Analog of thek⋅ptheory for a localized-orbital description of the band structure of zinc-blende-structure semiconductors

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Abstract
The k⋅p method is based on a completely general formulation but contains parameters defined in terms of series involving matrix elements of the momentum operator. On the other hand, current band-structure calculations lead to a knowledge of the Hamiltonian matrix in a finite basis set per unit cell. It is thus of great interest to devise a systematic method allowing one to relate directly the effective-mass tensors to these Hamiltonian matrix elements. This is done here by a formulation close to the original k⋅p theory, applied to a tight-binding description of the band structure. The effects due to the inclusion of spin-orbit coupling and strain are discussed. The origin of the crossing between the light- and heavy-hole bands under uniaxial strain is analyzed. Extensions of the method to other descriptions of the band structure, as well as to phonon-dispersion curves, are briefly presented.