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

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Abstract
The atomic and electronic structures of the {122} Σ=9 tilt and 〈111〉 Σ=7 and 〈011〉 Σ=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.