Calculation of the total energy of charged point defects using the Green's-function technique

Abstract

We present a method for calculating the energy of an isolated, charged, deep-level point defect in an otherwise-perfect infinite crystal. To simplify the evaluation, one can make the usual replacement of one-particle energy terms by a sum over occupied eigenvalues plus corrections for overcounting. However, this simplification leads to conceptual difficulties when the defect is charged. These are overcome by truncating the long-range tail of the defect potential. The correct screening charge does not appear automatically when a truncated potential is used, and so a constant potential shift is added to guarantee proper screening. Alternatively, one can evaluate the original kinetic-energy form of the functional. We do so and compare it with the eigenvalue formulation. A careful study of the effects of truncation indicates that, although the two formulations are equivalent for neutral systems, they are not so for charged systems. The calculated energy of charged defect must differ slightly when evaluated by the two methods. The truncation error is greater for the eigenvalue formulation than for the kinetic-energy formulation. However, this difference is expected to be in the (0.1-0.2)-eV range for reasonable truncation radii, and to be quite insensitive to atomic displacements. This may be sufficiently small and insensitive, depending on the situation being studied, that the greater numerical simplicity of the eigenvalue formulation would make it the method of choice. If not, the kinetic-energy formulation presents no major difficulties. Consequences of shifting the conduction-band eigenvalues, as a way of overcoming the small-band-gap problem inherent in the use of local-density-functional theory are explored.