Invariant embedding approach to secondary electron emission from metals

TL;DR

This paper develops an invariant embedding method to accurately calculate secondary electron emission yields from metals at low energies, emphasizing the roles of incoherent scattering and surface potential effects.

Contribution

It introduces an invariant embedding approach combined with a quasi-isotropic approximation to model electron emission, incorporating effects of coherent and incoherent scattering.

Findings

Experimental data are well reproduced with the model.

Incoherent scattering on ion cores is crucial for electron escape.

Surface Bragg gaps and defect scattering influence electron transmission.

Abstract

Based on an invariant embedding principle for the backscattering function we calculate the electron emission yield for metal surfaces at very low electron impact energies. Solving the embedding equation within a quasi-isotropic approximation and using the effective mass model for the solid, experimental data are fairly well reproduced provided (i) incoherent scattering on ion cores is allowed to contribute to the scattering cascades inside the solid and (ii) the transmission through the surface potential takes into account Bragg gaps due to coherent scattering on crystal planes parallel to the surface as well as randomization of the electron's lateral momentum due to elastic scattering on surface defects. Our results suggest that in order to get secondary electrons out of metals, the large energy loss due to inelastic electron-electron scattering has to be compensated for by incoherent elastic electron-ion core scattering, irrespective of the crystallinity of the sample.