Band mixing in semiconductor superlattices

Abstract

Much understanding of the electronic and optical properties of a semiconductor superlattice can be obtained by relating the superlattice electronic wave functions and band structure to those of the two bulk semiconductors from which it is constructed. In this paper, the relationship is studied within the framework of the empirical tight-binding model, which is solved using the reduced Hamiltonian technique. The superlattice wave functions are described as linear combinations of bulk Bloch functions with complex wave vectors, twenty (including spin) for each of the two constituent materials. The bulk Bloch-function composition of the superlattice wave function is studied as a function of layer thickness, alloy composition, and energy. The GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As and InAs-GaSb superlattices are examined in detail. Comparisons with simpler Kronig-Penney and envelope-function models are made. It is found that the lowest superlattice conduction-band states are primarily derived from the expected bulk states with wave vectors near the center of the Brillouin zone, with a small admixture of zone-edge components. The energies and general form of the wave functions are modified only slightly, except close to the interfaces. There, the admixture can significantly affect the interfacial boundary conditions beyond those employed by commonly used envelope-function approximations. Valence-band states are more complicated in that the superlattice periodic potential mixes the bulk heavy-hole, light-hole, and spin-orbit split-off bands, even at the superlattice Brillouin-zone center. Crossover effects occur in which a given superlattice subband can have a varying proportion of light-hole-like or heavy-hole-like character depending on superlattice layer thickness. The dispersion of the subbands away from the zone center also causes the mixing of bands and results in modifications of the superlattice band structure as compared with band structures produced by simpler models.