Periodic-cluster calculations of the valence states and native defects in diamond, silicon, germanium, ZnS, ZnSe, and SiC

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Abstract
We present the results of band calculations and of native defects on diamond, Si, Ge, ZnS, ZnSe, and SiC by means of periodic clusters. We study the convergence of the results with cluster size. For clusters as small as eight atoms, eigenvalues and eigenfunctions seem to be converged. Compared to nonperiodic clusters, the present technique has the advantage of establishing a one-to-one correspondence to the eigenvalues of a full band calculation (infinite-sized cluster). Compared to the full band calculation, the periodic-cluster technique is equivalent to a calculation with ‘‘special points’’ integration in the Brillouin zone. The periodic-cluster calculation is useful when a spectrum ‘‘discretization’’ is desired, for instance, in the calculation of defects. We illustrate this point by presenting the results of calculations on native defects in these semiconductors. Our results for the valence states are in excellent agreement with experiment. In other instances, our results are able to give a theoretical interpretation to experiment.