Tight-Binding Calculations of the Valence Bands of Diamond and Zincblende Crystals

The tight-binding approach to the problem of the electronic energy levels in solids is intuitively very appealing. The method provides a real space picture of the electronic interactions which give rise to the particular features of the energy band structure, density of states, etc. This is extremely useful in studies of how these features change when the electronic configuration is altered. The tight-binding method is most practical when only a few types of electronic interactions are dominant. In such a case an adequate description of the system of interest can be obtained by specifying a small number of interaction parameters. In this way a qualitative description of the valence bands can be obtained [l to 81 for niaterials in the diamond, zincblende, and other structures. In this paper we show that a tight-binding method using a few interaction parameters gives accurate results for the valence bands of the diamond and zincblende crystals C, Si, Ge, GaAs, and ZnSe. The tight-binding method we use is equivalent to that of Slater and Koster [GI. It can also be regarded as a more complete version of the Weaire and Thorpe [a] model in which interactions between more distant directed orbitals are included. It is necessary to include these extra interactions for a more complete description of the valence bands. I n Section 2 we give a brief review of the method and consider the effects of the various interactions on the density of states. We show that the inclusion of all the possible nearest-neighbor interactionsl) between sand p-tight-binding states is not sufficient to broaden the “p-like’’ bands along all symmetry directions. The resulting error in the energies is about 1 eV and occurs niostly for