Force constants and dispersion relations for the zincblende and diamond structures revisited

Abstract

The bulk atomic equations of motion are revisited in order to show explicitly, for high symmetry directions, the transformation of this three-dimensional problem into decoupled one-dimensional problems. The force constants of the corresponding one-dimensional equations are related to a larger number of force constants of the bulk problem. We illustrate how the three-dimensional force constants (and consequently the whole dynamical matrix) can be estimated from a few either experimental or theoretical points for semiconductors in the zincblende and diamond structures.