Theoretical study of grain boundaries in Si: Effects of structural disorder on the local electronic structure and the origin of band tails.

Abstract

The atomic and electronic structures of the {122} \ensuremath{\Sigma}=9 tilt and 〈111〉 \ensuremath{\Sigma}=7 and 〈011〉 \ensuremath{\Sigma}=3 twist boundaries in Si have been examined by using the transferable semiempirical tight-binding method. The effects of various kinds of structural disorder, except coordination defects, on the local electronic structure of Si at the interfaces have been analyzed, and the origins of band tails at grain boundaries in Si have been investigated. Odd-membered rings induce the changes in the shapes of the local densities of states (LDOS's), where the densities of states are increased at the two minima among the three peaks of the bulk valence-band DOS and are decreased at the s-p mixing peak. Four-membered rings generate the LDOS's of a particular shape, where the sharp s-like and p-like peaks are shifted toward the bottom and the top of the valence band, respectively, and the features between these two peaks are smoothed. Bond distortions, strictly bond stretchings and bond-angle distortions, generate states at the top of the valence band and at the bottom of the conduction band, inducing the peaks at the band edges in the LDOS's. Greatly stretched bonds generate so-called weak-bond states, which consist of the bonding and antibonding states inside the minimum band gap. These states are deeper in the band gap and are more spatially localized at the bond and neighboring atoms than the shallow band-edge states caused by smaller bond distortions.Dihedral-angle disorder does not induce such marked changes in the LDOS's, although there exists a slight shift of the p-like peak toward lower energy, which seems to be related to the suppression of bulklike states at the top of the valence band. The present relations between the structural disorder and the local electronic structure of Si also apply to general disordered systems such as amorphous Si. It can be said that the effects of the respective kinds of structural disorder have been shown much more clearly than in the previous studies of amorphous Si because here the respective kinds of disorder can be arranged and buried properly between the bulk crystals in the configurations of grain boundaries. Regarding band tails, it has been shown that the band-edge states caused by bond distortions can penetrate into the minimum band gap according to the degree of bond distortions, and that those in the coincidence-site-lattice (CSL) tilt boundaries do not penetrate into the minimum band gap because of small bond distortions. The band-edge states coming from bond distortions are frequently localized in the interface layers, although these are not necessarily localized in the directions parallel to the interface. Greater bond distortions existing isolated or sparsely in the interface generate states deeper in the band gap with stronger localization behavior in the directions parallel to the interface as in the case of the present weak-bond states. The band tails at grain boundaries in Si observed experimentally can be explained by the distribution of such distorted or weak bonds in general grain boundaries or at defects in the CSL tilt boundaries. This is the first theoretical study that has successfully explained the origins of the band tails at grain boundaries in Si.