Measured electron IMFPs for SiC - Wiley Online Library

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elastic peak electron spectroscopy (EPES), for the first time, the inelastic mean free paths (IMFPs) in bulk SiC with different structural properties (polycrystalline ...
SURFACE AND INTERFACE ANALYSIS Surf. Interface Anal. 2006; 38: 644–647 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/sia.2282

Measured electron IMFPs for SiC ´ M. Krawczyk,∗ L. Zommer, A. Kosinski, J. W. Sobczak and A. Jablonski Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland Received 30 June 2005; Revised 1 December 2005; Accepted 3 December 2005

Silicon carbide (SiC) is a wideband semiconductor that is very promising for many applications in optoelectronics and microelectronics. Since information on the electron transport processes in SiC is scarce, its systematic study is highly desirable. The aim of this work is to determine experimentally by elastic peak electron spectroscopy (EPES), for the first time, the inelastic mean free paths (IMFPs) in bulk SiC with different structural properties (polycrystalline and monocrystalline materials) and surface concentrations of its constituents. The relative EPES measurements were carried out in the electron energy range 0.2–2.0 keV with two different analyzers (double-pass cylindrical mirror analyzer (DCMA), spherical sector analyzer (SSA)) and the use of Ni standard. The measured IMFPs were uncorrected for surface excitations and compared with those calculated from the TPP-2M and G-1 predictive formulae using Fano plots. Good agreement was found between the measured and the calculated electron IMFPs in SiC exhibiting different structural properties. Copyright  2006 John Wiley & Sons, Ltd.

KEYWORDS: electron inelastic mean free path; SiC; electron spectroscopies; quantitative surface analysis; elastic peak electron spectroscopy

INTRODUCTION Silicon carbide (SiC) is a wide band-gap IV–VI compound semiconductor with large breakdown electric field, large saturated electron drift velocity and large thermal conductivity. Therefore, this semiconductor is expected to be an advanced material for high-power, high-temperature and high-frequency microelectronic devices and sensors. For the development of new devices using SiC, it would be very important to use surface sensitive electron spectroscopies, e.g. AES, XPS or electron energy-loss spectroscopy (EELS). The inelastic mean free path (IMFP) of electrons is one of the correction factors in quantitative analysis by surface sensitive electron spectroscopies.1 Werner2 and Gergely3 have specifically reviewed the electron transport processes in solids for surface analysis. An extensive database of IMFP values in a wide variety of materials (elements, inorganic compounds, organic compounds) has been already published.3,4 However, the IMFPs for SiC are still lacking. These values for different energies can be calculated using the TPP-2M5 and G-16 predictive formulae; however, IMFPs can also be measured experimentally by elastic peak electron spectroscopy (EPES).7 More recently, EPES has been successfully used to measure the IMFPs in bulk GaN crystals.8 Predictive formulae can be used to calculate the IMFPs in materials for which no IMFP calculations or measurements have been made. The TPP-2M formula was derived by fitting a modified form of the Bethe IMFPs to that calculated from Ł Correspondence to: M. Krawczyk, Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland. E-mail: [email protected] Contract/grant sponsor: Foundation for Polish Science.

Copyright  2006 John Wiley & Sons, Ltd.

the experimental optical IMFP data for 27 elemental solids and selected organic materials in the electron energy range 50–2000 eV.5 A number of parameters characterizing the examined sample has to be known (density, stoichiometry, band-gap energy, and the number of valence electrons per atom or molecule). The G-1 equation6 provides IMFP values for all elements and compounds in the energy range 200–2000 eV. This equation requires only a simple set of input parameters (density, stoichiometry). The aim of this work is to determine experimentally by EPES, for the first time, the IMFPs in bulk SiC with different structural properties and surface concentrations of its constituents. The surface excitation effects are not accounted for in the software package EPES. In addition, the EPES-measured IMFPs are compared with the IMFPs calculated from two predictive formulae, i.e. the TPP-2M equation5 and the G-1 equation.6 Finally, the scatter between the experimental IMFPs and those from predictive formulae are successfully determined.

EXPERIMENTAL Samples The samples used in this study were: (i) polycrystalline SiC sputtering target (25.4 mm dia ð 3.18 mm thick, 99.5%, metals basis) purchased from Alfa Aesar (A Johnson Matthey Company, Karlsruhe, Germany); (ii) SiC(0001) crystal with a size of 10 mm ð 10 mm ð ¾0.25 mm (one side mirror polished) purchased from MaTecK GmbH (Julich, Germany). ¨ The samples were sputter cleaned and amorphized by 1 keV ArC irradiation.

Measured IMFPs for SiC

Spectrometers The EPES measurements were carried out using two spectrometers with different analyzers – a double-pass cylindrical mirror analyzer (DCMA) and a spherical sector analyzer (SSA) – over a wide electron energy range E D 0.2–2.0 keV. Both the analyzers used normal angle of incidence but different acceptance angles and energy resolutions. The spectrometer DCMA PHI 15–255 G (USA) was applied using acceptance angles in the 42.3° š 6° range and the energy resolution E/E D 0.6%. The angle between the SSA MICROLAB 350 spectrometer (Thermo VG Scientific, UK) entrance and the surface normal was 60° . The external acceptance half-angle of this analyzer was 10° but its internal acceptance half-angle was changeable in the angle range 3° –7° . Relative EPES measurements using the MICROLAB 350 spectrometer were performed with the energy resolution E/E D 0.6–0.06%.

Quantitative surface analysis by XPS Surface composition of the SiC samples was investigated prior to and after the EPES measurements by XPS (VG Scientific ESCALAB-210 spectrometer).9,10 The XPS measurements were performed using the Al K˛ radiation source operated at a power of 300 W (15 kV, 20 mA). The angle between the X rays and the surface normal was 68° . Quantitative XPS analysis was based on the C 1s, Si 2p and O 1s photoelectron spectra. Data were analyzed using the ECLIPSE VG program, including satellite subtraction, Shirley background subtraction11 and fitting procedure. Quantification was performed using the multiline method.12

EPES measurements Relative EPES measurements were performed with the DCMA (monocrystalline SiC) and the SSA MICROLAB 350 (polycrystalline SiC) spectrometers. All measurement procedures applied here have been already described in detail elsewhere.8,13 The IMFP energy dependence for the studied SiC samples was obtained in the electron energy range of 200–2000 eV. The elastic peak intensity was isolated from the energyloss region of the measured energy spectrum with the Shirley background subtraction technique.11,14

EVALUATION OF THE IMFPs A detailed description of the procedure for determining the IMFP from the elastic peak intensity has been published elsewhere.15 Briefly, the procedure compares the elastically backscattered electron intensity ratios from a sample and a standard, measured at a given kinetic energy and experimental geometry with those calculated by the Monte Carlo algorithm for the same experimental conditions. The resulting dependencies of the elastic-electron backscattering probabilities on the IMFP are the so-called calibration curves. The Monte Carlo algorithm modified to describe multicomponent materials16 was applied using a single recommended IMFP value for the Ni standard that was calculated for each energy from the fitted parameters in Ref. 17. In the present Monte Carlo scheme, no surface effects

Copyright  2006 John Wiley & Sons, Ltd.

were considered and the total number of electron trajectories of 107 was assumed.16 During the development of the TPP-2M equation,5 the band-gap energy, Eg , and the number of valence electrons, Nv , of SiC are assumed. In the case considered, the parameter Eg equals 2.9 eV.18 For the studied carbide, Nv is calculated from the sum of contributions from each constituent element (i.e. Nv for each element multiplied by the stoichiometric coefficient for that element).17

RESULTS AND DISCUSSION Prior to EPES measurements, the SiC samples were sputter cleaned with 1 keV ArC ions. The XPS spectra recorded in the present work indicate that the composition of the sample surface was close to the Si40 C60 composition19 (in at.%) after having applied argon ion sputtering. As previously reported,19 XPS shows that the SiC films have slightly C-rich compositions in the surface region, but stoichiometric composition in the bulk. We have analyzed the energy dependence of the EPESdetermined IMFPs, assuming two different compound compositions (in at.%) such as Si40 C60 (the XPS-measured surface composition) and Si50 C50 (the ideal stoichiometry) with densities typical for SiC ( D 3.16 g/cm3 ),18 in the coordinates E/IMFP versus lnE (Fano plots). The Fano plots are shown in Figs 1 (polycrystalline SiC) and 2 (monocrystalline SiC). The measured IMFP values (i ) were fitted by a simple Bethe equation20 in the form: i D E/[E2p ˇ lnE]

1

where E is the electron energy (in eV), Ep D 28.8 (Nv /M)1/2 is the free-electron plasmon energy (in eV), Nv is the number of valence electrons per atom or molecule,  is the density (in g cm3 ), and M is the atomic or molecular weight. Values of the parameters E2p ˇ and  were obtained using the nonlinear least-squares (NLLS) algorithm from fits of the EPES IMFPs for each sample and are available in Table 1. Figures 1 and 2 show that the Bethe equation20 provides a satisfactory description of the energy dependence of the IMFP for SiC over the energy range 200–2000 eV. In addition to the measured IMFPs for each compound composition in the electron energy range under study, Figs 1 and 2 show the IMFP values calculated from the TPP-2M5 and the G-16 predictive formulae. The same stoichiometry and density were used in these formulae as in the theoretical model for the EPES method. To compare the IMFPs found from EPES with the corresponding calculated IMFPs, a statistical analysis of the data was made.4 The parameters calculated were the Table 1. Values of Ep2 ˇ and  found in the fits of Eqn (1) to the measured IMFPs for SiC and for electron energies between 200 and 2000 eV Sample Polycrystalline SiC Monocrystalline SiC

˚ 1 ) E2p ˇ (eV A

 (eV1 )

12.09 12.53

0.0493 0.0364

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Figure 1. Fano plots of measured and calculated IMFPs in polycrystalline SiC samples: (a) Si40 C60 ; (b) Si50 C50 . The symbols show measured IMFPs using relative EPES measurements (the DCMA, Ni standard). Dashed line: fitted function. Solid line: values calculated from the TPP-2M5 equation; dotted line: values calculated from the G-16 equation.

Figure 2. Fano plots of measured and calculated IMFPs in SiC(0001) single crystal samples: (a) Si40 C60 ; (b) Si50 C50 . The symbols show measured IMFPs using relative EPES measurements (the SSA, Ni standard). Dashed line: fitted function. Solid line: values calculated from the TPP-2M5 equation; dotted line: values calculated from the G-16 equation.

root-mean-square (RMS) deviation or the mean percentage deviation R. They were calculated from   r 1  RMS D  EPES  theory 2 r EPESD1

Table 2. Statistical analysis of the data. Calculations are made for a number of IMFPs, r D 9 (polycrystalline samples) and/or r D 5 (single crystal samples)

R D 100

  r 1   EPES  theory   r EPESD1  theory

2

where r is the total number of experimental values EPES for a given SiC composition, and theory denotes the IMFP value predicted from the TPP-2M equation5 or the G-1 equation6 at a particular electron energy. The RMS and R values resulting from Eqn (2) for two examined SiC stoichiometries are shown in Table 2. As shown in Figs 1 and 2, good agreement is found between the measured IMFPs in SiC and the corresponding calculated IMFPs from two predictive formulae. Generally, the measured IMFPs agree nicely with the calculated IMFPs for the studied SiC compositions, 40/60, and 50/50 (at.%), assuming polycrystalline and monocrystalline materials. The

Copyright  2006 John Wiley & Sons, Ltd.

Composition (at.%) Polycrystalline samples Si40 C60 Si50 C50 Average values: SiC(0001) single crystal samples Si40 C60 Si50 C50 Average values:

Deviation from TPP-2M5

Deviation from G-16

˚ RMS (A)

R (%)

˚ RMS (A)

R (%)

2.3 2.1 2.2

7.3 6.7 7.0

1.4 2.1 1.7

5.3 7.0 6.1

1.7 1.5 1.6

3.9 4.1 4.0

0.9 1.4 1.1

3.8 3.4 3.6

deviation of the measured IMFPs from the calculated IMFPs is highest for polycrystalline SiC (Table 2).

Surf. Interface Anal. 2006; 38: 644–647 DOI: 10.1002/sia

Measured IMFPs for SiC

The EPES method requires the correction of the surface excitation effect to determine the absolute values of the IMFPs or when the measurements were made without a standard.4 If a standard material is employed it is believed that the effects of surface excitations are likely to be small,21 if the sample material and the standard have similar inelastic-scattering properties. Since the IMFPs are determined in EPES measurements from the ratios of elastically backscattered intensities for the sample and the standard, the ratios of corrections to bulk IMFPs (to take account of surface excitations) for the two materials are likely to be close to unity. For the presently used Ni standard, we Ni have calculated the fSiC s /fs ratios, i.e. the surface electronic excitation (SEE) corrections,15 using values of the material parameters ‘a’22 and the surface excitation probabilities (SEP), Ps (˛, E).2,22,23 These calculations were performed for both the incident and the escaping electrons under the experimental configurations used. The ‘a’ values for SiC and Ni were found to be 0.22 š 0.05 and 0.31 š 0.05, respectively. Moreover, it Ni was found that the value of fSiC s /fs increased considerably from about 0.75 at 200 eV to about 0.88 at 2000 eV. Therefore, we may still correct the present EPES IMFPs for the surface excitation effects. Further improvement of these values are possible, and our work will be continued.

CONCLUSIONS (1) In general, the measured IMFPs agree well with the calculated IMFPs for two studied SiC compositions (stoichiometric 50/50, and the XPS-measured surface composition of 40/60), assuming polycrystalline and single crystal structures. In fact, the best agreement is found for both monocrystalline Si40 C60 and Si50 C50 samples with the density of stoichiometric SiC. (2) EPES proves to be a useful method for the experimental determination of the energy dependence of IMFPs in bulk SiC with different structural properties.

Copyright  2006 John Wiley & Sons, Ltd.

Acknowledgement One of the authors (A.J.) would like to acknowledge the partial support by the Foundation for Polish Science.

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