Theory of Defect Levels and the “Band Gap Problem” in Silicon

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Abstract
Quantitative predictions of defect properties in semiconductors using density functional theory have been crippled by two issues: the supercell approximation, which has incorrect boundary conditions for an isolated defect, and approximate functionals, that drastically underestimate the band gap. I describe modifications to the supercell method that incorporate boundary conditions appropriate to point defects, identify a common electron reservoir for net charge for all defects, deal with defect banding, and incorporate bulk polarization. The computed level spectrum for an extended set of silicon defects spans the experimental gap, i.e., exhibits no band gap problem, and agrees remarkably well with experiment.