Scattering model for the bound electronic states of an impurity complex in a crystal

Abstract

In previous work a Green's function method has been developed for the calculation of the bound one-electron eigenstates of a polyatomic molecule. This technique is now extended to the problem of determining the bound states associated with substitutional impurities in a crystal. The model is distinguished from more conventional methods of treating the impurity problem, in that an explicit knowledge of the Wannier functions or Bloch functions for the perfect crystal is not required. The one-electron wave functions for the impurity complex and those for the unperturbed part of the crystal are expanded on an equal basis in the partial-wave representation. The electronic spectrum of the perfect crystal enters only implicitly through the presence of “renormalized” molecular type structure factors which contain the resolvent for the energy band problem. Because there are no multicenter integrals in this method, one is not restricted in practice to considering only isolated impurities, but can treat as easily arbitrary clusters of impurities and perturbed atoms of the host crystal. More general types of crystal defects, such as interstitial impurities and vacancies, are also within the scope of the model.