Effects of surface states and of excitation on barrier heights in a simple model of a grain boundary or a surface

The model of a grain boundary (or of a surface) used here employs parallel quasi-Fermi levels but does not require the depletion approximation. Shockley–Read–Hall recombination via the surface states (including Auger effects) is utilized and the resulting surface trap occupation is displayed as a generalization of the well-known Fermi–Dirac distribution function. This enables one to cover equilibrium and steady-state conditions in one treatment. The barrier height has been given as a function of bulk doping, surface energy level density, and also as a function of excitation intensity. The latter is determined by the separation between the quasi-Fermi levels and can be due to incident light or carrier injection. A number of experimental curves have been fitted satisfactorily on the basis of the theory. Among the conclusions, we note that there is a maximum (with respect to doping) in the barrier height, and that illumination reduces the barrier height. The effect of the energetic position of the surface states is also traced here.