Structural and chemical trends in doped silicon nanocrystals: First-principles calculations

Electronic and structural properties of substitutional group-V donors sN, P, As, Sbd and group-III acceptors sB, Al, Ga, Ind in silicon nanocrystals with hydrogen passivation are explored using first-principles calculations based on hybrid density functional theory with complete geometrical optimization. The bonding near the impurity is similar to that found for the impurity in bulk crystalline silicon, with some quantitative differences. The N case shows large local distortions, as it does in the bulk, characteristic of a deep trap. For the other impurities, no evidence is found for a transition to atomic scale localization induced by the small size of the nanocrystal. The chemical trends of the donor and acceptor binding energies and the donor excited state energies in doped nanocrystals are similar to those in the bulk; however, the absolute magnitudes are substantially larger. The increase in the magnitude of the binding energy is mainly due to the quantum confinement effect combined with the reduced screening of the impurity potential in small nanocrystals. The screening of the impurity potential is carefully examined using the self-consistent electrostatic potential from the full calculations. Strong chemical and local-field effects are seen within the radius of the first neighbor bonds to the impurity atom. This explains the large increase in the donor excited state energy level splittings and the relative importance of the central cell contributions to the binding energies. The acceptor and donor orbitals have different atomic character on the impurity site, leading to substantially different acceptor and donor energy level splittings.