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The inelastic mean free path of electrons. Past and present research
Vacuum 84 (2010) 134–136
Contents lists available at ScienceDirect
Vacuum journal homepage: www.elsevier.com/locate/vacuum
The inelastic mean free path of electrons. Past and present research G. Gergely a, *, S. Gurban a, M. Menyhard a, A. Jablonski b, L. Zommer b, K. Goto c a
Research Institute for Technical Physics and Materials Science, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary Institute of Physical Chemistry, Polish Academy of Sciences, ul. Kasprzaka 44/52, Warsaw 01-224, Poland c Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan b
a b s t r a c t Keywords: Inelastic mean free path Elastic peak electron spectroscopy Surface excitation correction Quantification based on Goto’s data
The inelastic mean free path (IMFP) is a fundamental material parameter. Presently the IMFPs calculated by the TPP-2M predictive formula (NIST SRD 71) are generally used. Elastic peak electron spectroscopy (EPES) is proved to be adequate for experimental determination of the IMFP denoted by le. le is smaller then li (TPP-2M) values, due to surface losses, characterized by the SEP (surface excitation) Pse material parameter. The present research is focused on the experimental determination of Pse based on Tanuma’s work. The Tanuma factor fsT is the ratio of experimental Ie and calculated Ic elastic peak intensities Ie(E)/Ic(E). The detection angle dependent Ic is proportional to DU, the solid angle of detection. The angular Ic(E,DU,ad) was calculated applying the EPESWIN software of Jablonski. In our work, experimental data of Goto were analysed for Si and Ni. Recent angularly resolved AREPES results of Jablonski and Zemek were quantified by fitting them at the 42 CMA (cylindrical mirror analyser) angle to absolute data of Goto and applying fsT. The models and SEP material parameters published by Werner et al., Ding et al., Kwei et al., Jablonski–Zemek and Nagatomi–Goto (Ni) and our data obtained by modifying Chen’s data (Si) have been tested. The best approach was obtained using data of Werner for Si, and data of Nagatomi for Ni. The SEP corrected IMFPs leco were deduced. The EPES SEP parameters were valid for AREPES by averaging over ad ¼ 35–70 . EPES spectra are quantified by applying the backscattering yield. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction The inelastic mean free path of electrons IMFP li is a fundamental material parameter. It determines electron transport processes, the intensity of Auger (AES), XPS, elastic (EPES), REELS (inelastically backscattered electrons) peaks and the information depth in electron spectroscopies applied for quantitative surface and thin films analysis. The problems related to the IMFP determination are summarized by Powell and Jablonski [1]. In 1984 the experimental determination of the IMFP le was done using elastic peak electron spectroscopy (EPES) [2,5]. The IMFP and EPES are defined and standardised by ISO (18115/5.68 and /7.26:2001). The calculated values of the IMFP li were published by [1]; mostly the TPP-2M predictive formula [3] is applied. Early experimental results on the escape depth are summarized in [4,6]. Evaluations of EPES experiments, applying Monte Carlo (MC) simulation, have been developed by Jablonski. Nowadays his EPESWIN software is widely used for this purpose [7]. The brief survey of past research is given in Table 1. Survey on the electrospectrometers is given in [2]. The acronyms are standardised by ISO (18115: 2001 Surface chemical analysis Vocabulary page 1). * Corresponding author. Fax: þ36 361 392 2273. E-mail address: [email protected] (G. Gergely). 0042-207X/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.vacuum.2009.06.009
It is found that the experimentally determined IMFP le is smaller than the calculated li (TPP-2 M). The differences are attributed to surface losses of incident and escaping electrons. The effects of surface losses are characterized by the surface excitation parameter, SEP.
2. Determination of the SEP parameter for the elastic peak and IMFP The SEP is defined by ISO (18115/7.80:2001/PDAM2). Recent works on SEP are summarized in Ref. [10]. Two formulae are used for calculating the SEP parameter [11–14], containing material parameters ach, aW, b ¼ 0.5 and c ¼ 1. Kwei–Chen–Ding [11,13,14]:
Pse ¼ aEb =cosc a
(1)
Werner-Oswald [12]:
Pse ¼
1 pffiffiffi 0:171aW E cos a þ 1
(2)
For elastic backscattering studies the interaction between the incoming (in) and outgoing (out) electrons are different and thus:
G. Gergely et al. / Vacuum 84 (2010) 134–136
135
Table 1 Brief survey of the history of IMFP. Concept Clausius (1822–88), Seitz: Modern Theory of Solids 1940, Semiconductors Shockley 1956 Calculations: 1962 Quinn, since 1969 Ritchie, 1974-Powell, 1976-Penn, 1988-Penn Ashley 1979–88, [1] Tanuma, Powell, Penn TPP-2M (1994) [3]. Early experiments with the overlayer method, Seah–Dench [4], escape depth, not IMFP Experimental IMFP with EPES since 1984 [2,5]. Ie by RFA (retarding field analyser) [6] and elastic peak intensity ratio Ie, sample/Ie, reference using CMA (cylindrical mirror analyser) or HSA (hemispherical sector analyser) spectrometers [2]. Evaluation of EPES experiments by Monte Carlo simulation, Jablonski since 1965, nowadays EPESWIN [7]. Al, Ni, Cu, reference sample [2]. High-energy resolution, HSA spectrometer ESA 31 since 1995 [2]. Absolute intensity experiments with RFA spectrometer [6]. IMFP and SEP from REELS with Goto’s absolute intensity data by Nagatomi–Goto [8,9] for Ni Surface excitation correction (SEP) since 1994. Results summarized in [2]. Recent models and material parameters [8–14]. Review paper in [1].
Pse ¼ Psei ðinÞ þ Pseo ðoutÞ
(3)
The material parameters [8,10–14] have been fitted to quantitative EPES experiments [10] applying Goto’s database [9]. Goto’s electron spectra are presented in absolute units (%). They have been determined by measuring the primary electron current and the spectra with two different Faraday cups [2]. Recently Jablonski and Zemek published new parameters, deduced from AREPES experiments [15]. Our present work quantified these AREPES results, by fitting the Ie(E,ad) curves of Si and Ni at the ‘‘Goto CMA point’’. The angular variation of the elastic peak Ic(E,ad) was calculated for normal incidence and ad axis of detection with the conic solid angle DU, with 4 semiangle with respect to the axis. It was shown, that Ic(E,42 ,DU) for the 42 CMA angle of detection is proportional to the conic solid angle DU. The main results are summarized in the Table 2. They are: the deviations DIe(Da) from the linear relationship with the conical solid angle and semi-angle Da, the quality factors DIeco defined in Eqn. (4) (see later), and applying various SEP parameters. Data for 6 and 4.1 semi-angles, E ¼ 0.5 and 1 keV energies are shown also in Table 2. The quality factors are summarized in Section 4 (Conclusions). The experimental Ie(E,42 ) point of Goto is transformed to the conic solid angle of acceptance. The experimental Ie(E,ad) curve is fitted to this quantified point. The position of the quantified calculated Ic(E,42 ) is determined by the experimental Tanuma factor fsT. This is the ratio of Ic(E,42 ,DU)/Ie(E,42 ,DU) ¼ 1/fsT, [16]. The calculated Ic(E,ad) curve is fitted to this point. SEP correction of Ie elastic peak is made with Ieco(E,ad) ¼ Ie(E,ad)*fs(ad). Where, fs(E,ad) ¼ 1/exp(Pse(E,ad)) [16]. Our new procedure is illustrated in Fig. 1 and in the case of Si for 0.5 and 1 keV, displaying quantified Ic(E,ad), calculated Ic(E,ad) curves, and the SEP corrected Ieco(E,ad) ¼ fs(ad)*Ie(ad) curves, testing various SEP parameters [8,10–12] with Eqns. (2) and (3). Similar results were found on Ni using material parameters by Nagatomi and Goto [8], Werner et al. [12] and Salma and Ding [13] for SEP corrections. The quality factors DIeco of SEP correction were deduced from the deviations between SEP corrected Ieco(E,ad,DU) and calculated Ic(E,ad,DU) elastic peak intensities, applying Eqn. (4).
Averaging was made for the ad ¼ 35–70 angular range. The quality factor for SEP correction is:
DIeco % ¼ 100
n 1X Ieco Ic n i ¼ 1 Ic
(4)
DIe(ad) uncorrected is also shown in the Fig. 1. Our EPES and quantified AREPES results on Si and Ni are summarized in the Table 2, comparing the quality factors achieved with different material parameters. In our previous work [10], the material parameters for SEP correction of Si, Ni, Cu, Ag and Au were deduced from EPES experiments covering the energy range E ¼ 0.4–1.2 keV. The present paper is confined to AREPES of Si and Ni. As shown in Table 2, for Si the best quality factor for SEP correction was obtained with aW,Si ¼ 1.2 [12]. For Ni the quality factor achieved with Nagatomi’s work (aCh,Ni ¼ 4.3) were slightly lower than the quality factor based on works of Werner et al. [12] and Ding [13]. Testing the quantified AREPES experimental results, the same material parameters proved to be useful, but lower accuracy of SEP correction could be achieved, confirming the validity of these parameters. The IMFP was determined by EPES from the quantitative and SEP-corrected Ie*fs elastic peak intensities [10], applying the EPESWIN software [6]. The same can be made with the SEP-corrected AREPES results; however, this would be a more complicated and less accurate SEP correction. The experimental determination of le applies in many cases, reference samples and a HSA (hemispherical) analyser [2]. For quantification of the elastic peak intensity the quantified AREPES spectra are suitable. 3. Quantification of EPES based on the backscattering yield (BY) The elastic peak intensity can be quantified applying the RE backscattering yield BY [2], defined by ISO BY ¼ 50p NðEÞdE. N(E) denotes the ratio of backscattered electrons/incident electrons for 1 eV energy interval at E energy and detected within the negative hemisphere. Applying Goto’s database [9] N(E)CMA was
Table 2 DIe(a) deviations with Da semi-angle, fsT Tanuma correction factor. Sample Si EPES Si AREPES Si AREPES Ni EPES Ni AREPES Ni AREPES
E (keV)
DIc (6 )%
DIc (4 )%
0.5 1
0.4 1.9
6.4 6.5
0.5 1
1.27 1.2
3.7 1.9
fsT
DIeu
DIecoCh
DIecoW
1.448
24.2 33.1 29.1 34.4 31.8 36.6
5.45 4.04 5 7.12 14.56 11.3
4.53 2.37 0.9 9.58 13.9 8.1
1.355 1.485 1.597
DIecoD
DIecoK
DIeoJZ
12.2 26.3 18.1 9.58 8.84 20.6
15.7 20.4 29.3
Quality factors DIeco(a) for EPES E ¼ 0.4–1.2 keV. AREPES ad ¼ 35–70 angular range, ai ¼ 0 . Notations for SEP correction: u: uncorrected; Ch: aCh,Si ¼ 3.5 (our modified Chen), aCh,Ni ¼ 4.3 (Nagatomi [8]); W: aW,Si ¼ 1.2 (Werner [12]), aW,Ni ¼ 1(Werner [12]); JZ: aJZ,Si ¼ 0.724 (Jablonski, Zemek [15]), aJZ,Ni ¼ 4.116 (Jablonski, Zemek [15]); D (Ding [13]) and K (Kwei [14]) 6 parameters.
136
G. Gergely et al. / Vacuum 84 (2010) 134–136
Fig. 2. Quantified backscattering N(E) spectra of Si, Ep ¼ 2 keV. ip ¼ 1 mA. i(E) detected current [9]. Distribution of electrons detected with the CMA: N(E)CMA Ne(E) ¼ NCMA(E)/ Tr(E). The angle of emission detected is 42 6 . Fig. 1. Quantified AREPES spectra of Si. Angle of incidence ai ¼ 0 , E ¼ 0.5 and 1 keV. Elastic backscattering probability versus ad: experimental, calculated and SEP corrected curves. Notations are indicated on the fig.: experimental data taken from [15] and quantified. MC denotes Ic(ad) calculated with Monte Carlo simulation [7], Our work applied SEP with modified Chen [10], and material parameters of Werner [12]. The curves AREPES applied the material parameters used by [15].
determined for the solid angle 42.3 6 and energy resolution of DEs ¼ 0.0026E eV:
NðEÞCMA ¼ iðEÞ= ip *0:0026E
(5)
with notations: i(E) the measured current, and ip ¼ 1 mA primary current. Ne(E) ¼ N(E)CMA/Tr(E). Tr(E) is the transmission of Goto’s CMA [17]. Goto’s experimental i(E) results are converted to N(E)CMA and Ne(E) in absolute units for Si, E ¼ 2 keV, using Tr(E) provided by Goto. Nc(E) is the calculated distribution. Results are displayed in Fig. 2. BY was calculated for 10 elements by Zommer et al. [18]. In our present work BY was determined experimentally by integrating Ne(E) with the boundaries of 200 eV and Ep. Below 200, backscattering and secondary electron emission cannot be separated. Calculated correction was applied for the 50–200 eV range. N(E) refers to 2p solid angle, which can be obtained by applying the angular correction factor fZ of Zommer et al. [18], N(E) ¼ fZ*Ne(E). Our integrated N(E) results supply the BY. They are compared with calculated data. They are for Ep ¼ 2 keV: Si: 0.251, BY ¼ 0.186, and Ni: 0.347, BY ¼ 0.298. The calculated BY data are slightly lower than experimental ones [18]. 4. Conclusions Material parameters for SEP correction of Si and Ni have been determined by applying EPES and AREPES experiments. For Si, the material parameter value aW,Si ¼ 1.2 yielded the best quality factors for EPES (0.4–1.2 keV) and for AREPES (35–70 ), E ¼ 0.5 and 1 keV, using the Oswald–Werner relationship. The modified Chen material parameter aCh,Si ¼ 3.5 resulted in slightly higher deviations. For Ni, EPES aCh,Ni ¼ 4.3 (Nagatomi) proved to be the best approach. For AREPES no significant differences were found with material parameters of Werner (aW,Ni ¼ 1), Nagatomi and Ding. AREPES experiments confirmed the validity of material parameters for SEP correction obtained by EPES. Regarding the angular variation for AREPES, the Werner– Oswald relationship proved to be the best approach.
Acknowledgements This research program was supported by the PL-15 Cooperation Contract between the Polish and Hungarian Academy of Sciences. References [1] Powell CJ, Jablonski A. Evaluation of calculated and measured electron inelastic mean free path near solid surfaces. J Phys Chem Ref Data 1999;28:19. [2] Gergely G. Elastic backscattering of electrons: determination of physical parameters of electron transport processes by elastic peak electron spectroscopy. Prog Surf Sci 2002;71:31. [3] Seah M, Dench WA. Quantitative electron spectroscopy of surfaces: a standard database for electron inelastic mean free paths in solids. Surf Interface Anal 1979;1:2. [4] Tanuma S, Powell CJ, Penn DR. Calculations of electron inelastic mean free paths. V. Data for 14 organic compounds over the 50-2000 eV range. Surf Interface Anal 1994;21:165. [5] Jablonski A, Mrozek P, Gergely G, Menyhard M, Sulyok A. The inelastic mean free path of electrons in some semiconductor compounds and metals. Surf Interface Anal 1994;6:291. [6] Dolinski W, Nowicki H, Mroz S. Application of elastic peak electron spectroscopy (EPES) to determine inelastic mean free paths (IMFP) of electrons in copper and silver. Surf Interface Anal 1988;11:229. [7] Jablonski A. Determination of the electron inelastic mean free path in solids from the elastic electron backscattering intensity. Surf Interface Anal 2005;37:1034. [8] Nagatomi T, Goto K. Inelastic mean-free path and surface excitation parameters by absolute reflection electron-energy loss measurements. Phys Rev 2007;B75:23542. [9] Goto K. Common data processing system version 8. Available at:. [10] Gergely G, Gurban S, Menyhard M. Determination of surface-excitation parameters for elastic peak electron spectroscopy (EPES). Using the database of Goto. J Surf Anal 2008;15(No. 2):159. [11] Chen YF. Surface effects on angular distributions in X-ray–photoelectron spectroscopy. Surf Sci 2002;519:115. [12] Werner WSM, Kover L, Egri S, Toth J, Varga D. Measurement of the surface excitation probability of medium energy electrons reflected from Si, Ni, Ge and Ag surfaces. Surf Sci 2005;585:85. [13] Salma K, Ding ZJ, Li HM, Zhang ZM. Surface excitation probabilities in surface electron spectroscopies. Angular and energy dependences of the surface excitation parameter for electrons crossing a solid surface. Surf Sci 2006;600:1526. [14] Kwei CM, Li YC, Tung CJ. Angular and energy dependences of the surface excitation parameter for electrons crossing a solid surface. Surf Sci 2006;600:3690. [15] Jablonski A, Zemek J. Angle-resolved elastic peak electron spectroscopy: role of surface excitations. Surf Sci 2007;601:3409. [16] Tanuma S, Ichimura K, Goto K. Estimation of surface excitation correction factor for 200-5000 eV in Ni from absolute elastic scattering electron spectroscopy. Surf Interface Anal 2000;30:212. [17] Alkafri A, Ichikawa Y, Shimizu R, Goto K. Transmission measurements of the absolute CMA: simulation and experiments. J Surf Anal 2006;14:2. [18] Zommer L, Jablonski A, Gergely G, Gurban S. Monte Carlo backscattering yield (BY) calculations applying continuous slowing down approximation (CSDA) and experimental data. Vacuum 2008;82:201.
Contents lists available at ScienceDirect
Vacuum journal homepage: www.elsevier.com/locate/vacuum
The inelastic mean free path of electrons. Past and present research G. Gergely a, *, S. Gurban a, M. Menyhard a, A. Jablonski b, L. Zommer b, K. Goto c a
Research Institute for Technical Physics and Materials Science, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary Institute of Physical Chemistry, Polish Academy of Sciences, ul. Kasprzaka 44/52, Warsaw 01-224, Poland c Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan b
a b s t r a c t Keywords: Inelastic mean free path Elastic peak electron spectroscopy Surface excitation correction Quantification based on Goto’s data
The inelastic mean free path (IMFP) is a fundamental material parameter. Presently the IMFPs calculated by the TPP-2M predictive formula (NIST SRD 71) are generally used. Elastic peak electron spectroscopy (EPES) is proved to be adequate for experimental determination of the IMFP denoted by le. le is smaller then li (TPP-2M) values, due to surface losses, characterized by the SEP (surface excitation) Pse material parameter. The present research is focused on the experimental determination of Pse based on Tanuma’s work. The Tanuma factor fsT is the ratio of experimental Ie and calculated Ic elastic peak intensities Ie(E)/Ic(E). The detection angle dependent Ic is proportional to DU, the solid angle of detection. The angular Ic(E,DU,ad) was calculated applying the EPESWIN software of Jablonski. In our work, experimental data of Goto were analysed for Si and Ni. Recent angularly resolved AREPES results of Jablonski and Zemek were quantified by fitting them at the 42 CMA (cylindrical mirror analyser) angle to absolute data of Goto and applying fsT. The models and SEP material parameters published by Werner et al., Ding et al., Kwei et al., Jablonski–Zemek and Nagatomi–Goto (Ni) and our data obtained by modifying Chen’s data (Si) have been tested. The best approach was obtained using data of Werner for Si, and data of Nagatomi for Ni. The SEP corrected IMFPs leco were deduced. The EPES SEP parameters were valid for AREPES by averaging over ad ¼ 35–70 . EPES spectra are quantified by applying the backscattering yield. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction The inelastic mean free path of electrons IMFP li is a fundamental material parameter. It determines electron transport processes, the intensity of Auger (AES), XPS, elastic (EPES), REELS (inelastically backscattered electrons) peaks and the information depth in electron spectroscopies applied for quantitative surface and thin films analysis. The problems related to the IMFP determination are summarized by Powell and Jablonski [1]. In 1984 the experimental determination of the IMFP le was done using elastic peak electron spectroscopy (EPES) [2,5]. The IMFP and EPES are defined and standardised by ISO (18115/5.68 and /7.26:2001). The calculated values of the IMFP li were published by [1]; mostly the TPP-2M predictive formula [3] is applied. Early experimental results on the escape depth are summarized in [4,6]. Evaluations of EPES experiments, applying Monte Carlo (MC) simulation, have been developed by Jablonski. Nowadays his EPESWIN software is widely used for this purpose [7]. The brief survey of past research is given in Table 1. Survey on the electrospectrometers is given in [2]. The acronyms are standardised by ISO (18115: 2001 Surface chemical analysis Vocabulary page 1). * Corresponding author. Fax: þ36 361 392 2273. E-mail address: [email protected] (G. Gergely). 0042-207X/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.vacuum.2009.06.009
It is found that the experimentally determined IMFP le is smaller than the calculated li (TPP-2 M). The differences are attributed to surface losses of incident and escaping electrons. The effects of surface losses are characterized by the surface excitation parameter, SEP.
2. Determination of the SEP parameter for the elastic peak and IMFP The SEP is defined by ISO (18115/7.80:2001/PDAM2). Recent works on SEP are summarized in Ref. [10]. Two formulae are used for calculating the SEP parameter [11–14], containing material parameters ach, aW, b ¼ 0.5 and c ¼ 1. Kwei–Chen–Ding [11,13,14]:
Pse ¼ aEb =cosc a
(1)
Werner-Oswald [12]:
Pse ¼
1 pffiffiffi 0:171aW E cos a þ 1
(2)
For elastic backscattering studies the interaction between the incoming (in) and outgoing (out) electrons are different and thus:
G. Gergely et al. / Vacuum 84 (2010) 134–136
135
Table 1 Brief survey of the history of IMFP. Concept Clausius (1822–88), Seitz: Modern Theory of Solids 1940, Semiconductors Shockley 1956 Calculations: 1962 Quinn, since 1969 Ritchie, 1974-Powell, 1976-Penn, 1988-Penn Ashley 1979–88, [1] Tanuma, Powell, Penn TPP-2M (1994) [3]. Early experiments with the overlayer method, Seah–Dench [4], escape depth, not IMFP Experimental IMFP with EPES since 1984 [2,5]. Ie by RFA (retarding field analyser) [6] and elastic peak intensity ratio Ie, sample/Ie, reference using CMA (cylindrical mirror analyser) or HSA (hemispherical sector analyser) spectrometers [2]. Evaluation of EPES experiments by Monte Carlo simulation, Jablonski since 1965, nowadays EPESWIN [7]. Al, Ni, Cu, reference sample [2]. High-energy resolution, HSA spectrometer ESA 31 since 1995 [2]. Absolute intensity experiments with RFA spectrometer [6]. IMFP and SEP from REELS with Goto’s absolute intensity data by Nagatomi–Goto [8,9] for Ni Surface excitation correction (SEP) since 1994. Results summarized in [2]. Recent models and material parameters [8–14]. Review paper in [1].
Pse ¼ Psei ðinÞ þ Pseo ðoutÞ
(3)
The material parameters [8,10–14] have been fitted to quantitative EPES experiments [10] applying Goto’s database [9]. Goto’s electron spectra are presented in absolute units (%). They have been determined by measuring the primary electron current and the spectra with two different Faraday cups [2]. Recently Jablonski and Zemek published new parameters, deduced from AREPES experiments [15]. Our present work quantified these AREPES results, by fitting the Ie(E,ad) curves of Si and Ni at the ‘‘Goto CMA point’’. The angular variation of the elastic peak Ic(E,ad) was calculated for normal incidence and ad axis of detection with the conic solid angle DU, with 4 semiangle with respect to the axis. It was shown, that Ic(E,42 ,DU) for the 42 CMA angle of detection is proportional to the conic solid angle DU. The main results are summarized in the Table 2. They are: the deviations DIe(Da) from the linear relationship with the conical solid angle and semi-angle Da, the quality factors DIeco defined in Eqn. (4) (see later), and applying various SEP parameters. Data for 6 and 4.1 semi-angles, E ¼ 0.5 and 1 keV energies are shown also in Table 2. The quality factors are summarized in Section 4 (Conclusions). The experimental Ie(E,42 ) point of Goto is transformed to the conic solid angle of acceptance. The experimental Ie(E,ad) curve is fitted to this quantified point. The position of the quantified calculated Ic(E,42 ) is determined by the experimental Tanuma factor fsT. This is the ratio of Ic(E,42 ,DU)/Ie(E,42 ,DU) ¼ 1/fsT, [16]. The calculated Ic(E,ad) curve is fitted to this point. SEP correction of Ie elastic peak is made with Ieco(E,ad) ¼ Ie(E,ad)*fs(ad). Where, fs(E,ad) ¼ 1/exp(Pse(E,ad)) [16]. Our new procedure is illustrated in Fig. 1 and in the case of Si for 0.5 and 1 keV, displaying quantified Ic(E,ad), calculated Ic(E,ad) curves, and the SEP corrected Ieco(E,ad) ¼ fs(ad)*Ie(ad) curves, testing various SEP parameters [8,10–12] with Eqns. (2) and (3). Similar results were found on Ni using material parameters by Nagatomi and Goto [8], Werner et al. [12] and Salma and Ding [13] for SEP corrections. The quality factors DIeco of SEP correction were deduced from the deviations between SEP corrected Ieco(E,ad,DU) and calculated Ic(E,ad,DU) elastic peak intensities, applying Eqn. (4).
Averaging was made for the ad ¼ 35–70 angular range. The quality factor for SEP correction is:
DIeco % ¼ 100
n 1X Ieco Ic n i ¼ 1 Ic
(4)
DIe(ad) uncorrected is also shown in the Fig. 1. Our EPES and quantified AREPES results on Si and Ni are summarized in the Table 2, comparing the quality factors achieved with different material parameters. In our previous work [10], the material parameters for SEP correction of Si, Ni, Cu, Ag and Au were deduced from EPES experiments covering the energy range E ¼ 0.4–1.2 keV. The present paper is confined to AREPES of Si and Ni. As shown in Table 2, for Si the best quality factor for SEP correction was obtained with aW,Si ¼ 1.2 [12]. For Ni the quality factor achieved with Nagatomi’s work (aCh,Ni ¼ 4.3) were slightly lower than the quality factor based on works of Werner et al. [12] and Ding [13]. Testing the quantified AREPES experimental results, the same material parameters proved to be useful, but lower accuracy of SEP correction could be achieved, confirming the validity of these parameters. The IMFP was determined by EPES from the quantitative and SEP-corrected Ie*fs elastic peak intensities [10], applying the EPESWIN software [6]. The same can be made with the SEP-corrected AREPES results; however, this would be a more complicated and less accurate SEP correction. The experimental determination of le applies in many cases, reference samples and a HSA (hemispherical) analyser [2]. For quantification of the elastic peak intensity the quantified AREPES spectra are suitable. 3. Quantification of EPES based on the backscattering yield (BY) The elastic peak intensity can be quantified applying the RE backscattering yield BY [2], defined by ISO BY ¼ 50p NðEÞdE. N(E) denotes the ratio of backscattered electrons/incident electrons for 1 eV energy interval at E energy and detected within the negative hemisphere. Applying Goto’s database [9] N(E)CMA was
Table 2 DIe(a) deviations with Da semi-angle, fsT Tanuma correction factor. Sample Si EPES Si AREPES Si AREPES Ni EPES Ni AREPES Ni AREPES
E (keV)
DIc (6 )%
DIc (4 )%
0.5 1
0.4 1.9
6.4 6.5
0.5 1
1.27 1.2
3.7 1.9
fsT
DIeu
DIecoCh
DIecoW
1.448
24.2 33.1 29.1 34.4 31.8 36.6
5.45 4.04 5 7.12 14.56 11.3
4.53 2.37 0.9 9.58 13.9 8.1
1.355 1.485 1.597
DIecoD
DIecoK
DIeoJZ
12.2 26.3 18.1 9.58 8.84 20.6
15.7 20.4 29.3
Quality factors DIeco(a) for EPES E ¼ 0.4–1.2 keV. AREPES ad ¼ 35–70 angular range, ai ¼ 0 . Notations for SEP correction: u: uncorrected; Ch: aCh,Si ¼ 3.5 (our modified Chen), aCh,Ni ¼ 4.3 (Nagatomi [8]); W: aW,Si ¼ 1.2 (Werner [12]), aW,Ni ¼ 1(Werner [12]); JZ: aJZ,Si ¼ 0.724 (Jablonski, Zemek [15]), aJZ,Ni ¼ 4.116 (Jablonski, Zemek [15]); D (Ding [13]) and K (Kwei [14]) 6 parameters.
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G. Gergely et al. / Vacuum 84 (2010) 134–136
Fig. 2. Quantified backscattering N(E) spectra of Si, Ep ¼ 2 keV. ip ¼ 1 mA. i(E) detected current [9]. Distribution of electrons detected with the CMA: N(E)CMA Ne(E) ¼ NCMA(E)/ Tr(E). The angle of emission detected is 42 6 . Fig. 1. Quantified AREPES spectra of Si. Angle of incidence ai ¼ 0 , E ¼ 0.5 and 1 keV. Elastic backscattering probability versus ad: experimental, calculated and SEP corrected curves. Notations are indicated on the fig.: experimental data taken from [15] and quantified. MC denotes Ic(ad) calculated with Monte Carlo simulation [7], Our work applied SEP with modified Chen [10], and material parameters of Werner [12]. The curves AREPES applied the material parameters used by [15].
determined for the solid angle 42.3 6 and energy resolution of DEs ¼ 0.0026E eV:
NðEÞCMA ¼ iðEÞ= ip *0:0026E
(5)
with notations: i(E) the measured current, and ip ¼ 1 mA primary current. Ne(E) ¼ N(E)CMA/Tr(E). Tr(E) is the transmission of Goto’s CMA [17]. Goto’s experimental i(E) results are converted to N(E)CMA and Ne(E) in absolute units for Si, E ¼ 2 keV, using Tr(E) provided by Goto. Nc(E) is the calculated distribution. Results are displayed in Fig. 2. BY was calculated for 10 elements by Zommer et al. [18]. In our present work BY was determined experimentally by integrating Ne(E) with the boundaries of 200 eV and Ep. Below 200, backscattering and secondary electron emission cannot be separated. Calculated correction was applied for the 50–200 eV range. N(E) refers to 2p solid angle, which can be obtained by applying the angular correction factor fZ of Zommer et al. [18], N(E) ¼ fZ*Ne(E). Our integrated N(E) results supply the BY. They are compared with calculated data. They are for Ep ¼ 2 keV: Si: 0.251, BY ¼ 0.186, and Ni: 0.347, BY ¼ 0.298. The calculated BY data are slightly lower than experimental ones [18]. 4. Conclusions Material parameters for SEP correction of Si and Ni have been determined by applying EPES and AREPES experiments. For Si, the material parameter value aW,Si ¼ 1.2 yielded the best quality factors for EPES (0.4–1.2 keV) and for AREPES (35–70 ), E ¼ 0.5 and 1 keV, using the Oswald–Werner relationship. The modified Chen material parameter aCh,Si ¼ 3.5 resulted in slightly higher deviations. For Ni, EPES aCh,Ni ¼ 4.3 (Nagatomi) proved to be the best approach. For AREPES no significant differences were found with material parameters of Werner (aW,Ni ¼ 1), Nagatomi and Ding. AREPES experiments confirmed the validity of material parameters for SEP correction obtained by EPES. Regarding the angular variation for AREPES, the Werner– Oswald relationship proved to be the best approach.
Acknowledgements This research program was supported by the PL-15 Cooperation Contract between the Polish and Hungarian Academy of Sciences. References [1] Powell CJ, Jablonski A. Evaluation of calculated and measured electron inelastic mean free path near solid surfaces. J Phys Chem Ref Data 1999;28:19. [2] Gergely G. Elastic backscattering of electrons: determination of physical parameters of electron transport processes by elastic peak electron spectroscopy. Prog Surf Sci 2002;71:31. [3] Seah M, Dench WA. Quantitative electron spectroscopy of surfaces: a standard database for electron inelastic mean free paths in solids. Surf Interface Anal 1979;1:2. [4] Tanuma S, Powell CJ, Penn DR. Calculations of electron inelastic mean free paths. V. Data for 14 organic compounds over the 50-2000 eV range. Surf Interface Anal 1994;21:165. [5] Jablonski A, Mrozek P, Gergely G, Menyhard M, Sulyok A. The inelastic mean free path of electrons in some semiconductor compounds and metals. Surf Interface Anal 1994;6:291. [6] Dolinski W, Nowicki H, Mroz S. Application of elastic peak electron spectroscopy (EPES) to determine inelastic mean free paths (IMFP) of electrons in copper and silver. Surf Interface Anal 1988;11:229. [7] Jablonski A. Determination of the electron inelastic mean free path in solids from the elastic electron backscattering intensity. Surf Interface Anal 2005;37:1034. [8] Nagatomi T, Goto K. Inelastic mean-free path and surface excitation parameters by absolute reflection electron-energy loss measurements. Phys Rev 2007;B75:23542. [9] Goto K. Common data processing system version 8. Available at: