An expression for the Fourier coefficients of the absorptive potential due to electron-impact ionization in crystals is derived and the cross section is given in terms of these Fourier components. Absorptive potentials due to K-shell ionization and thermal diffuse scattering (TDS) are calculated with use of a hydrogenic model and an Einstein model, respectively. Inelastic potentials require integration over all states of the scattered electron and, for K-shell ionization, integration over all states of the ejected electron. These potentials are thus dependent on incident-beam energy, in contrast with the elastic potential. The projected spatial distribution of these potentials are plotted and compared with the elastic potential for CdTe, GaAs, Si, and diamond. The delocalization of the ionization absorptive potential is similar to that expected from classical impact-parameter arguments. The form of the TDS potential is substantially different from that due to elastic scattering, being extremely peaked on atomic positions with no absorption in the channels between atomic planes.

• Received 5 June 1990

DOI:https://doi.org/10.1103/PhysRevB.42.11644