Optical properties of silicon and germanium determined by high-precision analysis of reflection electron energy loss spectroscopy spectra

Abstract

We present a detailed analysis and comparison of four models describing the extension of the electron-energy loss function from the optical limit of q→0 into the (q,ω) plane to obtain the bulk and surface terms of differential inverse inelastic mean free paths. We found that the best model that describes accurately and times efficiently the calculation of the energy loss function of free-electron-like materials is the combination of the Penn algorithm [Phys. Rev. B 35, 482 (1987)] with the Ritchie-Howie method [Philos. Mag. 36, 463 (1977)]. Applying this model in our reverse Monte Carlo method, we determined, with high-precision, electron-energy loss functions of silicon and germanium based on the theoretical analysis of the high-energy resolution reflected electron energy loss spectroscopy (REELS) spectra, measured at 3, 4, and 5 keV incident electron energies. The refractive index n, the extinction coefficient k, and the complex dielectric function (ε = ε 1 + iε 2 ) were calculated from the obtained energy loss function in a wide energy loss range of 0-200 eV. The accuracy of the obtained results is justified with various sum rules. We found that the calculated optical data of Si and Ge fulfill the sum rules with an average accuracy of 0.11% or even better. Therefore, the use of these optical data in materials science and surface analysis is highly recommended for further applications.

Individual separation of surface, bulk and Begrenzungs effect components in the surface electron energy spectra

“…On the other hand, Monte Carlo (MC) simulation method is a powerful tool for the simulation of electron-solid and electron-surface interaction. It can deal with the multiple scattering effect more accurately, and can be used to obtain both the electron energy spectra 29 and secondary electron yields 42 – 44 which are in good agreement with the experimental results. The quantitative analysis of REELS spectra can be done based on a MC simulation method 24 , 30 .…”

“…( 2 )–( 4 ) can be obtained by an extension from the long wavelength limit , namely the optical ELF , by assuming a dispersion relation. In this work, a FPA-Ritchie-Howie method 29 is employed to extended the ELF, i.e. using the full Penn algorithm (FPA) 47 to extend the ELF for the calculation of the bulk DIIMFP while using Ritchie and Howie’s scheme 48 for the calculation of the surface excitation DIIMFP and Begrenzungs effect term .…”

A comparative study on Monte Carlo simulations of electron emission from liquid water

“…The FPA method can provide a more accurate description of electron inelastic process as compared to SPA method. 39 Nikjoo et al 40 also compared various algorithms for extending the optical data into q 6 ¼ 0 region. They found that the FPA model provides better representation of the experimental data.…”

Monte Carlo simulation study of reflection electron energy loss spectroscopy of an Fe/Si overlayer sample

“…In this work, the Mott's cross section 34 with the Thomas‑Fermi‑Dirac (TFD) atomic potential 35 was employed to quantitatively describe the electron elastic scattering behavior. This is exactly equivalent to the conditional MC simulation reported in our previous work 10–14,16,17,21–25,27,29 . After obtaining the electron inelastic scattering cross section and the electron elastic scattering cross section, the MC simulation could be performed.…”

“…This RMC method is based on an iterative process of improving the ELF by minimizing the differences between a simulated and a measured REELS spectrum, in which a conventional MC simulation of electron interaction with a semi‐infinite solid is employed as the iterative process. Based on this method, optical constants from 10 materials (SiO2, 10 Ag, 11 Fe, 12 Ni, 13 Cr, Co, Pd, 14,15 Ir, 16 Si, and Ge 17 ) have been extracted from their corresponding measured REELS spectra.…”