Theory of localized defects in solids

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Abstract
Short-range defects are found, for example, at solid surfaces and at deep and isoelectronic traps in the bulk. We have extended a new concept, introduced by Kohn and Onffroy, in order to treat local defects in three-dimensional solids. The new concept involves generalized Wannier functions, which can be obtained variationally. These functions vary from site to site in the (nonperiodic) solid and make a complete orthonormal basis set for the bound and continuum wave functions. Questions as to the validity of the method in three dimensions are answered. The basis functions are calculated via perturbation theory for local defects in a wide-band-gap insulator. An exact set of difference equations similar to the one-band Koster-Slater equations and to those presented by Kohn and Onffroy is derived for the many-band wave functions of the nonperiodic system. It is shown how to obtain charge densities and local densities of states without prior knowledge of the electron wave functions.