We have examined the electronic structure of the incoherent {Σ}=3 grain boundary in Ge in the framework of a reconstructed model which reproduces the main features of the high-resolution electron microscopy (HREM) image it exhibits. In particular, the sixfold rings of atoms are in a position almost identical to those observed in HREM. The optimum atomic structure has been determined by energy-minimization calculations in the Keating model. For the optimized geometry, the electronic structure computed using the recursion method shows that there are no localized states in the fundamental gap. The main perturbation induced by distortions in bond lengths and angles is a 1-eV shift in the peak of the density of the p states pointing in the [211] direction where the translation symmetry is broken. However, this shift towards the top of the valence band is too small to push these resonant states into the energy gap. Consequently the electrical activity of the incoherent {Σ}=3 grain boundary should be attributed to an impurity segregation near the most perturbed sites or to additional microdefects rather than to an intrinsic structural effect.
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Mauger et al. (1987) studied this question.