4-1 PSD of Kulite, Endevco, UF piezoresistive and UF Proximity sensor at 0 Volt without setup noise. .... 4-30 Power spectral density of UF proximity sensor with free membrane at zero biased voltage. ...... converting acoustic energy into electrical energy. When pressure is ...... http://www.lessemf.com/mag-shld.html,2005. 30.
CHARACTERIZATION OF NOISE IN MEMS PIEZORESISTIVE MICROPHONES
By ROBERT DIEME
A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2005
Copyright 2005 by Robert Dieme
To my wife, my parents, and Rev. John D. Gillespie.
ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Toshikazu Nishida, for his guidance and encouragement. I also would like to express my gratitude to Dr. Mark Sheplak, Dr. Gijs Bosman, and Dr. Kevin Jones, for their ideas and encouragement. I would also like to thank Dr. Louis N. Cattafesta III for help with my experiments. I also thank all Interdisciplinary Microsystems Group (IMG) students for their help and support. I thank my wife and parents for their prayers, support, and encouragement through my study. Special thanks go to Rev. John D. Gillespie for his advice. Finally, I thank God for the all of the graces He gives me.
iv
TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................................................................................. iv LIST OF TABLES............................................................................................................ vii LIST OF FIGURES ......................................................................................................... viii ABSTRACT...................................................................................................................... xii 1
INTRODUCTION ........................................................................................................1 Motivation.....................................................................................................................1 Previous Work ..............................................................................................................2 Objectives and Outline .................................................................................................9
2
NOISE IN PIEZORESISTIVE MEMS MICROPHONES.........................................11 Noise and Noise Power Spectral Density ...................................................................11 Noise Sources .............................................................................................................12 Thermal Noise .....................................................................................................13 Low Frequency Noise..........................................................................................14 Hooge’s model .............................................................................................14 McWhorter’s model .....................................................................................15 Shot Noise ...........................................................................................................19 Piezoresistive Microphone..........................................................................................20 MEMS Piezoresistive Microphone Voltage Output............................................22 MEMS Piezoresistive Microphone Sensitivity ...................................................24
3
EXPERIMENTAL NOISE SETUP............................................................................25 Shielding .....................................................................................................................25 Wiring System ............................................................................................................29 Voltage Supply ...........................................................................................................32 Setup Noise.................................................................................................................35 Noise Figure................................................................................................................42
v
4
MICROPHONES NOISE MEASUREMENT ...........................................................45 Noise in Microphones.................................................................................................51 UF Piezoresistive Microphone ............................................................................51 UF Proximity Sensor ...........................................................................................54 Endevco Piezoresistive Microphone ...................................................................56 Kulite Piezoresistive Microphone .......................................................................57 Acoustic Calibration ...................................................................................................60 Frequency Response............................................................................................61 Linearity ..............................................................................................................63 Minimum Detectable Signal................................................................................66 Dominant Noise Source in MEMS Piezoresistive Microphones................................67 Acoustic Isolation Test ........................................................................................67 Membrane Contribution to 1/f Noise ..................................................................69
5
CONCLUSION AND FUTURE WORK ...................................................................72
APPENDIX: PIEZORESISTIVITY ..................................................................................74 LIST OF REFERENCES...................................................................................................77 BIOGRAPHICAL SKETCH .............................................................................................80
vi
LIST OF TABLES Table
page
2-1
Manufacturers’ specifications for Endevco piezoresistive and Kulite piezoresistive microphones ......................................................................................24
3-1
Noise power spectral density at 60, 120 and 180 Hz with one, two and three faraday cages ............................................................................................................28
3-2
Pre-amplifier settings ...............................................................................................36
3-3
Spectrum analyzer setting ........................................................................................37
4-1
Our measured input and output impedances of UF piezoresistive microphone, UF proximity, Kulite and Endevco ..........................................................................45
4-2
Frequency range during measurement .....................................................................47
4-3
Acoustic calibration results of UF microphone, UF proximity, Endevco and Kulite microphones ..................................................................................................64
4-4
Sensitivity of the UF microphone, UF proximity, Endevco and Kulite microphones under the same bias voltage (3 V) ......................................................65
4-5
Sensitivity of the UF microphone, UF proximity, Endevco and Kulite microphones under same power dissipation (7 mW) ...............................................65
4-6
Minimum detectable signal (MDS) of UF microphone, UF proximity, Endevco and Kulite microphones at different bias voltages ...................................................66
4-7
Minimum detectable signals (MDS) when the microphones are operated under the same bias voltage (3 V) ......................................................................................67
4-8
Minimum detectable signals (MDS) when the microphones are subjected to the same power dissipation (7 mW)...............................................................................67
A-1 Piezoresistive coefficients of silicon ........................................................................75 A-2 Transverse and longitudinal piezoresistance coefficients of silicon for direction....................................................................................................................76
vii
LIST OF FIGURES Figure
page
2-1
Trapping-detrapping model for 1/f noise. ................................................................18
2-2
Piezoresistors configured in Wheatstone bridge. .....................................................21
2-3
Top view of a UF piezoresistive microphone...........................................................21
2-4
Cross-section of a UF piezoresistive microphone.....................................................21
3-1
PSD of UF microphone at 3 V shielded with one Faraday cage..............................27
3-2
PSD of UF microphone at 3 V shielded with two Faraday cages. ...........................27
3-3
PSD of UF microphone at 3 V shielded with three Faraday cages. .........................28
3-4
Power spectral densities of UF microphone at the same voltage bias with ground loop, floating equipments and one ground connection. ...........................................29
3-5
Power spectral density of UF microphone with ground loop...................................30
3-6
Power spectral density of UF microphone with floating equipments. .....................31
3-7
Power spectral density of UF microphone with one ground connection. ................31
3-8
UF microphone biased with a power supply, zinc/carbon and lead acid batteries...33
3-9
UF piezoresistive microphone biased at 2.64 Volt with a power supply.................34
3-10 UF piezoresistive microphone biased at 2.64 Volt with zinc/carbon battery...........34 3-11 UF piezoresistive microphone biased at 2.64 Volt with lead acid battery. ..............35 3-12 Small signal representation of the setup noise. ........................................................37 3-13 Noise voltage power spectral density measurement setup. ......................................38 3-14 Voltage noise power spectral density of setup. ........................................................38 3-15 Noise current power spectral density measurement setup. ......................................39
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3-16 Current noise power spectral density of setup. ........................................................39 3-17 Experimental setup for a 1 kΩ metal film resistor. ..................................................40 3-18 Small signal analysis of voltage noise power spectral density of 1kΩ metal film resistor. .....................................................................................................................40 3-19 Equivalent input voltage noise Svin in term of noise voltage. ..................................41 3-20 Equivalent input current noise SIin in term of noise current. ....................................41 3-21 Voltage noise PSD of a 1-kΩ metal film resistor without the subtraction of the equipment setup noise. .............................................................................................42 3-22 Noise of the metal resistor with setup noise subtracted. ..........................................42 3-23 Noise figure of 1 kΩ metal film resistor using the SR560 low noise preamplifier..43 4-1
PSD of Kulite, Endevco, UF piezoresistive and UF Proximity sensor at 0 Volt without setup noise...................................................................................................46
4-2
Noise figure of UF piezoresistive microphone, Kulite, Endevco, and UF proximity sensor using the SR560 low noise pre-amplifier. ....................................46
4-3
Large signal representation of bias network. ...........................................................47
4-4
Small signal representation of bias network. ...........................................................48
4-5
Small signal representation of bias network using a ∆-Υ transformation................48
4-6
Experimental setup of noise measurement...............................................................49
4-7
Experimental setup for an AC bridge measurement. The mathematical derivations have been obtained from Lorteije and Hoppenbrouwers.......................50
4-8
Power spectral density of UF piezoresistive microphone at different bias voltages.....................................................................................................................51
4-9
Voltage dependence of PSD for UF piezoresistive microphone at 12 Hz and binwidth 0.016 Hz....................................................................................................53
4-10 Hooge parameter of UF piezoresistive microphone.................................................53 4-11 Power spectral density of UF proximity sensor at different bias voltage (constant reverse bias of -0.5 V). .............................................................................................54 4-12 Voltage dependence of PSD for UF proximity sensor at 12 Hz and binwidth 0.016 Hz. ..................................................................................................................55
ix
4-13 Hooge parameter of UF proximity sensor................................................................55 4-14 Power spectral density of Endevco microphone at different bias voltage. ..............56 4-15 Voltage dependence of PSD for Endevco microphone at 12 Hz and binwidth 0.016 Hz. ..................................................................................................................57 4-16 Power spectral density of Kulite microphone (without the temperature compensation module) at different bias voltage. .....................................................57 4-17 Voltage dependence of power spectral density for Kulite microphone (without the temperature compensation module). ..................................................................58 4-18 Kulite noise power spectral densities compared to the DC setup noise...................58 4-19 Comparison of power spectral densities of UF microphone, UF proximity sensor, Endevco, and Kulite (without the temperature compensation module) microphones biased at 2.6 V. ...................................................................................59 4-20 1/f noise figure of UF piezoresistive microphone, UF proximity sensor, Endevco, and Kulite (without the temperature compensation module) microphones biased at 2.6 V. ...................................................................................60 4-21 Experimental setup used with the normal incidence plane wave tube.....................61 4-22 Magnitude frequency response (normalized sensitivity) of Endevco, UF proximity, Kulite (with and without the temperature compensation module) and UF piezoresistive microphone..................................................................................62 4-23 Phase frequency response of Endevco, UF proximity, Kulite (with and without the temperature compensation module) and UF piezoresistive microphone. ..........63 4-24 Linearity measurement of Endevco, proximity, Kulite (with and without the temperature compensation module) and UF piezoresistive microphone. ................63 4-25 Sensitivity of Endevco, UF proximity, Kulite (with and without the temperature compensation module) and UF piezoresistive as a function of pressure. ................64 4-26 Power spectral density of the Bruel and Kjaer 4138 condenser microphone and of the UF piezoresistive microphone. ......................................................................68 4-27 Coherence function between the B&K and UF piezoresistive microphone.............68 4-28 Power spectral density of the UF piezoresistive proximity sensor with free diaphragm.................................................................................................................69 4-29 Power spectral density of the UF piezoresistive proximity sensor with fixed diaphragm.................................................................................................................70
x
4-30 Power spectral density of UF proximity sensor with free membrane at zero biased voltage...........................................................................................................71 5-1
Focus ion beam (FIB) of an arc piezoresistor of the UF piezoresistive microphone...............................................................................................................73
5-2
Transmission electron microscopy (TEM) results of an arc piezoresistor of the UF piezoresistive microphone..................................................................................73
A-1 Polar plots of longitudinal and transverse piezoresistance coefficients for p-type (100) silicon..............................................................................................................75
xi
Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science CHARACTERIZATION OF NOISE IN MEMS PIEZORESISTIVE MICROPHONES By Robert Dieme May 2005 Chair: Toshikazu Nishida Major Department: Electrical and Computer Engineering Microelectromechanical systems (MEMS) have provided many benefits in measurement systems in acoustical, optical and electrical engineering. However, with the desire for better MEMS sensor performance where high resolution and small device size are required, multiple sensor parameters such as dynamic range, sensitivity, and noise must be considered. Our study focused on noise in MEMS devices. We examined noise sources in a piezoresistive MEMS device. Careful noise measurements are needed to accurately study noise in MEMS sensors. Techniques such as shielding, wiring system, biasing, and extraction of setup noise from the total measured noise play fundamental roles in accurate noise measurement. We measured and compared the noise power spectral densities of 4 piezoresistive microphones (2 university-experimental models and 2 commercial models) at low frequencies (bias dependence, Hooge parameter) and noted their high frequency thermal noise asymptote. We also measured microphone acoustic performance parameters such as sensitivity, linearity, and minimum detectable signal using a plane xii
wave tube. Excess noise at low frequencies in piezoresistive sensors with free and fixed membrane was found to be of electrical origin.
xiii
CHAPTER 1 INTRODUCTION The recent trend in integrated circuit (IC) technology is to fabricate small size devices while improving their performance and reliability, and at the same time making them affordable to consumers. Microelectromechanical systems (MEMS) are an extension of IC technology that allows the fabrication of miniature systems such as sensors and actuators, which are useful in a wide variety of engineering fields. These miniature systems include transducers on the micrometer scale (for example, piezoresistive pressure sensors, microphones, accelerometers, and cantilevers). Motivation Among many factors that limit MEMS performance transducers noise is critical since it determines the minimum signal that can be detected. Reducing noise while maintaining or improving device sensitivity will provide better signal-to-noise ratio and lower minimum detectable signal. However, to determine whether the sensor noise is at its theoretical minimum or if a better design can achieve lower noise, one must first understand the fundamental noise mechanisms and be able to take accurate noise measurements. Good data are obtained when equipment are properly chosen and correctly used in a good, well-shielded environment during the measurements. After establishing confidence in the accuracy of the measurements, we used the resulting data to verify the contribution of different noise sources in MEMS sensors, and to draw conclusions about their impact on sensor performance. Knowing the most dominant noise source in sensors allow us to focus 1
2 effort on the real issue when designing a low-noise device. One may put much effort in lowering a sensor noise floor, but end up being unsuccessful because the targeted noise to be reduced was not a major contributor to the overall noise of the sensor, or because the sensitivity was also reduced (leading to no improvement in the minimum detectable signal). Previous Work Noise in MEMS sensors has been studied by many scientists who have focused on specific noise sources, which they believe limit their device performance [1-4]. Optimization analysis to improve sensitivity and reduce noise was also done [5-7]. Harley and Kenny [5] showed methods used for fabricating high-sensitivity piezoresistive cantilevers to improve their sensitivity, bandwidth, and noise. They discussed geometric and process parameter effects on cantilever sensitivity, bandwidth, and noise. Later [1], they gave a more detailed analysis for the optimization of piezoresistive cantilevers. In their work, sensitivity, noise, bandwidth, and spring constant were subjected to optimization based on cantilever geometry, process design, and voltage operation. They provided formulas and graphs showing the effect of thickness, length, and width on cantilever sensitivity. Thinner cantilevers yielded to an improvement of the sensitivity. Cantilever leg lengths were chosen judiciously since a trade off between sensitivity and low frequency noise is involved through the number of carriers. For process optimization, shallow-doped cantilevers led to high noise, since the number of carriers was small. Deep-doped cantilevers led to low noise because of the large number of carriers. However, deep-doped cantilevers reduced the sensitivity since the sensitivity efficiency β derived by Tortonese [8] was smaller. There is therefore a trade off between noise and sensitivity. The same effect is seen with the choice of doping
3 concentration since the number of carriers plays a role in the noise and sensitivity readings. Harley and Kenny confirmed the presence of bulk 1/f noise in their cantilevers. They propose further studies on anneal to improve the quality of the crystal lattice in order to reduce the bulk 1/f noise. They also suggested that piezoresistive devices be biased according to their tolerance on power dissipation, to prevent either their destruction or the decrease of their performance, since at low frequencies the noise increases as the bias voltage squared. Chau and Wise [6] analyzed the limits of silicon capacitive and piezoresistive sensors when subjected to size reduction. The factors they discussed are pressure range, pressure sensitivity, pressure resolution, and the effect of built-in diaphragm stress (which mainly depends on parameters such as diaphragm length, diaphragm thickness for piezoresistive microphone, and plate separation for capacitive microphone). Chau and Wise stated that the pressure resolution is limited by various noise sources including sources of both mechanical (Brownian noise) and electrical (piezoresistor thermal noise, KT/C noise, circuit noise) origin. They provided tables showing the theoretical performance of ultraminiature and ultrasensitive capacitive and piezoresistive sensors assuming that the diaphragms are made of monocrystalline silicon and are free of built-in stress. In the ultraminiature (scaled size) case, the performances of the devices were analyzed as the diaphragms lengths are progressively reduced, while keeping steady pressure ranges. As for the ultrasensitive (scaled sensitivity) sensors, the diaphragm thickness was scaled down while the diaphragms length remained constant. Chau and Wise stated that the capacitive sensors were limited by circuit resolution while piezoresistive sensors were affected by offsets and temperature drifts in the
4 ultraminiature sensors case. In addition, ultraminiature capacitive sensors could not have their sizes reduced as much as the sizes of their piezoresistive counterparts. However, the theoretical study conducted by Chau and Wise reveals that ultraminiature capacitive sensors have higher sensitivity that the piezoresistive ones. In the case of the ultrasensitive sensors, the limits were set by pressure offsets and drift. Chau and Wise study suggested that when high sensitivity is required, capacitive sensors are preferable than the piezoresistive sensors. From the tables provided, among the noise mechanisms present, Brownian noise was less significant than the thermal noise, kT/C noise and circuit noise. Chau and Wise [9] extensively studied Brownian noise in ultrasensitive capacitive and piezoresistive sensors. A thorough analysis of a circular diaphragm surrounded by a rarified gas in which the mean free path of gas molecules was larger than the diaphragm diameter was done. The study was laid out in terms of deflection, kinetic and potential energy, capacitance, stresses, damping coefficient and a constant K, which depends on the properties and condition of the gas. As a result, a formula of the input pressure noise due to Brownian motion for both ultrasensitive capacitive and piezoresistive sensors was given for frequencies below the diaphragm fundamental resonance frequency. Chau and Wise presented numerical computation of Brownian noise in both types of sensors assuming that the built-in stress was negligible. The capacitive sensors revealed lower noise that the piezoresistive ones. Furthermore, their study showed that Brownian noise was less than the thermal noise of the piezoresistive sensors and the circuitry noise at low frequencies. Chau and Wise concluded that Brownian noise was not a factor that could
5 prevent further miniaturization and sensitivity improvement of solid-state pressure sensors. Chau and Wise [9] result differs from the one made by Barabash and Cobbold [2]. In their investigation of the limitation of ISFET and silicon pressure transducers, Barabash and Cobbold divided the noise sources of pressure transducers into two categories: extrinsic (Brownian noise) and intrinsic noise (Johnson noise). The study of the Brownian noise was conducted under the assumption that the mean free path is much smaller than the diaphragm radius. Barabash and Cobbold derived formula of the total mean square noise voltage and applied a specific example showing that the Brownian noise voltage was much larger than the Johnson noise. Thus, they claimed that Brownian noise was a limiting factor in silicon pressure transducers. However, Chau and Wise concluded that Brownian noise was less significant than the other major noise sources [9]. Hansen and Boisen [3] discusses noise in piezoresistive force microscopy. The noises sources were divided into three categories: vibrational noise, Johnson noise, and 1/f noise. In their device modeling, Hansen and Boisen considered cases of ideal and real devices with supported or free cantilever ends. The Johnson noise and flicker noise originating from the piezoresistors were expressed with the cantilever physical parameters. Hansen and Boisen point out the effect of bandwidth and temperature on the total deflection noise power. The study of the temperature effect has been conducted by analyzing the contributions of the thermal resistances of both the cantilever and the supporting structure. Hansen and Boisen gave an expression of the total deflection noise power as a function of temperature rise. For fixed design parameters of cantilevers,
6 comparisons of cantilevers with a single piezoresistor and full Wheatstone bridge piezoresistors showed that the noise, when dominated by Johnson noise that is temperature dependent, was lowered when a full Wheatstone bridge piezoresistors was used. This reduction of noise level comes to the fact that when a full Wheatstone bridge piezoresistors is used, the characteristic temperature parameter ∆Tc is reduced by half. A table comparing the noise performance of different cantilever designs showed a reduction in noise level for cantilevers with full Wheatstone bridge piezoresistor compared to cantilevers with single piezoresistor. Yu et al. [10], gave a detailed analysis on sensitivity and noise in piezoresistive cantilevers. The results obtained serve as a guideline for optimization design of cantilevers. Parameters involved in the process fabrication of cantilevers such as piezoresistor geometry, doping concentration, annealing, bias voltage and material properties are combined to study the trends in device performances. The experiments show the influences of the parameters quoted above on the Hooge factor, gauge factor, and minimum detectable deflection. In addition, the matrix of parameters was applied in the fabrication of cantilevers with three different material properties: single-crystal silicon, low-pressure chemical-vapor deposition (LPCVD) amorphous silicon and microcrystalline silicon. A series of experiments, graphs, tables and plots were used to draw conclusions of the optimization analysis. For instance, an increase in the volume of the piezoresistors lowered the 1/f noise, which is said to be the dominant noise at low frequencies. Their results showed that the doping dose did not affect much the Hooge factor. However, its increase lowered the 1/f noise. In addition, annealing at 1050° C for 30 minutes on an amorphous silicon resistor revealed an improvement in the 1/f noise and
7 Hooge parameter compared to an annealing at 950° C for 10 minutes on the same resistor type. Yu et al. suggested that single-crystal silicon; and LPCVD amorphous silicon and microcrystalline silicon were suitable for the fabrication of cantilevers where high resolution is required. However, their data showed that when the same annealing (950 oC for 10 minutes) and doping dose (5x1014 cm-2) are applied single crystal piezoresistor silicon had a lower Hooge parameter (5.7x10-6) than amorphous (1.3x10-3) and microcrystalline silicon (1.8x10-3) piezoresistors. Gabrielson [11] presented limiting factors in miniature acoustic and vibration sensors. In addition to an analysis of the mechanical-thermal noise, he discussed other noise in sensors (shot noise, 1/f noise, preamplifier noise, Johnson noise and optical noise). Gabrielson proposed two techniques: one based on the frequency response of the system or another based on a circuit simulation to estimate the noise of the sensor. In the latter, an equivalent circuit representation of the mechanical system was used. Thus, electrical and mechanical noise contributions were both evaluated. In demonstrating the presence of a pure 1/f noise in the membrane motion of condenser microphones and its effect on different microphones sizes, Zuckerwar and Ngo [12] separated the membrane noise from the pre-amplifier noise. The microphone noise was measured in an acoustic isolation vessel to keep the microphones at constant room temperature and pressure. Zuckerwar and Ngo [12] provided a formula of the power spectral density of the preamplifier output using a small circuit model of the measurement setup (condenser microphone and pre-amplifier). Based on that formula, Zuckerwar and Ngo extracted the membrane noise by subtracting the preamplifier noise power, obtained when no external voltage was applied across the capacitor, from the total
8 noise power output of the pre-amplifier, when an external power supply was used to apply a voltage between the capacitor membrane and back plate. The electromechanical coupling is zero when no external voltage is applied to the capacitor’s plates. Based on a plot illustrating the noise due to the membrane motion, the authors indicated the presence of a 1/f noise in the membrane motion in the frequency range over which the 1/f noise is dominant. From their experimental results, Zuckerwar and Ngo suggested that theories of 1/f noise in the electrical domain could be extended to the mechanical domain. In their most recent publication, Zuckerwar et al. [4] focused their background noise studies on piezoresistive, electret condenser, and ceramic microphones for which they provided small circuit representations of the noise in the microphone. In addition to the well-known noise mechanisms present in piezoresistive microphone (mechanical thermal noise, Johnson noise, and electrical 1/f noise), Zuckerwar et al. included a mechanical 1/f noise, which they said is correlated to the diaphragm damping resistance. Vandamme and Ooterhoff [13] supported the theory that 1/f noise is a bulk phenomenon and computed the Hooge factor on ion-implanted resistors with different annealing steps. Their results showed that high temperature annealing helped to reduce the Hooge factor, therefore the 1/f noise. They attributed the decrease of 1/f noise to the reduction of defects caused by high temperatures annealing. Belier et al. [14] showed methods such as preamorphization and annealing to fabricate piezoresistors for NanoElectroMechanical systems (NEMS) applications. The piezoresistors were employed in the fabrication of a piezoresistive cantilever. Measurements of the 1/f noise on boron fluorine (BF2) implanted piezoresistive cantilevers with and without
9 germanium preamorphization have been conducted. The results revealed lower 1/f noise on the samples with germanium preamorphization. Objectives and Outline Today, the relevance of noise sources for pressure sensors is worth discussing since sensor fabrication technology and applications fields face more challenges in terms of resolution, sensitivity, bandwidth and operation. In the previous section, various hypothesis and measurements are provided by authors to describe the limiting factors in pressure sensors. Harley and Kenny et al. [1], in their study of noise in piezoresistive cantilevers, which could be extended to piezoresistive microphones, found that electrical 1/f noise is the dominant noise factor among other noise sources such as thermal noise. Barabash and Cobbold [2] postulated from their investigation that the Brownian noise dominated the Johnson noise, and therefore was a limiting factor in the silicon pressure transducers. Chau and Wise [9] concluded otherwise since their study suggested that Brownian noise level was less significant than the thermal noise, kT/C noise and circuit noise; therefore Brownian noise was not a factor that could prevent further miniaturization and sensitivity improvement of solid-state pressure sensors. Zuckerwar and colleagues’ challenge [4] was based on proving the presence of a purely 1/f mechanical noise in the membrane motion of the pressure sensor and the frequency over which it was dominant. Depending on the bandwidth, piezoresistor fabrication process, and sensor dimension, the type of noise that limits the sensor performance can vary. However, the relative presence and importance of some noise sources such as the one proposed by Zuckerwar et al. need a particular attention. Different authors have suggested various noise sources that limit the sensors performance. One needs to find whether the dominant noise source is electrical or
10 mechanical of origin. This is important because when designing sensors with low minimum detectable signal, noise level must be considered. We investigate the mechanical and electrical noise sources in MEMS piezoresistive microphone using two commercial piezoresistive pressure sensors: Kulite (MIC -093) and Endevco (8510B-1) and two UF microphones: UF piezoresistive microphone [15, 16] and UF proximity sensor [17].
CHAPTER 2 NOISE IN PIEZORESISTIVE MEMS MICROPHONES Noise in MEMS sensors originates from different sources. The importance of understanding their origin helps in the design criteria to improve the noise performance and hence the fabrication of sensors with better signal to noise ratio and minimum detectable signal. The fundamental noise mechanisms that potentially limit the performance of the piezoresistive MEMS sensors are thermo-mechanical noise, Johnson noise, 1/f noise, and shot noise. Noise and Noise Power Spectral Density Noise can be described as unwanted signals (acoustic, electrical) that contaminate the desired signal. In the electrical domain, unwanted signals interfering with the desired signal can originate from the environment (electromagnetic interference) or from the electronic device itself via current or voltage fluctuations. These undesired signals can be large enough to obscure the desired signal thus impeding its measurement. Techniques to separate the signal of interest from external deterministic interferences include shielding and proper wiring. However, intrinsic non-deterministic noise that originates from the device cannot be avoided via shielding or proper wiring. Assuming proper shielding, the intrinsic non-deterministic noise limits the lower part of the dynamic range of a device. Since noise is a random process, analyzing it in the time domain does not give useful information regarding its average magnitude. Therefore, we employ the power spectral density function, which gives the magnitude of the random signal squared over a range of
11
12 frequencies for noise measurements. Power spectral density function as described by Bendat and Piersol [18] is given in Equation 2-1. Ψ 2x ( f , ∆f ) ∆f → 0 ∆f
Gx = lim
(2-1)
T
1 2 x ( t , f , ∆f )dt is the mean square value of a sample time T →∞ T ∫ 0
where Ψ 2x ( f , ∆f ) = lim
record between frequencies f and f + ∆f . Noise Sources Noise in semiconductor MEMS sensors is affected by various parameters such as conductivity, defect density, temperature, doping concentration, and bias voltage. With zero applied bias voltage and no external stimuli (light, thermal gradient) the semiconductor is in equilibrium and its properties remain constant independent of time. However, when bias or stimuli are applied, the semiconductor properties are no longer constant, and the system is said to be in non-equilibrium. Noise in MEMS sensors can be classified as equilibrium and non-equilibrium noise. Solid-state materials can be divided in three major groups: conductors such as aluminum, semiconductors such as silicon (elemental semiconductor) and gallium arsenide (compound semiconductor), and insulators such as SiO2. Conductors have low resistance. Their conductivity is on the order of 1x104 S/cm or higher. However, insulators have very high resistance with conductivities on the order of 1x10-8 S/cm or lower. Semiconductors are materials with conductivities lying between those of the insulators and the conductors (1x10-8 and 1x104 S/cm). Doping, temperature, and exposure to light can change the conductivity of semiconductor materials, rendering it
13 very attractive for electronic devices and transducers. Noises present in silicon semiconductors based MEMS microphones are presented next. Thermal Noise Johnson noise describes voltage fluctuations at the terminal of a conductor or semiconductor at equilibrium. These fluctuations are caused by the random vibrations of charge carriers in equilibrium with the lattice at temperature, T. Work by Nyquist [19] and Johnson [20] led to the expression of the thermal noise power spectral density given in Equation 2-2. Sth = 4 K B RT
⎡V 2 ⎤ ⎢⎣ Hz ⎥⎦
(2-2)
where kB is the Boltzmann constant, R is the resistance, and T is the temperature in Kelvin. Electrical thermal noise is independent of bias voltage since the agitation of the charge carriers by thermal lattice vibrations is present regardless of bias voltage. However, an increase in the temperature induces more agitation of the carriers, hence making the Johnson noise temperature dependent. Furthermore, Johnson noise frequency independent because lattice vibrations are random, thus not related to any single time constants. Mechanical thermal noise is the mechanical analogue of electrical thermal noise. By the fluctuation-dissipation theorem, any dissipative mechanism that results in mechanical damping must be balanced by a fluctuation force to maintain macroscopic energy balance, hence thermal equilibrium. In analogy with Equation 2-2, mechanical thermal noise is given in Equation 2-3.
14 S mth = 4 K B RmT
⎡N 2 ⎤ ⎢⎣ Hz ⎥⎦
(2-3)
where Rm is the equivalent mechanical resistance of the sensor. Low Frequency Noise Low Frequency noise is a frequency dependent non-equilibrium noise, which is predominant at lower frequencies. It is also known as1/f noise. The mechanism that generates 1/f noise is still an active area of research. Two widely discussed mechanisms of 1/f noise are the fluctuation in the mobility (∆µ) described by Hooge [21] and the fluctuation in the number of carriers (∆n) developed by McWhorter [22]. Hooge’s model Hooge [21] originally conducted experiments on noise in homogeneous samples at low frequency, which has an inverse frequency dependence (or 1/f). He suggested that this 1/f noise at low frequency is a bulk phenomenon [21] and is due to fluctuations in the mobility (∆µ)[23-25]. He gave an empirical formula for the noise power spectral density of 1/f noise in his publications [21] as illustrated in Equation 2-4.
SV =
αV 2 Nf
⎡V 2 ⎤ ⎣⎢ Hz ⎦⎥
(2-4)
Here α is an empirical material parameter varying from 1x10-6 to 1x10-3, V is the bias voltage, N is the number of carriers and f is the frequency. Hooge’s equation indicates a square bias voltage dependence for the low frequency noise. Thus, this noise mechanism is only present when a voltage is applied (for example, when a piezoresistive semiconductor MEMS microphone is biased). In addition, the noise power spectral density is inversely proportional to number of carriers
15 N. Thus, the low frequency noise depends on the doping concentration Ndoping and constant volume V, since N=Ndoping*V. McWhorter’s model McWhorter [22] conducted his experiments on germanium filaments and argued that 1/f noise is a surface effect. At the semiconductor surfaces and interfaces, physical defects give rise to electronic traps that capture and emit charge. He postulated that 1/f noise is caused by fluctuations of the number of charge carriers, due to trapping and detrapping of charge carriers at these traps. The difference between 1/f noise proposed by Hooge and McWhorter is illustrated via the resistance fluctuations in a p-type resistor. Hooge [21] gives a spectral power density of the fluctuation in the resistance R as shown in Equation 2-5. SR α = 2 R Nf
(2-5)
where S R is the noise power spectral density, α is a dimensionless parameter, f is the frequency, and N is the number of carriers. In a linear system, Ohm’s Law, V = R * I , holds and one can extend Equation 2-5 to Equation 2-6 shown below. S R SV S I α = 2 = 2 = 2 R V I Nf
(2-6)
In a p-type resistor (p>>n) with length l, width w and thickness t, the resistance R is R=
ρl wt
[Ω]
(2-7)
16 Here the resistivity ρ of a p-type resistor is expressed as ρ =
1
σ
≈
1
σp
=
1 qµ p p
where σ
is the conductivity, q is the charge of the carrier, µ p is the hole mobility, and p is the hole concentration. Thus, Equation 2-7 can be expressed in terms of mobility and hole concentration as shown in Equation 2-8.
l qwt µ p p
[ Ω]
(2-8)
∆µ p ∆ p ∆R =− − R µp p
(2-9)
R=
Fluctuations in ∆R is expressed in Equation 2-9. ∆R =
∂R ∂R ∆µ p + ∆p ∂µ p ∂p
=− =−
l l ∆µ p − ∆p 2 qwt µ p p qwt µ p p 2 R
µp
∆µ p −
R ∆p p
and
where ∆µ p is the fluctuation in mobility and ∆p is the fluctuation in the carrier concentration. It is seen that fluctuations in R may be caused by fluctuations in µp, p or both under bias conditions. The fluctuations in mobility can be explained as follows. The time interval between two successive hole collisions is called the relaxation time or mean free transit time and is denoted by τ. This relaxation time is determined by lattice and
17 impurity scattering. The mobility µp is related to the relaxation time τ as described in Equation 2-10.
µp =
q〈τ 〉 mp
(2-10)
where mp is the hole effective mass, q is the charge of the carrier, and is the average relaxation time. Therefore, fluctuations in induce fluctuations in µp as shown in Equation 2-11.
∆µ p =
q∆〈τ 〉 mp
(2-11)
Under applied voltage bias, carriers drift in the resulting electric field giving rise to a current I. This current is related to the mobility as shown in Equation 2-12 for a p-type semiconductor resistor.
I pdrift = qµ p pε A
(2-12)
where ε is the electric field, and A is the cross-sectional area of the resistor. Thus, from Equation 2-12, one sees that fluctuations in the current I pdrift are induced by fluctuations in the mobility ∆µ p , which is in turn related to fluctuations in the relaxation time ∆〈τ 〉 as shown in Equation 2-11. These time dependent fluctuations give rise to 1/f noise. The other possible source of 1/f noise is fluctuation in the number of carriers as proposed by McWhorter [22]. The Lorentzian generation-recombination spectrum resulting from the trapping and detrapping of the charges carriers at trap levels is given in Equation 2-13 [26].
18 SGR ( f ) = AGR
τt 2 1 + ( 2π f τ t )
(2-13)
where AGR is proportional to the density of the trap levels, and τ t is the tunneling time constant. Figure 2-1 describes the energy band diagram with two trap levels and their
E
I(t)=qµn
n
-
-
eAn(t)
-
Log PSD (V2 /Hz)
associated Lorentzian spectra with a corner frequency at f 3dB =
1 2πτ
.
1/f g-r 2
-
-
EC
g-r 1
g r ET1
Thermal noise
E T2
A
f3dB
f3dB
Log f (Hz)
B
Figure 2-1. Trapping-detrapping model for 1/f noise. A) Energy band diagram of trapping and detrapping at two trap levels, B) Lorentzian spectrum of two trap levels in comparison with thermal noise. Since electrons located in trap centers far from the conduction band require more energy for generation-recombination to occur, τ is larger for deeper trap centers than shallow trap centers as illustrated in Figure 2-1. Summing the noise power spectral densities for a continuum of trap levels, we observe the 1/f noise shape up to the cut off frequency where the curve rolls off as 1/f2. The 1/f noise observed at low frequency is caused by the fluctuation in the number carrier in the conduction band due to trapping and detrapping of carriers located at multiple trap levels. Both Hooge’s and McWhorter’s 1/f noise models are actively used for low frequency noise measurement in electronic devices [1, 10, 27].
19 However, since Hooge’s model describes the low frequency noise though parameters (voltage, number of carrier, Hooge parameter) that are easily manipulated during process fabrication or measurement of the electronic device, it is very attractive for analysis. Designers can reduce the low frequency noise by adjusting or modifying these parameters. The validation of the Hooge model can be verified experimentally. First, one observes that the noise power spectral density decays as the frequency increases. Second, a graph of the noise power spectral density at a particular frequency versus the applied voltage shows a voltage square dependence. In addition, for noise optimization purposes, the extraction of the Hooge parameter α gives insight into the process fabrication quality (defects density). Moreover, via simulation, one can choose the doping concentration and resistor volume to reduce the 1/f noise through the number of carrier while maintain good sensitivity (for example in MEMS piezoresistive microphones). Later in this thesis, we use Hooge’s model to analyze the measured noise power spectral densities and to verify whether the origin of the observed low frequency noise is electrical or mechanical in the MEMS piezoresistive microphone. Shot Noise Schottky [28] investigated noise in vacuum tubes. He discovered a fundamental noise mechanism arising from random emission of electrons from the cathode to the anode which is termed shot noise. In a semiconductor, when charge carriers cross a potential barrier independently and randomly, fluctuations occur in the average current I. These fluctuations give rise to shot noise which is a non-equilibrium noise. In particular, shot noise is observed in a p/n junction due to the fluctuations in the average current I induced by the random crossing
20 of carriers over a potential barrier. The shot noise power spectral density is given in Equation 2-14. S I = 2qI
⎡ A2 ⎤ ⎢⎣ Hz ⎥⎦
(2-14)
where q is the electron charge and I is the current. Equation 2-14 shows that shot noise is directly proportional to the average current I, hence is only present under bias conditions, and is frequency independent. Piezoresistive Microphone The transduction mechanism of the MEMS piezoresistive microphone is based on converting acoustic energy into electrical energy. When pressure is applied to the microphone, the diaphragm deflects producing a change in the resistance of the four piezoresistors configured in a Wheatstone bridge as shown in Figure 2-2 and located at the diaphragm edge where the stress is maximum. The change is the resistance is due to a property of material known as piezoresistivity. Information on piezoresistivity is provided in the Appendix. Two piezoresistors are positioned to sense the stress parallel to the current flow while the other two are placed to sense the stress perpendicular to the current flow. The Wheatstone bridge provides a null voltage across the bridge at zero pressure, Vout = 0 , when the bridge is balanced, i.e. R1 = R2 = R3 = R4 . When there is pressure incident on the microphone, the diaphragm deflects producing equal absolute value resistance change across the four piezoresistors. The resistance change in R1 and R3 have opposite signs to that of R2 and R4 . These resistance change produce a differential output voltage Vout = V1 − V2 across the bridge, where V1 and V2 are equal in magnitude but have opposite signs.
21
Figure 2-2. Piezoresistors configured in Wheatstone bridge. Top and cross-sectional views of a UF piezoresistive microphone are shown respectively in Figure 2-3 and 2-4 [16]. Bond Pad (250 µm x 250 µm)
Arc Resistor
Diaphragm (1 mm x 1 µm) Vent Channel (10µ m x 10µ m x 9.5 mm)
Taper Resistor
Figure 2-3. Top view of a UF piezoresistive microphone [16]. p+ Silicon
)
Nitride (2000 Å)
(1x1020 cm-3
Oxide (550 Å)
Aluminum (1 µm)
Nitride (1 µm)
n-Si
Figure 2-4. Cross-section of a UF piezoresistive microphone [16].
Oxide (7000 Å)
22 Details of the design of this piezoresistive microphone are presented by Saini [15]. In this analysis, it is assumed that the four piezoresistors of the Wheatstone bridge have equal unstressed resistance, thus we have a balanced bridge at zero applied pressure. MEMS Piezoresistive Microphone Voltage Output When pressure or force is applied to the microphone’s membrane, it induces stress and resulting strain on the membrane. These physical phenomena, stress and strain, have an impact on the piezoresistors located at the edge of the membrane where the stress is maximum. Strain is the change per unit length of the piezoresistors and is expressed as shown in Equation 2-15.
ε=
∆L L
(2-15)
where ∆L is the change in the original length of the piezoresistor and L is the original length of the resistor. The strain sensitivity, which is called the gauge factor G0, is expressed as shown in Equation 2-16. G0 =
( ∆R
R0 )
ε
(2-16)
where ∆R is the chance of resistance R and ε is the strain. The resistance of a semiconductor resistor is given in Equation 2-17. R=ρ
l wt
(2-17)
where ρ is the resistivity, and l , w and t are respectively the length, width and thickness of the resistor. The expression
∆R is obtained by differentiating Equation 2-17 and dividing the R
23 resulting expression by the resistance R as illustrated in Equation 2-18. ∆R ∆ρ ∆l ∆w ∆t = + − − R ρ l w t
(2-18)
Using the Poisson’s ratio, the strain sensitivity G becomes
G=
∆R
ε
∆ρ R = (1 + 2υ ) +
ρ
(2-19)
ε
In Equation 2-19, (1 + 2υ ) is due to the geometry change and
∆ρ
ρ
is due to the
piezoresistive effect. For metal, the piezoresistive effect is negligible and therefore the gauge factor can be expressed in term of its geometrical change only as shown in Equation 2-20. G=
∆R
ε
R = (1 + 2υ )
(2-20)
Since υ is less than 0.5, G for metal is about two. For semiconductor, the gauge factor, G, is dominated by the piezoresistive effect
∆ρ
ρ
and can have a magnitude in the range
of 100. The expression of sensor output voltage ∆Vout given in Equation 2-21 describes a linear relation between the input pressure on the membrane of the microphone and the output voltage of the Wheatstone bridge configuration. ∆Vout = G0εVbias
(2-21)
Using Equation 2-19, we express the bridge output voltage ∆Vout in terms of the change in resistance ∆R , the resistance R and the bias voltage Vbias. ∆Vout =
∆R Vbias R
(2-22)
24 Hence with application of an external bias the piezoresistive microphone provides a linear output voltage related with resistance change. If a mechanical transfer function relating ∆R to pressure is linear, then a linear acoustic transducer is achieved. MEMS Piezoresistive Microphone Sensitivity The sensitivity of a MEMS piezoresistive microphone is given by the ratio of the output voltage to the input pressure. The normalized sensitivity, which is the sensitivity divided by the bias voltage is shown in Equation 2-23. 1 Vout 1 ∆Vout 1 ∆R S= ≈ = Vbias p Vbias p R p
(2-23)
where Vbias is the voltage applied to the microphone, ∆Vout is the differential output voltage, and ∆R is the resistance modulation of the piezoresistor. In the next chapter, the experimental setup for careful noise measurement is discussed. Noise measurement on the UF piezoresistive microphone and three other sensors: UF proximity sensor, Endevco piezoresistive microphone and Kulite piezoresistive microphone will be discussed in Chapter 4. Table 2-1. Manufacturers’ specifications for Endevco piezoresistive and Kulite piezoresistive microphones Parameters Endevco Kulite Maximum voltage (V) 18 15 Input impedance (Ω) 2060 3112* Output impedance (Ω) 1832 1152 Sensitivity (µV/Pa) 26.9 4.3 *Input impedance of Kulite microphone with a temperature compensation module.
CHAPTER 3 EXPERIMENTAL NOISE SETUP In this chapter, we will explore experimental setup techniques to accurately measure noise power spectral density of a device under test. To reach our goal stated above, we justify the use of three Faraday cages, show the effect of ground loops, evaluate the noise levels when biasing the device under test with different types of voltage supply, determine the setup noise, and extract the noise of the device under test. The equipment used for the measurement are: three Faraday cages, low noise preamplifiers(SRS 560 and Brookdeal 5004), a dynamic signal analyzer (SRS 785), lead acid batteries, standard AA batteries, line-powered regulated power supply, metal film resistors, double shielded coaxial cables (RG-223/U), and BNC connectors. Shielding To reduce signal contamination from non-intrinsic noise sources, such as radio signals (AM, FM, Radar) at high frequencies, and power line interference at 60 Hertz and harmonics, shielding is necessary. It is accomplished by enclosing the equipment inside a Faraday cage, which is a conducting material box of sufficient thickness, to attenuate the electromagnetic radiation. The latter results from the combination of both electric and magnetic fields. Electrical current is produced in a conductor inductively through a time-varying magnetic field or capacitively via an electric field. Michael Faraday demonstrated in 1836 that charges are located on the outside surface rather than the interior of a conductor. This discovery is the reason why metal
25
26 boxes are used as shielding devices. However, each material has a penetration distance of electromagnetic radiation called the skin depth as shown in Equation 3-1.
δ=
c 2πσµω
(3-1)
where c is the speed of light, σ is the electrical conductivity, µ is the permeability, and ω is the angular frequency. At low frequency, the skin depth is larger, therefore shielding becomes more difficult. In our measurement setup, we covered our boxes with magnetic shielding foils [29] to improve the shielding capacity. For instance, at 10 Hz, the permeability of the magnetic shielding foil is 10,000. A plot illustrating the permeability versus frequency of the shielding foil and the material specification are given in [29]. From manufacturer’s specification sheet, the chemical composition of the magnetic shielding foils is nickel (80%), iron (15%), molybdenum (5%) and small amounts of sulfur, carbon, manganese, silicon, and phosphorous, and its thickness is 104.14 µm. The effect of three successively enclosed Faraday cages is shown by plotting the power spectral density of a device under test, showing the decrease in the electromagnetic interference pick up with increase in number of Faraday cage. We used three thin Faraday cages because it is easier to fabricate and implement than one thick Faraday cage. We provide three noise power spectral densities of the UF microphone when one, two and three shielded boxes are used. The microphone is biased at three volts with a lead acid battery and metal film resistors in an implementation of a voltage divider. The effects of one, two, and three Faraday cages are shown and compared in Figures 3-l, 3-2 and 3-3. Note that the curves are shown
27 separately to allow comparison of the magnitude of the interference peaks. When one Faraday is used, the power spectral density of the UF microphone is shown in Figure 3-1. 1.E-10 1.E-11
2
Sv (V /Hz)
1.E-12 1.E-13 1.E-14 1.E-15 1.E-16 1.E-17 1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-1. PSD of UF microphone at 3 V shielded with one Faraday cage. In Figure 3-1, one can observe a poor shielding. The 60 Hz harmonics are present up to 1 kHz. Better shielding is necessary to minimize the interferences. A similar measurement as the one above is performed except that in this case, we use two Faraday cages instead of one. Figure 3-2 shows the result of the experiment. The 60 Hz harmonics have decreased in number and their magnitudes lowered. In this case, we note that the low noise amplifier has been shielded along with the device under test. 1.E-10 1.E-11
2
Sv (V /Hz)
1.E-12 1.E-13 1.E-14 1.E-15 1.E-16 1.E-17 1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-2. PSD of UF microphone at 3 V shielded with two Faraday cages.
28 One can obtain a cleaner power spectral density by using three Faraday cages in Figure 3-3. Such experiment is performed under the same conditions as the previous measurements. 1.E-10 1.E-11
2
Sv (V /Hz)
1.E-12 1.E-13 1.E-14 1.E-15 1.E-16 1.E-17 1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-3. PSD of UF microphone at 3 V shielded with three Faraday cages. Using three Faraday cages, we observe a single peak at 60 Hz, with magnitude lower than the previous measurements. Table 3.1 summarizes the noise power spectral density at 60, 120 and 180 Hz when the measurement is conducted with one, two and three faraday cages. Table 3-1. Noise power spectral density at 60, 120 and 180 Hz with one, two and three faraday cages Number of Faraday PSD at 60 Hz PSD at 120 Hz PSD at 180 Hz cages (V2/Hz) (V2/Hz) (V2/Hz) 1 1.86E-11 5.63E-12 1.18E-13 2 1.50E-13 2.71E-15 4.31E-15 3 1.96E-14 1.59E-15 1.00E-15 From Table 3-1, one observes a drop in noise power spectral densities at 60, 120 and 180 Hz as the number of Faraday cages increases. Good shielding could also have been obtained with only one Faraday that has a shielding capacity equal to or higher than the three cages used in our experiment combined.
29 Now that we have a technique for proper shielding of the device under test, we will explore the effect of grounding. Wiring System To prevent electromagnetic contamination of noise measurement, one should pay particular attention to the wiring system of the setup. Bad wiring system can contribute to the enhancement of signal contamination by external noise sources. Two examples of bad wiring systems are ground loop and having no ground at all. In both cases, the 60 Hz interference is significant. In addition to the unclean power spectrum obtained when no ground connection is used, the latter constitutes a safety issue. Electrocution can result since during an electrical fault there is no path for the current to flow to ground. Usually, one ground connection is optimal. Figure 3-4 shows noise power spectral densities of the UF microphone at the same voltage bias when ground loop, floating equipment and one ground connection are implemented. 1.E-10
2
Sv (V /Hz)
1.E-11 Ground loop and Floating equipments
1.E-12 1.E-13 1.E-14
Single ground
1.E-15 1.E-16 1.E-17 1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-4. Power spectral densities of UF microphone at the same voltage bias with ground loop, floating equipments and one ground connection. In the figure above, we cannot clearly differentiate the ground loop plot to the no ground and one ground plot since their spectral densities overlap. However, there are differences in electromagnetic contaminations. Separate plots will be provided for
30 clarification. To investigate the effect of a ground loop, long power lines (~ 12 m) connected at different building outlets are used to power the equipments. In addition, a long single shielded BNC (~ 0.61 m) connected the device output to the low-noise amplifier and the spectrum analyzer. In this setup, we use the best shielding obtained from the last section, three Faraday cages, and a lead acid battery provides the bias voltage through a network of metal film resistors used in the voltage divider. The resulting noise power spectral density of this setup is shown in Figure 3-5. 1.E-10
2
Sv (V /Hz)
1.E-11 1.E-12 1.E-13 1.E-14 1.E-15 1.E-16 1.E-17 1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-5. Power spectral density of UF microphone with ground loop. In the ground loop figure, one observes power line harmonic peaks at discrete frequencies in multiples of 60 Hz up to 2 kHz and also leakage at certain frequencies. According to Faraday’s Law, the change in the magnetic flux in a coil of wire will induce a voltage within the coil of wire. This mechanism takes place in the setup from which Figure 3-5 has been measured. In fact, a changing AC field, originated from the power line, gives rise to potentials at multiple points in the BNC cables (~ 0.61 m) between the various building ground connections. Next, the effect of floating all the equipments is shown in Figure 3-6. In this case, power line harmonics are also seen. Even though there is no ground connection for all
31 the equipment, the external noise picked up by the long power lines and exterior surface of the Faraday cages contaminate the signal. 1.E-10
2
Sv (V /Hz)
1.E-11 1.E-12 1.E-13 1.E-14 1.E-15 1.E-16 1.E-17 1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-6. Power spectral density of UF microphone with floating equipments. To reduce noise contamination due to the environment, we use one ground connection, short power lines (~ 1.27 m) and BNC cables (~ 0.15 m) along with the three Faraday cages. The result of such a setup is illustrated in Figure 3-7. 1.E-10
2
Sv(V /Hz)
1.E-11 1.E-12 1.E-13 1.E-14 1.E-15 1.E-16 1.E-17 1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-7. Power spectral density of UF microphone with one ground connection. In the plot above, most of the 60 Hz and harmonic interference frequency peaks are no longer present and the remaining are reduced. This is because there is no ground loop, therefore a reduction of the 60 Hz magnetic coupling, and most of the electromagnetic interference not blocked by the Faraday cage is terminated at one single ground point. The suppression of ground loop constitutes a major effect in the cleanness
32 of the signal. The difficulty to completely suppress the 60 Hz interference at low frequency comes from the fact that the skin depth is larger in that range, therefore penetration of electromagnetic radiation in the conductor takes place. Therefore, the wiring system is important when performing noise measurements. It is important to make the proper choice of short and shielded cable while using a Faraday cage to shield the device under test against extrinsic noise sources. It is also important to provide a path to a single ground point to avoid ground loops and to limit risk of electrocution. Voltage Supply The choice of voltage supply used when performing noise measurement of a device is important. The voltage supply can add noise to the measurement. To illustrate the above statement, noise measurements were performed on a UF piezoresistive microphone at 2.64 Volt bias for three sources: (1) a line-powered regulated power supply, (2) zinc/carbon, and (3) lead acid batteries as shown in Figure 3-8. One can realize from the plot that using a line-powered power supply introduces significant electromagnetic interference. The power spectral densities obtained using zinc/carbon and lead acid batteries show less 60 Hz harmonics contaminations. Since it is difficult to distinguish them when plotted together, separate plots of all the measurements will be given for clarification of the data. When a line-powered power supply is used to bias the UF microphone, the resulting plot reveals the presence of strong 60 Hz harmonics even at high frequencies. This is due to the fact that the power supply connected to the 60 Hz line power of the building magnetically couple the 60 Hz fundamental and harmonics through an internal transformer.
33 1.E-09 1.E-10
2
Sv( V /Hz)
1.E-11 1.E-12 1.E-13 1.E-14
Power supply
1.E-15 1.E-16 1.E-17 1.E+01
Zinc/carbon and lead acid battery 1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-8. UF microphone biased with a power supply, zinc/carbon and lead acid batteries. In addition, multiple grounds arise from the fact that there are two ground points, one for the spectrum analyzer and a separate one for the power supply. One could operate the power supply in floating mode to obtain one single ground point from the spectrum analyzer. However, in that setup not only is there safety implications, but also the 60 Hz power line still contaminates the signal with 60 Hz and harmonic frequencies. Therefore, no improvement in the power spectral density is observed. Figure 3-9 shows a plot of the noise power spectral density when a line-powered power supply is used as the bias voltage. To reduce 60 Hz power line interference contamination, batteries may be used as the bias voltage. However, the choice of battery plays an important role in the noise level. Plots of power spectral densities at 2.64 volts using zinc/carbon and lead acid batteries are presented in Figures 3-10 and 3-11 respectively. Although both batteries types help reduce noise contamination, the lead acid battery is a better choice between the two since carrier trapping/detrapping is less dominant in the liquid (lead acid battery) than in the granular solid (Zinc/carbon battery). In addition, two advantages of using a lead acid battery are the larger capacity (long lasting) and the capability to recharge since noise measurements can be lengthy in time,
34 usually when the binwidth is very small and the number of averages large for better accuracy and require a reliable source of power. In fact, the resistance of a decaying battery increases, thus is likely to add noise into the signal. 1.E-09 1.E-10
2
Sv ( V /Hz)
1.E-11 1.E-12 1.E-13 1.E-14 1.E-15 1.E-16 1.E-17 1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-9. UF piezoresistive microphone biased at 2.64 Volt with a power supply. 1.E-09 1.E-10
2
Sv( V /Hz)
1.E-11 1.E-12 1.E-13 1.E-14 1.E-15 1.E-16 1.E-17 1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-10. UF piezoresistive microphone biased at 2.64 Volt with zinc/carbon battery. Using the results obtained from investigating shielding, wiring system and bias supply, we are confident on the necessary techniques for proper noise measurement. In the next section, in addition to the equipment setup, the internal settings of the low-noise amplifiers and spectrum analyzer are provided.
35 1.E-09 1.E-10
2
Sv ( V /Hz)
1.E-11 1.E-12 1.E-13 1.E-14 1.E-15 1.E-16 1.E-17 1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-11. UF piezoresistive microphone biased at 2.64 Volt with lead acid battery. Setup Noise In this section, we evaluate the setup noise. The setup noise power spectral density will be subtracted from the total power spectral density measured for the device under test. The preamplifier and spectrum analyzer setup noise will be given along with the bias voltage and detailed diagrams of the equipment setup. The setup noise is the contribution to the measured noise by the equipment used during the measurement. We measure both the current and voltage noise power spectral densities of the setup. In these measurements, the pre-amplifier and the spectrum analyzer are configured as shown in Table 3-2 and Table 3-3. The coupling is set to AC because we are interested in the time-varying signal. The differential inputs A-B allow the measurement of the microphone output voltage. If single ended input was used, then one of the output signals would have been set to ground. In addition, increased dynamic range is provided by the differential mode due to improved common mode noise rejection. When the SRS 560 is used during measurement, the filter is set as a band pass filter with lower and higher limits at 0.03 Hz and 300 KHz with ± 6 dB/octave roll off.
36 Table 3-2. Pre-amplifier settings Parameters SRS 560 Coupling AC Inputs A-B Bandwidth 0.03 Hz – 300 KHz Gain 1000 Input 100 MΩ, 25 pF Output 50 Ω
Brookdeal 5004 AC A-B 0.5 Hz – 1 MHz 1000 5MΩ, 50 pF 1 KΩ
The gain is set to 1000 ensuring that the output signal of the preamplifier is higher that the noise floor of the spectrum analyzer allowing accurate noise measurement. The input and output impedance of the pre-amplifiers are specified by the manufacturers. They are relevant to the analysis of the current and voltage setup noise, as we will see later in this section. The setup of the spectrum analyzer is illustrated in Table 3-3 below. The coupling is set to AC since we are interested in small signal fluctuation. In the spectrum analyzer, the single-ended input A is chosen. A Hanning window is selected for the measurement of the random signal because it provides good selectivity and reduces power spectral density leakage. A list of spans, FFT lines and bin widths is given in Table 3-3. The power spectral density is obtained by overlapping the measurements of the different spans. At low frequencies, the binwidth is smaller to ensure better frequency resolution and therefore good accuracy of the measurements. The first 10% of each measurement span are truncated to minimize error due to leakage at the lowest frequencies since the digital window filter, Hanning, is not infinitely sharp. Multiple such spans are overlapped to obtain the overall power spectral density. LabView is used to automate the measurements. The amplifier used in the remaining section to illustrate the setup noise is the SRS 560. The same principle may be applied to the Brookdeal amplifier.
37 Table 3-3. Spectrum analyzer setting Parameters Settings Coupling AC AC Input A A Window Hanning Hanning Span (Hz) 100 400 FFT Lines 800 800 Binwidth (Hz) 0.125 0.5 Averages 1700 5000
AC A Hanning 1600 800 2 10000
AC A Hanning 12800 800 16 30000
The small signal representation of an amplifier is shown in Figure 3-12. The amplifier noise model consists of input referred noise sources represented as voltage and current noise sources and an ideal noise-free amplifier. The input impedance of the amplifier is represented as Zin described in Figure 3-12.
Sva Spectrum Analyzer (SR785)
Pre-Amp (SR560)
Sia
Zin
G
Figure 3-12. Small signal representation of the setup noise. The voltage noise source Sva of the pre-amplifier, given by Equation 3-2, is obtained by shorting the input of the pre-amplifier, which allows the cancellation of Sia. In this case, the source resistance seen by the input of the pre-amplifier is very low (RS→0). The resistance measured at the input is 0.26 Ω. Figure 3-13 shows the voltage noise power spectral density measurement setup. Sva =
Svout G2
⎡V 2 ⎤ ⎢⎣ Hz ⎥⎦
(3-2)
38 Shielded Box
Shielded Box
A
Pre-Amp (SR560)
Spectrum A Analyzer (SR785)
B
Chassis
Computer (LabView)
AC Out
AC Out
Figure 3-13. Noise voltage power spectral density measurement setup. The voltage power spectral density measured is shown in Figure 3.14.
1.E-15
2
Sv (V /Hz)
1.E-14
1.E-16
1.E-17 1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-14. Voltage noise power spectral density of setup. To measure the current noise power spectral density of the setup, the input of the pre-amplifier is open circuited. This permits cancellation of the voltage noise source Sva, allowing measurement of only the current power spectral density Sia. The setup of this experiment is shown in Figure 3-15. The source resistance for the open-circuit case seen by the input of the amplifier is infinite. Equation 3-3 gives the current noise power spectral density.
39 Sia =
Svout S = iout2 2 2 RinG G
⎡ A2 ⎤ ⎣⎢ Hz ⎦⎥
(3-3)
where Svout is the measured voltage noise power spectral density, Rin is the input impedance of the pre-amplifier, and G is the gain of the pre-amplifier. The measured current power spectral density is shown in Figure 3-16. Shielded Box
Shielded Box
A
Pre-Amp (SR560)
Spectrum A Analyzer (SR785)
B
Chassis
Computer (LabView)
AC Out
AC Out
Figure 3-15. Noise current power spectral density measurement setup.
1.E-31
2
Si (A /Hz)
1.E-30
1.E-32
1.E-33 1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-16. Current noise power spectral density of setup. The experimental setup with a 1 kΩ metal film resistor as source resistance is shown in Figure 3-17.
40 Shielded Box
Shielded Box
Shielded Box
A
Rmfr
Pre-Amp (SR560)
A
B
Spectrum Analyzer (SR785)
Chassis
Computer (LabView)
AC Out
AC Out
Figure 3-17. Experimental setup for a 1 kΩ metal film resistor. The noise equivalent circuit corresponding to Figure 3-17 is shown in Figure 3-18. Sva
Pre-Amp (SR560)
Rdut Sia
Zin
G
Spectrum Analyzer (SR785)
SVRdut
Figure 3-18. Small signal analysis of voltage noise power spectral density of 1kΩ metal film resistor. Sva and Sia are respectively the voltage and current noise power spectral densities of the pre-amplifier, and SVRdut is the noise source associated with the device under test, in our case a 1 kΩ metal film resistor. Figure 3-18 can be represented by an equivalent input noise in term of noise voltage or noise current as shown respectively in Figures 3-19 and 3-20. The voltage noise PSD of the device under test, Rdut, can be extracted by subtracting the noise contribution of the setup as shown in Equation 3-4.
41
S dut = Svout − S setup
⎡V ⎤ ⎢⎣ Hz ⎥⎦
(3-4)
Svin =Sva+Sia (Rdut//Zin)2
Pre-Amp (SR560)
Rdut Zin
Spectrum Analyzer (SR785)
G
SVRdut
Figure 3-19. Equivalent input voltage noise Svin in term of noise voltage. SIin =Sia+Sva /(Rdut//Zin)2 Pre-Amp (SR560)
Rdut Sia
Zin
G
Spectrum Analyzer (SR785)
SIRdut
Figure 3-20. Equivalent input current noise SIin in term of noise current. The plot of the noise voltage power spectral density of the setup and power spectral density of a 1 kΩ metal film resistor without subtraction of the equipment setup noise is shown in Figure 3-21. Once the setup noise is subtracted from the total output noise, the remaining quantity is the noise of the 1 kΩ metal film resistor. The plot showing the noise power spectral density of the metal resistor after the setup noise has been subtracted is shown in Figure 3-22 compared with the fundamental thermal noise of the 1 kΩ resistor. This plot shows that when the setup noise is subtracted from the total output noise, the noise obtained using Equation 3-4 overlaps with the theoretical thermal noise predicted by Johnson [20] as illustrated in Figure 3-22.
42 1.E-13
2
Sv (V /Hz)
1.E-14 1 kΩ metal film with setup
1.E-15 Setup noise
1.E-16
1.E-17 1.E+00
1.E+01
1.E+02 1.E+03 Frequency (Hz)
1.E+04
1.E+05
Figure 3-21. Voltage noise PSD of a 1-kΩ metal film resistor without the subtraction of the equipment setup noise. 1E-13
2
Sv(V /Hz)
1E-14 1 kΩ metal film with setup noise
1E-15
1 kΩ metal film without setup noise
1E-16 Thermal noise
1E-17 1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-22. Noise of the metal resistor with setup noise subtracted. Noise Figure The noise figure is a qualitative measure of the contribution of the amplifier noise compared to the device under test noise for a measured signal. If the noise figure is low, this implies that the Johnson noise of the source (device under test) dominates the output noise; however, if the noise figure is large then the amplifier noise dominates the output noise. The noise figure is expressed in term of voltage as shown in Equation 3-5 in dB.
⎛ S ⎞ NF = 20 log10 ⎜ Vout ⎟ ⎝ SVsource ⎠
[ dB ]
(3-5)
43 where SVout is the voltage output noise and SVsource the voltage thermal noise source both with units Vrms/Hz1/2. Similarly, it can be computed in terms of noise power.
⎛ S ⎞ NF = 10 log10 ⎜ Pout ⎟ ⎝ S Psource ⎠
[ dB ]
(3-6)
where SPout is the noise output power and SPsource the thermal noise source both expressed Vrms2/Hz. Equation 3-7 shown below gives the noise figure derived from the experimental setup shown in Figure 3-18. ⎛ Total input noise power , including source noise ⎞ NF = 10 log10 ⎜ ⎟ Noise power of source noise ⎝ ⎠ ⎛ 4 K B RdutT ∆f + Sva + Sia ( Rdut // Rin )2 ⎞ = 10 log10 ⎜ ⎟ ⎜ ⎟ 4 K B RdutT ∆ ⎝ ⎠
(3-7)
⎛ S + Sia ( Rdut // Rin )2 ⎞ = 10 log10 ⎜1 + va ⎟ ⎟ ⎜ 4 K R T ∆ B dut ⎠ ⎝
[ dB ]
The noise figure, shown in Figure 3-23, of 1 kΩ metal film resistor has been computed to determine when the output noise is dominated by the Johnson noise of the microphone or by the amplifier noise. From Figure 3-23, the noise figure at 1 kHz is about 3 dB.
Noise Figure (dB)
1.E+01
1.E+00 1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-23. Noise figure of 1 kΩ metal film resistor using the SR560 low noise preamplifier.
44 This means that the contribution of the amplifier noise to the noise measured is small. Thus, for devices of about 1 kΩ or higher, the noise measured will not be dominated by the amplifier noise. Therefore, we will be able to measure their noise floor.
CHAPTER 4 MICROPHONES NOISE MEASUREMENT In this chapter, we measure the noise power spectral densities of four microphones: UF piezoresistive microphone [15, 16], UF proximity sensor [17], Endevco piezoresistive microphone (8510B-1) and Kulite piezoresistive microphone (MIC–093). Using the procedure outlined in Chapter 3, the setup noise will be subtracted from the resulting total power spectral density of each of the measurements, and the Hooge parameter α will be computed for the UF piezoresistive microphone and the UF proximity sensor. First, the noise power spectral densities of the Kulite, Endevco, UF piezoresistive, and UF proximity microphone were measured at zero bias. The measured input and output impedances of the microphones are shown on Table 4-1. Table 4-1. Our measured input and output impedances of UF piezoresistive microphone, UF proximity, Kulite and Endevco Microphones UF UF Proximity Kulite Endevco
Rin (Ω) 578 9623 3102 2057
Rout (Ω) 579 9634 1148 1820
Figure 4-1 shows the power spectral densities of UF piezoresistive microphone, Proximity, Kulite and Endevco without the setup noise and their corresponding theoretical thermal noise. In Figure 4-1, we observe that the higher the resistance of the device, the higher the PSD noise floor. This is because the observed asymptotic noise floor is due to the thermal noise corresponding to the output impedance of the microphones and is proportional to the resistance value. 45
46 1E-13
1E-15
2
Sv (V /Hz)
1E-14
Thermal noise
UF Proximity
1E-16
Endevco Kulite
1E-17 1E-18 1.E+00
UF Piezoresistive
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figures 4-1. PSD of Kulite, Endevco, UF piezoresistive and UF Proximity sensor at 0 Volt without setup noise. When the microphone is unbiased, the observed 1/f noise characteristic at low frequencies originates from the pre-amplifier. The noise figures of the microphones are plotted in Figure 4-2.
Noise Figure (dB)
1.E+02 1.E+01 UF Piezoresistive Kulite Endevco
1.E+00
UF Proximity
1.E-01 1.E-02 1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 4-2. Noise figure of UF piezoresistive microphone, Kulite, Endevco, and UF proximity sensor using the SR560 low noise pre-amplifier. As expected, the noise figure is lowest for the proximity sensor due to its highest output impedance of the four microphones investigated. Since the UF ultrasonic proximity sensor has the highest output resistance and the UF microphone the lowest
47 output resistance, their noise figures are respectively the lowest and highest in Figure 4-2. However, one should not design a device with large resistance to compete with the noise figure because even if the noise figure is smaller the downfall is that it is achieved by having a large thermal noise produced by the source. This high thermal noise may affect the signal-to-noise ratio. Since we are interested in investigating the transducer noise at frequencies below the human hearing range to capture and characterize the low frequency 1/f component, we will investigate the noise at frequencies starting from 0.01 Hz. Table 4.2 shows the frequency spans of the measurements. The data have been overlapped to obtain the power spectral density. Table 4-2. Frequency range during measurement Span (Hz) FFT lines Binwidth (Hz) 12.5 800 0.016 200 800 0.25 1600 800 2 12800 800 16 Prior to the measurement, we investigated the effect of the bias resistor (metal film resistor) on the output resistance of the microphone, Req. The large signal and small signal circuits are shown in Figure 4-3 and Figure 4-4. Rbias R1
R2
Vbias
Pre-amplifier R4
R3
Figure 4-3. Large signal representation of bias network.
48 In small signal analysis, the voltage source becomes a short as illustrated in Figure 4-4.
Figure 4-4. Small signal representation of bias network. The equivalent resistance seen by the pre-amplifier is found from the circuit above using a ∆-Υ transformation. The resulting circuit is shown in Figure 4-5.
a R1
Rea
Rec
b e R4
c
Red d
Req
Figure 4-5. Small signal representation of bias network using a ∆-Υ transformation. The expression of the equivalent resistance seen by the pre-amplifier is given in Equation 4-1. Req = ( Rbae // Rbde ) + Rec = ⎡⎣( R1 + Rea ) // ( R2 + Red ) ⎤⎦ + Rec
where
(4-1)
49 Rbae =R1 + Rea Rbde = R4 +Red R ea = ( Rac ∗ Rad ) ( Rac + Rcd + Rad ) R ec = ( Rca ∗ Rcd ) ( Rac + Rcd + Rad ) R ed = ( Rda ∗ Rdc ) ( Rac + Rcd + Rad ) By simulating cases of balanced and unbalanced Wheatstone bridge, we found that Rbias has no effect on the impedance seen by the amplifier when the Wheatstone bridge is balanced. We will use this result in our analysis. The noise power spectral density of the UF piezoresistive microphone, UF proximity, and Endevco piezoresistive sensors will be evaluated using the setup developed in Chapter 3 and shown in Figure 4-6. Shielded Box
Shielded Box
Shielded Box Rbias
A Pre-Amp (SR560)
Vbias
A Spectrum Analyzer (SR785) Chassis
B
Computer (LabView)
AC Out
AC Out
Figure 4-6. Experimental setup of noise measurement. However, for the Kulite piezoresistive microphone, instead of a DC bias voltage, we use an AC bias voltage. At DC bias voltage, we were unable to observe the low frequency noise of the Kulite microphone. This is due to the fact that the amplifier noise dominates at low frequencies, and therefore prevented the noise measurement of the
50 Kulite under DC bias voltage. To overcome this impediment, the microphone is biased with an AC bias voltage. The advantage of using an AC bias voltage is its capability to modulate the microphone low frequency noise to a frequency higher that the corner frequency of the pre-amplifier where it can be detected and measured. Figure 4-7 shows the setup for an AC bridge measurement. Shielded Box Shielded Box Shielded Box Microphone R1
SRS 785 R2
A
SRS 560 Spectrum Analyzer
Amp
VAC R3
Sv (V 2/Hz)
S v (V2/Hz)
fc-fn f c fc+fn
∆V = = =
Vi Rs Vc Rs Vc Rs
B
∆R =
Vc Rs
f (Hz)
Sv (V 2/Hz)
R4
fc-fn f c fc+fn
f (Hz)
Delta f (Hz)
fn
cos ( 2π f c t ) ∆R
∞
∑ cos ( 2π f t ) {a c
n
cos ( 2π f n t + ϕ n )}
c
+ f n ) t + ϕ n } + cos {2π ( f c − f n ) t − ϕ n }]
n =0 ∞
f0
an
∑ 2 [cos {2π ( f
⎛ ∆V ⎞ ⎜ ⎟ ⎝ V ⎠
2
⎛ ∆R ⎞ ⎟ ⎝ R ⎠
2
.
= ⎜ f c +∆f
f c + ∆f
n =0
Figure 4-7. Experimental setup for an AC bridge measurement. The mathematical derivations have been obtained from Lorteije and Hoppenbrouwers [30]. Lorteije and Hoppenbrouwers [30] describe the low frequency noise measurement using an AC signal. They show that an AC signal with carrier frequency fc, the noise power spectral density at frequencies fc –fn and fc +fn, where fn is a frequency component of the fluctuating resistance, is equal to the noise power spectral density at fn for a DC
51 bias voltage. Thus, Lorteije and Hoppenbrouwers call the noise power spectral density resulting from an AC bias voltage 1/∆f noise. Furthermore, Lorteije and Hoppenbrouwers, through experimental result on carbon-impregnated paper, under DC and AC bias voltages, have suggested that the noise power spectral density obtained when an AC signal is used as bias voltage is four times smaller than the noise power spectral density when a DC voltage is used. Therefore, one must multiply the low frequency AC measurement by four to obtain the noise measurement for DC bias voltage. Noise in Microphones UF Piezoresistive Microphone The piezoresistive microphone has been described in Chapter 2. Its voltage noise power spectral density is measured using the setup of Figure 4-6. 1.E-12
2.68 V
2
Sv (V /Hz)
1.E-13
1.75 V
1.E-14
0.87 V
1.E-15 1.E-16 1.E-17
Thermal noise
1.E-18 1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 4-8. Power spectral density of UF piezoresistive microphone at different bias voltages. One can observe that at high frequencies the noise power spectral density overlaps with the Johnson noise, after extracting the setup noise. The corner frequency where the thermal noise starts to dominate is around 1x104 Hz. The frequency range over which the 1/f noise dominates is very large. This will have a negative effect on the signal-to-noise
52 ratio not only because of the wide range over which the 1/f noise is present but also the high noise level at low frequencies. The signal-to-noise ratio expresses the signal strength with respect to the noise present in the system as given in Equation 4-2,
⎛V ⎞ SNR = 20 log ⎜ s ⎟ ⎝ Vn ⎠
(4-2)
where Vs is the signal and Vn is the noise level. The total RMS noise in a bandwidth, ∆f, is obtained by taking the square root of the power spectral density integrated over the bandwidth. The noise level can be large at low frequency because the 1/f noise increases as the frequency decreases. Equation 4-3 gives the RMS noise voltage when two dominant noise sources in piezoresistive sensors, 1/f and thermal noise, are considered. Vn = 4 K B R T BW +
⎛ f ⎞ ln ⎜ 2 ⎟ N ⎝ f1 ⎠
αV 2
(4-3)
where f1 is the lowest and f2 is the highest frequencies and BW, the difference between f2 and f1, is the bandwidth. When f2 is much larger than f1, the bandwidth can be approximated as f2. To show the voltage square dependence of the noise power spectral density as formulated by Hooge [21], the power spectral density is plotted versus voltage at a specific frequency in Figure 4-9. The noise voltage power spectral density values used in this graph are taken at 12 Hz. A power regression of the data gives a voltage dependence of 1.85 ± 0.60. The Hooge parameter α is computed to evaluate the process quality of the piezoresistor transducer in the piezoresistive microphone since the lower the value of α, the lower the noise, and the better the process quality. From Equation 2-5 we obtain the expression for the Hooge parameter α as shown in Equation 4-4.
53
α=
SV ∗ N ∗ f V2
(4-4)
where Sv is the noise voltage power spectral density, N is the number of carriers, f is the frequency at which the Hooge parameter is computed, and V is the bias voltage applied to the microphone.
2
Sv (V /Hz)
1.E-13
-15
1.85±0.60
Sv = 1.99*10 X 1.E-14
1.E-15 1.E-01
1.E+00
1.E+01
Voltage (V)
Figure 4-9. Voltage dependence of PSD for UF piezoresistive microphone at 12 Hz and binwidth 0.016 Hz. The plot of the Hooge parameter is shown in Figure 4-10. Hooge parameter Magnitude
1.E-02
1.E-03 5.E-01
2.E+00 Voltage (V)
4.E+00
Figure 4-10. Hooge parameter of UF piezoresistive microphone. The Hooge parameter when biased at 2.68 V is estimated to be 2.9x10-03 with an uncertainty of 2.78 %. The uncertainty was computed by applying the uncertainty
54 analysis techniques from Coleman and Steele [31] on the governing equation of the low frequency noise power spectral density described in Equation 4-4. The Hooge parameter value is large. It reflects the high 1/f noise levels seen in Figure 4-8. To obtain a lower Hooge parameter, a better process quality is required. UF Proximity Sensor The power spectral densities of the UF proximity sensor are measured with the same equipments and settings as the UF piezoresistive microphone. However, a bias is applied to the substrate for junction isolation. The substrate is biased at 6.71, 4.99, and 3.15 Volts when the sensor is biased respectively at 6.23, 4.45, and 2.65 Volts. This leads to a reverse bias voltage of about - 0.5 Volt that corresponds to a relative small leakage current of 0.96 nA. The voltage noise power spectral densities of the UF proximity sensor with different bias voltages are shown in Figure 4-11 at constant reverse bias of -0.5 V. 1.E-12 6.23 V 4.45 V
2
Sv(V /Hz)
1.E-13
2.65 V 1.E-14 1.E-15 Thermal noise 1.E-16 1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 4-11. Power spectral density of UF proximity sensor at different bias voltage (constant reverse bias of -0.5 V). The corner frequency is at 100 Hz. It is significantly lower than the corner frequency of the UF piezoresistive microphone. A plot comparing the noise levels all
55 four microphones at the same bias voltage will be given later in this chapter. The voltage dependence of the power spectral density is shown in Figure 4-12, giving a voltage power dependence of 1.86 ± 2.67.
2
Sv (V /Hz)
1.E-13
-16
1.86±2.67
Sv = 2.96*10 X 1.E-14
1.E-15 1.E+00
1.E+01 Voltage (V)
Figure 4-12. Voltage dependence of PSD for UF proximity sensor at 12 Hz and binwidth 0.016 Hz. We also compute and plot the Hooge parameter for the UF proximity sensor as shown in Figure 4-13. Hooge Parameter Magnitude
1.E-04
1.E-05 2.E+00
5.E+00
7.E+00
Voltage (V)
Figure 4-13. Hooge parameter of UF proximity sensor. The value of the Hooge parameter of the UF proximity sensor when biased at 2.65 with a constant reverse bias of 3.15 V is 6.75x10-05 with an uncertainty of 2.78 %, which is two orders of magnitude lower compared to the UF piezoresistive microphone. This leads to the conclusion that the piezoresistor silicon defect density is significantly lower
56 and the process quality correspondingly higher for the UF proximity sensor than the UF piezoresistive microphone. One key difference between the two devices is the use of a high temperature wafer-bonding step in the UF piezoresistive microphone. Endevco Piezoresistive Microphone Noise measurements have also been performed on a commercial microphone; Endevco (Model 8510B-1). Some of the microphone specifications have been provided in Chapter 2. The noise measurements are conducted using the same conditions as the previous microphones. The noise power spectral density obtained is shown in Figure 414. 1.E-12
6.96 V
2
Sv (V /Hz)
1.E-13
4.90 V
1.E-14
2.94 V
1.E-15 1.E-16
Thermal noise
1.E-17 1.E-18 1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 4-14. Power spectral density of Endevco microphone at different bias voltage. The corner frequency of the Endevco microphone is 1x103 Hz, which is higher than the corner frequency of the proximity sensor but still lower than the UF piezoresistive microphone. Its noise floor is lower than the noise floor of the UF piezoresistive microphone and UF proximity sensor. Since we do not know the number of carriers in the piezoresistor, we cannot compute the Hooge parameter. However, the voltage dependence of the PSD is provided in Figure 4-15 and indicates a power dependence of 1.48 ± 2.05.
57 1.E-15 -17
1.48±2.05
2
Sv(V /Hz)
Sv = 2.25* 10 X
1.E-16 1.E+00
1.E+01 Voltage (V)
Figure 4-15. Voltage dependence of PSD for Endevco microphone at 12 Hz and binwidth 0.016 Hz. Kulite Piezoresistive Microphone The noise power spectral density of the Kulite microphone without the temperature compensation module (MIC-093) has been obtained via amplitude modulation. The noise measurements are conducted with an AC bias voltage with frequency of 10 kHz and different amplitudes of 1.06, 1.87 and 2.68 volt peak. The noise power spectral density of Kulite microphone is shown on Figure 4-16 with corner frequency at 10 Hz. 1.E-12 2.68 V
2
Sv (V /Hz)
1.E-13
1.87 V
1.E-14
1.06 V
1.E-15 1.E-16
Thermal noise
1.E-17 1.E-18 1.E-01
1.E+00
1.E+01 1.E+02 Frequency (Hz) Delta Frequency (Hz)
1.E+03
1.E+04
Figure 4-16. Power spectral density of Kulite microphone (without the temperature compensation module) at different bias voltage.
58 The voltage dependence of the power spectral density provided in Figure 4-17. indicates a power dependence of 1.59 ± 0.73.
2
Sv(V /Hz)
1.E-14
Sv = 2.17 * 10
-16
X
1.59 ±0.73
1.E-15
1.E-16 1.E+00
1.E+01 Voltage (V)
Figure 4-17. Voltage dependence of power spectral density for Kulite microphone (without the temperature compensation module). One can observe from Figure 4-15 that the noise power spectral density of the Kulite is small. Figure 4-18 demonstrates that these noise levels at low frequency could not be observed under DC bias voltages since the setup noise dominates. 1.E-12 DC setup noise 2.68 V
1.E-14
1.87 V
2
Sv (V /Hz)
1.E-13
1.E-15
1.06 V
1.E-16 1.E-17 1.E-01
1.E+00
1.E+01 1.E+02 Frequency (Hz)
1.E+03
1.E+04
Figure 4-18. Kulite noise power spectral densities compared to the DC setup noise. A plot comparing the voltage noise PSD of the UF piezoresistive microphone, UF proximity sensor, Endevco and Kulite microphones is provided in Figure 4-19. We observe at low frequencies that the UF piezoresistive microphone has the higher noise level, followed by the UF proximity sensor, the Endevco microphone and then the Kulite microphone.
59 1.E-12
UF microphone UF proximity sensor Endevco microphone (8510B-1) Kulite microphone (MIC-093)
1.E-14
2
Sv (V /Hz)
1.E-13
1.E-15 1.E-16 1.E-17 1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
Frequency (Hz)
Figure 4-19. Comparison of power spectral densities of UF microphone, UF proximity sensor, Endevco, and Kulite (without the temperature compensation module) microphones biased at 2.6 V. It is worth noticing that the resistance of the UF piezoresistive microphone is the smallest among all the microphones. This graph reveals that, at low frequencies, the noise is dominated by the 1/f noise while, at high frequencies the noise is thermal noise. The main difference in the resistors beside their values is their types. The piezoresistors of the UF piezoresistive microphone are dielectrically isolated and the ones of the proximity sensor are junction isolated. The latter will incur shot noise but less 1/f noise since it has fewer traps surrounding it. The 1/f noise of the UF piezoresistive microphone is large possibly due to traps generated during the high temperature wafer-bonding step. The corner frequency of the UF piezoresistive microphone is also the largest compared to the other sensors. However, at high frequencies one sees a reverse in the magnitude of the noise. The UF piezoresistive microphone shows a lower noise since it has the smallest output resistance. This confirms the direct relation of the thermal noise with the output resistance value as shown previously in Equation 2-2. For further illustration of the 1/f noise contribution, we define a 1/f noise figure by subtracting the thermal noise power from the 1/f noise power of the device. It is represented mathematically by Equation 4-5.
60 ⎛ 1/ f noise ⎞ NF1 f = 20 log ⎜ ⎟ ⎝ thermal noise ⎠
(4-5)
This 1/f noise figure is different than the noise figure presented in Figure 3-23 and 4-2 where the device was not biased. The quantity plotted is the difference of the total measured noise power and the thermal noise power of the device. In Figure 2-20, we plot the 1/f noise figure for all four sensors biased at 2.6 V.
1/f Noise Figure (dB)
100 UF microphone UF proximity Endevco microphone (8510-B)
10
Kulite microphone (MIC-093)
1
0.1 0
25
50
75
100
Frequency (Hz)
Figure 4-20. 1/f noise figure of UF piezoresistive microphone, UF proximity sensor, Endevco, and Kulite (without the temperature compensation module) microphones biased at 2.6 V. From this plot one can see that for the sensors with higher noise voltage power spectral densities, their 1/f noise figures dominate at the low frequency range. It is worth noticing that, as the frequency gets larger, the 1/f noise figure of all the sensors will tend to zero. This is expected since beyond the corner frequency, the noise is essentially the thermal noise of the sensor. Acoustic Calibration In this section, we investigate the performance of the UF piezoresistive microphone, UF proximity, Endevco, and Kulite microphones through acoustic calibration. For the latter, the acoustic calibration is performed with and without its temperature compensation module (TCM). The parameters measured frequency response
61 and linearity of the microphones are used to compute the sensitivity and minimum detectable signal of the microphones. Frequency Response The calibration of the dynamic response of the UF piezoresistive microphone, UF proximity, Endevco and Kulite is performed with the use of a plane wave tube. A diagram illustrating the setup is shown in Figure 4-21. B&K MIC
DC Supply DUT Diff. Amp
Amp
PULSE MultiAnalyzer
Computer (LabShop)
Figure 4-21. Experimental setup used with the normal incidence plane wave tube. The microphones are mounted in the same plane at the end of the plane wave tube next to a 1/8-inch Bruel and Kjaer (4138 B&K condenser microphone) integrated with a B&K 2670 preamplifier. This setup allows both microphones to sense the same incident pressure. The plane wave tube with a cutoff frequency of 6.7 KHz is 96 cm long, with a 2.54 cm x 2.54 cm square duct. The formation of a standing wave is generated by a JBL 2126-J compression driver mounted at the other end of the tube. The microphones are biased using a Hewlett Packard E3630A DC power supply. The voltage settings are specified by the manufacturers to avoid damaging the microphones. The Kulite and the
62 Endevco microphones are biased at 10 volt; the UF proximity sensor at 9 volt with a 10.5 volt reverse bias on the substrate for junction isolation and the UF piezoresistive microphone at 3 volt. As for the B&K microphone, it is powered by a B&K PULSE multi-analyzer system. The outputs of the microphones are connected to a low noise amplifier, Standford Research System (SRS 560), in a differential mode. The gain of the low noise amplifer is set to 200 and its output connected to the B&K PULSE multianalyzer system, which processes the data via LabShop software. Prior to each microphone calibration, the B&K microphone is calibrated using a B&K 4228 pistonphone. During this measurement, a periodic random signal, supplied by a B&K PULSE multi-analyzer system and amplified by a Techron 7540 power amplifier to drive the speaker, is used. Also 800 FFT lines, 8000 averages, a span of 6.4 KHz, with center frequency 3.5 KHz, resulting in a maximum frequency of 6.7 KHz are used. Both normalized magnitude and phase frequency response of the microphones are shown in Figures 4-22 and 4-23.
Sensitivity(uV/Pa*V)
3
Endevco
2
Kulite without TCM UF proximity sensor UF piezoresitive Kulite with TCM
0 1000
2000
3000 4000 5000 Frequency (Hz)
6000
7000
Figure 4-22. Magnitude frequency response (normalized sensitivity) of Endevco, UF proximity, Kulite (with and without the temperature compensation module) and UF piezoresistive microphone.
63 UF piezoresitive
5
Endevco Phase (Degree)
UF proximity Kulite with TCM Kulite without TCM
0
-5 1000
2000
3000
4000 5000 Frequency (Hz)
6000
7000
Figure 4-23. Phase frequency response of Endevco, UF proximity, Kulite (with and without the temperature compensation module) and UF piezoresistive microphone. Linearity The setup for the linearity measurement is the same as above. However, in this case a 1 kHz sine wave source signal is used. The amplitude of the source signal is progressively increased and the pressure sensed by the microphone. The corresponding microphone output voltages are recorded until one sees a non-linear trend in the signal. Figure 4-24 shows the linearity plots of the Endevco, proximity, UF piezoresistive microphone and Kulite sensors up to 1500 Pa.
Sensor Outpu (uVrms)
40000
Endevco
30000
20000
Kulite without TCM
10000
UF proximity Kulite with TCM UF piezoresistive
0 0
200
400
600 800 1000 Pressure ( Parms)
1200
1400
1600
Figure 4-24. Linearity measurement of Endevco, proximity, Kulite (with and without the temperature compensation module) and UF piezoresistive microphone.
64 One observes that all the sensors exhibit linear responses up to 1500 Pa. The static sensitivity of the microphone is obtained by computing the slope of the linearity plots. However, another plot that one can explore is the plot of sensitivity versus the applied pressure to better visualize the linear response of the microphones to normal incident pressure. Such a plot is shown on Figure 4-25 for UF piezoresistive microphone piezoresistive, UF proximity sensor, Endevco and Kulite microphones. 3
Sensitivity (uV/Pa*V)
Endevco 2
Kulite without TCM
1
UF proximity UF piezoresistive Kulite withTCM 0 0
200
400
600 800 1000 Pressure (Parms )
1200
1400
1600
Figure 4-25. Sensitivity of Endevco, UF proximity, Kulite (with and without the temperature compensation module) and UF piezoresistive as a function of pressure. Table 4.3 summarizes the acoustic calibration of the microphones. Table 4-3. Acoustic calibration results of UF microphone, UF proximity, Endevco and Kulite microphones Parameters UF UF Endevco Kulite Kulite without microphone proximity with TCM* TCM* Excitation Voltage (V) 3 9 10 10 10 Input impedance (Ω) 578 9623 2057 3102 1148 Output impedance (Ω) 579 9634 1820 1148 1148 Sensitivity (µV/Pa) 1.69 6.40 26.9 4.23 11.6 Normalized Sensitivity 0.56 0.71 2.69 0.42 1.16 (µV/Pa*V) Measured up to 158 158 158 158 158 (dB SPL) *TCM (temperature compensation module).
65 In Table 4-3, the excitation voltages during the microphone sensitivity measurement are different. For a comparison point of view, it would be interesting to measure the microphone sensitivity under identical bias condition and power dissipation. In Table 4-4 and 4-5, we show the sensitivity of the UF microphone, UF proximity, Endevco, and Kulite microphones under the same bias voltage (3 V) and under the same power dissipation (7 mW). Table 4-4. Sensitivity of the UF microphone, UF proximity, Endevco and Kulite microphones under the same bias voltage (3 V) Parameters UF UF Endevco Kulite Kulite without microphone proximity with TCM TCM Sensitivity (µV/Pa) 1.69 2.32 8.60 1.26 3.40 Normalized Sensitivity 0.56 0.77 2.86 0.42 1.13 (µV/Pa*V) Table 4-5. Sensitivity of the UF microphone, UF proximity, Endevco and Kulite microphones under same power dissipation (7 mW) Parameters UF UF Endevco Kulite Kulite without microphone proximity with TCM TCM Excitation Voltage (V) 2.00 8.16 3.77 4.63 2.82 Sensitivity (µV/Pa) 1.39 6.32 10.9 1.95 3.17 Normalized Sensitivity 0.69 0.77 2.89 0.42 1.12 (µV/Pa*V) From Table 4-4, when all microphones are biased at 3 V, we observe a larger sensitivity from Endevco, followed by Kulite without TCM, UF proximity, UF piezoresistive microphone and Kulite with TCM. When the sensors are subjected to the same power dissipation (7 mW), as shown in Table 4-5, a larger sensitivity is observed from Endevco, followed by UF proximity, Kulite without TCM, Kulite with TCM and UF piezoresistive microphone. The UF piezoresistive is biased at 2 V. If it was biased at 3 V, then the UF proximity would have been biased at 12.24 V in order to have the same power dissipation in both sensors. However, 12.24 V is larger than the maximum bias
66 voltage applicable to the UF proximity sensor (10 V). A power dissipation of 7 mW allows us to bias the UF proximity sensor without exceeding its maximum bias constraint. Minimum Detectable Signal The minimum detectable signals are shown in Table 4-6 for UF piezoresistive microphone, UF proximity, Endevco and Kulite. They are computed in a binwidth of 2 Hz centered at 1 kHz with the microphone biased at different bias voltages as shown in Table 4-3. The minimum detectable signal is the ratio of the noise voltage to the sensitivity. It is expressed as shown in Equation 4-6. MDS =
Noise voltage Sensitivity
(4-6)
Table 4-6. Minimum detectable signal (MDS) of UF microphone, UF proximity, Endevco and Kulite microphones at different bias voltages Parameters
UF microphone
UF proximity
Excitation Voltage (V) MDS for 2 Hz bin centered at 1 kHz (SPL)
3 51.5
9 43.2
Endevco Kulite With TCM 10 10 23.8 38.1
Kulite Without TCM 10 29.3
In Table 4-6, the Endevco has the lowest MDS followed by the Kulite, the UF piezoresistive microphone and the proximity sensor. The minimum detectable signals when the microphones are operated under the same bias voltage (3 V) and same power dissipation (7 mW) are shown respectively in Table 4-7 and 4-8. From Table 4-7, when all microphones are biased at 3 V, we observe a lower MDS from Endevco, followed by Kulite without TCM, Kulite with TCM, UF piezoresistive microphone and UF proximity.
67 Table 4-7. Minimum detectable signals (MDS) when the microphones are operated under the same bias voltage (3 V) Parameters UF UF Endevco Kulite Kulite Without microphone proximity with TCM TCM Excitation Voltage (V) 3 3 3 3 3 MDS for 2 Hz bin centered 51.5 51.8 33.4 48.6 40.0 at 1 kHz (SPL) Table 4-8. Minimum detectable signals (MDS) when the microphones are subjected to the same power dissipation (7 mW) Parameters UF UF Endevco Kulite Kulite Without microphone proximity with TCM TCM Excitation Voltage (V) 2.00 8.16 3.77 4.63 2.82 Power Dissipation (mW) 7 7 7 7 7 MDS for 2 Hz bin centered 53.2 43.1 31.3 44.8 40.6 at 1 kHz (SPL) When the sensors are subjected to the same power dissipation (7mW), as shown in Table 4-8, a lower MDS is observed from Endevco, followed by Kulite without TCM, UF proximity, Kulite with TCM, and UF piezoresistive microphone. Dominant Noise Source in MEMS Piezoresistive Microphones The theory of the existence of a purely mechanical 1/f noise dominant at low frequency has been suggested by Zuckerwar et al. [4]. In this section, we demonstrate that the 1/f noise at low frequencies is electrical by nature and is dominant. Acoustic Isolation Test The noise measurement is performed in a Faraday cage. The purpose of the acoustic isolation test is to quantify the acoustic sound pressure in the Faraday cage using a sensitive B&K microphone (1/8-inch Bruel and Kjaer 4138 condenser microphone). This result reveals whether the experiment is acoustically shielded. The coherence between a calibrated Bruel and Kjaer 4138 condenser microphone and the UF piezoresistive microphone help us to see if there is an acoustic deterministic source of the
68 measured electrical noise, i.e. the acoustic analog of EMI. Figure 4-26 shows the power spectral density of the Bruel and Kjaer 4138 condenser microphone and of the UF
2
Spa (Pa /Hz)
piezoresistive microphone. 1.E+00 UF piezoresistive microphone (Vbias = 3 V) 1.E-01 B&K 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 1.E-07 1.E-08 1.E-09 1.E-10 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03
1.E+04
Frequency (Hz)
Figure 4-26. Power spectral density of the Bruel and Kjaer 4138 condenser microphone and of the UF piezoresistive microphone. We observe from Figure 4-26 that a low level acoustic signal is present inside the Faraday cage during the electrical noise measurement. Although, the acoustic isolation of our setup is not as good as the one of Zuckerwar et al. [12], the acoustic signal is much smaller than the equivalent signal of the UF piezoresistive microphone. Figure 4-27 shows the coherence function between the B&K and UF piezoresistive microphone. 1.00
Coherence
0.80 0.60 0.40 0.20 0.00 0
1
10
100
1000
10000
Freque ncy (Hz)
Figure 4-27. Coherence function between the B&K and UF piezoresistive microphone.
69 From the above figure, note that the coherence between the acoustic signal and the electrical noise is small for most frequencies. An exception occurs at 60 Hz. At that particular frequency, the coherence is larger and has a value close to 0.6. This coherence value at 60 Hz may be due to a common 60 Hz electrical contamination. Therefore, one may conclude that the acoustic interference contribution to the measured electrical noise is negligible. Having quantified the impact of the acoustic signal in our measurement, we will now see whether the origin of the 1/f noise is mechanical or electrical in nature. Membrane Contribution to 1/f Noise To investigate whether the dominant source of the 1/f noise is mechanical or electrical of origin, we perform power spectral density measurement on two UF piezoresistive proximity sensors of identical structures except that one has a free membrane and the other has fixed membrane. 1.E-12 1.E-13
2
Sv (V /Hz)
UF piezoresistive proximity with released membrane
8V 5V
1.E-14 1.E-15 0V
1.E-16 1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
piezoresistors
free n-Si Figure 4-28. Power spectral density of the UF piezoresistive proximity sensor with free diaphragm.
70 If the noise is mechanical of origin, then whether the sensors are biased or not, a 1/f noise characteristic must be present on the microphone with free membrane since the damping resistance, Ra, of the microphone diagram is related to the purely mechanical 1/f noise [4, 12]. Figure 4-28 shows the power spectral density of the UF piezoresistive proximity sensor with free diaphragm. Figure 4-29 shows the power spectral density of the UF piezoresistive proximity sensor with fixed diaphragm. 1.E-12
UF piezoresistive proximity with unreleased membrane
8V
2
Sv (V /Hz)
1.E-13
5V
1.E-14 1.E-15 0V
1.E-16 1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
piezoresistors
fixed n-Si Figure 4-29. Power spectral density of the UF piezoresistive proximity sensor with fixed diaphragm. Comparing Figures 4.28 and 4.29, we observe that excess noise is present in both mechanically fixed and free diaphragms. In addition, as the bias voltage increases, the power spectral density at low frequencies increases. For the cases when the microphones are not biased the excess noise coincides with thermal noise. In this case, the excess
71 noise as illustrated on Figure 4-30 for the sensor with free membrane corresponds to the excess noise of the low noise pre-amplifier (SRS 560). 1.E-12
1.E-14
2
Sv (V /Hz)
1.E-13
1.E-15 0V
1.E-16
Setup noise with SR 560 1.E-17 1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 4-30. Power spectral density of UF proximity sensor with free membrane at zero biased voltage. A similar plot is obtained for the sensor with fixed diaphragm at zero biased zero. On Figure 4-28 and 4-29, the setup noise has been removed. For the zero biased cases the power spectral densities show that the low noise is mainly the amplifier low noise. However, at frequencies higher than the corner frequency of the amplifier, the thermal noises of the sensors dominate. We can conclude from the measurements that the source of excess noise is electrical.
CHAPTER 5 CONCLUSION AND FUTURE WORK We have discussed noise measurement techniques such as using Faraday cages for shielding, lead acid battery for biasing, single point ground to avoid ground loops, and evaluation and subtraction of setup noise. These techniques are implemented during the noise power spectral density measurement of UF piezoresistive microphone, UF proximity sensor, Endevco piezoresistive microphone (8510B-1) and Kulite piezoresistive microphone (MIC-093). In addition, the settings of the low noise amplifiers (SRS 560 and Brookdeal 5004) and spectrum analyzer (SRS 785) are provided. Noise power spectral densities are obtained, voltage square dependent of the 1/f noise is shown, and Hooge parameters of the UF piezoresistive microphone, UF proximity sensor are computed. Using the power spectral densities measurement and the acoustic calibration of the microphone in a plane wave tube we have been able to compute the minimum detectable signal of the microphones, which is a key factor for a large the dynamic range of a MEMS sensor. To improve the dynamic range of MEMS piezoresistive microphones one should consider minimizing the noise. Since we have proven that the dominant noise in MEMS piezoresistive microphone is electrical of origin, special attentions should be on techniques to reduce the noise through new fabrication techniques of MEMS piezoresistive microphones. Geometrical and process fabrication parameters such as piezoresistor surface to volume ratio, pre-amorphization, annealing, and doping concentration impact the design of dielectrically isolated resistors and junction isolated 72
73 resistors. In addition, the study of the correlation between defects densities and 1/f noise enable the design of low noise process flows to fabricate low noise MEMS microphones. Figure 5-1 shows the results of a focus ion beam (FIB) and the defects in an arc piezoresistor of the UF piezoresistive microphone are shown using a transmission electron microscopy (TEM) as shown in Figure 5-2.
Sample Area Arc Resistor
Contact
Figure 5-1. Focus ion beam (FIB) of an arc piezoresistor of the UF piezoresistive microphone. Nitride Threading dislocation
SiO2
SiO2 Nitride
P+ Silicon
Figure 5-2. Transmission electron microscopy (TEM) results of an arc piezoresistor of the UF piezoresistive microphone. The combination of piezoresistor noise theory and measurements and the optimization approach used by Papila et al. [32] have the potential to yield optimally high performance piezoresistive microphones.
APPENDIX PIEZORESISTIVITY Piezoresistivity is a material property where the material resistivity changes with applied stress. Resistivity, as described in Equation A-1, is inversely proportional to the doping concentration n, carrier mobility µ, and electron charge q. Resistivity is related to the applied stress through piezoresistance coefficients.
ρ=
1
[Ω − cm]
nµ q
(A-1)
Silicon, which is a crystal with cubic symmetry, has three fundamental piezoresistive coefficients, π11, π12, and π44. Its piezoresistance coefficient matrix is shown below in Equation A-2 [33].
0 0 ⎤ ⎡σ 1 ⎤ ⎡ ∆ρ1 ⎤ ⎡π 11 π 12 π 12 0 ⎢ ∆ρ ⎥ ⎢π 0 0 ⎥⎥ ⎢⎢σ 2 ⎥⎥ ⎢ 2 ⎥ ⎢ 12 π 11 π 12 0 0 0 ⎥ ⎢σ 3 ⎥ 1 ⎢ ∆ρ3 ⎥ ⎢π 12 π 12 π 11 0 ⎢ ⎥=⎢ ⎥⎢ ⎥ 0 0 π 44 0 0 ⎥ ⎢ τ1 ⎥ ρ ⎢ ∆ρ 4 ⎥ ⎢ 0 ⎢ ∆ρ5 ⎥ ⎢ 0 0 0 0 π 44 0 ⎥ ⎢ τ 2 ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ 0 0 0 0 π 44 ⎥⎦ ⎢⎣ τ 3 ⎥⎦ ⎢⎣ ∆ρ 6 ⎥⎦ ⎢⎣ 0
(A-2)
where σ1=σxx, σ2=σyy, and σ3=σzz are the normal stresses, and τ1=τyz, τ2=τxz, and τ3=τxy are the shear stresses. The piezoresistance coefficient magnitude changes with orientation. To properly determine its value for different orientations, a coordinate transformation must be performed [34]. The piezoresistance coefficients for n-type and p-type silicon at a specific given resistivity are shown in Table A-1 [33].
74
75 Table A-1. Piezoresistive coefficients of silicon* π11 π12 ρ(Ω-cm) Silicon -11 -1 (10 Pa ) (10-11 Pa-1) p-type 7.8 6.6 -1.1 n-type 11.7 -102.2 53.4 *Smith [33].
π44 (10-11 Pa-1) 138.1 -13.6
The piezoresistance coefficient may be decomposed into a transverse piezoresistive coefficient, πt and a longitudinal piezoresistive coefficient πl when the stress is perpendicular or parallel to the electric field respectively. These transverse or longitudinal piezoresistance coefficients are given in Equation A-3 in terms of the piezoresistance coefficients π11, π12, π44, and the direction cosines (l,m) [34].
π t = π 12 − (π 44 + π 12 − π 11 )(l12l22 + m12 m22 + n12 n22 ) π l = π 11 + 2(π 44 + π 12 − π 11 )(l12 m12 + l12 n12 + m12 n12 )
(A-3)
The polar plots of longitudinal and transverse coefficient of piezoresistance coefficients for p-type (100) silicon are shown in Figure A-1 using the values of π11, π12, and π44 of Table A-1.
Figure A-1. Polar plots of longitudinal and transverse piezoresistance coefficients for ptype (100) silicon. Observing Figure A-1, one notices that the piezoresistance coefficients are larger in the direction and that the transverse piezoresistance coefficients are
76 approximately equal but have opposite sign compared to the longitudinal piezoresistance coefficient. This is a reason why the piezoresistors of the UF microphones are oriented in this direction in a Wheatstone bridge circuit configuration. Using Equation A-3, the transverse or longitudinal piezoresistance coefficients, as shown in Table A-2 along the direction on a (100) wafer for room temperature and lowly doped silicon. Table A-2. Transverse and longitudinal piezoresistance coefficients of silicon for direction Silicon πl (10-11 Pa-1) πt (10-11 Pa-1) p-type 71.8 -66.3 n-type -31.2 -17.6 Note for p-type silicon, πl is of opposite sign and almost same magnitude as
πt, which is not the case for n-type silicon where πl and πt have neither opposite sign nor similar magnitudes. For this reason, piezoresistors are typically oriented in the direction on p-type silicon. The piezoresistance coefficient varies inversely with doping concentration. From Equation A-1, we observe that as the doping concentration increases, the resistivity decreases, yielding a decrease in the resistance. Kanda [35] has investigated the dependence of the piezoresistive coefficients on doping concentration and temperature using Fermi-Dirac statistics. A recent study by of the doping dependence of the π coefficient by Harley and Kenny [1] is different from Kanda’s theoretical prediction at high concentrations. Harley and Kenny [1] fit the data obtained from Manson et al. [36], Tufte and Stetzer [37] and Kerr and Milnes [38] and show that at high doping concentration, the decrease of the piezoresistance coefficient is approximated by a linear relationship.
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BIOGRAPHICAL SKETCH Robert Dieme was born on February 28th, 1974, in Diourbel, Senegal. After finishing high school in 1995, he received the Associate of Arts certificate from Tallahassee Community College in December 1998. He graduated with a bachelor degree in electrical engineering from the University of Florida in December 2001. He then started the degree for Master of Science in electrical engineering at the University of Florida in the spring of 2002 under the guidance of Dr. Toshikazu Nishida. He wishes to pursue a PhD degree, concentrating in the optimization of noise in piezoresistors.
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