Electron inelastic interactions with overlayer systems

Abstract

An overlayer system composed of a thin film on the top of a semi-infinite substrate was studied in this work for electron inelastic interactions. Analytical expressions for the depth-dependent inelastic differential and integral inverse mean free paths were derived for both incident and escaping electrons. The interface ͑film-substrate͒ effect and the surface ͑vacuum-film͒ effect were analyzed by comparing the results of an overlayer system and a semi-infinite system. It was found that the interface effect extended to several angstroms on both sides of the interface for a 500 eV electron incident into or escaping from the vacuum-SiO 2 -Si and the vacuum-Au-Ni systems. An application of the spatial-varying inelastic differential inverse mean free paths was made by Monte Carlo simulations of the electron elastic backscattering from an overlayer system. Good agreement was found between results calculated presently and data measured experimentally on the elastic reflection coefficient.for zϽϪD/2, B͑,Q,,z ͒ϭ 21ͭ 2 cos ͫ ͑zϩD/2͒ z ͬ Ϫexp͓ϪQ͑zϩD/2͔͒ ͮ Ϫ 21 23 exp͑ϪQD͒exp͓Q͑zϪD/2͔͒ ⑀ 2 ͑ Q,,zϩD/2͓͒1Ϫ 21 23 exp͑Ϫ2QD͔͒ ϩ 23 exp͓Q͑zϪD/2͔͒Ϫ 23 21 exp͑ϪQD͒ ͭ 2 cos ͫ ͑zϩD/2͒ z ͬ Ϫexp͓ϪQ͑zϩD/2͔͒ ͮ ⑀ 2 ͑ Q,,zϪD/2͓͒1Ϫ 21 23 exp͑Ϫ2QD͔͒ ϩ ͫ 1 ⑀ 2 ͑q ,͒ ͬ , ͑10͒ for ϪD/2ϽzϽD/2 and 8249 21ͭ 2 cos ͫ ͑zϩD/2͒ z ͬ Ϫexp͓ϪQ͑zϩD/2͔͒ ͮ exp͓ϪQ͑zϩD/2͔͒Ϫ 21 23 exp͑Ϫ2QD͒ ⑀ 2 ͑Q,͕͒1Ϫ 21 23 exp͑Ϫ2QD͖͒ ϩ 23 exp͓Q͑2zϪD ͔͒Ϫ 23 21 exp͑ϪQD͒ ͭ 2 cos ͫ ͑zϩD/2͒ z ͬ Ϫexp͓ϪQ͑zϩD/2͔͒ ͮ exp͓Q͑zϪD/2͔͒ ⑀ 2 ͑ Q, ͓͒1Ϫ 21 23 exp͑Ϫ2QD͔͒ ϩ ͫ 1 ⑀ 2 ͑Q,͒ ͬ , ͑16͒ for ϪD/2ϽzϽD/2 and B͑,Q,,z ͒ϭ 23 ͓1ϩ 21 exp͑Ϫ2QD͔͒ ͭ 2 cos ͫ ͑zϪD/2͒ z ͬ Ϫexp͓ϪQ͑zϪD/2͔͒ ͮ exp͓ϪQ͑zϪD/2͔͒ ⑀ 3 ͑ Q, ͕͒1Ϫ 21 23 exp͑Ϫ2QD͖͒ Ϫ 21 ͓1ϩ 23 ͔ ͭ 2 cos ͫ ͑zϩD/2͒ z ͬ Ϫexp͓ϪQ͑zϩD/2͔͒ ͮ exp͓ϪQ͑zϩD/2͔͒ ⑀ 3 ͑ Q, ͓͒1Ϫ 21 23 exp͑Ϫ2QD͔͒ ϩ ͫ 1 ⑀ 3 ͑Q,͒ ͬ , ͑17͒ for zϾD/2.8250

Surface excitations in electron spectroscopy. Part I: dielectric formalism and Monte Carlo algorithm

“…To the best of our knowledge, no detailed discussion of the implications or the effect of this approximation exists in the literature. Moreover, several later models use this approximation with the sole justification of a reference to the aforementioned work or to works which in turn make a reference to it. Another approximation that is made in some works (sometimes tacitly) consists in replacing q by q ‖ in the last bracket in Eqn .…”

“…By choosing appropriate values for ( p 1 , p 2 , p 3 ), e.g. (0,1,0) for the Chen and Kwei model, and introducing further approximations as required, it is in principle possible to reproduce most of the subset of semiclassical models for surface excitations found in the literature . As pointed above, the model of Yubero and Tougaard is not suited for comparison within the presented framework, for it takes a different approach.…”

Monte Carlo simulation of energy loss of electrons backscattered from solid surfaces

“…Chen and Kwei derived a semi-classical expression for DIIMFP including the depth-dependence of surface excitation and found that the surface excitation effect was extended to both sides of the solid surface [9]. Intensity of electrons backscattered from solid surfaces [10] and from a binary compound [11], were calculated using a MC algorithm applying these depth dependent DIIMFP calculations and the straight line approximation in the surface region. A theoretical derivation of the DIIMFP for electrons moving across the solid surface was given by Li et al [1] on the basis of the dielectric response theory and the extended Drude dielectric functions.…”

Retardation effect on energy losses of electrons moving parallel to solid surfaces

“…[1][2][3][4][5][6] For the charged particle moving parallel to a semi-infinite solid, theoretical approaches [7][8][9] were proposed to calculate the induced potentials which resulted in surface plasmon excitations, i.e., collective oscillations of the quasifree electrons near the surface. Much attention has been paid to the inelastic interaction cross sections between the charged particle and the solid surface.…”