Deep electron level calculations for dislocations in Si and Ge recursion approach exploiting the translational symmetry

For crystals with dislocations, the tight-binding recursion method is reformulated to maintain the translational symmetry along the dislocation line. The method is applied to the deep electron levels at dislocations in Ge and Si. Because of the translation symmetry up to 110 pairs of significant recursion coefficients (an, bn) could be evaluated, revealing an asymptotic oscillatory behaviour of the coefficients. For unreconstructed and reconstructed 30°, 60° and 90° partial dislocations in Ge and Si, the one-dimensional bands of deep electron levels are presented as deduced from the continued-fraction density of states. Including the changes in the chemical shift brings the calculated deep level structure of the unreconstructed 90° partial into rather close agreement with the experimental findings.