Finding

Paper

Citations: 29

1959

Abstract

Abstract A review of the k·p approach to band structure will be given. An effective Hamiltonian for the cell-periodic part of the Bloch function consists of diagonal elements corresponding to the band energies at k = 0 and off diagonal elements of ( h m ) k·p connecting the bands and causing mutual repulsion unless symmetry forbids interaction. When ( h m ) k·p is small compared to the energy separation between bands, second order perturbation theory can be used to obtain effective masses. E vs. k2 expressions involve a small number of parameters which are determined by experiments such as cyclotron resonance. Perturbation theory can be improved upon by treating strongly interacting bands exactly and subsequently handling weak interactions by perturbation theory. Such a procedure inevitably increases the number of parameters to be determined. Optical band gap measurements are needed for this extension. In addition, absolute optical absorption determines momentum matrix elements between bands. The feasibility of using such an approach to determine band structure empirically throughout the zone will be examined. In addition to k.p, there are less important k dependent terms which must be considered in some cases. The linear k terms at k =0 in the III–V compounds are an example. The inclusion of exchange terms in the one particle Schroedinger equation introduces modifications in the above treatment. The interband matrix elements determining the effective mass contain contributions from both momentum and exchange terms, whereas optical absorption involves only the momentum matrix element. Exchange terms contribute first order perturbation corrections to the effective mass. Estimates of exchange effects indicate that they are small. The symmetry approach of LSputtinger may serve to indicate inadequacies of the one particle viewpoint.

Authors

E. Kane

Journal

Journal of Physics and Chemistry of Solids

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