Alternative electronic parts for multiphonon-broadened photoionization cross sections of deep levels in SiC

Analytical expressions for multiphonon-broadened photoionization cross sections of deep levels are generally represented by convolutions of temperature-independent electronic parts with thermally broadened Franck–Condon (FC) factors. As a simple analytical representation of the FC factors, we use here the semiclassical (Gaussian) approximation. For the electronic part we consider a variety of conventional alternatives such as the familiar Lucovsky model, Ridley’s billiard ball model, and Inkson’s model. From corresponding numerical analyses of experimental photoionization cross section data available for the $R$ center in 6H-SiC and a vanadium-related center in $4\mathrm{H}∕6\mathrm{H}\text{-}\mathrm{SiC}$ we conclude that, among these conventional models, Inkson’s model (for allowed transitions) is the only one that provides satisfactory fits to the experimental data. As a physically plausible alternative to the latter we also consider a Taylor series expansion for the electronic part, which is capable of accounting for competition (superposition) of qualitatively different components due to allowed and forbidden transitions. This alternative model leads, particularly for the vanadium-related center in $4\mathrm{H}∕6\mathrm{H}\text{-}\mathrm{SiC}$ , to a marked improvement of the numerical fit in conjunction with a significant change in the estimated optical ionization energy. We show a simple way of estimating FC shifts and the associated thermal ionization energies on the basis of the fitted semiclassical parameter sets.