New self-consistent approach to the electronic structure of localized defects in solids

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Abstract
We have developed a new method to calculate electronic states associated with localized defects. The method yields energy levels, wave functions, and electron charge densities with a precision which is equal to state-of-the-art results for bulk band structure or surface calculations and thus should eventually allow meaningful detailed comparison with experiments. The calculations are based on a scattering-type Green's-function formulation which describes the system of a single isolated defect in an otherwise perfect crystal. Self-consistency is achieved by an iterative recalculation of the valence charge and then of the defect potential. The Green's function, which expresses all of the necessary information about the perfect crystal, is here evaluated using an eigenfunction expansion employing high-precision wave functions and band structures obtained from a self-consistent, pseudopotential, local-density-functional calculation. The defect potential is calculated in the same approximation, using occupied electron states of the perturbed system. The use of this method is not restricted, however, to pseudopotentials. The possibility of extending it, e.g., in the direction of crystal ionic potentials with core electrons, seems quite real in the event that such extension should be needed, say, for studying the energetics of relaxation or reconstruction around the vacancy. The method is applied to the example of an isolated Si vacancy. This system has been chosen to facilitate comparison to earlier non-self-consistent, or self-consistent but artificially periodic, calculations. The results generally agree with these earlier works but are improved in various aspects.