A localized orbital description of Si

Abstract

AbstractIn order to describe the change in electronic structure arising from the presence of impurities in a metal or semiconductor it is convenient to have a localized basis representation of the host. To optimize such impurity calculations it is also necessary that this set of localized basis functions be as small as possible. The best representation of the electronic structure of the diamond and zinc‐blende semiconductors in terms of a small set of localized basis functions has been obtained by Chadi. In this method Bloch sums for describing the pseudo‐wave‐functions and energy bands are constructed from Slater orbitals of different symmetry centred on each atomic site. Using a variational approach to determine the decay constants parametrizing these various orbitals Chadi obtains an accurate description of the bandstructures with a simple four state per atom s–p basis set and reliable pseudo‐charge densities with only ten states per atom. These original calculations of Chadi are not, however, carried through to full convergence. Therefore this analysis is repeated for the case of Si and it is found that, while Chadi's results are indeed fortuitous, it is possible to accurately describe both the bandstructure and valence electron charge density of these semiconductors in terms of a minimum set of well localized basis functions.