Effects of the local configuration on the lattice dynamics of group-IV semiconductors

The relative importance of short-range order and local topology versus long-range order in determining the vibrational properties of group-IV semiconductors is investigated. We have developed a cluster-Bethe-lattice method which treats a cluster of atoms with the short-range order and local topology therein exactly. The rest of the system is treated within the Bethe-Peierls approximation which retains the short-range tetrahedral order. We have studied the lattice vibration spectra corresponding to clusters of different sizes in the diamond structure. We find that the presence of rings of bonds have clear and discernible effects not found previously. The main feature of the perfect-crystal density of states is already present in small ({~} 30 atoms) clusters. We can conclude that, as in the electronic case, the density of vibrational states is governed by the local configurations.