Effective energy loss function of silver derived from reflection electron

SURFACE AND INTERFACE ANALYSIS Surf. Interface Anal. 2006; 38: 632–635 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/sia.2315

Effective energy loss function of silver derived from reflection electron energy loss spectra ˝ esi, ´ 4 D. Varga4 and J. Toth ´ 4 Z. M. Zhang,1∗ Z. J. Ding,2 H. M. Li,3 K. Tok 1 Hefei National Laboratory for Physical Sciences at Microscale, Department of Astronomy and Applied Physics, University of Science and Technology of China, Hefei, Anhui 230026, China 2 Hefei National Laboratory for Physical Sciences at Microscale, Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China 3 High Performance Computing Laboratory, University of Science and Technology of China, Hefei, Anhui 230026, China 4 Institute of Nuclear Research of the Hungarian Academy of Sciences, (ATOMKI), H-4001 Debrecen, P.O. Box 51, Hungary

Received 30 July 2005; Revised 03 December 2005; Accepted 17 December 2005

The electron inelastic scattering in silver is studied both experimentally and theoretically. The reflection electron energy loss spectroscopy (REELS) spectra were measured using the ESA-31. It is shown that the surface excitation is enhanced with decreasing primary energy. For the higher resolution spectra with the narrower energy distribution of elastically scattered electrons, the Tougaard’s recursive formula describes inelastic scattering cross section from the measured energy loss spectrum as well as the extended Landau approach. At low primary energies, the differential inverse inelastic mean free path (DIIMFP) for low loss energies extracted by Tougaard’s recursive method is smaller than that by the extended Landau approach. The latter method is better for measured REELS spectra with a large full width at half maximum (FWHM) of elastic peak (e.g. for a CMA). The effective energy loss function (EELF) has been derived from these experiments based on the extended Landau approach. The Monte Carlo simulated REELS spectra with the derived EELF agree well with the experimental spectra. Copyright  2006 John Wiley & Sons, Ltd.

KEYWORDS: REELS; energy loss function; Monte Carlo; Tougaard’s recursive method; extended Landau approach; inelastic scattering; silver

INTRODUCTION Reflection electron energy loss spectroscopy (REELS) has now become one of the most powerful tools for analysis of the surface region of solids. By bombarding a surface with incident electrons, the emitted electrons suffer energy losses because of the excitations of bounded electrons of the atoms and free electrons (conductive electrons) of the solid and thus carry information on the electronic properties of the surface. During transportation of the electrons going out of the solid, the electron energy distribution is distorted by suffering energy losses through inelastic scattering processes. Recently, a dielectric response theory was employed to describe the inelastic scattering process1 – 3 and the energy spectra of the emitted electrons. The calculations agreed with the experimental spectra for high primary energies and at Ł Correspondence to: Z. M. Zhang, Department of Astronomy and Applied Physics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China. E-mail: [email protected] Contract/grant sponsor: National Natural Science Foundation of China; Contract/grant numbers: 10574121, 902060090. Contract/grant sponsor: Natural Science Foundation of Anhui Province of China; Contract/grant number: 05021015. Contract/grant sponsor: The Hungarian Scientific Research Found; Contract/grant number: OTKA No. T038016. Contract/grant sponsor: Bolyai. Contract/grant sponsor: Hungarian Academy of Sciences; Contract/grant number: CHN-28/2003.

Copyright  2006 John Wiley & Sons, Ltd.

large energy losses; but a large discrepancy was found for low primary energies and at low losses. Many authors4 – 8 have pointed out that the reason is the optical energy loss function used in the modeling of inelastic scattering, which describes only the bulk electronic excitation without considering the surface effect. The improvement for quantitative surface analysis is significant when surface excitation is included. In this respect, some workers9 – 11 have modeled surface excitation effect. Chen et al.9,10 have taken into account additional inelastic scattering probability due to surface effect by the use of a surface excitation parameter. Ding11 has also investigated the contribution from surface effects with self-energy formalism in surface electron spectroscopy. In his recent paper, Werner12 extracted the normalized differential mean free path for bulk scattering and the differential surface excitation probability from REELS spectra. Two REELS spectra under different experimental conditions are simultaneously deconvoluted in his procedure. Although these methods describe experimental results very well, they are very complex and expatiatory in form and thus can hardly be applied in practical analysis. Additionally, Tougaard7,13,14 considered the possibility of extracting quantitative information on the electron scattering properties in a solid through the analysis of experimental electron spectra based on the Landau theory. Yoshikawa and Shimizu8,15 have also obtained the effective energy loss

Effective energy loss functions extracted from REELS spectra

function (EELF) for including both the surface and bulk excitations from the measured REELS spectra by an extended Landau approach.8,15,16 The two methods are based on a univariate power series in Fourier space, however, they are simple and efficient to use. In this paper, REELS spectra were measured at different primary energies for silver. The extracting differential inverse inelastic mean free paths (DIIMFP) between the above two methods are compared. At lower primary energies, the DIIMFP at low energy losses obtained by Tougaard’s method is smaller than that by the extended Landau approach. The extended Landau approach is better for measured REELS spectra with a large full width at half maximum (FWHM) of elastic peak (e.g. for a CMA). The EELF was obtained from the measured spectra by the extended Landau approach, and a Monte Carlo (MC) simulation with such EELF reproduces the measured spectra well by using the derived EELF.

EXPERIMENTAL REELS spectra were measured with the ESA-31, a home built spectrometer based on a 180° hemispherical analyzer17 that works in fixed retardation ratio mode. The electron beam was produced by an electron gun with tungsten filament (LEG 62 VG Microtech). Prior to electron spectroscopic analysis, in situ cleaning of the sample surface was performed using 2 keV energy ArC ion sputtering. The cleanness of the surface of the specimen of Ag was tested by XPS measurement. The angles of incidence of the primary electron beam were 0 and 50° while the angles of analyzer axis were at 50 and 0° with respect to the surface normal of the sample, respectively, achieved by rotating the sample. REELS spectra of Ag polycrystalline were recorded for the electron primary energy of 500, 1000 and 1500 eV; the half-cone analyzer acceptance angle was 1.5–1.8° in the energy dispersive direction and 4–5° in the nondispersive direction. The measured REELS spectra have been corrected by considering electron transmission. The detail has been described elsewhere.17

THEORETICAL Tougaard’s deconvolution method Tougaard et al.7,13 have obtained a recursive deconvolution formula to calculate the inelastic scattering cross section from a measured REELS spectrum as follows: in L KE0 E D in C L

jE

E 0

E

in L KE0 EjE0 dE0 in C L EC 0 jE0 dE0 E 0

1 where KT is the probability that an electron loses energy T EC per unit path length travelled in the solid. E0 jE0 dE0 is the 0

integrated intensity of the elastic peak in REELS spectrum. The inelastic mean free path (IMFP), in , is given by the integration 1 KTdT 2 in D 0


Extended Landau approach Similar to Tougaard’s method, Yoshikawa and Shimizu obtained the following formula by using the Landau formula in the description of electron inelastic scattering,8,15 Q D Fs Q Js

1

n Q ˛n [in Ks]

3

nD0

Q Q Q where Js, Fs and Ks are Fourier transforms of the measured REELS spectrum jE, the energy distribution of primary electrons FE, and DIIMFP KE, respectively. s is the Fourier parameter conjugate to the energy. The correction factor ˛n adjusts for the elastic scattering effect and indicates how many times reflected electrons undergo n inelastic scattering events in a specimen before emerging from the surface. Therefore, it is ˛n that is to be calculated preliminarily from the MC simulation for the identical experimental conditions. Q and Fs Q derived from the experimental spectra, Using Js Q and ˛n calculated from the MC simulation, Ks in Eqn (3), or KE, is derived by solving Eqn (3). A recursion formula for the determination of in KE was given as follows:4 rn

k

˛m Y0 m, n

mD0

xn D

k

4

˛m Ym, n

mD1

where xn and rn are, respectively, the n-th term in the discrete data of in KE and RE. Ym, n and Y0 m, n satisfy the following relation, Zm, n D Ym, nxn C Y0 m, n

5

Here, Zm, n corresponds to the n-th term of summation of m-fold self-convolution of in KE.

Effective energy loss function The absolute value of the DIIMFP, KE, obtained from Eqns (4) and (5) is determined by the IMFP so as to satisfy Eqn (2). We used the reference IMFP values reported by Tanuma et al.18 Once KE is obtained, one can derive the EELF, Imf1/εeff g, by numerically solving the integration equation,2,3,19,20 KE D

h¯ ω 1 Im EE h¯ ω ε¯hω 0 2 h¯ 2 ð d¯hω  2kq q E 2m 1 2a0 E

1

6

where a0 is the Bohr radius and E is the kinetic energy of an electron.

RESULTS AND DISCUSSION Figure 1 shows the normalized frequency of inelastic scattering events at different primary energies for silver, which is

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Figure 1. Distribution of the relative number of inelastic collisions in Ag at different primary energies.

Figure 2. Differential inelastic scattering cross sections for Ag obtained by use of Tougaard’s method and the extended Landau approach at different primary energies. The area under the curve between 0–100 eV is normalized to unit.

obtained from MC simulations. It is apparent that the inelastic collisions increase so the peak shifts to the larger collision numbers with decreasing primary energy. Figure 2 compares the DIIMFP calculated by using Tougaard’s recursive method, Eqn (1), and the extended Landau method, Eqn (3), from the measured REELS spectra at several different primary energies for Ag. It is clearly seen that the difference between the two methods is quite small for high primary energies; but for low primary energies, the DIIMFP at low energy losses derived by Tougaard’s method is smaller than that by the extended Landau approach. The reason is that the surface effect is stronger at lower electron energies, this leads to the number of inelastic collisions deviated from the exponential distribution, which


Figure 3. Comparison of the effective energy loss function (EELF) obtained from the REELS spectra with the bulk energy loss function (BELF) at different primary energies for Ag.

is originated from the theoretical work of Tofterup21 and is the basis of Tougaard’s method, as indicated by Vicanek.22 In our previous work,23,24 we had pointed out that some details at low energy losses are neglected in Tougaard’s method because the fine structures due to interband and intraband transitions can be covered by the elastic peak at low energy resolution. In that paper, the REELS spectra were measured by a CMA with a lower energy resolution of 0.25%, so the observed difference was attributed to this reason. While in the present work, a hemispherical analyzer with a higher energy resolution of 0.04–0.06% is employed, and the energy distribution of primary electrons is very narrow, about 0.36 eV, as well. Figure 2 thus indicates that, for such high resolution energy spectra, Tougaard’s method and the extended Landau approach agrees in extracting the inelastic scattering cross section from the experimental REELS spectra. The EELF obtained by Eqn (6) is shown in Fig. 3. For comparison, the optical bulk energy loss function (BELF) derived from optical dielectric constants25 is also plotted. It is clear that the contribution from surface excitation is significant and increases with decreasing primary energy. Figure 4 shows the REELS spectra calculated by the MC simulation based on the use of the EELF that was obtained. The results clearly indicate that the present MC simulation closely describes the experimental REELS spectra.

CONCLUSION The REELS spectra were measured at different primary energies for silver. The differential inelastic scattering cross sections were obtained by the use of Tougaard’s method and extended Landau approach from these REELS spectra. For high resolution spectra, both the methods coincide with each other; while for low resolution spectra, the present extended Landau approach should give a better result. The EELFs for different primary energies are thus obtained. The contribution to the EELF from surface excitation is significant and increases with decreasing


Effective energy loss functions extracted from REELS spectra

No. T038016), the grant ‘Bolyai’ from the Hungarian Academy of Sciences, and TeT Grant No. CHN-28/2003.

REFERENCES

Figure 4. Comparison of the MC simulated REELS spectra with the experimental measured spectra at different primary energies for Ag.

primary energy. MC simulations with the obtained EELF reproduce the experimental spectra, indicating that the present simulation describes inelastic scattering process well.

Acknowledgements This work was partially supported by the National Natural Science Foundation of China (Grant Nos 10574121 and 902060090), Natural Science Foundation of Anhui Province of China (Grant No. 05021015), the Hungarian Scientific Research Found (OTKA


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