A complete spatial description of the empirical-local-pseudopotential Hamiltonian in zinc-blende–structure semiconductor materials based on the tight-binding theory is presented. The ${\mathrm{sp}}^3$ Gaussian orbitals are employed to construct the Bloch basis functions which are subsequently used in obtaining the Hamiltonian matrix. The spatial correlation of the neighbor quasiatomic wave functions is estimated. It is shown that to produce an energy-band structure comparable to that of the plane-wave basis, a cluster of at least 135 primitive cells is required. The intermediate-range interactions are important in determining the dispersion of the band structure. We evaluated the GaAs energy band as an illustration.

• Received 11 April 1988

DOI:https://doi.org/10.1103/PhysRevB.38.12487