Absolute determination of optical constants by reflection electron energy loss spectroscopy

Abstract

We present an absolute extraction method of optical constants of metal from the measured reflection electron energy loss (REELS) spectra by using the recently developed reverse Monte Carlo (RMC) technique. The method is based on a direct physical modeling of electron elastic and electron inelastic scattering near the surface region where the surface excitation becomes important to fully describe the spectrum loss feature intensity in relative to the elastic peak intensity. An optimization procedure of oscillator parameters appeared in the energy loss function (ELF) for describing electron inelastic scattering due to the bulk-and surfaceexcitations was performed with the simulated annealing method by a successive comparison between the measured and Monte Carlo simulated REELS spectra. The ELF and corresponding optical constants of Fe were obtained from the REELS spectra measured at incident energies of 1000, 2000 and 3000 eV. The validity of the present optical data has been verified with the f-and ps-sum rules showing the accuracy and applicability of the present approach. Our data are also compared with previous optical data from other sources.There is a continuous interest and effort on the determination of optical constants of solids due to their importance in both fundamental researches and applications. Optical methods based on reflectance and absorption spectroscopy with ellipsometry were extensively employed up to now and the measured data for metals and semiconductors were compiled to form a database of optical constants.1,2 However, many materials still lack the data in the intermediate photon energy range around 20~50 eV. Furthermore, the available data usually consist of different energy regions measured by different groups and means and, a)

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

“…which is the formula used in our previous works [48][49][50][51][52]. For nonconductors, the refractive index n is much greater than the extinction coefficient k at low frequencies, Re[−1/ε(0)] is approximately equal to 1/n 2 (0), and Eq.…”

“…In our previous works [48][49][50][51][52], we used Ritchie and Howie's scheme [24] to extend the momentum transferdependent ELF from an optical ELF. The numerical integrations in Eqs.…”

“…where ω 2 qi (q, ω pi ) = ω 2 pi + 2E F q 2 /3 + q 4 /4 describes the plasmon dispersion, and E F is the Fermi energy. In our previous simulations [48][49][50][51][52], γ i was taken into account as a constant. In this work, for a more general comparison, a dispersion relation [24] of γ i (q) = (γ 2 i + q 4 /4) 1/2 is used.…”

“…The Ritchie-Howie method is used due to its high efficiency for obtaining the surface ELF. We note that, as the extraction of the ELF by the RMC method from REELS takes a lot of iteration [46,48], the use of the Ritchie-Howie method for the surface DIIMFP σ surf is a necessary compromising solution for saving computation time in our RMC simulation.…”

“…The simulated annealing method [47] was employed for adjusting the parameter set of the ELF to obtain the best fit. Later Xu et al [48,49] further improved the RMC method by considering the semiclassical electron inelastic scattering model. The extended RMC method has been successfully applied to various metallic solids [49][50][51][52].…”