Dzwig, Peter (1977) The overlap integrals for the Auger effect in gallium phosphide. University of Southampton, Doctoral Thesis.
Abstract
For the first time a direct calculation of the overlap integrals occuring in the Auger effect in the III-V compound Gallium Phosphide has been made. Theoretical investigation of the properties of the overlap integrals has been made and previous theoretical result sextended. The numerical approach has been via the Kop method of band structure calculation. This approach has enabled the integrals themselves to be evaluated and their sensitivity to band structure parameter changes in the region of high electronic concentration in the conduction and investigated. Whilst it has proved impossible to obtain an algebraic expression for the overlap integrals via curve-fitting their chief properties are described qualitatively. The numerical results obtained are included in a Monte Carlo calculation for the Auger recombination coefficient for the hole-hole-electron process in Gallium Phosphide B2 , yielding B2 - 1.65 x 10-33cm6s 1. This is taken, together with the work of other investigators, to indicate that the Auger effect is not the main recombination channel in Gallium Phosphide and that other processes must be invoked to account for experimental results. Theoretically, general properties of the overlap integrals are investigated and some previous results are extended to include relativistic effects and Umklapp terms in the integrals. It is shown that the latter cannot be included in a Kop approach since their presence leads to a set of simultaneous linear equations which are singular and cannot be solved owing to insufficient conditions for an arbitrary Umklapp term. Certain previous theoretical work is ammended in the light of this calculation and is shown to be in agreement with the above result for B2e.
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