Calculating the properties of defects in semiconductors at finite temperatures

Today's method of choice to calculate the ground-state properties of localized defects in semiconductors involves periodic supercells to approximate the host crystal and first-principles density-functional theory to solve the electronic problem. This approach is quite successful at predicting equilibrium geometries, formation, binding and various activation energies, local vibrational modes, charge and spin densities and, to a lesser extent, electrical properties of native defects, impurities and small complexes in their stable and metastable configurations. However, the free energies are rarely included. Therefore, the predictions are strictly valid only at T=0K and exclude the total zero-point energies. This paper discusses how vibrational free energies (at constant volume) can be routinely calculated within the supercell/density- functional method. When additional contributions, such as configurational entropies, are included, the energetics of defects can be predicted at finite temperatures.