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Elastic electron backscattering from flat and rough Si surfaces
Journal of Electron Spectroscopy and Related Phenomena 152 (2006) 100–106
Elastic electron backscattering from flat and rough Si surfaces A. Jablonski a,∗ , K. Olejnik b , J. Zemek b a
b
Institute of Physical Chemistry Polish Academy of Sciences, ul. Kasprzaka 44/52, 01-224 Warszawa, Poland Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnicka 10,162 53 Prague 6, Czech Republic Received 14 November 2005; received in revised form 8 April 2006; accepted 10 April 2006 Available online 29 April 2006
Abstract In earlier studies, it has been found that the surface roughness influences only weakly the inelastic mean free path values resulting from elastic peak electron spectroscopy. To address this issue, in the present work, the elastic electron backscattering intensity has been systematically studied in numerous experimental configurations. Measurements were made for the flat Si sample, and for the Si sample with well-defined roughness in the form of long trapezoidal channels. Such structure is a good representation for one-dimensional models used in theoretical description of the surface roughness effects in XPS. It has been found that there is a pronounced influence of the surface roughness on the electron backscattered intensity at the primary beam incidence different from normal. These results were observed at energies of interest for surface sensitive electron spectroscopies, i.e. 200, 500 and 1000 eV. Additionally, the elastic backscattering probability for a flat surface was found to agree well with the theoretical predictions. Correction for the surface energy losses further improved the agreement between theory and experiment. © 2006 Elsevier B.V. All rights reserved. Keywords: Surface roughness; Elastic electron backscattering; Monte Carlo simulations; Electron transport
1. Introduction The surface roughness is a factor which is very difficult to control in practical surface analysis. The main reason is that the surface structure depends on the procedure of preparation, and it would be very difficult, if ever possible, to propose an accurate description of the roughness in the mathematical formalism of electron spectroscopies. In early days of Auger electron spectroscopy, it has been proposed to introduce a surface-roughness factor, R, into the formalism quantifying this technique [1]. However, the concept of a single factor does not seem to be followed in a later literature. A number of studies were addressed towards the influence of the surface roughness on the photoelectron signal intensity. The surface roughness may affect the monitored photoelectron intensity in a number of ways: 1. a particular area on the surface may be shaded from the incident X-rays; 2. photoelectrons ejected from a given area may be recaptured by the adjacent surface protrusions; ∗
Corresponding author. Tel.: +48 22 343 3331; fax: +48 22 343 3333. E-mail address: [email protected] (A. Jablonski).
0368-2048/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2006.04.003
3. photoelectrons can be elastically scattered on the adjacent protrusions. This problem is very difficult to describe theoretically. A convenient practice to evaluate the surface roughness was to assume a simple model of rough surface which makes possible the theoretical description of the photoelectron intensity. Ebel et al. [2] adjusted the model of variable cubes, used earlier in X-ray fluorescence analysis, to the formalism of XPS. In this model, the surface roughness is varied by rotation of adjacent cubes around an axis parallel to the surface. This model turned out to be useful also in evaluation of photoelectron intensity from rough surfaces with overlayer [3]. A concept of one-dimensional rough surfaces was extensively analyzed by Fadley et al. [4]. Comparison of the overlayer thicknesses determined by XPS on smooth and artificially roughened surfaces proved that the surface roughness limits the XPS configurations useful for measurements [5]. In fact, only the normal emission angle should be recommended for such studies. Additionally, surface roughness leads to the overestimation of the measured thickness, as compared to smooth surfaces. The problem of the overlayer thickness measurements was also studied by Gunter and Niemantsverdriet [6]. These authors performed the Monte Carlo analysis for a statistically created one-dimensional model of a rough sur-
A. Jablonski et al. / Journal of Electron Spectroscopy and Related Phenomena 152 (2006) 100–106
face. They found that the error caused by the surface roughness is distinctly smallest when the experimental configuration with the emission angle of 35◦ is used. This observation was found to be weakly dependent on the extent of the surface corrugation. Werner [7] generalized the above result by proposing the term of “magic angle” for this experimental geometry. In a recent work, Olejnik et al. [8] studied, experimentally and theoretically, the angular dependence of photoemission from well defined threedimensional structures on the silicon surface. The authors have shown that, in fact, the “magic angle” depends on the character of the surface roughness, and in the studied cases varied between 31◦ and 56◦ . In recent years, we observe a growing interest in techniques based on measurements of the elastic electron backscattering probability for studied surfaces. These techniques are known under the acronym EPES (elastic peak electron spectroscopy). A spectacular application of this technique is the determination of the inelastic mean free path (IMFP) of electrons in a solid (Ref. [9] and references therein). In a typical experiment, a solid surface is bombarded with a beam of monoenergetic electrons, and the intensity of the so-called elastic peak is monitored. It is of critical importance to define, possibly accurately, the experimental configuration. One can expect that the surface structure may have a major influence on the resulting IMFPs. In contrast, rather minor effects of the roughness were reported in the literature. Dolinski et al. [10] studied the scraped and sputtered samples of Ag and Cu; both procedures must have resulted in a difference in surface roughness. Despite this fact, similar IMFP values were obtained for these surfaces. Jiricek et al. [11] sputtered two samples of silicon with different doses of Ar+ ions which resulted in different roughness. The amplitude of roughness was estimated to be 1.7 and 2.2 nm. No substantial influence on the IMFPs obtained from EPES has been found. Similar study has been performed Zemek et al. [12] for two Si samples with a distinctly different roughness: a polished Si sample with roughness amplitude of 5.5 nm, and grinded sample with roughness amplitude of 760 nm. Again, the IMFP values for both samples were found to be similar. Thus, it seems that the EPES procedure for determining the IMFP is not affected by the surface roughness. In the reported measurements of the IMFPs using the EPES method, the beam of primary electrons was located along the surface normal. Thus, the shading of primary electrons by the surface protrusions is minimized. We may expect that a more pronounced difference between elastic backscattering probabilities for surfaces of different roughness can be observed for glancing incidence of primary electrons. The purpose of the present work is to perform a systematic study of the surface roughness effects in numerous experimental configurations defined by the primary beam incidence angle and the electron emission angle. 2. Experimental Two samples were prepared from the same silicon wafer: 1. a flat Si (1 0 0) sample, 10 mm × 10 mm, with average surface roughness below 1 nm, and
101
Fig. 1. Idealized model of a rough silicon surface. (a) The AFM image; (b) the calculated profile in a direction perpendicular to the trapezoidal channels.
2. rough Si sample, 10 mm × 10 mm, with a well-defined structure of trapezoidal channels. The structure of parallel channels was prepared on the Si (1 0 0) surface with photolithography. The image, recorded ex situ with the AFM in the contact mode (Topometrix Explorer), is shown in Fig. 1(a). The linescan, shown in Fig. 1(b), was extracted from the surface image using software provided by the AFM producer. As follows from this illustration, the channels had a triangular shape with average depth of about 6 m. The distance between channels was about 12.5 m. Measurements of the elastic peak intensity were carried out in an ADES 400 angle-resolved photoelectron spectrometer (V.G. Scientific, UK) equipped with a rotatable hemispherical electron energy analyzer, an electron gun, and an ion gun for sputtercleaning (AG-2, V.G. Scientific, UK). Before the EPES measurements, a thin native surface oxide (∼1 nm thick) and a slight carbon surface contamination were removed in-situ by sputtercleaning (Ar ion beam, 5000 eV ion beam energy, 10 A/cm2 ion beam current density, angle of incidence of 60◦ measured from the surface normal). To avoid the effect of shadowing in the case of roughened sample, the ion beam was located in a plane parallel to the channels. The surface cleanness was checked by XPS. Elastically backscattered electrons were collected by the analyzer within a small acceptance angle. The half-cone angle of the
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Si atoms. On normalization, we have W(θ) = 2π
1 dσe sin θ σe dΩ
(1)
where σ e and dσ e /dΩ is the total and differential elastic scattering cross-section. The following weight is associated with the kth trajectory: ⎧ ⎨ exp(−xk /λin ) if the electron entered the analyzer with acceptance angle Ω, ηk = (2) ⎩ 0 in all other cases. where xk is the length of the kth trajectory, and λin is the IMFP. The elastic backscattering probability is assumed to be equal to the mean value of the above weight. Suppose that n complete electron trajectories were generated for a given experimental configuration and electron energy. We have then: Fig. 2. Outline of the experimental setup.
n
η = ηk = analyzer was 4.1◦ . The spectra were recorded in the FAT mode at a pass energy of 20 eV. The electron source beam current was 0.1–1.0 A, and the electron beam diameter was 2–3 mm. The elastic peaks were recorded at the primary electron energies 200, 500 and 1000 eV. During measurements, the beam incidence angle, θ 0 , was fixed in one series of measurements while the emission angles α were varied in steps of 20◦ , by rotation of the analyzer between the direction of the electron beam and the emission angle of 80◦ . Measurements were made for five incidence angles θ 0 , i.e. 0◦ , 20◦ , 40◦ , 60◦ and 80◦ . Outline of the experimental setup is shown in Fig. 2. The electron beam, the direction to the analyzer, and the surface normal were located in one plane. This plane was perpendicular to the channels on the rough surface (i.e. in the direction of the scan, as shown in Fig. 1(a)). The angle of the incidence of the electron beam and the angle between the analyzer axis and the surface normal were assumed to be positive when the electron source and the analyzer were located on the opposite sides of the surface normal (Fig. 2). 3. Theory 3.1. Calculations of the elastic backscattering probability Measurements of the elastic backscattering signal intensity were accompanied by calculations performed for the same geometries and electron energies. The elastic backscattering probability was calculated for the model of ideally flat surface. A typical Monte Carlo algorithm, simulating the electron trajectories, was used for this purpose [9,13]. The elastic scattering events along the electron trajectory are assumed to be well described by the Poisson stochastic process. Thus, the distances between elastic collisions follow the exponential distribution with the mean value equal to the elastic mean free path. The distribution of the elastic scattering angles, θ, is assumed to be proportional to the elastic scattering cross section for the isolated
1 ηk n
(3)
k=1
In the present calculations, the elastic scattering cross sections were taken from the NIST database [14]. The IMFP values published by Tanuma et al. [15] were used in the MC simulations. They were calculated from the experimental optical data and are valid for electron transport in the bulk of the solid. 3.2. Surface energy losses It is well known now that the probability of electron energy losses is increased in the surface region [16–20], thus the elastically backscattered intensity is expected to be smaller than the intensity calculated from the MC algorithm described above. The electrons contained within the elastic peak are passing the surface region twice, which increases the probability of an energy loss. The probability of passing such trajectory without energy loss, as compared with trajectory in the bulk, is decreased by the factor [21]: fs = exp[−Psin (θ0 , E)] exp[−Psout (α, E)]
(4)
where Ps is the surface excitation probability (SEP) [17–19], and the superscripts “in” and “out” indicate the direction of an electron with respect to the surface. Different expressions were proposed for estimation of Ps [16–19]. We use here a simple expression of Chen [19] which in the present notation, can be written as follows: ach ach Psin (θ0 , E) = 1/2 , Psout (α, E) = 1/2 (5) E cos θ0 E cos α where the kinetic electron energy is expressed in eV, and ach is the√material depended parameter. For silicon, ach = 2.50 in units of eV [19]. Eventually, the elastic backscattering probability, corrected for the surface energy losses (ηSEP ), should be calculated from the relation: ηSEP = fs η
(6)
A. Jablonski et al. / Journal of Electron Spectroscopy and Related Phenomena 152 (2006) 100–106
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where the uncorrected probability is obtained from the MC calculations, and the correction fs is calculated from Eqs. (4) and (5). 4. Results The elastic backscattering intensities, η determined experimentally for the flat and rough surface are shown in Figs. 3–7. These data are so normalized that the backscattered intensity is arbitrarily assumed to be equal to unity at normal emission angle. An exception is made for the normal incidence angle when the normalization to unity in made for emission angle of 20◦ . This is due to an obvious fact that it is impossible to locate the electron gun and the analyzer simultaneously at normal to the surface (Fig. 2). The normalization used here is arbitrary, however, in
Fig. 4. Dependence of the elastic backscattering intensity on the emission angle, α, for the primary beam incidence angle θ 0 = 20◦ . Squares and dotted line: elastic peak intensity measured for the flat sample; triangles and dotted line: elastic peak intensity measured for the rough sample; full circles and solid line: the elastic backscattering probability calculated for the flat surface without correction for the surface energy losses; open circles and solid line: the calculated elastic backscattering probability corrected for the surface energy losses. Note that all dependences are normalized to unity at the emission angle of 0◦ .
Fig. 3. Dependence of the elastic backscattering intensity on the emission angle, α, for the primary beam incidence angle θ 0 = 0◦ Squares and dotted line: elastic peak intensity measured for the flat sample; triangles and dotted line: elastic peak intensity measured for the rough sample; full circles and solid line: the elastic backscattering probability calculated for the flat surface without correction for the surface energy losses; open circles and solid line: the calculated elastic backscattering probability corrected for the surface energy losses. Note that all dependences are normalized to unity at the emission angle of 20◦ . (a) Energy of 200 eV; (b) energy of 500 eV; (c) energy of 1000 eV.
this way, we conveniently compare the shape of the emission angle dependence of the elastic backscattering intensity. Figs. 3–7 show also the emission angle dependence of the elastically backscattered intensity resulting from the Monte Carlo calculations. Simulations were made, at a given incidence angle, in the range from −80◦ to 80◦ in steps of 5◦ . The same energies as in the experiments were considered, i.e. 200, 500 and 1000 eV. For each geometry and energy, 107 complete electron trajectories were simulated, to obtain a reasonable statistics. Typically, the standard deviation for the elastic backscattering probability calculated from Eq. (3) was about 2% or less. However, in some experimental configurations, the standard deviation was larger. For example, at 1000 eV and incidence angles θ 0 = 0◦ , 20◦ , and 40◦ the standard deviation exceeded 3%. The decreased accuracy in these conditions is
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Fig. 5. The same as Fig. 4 except for the primary beam incidence angle θ 0 = 40◦ .
responsible for the scatter in the calculated curves observed in Figs. 3(c), 4(c) and 5(c). Results of Monte Carlo simulations shown in Figs. 3–7 are normalized in the same way as the experimental values to facilitate comparison. To visualize the influence of surface energy losses, the calculated intensities corrected for SEP are also shown in the plots. As follows from Fig. 3, the influence of surface roughness on the measured backscattered intensity, in the geometries with normal incidence of the primary beam, is insignificant at energies 200 and 500 eV. A noticeable difference, although relatively small, is observed at 1000 eV. These results are consistent with earlier study [12] in which measurements were made for flat and rough Si surfaces at normal incidence of electrons. One should also stress the fact that the calculated dependence of the elastically backscattered intensity is well compared with the measured dependences. On close inspection of panels Fig. 3(b) and (c), we see that the measured angular dependence for a flat surface better compares with calculated dependence after correction for the surface energy losses. At the incidence angle of 20◦ , as shown in Fig. 4, the emission angle dependences measured for flat and rough surfaces are
Fig. 6. The same as Fig. 4 except for the primary beam incidence angle θ 0 = 60◦ .
practically identical only at 200 eV (Fig. 4(a)). At higher energies, there are considerable differences in the shape of curves measured for the studied samples. One should note that, again, the calculated angular dependences are close to the dependence measured for the flat sample. At energies 500 and 1000 eV, the measured dependence is closest to the calculated dependence after correcting for surface energy losses. For primary beam incidence angles of 40◦ , 60◦ , and 80◦ , the shape of the emission angle dependences measured for both samples are distinctly different at all considered energies (Figs. 5–7). Furthermore, the difference seems to increase with increasing energy. At θ 0 = 40◦ and 60◦ we see a reasonably good agreement of the shape of the measured dependence for the flat sample and the calculated dependence after correction for the surface energy losses. The measured emission angle dependence of η deviates from the calculated curves in the case of the incidence angle of θ 0 = 80◦ (Fig. 7). The measured dependence is a less pronounced function of α than the calculated dependence, particularly in the range of emission angles exceeding 40◦ . This may be partially due to a finite roughness of the flat sample (amplitude below 1 nm) and partially due to other experimental difficulties.
A. Jablonski et al. / Journal of Electron Spectroscopy and Related Phenomena 152 (2006) 100–106
Fig. 7. The same as Fig. 4 except for the primary beam incidence angle θ 0 = 80◦ .
5. Discussion and conclusions An important result of the present work is the demonstration of considerable influence of the surface roughness on the elastically backscattered electron intensity, in contrast with results published earlier [11,12]. We have found that the less pronounced effects of surface roughness are observed at normal incidence of the primary beam, and such geometry was used in earlier studies. This observation is a useful guidance for an experimental configuration for determination the IMFP from the EPES method. In fact, as follows from a review of the EPES measurements [9], the configurations with normal incidence were almost exclusively used in the IMFP measurements published until 1999 (two exceptions among 61 published measurements). This may partially justify a relatively good agreement of the IMFPs originating from EPES and calculated from the experimental optical data. Furthermore, a considerable majority of published IMFPs obtained from EPES stems from the experimental procedure of relative measurements. In this case, we measure the ratio of elastically backscattered intensity for a given sample and a standard, i.e. the solid for which the IMFPs
105
are known with good accuracy. Both samples cannot be ideally flat, however the effects of possible surface roughness, decreasing the signal intensity, are further reduced when taking the ratio. In the present work, we used an entirely arbitrary method for normalization, i.e. we assumed that η = 1 at normal emission angle (or the closest to normal). In this way, we can compare only the shape of the dependence of η versus α rather than the backscattered intensities for a particular emission angle. For this reason, we cannot recommend the range of emission angles for the EPES measurements. As indicated in compilation of experimental configurations used in EPES determination of the IMFP (Table 6 in Ref. [9]), around 50% of the reported IMFPs resulted from the measurements using the cylindrical mirror analyzer in which the emission angles are in vicinity of 42◦ . Furthermore, in the case of normal incidence, it has been found that the IMFPs resulting from EPES depend noticeably on the emission angle in the range of the emission angles below 20◦ [22]. At larger emission angles, the resulting IMFPs were more stable. Consequently, it seems to be safe to recommend the emission angles exceeding 20◦ for the determination of the IMFPs from EPES. Second important conclusion resulting from the experimental dependences η versus α refers to the energy dependence of the surface roughness effects. We see in Figs. 3–7 that the roughness effects increase with energy. There is no obvious explanation for this observation. It would be necessary to develop an algorithm for simulations of electron trajectories taking into account the roughness structure shown in Fig. 1. Such work is in fact planned in the future. We present here the measurements made for only one element, and these results, for obvious reasons, cannot be generalized to all solids. Tentatively, it may be justified to extend the present observations to low atomic number solids which have the electron transport properties similar to silicon. Furthermore, a surface with the regular structure of channels studied here is a good model for the one-dimensional concept of rough surfaces which was considered in the mathematical formalism of XPS [4]. In calculations of the η versus α dependences for a flat silicon surface, the same Monte Carlo algorithm was used as in calculations associated with the determination of the IMFP by the EPES method [13]. Generally, we see a reasonably good agreement between the shape of the calculated dependence and the measured dependences. Similar agreement between theory and experiment has been reported in a number of earlier studies [23–25]. Good performance of theory is a foundation for the method of determining the IMFP in which we reverse the problem: from measured backscattered intensity (or ratio of intensities) we obtain such value of the IMFP which ensures the best agreement with experiment. However, as follows from Fig. 7, there are major discrepancies between the shapes of η versus α dependences at θ 0 = 80◦ . A possible explanation for the difference between the theory and experiment can be ascribed to the fact that, at glancing incidence, it is difficult to locate the electron beam on the sample surface. Furthermore, at glancing emission angles, the elastically backscattered electrons may be then collected from a smaller area than the area irradiated by the beam. In effect, the shape of calculated curves distinctly deviates from experimental curve measured for the flat sample in the
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region of large emission angles. Consequently, the experimental configurations involving the glancing incidence and emission angles should be avoided in any quantification of the elastically backscattered intensity. The present results visualize that the correction for the surface energy losses improves the agreement between measured and calculated dependence of η versus α. We may expect that the universal correction for the surface energy losses would further improve the performance of the EPES method. Unfortunately, the presently available theoretical [16] or semiempirical [17] expressions are applicable only to selected solids. There is a clear need for further work in this direction. An extensive volume of the experimental material on η versus α dependences would be helpful in evaluating the proposed corrections for the surface energy losses. Acknowledgments One of the authors (A. J.) would like to acknowledge partial support by the Foundation for Polish Science. Two authors (K. O. and J. Z.) gratefully acknowledge the support by Institutional Research Plan No. AV0Z10100521 and by the Czech Science Foundation Project No. 202/06/0459. References [1] C.C. Chang, in: P.F. Kane, G.B. Larrabee (Eds.), Characterization of Solid Surfaces, Plenum Press, New York, 1974, p. 509. [2] H. Ebel, M.F. Ebel, E. Hillbrand, J. Electron Spectrosc. Relat. Phenom. 2 (1973) 277.
[3] M.F. Ebel, J. Wernisch, Surf. Interface Anal. 3 (1981) 191. ˚ [4] C.S. Fadley, R.J. Baird, W. Siekhaus, T. Novakov, S.A.L. Bergstr¨om, J. Electron Spectrosc. Relat. Phenom. 4 (1974) 93. [5] M.F. Ebel, G. Moser, H. Ebel, A. Jablonski, H. Oppolzer, J. Electron Spectrosc. Relat. Phenom. 42 (1987) 61. [6] P.L.J. Gunter, J.W. Niemantsverdriet, Appl. Surf. Sci. 89 (1995) 69. [7] W.S.M. Werner, Surf. Interface Anal. 23 (1995) 696. [8] K. Olejnik, J. Zemek, W.S.M. Werner, Surf. Sci. 595 (2005) 212. [9] C.J. Powell, A. Jablonski, J. Phys. Chem. Ref. Data 28 (1999) 19. [10] W. Dolinski, S. Mroz, M. Zagorski, Surf. Sci. 200 (1988) 361. [11] P. Jiricek, J. Zemek, P. Lejcek, B. Lesiak, A. Jabło´nski, M. Cernansky, J. Vac. Sci. Technol. A20 (2002) 447. [12] J. Zemek, P. Jiricek, A. Jablonski, B. Lesiak, Surf. Interface Anal. 34 (2002) 215. [13] A. Jablonski, Surf. Interface Anal. 37 (2005) 1035. [14] A. Jablonski, F. Salvat, C.J. Powell, NIST Electron Elastic-Scattering Cross-Section Database, Version 3.1 Standard Reference Data Program Database 64, US Department of Commerce, National Institute of Standards and Technology, Gaithersburg, MD, 2003, web address: http://www.nist.gov/srd/nist64.htm. [15] S. Tanuma, C.J. Powell, D.R. Penn, Surf. Interface Anal. 17 (1991) 911. [16] Y.F. Chen, Surf. Sci. 380 (1997) 199. [17] W.S.M. Werner, W. Smekal, C. Tomastik, H. Stori, Surf. Sci. 486 (2001) L461. [18] W.S.M. Werner, Surf. Interface Anal. 31 (2001) 141. [19] Y.F. Chen, Surf. Sci. 519 (2002) 115. [20] W.S.M. Werner, L. Kover, S. Egri, J. Toth, D. Varga, Surf. Sci. 585 (2005) 85. [21] S. Tanuma, S. Ichimura, K. Goto, J. Surf. Anal. 5 (1999) 48. [22] A. Jablonski, P. Jiricek, Surf. Sci. 412/413 (1998) 42. [23] A. Jablonski, J. Gryko, J. Kraaer, S. Tougaard, Phys. Rev. B39 (1989) 61. [24] A. Jablonski, Phys. Rev. B43 (1991) 7546. [25] W.S.M. Werner, I.S. Tilinin, M. Hayek, Phys. Rev. B50 (1994) 4819.
Elastic electron backscattering from flat and rough Si surfaces A. Jablonski a,∗ , K. Olejnik b , J. Zemek b a
b
Institute of Physical Chemistry Polish Academy of Sciences, ul. Kasprzaka 44/52, 01-224 Warszawa, Poland Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnicka 10,162 53 Prague 6, Czech Republic Received 14 November 2005; received in revised form 8 April 2006; accepted 10 April 2006 Available online 29 April 2006
Abstract In earlier studies, it has been found that the surface roughness influences only weakly the inelastic mean free path values resulting from elastic peak electron spectroscopy. To address this issue, in the present work, the elastic electron backscattering intensity has been systematically studied in numerous experimental configurations. Measurements were made for the flat Si sample, and for the Si sample with well-defined roughness in the form of long trapezoidal channels. Such structure is a good representation for one-dimensional models used in theoretical description of the surface roughness effects in XPS. It has been found that there is a pronounced influence of the surface roughness on the electron backscattered intensity at the primary beam incidence different from normal. These results were observed at energies of interest for surface sensitive electron spectroscopies, i.e. 200, 500 and 1000 eV. Additionally, the elastic backscattering probability for a flat surface was found to agree well with the theoretical predictions. Correction for the surface energy losses further improved the agreement between theory and experiment. © 2006 Elsevier B.V. All rights reserved. Keywords: Surface roughness; Elastic electron backscattering; Monte Carlo simulations; Electron transport
1. Introduction The surface roughness is a factor which is very difficult to control in practical surface analysis. The main reason is that the surface structure depends on the procedure of preparation, and it would be very difficult, if ever possible, to propose an accurate description of the roughness in the mathematical formalism of electron spectroscopies. In early days of Auger electron spectroscopy, it has been proposed to introduce a surface-roughness factor, R, into the formalism quantifying this technique [1]. However, the concept of a single factor does not seem to be followed in a later literature. A number of studies were addressed towards the influence of the surface roughness on the photoelectron signal intensity. The surface roughness may affect the monitored photoelectron intensity in a number of ways: 1. a particular area on the surface may be shaded from the incident X-rays; 2. photoelectrons ejected from a given area may be recaptured by the adjacent surface protrusions; ∗
Corresponding author. Tel.: +48 22 343 3331; fax: +48 22 343 3333. E-mail address: [email protected] (A. Jablonski).
0368-2048/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2006.04.003
3. photoelectrons can be elastically scattered on the adjacent protrusions. This problem is very difficult to describe theoretically. A convenient practice to evaluate the surface roughness was to assume a simple model of rough surface which makes possible the theoretical description of the photoelectron intensity. Ebel et al. [2] adjusted the model of variable cubes, used earlier in X-ray fluorescence analysis, to the formalism of XPS. In this model, the surface roughness is varied by rotation of adjacent cubes around an axis parallel to the surface. This model turned out to be useful also in evaluation of photoelectron intensity from rough surfaces with overlayer [3]. A concept of one-dimensional rough surfaces was extensively analyzed by Fadley et al. [4]. Comparison of the overlayer thicknesses determined by XPS on smooth and artificially roughened surfaces proved that the surface roughness limits the XPS configurations useful for measurements [5]. In fact, only the normal emission angle should be recommended for such studies. Additionally, surface roughness leads to the overestimation of the measured thickness, as compared to smooth surfaces. The problem of the overlayer thickness measurements was also studied by Gunter and Niemantsverdriet [6]. These authors performed the Monte Carlo analysis for a statistically created one-dimensional model of a rough sur-
A. Jablonski et al. / Journal of Electron Spectroscopy and Related Phenomena 152 (2006) 100–106
face. They found that the error caused by the surface roughness is distinctly smallest when the experimental configuration with the emission angle of 35◦ is used. This observation was found to be weakly dependent on the extent of the surface corrugation. Werner [7] generalized the above result by proposing the term of “magic angle” for this experimental geometry. In a recent work, Olejnik et al. [8] studied, experimentally and theoretically, the angular dependence of photoemission from well defined threedimensional structures on the silicon surface. The authors have shown that, in fact, the “magic angle” depends on the character of the surface roughness, and in the studied cases varied between 31◦ and 56◦ . In recent years, we observe a growing interest in techniques based on measurements of the elastic electron backscattering probability for studied surfaces. These techniques are known under the acronym EPES (elastic peak electron spectroscopy). A spectacular application of this technique is the determination of the inelastic mean free path (IMFP) of electrons in a solid (Ref. [9] and references therein). In a typical experiment, a solid surface is bombarded with a beam of monoenergetic electrons, and the intensity of the so-called elastic peak is monitored. It is of critical importance to define, possibly accurately, the experimental configuration. One can expect that the surface structure may have a major influence on the resulting IMFPs. In contrast, rather minor effects of the roughness were reported in the literature. Dolinski et al. [10] studied the scraped and sputtered samples of Ag and Cu; both procedures must have resulted in a difference in surface roughness. Despite this fact, similar IMFP values were obtained for these surfaces. Jiricek et al. [11] sputtered two samples of silicon with different doses of Ar+ ions which resulted in different roughness. The amplitude of roughness was estimated to be 1.7 and 2.2 nm. No substantial influence on the IMFPs obtained from EPES has been found. Similar study has been performed Zemek et al. [12] for two Si samples with a distinctly different roughness: a polished Si sample with roughness amplitude of 5.5 nm, and grinded sample with roughness amplitude of 760 nm. Again, the IMFP values for both samples were found to be similar. Thus, it seems that the EPES procedure for determining the IMFP is not affected by the surface roughness. In the reported measurements of the IMFPs using the EPES method, the beam of primary electrons was located along the surface normal. Thus, the shading of primary electrons by the surface protrusions is minimized. We may expect that a more pronounced difference between elastic backscattering probabilities for surfaces of different roughness can be observed for glancing incidence of primary electrons. The purpose of the present work is to perform a systematic study of the surface roughness effects in numerous experimental configurations defined by the primary beam incidence angle and the electron emission angle. 2. Experimental Two samples were prepared from the same silicon wafer: 1. a flat Si (1 0 0) sample, 10 mm × 10 mm, with average surface roughness below 1 nm, and
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Fig. 1. Idealized model of a rough silicon surface. (a) The AFM image; (b) the calculated profile in a direction perpendicular to the trapezoidal channels.
2. rough Si sample, 10 mm × 10 mm, with a well-defined structure of trapezoidal channels. The structure of parallel channels was prepared on the Si (1 0 0) surface with photolithography. The image, recorded ex situ with the AFM in the contact mode (Topometrix Explorer), is shown in Fig. 1(a). The linescan, shown in Fig. 1(b), was extracted from the surface image using software provided by the AFM producer. As follows from this illustration, the channels had a triangular shape with average depth of about 6 m. The distance between channels was about 12.5 m. Measurements of the elastic peak intensity were carried out in an ADES 400 angle-resolved photoelectron spectrometer (V.G. Scientific, UK) equipped with a rotatable hemispherical electron energy analyzer, an electron gun, and an ion gun for sputtercleaning (AG-2, V.G. Scientific, UK). Before the EPES measurements, a thin native surface oxide (∼1 nm thick) and a slight carbon surface contamination were removed in-situ by sputtercleaning (Ar ion beam, 5000 eV ion beam energy, 10 A/cm2 ion beam current density, angle of incidence of 60◦ measured from the surface normal). To avoid the effect of shadowing in the case of roughened sample, the ion beam was located in a plane parallel to the channels. The surface cleanness was checked by XPS. Elastically backscattered electrons were collected by the analyzer within a small acceptance angle. The half-cone angle of the
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Si atoms. On normalization, we have W(θ) = 2π
1 dσe sin θ σe dΩ
(1)
where σ e and dσ e /dΩ is the total and differential elastic scattering cross-section. The following weight is associated with the kth trajectory: ⎧ ⎨ exp(−xk /λin ) if the electron entered the analyzer with acceptance angle Ω, ηk = (2) ⎩ 0 in all other cases. where xk is the length of the kth trajectory, and λin is the IMFP. The elastic backscattering probability is assumed to be equal to the mean value of the above weight. Suppose that n complete electron trajectories were generated for a given experimental configuration and electron energy. We have then: Fig. 2. Outline of the experimental setup.
n
η = ηk = analyzer was 4.1◦ . The spectra were recorded in the FAT mode at a pass energy of 20 eV. The electron source beam current was 0.1–1.0 A, and the electron beam diameter was 2–3 mm. The elastic peaks were recorded at the primary electron energies 200, 500 and 1000 eV. During measurements, the beam incidence angle, θ 0 , was fixed in one series of measurements while the emission angles α were varied in steps of 20◦ , by rotation of the analyzer between the direction of the electron beam and the emission angle of 80◦ . Measurements were made for five incidence angles θ 0 , i.e. 0◦ , 20◦ , 40◦ , 60◦ and 80◦ . Outline of the experimental setup is shown in Fig. 2. The electron beam, the direction to the analyzer, and the surface normal were located in one plane. This plane was perpendicular to the channels on the rough surface (i.e. in the direction of the scan, as shown in Fig. 1(a)). The angle of the incidence of the electron beam and the angle between the analyzer axis and the surface normal were assumed to be positive when the electron source and the analyzer were located on the opposite sides of the surface normal (Fig. 2). 3. Theory 3.1. Calculations of the elastic backscattering probability Measurements of the elastic backscattering signal intensity were accompanied by calculations performed for the same geometries and electron energies. The elastic backscattering probability was calculated for the model of ideally flat surface. A typical Monte Carlo algorithm, simulating the electron trajectories, was used for this purpose [9,13]. The elastic scattering events along the electron trajectory are assumed to be well described by the Poisson stochastic process. Thus, the distances between elastic collisions follow the exponential distribution with the mean value equal to the elastic mean free path. The distribution of the elastic scattering angles, θ, is assumed to be proportional to the elastic scattering cross section for the isolated
1 ηk n
(3)
k=1
In the present calculations, the elastic scattering cross sections were taken from the NIST database [14]. The IMFP values published by Tanuma et al. [15] were used in the MC simulations. They were calculated from the experimental optical data and are valid for electron transport in the bulk of the solid. 3.2. Surface energy losses It is well known now that the probability of electron energy losses is increased in the surface region [16–20], thus the elastically backscattered intensity is expected to be smaller than the intensity calculated from the MC algorithm described above. The electrons contained within the elastic peak are passing the surface region twice, which increases the probability of an energy loss. The probability of passing such trajectory without energy loss, as compared with trajectory in the bulk, is decreased by the factor [21]: fs = exp[−Psin (θ0 , E)] exp[−Psout (α, E)]
(4)
where Ps is the surface excitation probability (SEP) [17–19], and the superscripts “in” and “out” indicate the direction of an electron with respect to the surface. Different expressions were proposed for estimation of Ps [16–19]. We use here a simple expression of Chen [19] which in the present notation, can be written as follows: ach ach Psin (θ0 , E) = 1/2 , Psout (α, E) = 1/2 (5) E cos θ0 E cos α where the kinetic electron energy is expressed in eV, and ach is the√material depended parameter. For silicon, ach = 2.50 in units of eV [19]. Eventually, the elastic backscattering probability, corrected for the surface energy losses (ηSEP ), should be calculated from the relation: ηSEP = fs η
(6)
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where the uncorrected probability is obtained from the MC calculations, and the correction fs is calculated from Eqs. (4) and (5). 4. Results The elastic backscattering intensities, η determined experimentally for the flat and rough surface are shown in Figs. 3–7. These data are so normalized that the backscattered intensity is arbitrarily assumed to be equal to unity at normal emission angle. An exception is made for the normal incidence angle when the normalization to unity in made for emission angle of 20◦ . This is due to an obvious fact that it is impossible to locate the electron gun and the analyzer simultaneously at normal to the surface (Fig. 2). The normalization used here is arbitrary, however, in
Fig. 4. Dependence of the elastic backscattering intensity on the emission angle, α, for the primary beam incidence angle θ 0 = 20◦ . Squares and dotted line: elastic peak intensity measured for the flat sample; triangles and dotted line: elastic peak intensity measured for the rough sample; full circles and solid line: the elastic backscattering probability calculated for the flat surface without correction for the surface energy losses; open circles and solid line: the calculated elastic backscattering probability corrected for the surface energy losses. Note that all dependences are normalized to unity at the emission angle of 0◦ .
Fig. 3. Dependence of the elastic backscattering intensity on the emission angle, α, for the primary beam incidence angle θ 0 = 0◦ Squares and dotted line: elastic peak intensity measured for the flat sample; triangles and dotted line: elastic peak intensity measured for the rough sample; full circles and solid line: the elastic backscattering probability calculated for the flat surface without correction for the surface energy losses; open circles and solid line: the calculated elastic backscattering probability corrected for the surface energy losses. Note that all dependences are normalized to unity at the emission angle of 20◦ . (a) Energy of 200 eV; (b) energy of 500 eV; (c) energy of 1000 eV.
this way, we conveniently compare the shape of the emission angle dependence of the elastic backscattering intensity. Figs. 3–7 show also the emission angle dependence of the elastically backscattered intensity resulting from the Monte Carlo calculations. Simulations were made, at a given incidence angle, in the range from −80◦ to 80◦ in steps of 5◦ . The same energies as in the experiments were considered, i.e. 200, 500 and 1000 eV. For each geometry and energy, 107 complete electron trajectories were simulated, to obtain a reasonable statistics. Typically, the standard deviation for the elastic backscattering probability calculated from Eq. (3) was about 2% or less. However, in some experimental configurations, the standard deviation was larger. For example, at 1000 eV and incidence angles θ 0 = 0◦ , 20◦ , and 40◦ the standard deviation exceeded 3%. The decreased accuracy in these conditions is
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Fig. 5. The same as Fig. 4 except for the primary beam incidence angle θ 0 = 40◦ .
responsible for the scatter in the calculated curves observed in Figs. 3(c), 4(c) and 5(c). Results of Monte Carlo simulations shown in Figs. 3–7 are normalized in the same way as the experimental values to facilitate comparison. To visualize the influence of surface energy losses, the calculated intensities corrected for SEP are also shown in the plots. As follows from Fig. 3, the influence of surface roughness on the measured backscattered intensity, in the geometries with normal incidence of the primary beam, is insignificant at energies 200 and 500 eV. A noticeable difference, although relatively small, is observed at 1000 eV. These results are consistent with earlier study [12] in which measurements were made for flat and rough Si surfaces at normal incidence of electrons. One should also stress the fact that the calculated dependence of the elastically backscattered intensity is well compared with the measured dependences. On close inspection of panels Fig. 3(b) and (c), we see that the measured angular dependence for a flat surface better compares with calculated dependence after correction for the surface energy losses. At the incidence angle of 20◦ , as shown in Fig. 4, the emission angle dependences measured for flat and rough surfaces are
Fig. 6. The same as Fig. 4 except for the primary beam incidence angle θ 0 = 60◦ .
practically identical only at 200 eV (Fig. 4(a)). At higher energies, there are considerable differences in the shape of curves measured for the studied samples. One should note that, again, the calculated angular dependences are close to the dependence measured for the flat sample. At energies 500 and 1000 eV, the measured dependence is closest to the calculated dependence after correcting for surface energy losses. For primary beam incidence angles of 40◦ , 60◦ , and 80◦ , the shape of the emission angle dependences measured for both samples are distinctly different at all considered energies (Figs. 5–7). Furthermore, the difference seems to increase with increasing energy. At θ 0 = 40◦ and 60◦ we see a reasonably good agreement of the shape of the measured dependence for the flat sample and the calculated dependence after correction for the surface energy losses. The measured emission angle dependence of η deviates from the calculated curves in the case of the incidence angle of θ 0 = 80◦ (Fig. 7). The measured dependence is a less pronounced function of α than the calculated dependence, particularly in the range of emission angles exceeding 40◦ . This may be partially due to a finite roughness of the flat sample (amplitude below 1 nm) and partially due to other experimental difficulties.
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Fig. 7. The same as Fig. 4 except for the primary beam incidence angle θ 0 = 80◦ .
5. Discussion and conclusions An important result of the present work is the demonstration of considerable influence of the surface roughness on the elastically backscattered electron intensity, in contrast with results published earlier [11,12]. We have found that the less pronounced effects of surface roughness are observed at normal incidence of the primary beam, and such geometry was used in earlier studies. This observation is a useful guidance for an experimental configuration for determination the IMFP from the EPES method. In fact, as follows from a review of the EPES measurements [9], the configurations with normal incidence were almost exclusively used in the IMFP measurements published until 1999 (two exceptions among 61 published measurements). This may partially justify a relatively good agreement of the IMFPs originating from EPES and calculated from the experimental optical data. Furthermore, a considerable majority of published IMFPs obtained from EPES stems from the experimental procedure of relative measurements. In this case, we measure the ratio of elastically backscattered intensity for a given sample and a standard, i.e. the solid for which the IMFPs
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are known with good accuracy. Both samples cannot be ideally flat, however the effects of possible surface roughness, decreasing the signal intensity, are further reduced when taking the ratio. In the present work, we used an entirely arbitrary method for normalization, i.e. we assumed that η = 1 at normal emission angle (or the closest to normal). In this way, we can compare only the shape of the dependence of η versus α rather than the backscattered intensities for a particular emission angle. For this reason, we cannot recommend the range of emission angles for the EPES measurements. As indicated in compilation of experimental configurations used in EPES determination of the IMFP (Table 6 in Ref. [9]), around 50% of the reported IMFPs resulted from the measurements using the cylindrical mirror analyzer in which the emission angles are in vicinity of 42◦ . Furthermore, in the case of normal incidence, it has been found that the IMFPs resulting from EPES depend noticeably on the emission angle in the range of the emission angles below 20◦ [22]. At larger emission angles, the resulting IMFPs were more stable. Consequently, it seems to be safe to recommend the emission angles exceeding 20◦ for the determination of the IMFPs from EPES. Second important conclusion resulting from the experimental dependences η versus α refers to the energy dependence of the surface roughness effects. We see in Figs. 3–7 that the roughness effects increase with energy. There is no obvious explanation for this observation. It would be necessary to develop an algorithm for simulations of electron trajectories taking into account the roughness structure shown in Fig. 1. Such work is in fact planned in the future. We present here the measurements made for only one element, and these results, for obvious reasons, cannot be generalized to all solids. Tentatively, it may be justified to extend the present observations to low atomic number solids which have the electron transport properties similar to silicon. Furthermore, a surface with the regular structure of channels studied here is a good model for the one-dimensional concept of rough surfaces which was considered in the mathematical formalism of XPS [4]. In calculations of the η versus α dependences for a flat silicon surface, the same Monte Carlo algorithm was used as in calculations associated with the determination of the IMFP by the EPES method [13]. Generally, we see a reasonably good agreement between the shape of the calculated dependence and the measured dependences. Similar agreement between theory and experiment has been reported in a number of earlier studies [23–25]. Good performance of theory is a foundation for the method of determining the IMFP in which we reverse the problem: from measured backscattered intensity (or ratio of intensities) we obtain such value of the IMFP which ensures the best agreement with experiment. However, as follows from Fig. 7, there are major discrepancies between the shapes of η versus α dependences at θ 0 = 80◦ . A possible explanation for the difference between the theory and experiment can be ascribed to the fact that, at glancing incidence, it is difficult to locate the electron beam on the sample surface. Furthermore, at glancing emission angles, the elastically backscattered electrons may be then collected from a smaller area than the area irradiated by the beam. In effect, the shape of calculated curves distinctly deviates from experimental curve measured for the flat sample in the
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region of large emission angles. Consequently, the experimental configurations involving the glancing incidence and emission angles should be avoided in any quantification of the elastically backscattered intensity. The present results visualize that the correction for the surface energy losses improves the agreement between measured and calculated dependence of η versus α. We may expect that the universal correction for the surface energy losses would further improve the performance of the EPES method. Unfortunately, the presently available theoretical [16] or semiempirical [17] expressions are applicable only to selected solids. There is a clear need for further work in this direction. An extensive volume of the experimental material on η versus α dependences would be helpful in evaluating the proposed corrections for the surface energy losses. Acknowledgments One of the authors (A. J.) would like to acknowledge partial support by the Foundation for Polish Science. Two authors (K. O. and J. Z.) gratefully acknowledge the support by Institutional Research Plan No. AV0Z10100521 and by the Czech Science Foundation Project No. 202/06/0459. References [1] C.C. Chang, in: P.F. Kane, G.B. Larrabee (Eds.), Characterization of Solid Surfaces, Plenum Press, New York, 1974, p. 509. [2] H. Ebel, M.F. Ebel, E. Hillbrand, J. Electron Spectrosc. Relat. Phenom. 2 (1973) 277.
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