A real space calculation of vibrational structure of crystalline and non-crystalline silicon

The vibrational structure of crystalline and non-crystalline Si has been calculated in the real space using Nex's recursion scheme. Born or delaunay type of interaction between the vibrating atoms has been considered upto nearest neighbours. The large size matrix has been considered to reproduce the phonons in the crystalline Si. It also simulates the vibrational spectrum of non-crystalline Si with smaller network and is very similar to those of amorphous Si. With the increase of size of Si matrix the two LA and two TO sharp peaks emerge out in the calculated DOS which are absent for the smaller size cluster. The reported vibrational structure for the large Si matrix is in agreement with that obtained by exact calculations in k-space using Brillouin zone integration by Thorpe.