One-dimensional overlap functions and their application to Auger recombination in semiconductors

The theoretical lifetime of excess carriers in semiconductors limited only by the Auger recombination mechanism previously discussed by the present authors, depends on a temperature-independent parameter. This involves certain overlap integrals. They are of the form ∫u*(k1, r) u(k2, r) dr, where the u’s are the modulating parts of Bloch wave functions. The integrals are calculated in this paper on the basis of a Kronig-Penney model. The value of the parameter obtained is shown to be rather insensitive to many details of the model used. When the value found is inserted into the previously published theory of lifetimes in InSb, very good agreement is obtained with the more detailed experimental results which have recently become available. This strongly suggests that the dominant recombination mechanism in InSb at elevated temperatures has been identified. A more general analysis of the properties of the overlap integrals is also given in this paper.