Vibrational properties of impurities in semiconductors

The most commonly used first-principles technique to predict the properties of impurities in semiconductors involves periodic supercells to represent the host crystal, classical molecular dynamics (MD) to describe the nuclear motion, with ab initio-type pseudopotentials and density-functional theory to treat the electronic problem. Calculating the entire dynamical matrix of the supercell is most useful. Indeed, the eigenvalues of this matrix give all the local, pseudolocal, and resonant vibrational modes associated with the impurity, and allow the calculation of the phonon density of states, from which the vibrational free energy can be obtained. Further, the eigenvectors of the dynamic matrix are used to quantify the 'localization' of specific vibrational modes and prepare the supercell in thermal equilibrium at a temperature T, up to a few hundred degrees kelvin. This supercell preparation allows non-equilibrium MD simulations to be performed. Applications include the calculation of vibrational lifetimes and of thermal conductivities. This paper describes the essential ingredients of such calculations.