Activation entropies for diffusion in cubic silicon carbide from first principles

The properties of defects in materials are crucial in order to determine their performance and behavior, especially at extreme conditions (at high temperature, under irradiation or with other types of constraints). Formation and migration energies of defects are studied routinely using first-principles calculations. However, most of the time, they are studied by static zero-temperature calculations, and the entropic contributions to the free energies are completely neglected. In this paper we address the first-principles calculation of the vibrational part of the free energies of formation and migration of silicon and carbon interstitials in silicon carbide. The latter is an important material for high-temperature applications. We find that formation free enthalpies can vary by up to 1 eV, in the range from 0 to 2000 K, while migration free energies vary by only a few tenth of an electron volt. Our results give us not only the activation energies for diffusion but also diffusion prefactors. The comparison with experimental results shows good agreement for carbon self-diffusion while for silicon self-diffusion our results underestimate by three orders of magnitude the experimental values, suggesting that defects other than the interstitials are the dominant diffusing species. As a last point, in the light of our results, we discuss empirical models concerning diffusion coefficients and entropy-energy relations.