Effect of frustration on the band edge in amorphous semiconductors

The existence of odd-membered rings leads to an erosion of antibonding states in a simple tight-binding Hamiltonian on a random network. We obtain better estimates of the magnitude of this erosion by systematically introducing fivefold rings into a diamond lattice with a supercell containing 8000 atoms. It is shown that the position of the band edge moves roughly linearly with the number of fivefold rings and that the slope agrees with that obtained from perturbation theory.