Energy band structure of diamond, cubic silicon carbide, silicon, and germanium

Abstract

We have developed a method for determining the band structure of crystals which combines the best features of a first-principles approach with the best features of an empirical approach. The first step in our method is a first-principles OPW band calculation based on the free-electron exchange approximation. In the second step, we depart from a purely first-principles approach, and introduce a small empirical correction which brings key features of the calculated energy level scheme into exact (or close) agreement with the most reliably established features of the experimental level scheme. In addition to obtaining reliable energy band models valid over a wide energy range, we obtain the electronic wave functions for a large number of levels, the core and valence electronic charge distributions, and many other “first-principles” quantities. Following a summary of the shortcomings of purely first-principles and purely empirical band calculations, we sketch the essential features of our intermediate treatment. Recent studies of the band structure of diamond, cubic silicon carbide, silicon, and germanium-carried out both by our method and other methods-are then discussed and compared. It is shown how improved band models for these crystals can be generated with the aid of some crucial information about the band structure derived from experiment. Finally, we observe that although the use of a universal exchange potential is an important simplification, and one that has greatly accelerated recent progress in energy band calculations, this approximation is to some extent an oversimplification. It appears likely that some of the empirical corrections that we now have to introduce in order to bring theory and experiment closer together could be reduced substantially if we could define one exchange potential for s-like electrons, another for p-like electrons, and still another for d-like electrons. This idea of l-dependent exchange potentials represents a middle ground between the Hartree-Fock extreme of different exchange potentials for different orbitals, and the Slater extreme of the same exchange potential for all orbitals.