Point defect calculations in diamond-type crystals by the extended Huckel method 1: General theory and the vacancy problem

The applicability of the extended Huckel method for the calculation of the electronic properties of point defects in diamond-type crystals is discussed. A detailed study of the isolated vacancy in both the diamond and silicon lattice shows that the results obtained depend upon the size of the cluster chosen and the approximations made at the boundary of the system. Clusters with up to 47 host lattice atoms are considered. A cluster of 41 atoms, which includes all atoms directly bonded to the second neighbours from the point defect, is considered to be the most suitable system. On the basis of a comparison of ab initio and extended Huckel calculations for small molecules, it is argued that studies involving distortions are beyond the validity of the simple method used here. At best, the results from extended Huckel studies for point defects in diamond type crystal should be considered to be semiquantitative.