ACCURACY OF THE CHEMICAL-PSEUDOPOTENTIAL METHOD FOR TETRAHEDRAL SEMICONDUCTORS

Simple two-center tight-binding models have often been used in electronic-structure calculations, although uncertainty about the foundations of the tight-binding method has severely limited progress. This uncertainty has been much reduced following the recent successes of the non-self-consistent Harris scheme but several important questions still remain. In particular, the accuracy of the (almost ubiquitous) two-center approximation is still in doubt. It has often been argued that although this is a poor approximation when applied crudely, it can be justified within the more sophisticated context of chemical-pseudopotential theory. The argument looks sensible, but clear quantitative tests only became possible with the advent of the Harris scheme. This paper reports a careful series of tests of the accuracy of the two-center approximation for germanium, and shows that neither the crude version nor the more sophisticated chemical-pseudopotential version is accurate enough to be useful. The remarkable success of two-center tight binding in predicting the structures and surface reconstructions of semiconductors is, therefore, still mysterious.