Theoretical study of the electronic structure of a high-angle tilt grain boundary in Si

We have constructed a model of a high-angle tilt boundary in Si and have examined its atomic and electronic structure. The 38.94° grain boundary studied contains fivefold and sevenfold rings of atoms in positions almost identical to those observed in high-resolution transmission electron microscopy. The grain boundary is continuous on a microscopic scale and does not contain any dangling bonds. The atomic positions on the two sides of the boundary are similar to those resulting from the joining of two crystals, aligned approximately in the directions of their respective [111] and [110] axes, along their common (221) surface. The two crystals have commensurate lattice sites on this surface. As a result, the grain boundary propagates on a macroscopic scale with no dislocations or strain due to lattice mismatch. We have performed energy-minimization calculations to determine the optimum atomic structure of the grain boundary. The calculated electronic structure for the optimized geometry has no defect states in the bulk band gap. The calculated surface energy per unit area of 0.02 eV/${\mathrm{\AA }}^2$ for the grain boundary is appreciably lower than that obtained for any of the free surfaces of Si because of the absence of dangling bonds at the grain boundary. Static charge fluctuations of $-0.14\mathrm{}\left|e\right|\mathrm{}$ and $0.06\left|e\right|\mathrm{}$ are found at the boundary.