Electronic structure of the Σ=9 high-angle tilt grain boundary in germanium

Abstract

The electronic structure of the Σ=9 (38.94°) high-angle tilt grain boundary (GB) in germanium is studied in a tight-binding model with atom positions optimized with a tight-binding molecular dynamics scheme. This boundary, containing fivefold and sevenfold rings, has been observed in high-resolution electron microscopy experiments. We find from geometry optimization a volume expansion of 0.28 A ̊ at the GB consistent with the measured value of 0.4±0.2 A ̊ . The calculated GB energy is about 1.06 eV per GB unit cell, which corresponds to the interface energy of γ≈ 350 ergs/cm 2. This is somewhat smaller than typical surface energies of the group IV semiconductors as might be expected. We find that although the GB does not introduce any localized states in the fundamental gap, it does so at specific k points in the interface Brillouin zone.