Correlation between bond distortion and the band-tail electronic density of states in amorphous silicon: a tight-binding recursion study

We study the spatial structure of the electronic states in amorphous silicon using a tight-binding Hamiltonian and the recursion method. A realistic cluster consisting of 4096 atoms in a periodic cubic supercell, obtained using reverse Monte–Carlo methods, is used as a model of amorphous silicon [B.R. Djordjevic, M.F. Thorpe, F. Wooten, Phys. Rev. B 52 (1995) 5685]. The local density of states for each of the 16 384 orbitals is computed. Our aim is to provide some insight into the nature of the band tail states and we particularly address the following issues. We examine the relative contributions of the p-orbitals and the s-orbitals to the density of states in the region of the band tail and gap. We investigate the geometric nature of these states. Finally, we study the correlation between the structural distortions in the amorphous silicon cluster and the spatial distribution of the band tail and gap states. Our results show that the p-orbitals contribute a large fraction of the density of states in the valence band tail. This fraction decreases as the energy increases across the gap into the conduction band. We observe the expected change from extended states deep in the valence and conduction band to localized states in the band gap. An attempt was made to characterize this change in terms of the fraction of the total density of states required for a percolating nearest-neighbor path in the cluster as a function of the energy. No abrupt change was observed in this quantity for energies in the region of the band tails. Although there are 4096 atoms in the cluster, 90% of the density of states in the band tail and gap is localized on only 416 atoms, that is, we find a backbone of atoms in the cluster responsible for a large fraction of the states in this energy range. We also find a strong correlation between atoms contributing a high density of states in the band tail and gap region and atoms with a large bond angle distortion.