Scattering-theoretical method for semiconductor surfaces: self-consistent formulation and application to Si(001)-(2×1)

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Abstract
A self-consistent-field method for the calculation of electronic properties of semi-infinite crystals with reconstructed surfaces is described in detail and applied to the Si(001)-(2×1) surface. The method is based on local-density-functional theory and a Green-function scattering-theoretic formulation is employed. Wave functions and operators are represented in a localized-Gaussian-orbital basis set. The calculations yield the self-consistent surface potential, charge densities, surface band structure, and wave-vector-, atom-, and orbital-resolved layer densities of states with an extreme spectral resolution. Surface bound states and surface resonances are determined unambiguously and accurately even for states whose wave functions are very extended. In order to be able to point out advantages of our method by comparison with the results of other techniques, we have carried out self-consistent slab calculations with varying slab thicknesses as well. The present method is shown to be very efficient and accurate in describing the whole electronic spectrum of the surface. The efficiency of the method stems largely from the fact that it exploits both the full three-dimensional periodicity of the underlying bulk crystal and the short range of the deviation of the surface potential from the bulk or vacuum potentials, respectively. Thus all bulk properties are built in from the start via a band-structure calculation as a well-defined reference and they are preserved. One then focuses on the changes produced by the surface potential. Since the bulk and surface effects are separated analytically in the Dyson equation for the surface Green function, the interpretation of the results is straightforward and unambiguous. The virtues of the scattering-theoretical method are exemplified by a detailed discussion of our results for the technologically most important Si(001)-(2×1) surface in comparison with our own slab calculations and with other results from the literature.