The atomic and electronic structures of {122}  = 9 tilt, and <111>  = 7 and <011>  = 3 twist boundaries were studied by using the transferable semi-empirical tight-binding method. The effects of various types of structural disorder, except coordination defects, upon the local electronic structure at the interface were analyzed, and the origins of band tails at grain boundaries were investigated. It was found that odd-membered rings induced changes in the shapes of the local densities of states, where the densities of states were increased at the 2 minima among the 3 peaks of the bulk valence-band density of states and were decreased at the s-p mixing peak. Four-membered rings generated local densities of states of a particular shape, where the sharp s-like and p-like peaks were shifted towards the bottom and the top of the valence band, respectively, and the features between these 2 peaks were smoothed. Bond distortions (stretchings and bond-angle distortions) generated states at the top of the valence band and at the bottom of the conduction band, thus inducing peaks at the band edges in the local densities of states. Highly stretched bonds generated so-called weak-bond states which consisted of bonding and anti-bonding states within the minimum band-gap. These states were deeper in the band gap and were more spatially localized at the bond and neighboring atoms than were the shallow band-edge states which were caused by smaller bond distortions. Dihedral-angle disorder did not produce such marked changes in the local densities of states, although there existed a slight shift of the p-like peak towards lower energies. This seemed to be related to the suppression of bulk-like states at the top of the valence band. The present relationships between structural disorder and local electronic structures also applied to general disordered systems such as amorphous Si. It could be said that the effects of the various types of structural disorder had been demonstrated much more clearly, than in previous studies of amorphous Si, because the various types of disorder could here be arranged and buried properly between the bulk crystals in the configurations of grain boundaries. With regard to band tails, it was shown that the band-edge states which were caused by bond distortions could penetrate into the minimum band gap according to the degree of bond distortion. Also, those that were in the coincidence site lattice tilt boundaries did not penetrate into the minimum band gap because of small bond distortions. The band-edge states which arose from bond distortions were frequently localized in the interface layers, although these were not necessarily localized in directions which were parallel to the interface. Greater bond distortions which were isolated or sparsely present in the interface generated states that were deeper in the band gap; with a stronger localization in directions that were parallel to the interface - as in the case of the present weak-bond states. The band tails at Si grain boundaries, which were observed experimentally, could be explained by the distribution of such distorted or weak bonds in general grain boundaries or at defects in the coincidence site lattice tilt boundaries. It was concluded that this was the first theoretical study that had successfully explained the origins of band tails at grain boundaries in Si.

M.Kohyama, R.Yamamoto: Physical Review B, 1994, 50[12], 8502-22