Electron surface scattering kernel for a plasma facing a semiconductor

Employing the invariant embedding principle for the electron backscattering function, we present a scheme for constructing an electron surface scattering kernel to be used in the boundary condition for the electron Boltzmann equation of a plasma facing a semiconducting solid. The scheme takes the solid's microphysics responsible for electron emission and backscattering from the interface within a randium-jellium model into account and is applicable to dielectrics and metals as well. As an illustration, we consider silicon and germanium, describing the interface potential by a Schottky barrier and including impact ionization across the energy gap as well as scattering on phonons and ion cores. The emission yields deduced from the kernel agree well enough with measured data to support its use in the electron boundary condition of a plasma facing silicon or germanium.