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Surface excitations in electron backscattering from silicon surfaces
Surface Science 562 (2004) 92–100 www.elsevier.com/locate/susc
Surface excitations in electron backscattering from silicon surfaces J. Zemek a
a,*
, P. Jiricek a, B. Lesiak b, A. Jablonski
b
Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, Cukrovarnicka 10, 162 53 Prague, Czech Republic b Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland Received 16 January 2004; accepted for publication 7 May 2004 Available online 9 June 2004
Abstract Surface excitation effects in surface-sensitive electron spectroscopy (XPS, AES, EPES, EELS) influence substantially the measured peak intensities or peak areas. To obtain reliable quantitative information from the electron spectra, the measured intensities should be corrected for these effects. For this purpose, Chen has suggested a simple procedure based on the knowledge of the surface excitation parameter, SEP. The SEP depends on electron energy, the impact and the emission angle of electrons, and a material studied. The SEP can be calculated from the theory or it can be obtained semi-empirically. In this contribution, we compare both procedures. They are applied on measured electron backscattering probabilities from silicon surface with respect to copper and gold standards. Corrected peak areas are finally used for evaluating of inelastic mean free paths for silicon, and compared with the available literature data. Results show that the semi-empirical approach to the SEPs leads to a better agreement with the predicted behavior. 2004 Elsevier B.V. All rights reserved. Keywords: Electron–solid interactions; Electron–solid scattering and transmission – elastic; Electron–solid scattering and transmission – inelastic; Monte Carlo simulations; Electron bombardment; Silicon
1. Introduction Measurements of the elastically backscattered electron intensities from solid surfaces are the basis for the frequently used technique for determination of the electron inelastic mean free path (IMFP). These measurements are accompanied with calculations of this intensity using theoretical models of electron transport. An input
*
Corresponding author. Fax: +42-4202-3123184. E-mail address: [email protected] (J. Zemek).
parameter for these calculations is the IMFP value adjusted so that the theoretical model leads to the same intensity as the measured intensity. To simplify the experimental procedure, we measure the ratio of intensities for a studied sample and the standard material. This method is known as the relative method, where a sample and a standard material is measured at the same experimental geometry and their intensity ratios are evaluated. The above method is known as elastic peak electron spectroscopy, EPES or EPES IMFP, and it has been reviewed by Gergely [1].
0039-6028/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2004.05.093
J. Zemek et al. / Surface Science 562 (2004) 92–100
The IMFPs can also be calculated from optical data [2] and from predictive formulae, i.e. the TPP-2M [3] and the G1 of Gries [4]. A compilation and analysis of available IMFP data obtained by the EPES, published recently by Powell and Jablonski [5], indicates a large scatter between the predicted and measured values. Generally, it originates from statistical and systematic errors due to uncertainty of electron elastic backscattering probability measurements, model of a solid, model of electron transport in a solid, accuracy of electron elastic scattering cross-sections and accuracy of input parameters to the algorithm simulating the electron transport. A critical review of the current status of theoretical models used for the IMFP determination has been published recently [6]. Therefore, below we have paid attention to important aspects of the EPES experiment. There are two main sources of systematic errors in the experiment originating from (i) the spectrometer and (ii) the sample (standard). Due to the ratio method used in this work, no substantial contribution to the scatter is expected from the experimental geometry and instrumental parameters as a spectrometer transmission function, an electron multiplier gain, stability and intensity of the primary electron beam current, etc. The sample and/or the standard, as a source of the scatter, appears to be more complex. Recently, possible influence of the surface roughness [7] and doping level [8] has been studied on exemplary silicon samples. Results show that the influence of the surface roughness and the doping level is low, or negligible. Actual surface composition of the sample can be properly analysed by XPS and/or AES and considered in the MC calculations [9]. Density of the sample, used as the input parameter in the MC calculations, can influence the resulting EPES IMFPs [4,9]. The sample and the standard surfaces are usually in situ prepared by sputter cleaning. Sputtering can modify the surface density. Particularly, it is known from amorphous silicon research that the density deficit can reach 20% or even more [10] with respect to the single crystal analog. Although a surface density can differ substantially from its bulk value, the bulk values are used for calcula-
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tions since the reliable methods for evaluating the actual surface density values are not commonly available. Another parameter influencing strongly the measured intensities results from the ordered arrangements of atoms in a surface region of samples and standards because the EPES method is confined to incoherent electron elastic scattering. The crystalline structure produces diffraction and/or directional channeling effects, etc. All these effects influence the intensity of the elastic peak [11]. Studies conducted to nickel [12] and titanium [13] showed that the texture and the grain size of polycrystalline materials should be controlled during the measurement. Therefore, metals used for the EPES measurements should have a fine polycrystalline structure. For semiconductors, as illustrated on several III–V compounds, the ordering effects can be eliminated by amorphisation of a surface region of samples by ion beam sputtering or by setting the experimental geometry at minima of the Renninger plots, where incoherent elastic scattering occurs [11]. Finally, the surface excitation by electrons crossing the surface has substantial impact on measured intensities in EPES, XPS, AES and EELS. The surface excitation effects have been pointed out firstly by Ritchie [14], and verified experimentally by Powell and Swan [15]. Although details of electron transport in the surface region of ±0.5 nm (above and beneath the surface) remains a subject for debating [1,16,17], a simple correcting procedure based on the surface excitation parameter (SEP) has been suggested by Chen [18] and already applied to XPS. However, the correction can be easily applied to the EPES spectra. In this work, following our recent preliminary results on silicon [19], we review and compare surface excitation corrections of electron elastic backscattering ratios applied to a silicon sample and a copper or a gold standard. Two approaches to the SEP, theoretical [18] and semi-empirical [20], are compared and used for the surface excitation correction of measured intensity ratios and finally, electron energy dependence of the IMFP in silicon.
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2. Surface excitation corrections The probability for an electron leaving the solid surface without any surface excitations is described by the surface excitation parameter, SEP, or PS ðE; hÞ [18]. The SEP represents the average number of surface excitation events experienced by an electron with energy E incoming and/or leaving the surface at an angle h [21]. Since the electron crosses the surface twice in EPES, the SEP consists of two components for incoming, PSin ðE; hin Þ, and outcoming electrons, PSout ðE; hout Þ, respectively: PS ðE; hÞ ¼ PSin ðE; hin Þ þ PSout ðE; hout Þ
ð2Þ
where kinetic energy E is in eV, ach is the material dependent fitting parameter, ach equals to 2.50, 2.45, and 3.06 for silicon, copper, and gold, respectively. On the base of extensive measurements of reflection energy loss spectra (REELS) for selected metals and semiconductors, Werner et al. [20] extracted the SEP values from the ratio of the number of electrons that induced a surface excitation to those elastically reflected. The SEP values have been fitted with respect to the modified Oswald’s expression [22]. PS ðE; hÞ ¼ 1=ð0:173aH E1=2 cos h þ 1Þ
Iexp ¼ IMC exp½PS ðE; hÞ
ð4Þ
where IMC is the Monte Carlo calculated intensity. The resulting IMFP values should compare well with IMFP values for the bulk [2,4,5].
ð1Þ
were E is the electron energy, hin and hout is the impact and the emission angle. With a model dielectric function, the SEP have been calculated for several metals and semiconductors by Chen [18]: PS ðE; hÞ ¼ ach E1=2 cos1 h
surface excitations were not taken into account. Therefore, to compare the EPES IMFP values with those (bulk-like) derived from the optical data, we applied the surface excitation corrections to the measured intensities, Iexp , of the sample and the standard according to the expression:
ð3Þ
where kinetic energy E is in eV, aH is the material dependent fitting parameter, and aH equals to 1, 2 and 1.5 for Si, Cu, and Au, respectively. For the nearly free electron materials their results agree reasonably with the free electron theory while significant deviations for the other materials were observed. The probability for an electron incoming and leaving the solid surface without any surface excitations can be expressed [18] as exp½PS ðE; hÞ. Corrections for the surface excitation effects can be applied to the measured or MC calculated intensity ratios. In the present MC calculations the
3. Experimental The XPS and EPES measurements were carried using an ADES-400 spectrometer (V.G. Scientific, UK), equipped with a Varian Auger electron gun, X-ray source (MgKa and AlKa radiation), Ar ion source and a hemispherical high-energy resolution analyser. The XPS analysis was used to check a surface cleanness of the sample and the standards. The analyser was operated with the acceptance angle ±4.1 at the pass energy 5 eV (EPES) or 100 eV (XPS). The silicon sample 10 · 10 mm2 was cut from a Si(1 1 1) wafer. The Cu standard was a 500 nm thick polycrystalline copper layer deposited by a vacuum evaporation on Si(1 1 1) wafer. The gold standard was cut from a 0.5 mm thick gold sheet. Before the EPES measurements, the surfaces were sputter-cleaned by Ar ion beam at 60 with respect to the surface normal, using the ion beam energy of 5000 eV, and the ion beam density of 10 lA cm2 at the cleaned surface until no evidence for surface contamination was detected in XPS spectra. The EPES measurements were made for relatively low electron energies from 200 to 1000 eV, where pronounced surface excitation effects are expected (see Eq. (2) or (3)). The electron source operated with an electron beam current 0.1–1.0 lA, and the beam spot diameter 2 mm. The incidence angle of the primary electron beam was 0 and the emission angle was 50, both with respect to the surface normal. The typical full width at half-maximum (FWHM) of the elastic peak in the
J. Zemek et al. / Surface Science 562 (2004) 92–100
whole energy range used was 0.5 eV. The area under the elastic peak was calculated after subtracting the Shirley background.
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intensities from the sample and the standard. The MC algorithm requires the following input parameters: surface composition and density of the investigated sample, IMFPs for standards and geometry of analysis.
4. EPES method 5. Results and discussion In Fig. 1, the SEP dependencies on energy are displayed for silicon, copper and gold using Chen (Eq. (2)) and Werner et al. (Eq. (3)) procedure calculated for the geometry used in the present work, hin ¼ 0, hout ¼ 50. Although the shape of energy dependencies is similar, pronounced
Werner SEPs 0.6
PS(E,θin,θout)
Si Cu Au
0.4
0.2
Chen SEPs 0.6
PS(E,θin,θout)
Principles of typical Monte Carlo algorithm for simulating the electron backscattering events were described by Powell and Jablonski [5]. In the algorithm presently applied, a modification described by Jablonski and Jiricek [23] was used to accelerate the calculations. Any theoretical model describing the elastic backscattering probabilities requires knowledge of elastic scattering cross-sections for atoms constituting the solid. These parameters were taken from the NIST database containing the cross-sections corresponding to the Dirac–Hartree–Fock potentials [24]. These potentials, calculated for isolated atoms, approximate the interaction between an electron and the ionic cores, screened by the solid state and core electrons that represent the scattering centres inside the solid. The detailed analysis of reliability of cross-sections calculated for these potentials, and also for the Thomas–Fermi–Dirac potential frequently used in simulations of electron transport, has been recently published [25]. In the MC algorithm simulating electron transport in a solid, electron exhibits multiple elastic collisions along the trajectory with the distance between elastic collisions described by exponential distribution. In the solid, homogeneously distributed atoms and ideally flat surface are assumed. To determine the IMFPs using the EPES method with a standard at each energy, a set of electron elastic backscattering intensity ratios for investigated sample and standard is calculated using MC algorithm. For Au and Cu standards the recommended IMFPs [5] are used. For an investigated sample a set of IMFPs in the range is assumed. For a given energy, the cal5–300 A culated dependence of ratio of electron backscattering intensity from the sample and the standard is called the calibration curve. The IMFPs are determined by comparing the calculated ratios to the ratios of measured electron backscattering
0.4
0.2
100
300
500
700
900
1100
Energy(eV)
Fig. 1. Energy dependence of the surface excitation parameter calculated for silicon, copper and gold by Eq. (3) (Werner SEPs) and by Eq. (2) (Chen SEPs). hin ¼ 0, hout ¼ 50 measured from the surface normal.
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differences are found for the particular elements. In case of the Werner et al. [20] approach, the SEP values for silicon dominate in all energy range considered with respect to those of gold and copper. Contrary, the highest Chen SEP [18] values are for gold. Angular dependencies of the SEP calculated from Eqs. (2) and (3) are displayed in Fig. 2(a) and (b) for electron energy of 200 and 1000 eV, respectively. As for the energy dependencies, their shape is similar. However, the Chen SEPs reveal more expressive angular dependencies for all elements considered at higher emission angles and low electron energy. In Fig. 3, the resulting correction factors calculated from Eqs. (1)–(4) for the elastic electron intensity ratios of the silicon with respect to copper
1.5
or gold standard are shown for electron energy range 200–1000 eV, impact angle 0, and emission angle 50. Large differences (as high as 20%) are seen for both considered SEP values used in the correcting procedure, particularly at low electron energy. Specifically, the resulting corrections derived from the Chen SEPs are weak (close to 1), while those from Werner et al. are more pronounced. Fig. 4 compares energy dependence of measured electron elastic backscattered probability ratios and those MC calculated uncorrected and corrected using the Chen (Eq. (2)) or Werner (Eq. (3)) SEPs for the silicon sample and the copper or gold standard. A huge difference between the MC uncorrected and the measured ratios is seen in a low-energy region where the surface excitation
1.5
(a)
Werner SEPs
EK=1000 eV Si Cu Au
1.0
(b)
Werner SEPs
EK= 200 eV
1.0
0.5
0.5
0.1
0.1
1.5
1.5
Chen SEPs
Chen SEPs
1.0
1.0
0.5
0.5
0.1
0.1 0
20
40 out (deg)
60
80
0
20
40
60
80
out (deg)
Fig. 2. Emission angle dependence of the surface excitation parameter calculated for silicon, copper and gold at E ¼ 200 eV (a) and 1000 eV (b) by Eq. (3) (Werner SEPs) and by Eq. (2) (Chen SEPs). hin ¼ 0, measured from the surface normal.
J. Zemek et al. / Surface Science 562 (2004) 92–100
97
3.0
1.2
Au standard
Au standard
experiment MC corrected, Werner SEPs MC corrected, Chen SEPs MC uncorrected
Werner SEPs Chen SEPs
ISi/IAu (a.u.)
exp(-PSi)/exp(-PAu)
1.1
1.0
2.0
1.0
0.9 0
0.8 1.6
Cu standard 1.1
Cu standard
ISi/ICu (a.u.)
exp(-PSi)/exp(-Pcu)
1.0
0.9
1.0
0.8 0 100
0.7 100
300
500
700
900
1100
Energy (eV) 300
500
700
900
1100
Energy (eV)
Fig. 3. Energy dependence of the surface correction factor calculated by Eq. (1) for the silicon sample and a standard using Chen and Werner SEPs. hin ¼ 0, hout ¼ 50 measured from the surface normal.
effects are more pronounced (Fig. 1). The MC data corrected using the Werner SEPs are moved toward the measured data for both standards used. A slight shift of the MC data corrected using the Chen SEPs toward the measured ratios for the cupper standard is consistent with Fig. 3. For the gold standard, however, the shift is in the opposite direction. Resulting values of the EPES IMFP are shown in Fig. 5. Here, the uncorrected and both corrected IMFP data are compared with those bulk-like calculated from the optical data by Tanuma et al. [2]. The EPES IMFP silicon data evaluated with respect to the copper standard are in close vicinity of the Tanuma et al. data. The uncorrected data
Fig. 4. Measured electron elastic backscattered probability ratios and those MC calculated uncorrected and corrected by using the Chen or Werner SEPs for the silicon sample and the copper or gold standard.
are systematically below Tanuma et al. values. This is the expected result because the uncorrected data for surface excitation effects result in lower IMFP values with respect to those bulk-like represented here by Tanuma et al. IMFPs [2]. A different picture is seen in the silicon IMFP data evaluated with respect to the gold standard. The uncorrected data are substantially below those bulk-like. Though, the corrections based on the Werner SEPs shift the data towards those bulklike, the shift is not sufficiently large to reach a close vicinity of Tanuma et al. data. Results of the EPES IMFP values uncorrected, as well as corrected and those from Tanuma et al. are compared also quantitatively. The scatter between selected couple of data sets considered were calculated from the root-mean square deviation
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J. Zemek et al. / Surface Science 562 (2004) 92–100
Inelastic mean free path λ(A)
30 20
10
5
" #1=2 r 1 X 2 ðk1 k2 Þ RMS ¼ r j¼1
ð5Þ
X r 1 k1 k2 R ¼ 100 r j¼1 k1
ð6Þ
uncorrected corrected, Werner SEPs corrected, Chen SEPs Tanuma et al.
1 100
30
Inelastic mean free path λ(A)
Au standard
200
500
1000
Cu standard
20
10
5 uncorrected corrected, Werner SEPs corrected, Chen SEPs Tanuma et al.
1 100
200
500
1000
Energy (eV) Fig. 5. Energy dependence of the inelastic mean free path for silicon with respect to copper or gold standard.
(RMS) and percentage deviation (R) using formulae [5]:
where k1 and k2 are the IMFPs evaluated for the same electron energy and different set of input parameters, or optical Tanuma et al. [2] IMFPs, r is the number of IMFPs used in the calculation. The scatter between the measured IMFPs due to difference in the surface excitation effects is listed in Table 1. The closest agreement is reached between corrected data using the Werner SEPs (Cu standard) and Tanuma et al. data [2]. For both standards used, the corrections based on the Werner SEPs result in improved agreement to the bulk-like data. Contrary, the corrections based on the Chen SEPs have led to rather worse results with respect to the bulk-like data. Recently, Jung et al. [26] has applied similar approach to the surface excitation corrections for silicon used as a standard in the EPES IMFP experiment. They have applied both the Chen and Werner et al. SEPs to correct the surface excitations at the silicon surface and found a large difference in the SEP values derived by Chen and Werner et al. As a consequence, the IMFP values for SiO2 sample (measured with respect to the silicon standard corrected by the Chen SEPs) were larger than those derived from the Werner et al. SEPs. In our preliminary study of silicon measured
Table 1 Deviations between the EPES IMFPs: uncorrected, corrected using Werner et al. and Chen SEPs, and Tanuma et al. optical IMFPs Standard Correction Reference Reference correction Reference IMFPs RMS (A) R (%) standard Cu Cu Cu Cu Au Cu Au Cu Au
Uncorrected Werner et al. SEPs Chen SEPs Uncorrected Uncorrected Werner et al. SEPs Werner et al. SEPs Chen SEPs Chen SEPs
Au Au Au – – – – – –
Uncorrected Werner et al. SEPs Chen SEPs – – – – – –
RMS and R values were calculated using Eqs. (5) and (6).
– – – Tanuma Tanuma Tanuma Tanuma Tanuma Tanuma
et et et et et et
al. al. al. al. al. al.
2.92 4.68 3.61 1.78 4.68 1.43 3.38 1.71 5.25
27.64 34.02 33.24 16.44 63.66 8.88 40.47 15.63 77.07
J. Zemek et al. / Surface Science 562 (2004) 92–100
with respect to copper and aluminium standard [19] we applied the surface excitation corrections based on Chen and or Werner et al. SEPs. This procedure was expected to improve agreement of the IMFPs with the IMFPs resulting from the optical data, however the SEPs were applied there incorrectly. From above discussion, a question arises whether the theoretical approach of Chen or the semi-empirical procedure developed by Werner et al. describe the SEPs properly. Except extensive experimental work of Werner et al. [20], combined with a sophisticated deconvolution of REELS spectra based on reliable optical data, there is a lack of next SEP experimental data for a possible verification. For silicon, there is only work estimating the SEPs by Gurban et al. [27]. The SEPs are evaluated from the ratio of the integrated surface plasmon peak to the electron elastic peak area. The dominated bulk loss signal measured at sufficiently high electron energy is used for separating the surface plasmon losses from the REELS spectra [28]. This method is limited to materials exhibiting predominantly plasmon losses in their REELS spectra. The authors provide no information about the experimental geometry. Therefore, the comparison is difficult. In the present experiment, the Werner et al. SEPs behave reasonably. They have led to the expected shift of the surface effect corrected EPES IMFPs. Further work is needed to elucidate the reasons why the theoretical approach failed for materials considered in the present work.
6. Summary and conclusions In the present work, two approaches to the surface excitation parameters, suggested by Chen and Werner et al., were compared for silicon, copper and gold. The both sets of the SEPs were then applied for correction of the electron elastic backscattering probability and finally to obtain the EPES IMFP values for silicon. A comparison of the correcting factors deduced from the Werner et al. and Chen approach and their application to the EPES IMFP data indicates that at least for
99
three materials measured here the corrections based on the Werner et al. semi-empirical approach to the SEP agree well with the expected behavior. Properly applied surface excitation corrections to the measured or the MC calculated electron elastic backscattering probability should led to close agreement with the bulk-like IMFP data derived from optical properties of a material under study. On the other hand, the uncorrected measured electron elastic backscattering probabilities can be compared with those MC calculated if the surface losses are inherently accounted for in the electron transport model.
Acknowledgements The authors (J. Z., P. J.) acknowledge support of project GACR 202/02/237. One of the authors (A. J.) would like to acknowledge partial support by the Foundation for Polish Science.
References [1] G. Gergely, Prog. Surf. Sci. 71 (2002) 31. [2] S. Tanuma, C.J. Powell, D.R. Penn, Surf. Interface Anal. 17 (1991) 911. [3] S. Tanuma, C.J. Powell, D.R. Penn, Surf. Interface Anal. 21 (1994) 165. [4] W.H. Gries, Surf. Interface Anal. 24 (1996) 38. [5] C.J. Powell, A. Jablonski, J. Phys. Chem. Ref. Data 28 (1999) 19. [6] A. Dubus, A. Jablonski, S. Tougaard, Prog. Surf. Sci. 63 (2000) 135. [7] J. Zemek, P. Jiricek, A. Jablonski, B. Lesiak, Surf. Interface Anal. 34 (2002) 215. [8] J. Zemek, P. Jiricek, B. Lesiak, A. Jablonski, Surf. Interface Anal. 36 (2004), in press. [9] B. Lesiak, A. Jablonski, J. Zemek, P. Jiricek, J. Pavluch, Surf. Interface Anal. 33 (2002) 381. [10] O. Renner, J. Zemek, Czech. J. Phys. B 23 (1973) 1273. [11] G. Gergely, A. Barna, A. Sulyok, C. Jardin, B. Gruzza, L. Bideux, C. Robert, J. Toth, D. Varga, Vacuum 54 (1999) 201. [12] P. Jiricek, J. Zemek, P. Lejcek, B. Lesiak, A. Jablonski, nansky, J. Vac. Sci. Technol. A 20 (2002) 447. M. Cer nansky, Surf. [13] B. Lesiak, J. Zemek, P. Jiricek, M. Cer Interface Anal. 36 (2004), in press. [14] R.H. Ritchie, Phys. Rev. 106 (1957) 874. [15] C.J. Powell, J.B. Swan, Phys. Rev. 115 (1959) 869. [16] M. Vicanek, Surf. Sci. 400 (1999) 1.
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[17] W.S.M. Werner, C. Eisenmenger-Sittner, J. Zemek, P. Jiricek, Phys. Rev. B 67 (2003) 155412. [18] Y.F. Chen, Surf. Sci. 519 (2002) 115. [19] J. Zemek, P. Jiricek, B. Lesiak, A. Jablonski, Surf. Sci. 531 (2003) L335. [20] W.S.M. Werner, W. Smekal, C. Tomastik, H. Stori, Surf. Sci. 486 (2001) L461. [21] R.F. Egerton, Electron Energy-Loss Spectroscopy in the Electron Microscope, Plenum Press, New York, 1986. [22] R. Oswald, Ph.D. Thesis, Eberhard-Karls-Universitat Tubingen, 1992. [23] A. Jablonski, P. Jiricek, Surf. Sci. 412/413 (1998) 42.
[24] NIST Electron Elastic-Scattering Cross-Section Database, Standard Reference Data Program (SRD 64), National Institute of Standards and Technology: Gaithersburg, MD, 2002, v. 3.0. [25] A. Jablonski, F. Salvat, C.J. Powell, J. Phys. Chem. Ref. Data 33 (2004) 409. [26] R. Jung, J.C. Lee, G.T. Orosz, A. Sulyok, G. Zsolt, M. Menyhard, Surf. Sci. 543 (2003) 153. [27] S. Gurban, G. Gergely, M. Menyhard, J. Adam, M. Adamik, Cs. Daroczi, J. Toth, D. Varga, A. Csik, B. Gruzza, Surf. Interface Anal. 34 (2002) 206. [28] G. Gergely, M. Menyhard, S. Gurban, A. Sulyok, J. Toth, D. Varga, S. Tougaard, Solid State Ionics 141 (2001) 47.
Surface excitations in electron backscattering from silicon surfaces J. Zemek a
a,*
, P. Jiricek a, B. Lesiak b, A. Jablonski
b
Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, Cukrovarnicka 10, 162 53 Prague, Czech Republic b Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland Received 16 January 2004; accepted for publication 7 May 2004 Available online 9 June 2004
Abstract Surface excitation effects in surface-sensitive electron spectroscopy (XPS, AES, EPES, EELS) influence substantially the measured peak intensities or peak areas. To obtain reliable quantitative information from the electron spectra, the measured intensities should be corrected for these effects. For this purpose, Chen has suggested a simple procedure based on the knowledge of the surface excitation parameter, SEP. The SEP depends on electron energy, the impact and the emission angle of electrons, and a material studied. The SEP can be calculated from the theory or it can be obtained semi-empirically. In this contribution, we compare both procedures. They are applied on measured electron backscattering probabilities from silicon surface with respect to copper and gold standards. Corrected peak areas are finally used for evaluating of inelastic mean free paths for silicon, and compared with the available literature data. Results show that the semi-empirical approach to the SEPs leads to a better agreement with the predicted behavior. 2004 Elsevier B.V. All rights reserved. Keywords: Electron–solid interactions; Electron–solid scattering and transmission – elastic; Electron–solid scattering and transmission – inelastic; Monte Carlo simulations; Electron bombardment; Silicon
1. Introduction Measurements of the elastically backscattered electron intensities from solid surfaces are the basis for the frequently used technique for determination of the electron inelastic mean free path (IMFP). These measurements are accompanied with calculations of this intensity using theoretical models of electron transport. An input
*
Corresponding author. Fax: +42-4202-3123184. E-mail address: [email protected] (J. Zemek).
parameter for these calculations is the IMFP value adjusted so that the theoretical model leads to the same intensity as the measured intensity. To simplify the experimental procedure, we measure the ratio of intensities for a studied sample and the standard material. This method is known as the relative method, where a sample and a standard material is measured at the same experimental geometry and their intensity ratios are evaluated. The above method is known as elastic peak electron spectroscopy, EPES or EPES IMFP, and it has been reviewed by Gergely [1].
0039-6028/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2004.05.093
J. Zemek et al. / Surface Science 562 (2004) 92–100
The IMFPs can also be calculated from optical data [2] and from predictive formulae, i.e. the TPP-2M [3] and the G1 of Gries [4]. A compilation and analysis of available IMFP data obtained by the EPES, published recently by Powell and Jablonski [5], indicates a large scatter between the predicted and measured values. Generally, it originates from statistical and systematic errors due to uncertainty of electron elastic backscattering probability measurements, model of a solid, model of electron transport in a solid, accuracy of electron elastic scattering cross-sections and accuracy of input parameters to the algorithm simulating the electron transport. A critical review of the current status of theoretical models used for the IMFP determination has been published recently [6]. Therefore, below we have paid attention to important aspects of the EPES experiment. There are two main sources of systematic errors in the experiment originating from (i) the spectrometer and (ii) the sample (standard). Due to the ratio method used in this work, no substantial contribution to the scatter is expected from the experimental geometry and instrumental parameters as a spectrometer transmission function, an electron multiplier gain, stability and intensity of the primary electron beam current, etc. The sample and/or the standard, as a source of the scatter, appears to be more complex. Recently, possible influence of the surface roughness [7] and doping level [8] has been studied on exemplary silicon samples. Results show that the influence of the surface roughness and the doping level is low, or negligible. Actual surface composition of the sample can be properly analysed by XPS and/or AES and considered in the MC calculations [9]. Density of the sample, used as the input parameter in the MC calculations, can influence the resulting EPES IMFPs [4,9]. The sample and the standard surfaces are usually in situ prepared by sputter cleaning. Sputtering can modify the surface density. Particularly, it is known from amorphous silicon research that the density deficit can reach 20% or even more [10] with respect to the single crystal analog. Although a surface density can differ substantially from its bulk value, the bulk values are used for calcula-
93
tions since the reliable methods for evaluating the actual surface density values are not commonly available. Another parameter influencing strongly the measured intensities results from the ordered arrangements of atoms in a surface region of samples and standards because the EPES method is confined to incoherent electron elastic scattering. The crystalline structure produces diffraction and/or directional channeling effects, etc. All these effects influence the intensity of the elastic peak [11]. Studies conducted to nickel [12] and titanium [13] showed that the texture and the grain size of polycrystalline materials should be controlled during the measurement. Therefore, metals used for the EPES measurements should have a fine polycrystalline structure. For semiconductors, as illustrated on several III–V compounds, the ordering effects can be eliminated by amorphisation of a surface region of samples by ion beam sputtering or by setting the experimental geometry at minima of the Renninger plots, where incoherent elastic scattering occurs [11]. Finally, the surface excitation by electrons crossing the surface has substantial impact on measured intensities in EPES, XPS, AES and EELS. The surface excitation effects have been pointed out firstly by Ritchie [14], and verified experimentally by Powell and Swan [15]. Although details of electron transport in the surface region of ±0.5 nm (above and beneath the surface) remains a subject for debating [1,16,17], a simple correcting procedure based on the surface excitation parameter (SEP) has been suggested by Chen [18] and already applied to XPS. However, the correction can be easily applied to the EPES spectra. In this work, following our recent preliminary results on silicon [19], we review and compare surface excitation corrections of electron elastic backscattering ratios applied to a silicon sample and a copper or a gold standard. Two approaches to the SEP, theoretical [18] and semi-empirical [20], are compared and used for the surface excitation correction of measured intensity ratios and finally, electron energy dependence of the IMFP in silicon.
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2. Surface excitation corrections The probability for an electron leaving the solid surface without any surface excitations is described by the surface excitation parameter, SEP, or PS ðE; hÞ [18]. The SEP represents the average number of surface excitation events experienced by an electron with energy E incoming and/or leaving the surface at an angle h [21]. Since the electron crosses the surface twice in EPES, the SEP consists of two components for incoming, PSin ðE; hin Þ, and outcoming electrons, PSout ðE; hout Þ, respectively: PS ðE; hÞ ¼ PSin ðE; hin Þ þ PSout ðE; hout Þ
ð2Þ
where kinetic energy E is in eV, ach is the material dependent fitting parameter, ach equals to 2.50, 2.45, and 3.06 for silicon, copper, and gold, respectively. On the base of extensive measurements of reflection energy loss spectra (REELS) for selected metals and semiconductors, Werner et al. [20] extracted the SEP values from the ratio of the number of electrons that induced a surface excitation to those elastically reflected. The SEP values have been fitted with respect to the modified Oswald’s expression [22]. PS ðE; hÞ ¼ 1=ð0:173aH E1=2 cos h þ 1Þ
Iexp ¼ IMC exp½PS ðE; hÞ
ð4Þ
where IMC is the Monte Carlo calculated intensity. The resulting IMFP values should compare well with IMFP values for the bulk [2,4,5].
ð1Þ
were E is the electron energy, hin and hout is the impact and the emission angle. With a model dielectric function, the SEP have been calculated for several metals and semiconductors by Chen [18]: PS ðE; hÞ ¼ ach E1=2 cos1 h
surface excitations were not taken into account. Therefore, to compare the EPES IMFP values with those (bulk-like) derived from the optical data, we applied the surface excitation corrections to the measured intensities, Iexp , of the sample and the standard according to the expression:
ð3Þ
where kinetic energy E is in eV, aH is the material dependent fitting parameter, and aH equals to 1, 2 and 1.5 for Si, Cu, and Au, respectively. For the nearly free electron materials their results agree reasonably with the free electron theory while significant deviations for the other materials were observed. The probability for an electron incoming and leaving the solid surface without any surface excitations can be expressed [18] as exp½PS ðE; hÞ. Corrections for the surface excitation effects can be applied to the measured or MC calculated intensity ratios. In the present MC calculations the
3. Experimental The XPS and EPES measurements were carried using an ADES-400 spectrometer (V.G. Scientific, UK), equipped with a Varian Auger electron gun, X-ray source (MgKa and AlKa radiation), Ar ion source and a hemispherical high-energy resolution analyser. The XPS analysis was used to check a surface cleanness of the sample and the standards. The analyser was operated with the acceptance angle ±4.1 at the pass energy 5 eV (EPES) or 100 eV (XPS). The silicon sample 10 · 10 mm2 was cut from a Si(1 1 1) wafer. The Cu standard was a 500 nm thick polycrystalline copper layer deposited by a vacuum evaporation on Si(1 1 1) wafer. The gold standard was cut from a 0.5 mm thick gold sheet. Before the EPES measurements, the surfaces were sputter-cleaned by Ar ion beam at 60 with respect to the surface normal, using the ion beam energy of 5000 eV, and the ion beam density of 10 lA cm2 at the cleaned surface until no evidence for surface contamination was detected in XPS spectra. The EPES measurements were made for relatively low electron energies from 200 to 1000 eV, where pronounced surface excitation effects are expected (see Eq. (2) or (3)). The electron source operated with an electron beam current 0.1–1.0 lA, and the beam spot diameter 2 mm. The incidence angle of the primary electron beam was 0 and the emission angle was 50, both with respect to the surface normal. The typical full width at half-maximum (FWHM) of the elastic peak in the
J. Zemek et al. / Surface Science 562 (2004) 92–100
whole energy range used was 0.5 eV. The area under the elastic peak was calculated after subtracting the Shirley background.
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intensities from the sample and the standard. The MC algorithm requires the following input parameters: surface composition and density of the investigated sample, IMFPs for standards and geometry of analysis.
4. EPES method 5. Results and discussion In Fig. 1, the SEP dependencies on energy are displayed for silicon, copper and gold using Chen (Eq. (2)) and Werner et al. (Eq. (3)) procedure calculated for the geometry used in the present work, hin ¼ 0, hout ¼ 50. Although the shape of energy dependencies is similar, pronounced
Werner SEPs 0.6
PS(E,θin,θout)
Si Cu Au
0.4
0.2
Chen SEPs 0.6
PS(E,θin,θout)
Principles of typical Monte Carlo algorithm for simulating the electron backscattering events were described by Powell and Jablonski [5]. In the algorithm presently applied, a modification described by Jablonski and Jiricek [23] was used to accelerate the calculations. Any theoretical model describing the elastic backscattering probabilities requires knowledge of elastic scattering cross-sections for atoms constituting the solid. These parameters were taken from the NIST database containing the cross-sections corresponding to the Dirac–Hartree–Fock potentials [24]. These potentials, calculated for isolated atoms, approximate the interaction between an electron and the ionic cores, screened by the solid state and core electrons that represent the scattering centres inside the solid. The detailed analysis of reliability of cross-sections calculated for these potentials, and also for the Thomas–Fermi–Dirac potential frequently used in simulations of electron transport, has been recently published [25]. In the MC algorithm simulating electron transport in a solid, electron exhibits multiple elastic collisions along the trajectory with the distance between elastic collisions described by exponential distribution. In the solid, homogeneously distributed atoms and ideally flat surface are assumed. To determine the IMFPs using the EPES method with a standard at each energy, a set of electron elastic backscattering intensity ratios for investigated sample and standard is calculated using MC algorithm. For Au and Cu standards the recommended IMFPs [5] are used. For an investigated sample a set of IMFPs in the range is assumed. For a given energy, the cal5–300 A culated dependence of ratio of electron backscattering intensity from the sample and the standard is called the calibration curve. The IMFPs are determined by comparing the calculated ratios to the ratios of measured electron backscattering
0.4
0.2
100
300
500
700
900
1100
Energy(eV)
Fig. 1. Energy dependence of the surface excitation parameter calculated for silicon, copper and gold by Eq. (3) (Werner SEPs) and by Eq. (2) (Chen SEPs). hin ¼ 0, hout ¼ 50 measured from the surface normal.
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differences are found for the particular elements. In case of the Werner et al. [20] approach, the SEP values for silicon dominate in all energy range considered with respect to those of gold and copper. Contrary, the highest Chen SEP [18] values are for gold. Angular dependencies of the SEP calculated from Eqs. (2) and (3) are displayed in Fig. 2(a) and (b) for electron energy of 200 and 1000 eV, respectively. As for the energy dependencies, their shape is similar. However, the Chen SEPs reveal more expressive angular dependencies for all elements considered at higher emission angles and low electron energy. In Fig. 3, the resulting correction factors calculated from Eqs. (1)–(4) for the elastic electron intensity ratios of the silicon with respect to copper
1.5
or gold standard are shown for electron energy range 200–1000 eV, impact angle 0, and emission angle 50. Large differences (as high as 20%) are seen for both considered SEP values used in the correcting procedure, particularly at low electron energy. Specifically, the resulting corrections derived from the Chen SEPs are weak (close to 1), while those from Werner et al. are more pronounced. Fig. 4 compares energy dependence of measured electron elastic backscattered probability ratios and those MC calculated uncorrected and corrected using the Chen (Eq. (2)) or Werner (Eq. (3)) SEPs for the silicon sample and the copper or gold standard. A huge difference between the MC uncorrected and the measured ratios is seen in a low-energy region where the surface excitation
1.5
(a)
Werner SEPs
EK=1000 eV Si Cu Au
1.0
(b)
Werner SEPs
EK= 200 eV
1.0
0.5
0.5
0.1
0.1
1.5
1.5
Chen SEPs
Chen SEPs
1.0
1.0
0.5
0.5
0.1
0.1 0
20
40 out (deg)
60
80
0
20
40
60
80
out (deg)
Fig. 2. Emission angle dependence of the surface excitation parameter calculated for silicon, copper and gold at E ¼ 200 eV (a) and 1000 eV (b) by Eq. (3) (Werner SEPs) and by Eq. (2) (Chen SEPs). hin ¼ 0, measured from the surface normal.
J. Zemek et al. / Surface Science 562 (2004) 92–100
97
3.0
1.2
Au standard
Au standard
experiment MC corrected, Werner SEPs MC corrected, Chen SEPs MC uncorrected
Werner SEPs Chen SEPs
ISi/IAu (a.u.)
exp(-PSi)/exp(-PAu)
1.1
1.0
2.0
1.0
0.9 0
0.8 1.6
Cu standard 1.1
Cu standard
ISi/ICu (a.u.)
exp(-PSi)/exp(-Pcu)
1.0
0.9
1.0
0.8 0 100
0.7 100
300
500
700
900
1100
Energy (eV) 300
500
700
900
1100
Energy (eV)
Fig. 3. Energy dependence of the surface correction factor calculated by Eq. (1) for the silicon sample and a standard using Chen and Werner SEPs. hin ¼ 0, hout ¼ 50 measured from the surface normal.
effects are more pronounced (Fig. 1). The MC data corrected using the Werner SEPs are moved toward the measured data for both standards used. A slight shift of the MC data corrected using the Chen SEPs toward the measured ratios for the cupper standard is consistent with Fig. 3. For the gold standard, however, the shift is in the opposite direction. Resulting values of the EPES IMFP are shown in Fig. 5. Here, the uncorrected and both corrected IMFP data are compared with those bulk-like calculated from the optical data by Tanuma et al. [2]. The EPES IMFP silicon data evaluated with respect to the copper standard are in close vicinity of the Tanuma et al. data. The uncorrected data
Fig. 4. Measured electron elastic backscattered probability ratios and those MC calculated uncorrected and corrected by using the Chen or Werner SEPs for the silicon sample and the copper or gold standard.
are systematically below Tanuma et al. values. This is the expected result because the uncorrected data for surface excitation effects result in lower IMFP values with respect to those bulk-like represented here by Tanuma et al. IMFPs [2]. A different picture is seen in the silicon IMFP data evaluated with respect to the gold standard. The uncorrected data are substantially below those bulk-like. Though, the corrections based on the Werner SEPs shift the data towards those bulklike, the shift is not sufficiently large to reach a close vicinity of Tanuma et al. data. Results of the EPES IMFP values uncorrected, as well as corrected and those from Tanuma et al. are compared also quantitatively. The scatter between selected couple of data sets considered were calculated from the root-mean square deviation
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J. Zemek et al. / Surface Science 562 (2004) 92–100
Inelastic mean free path λ(A)
30 20
10
5
" #1=2 r 1 X 2 ðk1 k2 Þ RMS ¼ r j¼1
ð5Þ
X r 1 k1 k2 R ¼ 100 r j¼1 k1
ð6Þ
uncorrected corrected, Werner SEPs corrected, Chen SEPs Tanuma et al.
1 100
30
Inelastic mean free path λ(A)
Au standard
200
500
1000
Cu standard
20
10
5 uncorrected corrected, Werner SEPs corrected, Chen SEPs Tanuma et al.
1 100
200
500
1000
Energy (eV) Fig. 5. Energy dependence of the inelastic mean free path for silicon with respect to copper or gold standard.
(RMS) and percentage deviation (R) using formulae [5]:
where k1 and k2 are the IMFPs evaluated for the same electron energy and different set of input parameters, or optical Tanuma et al. [2] IMFPs, r is the number of IMFPs used in the calculation. The scatter between the measured IMFPs due to difference in the surface excitation effects is listed in Table 1. The closest agreement is reached between corrected data using the Werner SEPs (Cu standard) and Tanuma et al. data [2]. For both standards used, the corrections based on the Werner SEPs result in improved agreement to the bulk-like data. Contrary, the corrections based on the Chen SEPs have led to rather worse results with respect to the bulk-like data. Recently, Jung et al. [26] has applied similar approach to the surface excitation corrections for silicon used as a standard in the EPES IMFP experiment. They have applied both the Chen and Werner et al. SEPs to correct the surface excitations at the silicon surface and found a large difference in the SEP values derived by Chen and Werner et al. As a consequence, the IMFP values for SiO2 sample (measured with respect to the silicon standard corrected by the Chen SEPs) were larger than those derived from the Werner et al. SEPs. In our preliminary study of silicon measured
Table 1 Deviations between the EPES IMFPs: uncorrected, corrected using Werner et al. and Chen SEPs, and Tanuma et al. optical IMFPs Standard Correction Reference Reference correction Reference IMFPs RMS (A) R (%) standard Cu Cu Cu Cu Au Cu Au Cu Au
Uncorrected Werner et al. SEPs Chen SEPs Uncorrected Uncorrected Werner et al. SEPs Werner et al. SEPs Chen SEPs Chen SEPs
Au Au Au – – – – – –
Uncorrected Werner et al. SEPs Chen SEPs – – – – – –
RMS and R values were calculated using Eqs. (5) and (6).
– – – Tanuma Tanuma Tanuma Tanuma Tanuma Tanuma
et et et et et et
al. al. al. al. al. al.
2.92 4.68 3.61 1.78 4.68 1.43 3.38 1.71 5.25
27.64 34.02 33.24 16.44 63.66 8.88 40.47 15.63 77.07
J. Zemek et al. / Surface Science 562 (2004) 92–100
with respect to copper and aluminium standard [19] we applied the surface excitation corrections based on Chen and or Werner et al. SEPs. This procedure was expected to improve agreement of the IMFPs with the IMFPs resulting from the optical data, however the SEPs were applied there incorrectly. From above discussion, a question arises whether the theoretical approach of Chen or the semi-empirical procedure developed by Werner et al. describe the SEPs properly. Except extensive experimental work of Werner et al. [20], combined with a sophisticated deconvolution of REELS spectra based on reliable optical data, there is a lack of next SEP experimental data for a possible verification. For silicon, there is only work estimating the SEPs by Gurban et al. [27]. The SEPs are evaluated from the ratio of the integrated surface plasmon peak to the electron elastic peak area. The dominated bulk loss signal measured at sufficiently high electron energy is used for separating the surface plasmon losses from the REELS spectra [28]. This method is limited to materials exhibiting predominantly plasmon losses in their REELS spectra. The authors provide no information about the experimental geometry. Therefore, the comparison is difficult. In the present experiment, the Werner et al. SEPs behave reasonably. They have led to the expected shift of the surface effect corrected EPES IMFPs. Further work is needed to elucidate the reasons why the theoretical approach failed for materials considered in the present work.
6. Summary and conclusions In the present work, two approaches to the surface excitation parameters, suggested by Chen and Werner et al., were compared for silicon, copper and gold. The both sets of the SEPs were then applied for correction of the electron elastic backscattering probability and finally to obtain the EPES IMFP values for silicon. A comparison of the correcting factors deduced from the Werner et al. and Chen approach and their application to the EPES IMFP data indicates that at least for
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three materials measured here the corrections based on the Werner et al. semi-empirical approach to the SEP agree well with the expected behavior. Properly applied surface excitation corrections to the measured or the MC calculated electron elastic backscattering probability should led to close agreement with the bulk-like IMFP data derived from optical properties of a material under study. On the other hand, the uncorrected measured electron elastic backscattering probabilities can be compared with those MC calculated if the surface losses are inherently accounted for in the electron transport model.
Acknowledgements The authors (J. Z., P. J.) acknowledge support of project GACR 202/02/237. One of the authors (A. J.) would like to acknowledge partial support by the Foundation for Polish Science.
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