The method of moments for semi-conductors and localized states

Abstract

It is shown how to approximate density of states curves by delta function models fitted to a few moments of the true curve. Application is made to the tight-binding approximation. The method gives analytical expressions for the cohesive energy of semi-conductors in the Hartree approximation, the position of bound states due to defects and also information about the population of the states. In the simplest models the results are obtained with a relative error in the range from one to ten per cent. The models presented here can be generalized easily and applied to other problems such as the study of surface states and localized vibrational states due to impurities