Bond-Orbital Model and the Properties of Tetrahedrally Coordinated Solids

A model electronic structure is explored which attempts to relate a wide range of properties to a few parameters of covalent and polar solids. The model is based upon tight-binding combinations of bonding hybrid orbitals. Of the many overlap matrix elements which enter, only three are retained; the three are associated with covalency, polarity, and metallicity. Many properties may be computed quite simply in terms of the parameters of the model, and measured values of the properties can then be used to determine the parameters. In this study the matrix elements associated with metallicity are obtained directly from the atomic-term values; those associated with covalency and polarity are obtained from the static dielectric constant using essentially the approach of Phillips, but in terms of the formula for the dielectric constant appropriate to this model. Also calculated in terms of the model were the valence energy bands themselves, obtained explicitly for silicon and for gallium arsenide. In treating other properties the unitarity of the final diagonalization was utilized to avoid carrying it out explicitly. The dipole moment of the individual bonds was defined and calculated as was an effective ionic charge and the macroscopic transverse charge. The cohesive energy was also obtained for ionic and metallic structures as well as for the covalent tetrahedral structures. Criteria for the stability of each structure were thereby obtained. The model also explains why some properties scale approximately linearly with the ionicity defined by Phillips.