Superlattice Calculation in an Empirical spds Tight-Binding Model
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(2) Scuola Normale Superiore and Istituto Nazionale per la Fisica della Materia, Piazza dei Cavalieri 7, 1-56126 Pisa, Italy
ABSTRACT We propose an empirical tight-binding method for tetrahedrally coordinated cubic materials and apply it to group IV and III-V semiconductors, extending existing calculations by the inclusion of all five d-orbitals per atom in the basis set. The symmetry character of the conduction states at the surface of the Brillouin zone is considerably improved
compared to calculations in smaller bases, and the corresponding band positions can be obtained within the experimental uncertainties. Because the distance dependence of the
tight-binding parameters is derived from deformation potentials, the model is particularly suited for an investigation of strained superlattices where the states at direct or pseudodirect conduction band minima are composed of wavefunctions of all the minima at F, X, and L of the constituents. Investigations of GaAs/AlAs and short-period superlattices indicate a strong mixing between the conduction band valleys in the miniband structure, and the results are in better agreement with experiments than state-of-the-art empirical pseudopotential calculations.
INTRODUCTION During the last decades, empirical tight-binding (TB) methods have been used for an approximate understanding of materials properties of various crystal symmetries [1-3]. A
major problem for quantitative applications concerning cubic semiconductors has been the 3 required extension of the atomic basis from the minimal size sp [2,4] towards higher-lying
atomic states like the next s-shell in an sp3 s* basis [5], d-states of rz-symmetry in sp3& [6] and the recent parametrization including sp3d5s* states [7]. Group theoretical arguments demonstrate that the latter sp3d's* basis is needed for a good approximation to numerical completeness, and various deficiencies of the smaller TB models have been resolved, e.g. the decomposition of valence and conduction wavefunctions into different atomic symmetries of cation and anion [7]. A crucial step in the parametrization of our sp3ds* nearest-neighbour TB model was the investigation of the free-electron band structure along the lines indicated in older empirical TB calculations. This allowed an analytic derivation of universal parameters for zincblende- and diamond-like semiconductors. In particular, the on-site energies of the d-states and all their interaction parameters were deduced from the higher free-electron conduction bands [7]. As these bands remain free-electron like in cubic semiconductor materials, the corresponding TB parameters are typical for all materials of this symmetry class. Because the d-d-interaction parameters interfere constructively at some points of the Brillouin zone, the corresponding splittings are by far too large to be obtained in low order perturbation theory. The lowest bonding d-state at the high symmetry points of the Brillouin zone occurs at X, leading to a dominating d-contribution to the X6&wav
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