ANALOG OF THE K.P THEORY FOR A LOCALIZED-ORBITAL DESCRIPTION OF THE BAND-STRUCTURE OF ZINC-BLENDE-STRUCTURE SEMICONDUCTORS

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.