Electron states associated with 90°partial dislocations in germanium

Abstract

The unreconstructed 90\ifmmode^\circ\else\textdegree\fi{} partial dislocations in germanium are examined by means of a linear combination of atomic orbitals electron Hamiltonian with ten Gaussian-type atomic orbitals for every atom, which for a perfect crystal yields accurate results for both the valence- and conduction-band states. A pair of alternate unreconstructed 90\ifmmode^\circ\else\textdegree\fi{} partial dislocations with corresponding stacking faults are incorporated via a supercell containing 256 atoms. When the bound electron states were evaluated, the translation symmetry both along the dislocation line and in the plane perpendicular to the dislocation line was exploited. A powerful mathematical approach for large sparse matrices makes it possible to treat this supercell, its size being large enough to decouple the interactions between neighboring dislocations. The deep energy levels in the gap and the resonant states were extracted with use of the Lanczos algorithm and a continued-fraction representation of the local density of states. Two defect bands for the 90\ifmmode^\circ\else\textdegree\fi{} partial dislocation in germanium were obtained. In the center of the one-dimensional Brillouin zone the two bands are widely split and are joined together at the zone boundary. The upper band is a resonant state near the center of the zone and becomes a bound state at the zone boundary. The lower band is a bound state over the entire zone.