Lattice dynamics of Ge and Si using the Born-von Karman model

The Born-von Karman model of lattice dynamics of diamond structure has been extended to include up to 12th-neighbor interactions. Applications to Ge and Si using eighth-neighbor interactions have been carried out. We obtained very good fits to the experimental values of phonon dispersion curves and elastic constants. However, in agreement with the conclusions of Herman, a reasonable fit can only be obtained using at least up to fifth-neighbor interactions. The special significance of the fifth neighbor is attributed to its structure. With the fitted force constants, we have calculated the phonon density of states using the high-resolution Gilat-Raubenheimer method. The calculated Debye temperatures and specific heats compare well with the experimental values.