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

Abstract

The theory describing energy losses of charged non-relativistic projectiles crossing a planar interface is derived on the basis of the Maxwell equations, outlining the physical assumptions of the model in great detail. The employed approach is very general in that various common models for surface excitations (such as the specular reflection model) can be obtained by an appropriate choice of parameter values. The dynamics of charged projectiles near surfaces is examined by calculations of the induced surface charge and the depth- and direction-dependent differential inelastic inverse mean free path (DIIMFP) and stopping power. The effect of several simplifications frequently encountered in the literature is investigated: differences of up to 100% are found in heights, widths, and positions of peaks in the DIIMFP. The presented model is implemented in a Monte Carlo algorithm for the simulation of the electron transport relevant for surface electron spectroscopy. Simulated reflection electron energy loss spectra are in good agreement with experiment on an absolute scale. Copyright © 2012 John Wiley & Sons, Ltd.

Absorption of an Electron by a Dielectric Wall

“…Jk, 79.20.Hx, 52.40.Hf The interaction of electrons with surfaces plays a key role in applied science. Various methods of surface analysis [1][2][3] are based on it as well as a number of materials processing techniques [4]. In these applications the electron energy is above 100 eV and backscattering and secondary electron emission, the physical processes involved, are sufficiently well understood [5][6][7][8][9][10][11][12].…”

“…1a the wall (plasma) to occupy the z < 0 (z > 0) half space, measuring energy in Rydbergs from the bottom of the conduction band, that is, setting E cb = U w − χ ≡ 0, length in Bohr radii, and mass in electron masses, the transmission probability for a plasma electron hitting the wall, and having thus kinetic energy E − χ > 0, is given by [35] T (E, ξ) = 4m e kp (m e k + p) 2 (1) with k = √ E − χ ξ and p = √ m e E η the z−components of the electron momenta outside and inside the wall. In (1) the signs of k and p are always the same.…”

Surface excitations in the modelling of electron transport for electron-beam-induced deposition experiments

“…The inclusion of surface excitations implies a modification of the sampling algorithm in the vicinity of the surface (typically 15 Å above and below the surface), as schematically shown in Figure 1. Technical details on the implementation of the algorithm for the simulation of surface energy losses can be found elsewhere in great detail [ 30,31,50]. Here the focus is on the effect of surface excitations on the reflection-electron-energy-loss spectrum (REELS).…”

“…Assuming a projectile that moves with a velocity v along a trajectory r = vt , one can conveniently solve the Maxwell equations in Fourier space to obtain the following expression for the induced electric field [31] (1) (1) where ρ(q,ω) is the Fourier transform of the projectile charge density ρ(r,t ) = Z 0eδ(r−vt ), where Z 0 is the projectile charge in units of the modulus of the electron charge, e, and v is the velocity of the projectile. To obtain this expression, the following approximations were considered: (1) The Coulomb gauge was adopted and the contribution from the vector potential was neglected.…”

“…The existence of surface excitations was predicted in the late 1950s [8]; experimental evidence was obtained shortly thereafter [9,10]. In order to model surface excitations in electron spectroscopies, several models have been developed to date [ 11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]. Various approaches are considered, often with underlying simplifications, evoked on physical or technical grounds, in the interest of making calculations feasible in a finite time.…”