Electron inelastic mean free path, electron attenuation length, and low-energy electron-diffraction theory

Abstract

Low-energy electron diffraction (LEED) theory is used for describing the electron transport in crystalline solids with the purpose of determining the electron attenuation length. The inelastic scattering of the primary electron in the electron gas of the material is introduced into the LEED theory in terms of the electron inelastic mean free path derived by Tanuma, Powell, and Penn from the Lindhard dielectric function and optical data [Surf. Interface Anal. 17, 911 (1991)]. The theorem of flux reversal for electrons in situations of inward and outward propagation is deduced from local inversion symmetry and specific boundary conditions at the sources. The theory is applied to 50\char21{}400 eV electrons incident on the three low-index surfaces of copper, and a fair agreement is found with a previous Monte Carlo simulation of the electron transport in amorphous copper. In addition to the inelastic electron-electron gas scattering, the inelastic electron-phonon scattering has a significant effect on the attenuation length in a crystalline material. The temperature parameter, necessary in a LEED calculation, does not occur in current Monte Carlo simulations. Common scattering potential models, at low energy, for LEED and for Auger electron spectroscopy and x-ray photoemission spectroscopy are discussed.