A level spectrum versus a single level in recombination

Abstract

The crucial importance of surface recombination in many solid-state devices is well known. Therefore one needs to know the differences between recombination via a spectrum of states and recombination via a single level. The generalised Shockley-Read recombination rate U1 via Nt states located at a single energy level Et is compared with the analogous rate Usp obtained when the Nt states are spread over a range of energies Etl, Etu in the forbidden gap. The same recombination coefficients, electron and hole concentrations, etc., are used in both cases. The ratio R=U1/Usp is studied. Among the conclusions are that R as a function of the location of Et is peaked at midgap if Usp refers to a uniform spectrum in the forbidden gap, and the capture cross sections for holes and electrons are of the same order. This arises from the efficient recombination for midgap states. For the same reason R drops below unity if Et lies near the band edges. For a strongly n-type or a strongly p-type surface the replacement of the spectrum by a single level is normally reasonable. The effects on R of energy-dependent capture coefficients and a non-uniform spectrum of trapping states are also considered. Although developed for surface recombination, the theory is also applicable to bulk recombination via an appropriate change of units for Nt.