Poisson-Schrödinger andab initiomodeling of doped Si nanocrystals: Reversal of the charge transfer between host and dopant atoms

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We present ab initio density functional calculations that show P (Al) dopant atoms in small hydrogen-terminated Si crystals to be negatively (positively) charged. These signs of the dopant charges are reversed relative to the same dopants in bulk Si. We have therefore developed a self-consistent Poisson-Schr\"odinger model that allows us to bridge these two regimes of different charge character. Our Poisson-Schr\"odinger model is based on a nonorthogonal tight-binding model that reproduces the band structure of silicon very well, and we have also developed parameters for P, Al, and H. Using this model, we predict this reversal of the dopant charge to occur at crystal sizes of the order of 100 Si atoms. We explain it as a result of the competition between fundamental principles governing charge transfer in bulk semiconductors and molecules. Based on these general considerations, we expect it to occur in nanocrystals of most semiconductors. We also calculate band-edge energies and dopant-level energies for a number of crystallites containing 29--888 Si atoms.