image of the dierently doped regions. All 1D-based techniques require a special test structure. The applicability of a number of techniques is limited because of a limited theoretical understanding of the underlying physical phenomena.

30


Table 2.1: Intercomparison of two-dimensional dopant (D) and carrier (C) pro ling methods (NA = not available). Method Res. (nm) Range (cm,3 ) Conc. res. D/C Quanti able

1D-based techniques

Imaging SIMS 100 NA 2D-SIMS 30-50 1016 , 1021 2D-tomography SIMS 50 NA 13 Lateral SIMS 5-10 10 , 1016 cm,2 2D-SRP < 100 nm 1014 , 1020 near- eld -wave impedance 1000 1015 , 1021

linear linear linear linear linear power

D D D D C C

yes yes yes yes yes yes

SCM SSHM STM - atom counting - STS - STP KPM SRM SPVM Chemical etch + SPM

NA 18 10 , 1:5 1019 NA NA 1015 , 1020 NA NA 17 10 , 1021

power power linear log. limited limited limited limited limited

C C D C C C C C C

limited no yes limited limited limited no limited limited

C C

NA NA

limited limited limited limited limited limited

C C C

limited limited limited no no no

C

yes

C

yes

SPM techniques 10 1015 , 1020

5 atomic 10 10 100 50-100 NA 10-20

EM techniques 25 1017 , 1021 10-20 1017 , 1021 10-20 4 1016 , 1021 20-40 1017 , NA

Chemical etch + SEM + TEM FE-SEM Combined TEM/FIB Electron holography EBIC

1-10 100

inverse modeling with C , V

Inverse modeling techniques NA

NA

Target values of the ideal technique 5-10 1014 , 1021 linear

2.6. CONCLUSIONS: COMPARISON OF 2D PROFILING METHODS

31

Table 2.2: Intercomparison of two-dimensional dopant and carrier pro ling methods (continued from table 2.1).

Method

Comments and problems

1D-based techniques

Imaging SIMS 2D-SIMS 2D-tomography SIMS Lateral SIMS 2D-SRP near- eld -wave impedance

Sensitivity limited by target volume Special structures required Special structures required, complex sample preparation Only the lateral dose distribution is measured Special structures required Limited spatial resolution

SCM SSHM STM - atom counting - STS - STP KPM SRM SPVM Chemical etch + SPM

Uncertainties at junctions, poor quanti cation procedure No quanti cation procedure Only on GaAs, not on Si Only junction delineation and type (n or p) identi cation Only junction delineation Poor quanti cation procedure, stray- elds limit the resolution No quanti cation procedure Only junction delineation and type (n or p) identi cation Dicult to quantify

Chemical etch + SEM + TEM FE-SEM Combined TEM/FIB Electron holography EBIC

SPM techniques

EM techniques

Only qualitative Only qualitative Robust model for quanti cation is not available Only illustrated on InP, no quanti cation procedure No quanti cation procedure available Only junction delineation

Inverse modeling techniques

inverse modeling with C , V Resolution and accuracy are unknown, long calculation times

Target values of the ideal technique

Fully quanti able, applicable to arbitrary structures

Chapter 3

SSRM instrumentation & measurement procedure 3.1 Introduction: the SSRM concept The present applications of Atomic Force Microscopy (AFM) have demonstrated that the technology exists to bring a sharp probe into contact with a sample and to scan it reproducibly over its surface with nanometer precision in the lateral direction, while maintaining a constant (low) force on the sample. When the AFM is equipped with a conductive probe, local resistance measurements can be performed with high resolution on two-dimensional semiconductor structures. A typical example (measured on a cross-sectioned device) is presented in gure 3.1. This gure shows the sample topography and the simultaneously measured resistance pro le. The scan size is 33 m2 and contains 512512 measurement points (pixel-to-pixel distance ' 6 nm). The sample under study consists of an n-type substrate (2 1014 atoms/cm3 ), implanted through a SiO2 mask with As (3 1015 atoms/cm2 , 20 keV) and annealed for 21 seconds at 1050 C in a N2 atmosphere. The implanted wafer is covered with an undoped poly-silicon layer with a thickness of about 3 m. The topographic image shows the SiO2 mask as a protrusion, slightly higher than the surrounding Si and poly-silicon. The quality of this topographic image is poor as compared to standard AFM topography measurements. This originates from the large forces which are used in SSRM pro ling as compared to standard AFM imaging. The resistance image shows the implanted area as a low-resistance region, the undoped poly-silicon and the SiO2 mask as very high resistance regions, and the Si substrate as a high resistance region. Contour lines of constant resistance are visible in the implanted area. By combining both images, the carrier pro le can be determined with respect to the geometry of the structure under study. In order to meet the goals of this work, as formulated in chapter 1, a commercial AFM is equipped with a conductive tip such that current ow (or resistance) can be measured locally through a contact area with a radius of about 10 nm. In a simple model, the measured resistance is composed of the contact resistance in series with the spreading resistance. The spreading resistance is proportional to the local sample resistivity and can thus be used for carrier pro ling purposes, while the contact resistance is a much more complicated function 33

CHAPTER 3. INSTRUMENTATION & MEASUREMENT PROCEDURE

34

Figure 3.1: Two-dimensional SSRM pro le of a cross-sectioned device. (a) shows the measured sample topography with the SiO2 mask being slightly higher than the Si substrate and the poly-silicon capping layer. (b) displays the simultaneously measured SSRM resistance map, showing the implanted areas as low-resistance regions (scan size: 33 m2 ).

of the sample resistivity. Only at high forces, the spreading resistance dominates over the contact resistance. Consequently, hard probes, which can withstand these high forces, are required for stable SSRM operation. In this chapter, a detailed investigation is presented regarding the experimental setup and the choice of the probe material. The choice of the material is relevant with respect to the contact resistance, possible degradation of the tip (for instance oxidation), hardness and deformation resistance (since larger pressures than during normal AFM operation are applied), possibility to shape the material in the correct form, and control of the radius of curvature. The development of a good conductive tip is one aspect in the design of the SSRM technique. Equally important is to know how such an SSRM measurement should be performed. It is clear for instance that, before contact is made, the AFM feedback loop is open so that the rst contact is made without force control. Also, as the resolution is closely associated with the precise movement of the tip, a detailed procedure for the tip-movement is required. The operational principles of the SSRM technique, determined and evaluated in this chapter, include:

instrumental setup SSRM probes sample preparation probe movement imaging artefacts

3.2. THE ATOMIC FORCE MICROSCOPE

35

3.2 The Atomic Force Microscope In standard atomic force microscopy (AFM) the surface topography of a sample is revealed by the movements of a ne tip touching the surface and mounted on a soft spring known as a cantilever. The tip is moved relative to the sample by a piezoelectric tube scanner that executes a raster pattern in the horizontal xy plane after the tip and sample have been brought into contact. A schematic setup of an AFM in which the sample is xed onto a piezoelectric tube is drawn in gure 3.2. A topographic image of the surface is obtained by representing the cantilever excursions at each point as the tip sweeps the surface. The de ections of the spring correspond to varying forces, hence the name force microscopy. The spring de ections can be detected in several manners. The most widely used technique is the optical lever de ection method [Meyer 88, Alexander 89]. In this mode, the spring de ections are detected by shining a laser beam on the free end of the cantilever and comparing the output signals of a two-segment photodiode that detects the light re ected o the cantilever. When using a four-segment photodiode, the lateral force can be detected simultaneously with the normal force [Kolbe 92]. Other de ection detection modes are: laser interferometry [McClelland 87], capacitive detection [Joyce 91], tunneling current detection [Binnig 86b], and piezoelectric detection [Tortonese 93, Itoh 94]. laser photodiodes b

lens

a

-

L

+

l

cantilever with integrated tip sample

Va-b

setpoint

+

piezo-tube

-

Feedback

Figure 3.2: Schematic of an Atomic Force Microscope (AFM) with optical detection of the lever de ection.

Figure 3.3 shows a magni cation of the probe-sample setup. SSRM is usually operated on the cross section of a piece of silicon cut out of a wafer. The original wafer top surface and the cross section surface are indicated in the gure. The AFM probe consists of a cantilever and a tip. Orthonormal axes are de ned for the sample and for the probe. For the sample, the z -direction is de ned to be perpendicular to the surface on which the measurement is performed (i.e. the cross-sectional surface). The y-direction lies in this surface and is chosen

36


perpendicular to the sample edge. For the probe, the z axis is taken equal to the one for the sample. The x axis is parallel to the cantilever beam. Z X cantilever tip

Y

}probe cross section original top surface

Z Y X

Figure 3.3: Sample layout showing the de nition of the dierent surfaces and directions used throughout this book.

Under normal imaging conditions, the cantilever movements during scanning are reduced as much as possible in order to maintain a constant imaging force. In this way, harmful interactions with the surface can be minimized. As is apparent from gure 3.2, the laser beam focused on the re ecting cantilever top hits the beam-position detector under a slightly dierent angle when the tip is lifted up by elevated terrain on the sample surface, producing a new dierence signal Va,b . The signal is used as input to a feedback circuit which, by adapting the length of the piezo tube, maintains the cantilever de ection close to a particular reference position determined by the setpoint value of the feedback. In this way, the force exerted by the tip on the sample is essentially constant during scanning. These provisions open the way to control and modify the pressure in a micro contact implemented as a spring-loaded tip/sample contact. Obviously, the range of available forces depends on the spring constant of the cantilever. From elastic theory it is known that for small de ections of a cantilevered beam ( xed at one end, free at the other end) the change of the slope at its very end is given by equation 3.1 wherein z is the vertical displacement of the tip, and l is the cantilever length [Feynman 72]. (3.1) = 32zl The sensitivity of the measurement depends on the ratio of the laser spot displacement at the detector to the actual movement of the tip. Accordingly, the ampli cation A can be written as equation 3.2 for small de ections of the cantilever. In this equation L represents the distance from the free cantilever end to the photodiode (L and l are indicated in gure 3.2). (3.2) A = 2L = 3L

z

l

For a cantilever that at rest is inclined over a small angle with respect to the plane of the sample surface, equation 3.2 needs to be corrected by a factor cos (), which is usually


37

close to unity. The relation shows the importance of the choice of a favorable Ll ratio: the cantilever should be as short as practicable to have an optimum sensitivity, while L may be large. The value of L should be chosen such that the laser spot remains entirely subtended by the photodiode and is typically a few centimeters. Once a mechanical contact between tip and sample has been established and the feedback loop is closed, the load exerted by the tip on the sample can be ne-tuned by choosing a dierent setpoint value as a reference. The imaging force is computed according to equation 3.3 where k is the cantilever spring constant, and z the vertical displacement of the tip.

F = kz = kpVz

(3.3)

The factor p is the piezoelectric coecient of the scanner relating the extension of the piezo tube to the driving voltage Vz . For the scanners used in this work, p is always close to 10 nm/V and Vz can be varied from -220 V to +220 V. The dierence Vz is taken as the dierence between Vz at the working point and Vz at the instant of making the mechanical contact. This point is not necessarily identical to the value corresponding to breaking the contact since various causes for hysteresis can be cited. One reason may be that the contact has been inelastic and that the sample became indented on impact, another reason lies in the attractive eect of a liquid lm adhering to the tip/sample contact region. It is clear that by choosing a dierent setpoint voltage the Vz value can be varied, and thus so can the force in a particular experiment. In practice, the value of Vz before mechanical contact has been established is inaccessible, since under open loop conditions the driving voltage will diverge to either + or - the supply voltage. Therefore, this value must be deduced from a corresponding value for Va,b , which may be obtained from a curve relating the observed dierence voltage Va,b to the piezo excursion Vz for a particular experimental setup (including the speci c laser spot position chosen on the cantilever) when mechanical contact has been made. This point will be discussed in more detail when dealing with force curves in section 3.6.1. Two AFM systems were used in this work. In the rst instrument (MultimodeTM , Digital Instruments Inc.), the sample is mounted on { and can be moved by { a piezoelectric tube, while the probe remains at a xed position ( gure 3.4). Dierent piezoelectric tubes with dierent scan ranges (xy: 2{150 m; z: 0.5{4 m) can be mounted on the instrument. This instrument is limited to small samples (maximum 11 cm2 ) with a limited height (maximum 8 mm). In the second instrument (DimensionTM 3000, Digital Instruments Inc.), the probe is xed to { and moved by { a piezoelectric tube, while the sample remains at a xed position ( gure 3.5). The main advantage of this setup is that larger and higher samples can be used. An optical microscope (100{800 magni cation) is used in both instruments to facilitate the positioning of the probe on the sample and to locate a particular area on the sample. For the Multimode instrument, the use of an extra optical stereo microscope (20{40 magni cation), looking at the sample under an angle of 45 , facilitates the manual (coarse) approach of the probe to the position of interest on the sample. In the DimensionTM instrument this is done by a motorized movement. An important drawback of the MultimodeTM instrument is caused by the fact that the sample, which can have dierent heights, is slightly tilted by the piezo during scanning. Hence, high samples (e.g. 7.5 mm)

38


require xy scale corrections for tilting eects. Figure 3.6 shows the line scans measured on a calibration standard which was placed at dierent heights using the same piezo tube (which was calibrated for low samples). On the higher samples an area which is 10% larger is observed. A possible solution, is to calibrate the piezo tube for dierent sample heights and to select the calibration parameters which correspond to the height of the sample to be measured. This problem is completely avoided by mounting the probe on the piezo-element while the sample is kept at a xed position, as is done in the DimensionTM instrument.

b) cantilever with integrated tip c) sample a) piezo tube

Figure 3.4: Digital Instruments MultimodeTM AFM. The piezo tube (a) cantilever holder (b) and sample (c) are indicated.

a) piezo tube

b) cantilever with integrated tip c) sample

Figure 3.5: Digital Instruments DimensionTM 3000 AFM. The piezo tube (a) cantilever holder (b) and sample (c) are indicated.

In a well-designed AFM or STM, tip-to-sample position control should be better than the resolution desired. High-performance instruments aim for a resolution of about 0.1 A normal to the sample surface and about 1 A laterally. These tolerance requirements can only


39

300 200

height (nm)

100 h2

1

2

3

4

5

6

8

7

9

10

11

12

sample

h1

0 piezo-tube

200 100 1

0 0

2

3

20

4

5

40

6

7

60

8

9

80

10

11

100

distance (µm)

Figure 3.6: (a) Line scans of a calibration sample measured with the MultimodeTM AFM (piezo xy scan range: 150 m). With a normal sample height h1 = 1:5 mm (solid line) only 11 steps are imaged, while 12 steps are found if the sample height is h2 = 7:5 mm (dashed line). (b) Schematic presentation of the sample tilt due to bending of the piezo tube.

be satis ed when ill-de ned disturbances such as building vibrations, acoustic noise, and temperature drift, as well as hysteresis and creep of the piezoelectric translation elements are eliminated. Vibrations can be minimized by using an appropriate damping system. Typical sources of vibrations are: building vibrations excited by machines running at or near line frequency (ventilation systems, pumps, etc.), and by the associated harmonics and sub-harmonics (typically 10{100 Hz) and vibrations caused by irregular motions such as those created by persons walking and working in the laboratory (typically 1{5 Hz). The in uence on the tip-to-sample distance of these external perturbations is reduced by using small dimensions and sucient stiness of the SPM structure [Pohl 86]. Also, a damping system on which the SPM is mounted must be used. The resonance frequency (fd ) of the damping system should be as small as possible in order to isolate the SPM eciently from the vibrations. This can be achieved by combining a high total mass (m) with a low damper spring constant (kd ) as is apparent from equation 3.4. A good solution has been found in using a tripod system in which the SPM is placed on a heavy platform which is suspended by three long (1 to 1.5 m) bungee cords. Also, a special vibration isolation table, whose platform is enclosed within an acoustic hood, has been used. s 1 (3.4) fd = 2 kmd

Perturbations in SPM images can also originate from drift. This eect is particularly strong when using a slow scanning speed. A major source of drift can be the slow temperature variations of an SPM. Therefore, a careful design is necessary in which symmetric arrangements are combined with low thermal expansion coecient materials, and in which all electronics which produce heat are thermally isolated from the tip-to-sample control

40


hardware. Another disturbing factor is formed by the hysteresis and creep of the piezoelectric translation elements. The importance of these eects will be discussed in section 3.7.1.

3.3 Resistance measurement unit The local spreading resistance is usually determined by measuring the current owing through the tip-sample point contact at a xed low bias (5{50 mV). Since a large dynamic range is necessary (the spreading resistances may vary from 100 to over 1 G if the probe is positioned in regions with a carrier concentration varying from 1021 down to 1014 atoms/cm3 ), the current measurement unit must be able to handle currents from the 10 pA to 100 A range. Therefore, a suitable current ampli er must be carefully selected. Low-noise components in combination with careful shielding of sample, probe and circuit are required in combination with a reasonable measuring speed. Since the resistance measurement is performed in DC mode, the speed of the circuit is determined only by the rate at which the probe is moved. Typically, the probe is moved at 1 m/s and 500 data points per m are measured, thus requiring a measurement speed of 500 Hz. As the carrier concentration varies over several orders of magnitude, the spreading resistance R (which, to a rst approximation, is inversely proportional to the carrier concentration) is best measured in a logarithmic way. Consequently, the sensitivity (S ) of the resistance measurement unit is de ned as out S = @ @V log(R) :

(3.5)

In principle, one could also measure the resistance by controlling the voltage across the tip-sample contact in such a way that the current is kept at a xed predetermined value. The voltage is then a measure of the local spreading resistance. This approach is not preferred because, in general, the tip-sample current-voltage behavior is strongly nonlinear and might result in high voltages if the reference current is taken too high. These high voltages might disturb the carrier pro le which is being measured, resulting in a false measurement. For the same reason, the resistance measurements are not performed at large bias voltages, but at low values (5{50 mV).

3.3.1 Linear voltage or current ampli er In its most simple form, the resistance measurement unit is based upon a voltage divider ( gure 3.7a) or upon a current-to-voltage convertor ( gure 3.7b). In the rst approach, a resistance Rs is placed in series with the unknown tip-sample resistance R, and the voltage Vout across the resistor is fed to a voltage ampli er. The output of the ampli er is a direct measure for R through equation 3.6 where Vb is the applied bias voltage. This output is connected to an AD convertor which enables one to store the resistance data as the probe is moved across the sample surface. The AD convertor is triggered by the AFM such that the sample topography and spreading resistance are measured simultaneously.

3.3. RESISTANCE MEASUREMENT UNIT

41

(3.6) R = Rs VVb , 1 out In a second approach, the current is measured using a standard current-to-voltage convertor in which a shunt resistor Rsh is placed in the (negative) feedback loop of a low-current ampli er (e.g. model AD549 from Analog Devices or model OPA128 from Burr Brown which both have a bias current smaller than 100 fA). The output of the ampli er is given by equation 3.7. If R is too small, the output of the ampli er (Vout ) saturates to a value close to the supply voltage. (3.7) R = ,Rsh VVb out Both linear methods are simple and fast, but have some important disadvantages. First, using a voltage divider ( gure 3.7a), the voltage across the tip-sample resistance R is not constant but can vary between 0 and Vb volts, dependent on the value of R. Consequently, the resistance values in regions with varying carrier concentration will be measured at dierent bias voltages, complicating the calibration and quanti cation of the resistance data into carrier concentration values. Second, the sensitivity depends on the value of R. A good sensitivity is obtained in the voltage-divider approach when R is close to Rs , while the sensitivity rapidly degrades if R and Rs dier from each other. In the current-to-voltage convertor approach, the sensitivity decreases proportionally to R1 . A logarithmic current ampli er, on the other hand, has a constant sensitivity for all resistance values. This is illustrated in gure 3.8 where the ampli er output is plotted as a function of R. The linear ampli er can be used if only small resistance variations are expected (Rs is then chosen equal to the expected average resistance value), or if a high sensitivity is required for a particular (limited) resistance range and sensitivity is of less importance for resistance values which fall out of this range. (a)

(b) -

+ R

R

to ADC

Rs -

Vb

R sh to ADC

+ Vb

Figure 3.7: (a) Voltage divider with linear voltage ampli er, and (b) linear current-to-voltage ampli er used to measure the tip-sample resistance.

An alternative approach - facing with similar sensitivity problems - is to make use of a standard resistance bridge (such as the Wheatstone bridge). Hereby, the sensitivity is again determined by the choice of a reference resistance.

3.3.2 Logarithmic current ampli er

The best results can be obtained using a logarithmic current ampli er. Several logarithmic current and/or voltage ampli ers integrated in one IC are commercially available. For


42

1.0

amplifier output (a.u.)

0.8

0.6

0.4

0.2

0.0 2 10

10

3

4

10

5

6

10 10 10 spreading resistance (Ω)

7

8

10

9

10

Figure 3.8: Ampli er output for a linear voltage ampli er for which Rs = 100 k (solid line), linear currentto-voltage ampli er for which Rsh = 10 k (dashed line) and logarithmic current ampli er (dotted line), illustrating the sensitivity.

example, the AD755 and AD759 ampli ers from Analog Devices and the LOG100 and 4127 models from Burr Brown oer a logarithmic ampli cation over 6 decades of current (1 nA to 1 mA). These ICs can be used without external components (except for a trimming resistor) as a single-stage current ampli er ( gure 3.9a). To extend the current range to smaller values a pre-amplifying stage can be used. Therefore, an ultra-low bias current operational ampli er can be used as shown in gure 3.9b. The current ampli cation of this stage is given by , RR21 . By choosing R1 = 100 R2 , the probe currents (10 pA { 100 A) are ampli ed to a level which corresponds to the dynamic range of the logarithmic current ampli er (1 nA { 10 mA). (a)

(b)

R

log(I)

R1

R

to ADC

-

+ Vb

R2 log(I)

to ADC

Vb

Figure 3.9: Schematic circuit layout of the logarithmic current ampli er. (a) Single-stage logarithmic current ampli er. (b) Dual-stage ampli er with a ultra-low bias current pre-ampli er, and a logarithmic current ampli er.

We selected the LOG100 model which has a reasonable speed (3 dB bandwidth always larger than 500 Hz) and a maximum logarithmic conformity error of 5%. No external components (except for a 8 M reference resistor and a 1 nF frequency compensation capacitor) are required. The printed circuit board was made such that it ts into the commercial DimensionTM AFM and such that the SSRM probes can easily be mounted on it. The diagram is presented in gure 3.10. The transfer characteristic is plotted in

3.3. RESISTANCE MEASUREMENT UNIT

43

Figure 3.10: Top- and bottom view of the printed-circuit board for a logarithmic current ampli er (based on the LOG100 IC from Burr Brown) which ts onto the DimensionTM AFM. The indicated connections are: +Vsupply , -Vsupply , ground, output and input (connected to the probe).

gure 3.11. The scale factor is about 3 Volts/decade. Note that positive input signals are required, i.e. the current must ow as indicated in gure 3.9. Using this ampli er, the maximum data rate is 500 measurements/second, which corresponds to a scan rate of about 1 Hz if 512 pixels are taken for each line scan. 10 STM amplifier LOG100 amplifier

output voltage (V)

5

0

-5

-10 10-11

10-10

10-9

10-8 10-7 10-6 input current (A)

10-5

10-4

10-3

Figure 3.11: Transfer characteristic (output voltage versus input current) of the logarithmic ampli er. The solid line corresponds to the LOG100 ampli er, the dashed lines to the STM ampli er.

Since the logarithmic current ampli ers only accept one polarity of input current, an electronic switch is needed to reverse the polarity if the input voltage is of the wrong sign. In principle, this is not necessary since the SSRM resistance measurement can always be performed at the same polarity. However, the exibility of the technique improves if both current polarities are allowed. Standard practice uses an absolute-value circuit in front of the logarithmic ampli er to rectify the bipolar signal. This requirement can be satis ed with a current inverter, switching diodes and a bidirectional current source, as shown in gure 3.12 [McDonald 80]. For the dual transistor a good parameter match is required (for example a LM394 can be used, or the logarithmic ampli er 4127 (Burr Brown) which

44


includes a current inverting option). The ampli er must have a low-oset voltage and a low bias current (for example, the 3527AM model), diode-connected JFET (e.g. BF245) should be used as the diodes to provide high accuracy.

I in +

I out

Figure 3.12: Current inverter which ensures that current always ows into the logarithmic ampli er regardless of the polarity of the input current.

A low-noise logarithmic current ampli er, originally developed for STM applications [Duerig 97] was found to be a good alternative. A schematic circuit layout is shown in gure 3.13. This ampli er accepts currents with positive or negative polarity. The convertor employs the standard virtual ground con guration with a chain of ultralow-leakage diodes that provide the non-linear feedback. One of the best diodes for this purpose is the BAV45 (Philips), which has a saturation current of typically 0.1 pA. The diode chain is shunted by a 1 G resistor to achieve stable operation below 0.5 nA. Here the transfer characteristic is linear whereas above typically 1 nA the characteristic is almost perfectly logarithmic with a conversion factor of approximately 0.7 V/decade. To obtain a suciently high bandwidth, typically 2 kHz, below 1 nA increasing to 100 kHz at 1 A, the parasitic capacitance of the diodes must be counterbalanced by means of an additional inverting ampli er (OP27) and a variable feedback capacitance (20 pF) at the input terminal. The frequency compensation is adjusted by increasing this capacitance to just below the point at which self-oscillation sets in. The circuit diagram is drawn in gure 3.13. The transfer characteristic is plotted in gure 3.11. 2k2

2k2

-

10x

OP27 20 pF

+

2k2

1G -

2k2

OP111

-

+

OP27

to ADC

+

Figure 3.13: Logarithmic current ampli er with discrete components, originally developed for STM applications.

3.4. PROBES

45

3.4 Probes The probe is one of the most crucial components in SPM to obtain high quality measurements. The tip of the probe must be extremely sharp (ultimately ending in one atom), show no wear, and must be mounted on a cantilever beam. Furthermore, every dierent scanning mode has its speci c probe requirements. In this section, standard AFM probes are brie y described rst. In a second part, a detailed description is given of the probes which were designed and used for carrier pro ling with the SSRM technique: metal and metal-coated probes, diamond and diamond-coated probes. Depending on the intended application, the cantilevers which are used should meet the following general criteria [Albrecht 90]:

Low spring constant: In order to measure small topography changes, the cantilever must bend with a relatively low force constant. Values of 10,2 to 102 N/m are appropriate for atomic resolution imaging. The spring constant of a cantilever beam with a rectangular cross section is given by equation 3.8 , whereby E is the Young's modulus of the cantilever material, h the height, w the width and l the length of the cantilever beam (see gure 3.14). 3

k = Ewh 4l3

(3.8) w h

l

apex angle

a

Figure 3.14: Standard AFM cantilever with rectangular cross section (length l, width w, height h and tip height a).

High resonant frequency: The scan rate of the AFM probe is limited by the lowest mechanical resonant frequency of the cantilever. If the scanning rate is too high or the resonant frequency is too low, the inertia of the cantilever will cause the tip to exert large forces on steeply sloped protrusions, and prevent the tip from tracking steep downwards slopes. Furthermore, fast imaging rates are preferred since the eects of thermal drift are more pronounced with slow scanning speeds. When the AFM is scanned in contact mode the resonant frequency of the cantilever increases to a much higher value, since the end of the cantilever is no longer free to vibrate. The response of the cantilever in traversing a step on the sample surface is, however, still determined by the natural resonance frequency. The combination of a low spring constant and a high resonant frequency can be obtained

46


by reducing the mass of the cantilever as much as possible. The natural and contact mode resonance frequency for a cantilever beam with a uniform cross section are given respectively by equation 3.9 and 3.10 [Marti 94]. s 1 (3.9) fr = 2 0:24k m s 1 (3.10) fr = 2 0:013k m

High mechanical quality factor Q: For non-contact scanning modes the mechanical

Q of the cantilever should have a high value, such that the sensitivity of the measurements increases. In contacting modes, however, the Q is of less importance.

High lateral and torsional stiness: A cantilever with a high lateral and torsional stiness is desirable to reduce the eects of lateral forces. For example, frictional forces can cause appreciable lateral bending of the cantilever, leading to image artefacts. A high lateral stiness can be obtained by a small height h and a large width w of the cantilever or by changing the cantilever shape from a rectangular to a V-shape. A high torsional stiness can be obtained by reducing the tip height a. Short cantilever: The sensitivity of the cantilever (expressed in V/nm) improves if shorter cantilevers are selected (see formula 3.2).

Incorporation of a mirror: When optical beam de ection is used to measure cantilever

de ection, a re ective surface is needed. A metallic surface provides the best re ectivity. Note that a rough surface might deform the shape of the laser spot, leading to a change in optical lever sensitivity [D'Costa 95]. If a metallic coating (typically gold) is deposited on the cantilever in order to improve the re ectivity, care has to be taken that the cantilever does not deform because of stress induced during the metal deposition step.

Sharp protruding tip: A sharp tip must be formed at the end of the cantilever. When the tip is dull, the image obtained is a convolution of the sample surface and the shape of the tip.

For SSRM, which is a current-carrying contact mode technique, the probes should ful ll a number of additional requirements:

High spring constant: The range of forces which can be applied by the probe is deter-

mined by the spring constant of the cantilever. Indeed, if the spring constant is too low for a particular force, the cantilever will bend to such an extent that the re ected laser spot moves o the photodetector (in this way opening the feedback loop). However, upon

3.4. PROBES

47

increasing the spring constant, the sensitivity to small changes in topography reduces correspondingly. The high forces which are required for stable SSRM operation necessitate a high spring constant (1 to 100 N/m).

Electrically conducting: The tip and cantilever must be highly conducting so that their

resistance can be neglected in the total measured resistance. Both doped semiconductors and metals are candidate materials to fabricate the tips and cantilevers. Poor conducting or isolating probes can be considered as well if they are coated with a conductive layer.

High hardness: The tips must be able to withstand the high forces which are involved in the SSRM mode. Their hardness should be at least equal to that of the indented material (most frequently Si).

The probes which were used in this work can be divided into two categories: metal probes and diamond probes. The probes are presented in the next sections. The mechanical and electrical characteristics are described in chapter 4.

3.4.1 Standard AFM probes Standard AFM probes are usually made from Si3N4 or Si using a batch fabrication process [Wolter 91, Albrecht 88]. Both direct and indirect fabrication technologies are used. In the direct way the tips are created in silicon by wet and/or dry etching, usually by undercutting an etch mask. Robust KOH etched tips are preferable for scanning on nearly planar sample surfaces, whereas the reactive ion etched tips have smaller opening angles, making them useful for scanning steep topography changes. In the indirect way a tip shaped hole is rst etched in silicon and thereafter lled with the desirable tip and cantilever material. Later, the silicon substrate (which only serves as a mould) is totally removed in a wet etchant. The advantage of this process is a large versatility in choice and combination of the tip material. However, a disadvantage in the indirect method, is the lack of freedom in shaping the tip mould: the aspect ratio is xed and low. For electrical applications, Si probes can be made conducting through doping. However, their application to SSRM is impossible. The major drawback of these probes is found in the limited hardness and limited resistance to wear of sharp Si probes.

3.4.2 Metal and metal-coated probes Many of the recently developed AFM schemes require conducting cantilevers [Thomson 95b]. In most of these methods, metal probes or metal-coated probes are used. A major advantage of metal probes over other types of probes is that they are made of low resistive material (typically 10,6 cm). On the other hand, metal probes might be sensitive to wear when they are used in contact mode AFM.

48


Metal probes A wide range of fabrication techniques can be used to prepare very sharp metal probes for STM or AFM. The most common methods include electrochemical etching and mechanical shearing. Many electrochemical polishing procedures, solutions, and conditions which have been known for a long time for tip preparation in eld ion microscopy and eld-emission electron microscopy are also applicable to STM or AFM [Niemeck 54]. A description of various tip-etching procedures can be found in the book by Tsong [Tsong 90]. Table 3.1 compares the elasticity modulus and the hardness of dierent metals (silicon and diamond are added as a reference). Tungsten tips have been used to a great extent in STM because of their high stiness. Platinum, although a softer metal, is a preferable material to tungsten because it is inert to oxidation. The addition of Ir to form a Pt/Ir alloy adds stiness while maintaining a chemically inert material. In this work, Ir and Pt/Ir probes were fabricated and tested. Table 3.1: Comparison of elasticity modulus and hardness of dierent metals (from [Weast 74]). Silicon and diamond are added for comparison.

Material Young's modulus Mohs hardness Knoop hardness (GPa) (a.u.) (GPa) W 360 Ti 115 Pt 145 4.3 0.18 Ni 207 5.5 0.56 Ir 528 6-6.5 0.65 Co 210 8 1.45 TiN 9 1.80 WC 9 1.88 Si 130 7 0.85 diamond 1140 10 6{10

Etched Pt/Ir probes A simple, fast and inexpensive method using innocuous chemicals was used to fabricate sharp Pt/Ir and Ir tips. The tips are formed in a two step process whereby the tip is rst etched in a bulk solution to obtain the basic shape [Musselman 90]. A piece of Pt/Ir (90:10) wire (diameter 25 or 50 m) is suspended in an unstirred, saturated CaCl2/H2 O/HCl solution (60:36:4 by volume) at room temperature. The rst step consisted of bulk etching of the Pt/Ir wire against a carbon rod electrode at 2 V (RMS) at 50 Hz for 20 minutes in 20 ml of aqueous CaCl2/HCl to obtain the general shape. After the etching step the tip is rinsed in distilled water to remove the residual etchant solution. The second step involves micro-polishing of the tip in a thin lm of etchant held by a Pt/Ir loop with a diameter of 5 mm ( gure 3.15). A micro-manipulator is used to position the tip precisely and dip only the very end of the tip into the etchant lm. An AC potential of 1.5 V (RMS) is applied between the tip and the loop. While following the process through a stereomicroscope (80 magni cation), the tip is pulled out of the etchant as far as possible so that the tip surface is being wetted as little as possible. The etchant must

3.4. PROBES

49

be refreshed periodically since the solution detoriates as the chloride ion concentration is depleted due to the formation of various platinum chloride complexes. Also gas and black particles appear during electrolysis. After the nal etching step, the tip is rinsed again in distilled water to remove the residual etchant solution. The tip quality is checked under the optical microscope and the SEM. Figure 3.16 shows a low and high magni cation SEM image of a Pt/Ir tip after the micro-polishing treatment. etchant

probe etch loop micro manipulator

AC

Figure 3.15: Schematic setup for the micro-polishing step of Pt/Ir tip fabrication. The etchant is a CaCl2 /H2 O/HCl solution.

Figure 3.16: Low and high magni cation SEM image of an electrochemically etched Pt/Ir probe (wire diameter 25 m) after the micro-polishing step. Tip radii smaller than 10 nm can be obtained using this method.

Before etching, the metal wires were squeezed (except for the free end of the wire) to form a at cantilever surface which is needed for the re ection of the laser beam. The free end of the metal was subsequently bent under 90 to form the tip. A small piece of squeezed Pt was glued on top of some of the cantilevers (using a micro-manipulator) to form a larger mirror surface. The cantilever is glued onto a glass cantilever support, which is cut to t into the AFM. Dierent spring constants of the cantilevers were obtained by using wires with various lengths and diameters. A fully operational example is shown in gure 3.17.

50


Figure 3.17: Electrochemically etched Pt/Ir AFM probe integrated on a cantilever formed by bending the wire under 90 and attening to form a re ecting surface.

Etched Ir probes Iridium is highly suitable as a tip material. Apart from having a high Young's modulus (see table 3.1), it is well known that Ir is particularly resistant to corrosion and to oxidation (in contrast to, for example, osmium and tungsten). Tips are fabricated by micro-electrochemical etching in 4 molar KOH in water at room temperature at 1 kHz and at about 0.5 V (RMS) in two stages: the rst etching is performed in a droplet of the electrolyte, the second in an etchant lm. In both steps the electrolyte is held by a platinum loop. While some gas evolution is noticed under the conditions of the electrolytical process, a blue color develops in the solution pointing to the formation of Ir complexes. Cantilever beams are formed in the same way as for the Pt/Ir tips. Metal-coated probes Standard Si AFM probes can easily be coated by evaporation or sputter deposition of a metal layer. Probes with dierent coatings were used: Au, Au/Cr, W, Ti, Ni, Co, Ti/W, and W/C. The major drawback of these probes is the increase in probe radius during coating. For example, if a Si probe with a radius of 10 nm is coated with a 50 nm thick metal layer, the resulting probe radius is about 60 nm.

Full-metal probes Recently, several groups have fabricated metal cantilevers with an integrated tip using a batch process [Hantschel 97, Tang 97, Boisen 96a, Boisen 96b]. These tips can be fabricated directly [Boisen 96a] or indirectly [Boisen 96b]. The advantage of such a concept is that a small tip radius and a well-de ned cantilever geometry can be obtained simultaneously (whereas the tip radius is quite large for metal-coated probes, and the cantilever geometry ill-de ned for etched metal wires). All metal probes used in this work (etched wires, metal-coated probes and full-metal probes)

3.4. PROBES

51

were found to be too fragile for SSRM operation on Si. The probes deformed rapidly upon applying the force which is required for stable SSRM operation (i.e. the force at which a clear relation between resistance and local sample resistivity is observed). The etched metal tips became bent, while the tip radius of the metal-coated and full-metal probes were observed to increase dramatically. Even when using metals with the highest resistance to wear the same behavior was observed.

3.4.3 Diamond and diamond-coated probes In order to overcome the tip wear problem, several groups are preparing diamond tips for various SPM applications as well as for eld emitter arrays. Diamond has the highest hardness (6{9 GPa) and Young's modulus (1140 GPa), the highest thermal conductivity (20 W/cm at 300 K), the lowest dielectric constant (5.66) and the highest breakdown eld (107 V/cm) of known semiconductors [Eremets 91]. These speci cations, combined with the chemical inertness, makes diamond a very interesting material for the fabrication of SPM tips for electrical applications. Table 3.1 compares the hardness and elasticity modulus of diamond with other relevant SPM tip materials. The dierent types of diamond probes available can be divided into three categories: full diamond probes (without cantilever), tip-cantilever systems (Si, metal,...) coated with a thin diamond layer, and diamond tips integrated on a diamond cantilever. Table 3.2 gives an overview of the dierent types of diamond probes. Table 3.2: Comparison of dierent types of diamond SPM probes.

Type Fractured diamond

reference

[Binnig 86a, Marti 87] Bulk diamond [Kaneko 90a] CVD diamond on bulk [Visser 92] diamond Isolated diamond crys- [Germann 92, tals on W or Si Liu 94a] CVD diamond on Si [Niedermann 96] Integrated diamond [Kulisch 97, Niedermann 97]

tip radius resistivity Comments (nm) ( cm) badly de ned geom. 100 12

0.034

30

-

20-200 20-30

0.03 0.1

no batch process no batch process low yield batch process batch process

Bulk diamond probes Since the early days of SPM, probes have been formed by fracture of bulk diamond [Binnig 86a, Marti 87]. However, the geometry and surface chemistry of such tips are not well de ned

52


[Germann 92]. Also, the resistivity of these probes is generally too high for electrical applications such as SSRM. Probes for STM have also been produced by growing boron doped homo-epitaxial lms on bulk diamond tips [Visser 92]. The diamond layer is grown epitaxially on an insulating natural diamond substrate of (110) orientation in a hot lament CVD reactor. A low resistivity (0.034 cm) is realized by heavy boron doping (the boron concentration is measured to be 6 1020 ions/cm3 ). The actual tip is formed by conventional diamond polishing and grinding and is found from indentation studies to have a radius of 12 nm (although SEM images of the same tips indicate a typical radius of 80 nm). STM probes have also been produced from bulk diamond [Kaneko 90a]. These probes were commercialized by Adamant Kogyo Co., Tokyo for STM applications. The diamond is brazed onto a titanium cylinder of 2 mm in length and 0.5 mm in diameter and is ground to a three-sided pyramid whose point is sharpened to a radius of about 100 nm. After completing the machining, the tips are implanted with boron (80 keV, 1:18 1016 ions/cm2 ) [Allos 94]. The tips come with a wire pressed into a central hole in the titanium cylinder, which must be removed before mounting the tip. In order to be able to use these probes for SSRM, we have shortened the tip as much as possible (to 1.5 mm) and ground it at with sandpaper resulting in a square cross section. The purpose of this procedure was to reduce the weight of the tip as much as possible. Glass supports from commercial cantilevers were used as substrates so that the fabricated cantilever units would t into a commercial AFM system. The cantilever itself can be formed by a small rectangular plate [Kaneko 90b] or can be formed by glueing two U-shaped Pt/Ir wires parallel to each other onto the top and bottom of the glass support with non-conductive epoxy (Torr Seal). By choosing the appropriate wire diameter and length it was possible to select the stiness of the cantilever. A double spring construction was chosen in order to increase the stiness of the cantilever in the xy plane. Earlier designs using dierent geometries failed because on contact with the sample the titanium cylinder twisted away from the normal to the plane. The titanium cylinder with diamond tip was then carefully tted into the space provided by the two loops of wire. In some units the cylinder was cemented with epoxy to the upper U-shaped wire, and to the lower one it was glued with metalizing conductive adhesive resin (silver epoxy). The epoxy was allowed to set at room temperature for fear of disrupting the brazing between the diamond and the titanium base by heating. The resin ensured an electrical contact between the diamond tip and the external circuitry by way of the titanium, the conducting epoxy, and the Pt/Ir beams onto which ne copper wires were silver pasted. In the most perfected version of the cantilevers, however, the current was carried by a curly gold wire of 30 m in diameter in order to avoid complications of thermal expansion of the cantilever beam caused by Joule heating. The gold wire was xed with silver conductive resin to the central cavity of the titanium cylinder and glued to the glass base for contact to the usual thin copper wires. A squeezed Pt/Ir mirror shielding the sample from illumination by the laser beam and used for detecting the cantilever de ections was fastened to the upper pair of cantilever beams. The metallic mirror on the cantilever did not allow any of the laser light to reach the sample. A schematic representation of the conducting AFM tip with implanted diamond is shown in gure 3.18.

3.4. PROBES

53 Pt mirror

glass holder Au wire 4 Pt wires Ti base diamond tip

Figure 3.18: Schematic diagram of conducting cantilever with implanted diamond tip mounted on a standard cantilever support with 4 Pt wires. A piece of squeezed Pt/Ir wire acts as a mirror. A curly gold wire ensures electrical contact between tip and external circuitry.

Table 3.3 gives an overview of the dierent tip con gurations constructed in the way described here. The table includes the computed force constants and indicates whether or not a tungsten lm (thickness 35 nm) was sputter deposited on the tip to further improve its conductivity. In gure 3.19 both a top view and a side view of cantilever IV are shown. Table 3.3: Characteristics of cantilevers with implanted diamond tip.

tip apex angle cantilever spring const. weight W coating ( ) (m) (N/m) (mg) O 60 20 (W) 110 no I 60 100 (Pt/Ir) 10000 no II 60 50 (Pt/Ir) 1220 0.53 no III 60 25 (Pt/Ir) 220 0.26 no IV 80 25 (Pt/Ir) 200 0.42 no V 60 50 (Pt/Ir) 1500 0.32 yes VI 80 25 (Pt/Ir) 200 0.23 yes

CVD diamond-coated probes The chemical vapor deposition (CVD) of isolated diamond crystals on the apex of W [Germann 92, Liu 94a, Liu 94b] or Si [Givargizov 95] tips, is dicult because there is no control of the orientation of the crystals with respect to the tip and because the creation of nucleation sites on the substrate material is dicult to realize. Often, a poor yield and reproducibility is observed when using this fabrication method and the crystals are frequently deposited on the sides of the tips rather than on their apex. In a similar method, CVD diamond is deposited by the hot lament CVD method on silicon probes [Niedermann 96]. The deposition takes place at typically 830 C in a mixture of 1% CH4 and 99% H2 [Mueller 96]. For these conditions, the growth rate is of the order

54


Figure 3.19: Conducting cantilever with implanted diamond tip (tip IV from table 3.3): (a) side view and (b) top view before the mirror is mounted on top of the wires.

of 1 m/h. The coatings have a limited purity, because the heated lament evaporates to a small extent. Alternatively, a microwave and electron cyclotron resonance CVD process can be used [Mueller 93, Hintermann 93]. These coatings are very uniform (10% of average thickness) over large areas (200 mm or more), smooth, and of high purity, but the growth rate is very low (about 100 nm/h). A dense nucleation of the diamond without damaging the silicon substrate is required to obtain continuous ultra-thin lms and is achieved by a priming procedure. The lms are boron doped in situ during growth, with a boron concentration of 1-10 ppm in the gas phase. The electrical and mechanical properties of CVD diamond and single crystal diamond are very close to each other [Hintermann 93]. For example, the Knoop hardness is 5{10 GPa for CVD diamond and 5.7{10.4 GPa for single crystal diamond. The Raman spectrum measured on a 150 nm thick diamond-coating on a silicon substrate ( gure 3.20) shows a strong peak at 1332 cm,1 corresponding to the carbon sp3 bond, indicating that there is a considerable amount of crystalline diamond in the lms. The limited intensity of this peak (compared to crystalline diamond) is related to the ne grain size of the lms [Namba 92]. A broader (and lower) peak, corresponding to the sp2 or graphite content, is observed around 1600 cm,1 . The spectrum shows two relatively strong peaks at about 1200 and 550 cm,1 , which are normally not expected for graphite or diamond. These peaks re ect the existence of defects (and impurities) in the coating lm, originating from the high boron dose which is used to maximize the electrical conductivity of the lms. The resistivity of the diamond layers prepared in this manner is about 0.03 cm. The speci cations of the diamond-coated probes used in this work are summarized in table 3.4. Two dierent tip geometries were used. The tips of probes I through IV have a large apex angle (40{50 ), while probes V have a much sharper tip apex (10{20 ). The tip radius is comparable for both geometries. Figures 3.21 and 3.22 show a low- and highmagni cation SEM image of both types of geometry. Although the macroscopic tip radius observed in these images is in the range of 100{200 nm, the tip often exhibits a nanoroughness in the 10 nm regime due to small (sharp) diamond particles. The tips with the

3.4. PROBES

55 A 1000

B

intensity (a.u.)

C 800

D

600

400 400

600

800

1000

1200

1400

1600

1800

wavenumber (cm-1)

Figure 3.20: Raman spectrum of a CVD diamond layer (thickness: 150 nm, substrate: silicon) showing the graphite (D) and diamond (C) peaks. Peaks A and B are related to the presence of defects.

smallest apex angles (type V) were found to break o easily when used for SSRM. The tips with a larger apex angle (types I through IV), were found to be more rigid and are therefore preferred. Table 3.4: Characteristics of CVD diamond-coated silicon cantilevers with integrated tip (probes I{IV are fabricated at CSEM, Neuchâtel, Switzerland, probes V at Nanosensors, Wetzlar, Germany).

tip I II III IV V

l

(m) 110/215/405/615 175/290/490/700 175/290/490/700 125/200/275/350 125/225

w

(m) 40 40 40 15 30

t

(m) 12 6 6 6 4/3

wafer ( cm) n 4.0 p 0.04 p 0.04 p 0.05 p 0.1{0.2

tcoat

(nm) 500 70 120 100 100

k

(N/m) 2207/286/44/13 68.5/15.1/13.1/1.1 68.5/15.1/13.1/1.1 72.6/17.7/6.8/3.3 42/3

fr

(kHz) 1388/363/102/44 274/100/72/17 274/100/72/17 528/206/109/63 330/75

Cantilevers made from diamond or silicon are very sti and brittle. As a consequence, careful handling is required because they break o easily (compared to cantilevers made from Si3N4 or metal). The uniformity of the diamond-coatings can be evaluated from the AFM topography of the surface of a silicon cantilever coated with 120 nm diamond ( gure 3.24). This image clearly shows the diamond grains which are formed at the nucleation sites. Between neighboring grains, openings are observed which can be as deep as the thickness of the coating layer. For the CVD deposition process used, coating layers which are thinner than 100 nm always have a large number of these openings, leading to a remarkably higher sheet resistance compared to thicker layers. Hence, a minimum thickness is required. However, if the thickness is too large, the probe radius increases and the best achievable resolution is poor. For example, a coating thickness of 500 nm resulted in a probe

56


Figure 3.21: Low and high magni cation SEM image of a diamond-coated cantilever with integrated tip (type IV from table 3.4, fabricated at CSEM, Neuchâtel, Switzerland). The probe has a large apex angle (40{50 ). The high magni cation image shows dierent diamond grains which might result in a small tip radius.

Figure 3.22: Diamond-coated cantilever with integrated tip (type V from table 3.4, fabricated at Nanosensors, Wetzlar, Germany). The probe has a small apex angle (10{20 ).

3.4. PROBES

57

radius of about 350 nm. Figure 3.23 shows the probe radius(a) as a function of the coating thickness as measured on a SrTiO3 calibration standard with atomically sharp steps with a well-de ned angle of = 25:6 [Sheiko 93]. The rounding of the atomically sharp steps can be used to calculate the tip radius with nanometer precision. The radius is given by equation 3.11 where d is the size of the rounded region.

d a = 2 sin( )

(3.11)

2

From these eects, it may be concluded that the ideal diamond-coating thickness is 100{150 nm. In this case, the uniformity is guaranteed (and thus a low sheet resistance) while the probe radius remains reasonably small. Finally, the roughness of the diamondcoating degrades the quality of the top surface of the cantilever as a mirror. Therefore, it is recommended to deposit an additional metal coating (e.g. Al or Au) on this surface to improve the re ectivity.

300

(c)

tip radius (nm)

250

measured fit

200 150 100

height (nm)

50 4 2 0 -2 -4 0

(b) 25.6

0 0

o

100

200

300

400

500

coating thickness (nm) 29 nm

100

200 distance (nm)

300

400

Figure 3.23: (a) AFM topography of a SrTiO3 calibration sample with a diamond-coated Si probe (scan size: 500500 nm2, coating thickness: 120 nm). (b) Section taken at the white line indicated in (a). The probe radius is calculated to be a = 2 sind=2 = 029 :45 = 65 nm. (c) Radius of the diamond-coated probes as a function of coating thickness.

Diamond cantilevers with integrated tip A dierent approach enables the fabrication of diamond tips with small radii of curvature integrated on diamond cantilevers [Oesterschulze 97, Kulisch 97, Niedermann 97]. It follows an analogous process for the production of all-metal probes [Hantschel 97, Tang 97] wherein standard Si processing techniques are used. One starts with a silicon wafer coated with a

58


Figure 3.24: Surface structure of a 120 nm thick CVD diamond layer as measured with AFM (scan size: 22 m2 ).

thermal oxide in which a hollow pyramid with a top angle of 70:6 is etched anisotropically using KOH (40 wt. %, 60 C). Next, the window for the future cantilever is opened and the wafer is subjected to a priming treatment in order to enhance diamond nucleation in a later stage since diamond nuclei hardly grow on a mirror-polished silicon surface [Yugo 91]. Both ultrasonic treatment with diamond paste [Ijima 91] and a pre-deposition plasma CVD process of several minutes with a higher CH4 content [Yugo 91] have proved to be successful. Subsequently, a 3{5 m diamond lm is deposited by hot- lament CVD or microwave CVD. A high boron dose is applied during the deposition to ensure the conductivity of the probes. Finally, the remaining SiO2 is removed and the silicon is etched o using KOH to release a freestanding diamond cantilever with a diamond tip. Tips with a radius of curvature of 20{ 30 nm have been be obtained in this manner. These probes have the advantage of combining a small tip radius with a large apex angle and a good crystalline diamond structure.

Figure 3.25: Low and high magni cation SEM image of a diamond cantilever with integrated diamond tip (fabricated at CSEM, Neuchâtel, Switzerland).

The speci cations of the diamond cantilevers with integrated tip which were used in this work are summarized in table 3.5. The geometry is displayed by the SEM images in gure 3.25.

3.4. PROBES

59

Table 3.5: Characteristics of diamond cantilevers with integrated diamond tip (fabricated at CSEM, Neuchâtel, Switzerland).

tip length (m) k (N/m) fr (kHz) I 500 0.17 11.2 II 220 1.97 57.8 III 150 6.22 124.3

Conclusion: the ideal SSRM probe

In conclusion, the ideal probe for SSRM has the following speci cations, summarized in table 3.6. First, it must be made of an extremely hard material in order to be able to withstand the high pressures which are involved in the SSRM measurements. Second, the material must be electrically conducting, with its resistivity as low as possible. Third, the tip radius must be as small as possible to make high spatial resolution feasible. Table 3.6: Speci cation for the ideal SSRM tip-cantilever system.

property material resistivity spring constant tip height tip radius tip apex angle cantilever shape cantilever length cantilever width cantilever thickness mirror surface

3.4.4 Dual probe

speci cation doped diamond 10,3 cm 10{100 N/m 5{10 m 10{25 nm 30{60 rectangular beam 150{300 m 20{40 m 3{6 m Au coating (20{100 nm)

The concept of a dual head for SSRM is inspired by the standard operation of conventional SRP where a pair of probes is stepped over a beveled surface. The dual probe arrangement can be used when the resistance measured in a single probe con guration is dominated by any part of the complete current path between the probe and the back contact, aside from the local spreading resistance experienced by the probe. In this way, one avoids the need of a back contact. There are two possible modes. The two probes can be stepped or scanned simultaneously, or one probe can have a xed position, while the other probe steps or scans across the sample. Until now, this type of probes is not available. We constructed, for the rst time, a dual probe to operate in the rst mode. Figure 3.26 shows a schematic representation of this dual probe incorporating two implanted diamond tips. By using two opposing arms of a micromanipulator it was possible to adjust a pair of the polished faces of the triangularly shaped tip extremities such that they were facing each other at close

60


distance (17 m). The tips were glued to each other in this position with insulating epoxy resin.

Figure 3.26: SSRM dual probe with implanted diamond probes.

The major problems in both approaches, are bringing the tips together as close as possible and the identi cation and control of the position of one tip with respect to the other one (in three dimensions). A partial solution to such diculties is proposed by Tsukamoto et al. using the sum and dierence of tunneling currents to control piezo elements that regulate both tip/sample distance and sample inclination [Tsukamoto 91]. This concept is however in a development stage and cannot yet be applied in the SSRM technique.

3.5 Sample preparation Scanning probe microscopes have been increasingly employed for high resolution imaging of semiconductors and semiconductor devices. In most cases, imaging is done in plan view, i.e. on wafer surfaces, and sample preparation for imaging is trivial. For carrier pro ling, however, the region of interest (often subsurface) must be accessible to the pro ling instrument. The SPM-based carrier pro ling methods, in particular SSRM, require a cross section through the sample to expose this region. Cross section preparation of semiconductors usually involves cleaving and/or polishing. The most important criteria for the cross-sectional surface are: low roughness, no surface damage, cleanliness. The two major sample preparation steps are the cross section preparation and the attachment of a current collecting contact to the sample.

3.5.1 Cross section preparation The dierent steps in the cross section preparation used for SSRM are schematically represented in gure 3.27. The same procedure can be used for other cross-sectional imaging methods such as SCM, dopant selective etching and Kelvin probe force microscopy. The principal steps can be summarized as:

Cleaving or sawing the wafer at the region of interest. A thin quartz glass plate or dummy wafer is cleaved or cut in the same way to have strips of the same size.

3.5. SAMPLE PREPARATION

61

Glueing a piece of the wafer and a piece of quartz glass (or dummy wafer) together,

face-to-face, thus protecting the wafer surface with the device against damage during the polishing procedure.

Soldering a current-collecting back contact. Polishing the cross section using dierent grain-size abrasive papers or polishing slurries.

Cleaning (a)

(b)

(c)

(d)

dummy glue back contact

(e)

(f)

or

Figure 3.27: Schematic representation of the cross section preparation procedure before polishing: (a) selection of the region of interest, (b) sawing or cleaving, (c) glueing against a dummy wafer or a thin piece of quartz glass, (d) back contact soldering, and polishing using (e) a special holder or (f) epoxy embedding.

62


As for cross-sectional TEM sample preparation [Romano 90], the dierent steps must be carried out with great care in order to arrive at a well-prepared cross section. It is clear that this requires some experience from the operator and can be considered more as an art than science. More details on each of these steps are given below.

Sawing of the wafer First, an area of the silicon wafer on which the pro le is desired is selected. A small piece is cut out of the wafer by scribing and breaking or sawing. A typical sample size is 55 mm2 . The sawing of the wafer is performed with a wire (or thinblade) diamond saw used for cutting integrated circuits. The principle advantage of using a diamond saw instead of cleaving the sample is that cuts can be performed in any desired crystallographic direction and not only in the main crystallographic directions. The cut plane is chosen parallel to the desired cross section plane, at a distance of 50{200 m (only limited by the accuracy of the positioning of the saw). This has been found to be a good compromise between the time required for the preparation and the reproducibility. The structure can also be located further away, but then longer polishing times are required. The roughness of the cross section after sawing or cleaving is generally too high for any SPM application. Hence, additional polishing is necessary. If structures with bonding pads are prepared, care has to be taken that the bonding pads are on the selected piece (and not on the removed wafer material) such that they can still be used for connecting the current-collecting back contact. Glueing When polishing the cross section of a single piece of silicon, the sample edge

easily chips o or becomes rounded. Since most structures are positioned at or close to the sample edge (i.e. the top surface), the sample edge must be protected from chipping. One possible approach to this problem is to glue an extra piece of silicon (dummy) or quartz glass onto the top surface. This piece protects the original silicon sample from damage during the polishing steps. A stereo microscope (magni cation 30) is used to facilitate the alignment of the edges of the dummy and the sample. The choice of dummy and glue material and the thickness of the glue layer are important. In this work, M-bond 610 adhesive (Measurements Group, Inc.) was used successfully. The main advantages of this type of glue are: (i) that it is transparent to light, (ii) that it forms a thin layer ( 1m) when the two pieces are pressed together, (iii) that the glue does not lose glueing power. The glue layer must be uniform and have no openings over the complete sample surface. Therefore, the samples must be cleaned thoroughly before glueing to remove all contaminants which are present after sawing or cleaving the sample. The glued stack is clamped rmly (e.g. using a paper clip) during the curing of the glue to reduce the thickness of the glue layer as much as possible. The thickness of the glue layer must be as small as possible. If at surfaces are used, a thickness of 100 nm can routinely be obtained. The glued stack is introduced in a furnace set at 150 C for about 15 minutes. This makes the glue hard enough for the mechanical polishing procedure. Note that a stack of more than two samples can be formed, in this way reducing the total sample preparation time. The quality of the glass piece is important in the described preparation technique because of two reasons: rst, if transparent, it allows one to observe the structure during the polishing procedure and secondly, it protects the active surface against undesired damage


63

during polishing. The polishing rate of the glass dummy is close to the one of silicon (when using the settings described in the next paragraph). An additional advantage of the stacked setup, is that the AFM probe can easily be kept in contact with the sample, whereas the probe loses contact when no dummy sample is used and the structure to be scanned is located at the sample edge. Consequently, the probe lifetime is much larger. In this context, it is worth mentioning that the topography should be as at as possible to reduce probe wear.

Polishing In principle, a technique similar to the SRP sample preparation method can be used [Pawlik 92, ASTM 674]. In conventional SRP, silicon samples are polished using a ne-grain diamond compound in a non-aqueous uid. Polishing of silicon slices or other large-area specimens is done against a polishing cloth; bevel polishing of small specimens is done against a glass surface. When polishing is complete, residual polishing compound is removed by organic solvent. The most important dierence in the SRP and SSRM sample preparation is that a beveled surface is needed for SRP, whereas a cross-sectional surface is needed for SSRM. Also, it is expected that the smaller probe size of SSRM makes the technique more sensitive to small topography variations, hence requiring a atter surface. After glueing, the sample stack is xed into a special sample holder ( gure 3.27e) which can also be mounted on the AFM system, such that the sample can easily be repolished between successive measurements. The sample must be xed rmly (using two adjustment screws) such that it can not move during the polishing procedure. The holder ts into an outer ring which can be held manually or clamped mechanically by the polishing machine. (Vacuum) grease is used between the polishing holder and the outer ring to avoid tilting and shaking of the holder during the polishing steps. Alternatively, the stack is embedded in epoxy resin using a small piece of tube (diameter 1 cm, height 0.5 cm) as shown in gure 3.27f. Standard epoxy resin can be used. We used epoxy which required 8 hours of drying time at 75 C. If the sample contains a device structure which must be bonded to form the back contact, the approach using epoxy is preferred; rst the sample is bonded, then the bonded sample is embedded in epoxy such that the bonding wires can be contacted without removing the epoxy. The holder can be moved manually over xed polishing pads or can be held xed on a rotating polishing plate. The former method is preferred for the coarse polishing steps (large grain size) while the latter is preferred for the ner steps. The range of speed of revolutions is 20{100 rotations per minute (which corresponds to speeds of 0.1{0.5 m/s at the sample). If the initial cross-sectional surface is rough, the rst polishing step must be performed with abrasive paper with a large grain size (e.g. 15 m). It is used for a very short time (5{30 s) to remove the largest topography variations. Then, abrasive papers with decreasing grain sizes are used (e.g. rst 9 m, then 0.3 m). Either aluminum oxide (Al2 O3 ) or silicon carbide (SiC) papers can be used. Because the nest abrasive still leaves some tiny scratches, an additional polishing step can be used in order to obtain a mirror like surface. This can be performed with oxide polishing on a polishing cloth. The polishing action is achieved through a combination of chemical treatment and gentle abrasive action. Colloidal silica with a grain size which can be as small as 0.04 m (e.g. Syton X30) are frequently used in microelectronics for very ne polishing. The weight and speed must be reduced to avoid destruction of the specimen.

64


A stereo microscope (magni cation 30) and a high magni cation microscope (magni cation 500) with dark eld imaging option are used to quickly evaluate the quality of the polished surface. Some experience is required from the operator to decide when a particular surface has been polished long enough and is ready to go to the next polishing step. In between dierent polishing steps, the sample must be thoroughly rinsed in water in order to remove residual grains. The quality of the polished cross section is illustrated by the AFM roughness measurements presented in gure 3.28 for dierent phases in the polishing procedure. The sample was cleaned to remove residues every time before the AFM measurement was performed. The RMS roughness and peak-to-valley numbers are summarized in table 3.7. For comparison, a round-robin (with 24 dierent institutes) of conventional SRP indicated an average RMS roughness value of 3.48 nm (peak-to-valley value: 20.81 nm [Clarysse 98b]). Note that a particular polishing paper can only be used for a limited time before it loses its polishing capability.

Figure 3.28: Cross section AFM topography images showing the eect of dierent polishing steps: (a) after the use of 9 m Al2 O3 abrasive paper, (b) 0.1 m diamond polishing pad, (c) 0.3 m Al2 O3 paper, (d) 0.05 m Al2 O3 polishing slurry, and (e) Syton (scan size: 1010 m2). The depth scale for (a),(b) is 50 nm, for (c),(d) and (e) 10 nm.

Regions with dierent materials in structured silicon samples show some preferential polishing due to a dierence in polishing rate. An example is shown in gure 3.29 which shows the topography after polishing of a silicon sample with buried SiO2 stripes, covered with poly-silicon. The nal polishing step was performed with Al2 O3 paper, 0.3 m grain size. No height dierence is observed between the crystalline and poly-silicon regions,


65

Table 3.7: Peak-to-valley (PTP), mean (Ra) and RMS roughness of the sample surface after dierent polishing steps (all measured on a 1010 m2 area).

Al2 O3 paper Al2 O3 slurry diamond Syton FIB SRP grain size (m) 9 0.3 0.05 0.1 0.04 RMS (nm) 1.58 0.34 0.24 2.62 0.23 0.16 3.48 Ra (nm) 1.12 0.27 0.16 2.08 0.17 0.13 2.72 PTP (nm) 21.65 3.17 2.43 19.20 2.51 0.96 20.81 but the SiO2 layers are about 2 nm higher. The observed heights facilitate the precise positioning of the probe on the structure under study, and are too small to in uence the SSRM measurements. Another consequence of dierent materials present on the sample cross section is the following: during the polishing procedure, some (soft) materials might be smeared out onto others (brittle ones). In particular metallic regions, such as W plugs or Al metallization layers, are found to be sensitive to this eect. The smearing can be minimized by reducing the load acting on the sample during the nal polishing step. None of the dierent polishing procedures which were used showed a dopant-dependent polishing rate. Thus, the polished silicon region always has a at topography (except for polishing scratches).

Figure 3.29: Cross section topography after the nal polishing step of a structured silicon sample illustrating the material dependence of the polishing rate (scan size: 44 m2 ). The sample has a trench lled with a thin layer of SiO2 and further lled with poly silicon. On average, the SiO2 is 2 nm higher than the surrounding silicon.

Finally, it is worth mentioning that the best results (i.e. the lowest surface roughness, without edge rounding) can be obtained if one considers the following polishing tricks: (i) The polishing direction should be perpendicular to the sample edge and away from the sample structure. If regions of metals are present on the sample, the polishing direction should be such that the metal debris is moved away from the region of interest. (ii) The more water is used, the less damage to the sample surface is observed. (iii) The coarse polishing steps can be performed at high loads, the ner ones at lower loads (note that the standard pressure is about 500 kPa (weight of the holder = 300 g, sample area = 6 mm2 ). (iv) Frequent rinsing of the polishing plate in water to remove residuals and contamination-free

66


storage, improves the polishing quality. (v) Rounding of the sample edge is pronounced if Syton is used. Therefore, the use of Syton should be avoided if the structure to be imaged is positioned at the very edge of the cross section. Sometimes, it is preferred to polish under a small angle in order to enlarge the depth scale of the structure. In this case, the sample can be glued on a beveling block as is done in the conventional SRP preparation procedure. A beveling block which ts onto the polishing holder used for cross section preparation is shown in gure 3.30. The same polishing procedure as for cross sections is used. No dummy is needed to protect the sample edge from chipping. The polishing direction should be from beveled surface to the wafer top surface (perpendicular to the bevel edge). Depending on the dierent polishing steps used, the bevel edge might show a small or large rounding. This bevel rounding must be taken into account and be corrected for when SSRM is performed close to the bevel edge (see chapter 7). bevel angle

Figure 3.30: Sample mounting block to polish a bevel surface at a small bevel angle.

Cleaning Residues are removed by ultrasonic cleaning in ethanol and de-ionized (DI) water. Replicating tape with aceton has also proven to be useful for removal of contaminants on the sample surface: First, a droplet of aceton is put onto the sample, then a piece of replicating tape is put onto the droplet and heated to about 100 C. Finally, the tape is pulled o and the sample is rinsed in DI water. Some of the samples were treated with a short dip in diluted HF in order to passivate the cross-sectional surface. No eect on the measured resistance at xed force or on the resistance vs. force curve has been observed, such that the HF dip was not included in the standard sample preparation procedure. The polishing and cleaning procedure must be performed brie y (same day) before the SSRM measurement takes place. Indeed, dierent results were obtained when some of the SSRM measurements were repeated on the same sample with the same probe after leaving the samples in a laboratory environment in ambient conditions for a couple of days, while the original results were reproduced on samples which were shortly re-polished and cleaned prior to the measurement. This ageing eect was observed to be a slow eect, allowing to perform reproducible measurements over a period of about 1 day after the polishing and cleaning procedure. Focused Ion Beam sample preparation Another promising sample preparation procedure is focused ion beam (FIB) milling or ion milling with Ar+ (as commonly used for TEM sample preparation). Liquid nitrogen cooling during milling might improve the quality of the cross section. The roughness of a FIB


67

prepared cross section as measured with an AFM is illustrated in gure 3.31. This section was prepared with a FEI-200 with a 30 keV Ga beam. The RMS roughness value is 0.16 nm, the peak-to-valley value 0.96 nm. These values are much lower than the ones obtained for the polished cross section (cf. table 3.7). The main problem associated with ion milling is in controlling preferential sputtering eects. Indeed, in order to position the section properly one needs to direct the Ga beam from the top surface of the structure. Orienting the Ga beam perpendicular to the top surface also helps to avoid additional doping by Ga. Dierent stopping of the beam through the wide variety of materials present in fully processed devices gives rise to a local change in sputter rates. Therefore, the resulting cross sections exhibit an additional topography caused by the top layers. An example is shown in gure 3.32. Sharp steps as high as 12 nm could be revealed by AFM in the silicon surface due to top layers of W and Al as compared to the lower regions underneath poly-silicon. The sharp steps aect the accuracy of the probe positioning in the region of interest and can lead to probe damage.

Figure 3.31: Cross section topography measured with AFM after FIB preparation (scan size: 1010 m2 ). In this gure, the sputtering beam (Ga) is oriented from top to bottom.

3.5.2 Back contact The electrical characterization of semiconductor samples by means of a single probe requires a counter electrode to conduct the current. It is necessary that the contribution from this contact to the overall impedance remains negligible under all circumstances. No satisfactory results were obtained by using silver paint on the back surface of the sample. Preliminary etching with diluted HF did not improve this situation. A good bond resulted when the contact was made by ultrasonic soldering. An ultrasound soldering iron (model S4040 from Sonobond Corp., West Chester PA, USA) was used to produce high quality contacts. Ultrasound soldering irons and dierent soldering alloys can be purchased from Fibrasonics, Inc. Chicago ILL, USA. A soldering alloy (melting point 93 ) consisting of 44% In, 42% Sn and 14% Cd required minimal heating of the sample and led to high quality ohmic contacts without preliminary etching. In practice, solder is applied ultrasonically to the back of the sample on a second cleavage plane, short-circuiting all dierently doped regions. It is claimed that the native oxide layer is mechanically destroyed by the vigorous oscillations

68


height (nm)

12

(b)

8 4 0 0

500

1000 1500 distance (nm)

2000

2500

Figure 3.32: (a) Cross section topography after FIB preparation illustrating the importance of preferential sputtering eects on surface atness (scan size: 1010 m2 ). In this gure, the sputtering beam (Ga) is oriented from top to bottom. The MOS structure is positioned at the top. (b) Section from A to A'. The higher regions correspond to the material underneath a top layer of W and Al, the lower regions correspond to the material underneath poly-silicon.

of the soldering iron at ultrasound frequency. An alternative for establishing good contacts on a silicon surface consisted in using the wire bonding technique were material is fused in a virgin contact on silicon obtained by ultrasonic vibration. Aluminum wires of 30 m in diameter were repeatedly bonded to the surface. Hereby, the sole limitation is the requirement that the structure to be analyzed is suciently wide such that the pro le in the direction perpendicular to the cross section of the sample is uniform. If this is not the case, the current ow might be in uenced by the underlying pro le and the quanti cation of the data will become more complicated. The back contact can be attached either before or after the polishing steps. Ultrasound soldering was found to be easier on roughly polished samples as opposed to plain wafer surfaces. The electrical behavior of both ultrasound soldered and wire bonded contacts is comparable. After attaching the back contact, the sample is glued onto a small metal disk with silver paint or mounted on a polishing holder. The metal disk is isolated from the AFM electronics and is connected to the external electronics. It is also interesting to note that there are two possible sample preparation procedures if the sample must be contacted from the top surface (e.g. when there are bonding pads to which the back contact must be soldered): (i) one can use a small piece of glass for the dummy. It may cover only the structure of interest and not the bonding pads or area on the wafer which is needed to attach the back contact. (ii) one can use another type of glue which can be dissolved after the polishing procedure. For this purpose, transparent nail polish has been successfully used (it is transparent to light, gives a very thin glue layer and can easily be dissolved using aceton).


69

Quality control of the back contact Two experimental techniques were used to verify the quality of the procedure to make a contact on the back of a sample.

(i) Control of a sample with four electrodes The quality of the ultrasonic soldered back contact was controlled in the following way. First, four contacts were soldered on a homogeneously doped sample as shown in the insert of gure 3.33. Two contacts were made on the bottom surface and two contacts on the polished top surface. No etching was performed prior to this step. Second, I{V curves were measured between all possible pairs of contacts (AB, AC, AD, BC, BD and CD). Typical curves are shown in gure 3.33 for an n-type silicon sample (10.1 cm). All curves show either an ohmic or a slightly rectifying characteristic. The values of the measured resistances can be used to calculate the resistances of the lump model in gure 3.33: the contact resistances are RA = 78 , RB = 112 , RC = 84 , RD = 100 and the bulk resistance RE equals 257 . The bulk value is of the same order as the value calculated from the simple Pouillet formula 10:6 cm0:5 cm R = L A = 0:25 cm0:064 cm = 331 . The contact resistances are of the order of 100 . These values are negligible compared to the total resistances which are measured with SSRM. 3 A 2 C

current (mA)

1 0

B E

D

A

B

C

D

-1 -2 -3 -1.0

-0.5

0.0

0.5

1.0

voltage (V)

Figure 3.33: I{V curves for dierent pairs of ultrasonically soldered contacts on n-type silicon (10.1 cm). Note that the presence of one slightly under-performing contact is apparent from 3 weakly rectifying characteristics. Insert: diagram of the contact positions with equivalent circuit.

(ii) Control by SRP The presence of considerable back contact resistance is diagnosed

by comparing the value of the resistance measured between two SRP probe contacts placed on top of the sample under a predetermined load with the sum of the individual resistances of the current paths through each probe separately towards the back contact. During this measurement the probe polarity is maintained to take into account possible rectifying

70


properties of the probe contacts. The back electrode is kept oating while the two-probe measurement is being performed. A series of homogeneously doped silicon samples were prepared with back electrodes using the ultrasound soldering method. The electrical quality of these contacts was controlled by comparing single and two-probe resistance measurements taken with a standard SRP apparatus (working load equals 5 g, bias voltage equals 5 mV). the results are collected in table 3.8 as a function of the sample resistivity. The table includes the percentage deviation between the sum of the individual resistance values and the global resistance.

R R1

R2

back contact

Figure 3.34: Schematical representation of a two-probe assembly on sample with back contact to identify the back contact resistance. Table 3.8: Comparison of resistances of single and double point probe contacts on doped silicon to identify the back electrode contact resistance. Measurements performed with standard SRP.

p-type silicon (100) resistivity resistance ( )

cm front probe back probe both probes sum % (R1 ) (R2 ) (R ) (R1 + R2 ) deviation 0.01 56 111 160 167 4 1.03 1022 1207 2375 2229 -7 4.78 17740 23090 39770 40830 3 10.1 115100 310600 392800 425700 8 23.4 195700 791000 798600 986700 19 n-type silicon (100) resistivity resistance ( )

cm front probe back probe both probes sum % (R1 ) (R2 ) (R ) (R1 + R2 ) deviation 0.082 429 624 1021 1053 3 1.03 4018 5737 9239 9755 5 6.0 52820 96440 153300 149260 -3 9.3 69090 96260 165600 165350 0 42.0 452600 1101000 1735000 1553600 -12

From this table it may be concluded that the back electrode resistance is negligible


71

with respect to the spreading resistance of the SRP probe contact. The eect of the bulk resistance of the sample can be eliminated in a similar fashion by noting the random distribution of the percentage deviation. The uncertainty of the larger resistance values is always relatively larger than for small resistances. Note that the spreading resistance values measured with SSRM are much larger than the ones measured by conventional SRP, so that the resistance of the back contact is also negligible in SSRM.

3.5.3 Conclusion In conclusion, a simple and fast sample preparation procedure is found. The complete sample preparation procedure takes 30{60 minutes per sample. No special equipment, except the commercially available one is required. All materials and tools which are needed for sample preparation are summarized in table 3.5.3. Evidently, other (similar) instruments can also be used. Table 3.9: Tools required for SSRM sample preparation

function sawing dummy glueing

time (min) 5{10

mounting polishing

2 20 15{25

back contact

5

cleaning

5

evaluation

5{10

tool manufacturer diamond saw Well quartz glass M-bond 610 adhesive Meas. Group, Inc. (Raleigh NC) hot plate sample holder home made epoxy resin Struers (Copenhagen, Denmark) Aluminum oxide paper Buehler Ltd. silicon carbide paper oxide polishing diamond polishing Mecapol P200 polisher Presi (Grenoble, France) glass plate soldering iron (S4040) Sonobond Corp. (West Chester PA) soldering alloy In/Sn/Cd Fibrasonics, Inc. (Chicago ILL) di water ethanol replicating tape Ladd Res. Ind., Inc. (Vermont) optical microscope stereo microscope

72


3.6 Probe Movement 3.6.1 First contact & determination of the applied force First contact

The rst contact between the probe and the sample, prior to AFM or SSRM imaging must be established carefully. As the AFM feedback loop is open before contact, the feedback parameters must be chosen such that the feedback response is gentle (e.g. critically damped) and probe damage is avoided. Furthermore, the force at rst contact is taken as low as possible. During the approach of the probe towards the sample, the tip-sample voltage is set to zero in order to avoid electrostatic forces which can cause the probe to jump towards the sample. Before performing the SSRM measurement, the area of interest is sought by scanning the sample in normal AFM operation. In contact mode the force is taken as low as possible. Tapping mode can be chosen to further reduce the force. Piezo oset voltages are used to move the probe to the position of interest. Only after a stable topographic image can be obtained, SSRM imaging can be started.

What is a force curve ? An important merit of the AFM technique for the present purposes consists in the technology to keep the force constant during the resistance measurements. A qualitative description of the calculation of the applied force has already been given in paragraph 3.2. At the start of an experiment under constant force, only the force setpoint value is known. The feedback mechanism will stop the approach of the probe to the sample as soon as this value is attained. Once the mechanical contact is established between probe and sample the experimental relation between the piezo voltage (Vz ) and the de ection detector voltage (Va,b ) is recorded, by cycling the value of Vz . These curves are known as force curves. An example is shown in gure 3.35. The cantilever de ection signal Va,b is proportional to the applied force (250 N/V), whereas Vz is proportional to the piezo displacement (typically 9 nm/V).

How is the applied force determined ? From the force curve in gure 3.35 the value of Vz before contact can be determined. This value is taken as the zero point for the calculation of the force. The force at which the experiment is carried out is deduced from the dierence between the zero point and the voltage Vz actually applied to the piezo during the experiment. The procedure is correct if the relation between Va,b and Vz is linear; the slope in units Va,b per unit piezo displacement is de ned as the sensitivity (s) of the instrumental setup. The ideal behavior is observed for a diamond probe on a diamond substrate as illustrated in curve a in gure 3.35. The force can be calculated according to equation 3.3. In case the diamond probe induces deformations in the sample, the relationship between Vz and Va,b is no longer linear as illustrated in curve b in gure 3.35. Under these conditions the rst loading and unloading cycle is dierent from the subsequent ones. In the following, only the rst loading and unloading is discussed. The displacement of the cantilever is no longer identical to the displacement of the z -piezo. Elastic deformations in the sample

3.6. PROBE MOVEMENT

73

Figure 3.35: Force curve for a repeated contact: cantilever de ection as a function of applied piezo voltage. The curves were taken with a diamond tip on (a) diamond, and on (b) silicon. Loading and unloading curves overlap.

show up as curvature in the force curve without hysteresis. If the curve shows hysteresis, it indicates that plastic deformations occur as well ( gure 3.36).

Figure 3.36: Force curve for the rst contact between a diamond probe and (a) diamond, and (b) silicon. Loading and unloading overlap for the diamond substrate, but show hysteresis for silicon.

Thus, the sensitivity of the particular setup must be determined with the help of an in nitely hard substrate, say diamond. The Va,b value that is observed before contact on the plastic sample is made, is now chosen as zero point. A line with a slope corresponding to the sensitivity is drawn through this point, so that the force for each experiment can be determined as previously on the one condition that Vz must be taken as Vas,b , wherein Va,b is the setpoint value and s the instrumental sensitivity measured on an in nitely hard substrate. Alternatively, it was found that for the diamond probes the ideal slope of the Va,b =Vz

74


relationship can be approximated by the measured slope on silicon at relatively high loads (for example of the order of 250 N for a spring constant of order 1 kN/m). The softer the cantilever the faster the linear part of the relationship will be reached. The eects of (i) the liquid contaminant layer on surfaces in ambient conditions, and of (ii) van der Waals attractive forces can be neglected in the force calculation. At the relatively high forces used here this is quite justi able.

3.6.2 From one point to the next Several modes can be used to move the probe from one measurement position to the next. One of the standard AFM scanning procedures - contact mode or tapping mode (also known as intermittent contact mode) - can be used, or one can use a stepping mode. Each of the methods is described in detail in what follows.

Contact mode In contact mode the force is kept constant by the feedback electronics and the tip-sample resistance can be measured continuously or at discrete steps in time. Ideally, this force corresponds to the normal force. In reality, lateral and torsional forces are also involved. The main advantage of this mode is that the normal AFM operation is used, including a high speed. The disadvantage is that the lateral force acting on the probe can become high such that the probe wears o rapidly. Also, the behavior of the contact (mechanically and electrically) might be dierent for a sliding and xed contact, complicating the interpretation of the measured resistance data (see section 4.1.4). Since the scanning mode is a normal AFM operation, the eect of piezo drift and piezo non-linearities can be compensated by a software routine or hardware as is frequently done in normal AFM operation. Note that these eects increase if the scan speed is reduced to very low values, as is done in the stepping mode. Figure 3.37 shows the topography of a sample, before and during the SSRM measurement. Scratches originating from the polishing procedure and small contaminants can be seen in gure 3.37a. Both are reduced during the SSRM measurement. Furthermore, the height of the higher parts of the structure (in this case SiO2 stripes) is reduced during scanning. The topography observed after the SSRM measurement shows a crater with its shape equal to the shape of the scanned area. The material which is removed from the crater is found back at the edges of the crater. The depth of the crater is typically 1.5{4 nm per cycle. The topography of a typical crater and a cross section of the same crater is shown in gure 3.38. In this plot we see (from left to right): the original polished surface, the piled up material at the crater edge, and the crater. Clearly, the crater depth increases strongly if higher forces are applied to the probe [Andoh 95, Kaneko 96]. Careful selection of the scan parameters is important to the successful application of contact mode AFM, and in particular of SSRM. For constant-force imaging the gain settings in the feedback control should be as high as possible. There are two gains: an integral and proportional gain. First, the integral gain is increased until just below the level at which the piezo starts to oscillate. Then, the proportional gain is set in the same way. In general, the scan rate must be decreased as the scan size is increased. Although high scan rates are preferred because they reduce the drift of the piezo elements, the scan rate in SSRM is kept

3.6. PROBE MOVEMENT

75

Figure 3.37: Topography (a) before and (b) during and a SSRM measurement (scan size 66 m2 ).

Figure 3.38: (a) Topography of the crater left after a single SSRM measurement (scan size 55 m2 ). The section from A to A' is drawn in (b).

76


small (compared to low-force contact mode imaging) to avoid probe damage. Typically scan speeds of 1 m per second are used (leading to an imaging speed of about 10 minutes for a 11 m2 image with 512512 pixels). It is important to reduce the force as much as possible when the probe has to travel over a distance in between dierent scans on the same sample. Zooming in and out, rotating, and piezo-oset commands should not be executed when the full force is applied on the probe. In principle, the force should only exceed the threshold force when the actual resistance measurements are performed. Furthermore, probe damage can be limited by avoiding to scan across steep topography changes such as sample edges.

Tapping mode In tapping mode the cantilever is oscillated close to the sample at - or near - its resonant frequency (usually tens or hundreds of kHz), touching the sample once every cycle. The amplitude of the cantilever de ection is kept constant by a feedback loop and is a measure for the sample topography. In this way, an intermittent contact is formed between tip and sample with a constant force (or energy transfer), which is usually taken very small. The advantage of such a concept for SSRM could be that the lateral force is minimized (though not completely eliminated), reducing the chance to damage the probe. However, the time during which the probe makes a contact (typically 1{10 s) is too short to allow a good resistance measurement. The fundamental limitation is formed by the resistance measurement unit which must be able to measure current over a very wide range, at high speed. The logarithmic ampli ers discussed in section 3.3, provide a constant sensitivity over the full range, but are limited in speed to about 500 Hz.

Stepping mode The force acting on the probe can also be reduced as much as possible when the probe is moved from one position to the next. In this way, damage caused during the sliding at high forces is avoided. The force can be increased again to the measurement level (i.e. above the threshold force) as soon as the new position is reached and the probe stopped moving laterally. This mode is named stepping mode. A schematic diagram is shown in gure 3.39. There are two main problems associated with this approach. First, upon reducing the force, the very end of the tip moves laterally over a distance x (see gure 3.39), determined by the spring constant of the cantilever, the amount of force and the angle at which the cantilever is inclined with respect to the sample surface. This value can reach values as high as hundreds of nm and thus reduce the spatial accuracy of the technique considerably. Secondly, extra electronics are needed to synchronize the resistance measurement unit with the probe movement. In our setup a trigger pulse is generated every time the force is increased above the threshold value. The pulse triggers the resistance measurement unit which starts the measurement and sends back another trigger pulse when the measurement is nished. For this purpose the lithoscript macro-language of the Nanoscope AFM was used. Figure 3.40 shows the resistance measured in the stepping mode (scan rate: 2 s/pixel) and in the scanning mode (scan speed: 1 m/s) when scanning a homogeneously doped

3.6. PROBE MOVEMENT

77 (b)

(a) ∆x

Figure 3.39: Schematic diagram showing the probe and piezo in stepping mode SSRM at the time of the resistance measurement (a), and when the probe is moved from one position to the next at reduced force (b).

silicon sample. In both modes the same probe was used at exactly the same working load. The measured resistance values and 95% con dence intervals for the stepping and scanning mode are respectively 34637 k and 33215 k . The signal to noise ratio is slightly higher for the scanning mode compared to the stepping mode, but the same resistance value is observed. 500

stepping mode scanning mode

resistance (kΩ)

450

400

350

300

250 0

500

1000

1500

distance (nm)

Figure 3.40: Resistance scan measured in the scanning mode (scan speed: 1 m/s) and stepping mode (scan rate: 2 s/pixel) measured with the same probe at the same load on a uniformly doped sample.

In summary, the contact mode is the preferred method because it provides the best controlled resolution and can easily be implemented without modi cations.

78


3.7 Imaging artefacts Several artefacts can be reported for SSRM imaging. The most important artefacts are related to piezo non-linearities, tip convolution, sample wear and friction.

3.7.1 Piezo non-linearities Piezoelectric materials may cause several artefacts in SPM images. First, piezoelectric materials do not move perfectly linear with the applied voltage. One of the most evident consequences is that straight lines on the sample will appear to be curved in the image. Distances which should be exactly the same, can be dierent in the center and at the sides of the image. Furthermore, crosstalk between the x- and y-movements results in an incorrect angle between horizontal and vertical lines which should be perpendicular to each other. Piezo creep is another well-known problem: apart from the instantaneous response there is also a slow response (which extends over minutes) of the piezo to the applied voltage. This causes drift of the tip with respect to the sample between successive measurements. This is illustrated in gure 3.41a in which an AFM image of a series of SSRM indentation marks are displayed. The indentations were made using SSRM in the stepping mode, whereby the probe followed a pattern shown in gure 3.41b. In this example, the piezo voltages applied to move the probe were not corrected for any of the non-linearities (the AFM image was collected with a calibrated scanner, which corrects for the non-linearities). As a result, there is a large discrepancy between the actual positions and the intended positions of the indentations. (b)

Figure 3.41: (a) Indentation marks left after SSRM operated in the stepping mode wherein the probe followed the pattern shown in (b). The topography was measured with standard AFM (scan size = 22 m2 ).

Another problem is related to hysteresis of the piezo elements, which leads to considerably dierent images when the tip is scanning from left to right across the surface or when it is scanning from right to left. To avoid these eects, corrections must be applied. This can be done by a software or hardware system. Systems with a software correction for scanner non-linearities require

3.7. IMAGING ARTEFACTS

79

calibration of the piezoelectric scanner. In the plane of the sample, this calibration can be done by scanning a sample for which the distances between certain features are known exactly. At the atomic scale, graphite can be used, because atomic resolution can easily be achieved. At larger scales, calibration gratings are provided with typical distances between the features of 1 m or even 10 m for the largest scanners. This information is stored in a le, or lookup table, or modeled into equations [Akila 95]. Afterwards, the system can compensate for non-linearity while collecting data by adjusting the voltage applied to the scanner in accordance with the le or the look-up table. Software solutions in general are relatively simple and inexpensive to implement. Their main disadvantage is that they compensate only partially for scanner non-linearities. The corrections are strongly dependent upon the scan speed, scan direction, and whether the scanner was centered within its scan range during calibration. As a result, software corrections are most accurate only for scans that reproduce the conditions under which the calibration was done. A scanner should be re-calibrated when scan conditions change. Systems with hardware solutions sense the actual position of the scanner with external sensors. The signal read from the sensor of each axis is compared to a signal that represents the intended scanner position along that axis. A feedback system applies voltage to the scanner to drive it to the desired position. In this way, the scanner can be driven in a linear fashion. The external sensors themselves must be stable and immune to all sources of nonlinearity, since their purpose is to improve the linearity of the SPM. Because the scanner's actual position is measured, systems using hardware sensors compensate for intrinsic nonlinearity, hysteresis, creep, aging, and cross coupling. They can reduce the total nonlinearity of the system to less than 1%. Techniques used for hardware correction include optical, capacitive, and strain-gauge techniques.

3.7.2 Friction Figure 3.42 shows the resistance measured on a uniformly doped silicon sample over a distance of 2 m with the scan direction parallel to the cantilever axis (curves A and B). The large dierence in both resistance pro les originates from a dierence in the normal force. If the probe is scanned in direction A, the normal force decreases by an amount set by the friction force acting on the probe. If the operating force is taken close to the threshold force, the force acting on the probe when scanned in this direction might be smaller than the threshold force resulting in very high resistance values. If the probe is scanned in direction B , the normal force increases by an amount set by the friction force acting on the probe. Upon changing the scan direction with 90 , the normal and lateral (or friction) force are separated and the normal force is equal to the setpoint. The measured resistances are equal, indierent of the scan direction (curves C and D). This method is preferred. Note that the change in normal force is limited by the friction coecient (see chapter 4).

3.7.3 Double tip & tip-convolution Most imaging artefacts in an SPM image arise from a phenomenon known as tip-convolution. Every data point in an image represents a spatial convolution of the shape of the tip and

80

CHAPTER 3. INSTRUMENTATION & MEASUREMENT PROCEDURE 160 A 150

resistance (kΩ)

D 140

C

130 120

B D

110

A

B C

100 0.0

0.5

1.0

1.5

distance (µm)

Figure 3.42: Resistance scan as a function of scan direction illustrating the eect of friction.

the shape of the feature imaged. As long as the tip is much sharper than the feature, the true edge pro le of the feature is represented. However, when the feature is sharper than the tip, the image will be dominated by the shape of the tip. For example, if there are two protrusions on the tip (equidistant from the surface), all of the features in the topography, and SSRM image will appear doubled. An example of this multiple-tip imaging artefact is shown in gure 3.43. This gure shows the SSRM resistance image measured on a shallow As implantation in a p-type silicon substrate, covered with SiO2 (scan size: 400400 nm2). The implanted area (dark region) is observed twice, indicating that the probe which was used had multiple tips. This is also clearly observed in the pro le measured along section AA', which is compared to the SIMS pro le in gure 3.43c. Tip-convolution can easily be recognized by a particular shape that is repeated throughout the topographic or SSRM resistance image. If the sample is rotated and imaged again, and the tip is dominating the image, the orientation of the particular shapes will be the same before and after rotation. If the image is a true representation of the surface, the shapes in the image will rotate along with the sample. If the SSRM image is dominated by tip-convolution eects, one has to change to another tip. Another example of extreme convolution can be observed in gure 3.44. The SSRM concentration pro le is compared to the SIMS pro le of a one-dimensional shallow boron implantation. The measurement was performed with a probe which was known to be blunted during previous measurements. As a result of the blunted probe (radius 300 nm), the measured peak is much lower (1 decade) and broader (about 200 nm at each side) than the one expected. In the presented example, the eect is clearly observed. More frequently, the convolution is less pronounced and it is hard to determine its precise range. Therefore a calibration sample is needed which allows one to measure the electrical tip radius precisely. Once the electrical radius is determined, this type of convolution can be corrected for to a certain extent as described in detail in chapter 5.5.

3.7. IMAGING ARTEFACTS

81

1019 1018 1017

SSRM SIMS 0

100

200

3

1020

concentration (at./cm )

1021

(c)

1016 300

depth (nm)

Figure 3.43: Double-tip SSRM image. (a) SSRM resistance image (scan size: 400400 nm2 ), (b) schematical sample layout, (c) Section from A to A' compared with SIMS, clearly showing two peaks in the SSRM concentration pro le.

1021

SSRM SIMS

concentration (at./cm3)

1020 10

19

10

18

10

17

10

16

1015 1014

-200

0

200

400

600

800

depth (nm)

Figure 3.44: One-dimensional SSRM pro le illustrating the eect of a large tip radius. The shallow pro le is broadened and the peak is lowered.

82


3.7.4 Sample wear One of the most disturbing SSRM artefacts is related to sample wear. If the sample wears o while performing the SSRM measurement, the results must be interpreted carefully. A typical example of sample wear is shown in gure 3.45 which was taken at a constant force (taken higher than the threshold force determined prior to the measurement). This image shows the resistance map measured on a 2D ion-implanted pro le. The rst part of the pro le (right part of the gure) is measured correctly, while the resistance values measured in the doped region increase to high values after scanning about half of the image. The sudden increase in resistance which is observed is believed to be related to the presence of debris accumulated at the very end of the tip.

Figure 3.45: Sample wear example. The measurement was started at the right hand side and continued towards the left hand side (scan size: 500500 nm2). The resistance in the doped region is observed to increase from right to left as the sample wears o and debris is accumulated at the tip.

3.8 Conclusions The SSRM instrumentation includes an AFM which is operated in the contact mode, a 5decade logarithmic current ampli er, and a doped diamond or CVD diamond-coated silicon probe. The ideal probes for SSRM are made form diamond which is made conducting through boron doping, and have a small tip radius (10{25 nm). Sample preparation for SSRM consists of the following steps: cleaving or sawing of the wafer at the region of interest, glueing a piece of the wafer and a piece of quartz glass or dummy wafer together (face-to-face), soldering a current collecting back contact using an ultrasound soldering iron, polishing the cross section using dierent grain-size abrasive papers or polishing slurries, cleaning of the sample cross section. This sample preparation procedure is simple and fast (30{60 minutes per sample). In SSRM the probe can be scanned in the stepping mode or in the contact mode. The contact mode is preferred because it provides the best controlled resolution, can easily be implemented without modi cations to the AFM system, and allows fast scan rates. An inherent disadvantage of the SSRM method { operated in the stepping or contact mode { is that the force on the probe must be increased to a high level (typically 10 N) to obtain

3.8. CONCLUSIONS

83

a stable resistance measurement. Consequently, craters are formed in the sample and the probe can get easily damaged. The most important artefacts which can be reported for SSRM imaging are related to piezo non-linearities, tip convolution, sample wear and friction. None of these artefacts forms a signi cant limitiation to the applicability of the SSRM technique for twodimensional carrier pro ling.

Chapter 4

Point contact characteristics The study and characterization of the electrical properties of small probe-semiconductor contacts ranges from the earliest investigations of semiconductors [Braun 74], through the invention of the transistor [Bardeen 48] to the more recent development of the scanning tunneling microscope [Binnig 82b]. However, practical device structures avoid the point contact wherever possible. Generally this is because of inadequate knowledge and control of the mechanical processes at the probe-semiconductor junction and poor surface atomic cleanliness. In SSRM the point contact is crucial and its characteristics are vital for the applicability of the technique as a carrier pro ling tool. Several physical mechanisms are working simultaneously resulting in a complicated point contact behavior. The dierent mechanisms can roughly be divided in three main categories: mechanical eects, electrical eects and thermal eects (such as local heating of the sample). Furthermore, environmental eects (humidity, temperature, sample illumination, contaminants on the sample, sample native oxide, etc.) contribute to the nal contact behavior. As a result, it is dicult to describe the complete point contact behavior at once. Therefore a gradual approach is used: rst the mechanical behavior of the contact is described and in a second section the electrical contact behavior is treated. Third, the electrical and mechanical behavior are combined in an electro-mechanical contact model. In a last section, the importance of dierent environmental (including thermal) eects is studied.

4.1 Mechanical The study of the SSRM point contact requires a detailed analysis of the mechanical behavior of the contact to get insight in the deformation of sample and probe and the size of the contact. Deformation of the probe might reduce the probe lifetime, while the size of the probe/sample contact sets a limit to the best attainable spatial resolution of the SSRM technique. The SSRM probe/sample contact can be modeled macroscopically by a rigid sphere indenting a at surface. As this is an issue of quite considerable importance in engineering many researchers have considered it since several decades. Recent reviews of general indentation theory have been given by Bhushan [Bhushan 96] and Johnson [Johnson 85]. 85

CHAPTER 4. POINT CONTACT CHARACTERISTICS

86

Typically, one can distinguish three subsequent regimes as one increases the load on the indenter [Sinclair 85, Follansbee 84]:

Initially one enters the elastic regime where the classical Hertz theory is valid. As the load on the indenter increases the stress eld under the contact will increase

until at a certain depth along the axis of symmetry, the local stress will exceed the uniaxial yield stress (Y ). This is the start of the elasto-plastic regime. In this regime, the plastically deformed region is surrounded by elastically deformed material.

Upon further increasing the load on the indenter, the plastically deformed region

reaches the surface and one enters the fully plastic regime. In this regime the pressure

attens out over the contact area and an increase of load is compensated by an increase of the plastically deformed region.

For conventional SRP the high loads (typically 50{100 mN) lead to the presence of all three regimes [Clarysse 92, Clarysse 96a]. Although the loads applied in SSRM are much smaller (as will be discussed in section 4.2), the small contact size results in a similar pressure distribution underneath the contact. In this section some general information is given on each of the three regimes before a detailed analysis of the SSRM contact (diamond indenter on a silicon substrate) is presented.

4.1.1 Elastic regime The rst analysis of the deformation and pressure of two elastic solids with well de ned geometries is due to Hertz at the end of the 19th century. For a spherical indenter (radius R) on a at surface, the contact is circular with a radius a (< R) given by equation 4.1 where F is the normal force acting on the indenter and E is the eective modulus de ned by equation 4.2. The parameters E and are Young's modulus of elasticity and the Poisson's ratio respectively; subscripts 1 and 2 refer to the two contacting bodies. The indentation depth is given by equation 4.3. Figure 4.1 shows a schematic diagram of the elastic indentation. F

R

δ a

Figure 4.1: Schematic diagram of a frictionless indentation of a rigid spherical indenter in a at surface.

4.1. MECHANICAL

87 1=3 a = 34FR E 1 = 1 , 12 + 1 , 22 E E1 E2

(4.1) (4.2)

1=3 2 2 (4.3) = aR = 9F 2 16RE The stress distribution at the surface and within the two solids can be calculated analytically [Hamilton 66]. From these calculations, it is found that the maximum principal shear stress (max ) is located under the probe on the axis of symmetry. For the case of silicon ( = 0:28, E = 124 GPa) the maximum (principal) stress is found at a depth of 0:48a below the probe and is given by equation 4.4 [Johnson 85]. (4.4) max = 0:15 aF2 As the normal load F is increased, the body with the lowest hardness may start to deform plastically. Obviously, for SSRM this is the silicon sample and not the diamond indenter (see table 3.1 for the hardness values of both materials). As the normal load is further increased, the plastic zone grows until the entire material surrounding the contact has gone through plastic deformation. The load at which the plastic ow or plastic yield begins is related to the yield point of the softer material through an appropriate yield criterion. Two of the yielding criteria most commonly employed are the Tresca's maximum shear stress criterion (plastic ow starts when the maximum shear stress, i.e. half the dierence between the maximum and minimum principal stresses, reaches the yield stress) and the von Mises shear strain energy criterion (plastic ow starts when the distortion energy equals the distortion energy at yield) [Hill 50]. The von Mises criterion predicts a shear stress which is about 15% higher than predicted by the Tresca criterion. The load to initiate yield (Fy ) for the case of silicon (Y = 4:41 GPa) can be found by combining equations 4.4 and 4.1 and Tresca's criterion: max = Y2 . The result is given by equation 4.5 (R in nanometer, Fy in nN). The maximum penetration depth (ay ) before onset of plastic deformation is found by using equations 4.3 and 4.5 and is given by equation 4.6. The corresponding mean pressure at the surface (py ) is given by equation 4.7, the radius of the contact by equation 4.8. For example, a typical probe radius of 50 nm results in Fy = 0:3 N, y = 0:4 nm and ay = 4 nm. After repeated loading, the load required to initiate yielding increases and reaches a steady state value, slightly higher than after rst loading [Johnson 85].

!

2 Fy = 21:17 R2Y EY = 0:12 R2 nN 2 y = 6:32 R EY = 0:008 R Fy = 1:07 Y py = a 2

(4.5) (4.6) (4.7)


88

ay = 2:51 R EY = 0:08 R

(4.8)

4.1.2 Elasto-plastic and fully plastic regimes

If the load is increased above the load at which plastic ow starts (Fy ), the elastic theory from Hertz is no longer valid and must be replaced by an elasto-plastic theory. The deformation now strongly depends on the nature of the materials such as elastic, rigid, perfectly plastic, elastic-plastic, elastic-brittle, etc. An elastic-perfectly plastic uniaxial system has a stress-strain relation as shown in gure 4.2a; rst it deforms elastically according to its Young's modulus E and then, at tensile stress Y , it yields plastically at a constant yield or ow stress. At small loads the sample deforms elastically; then at higher loads, the critical stress is rst exceeded at a region below the center of the contact zone ( gure 4.3a). This corresponds to the onset of plastic deformation. As the load is increased further, the indentation becomes larger, and the plastic zone grows until the whole of the material surrounding the indenter undergoes plastic deformation ( gure 4.3b). The same is true for a real elastic-plastic system with stress-strain behavior as shown in gure 4.2b. (b)

Y

tensile stress

tensile stress

(a)

E

Y

E strain

strain

Figure 4.2: Schematic of stress-strain curve for (a) elastic-perfectly plastic and (b) real elasto-plastic solids. E is the Young's modulus of elasticity, Y is the yield stress.

For elasto-plastic and fully plastic contact analysis, the analytical equations describing the stress distribution are very complex and most numerical techniques are work intensive. These problems can be overcome by using nite element analysis. We used the multipurpose nite element code SYSTUS [SYSTUS] which has contact element features, capable of solving various types of contact by de ning material properties of the contacting surfaces. Figure 4.4 shows the stress contourlines and the yield region obtained for a 50 nm radius spherical indenter into silicon at a penetration depth of 1 nm. This result represents the fully plastic regime. Note that the plastically deformed region has approximately the same depth as width (10{15 nm). The basic shape of the shown plastic region is in agreement with other published results [Laursen 92]. Furthermore, this shape is found to change only very little when the contact type (with or without friction) and/or the precise shape of the indenter are changed. Both these parameters are not well known and hard to determine for the SSRM probe/sample contact. From Tabor [Tabor 70] and Sinclair et al. [Sinclair 85], the increase of the mean pressure p at the surface as a function of EY Ra for the case of a rigid sphere pressed against a at

4.1. MECHANICAL

(a)

89

F

(b)

F

Figure 4.3: Indentation of an elastic-perfectly plastic solid by a spherical indenter. The grey areas represent the plastically deformed regions. (a) Onset of plasticity below the surface at a mean pressure at the surface given by p ' 1:07 Y , and (b) at a higher load, full plasticity is reached and the plastic ow extends to the free surface (at this stage p ' 2:8 Y ).

Figure 4.4: Stress distribution obtained from nite element calculations in silicon under a hard spherical indenter with radius 50 nm in the fully plastic regime. The region shown covers an area of 5050 nm2. The maximal indentation depth was 1 nm, the contact radius was approximately 25 nm. The yield region lies within the contourline labeled D.

90


surface is known as the universal Meyer hardness curve, and is almost completely material independent. The latter dimensionless expression may be interpreted as the ratio of the , strain imposed by the indenter Ra to the elastic strain capacity of the material EY . The condition of full plasticity is reached at a load of about 200 times that at which onset of plastic deformation occurs. This corresponds to an increase of the radius a of the indentation by a factor of about 10. For our example (probe radius 50 nm) full plasticity is reached at F ' 60 N and a ' 40 nm. Based on a number of numerical analyses and experimental measurements, a relationship between hardness (H , de ned as the applied load divided by the area of the impression) and yield stress (Y ) was found: H ' 2:8 Y . Full plasticity is reached when the mean pressure at the surface equals H . The SSRM point contact goes through these three regimes as the load acting on the probe is increased by changing the reference point of the AFM feedback loop. Experiments have shown that a stable electrical contact requires that the elasto-plastic regime is reached (see section 4.2.2).

4.1.3 Diamond on silicon The situation for silicon is additionally complicated by the fact that high pressure experiments have shown that silicon (and also germanium) undergoes a phase transformation from the cubic structure Si(I) to the denser -tin structure Si(II) (22% volume reduction) at moderately elevated pressures [Hu 86]. The pressures needed to trigger the transformation depend on the nature of the stress state. Under pure hydrostatic conditions, the transformation takes place over the range 11.3{12.5 GPa, but this is reduced to values as low as 8 GPa when shear stresses are present. These transformation pressures have a special signi cance when compared to the indentation hardness (H ) of silicon which typically falls in the range 10{12 GPa. The signi cance is that the hardness, which represents the mean pressure developed under the indenter, is at least equal to or greater than the minimum pressure needed to induce the transformation to the -tin state. This suggests that a volume-reducing, pressure-induced phase transformation occurs beneath the indenter during an indentation experiment in which the elasto-plastic and/or fully plastic regime is reached. Silicon and also germanium are unique in this regard in that very few materials have hardnesses that exceed the transformation pressures. Upon release of the pressure a reversion to dierent structures is possible. In experiments with slow pressure release there is a transition from the -tin structure to a rhombohedral polymorph (Si-XII) at 8.5 to 10.8 GPa. The Si-XII phase transforms further to the body centered cubic phase (Si-III) at 2 GPa [Hu 86]. The Si-III phase has a density intermediate between Si-I and Si-II with approximately 8% reduction in volume over Si-I. During rapid pressure release, amorphous silicon is formed. A schematic representation of the dierent phases of silicon is presented in gure 4.5 [Kailer 97]. Evidence of the existence of the -tin phase under an indenter has been found through several approaches, such as the detailed study of the load-unload force versus penetration depth curves for a spherical indenter [Pharr 89, Weppelmann 93], transmission electron microscopy (TEM) analysis [Page 92, Clarke 88], electrical resistance measurements on rectifying gold-chromium contacts [Pharr 92], the observation of material extrusions immediately adjacent to the indenter [Pharr 91], and Raman spectrometry [Kailer 97]. We brie y

4.1. MECHANICAL

91

Si-II (metallic)

slo

w

Si-IV (hexagonal diamond)

un

loa

din

rapi

g

ing

load

d un

stress (GPa)

10

0

Si-I (cubic diamond)

amorphous Si

Si-XII (rhombohedral)

Si-III (body centered cubic)

Figure 4.5: Scheme of the phase transformations that occur during hardness indentations in silicon. During the indentation experiment Si transforms from the original diamond cubic Si-I structure to the hexagonal diamond Si-IV or the metallic -tin phase Si-II depending on local stress conditions. Upon unloading other forms, including the amorphous phase, Si-XII, and Si-III are reached.

discuss two of these studies into some more detail:

Load curves:

Several papers have reported an unusual reverse-thrust or pop-out phenomenon in the unload curve of load-unload force versus penetration measurements as they can be obtained by todays nano-indentation or AFM equipment [Pharr 89, Weppelmann 93]. This is a phenomenon which is typically observed on silicon only. Figure 4.6 shows the load-unload force versus displacement curve measured with an SSRM indenter on a silicon substrate using the AFM as a nano-indentation tool. Hereby a force curve was measured as described in section 3.6.1, after which the de ection of the cantilever was subtracted to obtain the elastic and plastic response of the sample. The deviation from the elastic response, i.e. the small twist in the loading curve and the hysteresis are evidence for the presence of an indentation-induced phase transformation in silicon. Both can be explained by the reduction of volume associated with the phase change in the silicon beneath the indenter manifested at the surface by a small increase of penetration and a corresponding increase in the contact radius.

Electrical measurements:

The performance of nano-indentation experiments with triangular shaped tips on and in between two gold-chromium contact pads (on a silicon substrate) between which the resistance could be measured has indicated that substantial resistance lowering occurs when the indenter crosses the metal-silicon interface [Pharr 92]. It has been shown that this process is reversible. This behavior can be attributed to the creation of a -tin phase under the indenter which is expected to have metallic properties. Consequently the metal-silicon interface is transformed from a rectifying Schottky into an ohmic contact during loading. It is to be expected that the -tin Si-II phase occurs under an SRP and SSRM contact


92 25

experimental elastic

load (µN)

20

15

10

5

0 0

10

20

30

40

50

displacement (nm)

Figure 4.6: Indentation load-displacement data for silicon measured with a standard SSRM diamond probe (probe IV from table 3.3) mounted on the AFM which is operated as a nano-indenter. The data exhibit a small twist in the loading curve (indicated by the arrow) and a strong hysteresis which are evidence for an indentation-induced phase transformation in silicon.

when the area of the imprint is small enough, i.e. the local pressure is high enough. From I{V measurements it has been found that for SSRM a threshold force must be exceeded in order to have an electrically stable contact (see section 4.2.2). This threshold force is large enough to cause plastic deformation and a -tin Si phase beneath the indenter. As discussed above, the plastically deformed region under an indenter is expected to be composed of the -tin Si-II phase. This phase has material properties which are substantially dierent from Si-I. The most apparent property is formed by its metallic behavior. This behavior can be observed experimentally during static compression using a diamond indenter technique [Gupta 80]. When compressing a thin piece of silicon one rst observes a linear decrease of the resistance on a linear-logarithmic pressure-resistance graph. This can be correlated to bandgap narrowing. Once the transition pressure has been reached an abrupt decrease of the resistance is observed. The dependence of the bandgap on the applied stress has been studied by Goro et al. [Goro 63]. It follows that for (100) silicon material a transition is observed at 12 GPa, while for (111) silicon material this value is lower, namely 8 GPa. Furthermore, it follows that the silicon transition pressure is highly shear stress dependent. The more shear stress, the lower the transition pressure. The low resistivity of 10,4 cm reported in reference [Minomura 62] indicates that Si-II behaves electrically as a metal.

4.1.4 Mechanical side eects Sliding contact

In a scanning mode, the force acting on the SSRM indenter is no longer purely normal, but has a lateral (friction) component. In a frictionless contact, the contact stresses and deformations are unaected by the sliding motion. Sliding motion or any tendency to slide

4.1. MECHANICAL

93

introduces a tangential force referred to as friction force Ff , which is proportional to the normal force: Ff = F where is a constant known as the coecient of friction. The tangential force at the contact surface aects the stress distributions and size and shape of the contact area. The contact area and the contact pressure distribution are no longer symmetrically placed, their center is displaced from the axis of symmetry and the contact pressure no longer has circular distribution. These dierences are function of the elastic properties and the friction coecient. Johnson [Johnson 85] has shown that the eect of tangential force on the normal pressure and the contact area is generally small, particularly when the coecient of friction is less than 1. The point of rst yield moves towards the surface as is increased, and reaches the surface when exceeds 0.3. Figure 4.7 shows the mean contact pressure at rst yield as a function of the coecient of friction [Johnson 85]. The same behavior is expected for the mean contact pressure at the onset of full plasticity. 1.0

p/Y

0.8

0.6

surface yield

subsurface yield

0.4

0.2

0.0 0.0

0.1

0.2

0.3

0.4

0.5

Coefficient of friction (µ)

Figure 4.7: Eect of sliding friction on the mean contact pressure for rst yield. For friction coecients larger than 0.3 the point of rst yield lies at the surface.

Clearly, the most important parameter in a sliding contact is the friction coecient . For the SSRM diamond/silicon contact, can be determined experimentally as follows: First, the lateral (friction) force detector of the AFM is calibrated for a particular SSRM probe by operating the AFM in the LFM mode and using the procedure described by Ogletree et al. [Ogletree 96]. Second, the same probe is used to scan a silicon sample which went through the complete SSRM sample preparation procedure. The friction coecient, calculated as the ratio of the friction force and the normal force, is found to be slightly dependent on the magnitude of the normal force and on the scanning speed. It varies between 0.05 and 0.2, leading to a maximum decrease of the mean pressure at rst yield or at the onset of full plasticity of only 10%. The highest values for were observed for the highest normal forces and at the highest scanning speeds. We conclude that the friction caused by the sliding motion of the probe decreases the load needed for rst and full plastic deformation to a very small extent. These results are con rmed by the experiments from Bhushan and Li [Bhushan 97] in which the friction coecient for a larger diamond tip

94


(radius: 1 m) sliding over a silicon sample was found to vary between 0.08 and 0.11.

Dopant eects Dislocation velocities in silicon are known to be strongly dependent upon doping levels and therefore it might be expected that hardness might also show some doping dependence. Since ion implantation results in a considerable disruption of the crystal structure by radiation damage processes, dislocation motion is expected to become more dicult resulting in an increased hardness [Hu 78]. Maugis et al. [Maugis 71] found that increasing dopant levels increased the hardness of silicon at room temperature. No sensitivity to the chemical nature of the dopant species has been found. Also, softening can occur if the ion implantation forms an amorphous layer. Amorphized silicon was measured to be 50% softer than the crystalline parent material [Burnett 87]. However, annealing is expected to remove the radiation damage in the non-amorphized material and to crystallize the amorphized silicon. Both would result in the hardness returning to close to that of bulk silicon. If any electrically active species were implanted their eects might now be expected to become apparent since the dominant radiation damage eect will have been removed. There is, however, no data on this. Bhushan and Li [Bhushan 97] measured a slightly higher hardness and elastic modulus and a slightly lower coecient of friction for undoped silicon as compared to p-type silicon (7 1019 atoms/cm3 ). It should, however, be noted that the maximum change in hardness (due to dopant concentration dierence) is limited to small values and was never observed in our own measurements.

Environmental and surface eects The hardness of the silicon samples may be aected by the test environment (e.g. dry or moist air). Hanneman et al. showed that the presence of adsorbed water could cause a 26% softening of the surface of silicon [Hanneman 68]. In addition, the surface preparation route may also aect the apparent hardness of silicon to a small extent. For example, a high sample roughness will result in a higher friction coecient. A thin contaminant lm present on the samples may change the micro-mechanical and tribological properties of the sample. The presence of an oxide lm results in a slightly higher hardness and elastic modulus [Draper 94, Leighly 73]. For thin oxide layers (i.e. < 2 nm) such as the native oxide, these changes are negligible for a 20 nm radius indenter [Draper 94]. In conclusion, small variations in the environmental and surface conditions have a limited in uence on the mechanical properties of the SSRM point contact.

Discussion One might wonder if this classical approach using continuum mechanics is still valid for the extremely small SSRM point contacts and whether no atomic approach should be used instead. Indeed, it has been reported in literature that the nanoscale mechanical properties of materials can be quite dierent than the bulk properties [Persch 94, Pethica 83, Schlesinger 91]. For example, the hardness and yield stress of silicon were observed to increase by more than 30% upon decreasing the dimension of the indenter from macroscopic

4.2. ELECTRICAL

95

values (radius > 500 nm) to microscopic values (radius < 100 nm) [Pethica 83]. However, all mechanical mechanisms mentioned above were found to remain valid.

4.2 Electrical One of the most important conditions for SSRM is that the conducting tip should make a good electrical contact on the sample and its contact resistance should be suciently low so that the measured resistance is dominated by the spreading resistance, which is a direct measure for the local sample resistivity or carrier concentration. If the contact resistance is not small compared to the spreading resistance, it should be a clear function of the sample resistivity such that the SSRM method remains a sensitive tool for carrier pro ling. The behavior of a at SRP probe/silicon contact under zero pressure will be treated rst. Second, pressure eects will be considered extensively. A complete analytical description of the electrical contact behavior is very complicated. Therefore the attention is focused on the experimental results.

4.2.1 Zero pressure

The total measured resistance Rtot is a sum of the back-contact resistance Rb , the spreading resistance Rs , the contact resistance Rc (also called barrier resistance) and the probe resistance Rp (equation 4.9).

Rtot = Rb + Rs + Rc + Rp (4.9) For an ideally at circular SSRM contact (under zero pressure) Rc and Rs are respectivelyde ned by equations 4.10 and 4.11 where is the sample resistivity (unit: cm) and 2 c = @V @J V =0 the contact resistivity (unit: cm ). The contact resistivity, also called the speci c contact resistivity, depends on dierent conduction mechanisms which dominate the contact depending on the dopant level of the substrate. Thermionic or eld emission for lowly or highly doped layers or a combination of both for intermediately doped layers. The value of c depends on both the applied voltage V and the barrier height 'B which, in its turn, depends on the dopant concentration, the presence of surface states, and the probe material. The density and energy distribution of the surface states are expected to be strongly in uenced by the polishing procedure. In a review of silicon properties [Sah 88] the amount of surface states is discussed which is considered to be applicable to the limiting case of a highly damaged SiO2/Si surface, i.e. a surface similar to the polished SSRM cross section, and was found to be as large as 1014 states/cm2 at room temperature. Furthermore, as the SSRM probe is made of highly doped diamond, the point contact is a diamond/silicon hetero-junction. It is clear that a full analytical description of the contact resistance is complicated. Therefore, the attention of this study will focus on the experimental results and on the electrical characteristics which are of importance for SSRM pro ling. c (4.10) Rc = a 2 (4.11) Rs = 4Sia

96

CHAPTER 4. POINT CONTACT CHARACTERISTICS Rp = Rp0 + diamond ka

(4.12)

The magnitude and the importance of the back contact resistance was discussed in section 3.5.2. Its value is typically smaller than 250 , which is negligible compared to the other terms in equation 4.9. The resistance of the probe (Rp ) is assumed linear and is the sum of the spreading resistance inside the diamond probe (which is proportional to a1 ) and a series term independent of the contact area. Indeed, the current not only spreads in the silicon substrate but also inside the diamond probe. Rp can thus be written as equation 4.12 wherein k is a constant factor depending on the precise shape of the tip apex and Rp0 is the constant term representing the resistance of the bulk of the probe, which can be determined by measuring the resistance when the probe is put down on a metal sample. Rp should be as low as possible to have a maximum sensitivity for SSRM. Again, one might ask whether the classical approach using continuum electronics is still valid for the extremely small SSRM point contacts. Should an atomic approach be used instead? Indeed, for very small contacts (i.e. if the contact radius is smaller than the mean free path ) the Sharvin formula for resistance (equation 4.13) will replace the spreading resistance formula [Sharvin 65]. The mean free path for electrons and holes in silicon is typically 7.6 nm and 5.5 nm [Sze 81], and slighty dependent on the sample resistivity. Since these values are smaller than the electrical radius of a typical SSRM contact (10{25 nm), the Sharvin formula normally does not apply. In the case of smaller contacts, equation 4.13 applies and has the same attractive property as the spreading resistance equation: the resistance increases monotonically with the sample resistivity, providing a highly sensitive method for carrier pro ling.

Rs = 43a(2 )

(4.13)

4.2.2 Under pressure From a mechanical point of view, the working load should be kept as low as possible in order to minimize wear and degradation of the probe and the sample during the measurement. From an electrical point of view on the other hand, it is expected that a minimum load is required to establish a stable, low-noise point contact. The electrical behavior of the point contact under pressure is studied by measuring current-voltage (I{V ) characteristics at dierent loads and as a function of sample type and resistivity. The silicon samples are homogeneously doped within the resistivity range 0.01{40 cm. B-doped (p-type) as well as P-doped (n-type) samples were used. All samples were polished on their (100) side and their resistivity was checked by conventional SRP. All measurements were performed with CVD diamond-coated silicon probes, except when explicitly mentioned. The presented results are representative for the qualitative behavior of all SSRM probes. However, the quantitative information might vary from probe to probe.

4.2. ELECTRICAL

97

Force dependence I{V curves can be collected as a function of the load applied on the probe. There are two possible approaches: for each I{V a separate indentation can be used or the force on the indenter can be gradually increased while it remains in the same position on the sample. Both approaches were studied. I{V curves were collected using a Keithley 237 electrometer driven by external software to collect and display the data. Careful guarding and shielding was used.

Metal samples First, I{V measurements were performed on metal samples in order to characterize the conductivity of the probes used. On metal samples the spreading resistance Rs and the back-contact resistance Rb are very small due to the small resistivity (typically 10,6 cm) and formula 4.9 reduces to Rtot = Rc + Rp. The I{V results measured on a at Pt sample as a function of the applied load, are shown in gure 4.8. The load was varied from 1 to 50 N. Figure 4.9 shows the same set of curves, now represented as the dynamic resistance @V @I versus V . In this type of plot a constant value corresponds to ohmic behavior, an asymmetric curve on the other hand stands for a nonlinear (rectifying) characteristic. Oscillations in this type of plots are the consequence of instrumental noise, both in current and in bias voltage, ampli ed by the dierentiating procedure. The measurements clearly show two distinct regimes. At low forces very little current ows and the I{V curves show a lot of noise and exhibit a non-ohmic nature, similar to I{V curves measured using the STM technique. At higher forces, much more current ows and the I{V curves are smoother and approximate ohmic behavior at the highest loads. The transition from one regime to the other appears at a particular (threshold) force (here between 1 and 2 N) and is accompanied by a resistance change of several decades. This behavior was observed for all probes, but the threshold force varies from probe to probe and typically lies between 5 and 25 N. The origin of the threshold is probably related to the presence of oxide or contamination on the probe and the sample. Once above a certain minimum load, the indenter pushes partially through this layer. Above the threshold force, all I{V curves have the same shape and scale with the applied force. When increasing the load to very high values, the I{V curve saturates. The saturation level is believed to correspond to the resistance of the probe (Rp ), which is at this stage much larger than the contact resistance (Rc ). For solid diamond probes saturation levels of 2{5 k are common, for CVD-diamond-coated probes 1{3 k , while no saturation was observed for metal probes (< 100 ). If this resistance is assumed to be dominated by the spreading resistance in the diamond probe (resistivity ' 0:01 cm), the electrical contact radius can easily be calculated using equation 4.12, leading to values of 5{25 nm for forces which are higher than the threshold force. In gure 4.10 the resistance data (at zero bias) are plotted versus the applied force (F ) and are tted to a power law function R = kF n (k and n are tting parameters). The exponent n equals -0.45 (' ,0:5). As R is inversely proportional to the contact radius, this relation indicates that the contact area is proportional to the applied force. This is in agreement with mechanics theories for plastic deformations [Marchand 83].


98

current (mA)

0.5

0.0

g

-0.5

f e d c b a

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

voltage (V)

Figure 4.8: I{V characteristics measured on platinum as a function of the applied load. The loads are (a) 50, (b) 25, (c) 15, (d) 8, (e) 4, (f) 2, and (g) 1 N. A diamond-coated silicon probe was used.

10

5

g 7 6 5 4

resistance (Ω)

3 2

104 7 6 5 4

f e

3

d c b a

2

3

10 -1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

voltage (V)

Figure 4.9: @V @I , V representation of the I{V characteristics of gure 4.8. The loads are (a) 50, (b) 25, (c) 15, (d) 8, (e) 4, (f) 2, and (g) 1 N. A diamond-coated silicon probe was used.

4.2. ELECTRICAL

99 5

10

measurement fit: R = k F-0.45

7 6 5 4

3 4 5 6 7

resistance (Ω)

1 2 2

104

3 7 6 5 4

4 5 6 7

contact radius (nm)

3

3

10 2 2

103

0

10

20

30

40

50

load (µN)

Figure 4.10: Contact resistance (at zero bias) as a function of load for a diamond-coated probe on a Pt sample (data obtained from gure 4.9). The data obtained at forces larger than 3 N are tted to a power law. The corresponding contact radius was calculated using the basic spreading resistance equation and assuming that = 0:01 cm.

Silicon samples In gure 4.11 a typical set of current-voltage I{V curves measured on a

p-type silicon sample (resistivity = 0.01 cm) is represented as a function of the load. The corresponding @V @I -V characteristics are shown in gure 4.12. The diamond-coated silicon cantilever which was used has a spring constant of 2200 N/m. The force-dependent behavior of these curves is representative for the measurements on all silicon samples with dierent probes of the same type. When the force is increased from 9 N (curve h) to 13 N (curve g) the contact abruptly changes from being nearly isolating to conducting. Below the transition the currents are very low. Above this transition the I{V curves are nearly identical except for a scaling factor which increases proportionally with the square root of the load (see gure 4.13). Similar results have been reported by Marchand and Truong for larger metal-semiconductor point contacts and can be interpreted as a con rmation that the plastic regime has been entered [Marchand 83]. The behavior of this curve as a function of the resistivity will be shown in the next section. The origin of the threshold load is probably related to the presence of native oxide or contamination on the probe and the sample. Above a certain minimum load the indenter pushes partially through this layer, and a behavior speci c for the sample under investigation appears. Below this load, the I{V curve is only weakly dependent on the underlying sample conductivity. In this context it is interesting to note that we were unable to image with the AFM the probe imprints made with loads below the transition point, whereas for higher loads clear imprints were found ( gure 4.14). This suggests that there was only very little plastic deformation below the transition load, as recently reported by Bhushan [Bhushan 94a] for diamond AFM probes on silicon. The aspect of the imprints is imposed by the diamond-coating and varies from a single imprint at low loads to multiple


100

0.4

current (mA)

0.2

0.0

-0.2

-0.4

h g f e d c b

-0.6 -1.5

a -1.0

-0.5

0.0

0.5

1.0

1.5

voltage (V)

Figure 4.11: I{V characteristics measured on p-type silicon ( = 0:01 cm) as a function of the applied load. The loads are (a) 150, (b) 100, (c) 75, (d) 50, (e) 25, (f) 19, (g) 13 and (h) 9 N. A diamond-coated silicon probe was used.

1010

dynamic resistance (Ω)

109 108 107 h 6

10 10

5

g

104

f d b a

103

-1.0

-0.5

0.0

0.5

1.0

voltage (V)

Figure 4.12: @V @I {V representation of the I{V characteristics of gure 4.11. The loads are (a) 150, (b) 100, (d) 50, (f) 19, (g) 13 and (h) 9 N.

4.2. ELECTRICAL

101 9

10

measured fit: R = k F-0.56

8

resistance (Ω)

10

107 106 105 104 103

0

20

40

60

80

100

120

140

160

load (µN)

Figure 4.13: Resistance measured at zero bias on p-type Si (0.01 cm) as a function of load. The data obtained at high forces pare tted to a power law and indicate that above a transition force of about 20 N, R is proportional to 1= F .

contacts at high loads. In all the experiments the rst touchdown occurred at the smallest possible load. Due to the non-vertical probe/sample approach in the Multimode AFM used in these experiments, a landing trace appears in the y direction before the feedback takes over. The recurring scratch, which is less than 20 nm wide, is thought to be made by one of the tip asperities. As a result of the very small contact area and the large stiness of the cantilever, the impact pressure here is at least 20 GPa, exceeding the yield strength of silicon. Material is being pushed forward by the sti cantilever until the feedback loop is closed and the predetermined load is imposed by the z piezo. In this way the volume of the expelled material always exceeds the volume of the pit. The piled-up material which can be attributed to amorphous silicon is abundantly present at low loads and often covers the whole imprint. Successive point contacts were made by manually shifting the tip in the y direction. A fast way of determining the force-dependent behavior of a particular probe is based on the measurement of force curves (cf. section 3.6.1). The resistance at a xed bias voltage is monitored simultaneously with the extension of the cantilever as the probe is moved up and down towards the sample. The standard SSRM resistance measurement unit is used. Parameters are: the total distance and starting position of the sample movement and the frequency of this oscillation. Figure 4.15 shows the force curve and the resistance pro le measured simultaneously with a diamond SSRM probe (spring constant 286 N/m). Note that the frequency must be chosen small, such that the external electronics are able to follow the resulting resistance changes. This procedure is recommended for checking the stability of the electrical behavior of the probe and should be used frequently when scanning in SSRM mode. Figure 4.16 shows the force and resistance pro les before and after a xed number of SSRM scanning cycles. Figure 4.17a displays the threshold force


102

Figure 4.14: Imprints made by a diamond-coated silicon tip on a sti cantilever (k = 2200 N/m) in silicon at increasing load: (a) 9, (b) 13, (c) 19, and (d) 31 N. AFM images are taken in contact mode with a standard AFM probe (scan size: 500 500 nm2). 109 60

8

107

40

106 20

5

resistance (Ω)

cantilever deflection (nm)

10

10

104

0 -40

-20

0

20

40

103

sample displacement (nm)

Figure 4.15: Force and resistance pro le as the diamond-coated SSRM probe (k = 286 N/m) is moved down towards the sample. The threshold is observed at a cantilever de ection of 26 nm, which corresponds to a force of 0:026 286 = 7:4 N.

4.2. ELECTRICAL

103

as a function of the number of SSRM images taken with this probe. The gure gives an idea of the stability and lifetime of the SSRM probes. In general, the threshold force is observed to increase slightly while scanning and the probe can be used for about 10{20 measurements without serious degradation. Sometimes a large increase in threshold force is observed (e.g. probe 3 in gure 4.17a). This degradation is re ected by an increase of the tip radius caused by wear. The corresponding (geometrical) radius of curvature was measured using the SrTiO3 calibration standard [Sheiko 93] and is shown in gure 4.17b. 109 108 7

10

resistance profile: before scanning after 5 SSRM images after 20 SSRM images

40

106

20

105

resistance (Ω)

cantilever deflection (nm)

60

104

0 -40

-20

0

20

40

103

sample displacement (nm)

Figure 4.16: Force and resistance pro les before scanning and after taking 5 and 20 SSRM images (2 2 m2) at 10 N.

The threshold force behavior is related to the nature of the sample and not to the nature of the probe. Indeed, the threshold observed on metal samples (Pt, Au) is much lower than the one observed on silicon. When using a metal probe, a similar threshold behavior is found when measuring on silicon. But, the probe shape degrades much faster than the diamond probes as can be seen by comparing the curves in gure 4.17. Clearly, the metallic probes are unable to sustain the stress necessary to establish a stable (ohmic) contact even on the highest doped materials.

Probe penetration The presence of a threshold force is the most striking fact of the force-dependent behavior of the SSRM point contact. This threshold force behavior can be explained by the presence of an oxide or contamination layer on the sample which must be penetrated to reach a stable measurement condition. Another possibility is the requirement for the formation of a -tin silicon phase, which is known to give much lower resistance values, but which requires high stresses in the silicon sample. In this section, probe penetration experiments are presented to con rm that the formation of such a -tin phase is the reason for the appearance of a threshold force. Therefore, the penetration depth of the probes in SSRM measurements is determined by measuring on silicon samples covered with a thin SiO2 layer of known


104 100

500

(a)

7 6 5 4

diamond probe 1 diamond probe 2 diamond probe 3 PtIr probe

(b) 400

2

tip radius (nm)

threshold force (µN)

3

10 7 6 5 4 3

diamond probe 1 diamond probe 2 diamond probe 3 PtIr probe

2

1

0

5

10 # nano-SRP images

15

300

200

100

20

0

0

5

10

15

20

# nano-SRP images

Figure 4.17: (a) Threshold force as a function of the number of images taken with 3 dierent diamond SSRM probes and one PtIr probe. (each image is 2 2 m2 and is taken at 10 N). The threshold force was determined as illustrated in gure 4.16 for diamond probe 1). (b) Corresponding probe radius as measured on a SrTiO3 calibration standard.

thickness. In a rst approach, a uniformly doped n-type sample with a thermal SiO2 layer of 20 nm was beveled under a small angle of 0 170 . By performing SSRM indentation experiments on the beveled surface at dierent distances from the bevel edge, the behavior for dierent oxide thicknesses can be measured. However, no reliable data could be obtained because of the surface roughness of the beveled surface and the destructive nature of the beveling procedure which degrades the quality of the oxide considerably. In a second approach, a set of uniformly doped n-type (100) wafers covered with a thermal oxide of varying thickness was selected. The thickness of the SiO2 layers was checked by ellipsometry and was found to be 2.0, 2.6, 3.5, 4.6, 8.8, and 20 nm. Two additional samples (same substrate) with no thermal oxide were added to this set; one with a native oxide and another one which was passivated by HF treatment shortly before the experiments. The variation of the resistance with the oxide thickness is shown in gure 4.18. Each data point represents the average of 5 measurements. The resistances were measured at a bias of 25 mV. No data are shown for the sample which has a 20 nm oxide layer (always out of range, i.e. > 109 ). The two additional samples (one with native oxide and a passivated one) showed resistance values close to the ones measured on the sample with 2 nm oxide. For all samples a threshold force behavior is observed; i.e. for a given force the spreading resistance increases very rapidly to a very high value. The asymptote value of a particular curve of gure 4.18 therefore yields the oxide thickness for which the probe can no longer establish an electrical contact to the substrate. In gure 4.19 these determined oxide thicknesses are plotted as a function of the probe loads. The indentation depth was determined from AFM topography measurements of the imprints left on the dierent samples and from force-displacement curves. These depths were found to be independent of

4.2. ELECTRICAL

105

the oxide thickness, but strongly dependent on the applied load. The load versus indentation depth is also drawn in gure 4.19. The large amount of scatter on these data is related to the fact that some of the expelled material may fall into the indention marks, in this way reducing the monitored depth. The indentation depth observed for a particular force is much deeper than the maximum oxide thickness for which a stable SSRM contact can be formed. For example, at a force of 100 N, an oxide thickness of 5 nm can be penetrated, while the indentation depth is 15 nm. Note that the actual penetration depth is even larger than the observed imprint depth because some of the material relaxes elastically after the indentation. We conclude that, in the presence of an oxide layer, SSRM operation requires a probe load which is higher than the one needed to penetrate the oxide layer. If the sample is passivated or has only a native oxide, the same behavior is observed as when the sample has a thin (2 nm) thermal oxide. This behavior con rms that the formation of a -tin phase, and not the presence of an oxide layer, is the reason for the appearance of a threshold force. 109

65 µN

8

resistance (Ω)

10

107

88 µN

106 105

125 µN 107 µN

142 µN

104 3

10

0

2

4

6

8

10

12

oxide thickness (nm)

Figure 4.18: Measured resistance values as a function of the thickness of the oxide on top of a highly doped n-type silicon (0.01 cm) substrate for dierent probe loads.

Resistivity dependence I{V measurements on homogeneously doped silicon were recorded for dierent sample resistivities. Figure 4.20 shows the I{V curves measured on dierent n-type and p-type silicon samples at a load of 25 N. V is again the voltage applied to the tip (while the sample is connected to ground). The dynamic resistance @V @I as a function of the applied bias for the same data is shown in gures 4.22 and 4.23. For comparison, the I{V data measured on the same set of samples with a solid diamond probe (at a load of 200 N) are shown in gure 4.21. From these measurements it is clear that if the sample resistivity changes, the I{V characteristics change drastically. If the sample resistivity is increased, less current

ows through the point contact. This forms the basis of the SSRM method, without which it can not be operated as a carrier pro ling tool.


106 200

force (µN)

150

100

50

0 0

10 oxide thickness (

20

30

) / indentation depth (

40 ) (nm)

Figure 4.19: Threshold force as a function of sample oxide thickness, and load versus indentation depth (measured with standard AFM).

The nonlinear behavior of the dynamic resistance of the n-type silicon is rather dierent from the p-type characteristics. The resistance values at zero bias are more peaked for highly resistive n-type than for p-type silicon pointing to the contribution of an extra barrier. This fact may be related to the p-type diamond probe creating a depletion region in the point contact on n-type material. Since low resistive samples can still be distinguished from each other, the conductive path in the AFM probe lies mainly within the diamond-coating, considering the 4 cm inner tip material. Upon decreasing the load down to the threshold value, the dispersion of the dynamic resistance with resistivity decreases gradually. Below the threshold force most curves started to overlap, making it useless for carrier pro ling. The dynamic resistance measured on both types of silicon is an order of magnitude higher for the CVD diamond-coated probes compared to the solid diamond probes for similar loads. The higher resistance is directly correlated with the smaller contact area that can be obtained with the diamond-coated probes. For SSRM operation a xed bias voltage must be chosen. In conventional SRP this voltage is typically 5{10 mV. Figures 4.22 and 4.23 illustrate that the maximum dynamic range can be obtained if the bias voltage approaches zero volts. In this context it is worth noting that over a voltage region kTq (' 26 mV at 300 K) from the origin (whereby k = Boltzmann's constant, T = absolute temperature, and q = electronic charge) all contact resistances can be shown to be linear [Henisch 84].

Calibration curve The key to the application of the spreading resistance technique is a calibration curve. It is a plot of the measured spreading resistance versus sample resistivity for n-type and p-type silicon. For conventional SRP the calibration curves are determined by measuring on certi ed homogeneously doped samples (obtained from and certi ed by the National

4.2. ELECTRICAL

200

107

(a)

(b)

(c)

(d)

(e)

(f)

0 -200 -400

current (µA)

150 100 50 0 -50 60 40 20 0 -20

-1.0

0.0 voltage (V)

1.0

-1.0

0.0

1.0

voltage (V)

Figure 4.20: I{V characteristics as a function of sample resistivity measured with a CVD diamond-coated probe at a load of 25 N. The n-type curves are represented by solid lines, the p-type curves by dashed lines. The resistivities for n- and p-type silicon are respectively: (a) 0.008 and 0.01 cm, (b) 0.082 and 0.1 cm, (c) 1.03 and 1.03 cm, (d) 6.0 and 4.8 cm, (e) 9.3 and 10.4 cm, (f) 42.0 and 23.4 cm.


108

200 (a) 0

(b)

-200 -400 current (µA)

150

(c)

(d)

60 (e) 40

(f)

100 50 0 -50

20 0 -20

-1

0 1 voltage (V)

-1

0 1 voltage (V)

Figure 4.21: I{V characteristics as a function of sample resistivity measured with a solid diamond probe at a load of 200 N. The n-type curves are represented by solid lines, the p-type curves by dashed lines. The resistivities for n- and p-type silicon are respectively: (a) 0.008 and 0.01 cm, (b) 0.082 and 0.1 cm, (c) 1.03 and 1.03 cm, (d) 6.0 and 4.8 cm, (e) 9.3 and 10.4 cm, (f) 42.0 and 23.4 cm.

4.2. ELECTRICAL

109

10

10

9


10

8

10

7

10

f e c b

6

10

105 104

a

103 -1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

voltage (V)

Figure 4.22: @V @I , V representation of the I{V characteristics of gure 4.20 measured on n-type silicon. The sample resistivities are: (a) 0.008, (b) 0.082, (c) 1.03, (e) 9.3, and (f) 42 cm.

10

10

9


10

108 107 106

g f

105

d

4

c b a

10

3

10 -1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

voltage (V)

Figure 4.23: @V @I , V representation of the I{V characteristics of gure 4.20 measured on p-type silicon. The sample resistivities are: (a) 0.01, (b) 0.1, (c) 1.03, (d) 4.8, (f) 23.4, and (g) 463 cm.

110


Institute of Standards and Technology [NIST] or Solid State Measurements [SSM]) ranging from 5000 cm to less than 0.001 cm. Typically, a supralinear interpolation between adjacent calibration points is used to calculate the resistivity which pertains to a measured resistance value. Figure 4.24 shows the n-type and p-type calibration curves for SSRM and SRP measured at typical loads (25 N for SSRM, 50 mN for SRP). The SSRM curves look very similar to the conventional SRP calibration curves, i.e. showing a monotonic relation between measured resistance and sample resistivity. Both the n-type and p-type SSRM calibration curves dier from the theoretical linear relation between resistivity and spreading resistance (equation 4.11). The deviation is smaller for the conventional SRP technique, but still present. These deviations have to be ascribed to the fact that the actual probe/semiconductor contact is far from being the ideal non-penetrating circular contact with radius a as is assumed for equation 4.11. The discrepancy between the n-type and p-type calibration curves has to be attributed to dierences in the contact properties [Mazur 66]. In conventional SRP relation 4.11 is adapted to take into account more accurately these discrepancies. This can be done through adding a barrier resistance factor or a variable radius or a combination of both;

barrier and xed radius: A barrier resistance component which equals the contact

resistance is inserted in equation 4.11. The nonlinearities in the calibration curves, i.e. the dierence between the ideal relation 4a and the actual measurement values, are attributed to such a barrier resistance eect. Such a barrier resistance term will be dependent on the sample resistivity and should always be positive.

R = 4a + Rbarrier ()

(4.14)

no barrier and variable radius: An alternative to account for the nonlinearities in the behavior of the calibration curves is to assume that the size of the contact is dependent on the sample resistivity (equation 4.15). However, the absence of a barrier resistance component is dicult to accept physically.

R = 4a()

(4.15)

barrier and variable radius: The combination of the former two models. R = 4a() + Rbarrier ()

(4.16)

It is interesting to note that in conventional SRP the n-type calibration curve consistently lies below the p-type curve, and the p-type curve typically displays a bump around 1 cm [Clarysse 96a]. No such systematic behavior was observed for the SSRM calibration curves. In gure 4.25 the calibration curves are plotted as a function of the applied load. Again, the transition load behavior which has already been discussed earlier can be seen. Below the threshold force, the resistance is little dependent on the sample resistivity and cannot be used for carrier pro ling. Above the transition force, the resistances are clearly resistivity

4.2. ELECTRICAL

111

9

10

8

10

resistance (Ω)

107

n-type SSRM p-type SSRM n-type SRP p-type SRP

6

10

105 104 103 102 1

10 0.001

0.01

0.1

1

10

100

resistivity (Ωcm)

Figure 4.24: Calibration curve: variation of the resistance (slope of the I{V curves at zero bias) with sample resistivity measured at 25 N. The data are extracted from the I{V curves in gures 4.22 and 4.23. A typical set of conventional SRP calibration curves is given for comparison.

9

10

p-type Si n-type Si

20 µN

resistance (Ω)

108 107 106

70 µN

105

200 µN

4

10

3

10 0.001

0.01

0.1

1

10

100

resistivity (Ωcm)

Figure 4.25: SSRM calibration curves as a function of the applied load. Curves measured with a full diamond probe (probe V from table 3.3).

112


dependent. The average slope of the calibration curves gradually changes from zero (i.e. no sensitivity) at forces lower than the threshold force, to about 1 for forces exceeding the threshold force. Maximum sensitivity is obtained at the highest forces. The force-pro le and the calibration curve are the ideal tools to check if a particular probe is suitable for SSRM. The force pro le displays the minimum force needed for SSRM, while the calibration curve shows the dynamic range and sensitivity at a xed force. In addition, a method is needed to evaluate the size of the probe apex. Tips can be imaged by SEM. However, this procedure cannot be used until after conducting the AFM experiments because an insulating lm may be formed on the tip from electron beam contamination in a contaminated vacuum. Another method makes use of a calibration standard with well known geometry. For example, a SrTiO3 sample can be used (see section 3.4.3). In gure 4.26 the calibration curves are displayed for dierent candidate SSRM probes. The probes are: CVD diamond-coated silicon, doped diamond, metal-coated doped diamond. Obviously, a good electrical performance (i.e. nearly linear calibration curve, low threshold force) must be accompanied by a good mechanical one (i.e. force withstanding, stable). The curves for the doped diamond probe are attened in the region of the lower resistivities, pointing to a series resistance on account of the diamond that is probably not suciently conductive. As a consequence, the dynamic range of this probe is limited to resistivity values higher than 0.1 cm (or 2 1017 atoms/cm3 for p-type and 9 1016 atoms/cm3 for n-type silicon). Upon decreasing the working load, the dynamic range shrinks even more. Therefore, some of the diamond tips were coated by sputter deposition of a thin (35 nm) layer of tungsten. The dynamic range of the coated probes is extended to at least 0.01 cm. The resistance measured between the coated probe and a platinum sample for a comparable size of imprints was 2.5 k . Hence, based on extrapolation of the calibration curves, it can be concluded that the dynamic range for this probe ends at resistivities a little below 0.01 cm. Furthermore, the calibration curves for the coated probes keep a high dynamic range and a nicely monotonic behavior at lower loads (70 N), indicating that they can be used at lower loads which implies a reduced imprint and contact area.

4.3 Electro-mechanical contact model As indicated before, the SSRM calibration curves exhibit strong nonlinearities which can be attributed to a barrier resistance term. In a simple model the total resistance is the sum of two components: a spreading resistance component and a barrier resistance component (cf. equation 4.16). The current spreading results in a spreading resistance which is only dependent on the sample resistivity and the contact radius, which is assumed to be constant. The barrier resistance term is related to the contact resistivity and is strongly dependent on the applied voltage, the sample type (n or p) and the sample resistivity. From the calibration curve in gure 4.27 it is clear that the radius can have a very small value. The minimum value of the contact radius can be determined by plotting the line given by R = 4a and which goes through the lowest calibration point. For the probe used in this experiment ( gure 4.27) a minimum value of 1 nm is found. This value is extremely small and known to be an underestimate of the real contact radius. The barrier resistance is obtained by subtracting the spreading resistance form the total resistance. The strong nonlinearities

4.3. ELECTRO-MECHANICAL CONTACT MODEL

113

9

10

8

resistance (Ω)

10

W-coated diamond uncoated diamond diamond-coated

107 106 105 4

10

103 0.001

0.01

0.1

1

10

100

resistivity (Ωcm)

Figure 4.26: SSRM calibration curves (only for n-type) for dierent probe types: (a) W-coated doped diamond, (b) doped diamond, (c) CVD diamond-coated silicon.

of the calibration curve indicate that the barrier resistance can be as high as 5 times the spreading resistance. The dynamic resistance curves presented in gures 4.22 and 4.23 show that the total resistance becomes much lower at higher voltages. As the spreading resistance is independent of the applied voltage, its value must be smaller than the smallest resistance value observed. In gure 4.28a the smallest resistance is plotted as a function of the sample resistivity. The values are determined from gure 4.23, after subtraction of the resistance of the diamond tip. The diamond resistance was determined on a Pt sample and was found to be 2.1 k for the particular probe used in these experiments. From this new spreading resistance curve the probe radius can be determined by tting the data by a line given by R = 4a . In this way, a radius of 140 nm is found for the data presented in gure 4.28. The appearance of these two dierent values for the contact radius (1 and 140 nm) can be explained by a rst-order electro-mechanical contact model presented in gure 4.29. Although the SSRM loads may seem unimportant, it should be emphasized that the size of the contact area is less than 100 100 nm2 which implies that pressures above 20 GPa are involved. Such large pressures at room temperature have a substantial in uence on the position and size of the silicon energy bandgap and cause a metallic -tin Si-II phase (see section 4.1.3). The transformed area corresponds roughly with the plastically deformed area and is electrically conducting. In particular, the interface between the -tin phase and the normal silicon behaves as an ohmic contact, independently of whether the doping type was n-type or p-type and the dopant concentration. Based on these points it is physically reasonable to assume two competing contact mechanisms: one related to the elastically deformed region and one related to the plastically deformed region. Both regions are indicated in gure 4.29a-b. The plastically deformed region is smaller than the elastically deformed region. In a rst approximation both regions are circular with radii ap and ae . From loadindentation curves and AFM imaging of the imprints left by an SSRM indentation it is


114

1010 9

10

Rtot at zero bias Rspr (radius = 1 nm)

resistance (Ω)

108 107 barrier resistance

106 105 4

10

103 102 0.001

0.01

0.1

1

10

100

1000

resistivity (Ωcm)

Figure 4.27: SSRM p-type calibration curve (solid line) and spreading resistance curve with minimum contact radius (dashed line). The spreading resistance curve is described by R = 4a where a is the contact radius (1 nm). The barrier resistance is the dierence between the total measured resistance and the spreading resistance.

1010 109

resistance (Ω)

10

Rtot at zero bias Rspr (radius = 140 nm) Rdia

8

107 106 105 104 10

3

102 0.001

0.01

0.1

1

10

100

1000

resistivity (Ωcm)

Figure 4.28: SSRM calibration curve (p-type) and spreading resistance curve at high bias voltages. The spreading resistances at high voltages are determined using the dynamic resistance curves from gure 4.23, after subtraction of the diamond resistance (2.1 k ). These data can be tted by R = 4a where a is the contact radius (140 nm).

4.3. ELECTRO-MECHANICAL CONTACT MODEL

115

known that ap is about 10{30 nm for the forces required for stable SSRM operation. In the plastically deformed region the silicon material is transformed into the -tin phase, which has a much lower resistivity and contact resistivity compared to the original Si material. cp The contact resistance (or barrier resistance) of this region is given by a 2p and remains high because of the small contact radius (ap ). In the elastically deformed zone there may be some pressure-induced bandgap narrowing as well as Fermi-level pinning due to surface ce is large because the contact resistivity ( ) is states. The contact resistance, given by a 2e ce large in this region. (a)

plastic ae

elastic

ap

(c)

(d) R diam

ρ B e = ce2 π ae

(b)

ae

ap

R diam

ρ B p = cp2 π ap

ρ B p = cp2 π ap

1 R p = ρ a1 - a e 4 p

ρ Rp = 4a p

ρ R e = 4a e

ρ

contact

Figure 4.29: Schematical top (a) and sectional (b) representation of the elastically and plastically deformed regions in the SSRM point contact. In the sectional view, the lateral variation of the contact resistivity (c) is plotted schematically. (c) Corresponding electrical lump model with barrier resistances Be and Bp and spreading resistances Re and Rp . (d) Electrical lump model at low probe/sample bias voltages.

The corresponding lump electrical model is presented in gure 4.29c. First, the diamond resistance (Rdiam ) is separated from the remaining part of the total resistance. This resistance is constant and independent of the sample properties. Second, the contact is split into two competing branches which correspond to the elastic and plastic zone of the contact. ce ), while the plastic one is composed of a barThe elastic branch is a pure barrier (Be = a 2e cp rier (Bp = a2p ) and a spreading resistance (Rp = 4 ( a1p , a1e )). The current is spread from the elastically deformed region towards the back contact by another spreading resistance (Re = 4ae ). Both barrier resistances are presented in the drawing as diodes which have a high leakage current. Indeed, if the point contacts are reversely biased, the total resistance is observed to decrease (see for example gure 4.23). The polarity of the diodes is dependent

116


on the type (n or p) of the Si sample. At high forward bias voltages the barrier resistances become very small, and the total resistance equals Re . This results in our example in an elastic contact radius (ae ) of 140 nm. At low bias voltages both barrier resistances are high and the current ow is divided between the elastically and plastically deformed regions of the contact. Hereby, the lower contact resistivity of the plastically deformed region results in a much higher current density and a higher current compared to the surrounding elastically deformed region. Indeed, at lower forces there is no plastically deformed material and only very low currents are observed. Thus, approximately no current ows through the elastically deformed contact zone and the model can be replaced by a more simple one as is shown in gure 4.29d. The total resistance is now split into a barrier resistance and a spreading resistance which is determined by the plastic contact radius (ap = 10{30 nm) which is also referred to as the electrical contact radius. In this model, the barrier resistance is much larger than the spreading resistance. This indicates that the value for the contact radius found above (1 nm) was indeed an underestimation of the plastic contact radius. The presented contact model indicates that the bias voltage must be limited to small values (-50{50 mV) in order to keep the active contact area restricted to the plastically deformed zone. At higher bias voltages, relatively more current ows through the elastically deformed region and the active contact area grows, resulting in a reduced spatial resolution. The signi cance of this model becomes clear when studying the quanti cation of the measured resistance values into carrier concentration values. For homogeneously doped samples, this transformation can be performed by interpolation of the calibration curves and the electro-mechanical contact model is not used. However, for non-homogeneously doped samples, one has to take into account that the current ow might be in uenced by nearby layers with a dierent carrier concentration. For example, nearby layers with a higher carrier concentration will lead to a smaller resistance value. This current spreading eect is discussed in detail in section 5.5. The current spreading depends strongly on the assumed contact model and in particular on the electrical contact radius.

4.4 Side eects

4.4.1 Sample illumination

If light falls on the sample under investigation, the sample can act as a photoconductor, i.e. carriers are generated by intrinsic or extrinsic photoexcitation, resulting in an increase in conductivity and thus a false SSRM measurement. The wavelength cuto is given by = hc 1:24 Eg = Eg m where Eg is the bandgap (in eV). For wavelengths shorter than , the incident radiation is absorbed and electron-hole pairs are generated. For the sample (silicon; Eg = 1:12 eV), Si = 1:11 m and visible light is absorbed, while for the probe (diamond; Eg = 5:47 eV), diamond = 0:227 m and no visible light is absorbed. If the illuminated sample has a pn junction, a photodiode is formed and the SSRM resistance measurements can be distorted seriously . A n+ p junction imaged with and without illumination is presented in gure 4.30. The measurement was performed at a standard SSRM bias voltage of +50 mV. The oscillating signal observed in the p-type substrate corresponds to a 50 Hz noise signal which was unintentionally coupled into the measurement. The incident light generates electron-hole pairs which might result in extra current ow through the SSRM probe in some

4.4. SIDE EFFECTS

117

regions of the pro le. The magnitude of this photocurrent is in uenced by the wavelength and intensity of the incident light, the polarity and magnitude of the bias voltage, and the carrier pro le and the presence of recombination centra in the device under study. In the presented structure, abnormally high currents are observed in the highly doped n-type region when the sample is illuminated with red (670 nm laserlight) or white (ambient) light. If the sample is shielded from all light by placing the complete AFM system in a dark enclosure, the observed current pro le can be used to calculate the correct carrier concentration pro le whereas the current pro les obtained under illumination result in abnormally high carrier concentration values. Throughout the experiments it became clear that n-type regions are particularly sensitive to these eects, whereas p-type regions often show no illumination dependence at all. This dierent behavior might originate from the fact that the probe is a p-type diamond, forming an additional pn junction when the probe is positioned in n-type regions. At present, not enough data are available to determine and explain the quantitative importance of this dierence. 2.5

no light red light ambient light red+ambient light

current (a.u.)

2.0

1.5

1.0

0.5

0.0 0

100

200

300

400

500

depth (nm)

Figure 4.30: One-dimensional SSRM pro le measured on a n+ p junction with and and without illumination (red laser light or white ambient light).

In conclusion, it is important to shield the sample from incident light. The SSRM measurement can easily be performed in a dark enclosure. The illumination of the optical microscope must be switched o during SSRM operation. Furthermore, the sample must be shielded from the laser beam (typically 670 nm, 1 mW maximum) which is needed for the optical detection of the cantilever de ection. This can be done in several ways. First, the cantilever beam can be made large enough and coated with a re ective coating such that it intercepts all incident laser light. An additional advantage of the re ective coating is that the intensity of the re ected light increases, leading to a more sensitive detection of the applied force. Also, the laser spot diameter can be focused on the cantilever to have a minimum diameter, such that no light falls o the cantilever. Second, the laser beam can be positioned on the cantilever away from the tip-end of the cantilever such that the laserlight cannot reach the area where the measurement is performed (the penetration depth


118

in silicon is about 5 m for 670 nm light). In this case, the sensitivity of the AFM force detection is slightly reduced. Alternatively, a non-optical de ection detection mechanism such as capacitive detection can be used [Joyce 91].

4.4.2 Time-dependence A time-dependent measurement of the spreading resistance of the SSRM point contact showed that it decreased gradually after contact was made, and reached a plateau after a fraction of a second ( gure 4.31). Hereby, the initial resistance can be a factor of 2 higher than the steady state value. The time constant ( ) was found to be 0.1{0.3 s and independent of the sample type and resistivity. The same behavior is also observed when the probe is no longer held at a xed position but scanned across the sample. In this case the steady state value is found to be independent of the scanning speed (which was varied from 0.1 to 10 m/s) and to equal the value observed for a xed point contact. From these ndings it can be concluded that the transient behavior does not in uence the SSRM measurement if the scanning mode (at scanning speeds between 0.1 and 10 m/s) is used. If the stepping mode is used, the resistance measurement at each position may only be performed after a small time (about 0.3 s) during which the transient behavior dies out. 10

resistance (kΩ)

8

6

4

τ 2

0 0.0

0.2

0.4

0.6

0.8

1.0

time (s)

Figure 4.31: Spreading resistance as a function of time for a diamond SSRM probe on a polished n-type

h100i silicon surface. The measuring voltage is 10 mV. The probe was not scanned.

A similar behavior was observed for conventional SRP where time constants are on the order of 100 s [Snauwaert 94], clearly much slower than for SSRM.

4.4.3 Unexpected piezo behavior The contact area and the measured resistance of the SSRM probe/semiconductor contact must be kept constant to perform a stable and reliable SSRM measurement. Normally, the AFM feedback loop keeps the force constant. It is however possible that slow deformations of

4.4. SIDE EFFECTS

119

the sample lead to an unstable contact with a varying contact area and resistance value. The stability of the SSRM probe/semiconductor contact was checked in the following manner. A rst probe/sample contact is made in the standard way at the lowest possible force. No scanning in the x or y direction is allowed. Subsequently, the force is increased to a preset value which is above the threshold force. The piezo voltage Vz and the current owing through the probe are monitored as a function of time. A systematic overshoot in Vz , which slowly levels o to a stationary value after a few minutes is observed. As illustrated in gure 4.32 the same phenomenon was again observed when choosing a new force level by repeatedly changing the value of the feedback setpoint. The evolution of the feedback voltage with time follows a behavior typical for creep [Vieira 86]. The amplitude of the overshoot is on the order of 10% of the DC oset voltage applied to the piezo element. It also appears from gure 4.32 that the phenomenon relaxes gradually after more switching cycles have been imposed, indicating a piezo memory eect. In order to test the interpretation that the changes of Vz exclusively re ect the creep movements of the piezo under electric stress and do not follow from plastic deformation of the sample, the experiment was repeated on a polished piece of diamond as sample, for which no indentation is expected. Exactly the same pattern of Vz as a function of time was observed. Also on much softer materials (e.g. Au) for which large indentations are expected, the same behavior was observed. Therefore, the evolution of Vz in time after a sudden DC oset must be attributed to creep and no slow plastic deformation of the sample is observed (in contrast to the ndings for conventional SRP [Snauwaert 94]). From these ndings, we conclude that the contact size and force (and thus the complete pressure distribution underneath the point contact) are constant in time. 50

1000

800

600 30 400

current (µA)

piezo voltage Vz (V)

40

20 200

10 0

50

100

150

200

250

300

350

0

time (s)

Figure 4.32: Response of feedback voltage (Vz ) to changes of load induced by repeatedly changing the setpoint value of the feedback loop on a silicon sample.

When current is drawn through the point contact, Vz again reacts to this new situation. Figure 4.33 shows the current as dierent bias voltages are switched on and o at a preset force such that the point contact between the diamond probe and a highly doped n-type silicon sample (resistivity = 0.008 cm) is essentially ohmic. A decrease in Vz is observed


120

that causes the withdrawal of the sample away from the probe to maintain a constant load. When the bias voltage over the point contact is switched o, the piezo voltage reverts to its original value (if one discounts the compensation for piezo creep). Such behavior precludes the possibility that heat dissipated in the resistive contact would have caused local melting of the sample so that the tip could penetrate more into the softening material. Under these conditions the piezo voltage would not have returned to its original value after the current stopped owing and heat dissipation halted. In order to con rm this viewpoint, the imprints left on silicon were compared for the case where no current passed with one where about 1 mA of current owed through the contact (see gure 4.34). The two imprints are very similar, indicating that no melting took place. 40 500

36

400

34

300

32 200

30 28

100

26 24 0

current (µA)

piezo voltage Vz (V)

38

0 100

200

300

time (s)

Figure 4.33: Changes in feedback voltage (Vz ) as current is drawn through a diamond probe in contact with silicon (p-type, resistivity = 0.01 cm) under various bias voltages (0.5, 1, 1.5, 2, 2.5 and 3 V). The load on the sample is 10 N. Note that the response to the current is superimposed on the compensation of subsiding creep. The amount of current is shown by the dashed line.

The change of the piezo voltage (Vz ) is plotted as a function of the current in gure 4.35 for dierent samples (Pt and p-type Si uniformly doped to dierent levels). All data can be tted by a quadratic function, suggesting that the piezo contraction is proportional to the squared current. Thus, the piezo contraction is also proportional to the power which is dissipated in the diamond tip (P = Rd I 2 ). The dissipated power is believed to cause a thermal expansion of the tip leading to the observed piezo contraction. Indeed, if the probe height enlarges, the AFM feedback will contract the piezo in order to keep the force constant. This behavior was observed for the two types of probes which are most frequently used for SSRM: solid diamond probes tted in a Ti base, and CVD diamond-coated Si probes. In normal operation, the Joule heating and the resulting increase in temperature are limited because of the small bias voltages which are being used. As the heat distribution has the same spreading behavior as the electrical current ow, the maximum temperature change is in rst approximation given by equation 4.17 whereby P is the heat dissipated in the probe.

4.4. SIDE EFFECTS

121

Figure 4.34: AFM images of the imprints made in silicon under a load of 50 N (scan size = 250 250 nm2). For the left imprint, no current owed, whereas a very large current (1 mA) owed during 60 s through the right imprint. The shape and size of both imprints is nearly identical.

T = P 4tha = 4thaRV

2

d

(4.17)

For example, the temperature change caused by the Joule heating at a typical bias voltage of 10 mV is smaller than 1 K (thermal resistivity = th ' 0:1 cmWK ). At 1 V bias (i.e. 0.5 mA current) the temperature change becomes a few tens Kelvin. The eect of this temperature change can be estimated using a nite element simulator which allows one to calculate the thermal expansion of the probe if the temperature is increased at the probe contact. The SYSTUS [SYSTUS] simulator was used to calculate the enlargement of the diamond probe; a local heating of 20 K was found to be able to cause a lengthening of the probe height of 40 nm. In rst approximation these values correspond to the observed values ( gure 4.35). In conclusion, the thermal expansion is only a minor eect with no notable in uence on the SSRM measurement. Furthermore, it is worth mentioning that this unexpected piezo eect was found to be more pronounced for the diamond probes constructed as shown in gure 3.18, compared to the batch-fabricated diamond-coated probes for the samepower dissipated.

4.4.4 Spreading Impedance Probe So far only DC characteristics of the point contact were studied. It is however possible that an AC measurement provides additional information on the sample under investigation. The additional information might include local reactance values, dielectric constants. . . . Another possible bene t of this approach might be that the eects due to the contact and surface region are separated in frequency from the bulk response. Indeed, if the contact (or barrier) eect and the bulk (or spreading) eect are both described as an R , C element with a dierent time constant, two peaks in the total reactance are observed [Thurber 91].

CHAPTER 4. POINT CONTACT CHARACTERISTICS 100

8 6

change in piezo voltage ∆Vz (V)

4 2

10

8 6

Pt p-Si 0.01 Ωcm p-Si 0.1 Ωcm p-Si 1 Ωcm p-Si 4.8 Ωcm p-Si 23.4 Ωcm

4 2

8 6

8 6

4

4

2

2

1

8 6

8 6

4

4

2

2

0.1 5

6 7 8 9

0.1

2

3

4

5

6 7 8 9

1

2

100

10

piezo contraction (nm)

122

1

current (mA)

Figure 4.35: Magnitude of the change in feedback voltage (Vz ) and piezo contraction (in nm) as a function of the current owing through the point contact. The presented data are measured with a solid diamond SSRM probe.

If these peaks occur at suciently dierent frequencies the spreading resistance can be separated from the contact resistance. This method is a standard approach used to study metal/semiconductor contacts [Thurber 91] and has also been used in an attempt to reduce the carrier spilling eects in conventional SRP [Czech 94]. As the logarithmic current ampli er can only be used for frequencies smaller than 500 Hz (cf. section 3.3), an alternative setup is required. Electrical impedance measurements have been performed with an HP-4192A impedance analyzer capable of performing AC frequency scans (maximum 13 MHz) at a xed DC bias. The high terminals have been connected to the probe, while the low terminals have been connected to the backcontact. Care has been taken to minimize side eects of stray capacitances by accurately calibrating the measurement circuit. Point contact measurements on uniformly doped samples have been performed. The frequency dependence of the measured AC impedance has been investigated under zero DC bias over a range from 100 Hz to 13 MHz with an AC amplitude of 50 mV. A typical example, measured on p-type silicon (1.03 cm), is shown in gure 4.36. Two curves are shown: the real resistance part (Rm ) and the imaginary reactance part (Xm ) of the complex impedance (Zm = Rm + jXm ). The curves show a behavior typical for a parallel R-C circuit: the resistance curve remains constant for low frequencies and decreases at rather high frequencies towards 0 . The reactance approaches zero for low frequencies and displays a distinct negative peak at a higher frequency. The corresponding equations are:

Rm = R2C 2R!2 + 1

(4.18)

2 2 Xm = R2RC 2C!2!+ 1

(4.19)

4.4. SIDE EFFECTS

123

1 . Ideally, R corresponds to the point contact And the negative peak occurs at fp = 2RC spreading resistance, while C corresponds to the spreading capacitance combined with the depletion capacitance at the point contact. In this case, fp is inverse proportional to the sample resistivity and can thus be used as an alternative measure for the carrier concentration. However, the extremely small capacitance values (typically < 10,14 F) lead to very high frequencies which are not detectable by the impedance analyzer used (the HP-4192A model is limited to frequencies below 13 MHz).

Rm Xm

600

impedance (kΩ)

400

200

0

-200

-400 1 10

10

2

3

10

4

10 frequency (Hz)

5

10

10

6

Figure 4.36: AC frequency scan showing the resistance and reactance curves measured with a 50 mV AC signal and zero DC bias at a SSRM point contact on p-type silicon (0.01 cm).

In practice, the stray capacitance (between tip and sample and between the thin wires) is considerably larger than the spreading capacitance, and dominates the AC behavior of the point contact. Hence, fp drops by several decades and is independent of the spreading capacitance. For example, the value for fp obtained from gure 4.36 is 450 kHz, leading to a capacitance value of 6:3 10,13 F. The magnitude of the stray capacitance was observed to dier strongly from sample to sample (and from setup to setup) and is dependent on the complete carrier pro le inside the sample. Consequently, this method is not suited for high-resolution carrier pro ling or for the extraction of local impedance properties inside semiconductor structures. A possible solution to perform impedance measurements is to combine the SSRM method with the SCM method. The advantage of the SCM method over the presented impedance measurement is that very small capacitance changes on a large capacitance background (the stray capacitance) can be detected. As SSRM is operated with a small DC bias and SCM with a DC and AC signal applied to the probe, and as SSRM requires a high force whereas SCM does not, these techniques are not fully compatible. Therefore the measurements must be performed sequentially instead of simultaneously. A possible approach is to rst scan the structure at low force and perform the SCM measurement, after which the same position is scanned again at higher force to perform the SSRM measurement. This method can switch from SCM to SSRM after nishing a single line-scan or after scanning a complete


124 two-dimensional area.

4.5 Conclusions The most important characteristics of the SSRM point contact are summarized below.

The force versus resistance curves of the SSRM point contact on silicon display a

threshold force. For forces smaller than the threshold force, the measured resistances are very high and cannot be used for carrier pro ling purposes, while the resistance measured at higher forces shows a clear relation with the sample resistivity and can thus be applied for carrier pro ling. The appearance of the threshold force is related to the transformation of the silicon beneath the point contact into an electrically conducting -tin phase. The formation of this phase is accompanied by a local plastic deformation of the sample and requires high stresses (on the order of 10 GPa). I{V characteristics measured on dierent uniformly doped silicon samples indicate that the maximum sensitivity for SSRM can be obtained at low biases (-50{50 mV). The SSRM calibration curves for n-type and p-type silicon show a monotonic relation between the sample resistivity and the measured resistance. These curves can vary strongly from probe to probe. The SSRM point contact can be described by an electro-mechanical contact model which includes contributions from the elastically and plastically deformed regions underneath the probe. Both contributions are described by a barrier resistance and a spreading resistance. At low bias voltages the plastically deformed region is dominating the contact behavior. The SSRM point contact reaches a stable resistance value within 0.1{0.3 s after the contact has been established. When using typical SSRM settings (-50{50 mV bias), no signi cant thermal eects have been observed. Sample illumination can introduce photocurrents which might lead to artefacts in the SSRM resistance map. Therefore the sample must be shielded from all incident light. A standard procedure to test a particular probe for SSRM consists of the following steps. First, the geometrical tip radius is measured by scanning a calibration sample such as a SrTiO3 sample with atomically sharp edges. Second, the conductivity of the probe is checked by measuring the resistance on a metal sample. The measured resistance represents the intrinsic resistance of the probe. Third, the threshold force (i.e. the minimum load at which stable SSRM measurements on silicon can be performed) is determined by increasing the load on the indenter until a sudden large increase in resistance is observed. Finally, p-type and n-type calibration curves are measured using a set of uniformly doped silicon samples or using two epitaxially grown samples with a well known staircase concentration pro le.

Chapter 5

Pro ling characteristics The SSRM method can in principle be applied in two applications, i.e. the determination of the vertical distribution of the carriers in an otherwise homogeneous structure (an application where SRP and SIMS can also be used) and the determination of the carrier distributions in two-dimensional structures. In this chapter, one-dimensional pro ling results are presented to illustrate the speci cations and limitations of the SSRM technique. These speci cations include dynamic range, sensitivity, concentration resolution, reproducibility, repeatability and quanti cation accuracy, and are de ned as follows:

Dynamic range is de ned as the range of carrier concentrations which can be detected by the pro ling method.

Sensitivity is de ned as the ratio of the change in the instrument response (i.e. the measured resistance) to a corresponding change in carrier concentration.

Concentration resolution is de ned as the ability to discriminate the carrier concentration level between two layers doped to (slightly) dierent concentration levels.

Repeatability refers to the ability to reproduce the measurement results using exactly the same experimental conditions (sample, probe, scan speed, force, etc.).

Reproducibility refers to the ability to reproduce the measurement results when successive measurements are made on dierent samples originating from the same wafer.

Spatial resolution & accuracy. Spatial resolution is de ned as the distance needed

to measure an abrupt dopant concentration step. This concentration step can have dierent heights. Spatial accuracy refers to the ability to determine the position of the measured carrier concentration with respect to the sample surface and mask edges.

Quanti cation accuracy is de ned as the accuracy of the complete (1D or 2D) car-

rier concentration pro le generated from the SSRM measurement data, with respect to the real carrier concentration pro le. 125

126

CHAPTER 5. PROFILING CHARACTERISTICS

5.1 Dynamic range and sensitivity In order to ensure universal applicability, SSRM must be able to cover a large concentration range, at least from 1016 to 5 1020 atoms/cm3 . In principle, both the SRP and the SSRM technique are comparative techniques in which the measured spreading resistance values are compared to the resistance values measured on samples with a well known carrier concentration using the same experimental settings. Typically, one uses a series of eight up to sixteen calibrated homogeneously doped silicon samples (as they are available from SSM [SSM] or NIST [NIST]) to calibrate the conventional SRP technique both for n-type and p-type material [Pawlik 92]. The same set of samples can be used for SSRM. Each sample has to be polished brie y, mounted on the AFM system, positioned, measured and removed. Depending on the number of calibration samples used, this procedure can take between one and three hours. Consequently, in practice there is a tendency to minimize the number of calibration measurements. In order to reduce the calibration time substantially, two structures (one n-type and one p-type) have been designed which allow one to measure the most critical part of the calibration curve with just a single sample for each impurity type [Clarysse 98a]. Both samples can be glued face-to-face forming a single stack, in this way further reducing the calibration time. This reduces the total calibration time for both impurity types to approximately 30 minutes. Figure 5.1 shows the involved dopant pro les. The samples are formed by epitaxial growth, combining a number of requirements. First, there is the very broad dynamic doping range asked for: 0.001 cm up to 10 cm, i.e. from 1015 atoms/cm3 up to 1020 atoms/cm3 (for p-type), which is ve orders of magnitude. Next, the dierent sublayers should be fairly homogeneously doped throughout each layer in order to have a at doping level of sucient width. The dierent calibration layers are separated from each other by thinner buer layers in order to reduce on-bevel carrier spilling eects when the structure is used for calibration of conventional SRP [Clarysse 98a]. These buer layers have a thickness of about 1 m and a dopant density of three times the dopant level of the next (above) calibration layer. A compromise was made regarding the number of dierent calibration levels between on the one hand the need to maximize the number of these levels in order to follow as accurately as possible any non-linearities in the calibration curve, and on the other hand the epi-layer growth restrictions. Figure 5.1 shows the resistance pro le as measured by SSRM on the p-type and ntype calibration sample. A standard SSRM probe with a spring constant of 17 N/m was used at a force of 2 N. First, a 2D image is recorded from which then the shown resistance pro le is extracted by averaging over 16 line scans resulting in a low noise pro le. Figure 5.1 indicates that the SSRM technique is able to distinguish clearly all seven dierent calibration levels. Also, the corresponding buer layers are clearly resolved. Since the probe contact is estimated to be smaller than 30 nm, the width of several micrometer of the calibration layers in cross-section guarantees that the measured resistances from the calibration layers can be used to generate an SSRM calibration curve, using the resistivities as obtained from the conventional SRP. From this type of plots, the calibration curves can be extracted. The n-type and p-type calibration curve, obtained from the data in gure 5.1, are drawn in gure 5.2. The SSRM curves are similar to the ones for SRP, but show considerably higher resistance values. Indeed, the radius of the SSRM contact (10{25 nm) is two orders of magnitude smaller

5.1. DYNAMIC RANGE AND SENSITIVITY 20

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Figure 5.1: Resistance pro le (dashed line) as obtained from SSRM measurement on a cross section on a staircase p-type (a) and n-type (b) structure versus the carrier concentration pro le (solid line) from the conventional SRP measurement.

than the typical SRP contact radius (1{2 m), resulting in a resistance which is more than two decades higher (the spreading resistance is inversely proportional to the contact radius). The staircase samples are ideal to compare the dynamic range and sensitivity of SSRM with other (two-dimensional) carrier pro ling techniques. Hereby, sensitivity is de ned as the ratio of the change in the instrument response (i.e. the measured resistance for SSRM) to a corresponding change in the stimulus (i.e. the carrier concentration). The slope of the calibration curves can be used to determine the sensitivity values. To illustrate this, the SSRM, SCM, and dopant selective etching methods are compared using the p-type calibration sample. Figure 5.3a shows the raw data, i.e. the AC bias necessary to maintain the same capacitance change in the closed loop SCM measurement. The observed dynamic range of these data is about 80, which is somewhat less than the typical value of 100, due to a combination of factors relating to surface states, capacitance sensor probing voltage and variations of the stray capacitance as the probe and cantilever are scanned across the sample. The data originate from a single scan ltered with a 16 pixel convolution lter. The six involved calibration layers are clearly visible in the raw data, although obviously the sensitivity is larger in the highly doped part of the pro le. For the application of the dopant selective etch method, it has been found that the combination of the steep slopes present in the staircase sample and the large etch depth changes ranging from a few nm up to 1 m makes it dicult for the AFM to still accurately resolve the lower dopant part due to tip convolution problems. Moreover, it was found that etching needs to be optimized to image either the high concentrations or the low concentrations [Trenkler 98b]. Therefore, an alternative (p-type) staircase sample has also been measured. This sample is identical to the one discussed up to now, but is missing the rst two (top) calibration layers. A polished cross section has been etched in a standard way for 30 s [Trenkler 98b]. The raw data, i.e. the etch depth, for this sample are shown in gure 5.3b.


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Figure 5.2: SSRM calibration curves (solid lines) obtained from the data in gure 5.1. The error bars indicate the 95% con dence intervals. The calibration curves for the conventional SRP technique are given for comparison (dashed lines).

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Figure 5.3: (a) AC bias pro le (solid line) as obtained from closed loop SCM measurement on a cross section of the p-type staircase structure versus the carrier pro le (dotted line) from the conventional SRP measurement. (b) Etch depth pro le (solid line) as measured with standard AFM on a p-type sample without the two rst (top) layers versus the carrier pro le (dotted line) from conventional SRP.

5.1. DYNAMIC RANGE AND SENSITIVITY

129

The remaining four calibration layers are clearly resolved. Note that whereas typically the detection limits of selective etching are at the level of 1017 atoms/cm3 , gure 5.3b shows quite clearly that concentration dierences down to 1015 atoms/cm3 can be resolved. This is mainly due to the long etching times used in this particular experiment. The response of each technique (SSRM: resistance; SCM: AC bias voltage; etching method: etch depth) is shown in gure 5.4 as the resistivity varies over 4 orders of magnitude. These values are obtained from the data on the p-type staircase sample. For completeness the conventional SRP calibration curve is also displayed. It follows that SCM, chemical etching and SSRM respectively display 2, 3 and 4 orders of dynamic range on their raw data. Note that for the etching method results from two dierent etching conditions had to be used (see above). For SSRM and SCM also the ideal theoretically expected behavior is indicated. The nearly linear dependence of the SSRM resistance on sample resistivity implies a constant sensitivity over the entire concentration range and no ampli cation of noise within the resistance to resistivity conversion. The deviation from linearity in the high concentration part for the etching method and in the low concentration part for SCM implies that for these methods sensitivity is reduced in those regions and S/N will be decreased relatively. On the other hand, the deviation of the SSRM calibration curve from the ideal linear dependence does imply that the ner details of the calibration curve need to be determined experimentally very precisely and have to be stable over a period of time. In this respect, SCM seems to have a more predictive capability (at least in the region from 0.01{10 cm) whereas in the highest concentration part some re nements to the theoretical modeling are necessary as well. 106 SSRM SCM SRP etching 1 etching 2

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Figure 5.4: p-type calibration curves extracted from the staircase measurements for SSRM, closed loop SCM, chemical etching, and conventional SRP. The dashed lines represent the (ideal) theoretically expected behavior for SSRM and SCM.


130

5.2 Concentration resolution The concentration resolution is de ned as the ability to discriminate the carrier concentration level between two layers doped to slightly dierent concentration levels. The target for the SSRM method is the ability to discriminate between carrier distributions that dier by no more than 20% over the concentration range from 1016 to 5 1020 atoms/cm3 . In the absence of a dedicated test structure with uniformly doped layers with certi ed concentration dierences of 20%, the concentration resolution is established as the average noise level on homogeneously doped substrates or uniformly doped layers. The noise level, de ned as the 3-deviation value of the measured resistance data, has been determined on homogeneously doped samples as a function of experimental conditions: sample preparation, applied force and scanning speed. The noise introduced by the resistance measurement unit was rst determined by replacing the tip-sample contact by a xed resistance, with precisely known value. These noise values were found to be negligible as compared to the noise level observed when the resistance of the tip-sample contact is measured. An overview of the results is given in table 5.1. For forces slightly above the threshold force, the noise level is high. The noise is observed to decrease upon increasing the working force. If the force is taken 50% higher than the threshold value, the 20% speci cation is reached. The scanning speed, varied from 1 to 5 m/s, has little or no in uence on the observed noise level. Table 5.1: Noise value (i.e. the 3-deviation value expressed in %) as a function of scanning speed and applied force, as measured on a homogeneously doped Si sample. The force is given relative to the threshold force (Ft) of the probe used in this experiment.

force = 1:1 Ft force = 1:5 Ft force = 2:0 Ft

speed = 1 m/s 2 m/s 5 m/s 72 141 91 27 31 23 13 8 15

In order to achieve these low noise values, a good surface preparation is crucial. Table 5.2 shows the noise level measured on the same sample, polished dierently and having a dierent sample roughness. The RMS value of the surface roughness should be better than 0.4 nm to suppress the noise level to below 20%. Table 5.2: Noise value as a function of sample preparation (roughness) at constant scanning speed (1 m/s) and force (1:5 Ft ).

RMS sample roughness (nm) noise (3 in %) 0.21 16 0.43 27 1.12 81

5.3. REPRODUCIBILITY AND REPEATABILITY

131

5.3 Reproducibility and repeatability 5.3.1 Repeatability Repeatability is veri ed by measuring one-dimensional test structures 10 times in quick succession. The percentage repeatability is calculated by rst nding the standard deviation in resistance measured at each pro le location. The 3-deviation spreading resistance of the 10 pro les is then divided by the average resistance of the 10 pro les at the corresponding location. The average value of this percentage pro le within the complete spreading resistance range is de ned as the repeatability. During this test, the sample and experimental conditions (tip radius, force, step density. . . ) are kept constant. Each measurement can be performed on a dierent location on the same sample, such that the measurement is not disturbed by the damage introduced by the previous measurement, or the successive measurements can be performed on the same location. Measurements are performed at a force which is twice as large as the threshold force such that the concentration resolution (i.e. the noise level) is low (as shown in table 5.1). Figure 5.5 shows the average spreading resistance pro le and the percentage repeatability pro le for the one-dimensional staircase structure presented earlier in gure 5.1a. This structure is of particular interest because it almost completely encloses the concentration range from 1014 to 1020 atoms/cm3 . In this example, the percentage repeatability was found to vary from 10 to 25% with an average value of 12.7%. The values obtained at the high and low concentration end of the curve (i.e. at the low and high resistance end) are slightly higher than the ones obtained for the mid-range. The repeatability is observed to be slightly better if successive measurements are taken at the same position. If a new location (on the same sample) is selected for each measurement, the repeatability can be improved by ignoring the rst scan and storing the second or one of the later scans for each position. Indeed, the rst scan is believed to be in uenced by the initial roughness of the sample and by the presence of contaminants. These contaminants are removed or reduced during this scan so that successive scans are less sensitive to these factors. However, when scanning at the same position (1D or 2D) for a long time (> 20 scans), the noise level is observed to increase again, often combined with unexpected large changes in the resistance values. This behavior is related to the large amount of debris generated during the long scanning time. The debris sticks to the probe and introduces an unstable electrical contact resulting in higher noise levels and large increases in resistance. The same procedure can be used for two-dimensional measurements. An overview of the average percentage repeatability is given in table 5.3. Table 5.3: SSRM repeatability as determined from 10 dierent measurements on the same test sample at a force which is twice the threshold force. The values are lower when the probe is not moved to a new position between the measurements.

new position same position rst scan second scan successive scans 1D 2D 1D 2D 1D 2D repeat. % 42% 49% 19% 29% 13% 18%


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Figure 5.5: One-dimensional SSRM repeatability test showing ve (out of ten) dierent resistance pro les (thin solid lines), the average spreading resistance pro le (thick solid line) and the percentage repeatability pro le (dashed line). In the presented example the probe was not moved to a new position after each scan . The resistances were measured on the one-dimensional p-type calibration structure presented in gure 5.1a.

5.3.2 Reproducibility Reproducibility is de ned here as the standard deviation on the spreading resistance measurements when successive measurements are made on dierent samples originating from the same wafer (which is assumed to be perfectly homogeneous) and/or at dierent times. The main dierence with the repeatability test is that the samples are re-polished in between reproducibility measurements. Obviously high reproducibility can only be achieved when high repeatability has been mastered. The determining factors are the reproducibility of the applied force, the lifetime and wear of the tip contact and the reproducibility of the sample preparation. An overview of the reproducibility test results is presented in table 5.4 which shows the average percentage reproducibility when using dierent samples and/or after realignment of the probe in the AFM instrument. In these experiments the probe is not changed. The percentage reproducibility is observed to be worse when the probes are realigned in between measurements and is only slightly dependent on the fact that dierent samples are taken or not. Table 5.4: SSRM reproducibility as determined from 10 dierent measurements (always second scan) at a force which is twice the threshold force. The measurements were taken on dierent samples (= or 6= sample) and/or after realignment of the probe in the AFM instrument (= or 6= probe).

= probe, 6= sample = 6 probe, = sample =6 probe, 6= sample 1D 2D 1D 2D 1D 2D reprod. % 24% 32% 34% 41% 37% 51%

5.4. SPATIAL RESOLUTION AND SPATIAL ACCURACY

133

5.4 Spatial resolution and spatial accuracy The electrical spatial resolution can be better than the geometrical resolution. This can be understood within the context of penetration through the native oxide whereby part of the visible geometrical deformation occurs in the oxide which however does not contribute to the electrical contact. Electrical resolution tests were performed on two types of samples; In a rst sample set the samples consist of a buried SiO2 layer with well known thickness. A second set of samples are MBE grown samples with abrupt doping steps. The spatial accuracy, i.e. the ability to position the measured carrier concentration pro le with respect to the sample geometry, is determined on samples with a well-de ned structure.

5.4.1 Buried SiO

2

The samples have a p-type substrate (1019 atoms/cm3 ) which is covered with a thin SiO2 layer (20, 10, 6, or 4 nm) and a polysilicon capping layer (1019 atoms/cm3 , thickness = 500 nm). If the probes are scanned across the SiO2 layer, a peak is observed in the resistance pro le. The width of the observed peak is a measure for the electrical tip radius or the spatial resolution of the particular probe used. The substrate and capping layer were highly doped to increase the contrast in resistance. Figure 5.6a shows the resistance scans measured on the dierent samples. The resistance pro les measured on the layers with a thickness of 20 nm display a clear resistance peak, while only a very small peak is observed on the 10 nm layer, and no peak is observed on the thinnest layers (6 and 4 nm). If the electrical contact is assumed to be circular and perfectly ohmic, the resistance pro le can be calculated by nite element simulations of the current distribution through the contact as the probe moves across the oxide layer. The simulation results obtained for an electrical probe radius of 10 nm are presented in gure 5.6b for a 5, 10, 20 and 30 nm thick SiO2 layer. If the probe radius is equal to the width of the oxide layer, the resistance measured at the oxide position is twice as high as the one measured far away from the oxide layer (the relative resistance peak equals 2). By comparing the simulated and experimental results, a good estimate for the electrical tip radius can be made. For the probe used in gure 5.6a, the relative resistance peak observed on the 20 nm oxide is higher than 2 while the resistance peak for the 10 nm oxide is smaller than 2. From these results it is concluded that the electrical tip radius lies between 10 and 20 nm. Unfortunately, these samples cannot be used for a two-dimensional spatial resolution test, since they vary only in one dimension. It is dicult to construct a sample which has a square oxide region whose dimensions are precisely known and which can then be used as a two-dimensional test for spatial resolution. A possible solution to circumvent this problem is to scan the one-dimensional structure with dierent orientations of the cantilever beam with respect to the sample edge.

5.4.2 Abrupt doping steps

An alternative test for the electrical spatial resolution involves the measurement of abrupt doping steps. For this purpose, two low-temperature MBE grown test samples were specially made at Sematech to judge the accuracy of various dopant pro ling methods [Diebold 96, Kump 95]. The samples were distributed to a number of groups as part of a round-robin


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Figure 5.6: (a) Resistance scans on p-type samples (1019 atoms/cm3 ) with a buried oxide of thickness 20, 10 and 6 nm. The presented results are an average of 8 parallel scans. The distance between two measurement points is 0.8 nm. The dashed lines show the average resistance level and twice this level. (b) Simulated resistance scans for a 10 nm tip radius scanning a 30, 20, 10 and 5 nm thick buried oxide layer. The resistance values are given in arbitrary units with the substrate value as a reference (= 1).

of various dopant pro ling methods. The rst structure contains abrupt boron doping steps (50 nm width) between 1020 , 1019 and 1018 atoms/cm3 which are meant to determine the spatial resolution as a function of the impurity concentration level. Spatial resolution was de ned by Sematech as the maximum of the rise or fall distance between the 16% and 84% concentration levels of an abrupt concentration step, and is a function of the concentration level. Note that it is impossible to make an abrupt carrier concentration step (on physical grounds, no discontinuities in the carrier concentration are allowed). Using Poisson's equation the maximum resolution which can be achieved can be calculated as a function of the dopant concentration level. The results are shown in gure 5.7. The SIMS pro le of the rst sample is shown in gure 5.8b. The carrier concentration pro le shows the abrupt boron doping steps and has a second peak with a linear concentration gradient from 1018 to 1020 and back down again to 1018 atoms/cm3 . Further, gure 5.8a shows the resistance data measured with the SRP (on a beveled surface) and SSRM method (on a polished cross section), the calculated SRP and SSRM carrier pro les are compared in gure 5.8b. The SSRM resistance pro le clearly reveals both peaks including the 50 nm wide abrupt steps in the rst peak. The conventional SRP resistance pro le lies much lower since the SRP probe contact is much larger than the SSRM contact. The abrupt steps are much less pronounced in the SRP resistance data. A generally good agreement is found between the SIMS, SRP and SSRM concentration pro les. From the three doping steps in the rst peak (from high to low concentrations), the spatial resolution was calculated to be 10.3, 18.6 and 20.6 nm. Note that the abrupt doping steps result in carrier concentration steps which are no longer abrupt and which have, in this case, a fall distance of respectively 4.5, 6, and 11 nm (as shown in gure 5.7). Table 5.5 lists these values. Using a simple Gaussian summation for


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Figure 5.7: Best (carrier concentration) attainable resolution as a function of the peak level and peak height of an abrupt doping step, as de ned by Sematech.

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Figure 5.8: SSRM, SRP and SIMS pro le of Sematech round-robin sample #1. The measured resistances are given in (a), the carrier densities in (b).

136


describing the convolution between the carrier pro le and our response function an estimate of the real SSRM resolution can be extracted. This resolution turns out to be about 15 nm. The saturation of the second peak in the SSRM pro le is believed to be a result of the type of ampli er which was used in this experiment. In this experiment the logarithmic current ampli er was replaced by a linear voltage ampli er which has a high sensitivity for a limited resistance range (20 k to 2 M ) and a much lower sensitivity outside this range (cf. section 3.3). As a consequence the integrated impurity dose from the SSRM method (1:4 1015 atoms/cm2 ) is smaller than those obtained from SIMS (2:2 1015 atoms/cm2 ) and SRP (2:6 1015 atoms/cm2 ). The SSRM carrier concentration pro le is compared to the one obtained by other 2D carrier pro ling methods in gure 5.9. The SCM data were measured by J. McMurray (University of Utah) and quanti ed by pinning the SIMS dopant pro le at 1019 atoms/cm3 (i.e. the rst dopant step) as a reference [Huang 96a]. Every other point is measured relative to this one point. Both steps appear in the SCM pro le, but they cannot be fully seen. The pro le is believed to be in uenced near the surface as well as along the deep edge by the size of the tip. The fact that the carrier density does not go up to the full 1020 atoms/cm3 in both peaks is believed to be related to some lateral depletion which is not accounted for in the SCM quanti cation model. The spatial resolution calculated as de ned above is given in table 5.5 and is found to be slightly higher than the one for SSRM. The selectively etched pro le shows very little details of both peaks. Note that there exists no quanti cation procedure for this technique such that only raw data are displayed. The dopant steps in the rst peak are not observed indicating a poor resolution as compared to the other two techniques. The results obtained with the selective etch method do not allow one to calculate the spatial resolution as de ned above. Table 5.5: Resolution (in nm) for dierent 2D carrier pro ling techniques, measured on Sematech round-robin sample #1. The best attainable resolution, calculated as presented in gure 5.7, is added for comparison. The deconvoluted value for the SSRM resolution is also given. p

peak conc. SSRM (x) SCM best attainable (y) SSRM deconv. ( x2 , y2 ) 1018 20.6 11 17.4 1019 18.6 25.3 6 17.6 1020 10.3 15.5 4.5 9.3 average 14.8

The second Sematech round-robin structure is a npn structure with a very shallow surface n-type layer. The sample consists of 1018 atoms/cm3 doped regions of boron and phosphorus doping and includes narrow boron-doped peaks to test for spatial resolution of small features. Figure 5.10a shows the measured SRP and SSRM resistance data, gure 5.10b the corresponding carrier concentration pro les. There are considerable dierences between the chemical (SIMS) and electrical (SRP and SSRM) concentration pro les. Based on the SIMS pro les an electrical junction is expected at a depth of about 100 nm. However, no electrical junctions are observed with SRP or SSRM. This is in agreement with electrical pro les obtained by other participants of the round-robin comparison [Kump 95]. The three boron peaks are detected by both the SRP and SSRM technique. However, the SSRM pro le shows a considerable peak broadening for the two thinnest peaks. Since the electrical probe


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Figure 5.9: SSRM, SCM and selectively etched pro le of Sematech round-robin sample #1. For SSRM and SCM the carrier concentration pro le is given, whereas for the selective etch method the raw data are presented.

radius (about 15 nm) and the width of the peaks are of the same size, the concentration values are averaged. This is illustrated by the simulated SSRM resistance pro le drawn in gure 5.10a. The simulated pro le is obtained by calculating the resistances for every point using a 3D nite element Poisson solver in combination with the calibration curve for the probe which was used and assuming a contact radius of 15 nm. The simulated pro le overlaps the measured pro le indicating that the contact radius is indeed close to 15 nm. Although a detailed deconvolution algorithm which restores the exact carrier pro le from the measured resistance pro le is available (presented in chapter 5.5), we were unable to apply it on this type of challenging concentration pro les as their steepness is presently outside the range of the correction factor database.

5.4.3 Spatial accuracy Adequate use of SSRM on small device structures requires the ability to determine the position of the measured carrier concentration with respect to the sample surface and mask edges. Standard topographical AFM imaging is an invaluable tool to achieve high precision localization and for instance zero point detection. In principle the SSRM tips are not designed for imaging which implies that the topographical resolution is not as good as normally obtained with standard AFM tips. In particular, the topographic image obtained during the SSRM measurement is of limited quality because of the high force used. Therefore it is standard practice to scan the structure at lower force prior to the SSRM measurement, hence obtaining a high resolution image of the structure's topography. The SSRM image is then taken at exactly the same position, using a higher force. In this way, the spatial


138 (a)

1020 simulated SSRM SSRM SRP

1019

resistance (Ω)

3


106

(b)

105

104

103

1018

10

17

10

16

SRP SSRM

1015 10

SIMS B SIMS P

2

0

200

400

600

depth (nm)

0

200

400

600

depth (nm)

Figure 5.10: SSRM, SRP and SIMS pro le of Sematech round-robin sample #2. The resistances are given in (a), the carrier densities in (b).

accuracy is equal to the electrical resolution. In another approach, the electrical signal can be used to detect the precise position of the measured pro le. For example, the sample can be coated with a thick (> 100 nm) oxide layer such that the measured resistance increases to in nity when the probe reaches the edge of the silicon region.

5.5 Quanti cation procedure 5.5.1 Introduction

This section deals with the transformation of the measured resistance data into a quantitative carrier or dopant concentration pro le. In SSRM, the resistance measured at a particular position on the sample cross section is not exclusively determined by the carrier concentration at this position, but by the entire surrounding carrier pro le. The correct evaluation of this spreading eect requires a detailed calculation, leading to a deconvolution algorithm which recovers the charge carrier pro le from the measured resistance pro le [DeWolf 96c, DeWolf 98a]. In this section, a general scheme for transforming a wide range of pro les is proposed.

5.5.2 Problem de nition

For semi-in nite uniformly doped samples (with resistivity ) the spreading resistance R of a non-penetrating circular (radius a) ohmic probe contact is known from theory and given by equation 5.1 [Henisch 57].

5.5. QUANTIFICATION PROCEDURE

139

(5.1) R = 4a In real life, the electrical properties of the probe-semiconductor contact depend on many dierent physical factors such as the precise probe shape, the surface state concentration and energy distribution, and the force applied on the probe. Equation 5.1 is no longer valid. The measured pro le must now be compared with a set of calibration measurements since it is extremely dicult to write down an equation which includes all of the non-idealities mathematically. Interpolation of the calibration curves, representing the resistances measured on a series of homogeneously doped samples over the resistivity range from 10,3 cm to 104 cm, is used to calculate the resistivity which corresponds to a measured resistance value. It is common practice to attribute the non-linearities in the calibration curve { i.e. the dierence in slope between the ideal relation 5.1 and the actual measurement values { to a barrier resistance component Rbarrier . This model was described in detail in sections 4.2.2 and 4.3 and leads to equation 5.2 whereby a corresponds to the electrical contact radius. (5.2) R = 4a + Rbarrier () For non-homogeneously doped samples the problem is even more complex. Since the SSRM measurements are performed on the cross section of a sample, other regions of the pro le (containing dierent carrier concentrations) are very near and the current might be primarily carried through the highly doped parts of the carrier pro le leading to a decrease in resistance. Thus, the resistance value measured at an arbitrary position x is no longer exclusively determined by the carrier concentration at x, but by the entire surrounding carrier pro le. Data points in lightly doped regions or in the proximity of a junction might be particularly sensitive to this eect. As a consequence, the calibration curves cannot be used directly to transform the measured resistance pro le into the correct resistivity pro le and a correction factor CF must be introduced in equation 5.2. Hereby, both the barrier resistance and the spreading resistance are assumed to be in uenced by the surrounding carrier pro le. Consequently, the total resistance is multiplied by the correction factor and the new formula for the measured resistance is given by equation 5.3. If the barrier resistance is assumed to be independent of the surrounding carrier pro le, equation 5.4 must be applied. In this case however, the eect of the correction factor on the total measured resistance is too small to explain the current spreading eects observed in the SSRM experiments. Further study is required to nd a physical explanation for this behavior. (5.3) R = CF (a; ) 4a + Rbarrier () (5.4) R = CF (a; ) 4a + Rbarrier () The correction factor CF is a function of the complete three-dimensional resistivity pro le and of the contact radius. The correct evaluation of the importance of this current spreading eect requires a detailed three-dimensional calculation of the current and potential distribution around the spreading resistance point contact, ultimately leading to


140

a deconvolution algorithm which converts the measured resistance pro le into the exact resistivity pro le. The carrier and dopant pro le are computed from the resistivity data using the Poisson equation and the mobility equation [Vandervorst 90]. It is important to note that the data quanti cation procedure of the conventional SRP method is faced with similar problems. However, the data interpretation algorithms developed so far for the SRP method can no longer be used for SSRM. The main dierences between SSRM and SRP are the reduced contact radius (20 nm compared to 2 m) and the fact that the resistance measurements are performed on a sample cross section instead of on a beveled surface as illustrated in gure 5.11. Whereas for the measurements on a beveled surface one could construct a deconvolution scheme based upon the applicability of one-dimensional solutions of the Laplace equation combined with cylindrical symmetry, as rst developed by Schumann and Gardner [Schumann 69], this is no longer true for SSRM. (a)

(b) x

bevel

original top surface y

original top surface

z

α bevel angle

cross section back contact

Figure 5.11: Schematic diagram of the conventional SRP (a) and SSRM (b) methods. In SRP the pro le can be assumed to vary only in one dimension (the vertical direction), while in SSRM the problem is twoor three-dimensional.

Finally, it is worth noting that the SSRM technique does not suer from stray- elds between the probe shaft and the surrounding sample surface which are a limit to the lateral resolution and to the quanti cation of other high resolution carrier pro ling techniques like SCM [Kopanski 96] and KPM [Hochwitz 96].

5.5.3 One-dimensional

The procedure for recovering the correct carrier (or dopant) pro le from a measured resistance pro le is split into two parts. In the rst part, the resistance pro le is calculated which pertains to a known carrier pro le (the forward problem). In the second part, the inverse problem of recovering the carrier pro le from a set of measured resistance data is solved. Before dealing with the actual deconvolution procedure, the importance of the current spreading is illustrated by some simple examples.

Current spreading simulation examples Before dealing with the deconvolution procedure, the importance of the current spreading for some simple examples is studied. Since the current spreading underneath the SSRM probe has a three-dimensional nature, analytical solution of the Poisson equation with the appropriate boundary conditions becomes very complex, if not impossible [Gelmont 93].


141

Conformal (Schwarz-Christoel) transformation solutions which can sometimes be used to simplify similar potential and eld problems [Nussbaum 95, Kober 57] also become extremely involved. An easy way to study the SSRM current distribution is found in 3D nite element simulation packages such as DESSIS [DESSIS] and DAVINCI [DAVINCI]. In this work the DESSIS simulator was used. Charge accumulation or depletion at boundaries are assumed to be second order eects and are therefore ignored. The mesh of the simulated structure is designed suciently large so that it approximates a semi-in nite solid. At the same time, the meshing is very ne (about 1/20th of the contact size) near the probesemiconductor contact where the largest changes in potential are expected. No signi cant change in results was observed upon further re nement of the mesh. Furthermore, the results obtained in test runs did not change when the outer nodes were assumed isolating or metallic. For these reasons it is believed that the mesh provides a very good approximation for a semi-in nite semiconductor substrate. Cylindrical symmetry was used whenever the problem allowed (for example on homogeneously doped samples). In a rst example, the current spreading through a circular ohmic contact placed on a homogeneously doped sample is calculated. Figure 5.12 shows the electrostatic contour plot and the current ow lines in a plane cutting through the center of the SSRM probe for three limiting cases: (a) isolating boundary, (b) semi-in nite uniformly doped material and (c) perfectly conducting boundary. The isolating or conducting boundary plane is perpendicular to the cross-sectional plane as shown in gure 5.11. By studying these simple - but extreme - situations in more detail an idea can be formed about the importance of the corrections needed for SSRM measurements. The correction factor CF (equation 5.3), which corrects the measured resistance data for the current spreading eect, equals 1 for a uniformly doped semi-in nite substrate ( gure 5.12b). When the sample has an isolating boundary, CF increases if the probe is moved towards the boundary and reaches 2 for the limiting case when the boundary is positioned exactly under the center of the probe ( gure 5.12a). If the isolating boundary is replaced by a perfectly conducting one, the correction factor CF becomes smaller than 1 and decreases towards zero when the probe touches the conducting boundary ( gure 5.12c).

Figure 5.12: Current distribution (solid lines) and potential contour lines (dashed lines) under a SSRM probe on three limiting case structures: (a) nearby isolating boundary, (b) semi-in nite uniform layer, (c) nearby perfectly conducting boundary.

Figure 5.13 shows the relation between the correction factor and the distance to the isolating or conducting boundary. Again, the boundary plane is perpendicular to the plane


142 2.0

correction factor

1.5

K=1

a

d

0.5 1.0 -0.5 -1 0.5

0.0 0.01

0.1

1

10

100

d/a

Figure 5.13: SSRM correction factors for a perfectly conducting (bottom curve) and perfectly isolating (top curve) boundary. The dashed lines show the correction factor for dierent resistivity ratios K de ned by equation 5.5

of the SSRM contact. Also given is the evolution of the correction factor as a function of the distance to nearby layers with well known resistivity. The resistivity ratio K is de ned by equation 5.5 where 1 and 2 respectively represent the resistivity of the contacted region and the nearby layer. K equals 1 if the boundary is isolating (2 ! 1) and equals -1 if the boundary is conducting (2 ! 0). The eect of the contact size is taken into account by scaling the distance with the contact radius a.

, 1 K = 2 + 2

1

(5.5)

Several conclusions can be drawn from gure 5.13. First of all, the correction factor CF is limited to values between 0:5 and 1:5 for reasonable distances (d > 0:1a). Secondly, although the appearance of a boundary (in particular a conductive one) near the probe has a strong in uence on the value of the correction factor, its eect is seen to die out quickly when the probe is moved away from the boundary. Third, upon decreasing the size of the contact radius, the sampling volume decreases and the eect of nearby layers reduces proportionally. In a second example, the correction factor is calculated for a contact placed on a semiin nite sample with a one-dimensional carrier pro le which has a constant resistivity gradient in one of the lateral directions (i.e. in a direction lying in the cross-sectional plane). Figure 5.14 shows the evolution of the correction factor as a function of the gradient. The eect of the contact size was taken into account by multiplying the gradient with the contact radius a (a gradient of n decades indicates that the resistivity changes n orders of magnitude over a distance equal to the probe radius). the relative resistivity gradient is varied between 0 ( at pro le) and 1:5 (which corresponds to a steepness of 10 nm/decade for a 15 nm probe radius). The correction factor equals 1 when the gradient is zero (uniformly


143

1.0

correction factor

0.8

0.6

0.4

0.2

0.0 10

2

3

4

5

6 7 8 9

2

100 resistivity gradient (nm/decade)

3

4

5

6 7 8 9

1000

Figure 5.14: SSRM correction factor calculated for 1D pro les with a constant resistivity gradient as a function of this gradient.

doped sample) and decreases towards zero when the resistivity gradient increases. Indeed, some part of the current will ow through the lower resistive region so that the measured resistances and the correction factors decrease.

forward problem The purpose of the forward method is to compute the resistance pro le which will be measured on a particular (known) carrier pro le. The most straightforward method to do this, is by calculating the current owing through the probe by solving the Poisson equation using a nite element Poisson solver for every position of the probe on the pro le. However, this is a time consuming method which leads to an unacceptable amount of calculation time. Another method makes use of a database (or lookup table) which stores the correction factor as a function of typical pro le characteristics. A given carrier (or resistivity) pro le is transformed into the resistance pro le by interpolation of the database and by applying the de nition of the correction factor (equation 5.3). Obviously, this method is much faster. The most critical step in this approach is the construction of the database and the assumption that a limited set of parameters can be found which describe nearly all practical pro les. In our work, a database was constructed in two steps: 1. A set of parameters which describe the resistivity pro le is de ned. 2. The correction factor database is constructed as a function of these parameters using 3D nite element calculations. In the rst step, parameters are searched which describe the resistivity pro le adequately. In this context, it is important to determine which parameters have a notable in uence on

144


the correction factors and at the same time describe the resistivity pro le as much as possible. Parameters which have little or no in uence on the spreading eect are avoided. Three signi cant parameters are: 1. The general shape of the resistivity pro le. 2. The distance to insulating or conducting boundaries. 3. The probe radius. A straightforward choice for the parameters describing the shape of the resistivity pro le (x) in a particular point x0 are the rst N coecients in the Taylor series expansion, for one-dimensional pro les given by equation 5.6 where f (x) = log((x)) (one normally uses the logarithmic values instead of the data themselves). 1 @ n f (x) (n = 1; 2; : : :) (5.6) n! @xn Note that the actual resistivity level (i.e. the zero order Taylor term) is not important. Indeed, the spreading of the current is determined only by the spatial variation of the resistivity and not by the local resistivity value. Because the eect of nearby regions on the measured resistance decreases rapidly when the distance to these regions grows (as illustrated by gures 5.13 and 5.14 for some simple examples), the shape of the pro le must be parameterized precisely only locally. All pro les can locally be matched as good as desired by taking more Taylor terms into account. For one-dimensional pro les, the rst two terms correspond to the local slope (decades/m) and curvature (decades/m2 ) of the resistivity pro le. For a wide range of real-life resistivity pro les only the rst and second order terms are signi cant and the contribution from higher order terms can be neglected. Whenever higher accuracy is necessary, higher order terms can be taken into account. In addition to the shape of the resistivity pro le, also the probe radius and the appearance of insulating or conducting boundaries such as oxide or metalization layers near the probe have to be taken into account. Clearly, the distance to such a boundaries is not included in the Taylor terms but can produce extra current spreading as was shown in gures 5.12 and 5.13. In the second step, a database is constructed which gives the evolution of the correction factor as a function of each of the parameters obtained in the rst step. A set of 3D nite element simulations were performed to study this evolution. The DESSIS device simulator was used in combination with the simulation experiment sequencing system NORMAN/DEBORA [NORMAN] which supports automatic design of experiments (DOE). DOE was used to determine which parameters of the input resistivity pro le must be varied (and also how) in order to minimize the number of simulations required to obtain a detailed database. For example, the probe radius is taken into account by taking relative values for each of the parameters: the relative slope is de ned as the product of the slope with the probe radius, the relative curvature as the product of the curvature with the squared probe radius, and the relative distance as the distance divided by the probe radius. More than 1000 simulations were carried out to set up the database for one-dimensional pro les. Figure 5.15 shows a fragment of the database for one-dimensional pro les. The correction


correction factor

10

1

0.1

(a)

145 (c)

(b)

C

C

C

B

B

B

A

A

A

-1.0

-0.5 0.0 0.5 slope (decades)

1.0 -1.0

-0.5 0.0 0.5 slope (decades)

1.0 -1.0

distance slope > 0 curvature > 0 -0.5 0.0 0.5 slope (decades)

1.0

Figure 5.15: Part of the SSRM correction factor database showing the correction factor as a function of the distance to an isolating boundary: (a) 10, (b) 1, and (c) 0 probe radii, and the slope and the curvature of the resistivity pro le: (A) 0.1, (B) 0.5, and (C) 1.0 decades.

factor is displayed as a function of the local slope and curvature of the pro le for three dierent distances between the center of the probe and an insulating boundary. The insert of gure 5.15c shows an example of a data point with a positive slope and curvature. When the probe is far away from the isolating boundary ( gure 5.15a), the correction factor becomes smaller if the slope increases (i.e. higher gradient) or if the curvature decreases ( atter resistivity pro le). Hereby, one has to remember that a smaller correction factor not necessarily corresponds to the smallest correction needed. Indeed, for the purpose of correcting data, it is a correction factor of 1 that is the smallest. The same behavior is observed if the probe moves closer to the boundary ( gure 5.15b) but the correction factor is now dierent for positive (lower resistivities towards the boundary) and negative slopes. Indeed, if the isolating boundary replaces some of the lower resistive material the current will drop resulting in higher correction factors. This eect is even more pronounced when the probe is positioned on the boundary ( gure 5.15c). The small non-smoothness of the correction factor curves can be ascribed to the limited number of data points and to small simulation errors. The resistance pro le which belongs to an arbitrary resistivity pro le can now be estimated as follows. First, the parameters (slopes, curvatures,...) are calculated for every data point using a numerical technique such as the central dierence method. Second, interpolation of the database is used for every data point to nd the correction factor pro le which pertains to the resistivity pro le. Finally, the resistance pro le is calculated by applying the correction factor de nition (equation 5.3). An example of the method is shown in gure 5.16. In this example, the resistance pro les were calculated using the forward method (calculation time: 1 second) and by solving the Poisson problem for every point (calculation time: 4 hours). The accuracy of the estimated resistance pro le is better than 10%. Figure 5.16c shows the correction factor for each data point.


146 100

105

4

(b)

(a)

(c)

10-2

correction factor

10

resistance (Ω)

resistivity (Ωcm)

-1

104

3

10

2

1

-3

10

-4

10

3

0.00 0.05 0.10 0.15 0.20 0.25 depth (µm)

102 0.00 0.05 0.10 0.15 0.20 0.25 depth (µm)

0 0.00 0.05 0.10 0.15 0.20 0.25 depth (µm)

Figure 5.16: Example of the forward method showing (a) the input resistivities, (b) the simulated (solid line) and estimated (circles) resistances and (c) the corresponding correction factors. The probe radius was 25 nm.

inverse problem The nal goal of this section is to be able to correct fully automatically for the current spreading eects. Therefore one has to solve the inverse problem: the transformation of the measured resistance data (k data points) into the correct dopant or carrier pro le. A conversion algorithm based upon the correction factor database is presented in gure 5.17. An adequate smoothing procedure is applied to the raw resistance values before they are processed by the actual correction algorithm. This smoothing step is essential since a minor change of the input resistance values can be the indication of a large resistivity change. It is thus essential that the smoothing step eliminates measurement noise, but does remove as little information as possible from the underlying physical pro le. Hence, an ecient constrained cubic spline smoothing method modi ed to improve its performance for SRP input data is selected [Clarysse 88, Dierckx 80]. In the second step, the smoothed resistance data are transformed into resistivity values. This is done by solving equation 5.3 towards . This corresponds to solving a set of k coupled non-linear equations, since the correction factor, which is enclosed in equation 5.3, is a function of the complete resistivity pro le. Since there exists no good general method for solving such systems, additional information speci c to our particular problem is needed. One possible way to solve the coupled set of equations compromises the following steps: 1. Calculate a starting value i (i = 1) for the resistivity pro le by using the calibration curve (equation 5.2) assuming there are no corrections (CF = 1). 2. Calculate the corresponding correction factor pro le CF (i ) by interpolation of the database.


147

measured resistance profile constrained cubic spline (ccs) smoothing smoothed resistance profile calibration curve first approximation for resistivity profile correction factor database correction factor profile

calculate new resistivity profile

repeat until convergence

ccs smoothing smoothed resistivity profile mobility and Poisson equations carrier profile dopant profile

Figure 5.17: Schematical representation of the inverse method for the conversion of SSRM resistance data into the carrier or dopant pro le.


148

3. Calculate a new resistivity pro le i+1 by applying equation 5.3 as follows:

i+1 = 4a CF (Ra; ) , Rbarrier (i ) i

(5.7)

4. Perform a constrained cubic spline smoothing on the new resistivity pro le i+1 . 5. Repeat steps 1-4 until a stopping criterion is ful lled. One possible stopping criterion is to compare i and i+1 and stop the repetition when a sucient agreement is observed, for example expressed in terms of the standard deviation: N X k=1

(i+1;k , i;k )2 "

(5.8)

Where i represents the complete resistivity pro le at step i in matrix notation. The small non-smoothness of the correction factor database (which can, for example, be observed in gures 5.13 and 5.15) does not in uence the convergence of the algorithm, if linear interpolation is used in step (ii). Note that the smoothing is essential since the calculation of the correction factors requires the computation of the rst and second order derivatives of the pro le. Finally, the carrier pro le n and the dopant pro le N can be calculated from the resistivity pro le by solving the mobility equation 5.9 together with the Poisson equation 5.10. (5.9) = n q +1 n q e e h h

r = , ""q (NA , ND + ne , nh) 2

0

(5.10)

Where the electron e and hole h mobilities are functions of the total dopant concentrations NA +ND and are obtained from ASTMs resistivity/dopant conversions [ASTM 723]. In order to illustrate the robustness of the algorithm a special example is shown in gure 5.18 corresponding to the case of a homogeneously doped sample with an insulating boundary at a depth of 0 nm, whereby we deliberately added 20% random noise to the resistance values before the correction was performed. Figure 5.18a shows the resistance pro le obtained with a probe radius of 20 nm. The resistivity pro les obtained after smoothing and using the calibration curve with and without the algorithm are given in gure 5.18b and show an accuracy of respectively 10% and 90% compared to the real pro le (i.e. constant resistivity). In a second example ( gure 5.19), the resistivity pro le is calculated from the simulated resistance pro le given in gure 5.16b. Again, random noise (10%) was added to the resistance data before the correction was performed. The resistance pro le is shown in gure 5.19a while the calculated and exact resistivity pro les are compared in gure 5.19b. The ratio between both resistivity pro les (insert of gure 5.19b) illustrates the accuracy of the inverse method.


149

0.20

50

(a)

(b)

real profile with algorithm without algorithm

resistivity (Ωcm)

resistance (kΩ)

40

30

0.15

0.10

20

0

200

400

0

200

400

depth (nm)

depth (nm)

Figure 5.18: Example of the inverse method. The simulated and raw (with 20% noise added) resistance pro les are given in (a). The real resistivity pro le (i.e. constant) and the resistivity pro les obtained by using the calibration curve with and without the correction algorithm are shown in (b).

100

105

(b)

(a)

real profile with algorithm

103

10-2

1.2 1.1

10

ratio

10

resistivity (Ωcm)

resistance (Ω)

10-1 4

-3

1.0 0.9 0.8

10

2

0

100 depth (nm)

200

10-4

0

0

100

100

200

200

depth (nm)

Figure 5.19: Example of the inverse method. The simulated and raw (with 10% noise added) resistance pro les are given in (a). The calculated (using the inverse algorithm) and exact resistivity pro les are drawn in (b). The insert in gure (b) shows the ratio of both resistivity pro les.


150

In a last example ( gure 5.20), a measured SSRM resistance pro le is quanti ed using both the presented quanti cation procedure and using the calibration curve without corrections. Both carrier pro les are shown in gure 5.20b. without algorithm with algorithm SIMS

20

concentration (at./cm-3)

10

1019

18

10

1017 0

100

200

300

depth (nm)

Figure 5.20: Shallow implantation as an example of the inverse method. The calculated (using the inverse algorithm) and the calculated (using the calibration curve) carrier concentration pro les are shown and compared to SIMS. The pro le obtained with the correction algorithm is more peaked and is closer to the SIMS pro le.

5.5.4 Two-dimensional The forward and inverse methods can also be used for two-dimensional pro les. The set of parameters which describe the 2D pro les adequately includes the distance to boundaries in the x and y direction (which can be isolating or conducting) and the rst and second order terms of the 2D Taylor series expansion. These parameters correspond to the slopes 2 f (x;y) . and curvatures in the x and y direction and the partial derivative @ @x@y The construction of the correction factor database for 2D pro les requires much more work since the number of parameters which needs to be taken into account is much higher. Without careful selection of the proper simulations which must be carried out, the total number of simulations becomes unacceptably large. In a possible solution for this problem, the current spreading for a particular point of the pro le is assumed to be dominated by the variation of the pro le in one direction (named main direction). The exact shape of the remainder of the 2D pro le has little or no in uence on the current spreading. Therefore, the 2D correction factor database can be limited to pro les whose slopes, curvatures and distances to boundaries in the main direction vary over the same range which was used for the 1D database, while the slopes and curvatures in the direction perpendicular to the main direction vary over a smaller range. Figure 5.21 shows a part of the database for two-dimensional pro les. The correction factor is drawn for semi-in nite samples (no boundaries) as a function of the slope and curvature in the main direction and the slope in


151

the perpendicular direction.

correction factor

10

1

C

B 0.1

A

0.01 -1.0

slope in perpendicular direction 0 decades 0.1 0.25 -0.5

0.0

0.5

1.0

slope in main direction (decades)

Figure 5.21: Extract of the SSRM correction factor database for 2D pro les. The correction factor is shown as function of the (relative) slope and the (relative) curvature of the resistivity pro le in the main direction: (A) -1.0, (B) 0.0, and (C) 1.0 decades, and the slope in the perpendicular direction.

The rst step in the transformation of 2D resistivity pro les into the corresponding resistance pro le requires the search of the main direction for each data point. The main direction is found by computing the correction factor in dierent directions (in the xy plane) and selecting the direction which shows the smallest correction factor (i.e. the largest current spreading eect). Figure 5.22 shows an example of the correction factors calculated for a 2D carrier concentration pro le using this method (calculation time: 3 seconds). A good agreement with the results obtained through direct calculation (calculation time: 3 hours) is observed. As soon as the main direction is known, the standard procedure can be used: calculation of the dierent parameters followed by interpolation of the 2D correction factor database. The inverse method can be applied to 2D resistance pro les in the same way as was done for 1D pro les.

5.5.5 The NSRP software package The forward and inverse algorithm were implemented in a software package, named NSRP, written in PASCAL and developed within a PC environment. The program allows one to smooth and transform one-dimensional resistance data into carrier concentration data and vice versa. User input is required to de ne the dierent smoothing conditions and the speci cations for the convergence of the transformation algorithm. For two-dimensional pro les the resistance pro le which pertains to a given resistivity or carrier concentration pro le can be calculated. Presently, the inverse procedure is not yet possible, and measured resistance pro les are transformed into carrier concentration values by using the calibration curves without correcting for current spreading eects. The incorporation of this correction


152

(b)

1.5 1.5 1

(c)2.5

2

1.5

(d)

2 1.5

1

0.9 1

0.5

0.5

1.1

1

Figure 5.22: Two-dimensional example of the correction factor calculations. (a) concentration pro le layout, the correction factors are given in (b) and (c) for the indicated region, (b) correction factors obtained through simulation (3 hours), (c) correction factors obtained through use of the semi-1D database approach (3 seconds), (d) ratio of both correction factor pro les showing an accuracy of 10% over the complete pro le.

requires an ecient two-dimensional smoothing algorithm and a time-ecient solution of the presented algorithm. These programming issues fall beyond the scope of this work.

5.6 Junction-isolated pro les The behavior of the SSRM resistance at junctions is of great importance since most real structures contain one or more junctions. Theoretically, the carrier concentration at the junction position goes down to the intrinsic level (1:5 1010 atoms/cm3 in Si), and the measured resistance should go up to very high values. In practice, leakage currents will reduce the resistances to somewhat smaller values. Figure 5.23 shows the SSRM measurement of a pn junction formed by a 20 keV B, 2 1015 atoms/cm2 implantation into a n-type substrate (concentration = 3 1014 atoms/cm3 ) and annealed at 900 C for 30 minutes. At the electrical junction position a small peak in the SSRM resistance curve is observed. Also shown is the dopant pro le as measured by SIMS and the carrier pro le obtained by solving Poisson's equation using the SIMS pro le as input. Note that the background signal of the SIMS measurement is omitted and an extrapolation line is drawn instead. A close resemblance for the SSRM pro le to the conventional SRP and SIMS measurements is observed, except for the dierence in junction depths. Indeed, the SSRM data show the expected decrease in the near surface region where the largest amount of boron is located and a rise toward the substrate value. The jump in carrier concentration from the SSRM data at the junction is a consequence of the dierent mobilities for electrons and holes and the (small)

5.6. JUNCTION-ISOLATED PROFILES

153

1021

109

1020

108

1019

107

1018

106 SIMS SRP SSRM concentration SSRM resistance

1017 10

16

10

15

1014 1013

105 10

4

10

3

resistance (Ω)

3

carrier concentrations (at./cm )

dierence in calibration curve for both types of silicon. The junction depths measured by the three techniques are: 410 nm for SRP, 570 nm for SIMS, and 950 nm for SSRM. The shallow depth for the standard SRP as compared to SIMS is due to the phenomenon of carrier spilling taking into account the bevel geometry [Hu 82, Casel 87]. As one goes further down along the bevel more and more material is removed and the highly doped top layer becomes thinner. At a certain depth the doped top layer becomes so small that reverse carrier spilling from the substrate dominates the junction, hence leading to a forward shift of its depth. Although in SSRM no bevel is applied, one still has to consider the eects of carrier diusion. Indeed, while the SIMS technique measures the 'immobile' dopant atoms, SSRM measures the 'mobile' carrier distribution. For structures with relatively steep dopant gradients, these carriers will redistribute in order to reduce this gradient, leading in this case to a displacement of the electrical junction depth to a larger depth. The magnitude of this displacement can be calculated by solving the Poisson equation for the assumed dopant pro le. For the presented example, the electrical junction depth was calculated (using the SIMS pro le) to be 1090 nm, i.e. 140 nm deeper than the measured one.

102 0

500

1000

1500

101 2000

depth (nm)

Figure 5.23: p+ n pro le measured on a cross section by SSRM with diamond-coated probe (load: 16 N). The raw resistance data and the processed carrier concentration pro le are displayed. The SIMS and conventional SRP data are given for comparison. The observed junction depths are: 410 nm for SRP, 570 nm for SIMS, 950 nm for SSRM.

The cross-sectional carrier junction shift on two frequently used submicron structures, i.e. abrupt junctions and junction isolated implants, has been calculated by solving Poisson's equation. The results are displayed in gure 5.24 for Gaussian-like implants and in gure 5.25 for abrupt junctions. For Gaussian-like implants it has been found that the particular parameters of importance are the slope of the Gaussian-like implant at the dopant junction and the dopant level in the substrate. Note that the dopant junction slope can be obtained from other pro le parameters such as the top gauss peak level and the depth posi-


154

tion of the atomic dopant pro le. From the simulations it follows that the largest junction shifts are to be expected for abrupt junctions when the substrate concentration level is low and the peak level high, and for Gaussian implants when the substrate concentration level is low and when a small gradient (expressed in nm/decades) is present.

substrate concentration (at./cm3)

1016 0.1

7 6 5 4

0.2

3 2

1015

0.3 7 6 5 4

0.4

3 2

14

10

10

0.8 0.9 2

0.5 0.6

0.7 3

4

5

6 7 8 9

2

100 gradient (nm/decade)

3

4

5

6 7 8 9

1000

Figure 5.24: Simulated cross-sectional carrier junction shift (in m) for junctions formed by a Gaussian implant as a function of the substrate concentration and the gradient of the pro le at the junction.

In this context it is worth noting that the small bias voltage (maximum 50 mV) at which the SSRM measurements are being performed are too low to alter the carrier distribution in the structure under study. Higher voltages can cause a lateral movement of the mobile carriers leading to an incorrectly measured carrier pro le. The pro le close to pn junctions is particularly sensitive to this eect. In SCM { which is usually operated at a few volts { this eect is present and results in a movement of the junction positions and the presence of unexpected bands in the carrier pro le [Kang 97, Kleiman 97]. As a consequence, the interpretation of the data measured at junctions is more straightforward for SSRM as compared to SCM.

5.7 Conclusions In conclusion, the most important characteristics of the SSRM carrier pro ling method are:

The dynamic range, i.e. the range of carrier concentrations which can be detected by SSRM, varies from 1015 to 1020 atoms/cm3 .

Due to the linear relation (in rst approximation) between the measured spreading resistance and the sample resistivity, the sensitivity is high over the complete dynamic range. No other two-dimensional carrier pro ling method is known which combines such a high dynamic range with such a high sensitivity.

5.7. CONCLUSIONS

155 7 6 5 4

0.2

3 2

1015 7 6 5 4

0.4 0

substrate concentration (at./cm3)

1016

0.6

3 2

0.8

14

10

1014

1015

1016

1017 1018 peak level (at./cm3)

1019

1020

1021

Figure 5.25: Simulated cross-sectional carrier junction shift (in m) for abrupt junctions formed by a epitaxial growth as a function of the substrate and peak concentration levels.

The concentration resolution, here determined as the average noise level observed

on homogeneously doped substrates, can be 20% or better if the applied working load is at least 50% higher then the threshold load, and the sample roughness better then 0.4 nm. The concentration resolution degrades fast if the sample roughness increases or if the working load is reduced.

The repeatability was found to vary from 13 to 29%. The repeatability is slightly better if successive measurements are performed on the same position without moving the probe. The reproducibility was found to vary from 24 to 51% and is observed to reach larger values when the probe is re-aligned between measurements and is only slightly dependent on the fact that dierent samples are pro led or if the same sample is pro led.

The spatial resolution as determined on thin buried oxide layers and on abrupt dopant steps was found to vary from 10 to 30 nm for a good SSRM probe. The

spatial accuracy, ie. the ability to determine the position of the measured carrier

pro le with respect to the sample surface and mask edges, was found to have similar values.

A quanti cation procedure to recover the dopant pro le from SSRM measurement

data is presented. The SSRM current spreading is studied using nite-element calculations resulting in a correction factor database, which stores the resistance correction factor as a function of typical pro le characteristics. Using a forward method that is based on interpolation of the correction factor database, a given resistivity pro le can be transformed into the corresponding resistance pro le. An iteration procedure, which makes use of the forward method, can be applied for the inverse problem of recovering the resistivity pro le from the measured resistance data.

156


The SSRM signal shows a small peak at pn junctions. The redistribution of the

mobile carriers as opposed to the xed dopant atoms (or carrier spilling) leads to a junction position which is larger than the one observed with SIMS. This junction shift can easily be calculated using Poisson's equation. This junction shift is opposite to the one observed in conventional SRP in which the carrier spilling is strongly in uenced by the presence of a bevel.

The speci cations of the SSRM technique are summarized in table 5.6. The speci cations of the SCM technique - where available - are added for comparison. Table 5.6: Summary of the most important SSRM pro ling characteristics.

speci cation SSRM SCM spatial resolution 10{30 nm 10{30 nm dynamic range 1015 , 1020 1015 , 1020 sensitivity linear non-linear reproducibility 13{29% { repeatability 24{51% { measurement time 20 min 20 min probe lifetime 10{20 scans { concentration resolution 20% {

Chapter 6

Applications and intercomparison 6.1 Introduction The two-dimensional capabilities of the SSRM method are studied using a number of case studies, relevant to nowadays silicon device processing. The samples and test structures which were pro led re ect the dierent types which are encountered in practice. Through these applications an attempt is made to indicate the applicability and the accuracy of SSRM with respect to the application under investigation. The structures include: ion implantation pro les, epilayers, MOS (PMOS, NMOS and DMOS) transistors, and bipolar transistors. The fabrication of the samples has been performed at various places and by dierent sources. Since there exists no other good, general applicable 2D pro ling method, standard 1D methods such as SIMS and conventional SRP were used for intercomparison of the results. Speci c two-dimensional results such as lateral diusion lengths and 2D contour lines, were compared to the results from alternative two-dimensional pro ling techniques (SCM, 2D-SRP and selective etching measurements). At present, it is however impossible to judge unambiguously the accuracy of any of these experimental eorts to characterize 2D carrier pro les. Details of the various techniques and references to the literature can be found in chapter 2. The presented case studies are focused on devices and structures which are based on silicon. The SSRM method can also be applied to other semiconductor materials (such as Ge, III-V, II-VI,. . . ). However, the point contact behavior can be strongly dierent. For example, the transformation into a conducting -tin phase under high pressures is only present for Si and Ge. Also, the barrier resistance might be strongly dierent for other materials. As a consequence, the dynamic range and sensitivity on other semiconductors will be dierent, requiring calibration of the probe on this type of materials. The possibilities of pro ling other semiconductors are illustrated in this chapter by the results obtained on InP laser structures.

6.2 Case study I: 2D diusions and implantations Example 1 In a rst series of boron implanted test structures the carrier pro le was de-

termined as a function of the diusion parameters. The pro les were formed by a self-aligned 157

158

CHAPTER 6. APPLICATIONS AND INTERCOMPARISON

boron implantation (40 keV, 4 1015 atoms/cm2 ) of a p-type substrate (1:5 1015 atoms/cm3 ) through a SiO2 mask (thickness = 600 nm, 10 m alternating mask and implantation window). Four dierent samples were prepared, each with a dierent anneal step: 15, 30, 120 and 360 min at 900 C, followed by a 15 seconds rapid thermal anneal (RTA) at 1100 C. The SSRM measurements were performed with a diamond-coated probe (cantilever 70 N/m). The SSRM pro le of the sample which received the longest anneal time (360 min) is shown in gure 6.1. The gure shows the topographic image and the resistance map which was measured simultaneously. Both images show the same 205 m2 region with 512128 pixels; i.e. a pixel-to-pixel distance of about 40 nm. The topographic image clearly displays the mask which was used for the self-aligned implantation. The topography allows one to identify the precise position of the measured carrier pro le with respect to the layout of the structure. The top region of the scanned area is measured as a very low region (o-scale) since the probe loses contact with the sample as it is scanned over the sample edge. In the resistance image ( gure 6.1b), the implanted region shows up as low-resistance area, while the resistance measured in the substrate region is much higher. The complete two-dimensional distribution of the charge carriers can be determined from this plot. The carrier concentration contour lines taken at 1:5 1015 atoms/cm3 are plotted in gure 6.2 for the four dierent samples. The vertical (or in-depth) and lateral diusion (under the implantation mask) can easily be determined from this type of measurements and can be plotted as a function of the anneal time ta ( gure 6.3). Hereby the diusion depth is de ned as the position where the implanted concentration reaches the substrate level, i.e. 1:5 1015 atoms/cm3 . The vertical diusion depths as obtained from SRP are givenpfor comparison. A linear relation is observed between each of the diusion depths and ta , with the lateral diusion always substantially smaller than the vertical diusion. This tendency was con rmed by scanning capacitance microscopy measurements, but is not con rmed by the values obtained by 2D-SRP [Privitera 93]. The lateral diusion observed with 2D-SRP is much larger than the one observed with SSRM and SCM. The accuracy of the lateral 2D-SRP pro le is believed to be limited by the uncertainty on the two contact radii and the width of the implantation window.

Figure 6.1: SSRM measurement of a 40 keV, 4 1015 atoms/cm2 Boron implanted sample (anneal time 360 min). Scan size: 205 m2. (a) sample topography. (b) SSRM resistance map.

6.2. CASE STUDY I: 2D DIFFUSIONS AND IMPLANTATIONS

159

oxide 0

15 min

-500 depth (nm)

30 min 120 min -1000 360 min -1500

-2000 -1000

-500

0

500

1000

lateral distance (nm)

Figure 6.2: Contour lines taken at a carrier concentration of 1:5 1015 atoms/cm3 as measured with SSRM on a 40 keV, 4 1015 atoms/cm2 Boron implanted sample which was annealed at 900 C for 15, 30, 120 and 360 min.

1.2

diffusion (µm)

1.0 0.8

lateral 2D-SRP depth 2D-SRP lateral SSRM depth SSRM lateral SCM depth SCM

0.6 0.4 0.2 0.0 0

20

40

60

80

100

120

140

time 1/2 ( s 1/2)

Figure 6.3: Vertical and lateral diusion depths as a function of anneal time at 900 C. The sample was implanted with 40 keV B, 4 1015 atoms/cm2 using a thick oxide (600 nm) as masking material.

160


Example 2 The in-depth (i.e vertical) and lateral diusion of As, P and B implantations

was studied as a function of implantation and annealing conditions. Therefore implantations were performed through a SiO2 mask (thickness 500 nm, 0.7 m alternating mask and implantation zone). All samples were covered with an undoped poly-silicon layer such that the probe does not fall of the sample when the edge of the implanted region is reached. This precaution improves the lifetime of the probe considerably. Two of the samples are selected as an example. Both samples received the same As implantation (5 1015 atoms/cm2 at 80 keV), but one of them received an extra P implantation (5 1014 atoms/cm2 at 20 keV). Both samples followed the same annealing procedure: 20 s at 1050 C. Since the substrate is n-type material (n-type epi layer, 22 cm on n+ bulk, 0.02 cm) there are no pn junctions. Figure 6.4 shows the two-dimensional SSRM resistance and carrier concentration pro le for the sample which received both implantations. The carrier concentration pro le was calculated from the measured resistance pro le using the n-type calibration curve of the probe which was used. A similar pro le was measured for the sample which received only the As implantation. Two contour lines (at 1017 and 1019 atoms/cm3 ) for both samples are drawn in gure 6.5. This gure illustrates that the high-concentration regions (mainly As) have a similar pro le, while the low-concentration regions (mainly P) are dierent. The vertical and lateral extension of the carrier pro le, measured on both samples along the indicated sections are drawn in gure 6.6. Upon comparing the pro les with and without the P implantation, we can clearly see the extra P implantation. In gure 6.6b the lateral and vertical pro les are compared for the sample which received both implantations (As and P). The As diusion is roughly the same in both directions, while the vertical P diusion is larger than the lateral diusion.

Figure 6.4: SSRM resistance (a) and carrier concentration (b) pro les of a test structure with an n-type substrate, implanted with As (5 1015 atoms/cm2 at 80 keV) and P (5 1014 atoms/cm2 at 20 keV) and annealed for 20 s at 1050 C. The scan size is 1.21.2 m2 .

These structures were also imaged with SEM after performing a dopant selective etch step [Frickinger 95]. Two typical results are presented in gure 6.7a and 6.7b which respectively show the structure which received the As implantation and the structure which received the double implantation (As and P). As the etch selectivity is limited to high car-

6.2. CASE STUDY I: 2D DIFFUSIONS AND IMPLANTATIONS

161

Figure 6.5: Contour lines (1017 and 1019 atoms/cm3 ) for both samples. The solid lines correspond to the sample which received the As implantation, the dashed lines correspond to the sample which received an additional P implantation.

1021

1021

As, SRP As, SSRM As+P, SRP As+P, SSRM

3

concentration (atoms/cm3)

1019 18

10

1017 1016 1015

1019 10

18

1017 1016 1015

14

10

As+P lateral vertical

(b) 1020 concentration (atoms/cm )

(a) 1020

0

200

400 600 depth (nm)

800

10

14

0

200

400 600 distance (nm)

800

Figure 6.6: Vertical and lateral SSRM and SRP pro les of two test structures: the one displayed in gure 6.4, and a similar one which did not receive the P implantation. Figure (a) shows the vertical pro les for both structures compared with the SRP results. Figure (b) compares the vertical and lateral extension of the SSRM pro le measured on the sample which received the double implantation (As and P).

162


rier concentration values (> 1018 atoms/cm3 for the settings used in this experiment), only limited information can be obtained. Two contour lines are drawn: one at 1018 and one at 2 1019 atoms/cm3 . From this comparison it is clear that the SSRM method provides far more information than the selective etch method. The SSRM method allows one to measure a quantitative carrier concentration pro le including contour lines at selected levels, whereas the selective etch method only provides a qualitative image of the highly doped region and provides only a limited number of contour lines at xed levels which must be calibrated using another 1D technique such as SIMS or SRP. The contour lines obtained with both methods are in reasonable agreement.

Figure 6.7: SEM image of the test structure which received (a) an As implantation, (b) an As implantation and an extra P implantation. (result from J. Frickinger [Frickinger 95]).

6.3 Case study II: NMOS and PMOS transistors In this case study two-dimensional measurements of the carrier distribution inside fully processed NMOS and PMOS transistors with gate lengths varying from 2 m down to 0.25 m are presented [DeWolf 97, DeWolf 98b]. The implantation and annealing steps which were used to construct the transistors are summarized in table 6.1 (p-type substrate). A TEM image ( gure 6.8) of the cross sectional layout of one of the transistors shows the tungsten plugs, the aluminum metallization, the poly-silicon gate and the silicide (CoSi2 ) source and drain contacts. Table 6.1: Speci cations of the MOS transistors (LDD = lightly doped drain, HDD = highly doped drain).

NMOS PMOS well-implant B, 3:2 1013 at 190 keV P. 2:2 1013 at 180 keV well-anneal 450 s at 1050 C 450 s at 1050 C 14 LDD-implant As, 1:2 10 at 40 keV BF2 , 8 1013 at 16 keV HDD-implant As, 4 1015 at 70 keV BF2 , 4 1015 at 20 keV junction anneal 10 s at 1100 C 10 s at 1100 C

6.3. CASE STUDY II: NMOS AND PMOS TRANSISTORS

163

Figure 6.8: TEM image of a 0.35 m MOS transistor which was used in the SSRM experiments. The dierent regions are: (a) W plugs, (b) Al metallization, (c) poly-Si gate, and (d) CoSi2 silicidation.

Figures 6.9a-d show several SSRM resistance images measured at 5 mV bias on the PMOS transistors with dierent gate-lengths. The eld region between two neighboring transistors is shown in gure 6.9d. All images were taken with the same (diamond-coated) probe at a force of 6{10 N. The tungsten plugs and aluminum metallization layers show a (very) low resistivity. Part of the plug material is not found back in the resistance images because it was removed during the polishing procedure or the cross section did not completely pass through the plug. As expected, the dielectric material between source, gate and drain contacts shows no conductivity at all (no current ows through the probe). In the lowly doped n-type substrate, only little current ows through the probe. The highly doped poly-silicon gates, the highly doped shallow implants and the lower doped n-well structure are revealed in detail. The sharp transition from the shallow p-type implants to the n-well structure can be explained by the very steep pro le which results in a large drop in the measured resistance. The interfaces between two dierent materials (e.g. between the dielectric and the silicide layers) are more diuse. This is believed to be a consequence of the polishing procedure. Dierent materials have dierent polishing rates and sometimes one layer is smeared out into another during the polishing steps. An interesting pro le feature can be seen in gure 6.9d. The shallow implant at the edge of the eld oxide follows exactly the shape of the surface (compare with the shape of the silicide layer in gure 6.8). Furthermore, the well implantation appears to have diused deeper under the eld oxide. This can be ascribed to oxidation enhanced diusion during the formation of the eld oxide. At this point it is interesting to note that when the measurements are repeated at lower load, the metal parts of the structure can still be delineated in the resistance image, while no (signi cant) dierence between the high and low resistive silicon regions of the device is observed. This is illustrated in gure 6.10a which displays a PMOS transistor (gate length = 0.5 m) measured at a load of 3 N (i.e. less than half of the load used for the images presented in gure 6.9: 6{10 N). In this gure, the metal plugs are clearly delineated as low-resistive regions, while the signal in the silicon is unstable. Considering the native oxide which must be penetrated and the metallic phase which must be formed when measuring on silicon, this agrees with what one expects. If scratches, originating from the polishing procedure, are present on the sample cross section, the resistance is also unstable at these positions. As mentioned before in chapter 3 and shown in gure 3.37, the SSRM measurement removes a small layer of the silicon and leaves a crater in the silicon with a depth of some nanometers. Consequently, if the scan area of a SSRM measurement overlaps with the scan


164

(a)

(b)

(c)

(d)

Figure 6.9: SSRM resistance map measured on PMOS transistors with a gate length of (a) 2.0 m (scan size: 55 m2 ), (b) 0.7 m (scan size: 22 m2 ), (c) 0.25 m (scan size: 11 m2 ). The eld region between two transistors (scan size: 4.54.5 m2 ) is shown in (d). Images taken at 6{10 N.


165

Figure 6.10: (a) Low force (3 N) SSRM image of a PMOS transistor with a 0.5 m gate length (scan size 44 m2 ). Only the metal plugs can clearly be observed. (b) SSRM image taken on the same transistor at normal force (8 N). The vertical streak (no or little current ow) originates from the debris left at the edge of a previous scan. (scan size 55 m2 ).

area of the previous one, part of the measurement is performed on virgin silicon while part of the measurement is performed in the crater. An example is shown in gure 6.10b. This gure shows a PMOS transistor with a gate length of 0.5 m. The right part of the gure was taken in the crater formed by a previous SSRM measurement, while the left part was untouched. At the edge of the crater, a white streak is observed, corresponding to a very low current signal. Indeed, at the edge of the crater, the silicon material (which is removed from the crater) is piled up and leads to an unstable, high resistive, contact. No signi cant dierence is observed between the data measured in the crater and the data measured on the virgin cross section. A small asymmetry is observed in the two-dimensional extension of the source and drain pro les of the PMOS transistors. The observed source (left) and drain (right) junctions of the 0.7 m PMOS transistor ( gure 6.9b) are drawn on top of each other in gure 6.11a. Therefore, the drain junction was rotated around the vertical axis. The drain pro le is steeper than the source pro le. This behavior was observed on dierent transistors of the same wafer. the asymmetry is also found in the IDS , VDS transistor characteristics which were measured after the cross section preparation ( gure 6.11b). The asymmetry can be explained by the fact that the wafer was not rotated during the 7 tilted source/drain implantations leading to some shadowing eects and asymmetrical pro les. Figure 6.12 shows the carrier concentration map (scan size 21 m2 ) of a 0.7 m NMOS transistor from the same set of transistors. Two sections are made through this image: the vertical carrier pro les through the gate and the source contact. Both pro les were calculated using the calibration curves without correction for current spreading eects. The source/drain concentration pro le has a typical Gaussian shape whereas the pro le through the poly-silicon gate is at. This can be explained by the higher diusion in the poly-silicon which leads to a uniform carrier distribution. The source pro le was also calculated us-

166

CHAPTER 6. APPLICATIONS AND INTERCOMPARISON 12

(b)

10

IDS (mA)

8 6 4 2 0 0.0

normal operation after exchanging source & drain 0.2

0.4

0.6

0.8

1.0

VDS (V)

Figure 6.11: Asymmetry in the junction pro le of the 0.7 m transistor: (a) shows the source and drain junction contour lines, (b) shows the IDS , VDS transistor characteristics in normal operation (solid lines) and after exchanging the source and drain (dashed lines).

ing the algorithm which corrects for the current spreading eect. Hereby a probe radius of 15 nm was taken. The corrected pro le is more peaked and comes closer to the SIMS pro le of the source implant. Figure 6.13 shows an SCM and SSRM image measured on exactly the same NMOS transistor. Because a thin layer of the sample is removed during the SSRM measurement, the SCM measurement was performed prior to the SSRM measurement. The source/drain junction is observed by SSRM as a thin band in which the resistance is high (black line). The black area observed in the top region of the image corresponds to the high resistance measured in the dielectricum which covers the device. In the SCM image, several bands (a bright and dark one) are observed close to the position of the junction. The junction contour line obtained from the SSRM measurement, drawn on top of the SCM image, shows that the inner edge of the bright band in this image corresponds to the junction contour line for the SCM settings used in this experiment (VDC = 0 V, VAC = 0:2 V). However, the shape and the position of the dierent bands in the SCM image are known to change as the settings are varied, leading to a more complicated interpretation of SCM images [Kleiman 97]. In the development of a deep submicron CMOS technology a trade-o between preventing short channel eects and hot carrier reliability has to be made for the NMOS. Lightly doped drain (LDD) structures with phosphorus are commonly used in 0.35 m technology to reduce the electric eld at the drain side and to decrease the degradation of the NMOS due to hot carrier generation. However, in a 0.25 m technology, these LDDs result in poor short channel behavior. A possible solution to this problem is to use an LDD-structure which is overlapped by the gate and which is surrounded by an oppositely doped halo [Hendriks 96]. The following implantation conditions were used in addition to the ones presented in table 6.1: LDD-implant: 20 keV P at 1014 atoms/cm2 , halo-implant: 30 keV B at 1013 atoms/cm2 . From the electrical transistor characteristics, the eective


167

(b)

concentration (at./cm-3)

10

I: gate II: source corrected source SIMS

20

1019

1018

10

17

0

100

200

300

400

500

depth (nm)

Figure 6.12: (a) SSRM concentration pro le of a 0.7 m NMOS (scan size 21 m2 ). The vertical pro les through the gate (I) and source (II) are shown in (b). The source pro le calculated by using the correction factor algorithm is more peaked and comes closer to the SIMS pro le of the source implant.

Figure 6.13: (a) SSRM concentration pro le of a 0.7 m NMOS (scan size: 11 m2 ). (b) SCM image of the same transistor (scan size: 1.41.4 m2 ). The solid line indicates the junction contour line as measured with SSRM.


168

gate length was calculated to decrease by 60 nm due to these implantations [Biesemans 96]. The SSRM method is the ideal tool to check the accuracy of this number and to make a detailed comparison of the carrier pro le of the transistors with and without LDD and halo. The SSRM results for the lateral pro le of an NMOS transistor with 0.35 m gate length are presented in gure 6.14. The lateral pro les measured on the transistors with and without the LDD and halo implantation show a dierence in eective gate length of 66 nm. This value con rms the value extracted from the electrical transistor characteristics. Note that, whereas the extraction method provides only information about the eective gate length, the SSRM method produces a full two-dimensional image of the carrier pro le.


1020

1019

295 nm 229 nm

1018

31 nm

17

10

35 nm without LDD & halo with LDD & halo

1016

-400

-200

0

200

400

distance (nm)

Figure 6.14: Lateral pro le taken at 15 nm under the gate oxide through an NMOS transistor (0.35 m gate length) with and without LDD and halo implantations. The dierence in eective gate length is 31 + 35 = 66 nm.

6.4 Case study III: round robin of 2D carrier pro ling techniques Recently, a round-robin was started on initiative from V. Ukraintsev (Texas Instruments, Dallas, USA) to evaluate and intercompare various two-dimensional dopant and carrier pro ling techniques [Ukraintsev 98b]. Nine research groups participate in this study, representing the following techniques: SCM, selective etching followed by TEM imaging, TCAD process simulation using the TSUPREM simulator, and SSRM. In rst instance, MOS transistor structures were distributed to the participants. One PMOS and one NMOS structure, both without source/drain silicide and contacts. The participants were asked to present the following data: (i) channel length, (ii) source, drain (S/D) and gate overlap, (iii) S/D junction depth, (iv) 2D dopant iso-concentration contours for S/D and channel regions, (v) lateral and vertical dopant pro les for these regions. Figure 6.15 summarizes the lateral and in-depth junction positions of both structures as measured with the dierent techniques.

6.4. CASE STUDY III: ROUND ROBIN

169

The lack of a two-dimensional dopant standard makes it impossible to judge unambiguously the accuracy of any experimental or theoretical eort to characterize 2D silicon dopant pro les. Therefore, the measured values are compared to the average of the values obtained by the dierent techniques. For the PMOS structure the average source/drain depth is 205 nm while the SSRM value is 165 nm. The average overlap distance is 103 nm while the SSRM value is 127 nm. For the NMOS structure these values are respectively 133 and 135 nm for the S/D depth and 92 and 110 nm for the overlap distance. This corresponds to dierences of 40, 24, 2, and 18 nm. 300

200

(a)

(b)

250 200

overlap (nm)

S/D depth (nm)

150

150 100

100

50 50 0

0

SIMS SUPREM SCM

SCM

SRM

SCM

SCM

SSRM

SUPREM SCM

SCM

SCM

SRM

SCM

SCM

SSRM

200 140

(c)

overlap (nm)

S/D depth (nm)

(d)

120

150

100

100 80 60 40

50

20 0

SIMS SUPREM

SCM

SCM

TEM

SCM

SSRM

0

SUPREM SCM

SCM

SCM

TEM

SCM

SSRM

Figure 6.15: S/D depth and overlap for PMOS (a and b) and NMOS (c and d) round robin structures obtained by TCAD simulation and by dierent pro ling techniques. The average value is indicated by the horizontal line.

From this intercomparison { which re ects the current state-of-the-art { it is clear that the site-to-site variations in pn junction position are noticeably higher than the spatial resolution requested by TCAD. The SSRM and SCM are found to provide in general more reliable results as compared to the SRM and TEM techniques. The site-to-site variations of the SCM results are large, indicating that the measurement procedure (including sample preparation) is very important for SCM. It is clear that, at present, there is no method which can be used as an absolute reference to evaluate the accuracy of a new carrier pro ling method such as SSRM. Therefore, more extensive round-robin studies which involve dierent laboratories and dierent carrier pro ling techniques must be carried out. The presented round-robin is only the rst step towards a useful intercomparison.

170


6.5 Case study IV: asymmetrical implantation Another test structure which was used for the intercomparison of various 2D carrier pro ling methods consists of a 0.3 m poly-silicon lm on a 20 nm oxide, patterned and etched down to the p-type substrate. A self-aligned arsenic implantation was performed (35 keV, 1015 ions/cm2 at 20 incidence) and the sample was annealed for 30 seconds at 1000 . The sample was fabricated at the Center for Integrated Systems at Stanford University. Figure 6.16 shows a 2.52.5 m2 image of the topography (left) and spreading resistance (right) measured simultaneously. The arrows in the topography image indicate the direction of the implantation. The poly-silicon mask layer shows a low resistance (bright area) with some dark lines or spots which are believed to occur at the interface between dierent grains in the poly-silicon. The arsenic implantation in the silicon substrate also shows up as a low resistance area, indicating a high carrier concentration. The asymmetry between the incidence side and the shadowing side is clearly observed. The pro le shows a large lateral extension under the poly-silicon at the incidence side (150 nm), while the lateral extension at the shadowing side is only 10 nm. The resistance measured in the substrate and in the capping glue layer is high (dark). The interface between the bright and dark areas corresponds to the junction contour line of the n-type implantation in the p-type substrate.

Figure 6.16: Topographic (left) and SSRM resistance (right) image of an asymmetrical implanted pro le (scan size: 2.52.5 m2 ).

The SCM (by A. Erickson, Digital Instruments), dopant selective etching and TCAD (by R. Alvis, AMD) results obtained on the incidence side of the same structure are shown in gure 6.17 for comparison. The SCM image shows a low signal (dark region) in the highly doped area. At the junction, a very broad band (thickness: 170 nm) of high signal is observed, complicating precise junction delineation. The sharp transition between both regions corresponds to a carrier concentration of about 2 1019 atoms/cm3 , but is known to be in uenced strongly by the parameter settings at which the SCM is operated (AC and DC voltages) [Kleiman 97]. The dopant selectively etched structure, imaged with TEM, shows contour lines in the region which is highly doped (> 1018 atoms/cm3 ) but no contrast for

6.6. CASE STUDY V: VERTICAL DMOS TRANSISTOR

171

lower concentration values.

Figure 6.17: (a) SSRM (scan size: 550 715 nm2 ), (b) SCM (scan size: 550 715 nm2), (c) dopant selective etching (scan size: 300 400 nm2 ), and (d) TCAD carrier pro les of the asymmetrical implanted pro le of gure 6.16. The thick solid line represents the junction contour line as measured by SSRM, the dashed line represents the sharp interface observed in the SCM image.

6.6 Case study V: vertical DMOS transistor In a nal example, analysis has been performed on DMOS devices supplied by Frits Van den Elshout (Philips, Nijmegen) in order to determine the carrier distributions inside these devices. The analysis is based on the use of SSRM and SCM. The topographical image in gure 6.18 (left side) shows quite clearly the Al-contact (black region) the underlying oxide (brown) and the polysilicon and underlying gate oxide. The SSRM image in gure 6.18 (right side) shows the electrically active regions. The dierent colors re ect dierent levels of resistivity; Black = highly conductive, White = low conductivity. One can quite clearly observe the highly doped n+ -substrate (black), the lower doped n-epilayer (dark brown) the p+ -body (which appears as highly resistive) the n+ -implant (black) the metal and the oxide regions as well as the highly conductive poly material. The highly resistive image of the p-body is dicult to understand except if for some reason the contact to this layer was poor which then also leads to high resistance values. Junction positions correspond to the sharp transition between the various color levels. In this gure the cross section was not entirely through the center of the hole such that the Al is not penetrating the n+ -layer. One should also notice that directly under the polysilicon gate there consistently appeared an extra doped region (right hand side of image 1.1).

172


Figure 6.18: Topographical (a) and SSRM (b) image of one vertical DMOS cell (1212 m2 scan).

Looking at a section more through the center of the VDMOS-cell ( gure 6.19) we can now clearly see the Al-contact penetrating into the n+ -layer (cf. the topographic image, left hand side). The shallow n+ region appears to be deeper indicating that there is an extra implant under the Al contact. The type (n or p of this extra implant can not be obtained from these SSRM measurements. The extra implant is more clearly observed (more color contrast) when changing the bias voltage from 50 mV to 500 mV as shown in gure 6.20. The I{V curves are no longer linear at this voltage and the current for the p-type curve is much lower than for the n-type as the contact is acting as a reversely biased junction for p-type regions. Therefore the signal in the p-type regions goes down, leading to a clear delineation of n and p-type regions.

Figure 6.19: Topographical (a) and SSRM (b) image of one vertical DMOS cell sectioned through the center of the cell. (66 m2 scan).

Figure 6.21 shows a schematic drawing of the dierent implant regions which are ob-

6.6. CASE STUDY V: VERTICAL DMOS TRANSISTOR

173

Figure 6.20: SSRM image of the cell shown in gure 6.19, taken at a higher bias voltage (500 mV instead of 50 mV). The p-type implant (bright area) can be clearly distinguished from the n-type implant (dark area).

served using SSRM. The upper image shows the cross section made through the center of the cell. The bottom image shows a cross section further away from the center. Besides the p-body and the shallow n+ implant, also an implant is observed under the poly-silicon gate and an extra implant is observed under the Al contact. The width of the latter is comparable to the width of the n+ region in the upper image. Based on the SSRM, it can not be determined if the implant is n-type or p-type, although image 6.20 suggests that it is a p-type implant.

Figure 6.21: Schematic representation of the dierent implant regions in the VDMOS cell. (a) Cross section made through the center of the cell. (b) Cross section further away from the center.

Similar results can be obtained with SCM using a Ni-coated silicon probe with a 10 nm radius ( gure 6.22) which is however unable to delineate the oxide/metal transition as well the dierence between metal and the highly doped n+ -layer. SCM does nicely delineate the junction position of the p-body as well as the extra implant under the polysilicon. However, at the junction formed by the p-body and the n-type substrate several bands (a bright one and a dark one) are observed. This behavior has also been observed in other

174


SCM measurements (see for example gure 6.13b and gure 6.17b). These bands make carrier pro ling and junction delineation using SCM complicated because the shape and the size of the observed bands are changing as the SCM settings are varied [Kleiman 97]. This behavior can be explained by the high voltages (a few volts) which are present on the tip during SCM operation. These high voltages can cause lateral movement of the carriers underneath the tip and in this way disturb the carrier pro le. The carrier pro le at pn junctions is particularly sensitive to this eect. 3D simulation of the SCM point contact close to pn junctions can provide the information which is required to transform the measured SCM pro les into quantitative carrier concentration pro les [Kleiman 97].

Figure 6.22: Topographic image (left) and SCM image (right) of a vertical DMOS cell (1212 m2 scan).

6.7 Case study VI: InP laser structures The SSRM method can also be applied for the determination of the two-dimensional carrier distribution inside III-V semiconductor structures. These materials are strongly dierent from Si such that the SSRM characteristics are dierent. The sample preparation of III-V semiconductor structures is simple. The samples are cleaved to expose an atomically at cross section through the device of interest. No polishing is required. Compared to the preparation of Si samples, this preparation is simple, fast, and perfectly reproducible. The SSRM image of a multilayer InP epi structure is shown in gure 6.23a. This is an i-n-i-n-p InP structure, where the i-layers are semi-insulating, Fe-doped, the n-type layers are Si-doped, and the p-type layer is Zn-doped, grown on an n-type substrate of InP(S). Figure 6.23b shows a line scan across the structure, while gure 6.23c shows a SIMS depth pro le of the epi structure. Note the excellent qualitative correlation between the SIMS and the SSRM pro les. Note also, that the resistance in a p-type layer is higher than that measured in n-type layers of similar dopant concentration. This is due to the much dierent electron versus hole mobility in InP (3500 and 50 cm2/Vs at 300K, respectively [Siegel 91]). Figure 6.24a shows an SSRM cross section image of a three-dimensional III-V structure

6.7. CASE STUDY VI: INP LASER STRUCTURES

175

1.4

(a)

current (µA)

1.2 1.0 0.8 0.6 0.4 0.2


0.0 0

1

2

3 4 depth (µm)

5

6

7

2 18

10

6 4

Zn Fe Si

2

1017 6 4 2

1016

0

1

2

3 4 depth (µm)

5

6

7

Figure 6.23: SSRM current pro le of an InP epi structure showing dierent n-type, p-type, and semiinsulating InP regions (dark = high current, bright = low current, 1515 m2 ). A metal probe was used at a bias of 5 V. The vertical pro le taken along the line AA' is displayed in (b). These data show a good qualitative agreement with the SIMS depth pro les shown in (c).

(a) 1.2 current (µA)

1.0 0.8 0.6 0.4 0.2 0.0 0

1

2 3 distance (µm)

4

5

Figure 6.24: Two-dimensional SSRM current pro le of an InP mesa-like structure showing diusion of the top p-type region into the semi-insulating region (5.65.6 m2). The lateral diusion pro le taken along the line AA' is displayed in (b).

176


used for a study of lateral Zn diusion from a highly Zn-doped layer into a semi-insulating, Fe-doped InP layer. This image demonstrates the SSRM's analytical power in 2-D imaging of carrier distributions in InP based structures, and in particular, to the analysis of lateral dopant diusion, which is becoming an issue of high interest. A lateral line scan through the region of Zn diusion is shown in gure 6.24b, exhibiting the characteristic steep-front Zn diusion pro le. Conversion of the resistance values into carrier concentration levels requires a calibration curve. In Si structures, this is routinely done by using specially grown reference samples that contain layers of varying carrier concentration. For III-V materials, a similar procedure should be followed. While the bias voltage applied to Si samples is usually below 100 mV, a much higher bias, of 1-5 V, had to be applied to III-V samples. At lower biases, the measured current was too low for accept signal-to-noise ratio. The reason for that is not yet well understood. It is interesting to note that the SSRM measurements on InP could be performed at very low forces. Diamond-coated tips mounted on cantilevers with a spring constant of 1.6 N/m were used at forces below 0.5`N, whereas the force had to be increased to 10 N to allow stable resistance measurements on Si. Metal (Cr) probes were also successfully applied and did not deform since they were operated at low forces. These facts indicate that a stable probe/InP contact needs a much lower pressure compared to a stable probe/Si contact. This can be explained by the fact that there is no thermal oxide on InP which must be penetrated and that no metallic phase must be formed in InP. We observed that even at very low probe forces the scanned surface was slightly damaged by the tip, possibly due to the softness of the material. As a consequence, the quality of repeated images taken from the same area deteriorated. The best images, with the highest signal-to-noise ratio, were the ones taken in the rst scan of a cross section area. It is likely that this problem can be overcome by using cantilevers with a lower spring constant, allowing it to scan at a lower force. We also found that for areas of interest near the edge of the sample's cross section, the image is much cleaner when the scan is done parallel, rather than perpendicular, to the sample's edge. This is due to the tip picking up debris at the edge.

6.8 Conclusions From the extensive series of case studies and intercomparison discussed in this chapter, the following conclusions can be drawn: The SSRM method allows one to determine the quantitative two-dimensional carrier pro le inside arbitrary semiconductor device structures. The SSRM method provides both two-dimensional junction contour lines and carrier concentration contour lines. The measured two-dimensional pro les can be used to make sections in a particular direction (often vertical or lateral). A good agreement between these pro les and the pro les measured with standard one-dimensional techniques such as SIMS and SRP is observed.

6.8. CONCLUSIONS

177

The speci cations determined on one-dimensional test structures (cf. chapter 5) re-

main valid for two-dimensional pro les. The most important speci cations are the spatial resolution (10{30 nm) and the dynamic range (1015 , 1020 atoms/cm3 ). The results from the intercomparison of SSRM with the most widely used alternative two-dimensional carrier pro ling methods { SCM and dopant selective etching { are summarized qualitatively in table 6.2. Table 6.2: Intercomparison of the two-dimensional speci cations of the most widely used two-dimensional carrier pro ling techniques.

SSRM SCM topographic information limited good metals and dielectrics high contrast no contrast junction delineation easy complicated quanti cation easy complicated

select. etch all details low contrast not possible complicated

SSRM can also be applied for carrier pro ling inside III-V semiconductor structures. SSRM applied on InP-based structures can be performed with metal probes at a much lower force compared to silicon pro ling.

Chapter 7

Related applications In this chapter two applications which are related to and based upon the SSRM technique are presented. In the rst application, the SSRM technique is applied on beveled samples as is routinely done in conventional SRP. In this way, the vertical (depth) and/or lateral dimension is magni ed, providing a very high spatial resolution. In the second application, local potential distributions inside operating devices are measured. In this method, the SSRM probe is connected to a voltage measurement unit which stores the measured voltage as the probe scans across the cross section of an operating device.

7.1 On-bevel high-resolution measurements 7.1.1 Introduction

The SSRM method, applied on cross-sectioned structures, is limited in spatial resolution to about 10{20 nm. This limit is related to the size of the tip radius. If higher resolution is desired in a particular direction, a beveling technique can be used to enlarge the scale in the selected direction (often the in-depth direction, as is routinely done in conventional SRP, or the lateral direction). The main problems associated with this approach are: (i) the structure must be large enough so that it is uniform over the whole length of the bevel; (ii) the redistribution of the mobile carriers relative to the xed impurities caused by the bevel geometry must be understood. Using this approach, some of the typical problems associated to conventional SRP could be solved. Indeed, the probe load during the on-bevel SSRM measurements is much lower as compared to conventional SRP, and the very small contact (nm versus m) and the accurate tip movements theoretically imply a higher depth resolution as well. The rst purpose of this section is to explore the advantages of such a concept with respect to one-dimensional shallow pro ling, as compared to conventional SRP [DeWolf 98c]. Second, it is studied how the beveling method can be applied for highresolution two-dimensional carrier pro ling.

7.1.2 One-dimensional By using a beveling technique with small bevel angles the SRP method can be used for one-dimensional carrier pro ling of ultra-shallow layers. However, its application is lim179

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CHAPTER 7. RELATED APPLICATIONS

ited by a number of artefacts which are currently not completely understood. Routinely generated SRP ultra-shallow pro les indicate abnormally high sheet resistance values as compared to those measured by the four point probe (FPP) or dierential Hall technique [Osburn 92, Clarysse 96b]. Furthermore, the SRP raw data often display a substantial increase in resistance while the probes are still stepping over the original surface as they approach the bevel edge [Clarysse 96b]. Both artefacts are believed to be related to the surface damage introduced by the beveling procedure. The surface damage at, between, and close by both contacts results in higher resistance values which lead to carrier concentration values lower than expected and thus higher sheet resistance values. The eect has a two-dimensional nature and increases when the pro les become more shallow. Another serious problem for determining the electrical characteristics of ultra-shallow structures with SRP is carrier spilling. On beveled samples, the phenomenon of carrier spilling has two parts: the redistribution of the mobile carriers relative to the xed impurities due to varying concentrations, and the on-bevel carrier spilling due to the change in eld as the various layers in the structure intersect the bevel surface [Casel 87, Pawlik 92]. The quanti cation of the on-bevel carrier spilling is hampered by the fact that the boundary conditions used for the solution of the Poisson equation are not exactly known. For instance, the assumption of a zero (electrical) eld at the surface is inappropriate for describing the probe-semiconductor contact under high loads and leads to an underestimation of the junction shift by a factor of 2{5 [Casel 87]. Recently, several groups have made progress toward understanding this phenomenon and a number of schemes have been proposed to correct SRP measurements for carrier spilling eects [Mazur 92, Choo 93, Berkowitz 90, Dickey 92, Mathur 92]. However, a general solution applicable to all types of pro les does not yet seem to be available [Clarysse 94]. A better way to resolve this problem is to try to reduce the carrier spilling phenomenon at the raw data collection level. The latter can be done by changing the bevel preparation procedure or by using lower weights. Indeed, it has previously been shown that the load (varied from 5 to 20 g) used in conventional SRP in uences the amount of on-bevel carrier spilling directly: the higher the load, the larger the spilling eect (larger junction shifts) [Clarysse 92]. Obviously the use of the SSRM method would be the ideal way to reduce the load during the measurements to very low values. The very small contacts (nm versus m for conventional SRP) and the accurate tip movements theoretically imply a higher depth resolution as well.

Measurement procedure Due to its similarity to standard SSRM, exactly the same instrumental setup can be used for on-bevel SSRM. As the measurements need to be performed on the magnifying bevel surface, often large distances need to be scanned and a wide range piezo (typical xy range: 140140 m2 , z range: 5 m) is thus required. The sample preparation procedure is slightly dierent from the standard SSRM procedure, but can also be divided in two steps. First, a bevel is polished on the sample. The standard beveling procedure as described by Pawlik [Pawlik 92] (see chapter 3) is applied so that the same surface quality is obtained for the SRP and SSRM measurements. The

7.1. ON-BEVEL HIGH-RESOLUTION MEASUREMENTS

181

smaller contact size combined with small probe movements allows for considerably larger bevel angles and provides a very high geometrical resolution. For example, a 100 nm deep pro le typically requires a magni cation of 500 in conventional SRP (stepsize 2.5 m, bevel angle 6'53") to attain a resolution of 5 nm, but a magni cation of only 50 is already suf cient in SSRM (stepsize 25 nm, bevel angle 1 08') to attain a much higher geometrical resolution (0.5 nm). Second, a large back contact is required since SSRM is a one-probe measurement. Careful soldering of the contact to all dierently doped layers { as described in section 3.5.2 { is necessary. If one of the layers is badly (or not) contacted by the back contact the measured resistance values for this layer might be too high and result in an underestimation of the carrier concentration. Using AFM technology to move the probe over the sample, an image of the sample topography can be made simultaneously to the resistance measurement. In this way, a resistance measurement and a measurement of the height of the sample is obtained for each position. A surface pro lometer or optical image re ection technique (both methods are routinely used in conventional SRP) is no longer required to measure the bevel angle. The SSRM setup has the additional advantage that the entire bevel pro le is measured precisely at the electrical measurement position and not just an average value for the bevel angle. This is similar to the concept of D'Avonzo et al. [D'Avonzo 80], although in the SSRM setup the topography measurement occurs at a much ner scale and with higher sensitivity due to the inherent AFM properties. The example in gure 7.1 shows the bevel topography and the measured resistance as a function of the distance scanned by the tip over the sample at a speed of 1 m/s. The topography scan shows (from left to right) the top surface, the rounded bevel edge (starting in point A) and the beveled surface. Since the bevel rounding extends to a depth of 50 nm it must be taken into account, especially for ultra-shallow layers which have a comparable depth. The topography information can be used in a conversion program to compute a variable depth scale [D'Avonzo 80]. Alternatively, a new resistance pro le with an equidistant depth scale can be set up by interpolation of the measured resistance data. For example, the resistance which corresponds to a depth of 10 nm (point B in gure 7.1) is found to be 45 k . The new (ideal, not measured) pro le can be used in the standard SRP quanti cation procedure as if it was measured on an ideal bevel surface without bevel rounding.

Data treatment Once the data are collected following the procedure presented in gure 7.1, the conventional SRP quanti cation procedure can be used. In this procedure, which is based on the algorithm introduced by Schumann and Gardner [Schumann 69], the probe separation s must be taken to be very large since we are using only one probe (radius a) which is far away from the back contact (typically 2 to 5 mm). Indeed, using the method of mirror images, the probe separation equals twice the distance between the SSRM probe and the back contact. As a consequence the Bessel terms of zero order in the integrandum of the general expression (equation 7.1) can be omitted, hereby simplifying the calculations [Schumann 69];


182

depth (nm)

0

A B

-50 -100 -150 -200

resistance (Ω)

106 6 4 2 5

10

6 4 2

104

0

B A

2 4 6 distance (µm)

Figure 7.1: Topography and resistance pro le measured simultaneously with the SSRM technique on a beveled surface (bevel angle: 2 140 ). The topography image shows from left to right: the original surface, the bevel rounding (starting in point A), and the bevel surface.

Z1 st 2st ! (7.1) R = 4a ,(t=a) sin(t) J1t(2t) , J0 (t a ) + J0 (2ta ) dt 0 where the function ,(t=a) is determined from the boundary conditions. In the calculations a constant radius of 10 to 25 nm is used combined with a resistivity dependent barrier [Pawlik 92, Clarysse 94]. The barrier re ects the fact that the calibration curves always lie above the reference line formed by the theoretical relation R = 4a , where a represents the probe radius. Note that the calculated SSRM concentration pro les depend very little on the choice of the model as the correction factors are close to 1. This will be clari ed in the next paragraph. Using a 2D scanning mode, several line-scans (perpendicular to the bevel edge) can be obtained each showing the same in-depth carrier pro le. The pro les can be averaged to obtain a better approximation of the real pro le by reducing the eect of measurement noise. Note however that sharp features might atten out since the averaging procedure acts as a low-pass lter. The principle is illustrated in gure 7.2. The sample is composed of (from right to left) a p-type substrate, a buried oxide layer (thickness 20 nm), a n-type poly-Si layer (thickness 340 nm) and an oxide capping layer (thickness 100 nm). A bevel angle of 1 50' was made to the sample, resulting in a 31 magni cation of the depth scale. Figure 7.2a shows the raw resistance data from 32 parallel line-scans (20 m long, spacing 100 nm) of 512 pixels. Figure 7.2a shows the SSRM carrier pro le obtained by averaging all line-scans to one resistance pro le which was then { after bevel rounding correction { used in the conventional SRP quanti cation procedure. The SIMS and SRP pro les are added to the gure for comparison. The SRP pro le lies about one decade below the SIMS dopant


183

pro le because of a limited activation of the dopants in the poly-Si layer. The discrepancy between the SRP and the SSRM pro le in the poly-Si is not understood.

1020 1019

(b)

18

concentration

10

1017 1016 15

10

14

10

1013

on-bevel nano-SRP SRP SIMS

1012 0.0

0.1

0.2

0.3

0.4

0.5

depth (µm)

Figure 7.2: On-bevel SSRM example. The 2D image (a) shows the raw resistance data of several parallel line-scans (scan size: 203.2 m2 ). The resulting SSRM carrier pro le is compared with SRP and SIMS in (b).

Comparison with conventional SRP The SRP and on-bevel SSRM techniques are compared using a series of one-dimensional carrier pro les. Hereby, the interest is focused on the ultra-shallow pro les. A rst set of ultra-shallow pro les was formed by 1 keV boron implantations with an implantation dose of 3 1014 atoms/cm2 [Collart 98] (samples supplied by E. Collart, Philips, The Netherlands). The samples consist of a 1 m thick homogeneously p-type doped layer (respectively 1017 and 5 1015 atoms/cm3 ) on top of a lightly doped p-type substrate (< 1015 atoms/cm3 ) as shown in gure 7.3c. Both samples were annealed at 1000 C for 10 seconds. The corresponding SRP and on-bevel SSRM pro les are shown in gures 7.3 and 7.4. For the rst (respectively second) sample, pro led with SSRM, a bevel angle of 2 14'18" (2 18'40") and a stepsize of 13 nm (45 nm) were used resulting in a vertical stepsize of 0.5 nm (1.8 nm). For the samples pro led with SRP the bevel angle was 4'54" (6'24"), the stepsize 2.5 m (1 m), and the vertical stepsize 3.6 nm (1.9 nm). A diamond-coated silicon probe was used at a force of 5 N (i.e. 4 orders of magnitude lower than the conventional SRP load of 50 mN). The raw data for the rst sample was already shown in gure 7.1. In gures 7.3 and 7.4 the SSRM pro les have been corrected for the bevel rounding which typically leads to a shift in the pro le towards the surface with 20 to 40 nm and an increased


184

surface concentration (factor 1.5{2 compared to the calculation without bevel rounding correction). The SSRM resistance values increase slightly while the probe is moved across the top surface (depth < 0 nm) as it approaches the starting position of the bevel rounding (depth = 0 nm). This increase is smaller than the one observed for SRP. The increase is believed to originate from the surface damage introduced by the beveling procedure. It is not yet clear why the eect is smaller for SSRM. After correcting for the bevel rounding, the SSRM resistance pro les were smoothed and transformed into carrier concentrations using the standard SRP quanti cation procedure. In gure 7.3 the measurements were virtually noise free. The SSRM resistance pro le in 7.4 unfortunately showed a high amount of noise near the bevel edge. This leads to an uncertainty on the calculated concentration pro le dependent on the smoothing algorithm used, with the surface concentration lying between 5 and 8 1019 atoms/cm3 (shown by the dierent solid lines in gure 7.4b). The SRP data were treated using the standard SRP quanti cation procedure (i.e. without bevel rounding correction). 2

105

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1017 1016 1015

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Figure 7.3: (a) Resistance pro les and (b) carrier concentration pro les measured with conventional SRP and on-bevel SSRM on an ultra-shallow p+p structure. The complete in-depth carrier pro le (as measured with SRP) is shown in (c).

Several points can be noted. First, the SRP and SSRM carrier concentration pro les show a similar depth distribution with the peak concentration in SSRM always being substantially higher than SRP. This could re ect that the SSRM data, in contrast to the SRP


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Figure 7.4: (a) Resistance pro les, (b) carrier concentration pro les, and (c) correction factor pro les measured with conventional SRP and on-bevel SSRM on an ultra-shallow p+p structure.


186


data, are corrected for bevel rounding. Also, this can be explained by a smaller probe penetration in SSRM as compared to SRP as well as a higher depth resolution resulting from the smaller sampling volume due to the very small contact. Indeed, the SSRM resistance values are 1.5 to 2 orders of magnitude higher than the SRP resistance data illustrating that the contact size is indeed reduced by 1.5 to 2 orders of magnitude (10{25 nm radius instead of 1 m). Also, the SSRM resistance data vary over a larger range. This results from the fact that the magnitude of the correction factors required to transform the conventional SRP resistance data into the corresponding carrier pro les is primarily determined by the probe radius and the shape of the concentration pro le. If the probe radius is reduced, the correction factor will be reduced as well. This is illustrated by the correction factor pro les for the SRP and SSRM method in gure 7.4c. The needed correction factors are reduced by a factor of 20. Whereas in SSRM the correction factors are limited to values smaller than 5, they can be as large as 100 in conventional SRP. Needless to say that such a large factor re ects a large sampling volume and hence leads to a loss in information on very steep pro les. For both pro les, the SRP and SSRM pro les underestimate the surface concentration and are shallower than the SIMS pro le ( gure 7.4b), leading to a lower integrated dose. The exact reason for this discrepancy is not yet understood. As both SRP and SSRM are applied on a beveled surface, carrier spilling eects will be active in both cases leading to the observed shift. A quantitative evaluation of this is not yet possible. The fact that the depth dierence between the SSRM and SRP pro les are relatively small, despite the large dierence in applied load, suggests that pressure enhanced carrier spilling eects are rather limited for these non junction-isolated samples. 10

18

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1.4

depth (µm)

Figure 7.5: p+n concentration pro les measured on a well structure with SRP, SIMS and on-bevel SSRM. A zero- eld predicted pro le is added for comparison.

To clarify the carrier spilling issue, a second set of (junction-isolated) samples which are known to be in uenced strongly by carrier spilling have been analyzed. Two typical examples are shown in gures 7.5 and 7.6. Figure 7.5 shows a typical well pro le obtained


187

Figure 7.6: SIMS, SRP and on-bevel SSRM measurement for a 60 nm ULSI source-drain structure. A zero- eld simulation is also shown. The dotted line represents an extrapolation of the SIMS measurement.

by implanting a n-type substrate with boron (6 1012 atoms/cm3 , 180 keV) through a 15 nm implantation oxide, while gure 7.6 shows a challenging structure from ULSI, i.e. a 60 nm deep source-drain pro le. Both examples illustrate that there is indeed a dierence in junction position between SRP and on-bevel SSRM. The SSRM junction position is closer to the zero- eld prediction (i.e. the apparent carrier pro le which one would measure on a beveled sample whose sample surface ful lls the ideal boundary conditions). In gure 7.6, a junction position dierence is observed between the SIMS dopant junction at 110 nm and the conventional SRP on-bevel carrier junction at 60 nm, i.e. a dierence of almost a factor of two. Comparing the conventional SRP and SSRM pro les, two points can be observed. First, and most important, the SSRM on-bevel carrier junction position is located at 90 nm, i.e. much deeper than the SRP junction. Second, the maximum level of the SSRM measurement does not go as high as the SRP does. This is related to the fact that the sensitivity in the low resistivity range is limited for the particular probe used in this experiment (full diamond probe: number IV, table 3.3). A similar behavior is observed for the well-pro le in gure 7.5. Also shown in both gures is a zero- eld simulation starting from the corresponding SIMS dopant pro le. Note that the zero- eld model can be considered to be the minimal carrier spilling pro le. Hence, even when SRP measurements could be performed pressure-less there would still be an amount of carrier spilling equal to the zero- eld predictions. As shown in gures 7.5 and 7.6 the SSRM pro le comes close to this minimal carrier spilling pro le, but does not yet overlap. Another example involves a p-type substrate, implanted with phosphorus (95 keV, 1012 atoms/cm2 ). SSRM measurements were performed at two dierent loads (70 and 200 N) on a beveled surface for which the bevel angle was 1 24'16". A solid diamond


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probe (number IV, table 3.3) was used. The results are shown in gure 7.7. Again, the SSRM on-bevel carrier junction positions (590 nm at 200 N, 690 nm at 70 N) are deeper than the SRP junction position (370 nm). Upon decreasing the SSRM load from 200 to 70 N the carrier junction depth comes closer to the zero- eld simulated junction position.

102 1200

depth (nm)

Figure 7.7: n+ p Junction measured by SRP (dashed line), on-bevel SSRM at a load of 70 N (circles) and 200 N (triangles), SIMS (solid line) and zero- eld calculations (dash-dotted line).

This observation is consistent over all samples analyzed as shown in gure 7.8. The explanation for this phenomenon is that the transition from SRP to SSRM does reduce the pressure induced eects, but as both techniques are applied on the same bevel the in uence of the surface preparation remains (explaining the dierence between the SSRM and zero eld junction depths in gure 7.8). Recent studies on carrier spilling eects have indeed led to the conclusion that surface properties do play an important role in this eect. Obviously a further reduction of the carrier spilling eects must include better surface preparation procedures leading to reduced surface damage and surface charge. Although still under investigation, the expected advantage of SSRM will be that other polishing methods can be considered, even if they lead to severe bevel rounding since this can be easily corrected for by the in-situ topography measurement. For example, it has been shown that Quso, Syton an Al2 O3 polishing materials give a very at bevel surface but result in a large bevel rounding.

7.1.3 Two-dimensional

Bevel surfaces can also be applied if a magni cation is desired in a particular direction. For example, if a high resolution in the vertical (depth) direction is wanted, one can measure on a standard bevel surface. Also a similar bevel can be made but now in such a direction that the bevel edge forms a small angle with respect to the structure under study, providing an


189

2

np 7e14

pn 3e15

junction depth (nm)

10009

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8 7 6 5 4 3 2

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Figure 7.8: Junction depths obtained from SRP, on-bevel SSRM, SIMS and zero- eld calculations for dierent samples. The samples are identi ed by their type (pn or np), substrate level (atoms/cm3 ) and the slope of the dopant pro le at the junction position (nm/decade).

expanded view of the vertical (depth) and lateral direction. An example, using a standard bevel, is shown in gure 7.9. This gure shows the SSRM resistance pro le measured on a NMOS transistor with a gate length of 1.0 m. The vertical dimension (y-direction) was magni ed by a factor of 13.7 by beveling the sample at an angle of 4 12'. No magni cation of the lateral dimension (x-direction) was used. The gure shows the low-resistive tungsten plugs as circular regions, the low-resistive source-drain implantation and gate regions. The resistance measured in the dielectric material is very high (bright area). The lateral direction can be enlarged at the same time by using a two-angle bevel surface, as is also done in the 2D-SRP method (cf. section 2.2.2) [Privitera 93]. The use of a bevel surface for structures with a two-dimensional dopant pro le has two major drawbacks. First, this method can only be used if the structure under study is uniform over a region which is long enough to allow for a bevel. For example, if a transistor (such as the one presented in gure 7.9) is beveled to enlarge the depth scale (over a distance of 250 nm) by a factor of 50, the transistor must be uniform over a minimum length of 0:25 50 = 12:5 m. This excludes the application on arbitrary devices which often have much smaller dimensions. Second, it is well known that the carrier pro le is disturbed by the presence of the (one-angle or two-angle) bevel [Hu 82]. For one-dimensional pro les this phenomenon has been studied extensively by dierent groups. When there is no surface charge on the oneangle bevel surface, one expects the eect of a bevel boundary to vanish as the bevel becomes 90 , and the potential lines to extent from the bulk straight to the sectioned surface ( gure 7.10). In this case, the electrical junction is located ahead of the metallurgical junction on the sectioned surface. A nite surface charge would change this situation. As the bevel angle decreases from 90 , the electrical junction position shifts away from the metallurgical junction position on the bevel. The shift levels o as the bevel angle


190

Figure 7.9: SSRM resistance map, measured on a beveled NMOS transistor (gate length 1 m). The bevel angle was 4 12', corresponding to a 13.7 magni cation in the vertical (y) direction (scan size: 1010 m2 ).

decreases to 5 and smaller, and becomes practically constant below 2 (corresponding to a magni cation of about 30) [Hu 82]. The bevel angle in conventional SRP is usually a small fraction of 1 and any variation of the bevel angle in this range has no eect on the carrier distribution on the beveled surface. (a)

(b)

Figure 7.10: Carrier spilling for (a) a cross-sectioned and (b) beveled structure with a one-dimensional dopant pro le. The dashed lines represent the electrical junction contour lines while the solid lines correspond to the chemical (dopant) junction positions. The arrows indicate the direction of the displacement of the junction.

For two-dimensional pro les the carrier spilling phenomenon is more complicated. Whereas one could use one-dimensional calculations to calculate the carrier redistribution in beveled one-dimensional pro les, for two-dimensional pro les the carrier redistribution in a cross section can only be calculated using a two-dimensional Poisson solver, while for beveled surfaces a three-dimensional Poisson solver is required. In gure 7.11 the carrier redistribution for cross-sectioned and beveled two-dimensional pro les is schematically presented. As a consequence, the reconstruction of the real carrier pro le from the measured on-bevel carrier pro le is very complicated. Extensive work is required to solve this problem. The example in gure 7.12 illustrates the 2D-carrier spilling for a MOS transistor structure formed by an arsenic implantation through a polysilicon mask (with a line width of 0.4 m) into a p-type substrate (1017 atoms/cm3 ). The on-bevel measured pro le is shown in gure 7.12a. Vertical (through the source) and lateral (10 nm under the gate) sections through this pro le are presented and compared to cross-sectional SSRM pro les in

7.1. ON-BEVEL HIGH-RESOLUTION MEASUREMENTS (a)

(b)

(c)

(d)

191

Figure 7.11: Schematic representation of the two-dimensional carrier spilling on (a) a cross-sectioned sample, (b) beveled sample (vertical scale is magni ed), (c) beveled sample (lateral scale is magni ed), and (d) beveled sample (lateral and vertical scale are magni ed). The dashed lines represent the electrical junction contour lines while the solid lines correspond to the chemical (dopant) junction positions. The arrows indicate the direction of the displacement of the junctions.

gures 7.12b and c. Upon comparing with the pro les measured with SSRM on a crosssectioned device, the expected discrepancy in vertical junction position is observed. The complete lateral pro les, and in particular the lateral junction positions, are observed to overlap, illustrating that the lateral carrier spilling eect is limited for this type of structures and bevel angles. However, not enough data nor calculations are available to decide which parameters { carrier gradient and concentration, bevel angles, etc. { have a strong in uence on this behavior and under which conditions a particular on-bevel measurement exhibits the reported behavior.

7.1.4 Conclusions The spatial resolution of one- and two-dimensional cross-sectional SSRM can be improved by application of the SSRM method on beveled surfaces. With respect to the conventional SRP technique, the probe weight and the contact size can be drastically reduced. In this way some of the limitations from conventional SRP for shallow 1D pro ling can be resolved. Probe conditioning is no longer required, larger bevel angles can be used, higher geometrical resolution can be obtained, and the bevel topography is measured in-situ which allows to correct the depth scale automatically for bevel rounding. The small SSRM contact results in a smaller sampling volume and hence smaller correction factors. The transformation from SRP to SSRM reduces the pressure enhanced carrier spilling component but since both techniques are applied on the same bevel, the in uence of the surface quality remains. Better surface preparation is required to further reduce the carrier spilling eects. The application of on-bevel SSRM for 2D carrier pro ling is limited by a poor understanding of the eect which the bevel geometry has on the carrier spilling.


192

1021


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20

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(c)

1019 1018 1017 1016

0

250 depth (nm)

-200 0 200 lateral distance (nm)

Figure 7.12: (a) SSRM resistance map, measured on a 2D arsenic implantation through a polysilicon gate (line width = 0.4 m). The bevel angle was 3 29', corresponding to a 16 magni cation in the vertical (y) direction (scan size: 22 m2 ). Source (S), gate (G) and drain (D) are labeled. The bevel edge is indicated by a dashed line. Figure (b) shows the vertical on-bevel (compressed in the y-direction) and cross-sectional SSRM pro les. Figure (c) shows the lateral on-bevel and cross-sectional pro les measured at 10 nm under the gate oxide.

7.2 Nanopotentiometry 7.2.1 Introduction The doping distribution inside semiconductor devices is engineered in order to establish the electrical properties of the devices. Therefore, it would be interesting to have not only a 2D dopant pro ling tool but also a technique able to characterize the 2D potential distribution inside a semiconductor device under operation. Most electrical characterization techniques measure I{V characteristics and evaluate the impact of process variations by extracting the signi cant parameters. They do not provide information on what is actually happening inside the device. A possible technique is presented here and named nanopotentiometry. The basic principle of nanopotentiometry is to monitor the potential distribution on the cross section of a device using a conductive AFM tip as a local voltage probe [DeWolf 96d, Trenkler 95, Trenkler 98a, Uchihashi 94]. Whereas other, similar, methods are based on non-contact mode AFM measurements, nanopotentiometry is based on a direct potential measurement in contact mode. A number of alternative techniques exist:

Kelvin probe force microscopy (KPM) was developed by Nonnenmacher et al. and

already described in chapter 2 [Nonnenmach 91]. The method uses a vibratingcapacitor method. They measured contact potential dierences on metal surfaces [Nonnenmach 91] and silicon pn diodes [Nonnenmach 92]. Vatel et al. applied the KPM technique to the potential distribution measurement of thin InGaAs resistor structures. Two-dimensional dopant pro les of silicon [Tanimoto 96, Henning 95] and GaAs [Mizutani 96] structures were also reported in literature.

7.2. NANOPOTENTIOMETRY

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Scanning tunneling potentiometry (STP) is another non-contact SPM technique, ca-

pable of measuring the potential distribution qualitatively inside working devices. The Scanning electron microscopy - dark voltage contrast (SEM-DVC) technique allows to measure the electrical eld and the potential distribution in silicon devices [Mil'shtein 95, Mil'shtein 97]. The measurements require the taking of an image of the silicon structure with all electrodes grounded and an image of the same structure under DC operation, the subtraction of one image from the other and the calibration of the contrast in accordance with the voltages at the electrodes. The main problem inherent to this technique is the limited quanti cation possibility and limited sensitivity to small voltage variations inside the devices under study. For each of these techniques a proof of concept can be found in literature, but, so far, no quantitative images of the potential distribution inside operating devices has been reported.

7.2.2 Instrumentation

The schematic setup of the nanopotentiometry technique is drawn in gure 7.13a. A conducting probe is scanned across a cross section made through the device under study. The device is put under operation by applying voltages to two or more contacts. The probe is electrically connected to a low bias-current ampli er with JFET input stage (e.g. model OP42 from Burr Brown) such that no current ows through the probe and the potential distribution inside the device remains undisturbed. The ampli er output is connected to one of the auxiliary input channels of the AFM such that the potential information can be displayed and stored simultaneously to the topographic information. A special cantilever holder with an integrated voltage-follower was constructed. This holder is constructed to t in the DimensionTM AFM from Digital Instruments. V

Figure 7.13: Schematical layout of the nanopotentiometry technique: a conductive AFM tip is connected to a voltmeter to measure the potential distribution inside a semiconductor device under operation.

7.2.3 Discussion

What is measured ? Ideally, the input resistance of the voltage measurement unit is in nite and no current ows through the probe. In this case, the potential of the probe is equal to the local potential in the semiconductor element underneath the probe and the potential distribution inside


194

the device under study remains undisturbed from the presence of the probe. A nite input resistance or the presence of a thin dielectric layer on the sample (or tip) surface might alter this situation. In this case the potential at the probe tip (Vtip ) will be set by the value of the input resistance of the ampli er (Ri ) and the sum of the resistance of the dielectric layer and the spreading resistance (Rs ) as follows: Vtip = RiR+iRs Vsample . As a result, the measured voltage is a convolution of the potential distribution inside the device, the quality of the oxide and the local spreading resistance. Clearly, Ri must be taken (much) larger than the maximum value of Rs. In this case, the probe yields the potential of the locality with which it is in contact only if the semiconductor is in electronic equilibrium. If it is not in equilibrium (e.g. because it is illuminated, or because it is situated in a junction depletion region, or for some other reason) then a so-called oating-potential (dierence) is generated at the probe contact, which interferes with the potential measurement. Thus, a current-less probe in contact with semiconducting material in which non-equilibrium prevails does not acquire the local potential, but arrives at some value which diers from it by the oating potential. The non-equilibrium within the semiconductor on which the probes are situated may be characterized by quasi-Fermi levels EF0 n and EF0 p . The probe reaches a compromise energy given by

nEF0 n + pEF0 p (7.2) n + p 0 and the corresponding oating potential would then be EF ,e EF wherein n and p are the electron and hole mobility [Henisch 84, Baron 70]. In this formulation, the nature of the contact barrier (Schottky barrier, or at-band condition, or accumulation layer) is not included. A detailed description and analytic estimates of oating potentials for all these conditions can be found in [Manifacier 84]. EF0 =

7.2.4 Sample preparation

The cross section can be prepared in the same way which is used for SSRM. However, for potentiometry there is one further requirement: one must be able to operate the device after sectioning. Therefore, electrical contacts must be attached to the device. In order to be as close as possible to normal operating conditions, standard wire and die bonding procedures can be used. All bonding pads must be located at the same side from the cross section. Since the bonding of the sample after cross-sectioning is dicult without damaging or contaminating the sample cross section, it is preferred to do the bonding prior to the cross section preparation. After bonding, the sample is usually embedded in epoxy as shown in gure 3.27f to facilitate the polishing procedure. The quality of the cross-sectional surface will have an impact on the electrical behavior of the devices where the potential measurements shall be performed. Therefore, I , V characteristics of the devices must be measured prior to and after the sample preparation procedure, and compared to ensure that the device is still operational. For example, IDS , VDS characteristics of MOS transistors repeatably indicated a strong increase in leakage current (typically from 0.1 nA to 100 nA) after preparation of the cross section by FIB or polishing [Trenkler 98a]. Except for this increase in leakage current and the general decrease of the current since part of the transistors was removed, the transistor characteristics did


195

not change considerably. Thus, careful sample preparation can still yield devices which are operational and which are useful for nanopotentiometry.

7.2.5 Force calibration The force needed for reproducible potential measurements on silicon devices under ambient conditions is determined by measuring force pro les while a xed voltage is applied to the sample. The voltage measured by the tip is monitored simultaneously with the force pro le, which shows the force acting on the tip as a function of the tip-sample distance. Figure 7.14a shows a force pro le in combination with the measured potential for a homogeneously doped silicon sample under a bias of 1 V. A diamond-coated silicon probe with a spring constant of 68.5 N/m was used. The data for increasing tip-sample distances (withdrawal) are omitted. When the probe jumps into contact with the silicon sample (distance 0 nm), the measured potential is still 0 V. The tip potential jumps to 1 V when the tip-sample force is further increased by lifting the sample towards the probe. A similar response was observed when the bias voltage on the sample was decreased to values as low as 1 mV. As discussed previously by O'Shea et al. [O'Shea 95a], there are two ways to explain this behavior. First, the very apex of the tip might not be conducting. Second, a thin insulating layer on the tip or sample may be present, through which tunneling can occur, only when the force is increased. Similar curves measured with the same tip on a Pt sample ( gure 7.14b) exclude the rst explanation and indicate that the extra sample displacement needed can be entirely attributed to the native oxide (and any other insulating contaminants) on top of the silicon sample. When using the same tip on a silicon sample on which an oxide layer was grown (thickness 4.6 nm), the extra sample displacement needed for potential measurements further increases ( gure 7.14c). Since the thickness and the quality of the native oxide on a cleaved or polished cross section in ambient conditions are not constant, the force chosen for reliable potential measurements is a little higher than the threshold determined by the presented method. All probes are inspected in this way both before and after scanning, to ensure that the electric properties of the tip are not altered during the measurement. As compared to the threshold force encountered in SSRM, the nanopotentiometry threshold force is found to be much smaller. For example, the probe which was used for the experiments presented in gure 7.14 had a SSRM threshold force of 6.1 N while the nanopotentiometry threshold force was only 1.9 N. Therefore, it is believed that no plastic deformation of the silicon sample is required for nanopotentiometry operation. Consequently, lower forces can be used (e.g. by taking a cantilever with a lower spring constant, or by reducing the force setpoint), resulting in a longer tip lifetime and a higher quality of the simultaneously measured topographic image.

7.2.6 Examples The strength of the nanopotentiometry method is illustrated by the one-dimensional measurement of the potential distribution inside an abrupt pn junction which has been prepared by epitaxial deposition of a boron-doped layer (1017 atoms/cm3 ) on a n-type substrate with a doping level of 1015 atoms/cm3 . An ion-implanted diamond tip was used at a force of


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Figure 7.14: Force pro le and measured potential on (a) bulk silicon sample, (b) platinum sample, and (c) bulk silicon sample with a 4.6 nm oxide layer. A diamond-coated silicon tip was used on a cantilever with a spring constant of 68.5 N/m.


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7 N. Figure 7.15 shows the potential distribution measured when 0.8 V and 1.7 V reverse bias is applied across the junction. One can clearly observe the potential drop across the depletion zone and its extension into the (lowly doped) n-type substrate.

potential (V)

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Figure 7.15: One-dimensional nanopotentiometry measurement of an abrupt p+n junction (located at a depth of 340 nm) under reverse bias.

The nanopotentiometry technique has also been applied to measure the potential distribution inside NMOS and PMOS transistors [Trenkler 98a]. A preliminary result for a NMOS transistor with 0.5 m gate length is presented in gure 7.16. A positive bias of 1 V was applied to the drain, while the source contact was connected to a common ground. In gure 7.16a the transistor was turned o by connecting the gate to the ground. Only the drain plug and the highly doped drain region are visible as bright features (i.e. high voltages). If the gate bias was increased to 0.75 V, the transistor was turned on ( gure 7.16b). The source contact and the highly doped source were also 'pulled up', which is believed to be due to the observed high contact resistance to the ground contact. This will be described in detail in the PhD thesis from T. Trenkler [Trenkler].

Figure 7.16: Two-dimensional nanopotentiometry measurement of a NMOS transistor under operation. (a) turned o: VDS = 1 V, VGS = 0 V, (b) turned on: VDS = 1 V, VGS = 0:75 V. From left to right the drain, gate, and source are displayed (scan size: 52.5 m2 ).

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7.2.7 Conclusions


Nanopotentiometry is another SSRM based tool for cross-sectional characterization of semiconductor devices. An experimental procedure has been developed to allow 2D potential mapping inside operating devices. The present results on MOS transistors demonstrate that nanopotentiometry provides insight into the actual working behavior of these devices. The sensitivity and the spatial resolution are presently limited by the nite size of the tip and by the quality of the surface preparation.

Chapter 8

General conclusions 8.1 Conclusions In this work, a new method for two-dimensional carrier pro ling with nanometer resolution is developed. This new method is named SSRM. The development includes the experimental setup, a detailed measurement procedure and a quanti cation procedure (including instrument calibration). The major achievements of the presented work can be summarized as follows:

The atomic force microscope (AFM) equipped with a conductive diamond probe can

be used in the contact mode to measure local spreading resistance values inside crosssectioned silicon structures. The spreading resistance values can be transformed into carrier concentration values using a well-de ned calibration procedure providing a one- or two-dimensional map of the carrier distribution. The ideal instrumental setup includes a logarithmic current ampli er and a borondoped diamond-coated silicon probe. The probe can be stepped or scanned from one measurement position to the next providing at the same time a geometrical image of the structure under study. The regions of interest in the sample are exposed by cross-sectioning and polishing to an RMS roughness smaller than 0.4 nm. Resistances are determined by measuring the current owing through the probe/semiconductor contact at low DC bias voltage (-50{50 mV). The resistance versus force behavior exhibits a strong decrease in resistance at a particular threshold force (typically varying from 5 to 25 N depending on the precise shape of the tip apex). Stable, low-noise, SSRM operation requires the use of a force which is higher than this threshold force (minimum 50% higher). The electromechanical model of the probe-semiconductor contact at these high forces postulates two eects operating in parallel. First, there is an ohmic spreading resistance in series with a barrier resistance which can be ascribed to the plastically deformed zone under the tip. This plastically deformed zone consists of a -tin silicon phase which has metallic electrical properties. The other component, corresponding to the elastically deformed region beneath the tip, is a large barrier resistance. This parallel combination is placed in series with a spreading resistance which is determined by the 199

CHAPTER 8. GENERAL CONCLUSIONS

200

size of the elastically deformed area. At low bias voltages, the plastically deformed region is dominating the contact behavior. The transformation of the measured resistance pro les into quantitative carrier concentration pro les makes use of calibration curves (one for each type of impurity) and a detailed quanti cation procedure which corrects for current-spreading eects. The calibration measurements are performed quickly using two specially prepared calibration samples. The correction algorithm makes use of a database storing the correction factor as a function of typical pro le characteristics (gradient, curvature, distance to isolating or conducting boundaries). Using a forward method which is based on interpolation of the database, a given resistivity pro le can be transformed into the corresponding resistance pro le. An iteration procedure which makes use of the forward method can be applied for the inverse problem of recovering the resistivity pro le from the measured resistance data. The speci cations of the SSRM method, summarized in table 8.1, ful l the requirements set by future generations of MOS technologies. Table 8.1: Intercomparison of SSRM with the present status of the most important 2D carrier pro ling methods and the demands from future generations of MOS technologies.

SSRM SCM selective etch 0.25 m 0.18 m

resol. (nm) 10{30 15{30 25 20 10

dyn. range conc. resol. quanti cation possibility 1015 , 1020 linear fully quanti able 1015 , 1020 power limited at junctions 1017 , 1020 poor none 1015 , 1020 linear 10 % accuracy 1015 , 1020 linear 5 % accuracy

The spatial resolution of one- and two-dimensional cross-sectional SSRM can be fur-

ther improved by application of the SSRM method on beveled surfaces. With respect to the conventional SRP technique, the probe weight and the contact size can be drastically reduced. In this way some of the limitations from conventional SRP for shallow 1D pro ling can be resolved. Probe conditioning is no longer required, larger bevel angles can be used, higher geometrical resolution can be obtained, and the bevel topography is measured in-situ which allows to correct the depth scale automatically for bevel rounding. The small SSRM contact results in a smaller sampling volume and hence smaller correction factors. The transformation from SRP to SSRM reduces the pressure enhanced carrier spilling component but since both techniques are applied on the same bevel, the in uence of the surface quality remains. Nanopotentiometry is another SSRM based tool for cross-sectional characterization of semiconductor devices providing insight into their actual working behavior. The potential distribution inside operating devices is monitored experimentally by a conductive AFM probe scanning the cross-sectioned device structure in contact-mode AFM. The probe is connected to a high-impedance voltage measurement unit, while the device under study is brought into operation by applying DC voltages to the appropriate regions (most often bonding pads or contacts).

8.2. FUTURE WORK AND OUTLOOK

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8.2 Future work and outlook The results achieved in this work are a step forward towards a general applicable twodimensional carrier pro ling method. The author believes that, although the SSRM and the SCM technique are still in a development stage, they are the leading candidates to become a general applicable two-dimensional carrier pro ling tool. Both techniques have a resolution close to the value asked for, can be applied on arbitrary structures, have the required dynamic range, and can deliver quantitative carrier concentration values. The SSRM has two important advantages compared to the SCM method: First, SSRM is less sensitive to surface preparation because higher forces are being applied. Second, the interpretation and quanti cation of the SSRM data at (or near) pn junctions is more straightforward, since the carrier pro le is less disturbed by the bias voltage (compared to the SCM method). Little work is required to implement the SSRM method into a commercial pro ling tool. For this purpose, the SSRM technique must rst be further optimized by improving the following aspects:

Further work is required to study the impact of the barrier resistance on the current spreading eect. The experimental results suggest that both the barrier resistance

and the spreading resistance in uence the current spreading. At present, a physical explanation of this behavior is not available. More work is necessary to obtain a high-yield batch fabrication method for diamondcoated probes. This work involves the development of both CVD diamond-coated silicon probes and diamond probes integrated on a diamond cantilever [Hantschel]. A software package must be developed which supports fully automated quanti cation of the measured resistances into carrier concentration values (one and twodimensional) including cubic spline smoothing, interpolation of the calibration curves and the correction factor database, and correction factor calculation. At present, there is no method which can be used as an absolute reference to evaluate the accuracy of a new carrier pro ling method such as SSRM. Therefore, extensive round-robin studies which involve dierent laboratories and dierent carrier pro ling techniques must be carried out. The eld of applications of SSRM can be further extended by incorporating a number of new options. This future work includes:

TCAD calibration: Until now, no characterization tool was available to measure

quantitative 2D carrier pro le information needed for the calibration of TCAD simulation packages. A major task of the SSRM technique could be to tune the models which are presently used in these simulators by pro ling a wide range of test structures. Combination with SCM and AC measurements: The SSRM method is in principle a DC method. However, if an AC method would be used one could measure the complete impedance, i.e the resistive and reactive part as a function of frequency. This has the possibility to provide more information than the present SSRM method.

202

CHAPTER 8. GENERAL CONCLUSIONS Preliminary experiments have indicated that diamond probes are well suited for SCM measurements. Thus, SCM and SSRM could be performed with the same probe in a semi-simultaneously way. For example, the structure under investigation could rst be scanned at low force, providing a good image of its geometry and at the same time an SCM image, after which the force is increased to the SSRM level for the SSRM measurement. One could do so by changing the force after a complete scan or after each line-scan. Two-probe setup: Sometimes, it is dicult to attach a back contact to the structure under investigation. For example, if a particular transistor is selected (which is, for example, defect) it might be very dicult to thin the transistor to such a thickness that one can reach the dierent regions from both cross sections (the one on which the measurement is performed and the one needed for the back contact). In such a situation, it would be helpful to dispose of a two-probe setup, in which the rst probe can be positioned on a particular area of the cross-sectioned device (for example on a cut through a plug) and the second probe can be moved and used to perform the SSRM resistance measurements. The rst probe might have a large contact area since it is only used as the current collecting probe, while the second probe must ful ll the normal SSRM probe speci cations. For example, a SRP probe could be used as the rst probe. For this purpose a rough positioning system might be sucient (for example based on a high magni cation optical microscope and a micromanipulator, as is routinely done to position both probes in conventional SRP). Quanti cation of 2D on-bevel SSRM: At present, not enough data nor calculations are available to decide which parameters { carrier gradient and concentration, bevel angles, etc. { have a strong in uence on the two-dimensional redistribution of carriers in beveled structures. Further work is required to delineate the importance of this problem and to set up a quanti cation procedure which corrects for this eect as is routinely done in conventional SRP for one-dimensional pro les. Further work is required to study the behavior of the nanopotentiometry method [Trenkler]. In particular, it needs to be studied to which extent the observed potential distributions are in uenced by the cross section preparation and by the presence of the probe on the cross-sectioned device.

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BIBLIOGRAPHY C.C. Williams, J. Slinkman, W.P. Hough, and H.K. Wickramasinghe, Lateral dopant pro ling on a 100 nm scale by scanning capacitance microscopy, J. Vac. Sci. Technol. A 8, 895 (1990). B. Wolf and P. Pau er, Speed dependency of abrasion during AFMscanning under high load, Cryst. Res. Technol. 31, 505 (1996). O. Wolter, Th. Bayer, and J. Gerschner, Micromachined silicon sensors for scanning force microscopy, J. Vac. Sci. Technol. B 9, 1353 (1991). C.P. Wu, E.C. Douglas, C.W. Muelller, and R. Williams, Techniques for lapping and staining ion-implanted layers, J. Electrochem. Soc. 126, 1982 (1979). A. Yagi, S. Tsukada, Y. Takahashi, S. Morita, Y. Sugawara, T. Okada, S. Imai, and N. Mikoshiba, Dierential conductance imaging under alternate current bias, J. Vac. Sci. Technol. A 8, 336 (1990). T. Yamamoto, Y. Suzuki, H. Sugimura, and N. Nakagiri, SiO2 /Si system studied by scanning capacitance microscopy, Jap. J. Appl. Phys. B 35, 3793 (1996). M. Yasutake, D. Aoki, and M. Fujihira, Surface potential measurements using the Kelvin probe force microscope, Thin Solid Films 273, 279 (1996). H. Yokoyama, M.J. Jeery, and T. Inoue, Heterodyne force-detection for high frequency local dielectric spectroscopy by scanning Maxwell stress microscopy, Jap. J. Appl. Phys. B 32, L1845 (1993). H. Yokoyama, T. Inoue, and J. Itoh, Nonresonant detection of electric force gradients by dynamic force microscopy, Appl. Phys. Lett. 65, 3143 (1994). E.T. Yu, M.B. Johnson, and J.-M. Halbout, Electrical pro ling of Si(001) pn junctions by scanning tunneling microscopy, Appl. Phys. Lett. 61, 201 (1992). E.T. Yu, K. Barmak, P. Ronsheim, M.B. Johnson, P. McFarland, and J.M. Halbout, Two-dimensional pro ling of shallow junctions in Si metaloxide-semiconductor structures using scanning tunneling spectroscopy and transmission electron microscopy, J. Appl. Phys. 79, 2115 (1996). E.T. Yu, Nanoscale characterization of semiconductor materials and devices using scanning probe techniques, Mat. Science Engin. 17, 147 (1996). S. Yugo, T. Kanai, T. Kimura, and T. Muto, Generation of diamond nuclei by electric eld in plasma chemical vapor deposition, Appl. Phys. Lett. 58, 1036 (1991).

Scienti c contributions Publications 1. P. De Wolf, J. Snauwaert, T. Clarysse, W. Vandervorst, and L. Hellemans, Characterization of a point-contact on silicon using force microscopy supported resistance measurement, Appl. Phys. Lett. 66, 1530 (1995). 2. P. De Wolf, J. Snauwaert, L. Hellemans, T. Clarysse, W. Vandervorst, M. D'Olieslaeger, and D. Quaeyhaegens, Lateral and vertical dopant pro ling in semiconductors by atomic force microscopy using conducting tips, J. Vac. Sci. Technol. A 13, 1699 (1995). 3. P. De Wolf, F. Chollet, and W. Vandervorst, AFMs reveal 3-D semiconductor features, Test & Measurement World 15(9), 41 (1995). 4. W. Vandervorst, T. Clarysse, P. De Wolf, L. Hellemans, J. Snauwaert, V. Privitera, and V. Raineri, On the determination of two-dimensional carrier distributions, Nucl. Instrum. and Methods B 96, 123 (1995). 5. T. Trenkler, P. De Wolf, J. Snauwaert, Z. Qamhieh, W. Vandervorst, and L. Hellemans, Local potential measurements in silicon devices using atomic force microscopy with conductive tips, Proceedings of the 25th European Solid State Device Research Conference (ESSDERC), Editions Frontieres, Gif sur Yvette, France, p. 477 (1995). 6. T. Clarysse, P. De Wolf, H. Bender, and W. Vandervorst, Recent insights into the physical modeling of the spreading resistance point contact, J. Vac. Sci. Technol. B 14, 358 (1996). 7. P. De Wolf, T. Clarysse, W. Vandervorst, J. Snauwaert, and L. Hellemans, Oneand two-dimensional carrier pro ling in semiconductors by nanospreading resistance pro ling, J. Vac. Sci. Technol. B 14, 380 (1996). 8. J. Snauwaert, N. Blanc, P. De Wolf, W. Vandervorst, and L. Hellemans, Minimizing the size of force-controlled point contacts on silicon for carrier pro ling, J. Vac. Sci. Technol. B 14, 1513 (1996). 9. P. De Wolf, F. Chollet, and W. Vandervorst, AFMs reveal 3-D semiconductor features, Test & Measurement Europe 4(5), 31 (1996). 227

228

BIBLIOGRAPHY

10. P. De Wolf, T. Trenkler, T. Clarysse, M. Caymax, W. Vandervorst, J. Snauwaert, and L. Hellemans, Quantitative carrier pro ling of silicon devices by Nano-SRP, Proceedings of the 3rd Workshop on Industrial Applications of Scanned Probe Microscopy, Ed. J. Dagata (1996). 11. P. De Wolf, T. Trenkler, T. Clarysse, M. Caymax, W. Vandervorst, J. Snauwaert, and L. Hellemans, Electrical characterization of sub-micrometer silicon devices by crosssectional contact mode AFM, Scanning Microscopy 10, 937 (1996). 12. W. Vandervorst, P. De Wolf, T. Clarysse, T. Trenkler, L. Hellemans, and J. Snauwaert, Carrier pro le determination in device structures using AFM-based methods, in Semiconductor Characterization: Present Status and Future Needs, Eds. W.M. Bullis, D.G. Seiler, and A.C. Diebold, p. 322, (1996). 13. P. De Wolf, T. Trenkler, W. Vandervorst, and L. Hellemans, ULSI-device characterization using Nano-SRP, Proceedings of the Electrochemical Society Vol. 97-12: Diagnostic techniques for semiconductor materials and devices, Eds. P. Rai-Choudhury, J. Benton, D. Schroder, and T.J. Shaner (1997). 14. P. De Wolf, T. Trenkler, W. Vandervorst, R. Tillmann, and A. Erickson, Comparison of semiconductor dopant pro les by scanning capacitance microscopy and nanospreading resistance pro ling, 9th Int. Conf. on STM and Related Techniques, Hamburg, July 1997. 15. W. Vandervorst, T. Clarysse, P. De Wolf, T. Trenkler, T. Hantschel, and R. Stephenson, Dopant/carrier pro ling for ULSI, Future Fab International 4, Vol. 1, 287 (1997). 16. P. De Wolf, T. Clarysse, and W. Vandervorst, Quanti cation of Nano-spreading resistance pro ling data, J. Vac. Sci. Technol. B 16, 320 (1998). 17. P. De Wolf, T. Clarysse, W. Vandervorst, L. Hellemans, Ph. Niedermann, and W. Hanni, Cross-sectional Nano-SRP dopant pro ling, J. Vac. Sci. Technol. B 16, 355 (1998). 18. P. De Wolf, T. Clarysse, W. Vandervorst, and L. Hellemans, Low weight spreading resistance pro ling of ultra-shallow dopant pro les, J. Vac. Sci. Technol. B 16, 401 (1998). 19. T. Clarysse, M. Caymax, P. De Wolf, T. Trenkler, W. Vandervorst, J.S. McMurray, J. Kim, C.C. Williams, J.G. Clark, and G. Neubauer, Epitaxial staircase structure for the calibration of electrical characterization techniques, J. Vac. Sci. Technol. B 16, 394 (1998). 20. T. Trenkler, P. De Wolf, W. Vandervorst, and L. Hellemans, Nanopotentiometry: Local potential measurements in CMOS transistors using atomic force microscopy, J. Vac. Sci. Technol. B 16, 367 (1998). 21. V.A. Ukraintsev, R.S. List, M. Chang, H. Edwards, R. San Marin, C.F. Machala, V. Zavyalov, J.S. McMurray, C.C. Williams, P. De Wolf, W. Vandervorst, D. Venables,

BIBLIOGRAPHY

229

S.S. Neogi, D.L. Ottaviani, J.J. Kopanski, J.F. Marchiando, B.G. Rennex, J.N. Nxumalo, Y. Li, and D.J. Thomson, Dopant characterization round-robin study performed on two-dimensional test structures fabricated at Texas Instruments, Proceedings of the Int. Conf. on Characterization and Metrology of ULSI Technology (ICCM) (1998). 22. R. Stephenson, P. De Wolf, T. Trenkler, T. Hantschel, T. Clarysse, and W. Vandervorst, Scanning probe microscopy of 1D and 2D carrier distributions, Materials Research Society (MRS), (symposium S: Nanoscale materials characterization using scanning probes), San Francisco, USA, April 1998. 23. P. De Wolf, M. Geva, T. Hantschel, W. Vandervorst, and R.B. Bylsma, Two-dimensional carrier pro ling of III-V structures using scanning spreading resistance microscopy, submitted to Appl. Phys. Lett. (1998).

Patents 1. Method for determining the resistance and carrier pro le of a semiconductor element using a scanning proximity microscope M. Meuris, W. Vandervorst, and P. De Wolf US-5585734 (Dec. 17, 1996) EP-466174 (Oct. 18, 1996) 2. Method for measuring the electrical potential in a semiconductor element L. Hellemans, P. De Wolf, T. Trenkler, W. Vandervorst US-5723981 (March 3, 1998) 3. A database and method for measurement correction for cross-sectional carrier pro ling techniques P. De Wolf, T. Clarysse, and W. Vandervorst US Patent Pending

BIBLIOGRAPHY

230

Curriculum vitae 8 oktober 1969 1987-1992 1992-1993 1993-1998 mei 1998

Geboren te Eeklo, Belgie Student aan de Universiteit Gent, Faculteit der Toegepaste Wetenschappen. Afgestudeerd in juli 1992 als Burgerlijk Elektrotechnisch Ingenieur, richting Zwakstroom. Vervulling legerdienst. Doctoraatsstudent aan de Katholieke Universiteit Leuven, Faculteit der Toegepaste Wetenschappen. Werkzaam als I.W.T.-bursaal in het Interuniversitair Micro-Elektronica Centrum (IMEC). Verdediging proefschrift: Two-dimensional carrier pro ling of semiconductor structures with nanometer resolution.

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