Defects in silicon: the role of vibrational entropy

Vibrational free energies are calculated from first-principles in the same Si periodic supercells routinely used to perform defect calculations. The specific heat, vibrational entropy, and zero-point energy obtained in defect-free cells are very close to the measured values. The importance of the vibrational part of the free energy is studied in the case of two defect problems: the relative energies of the H2 and H2∗ dimers and the binding energy of a copper pair. In both cases, the vibrational entropy term causes total energy differences to change by about 0.2 eV between 0 and 800 K. We also comment on the rotational entropy in the case of H2 and the configurational entropy in the case of the Cu pair. These examples illustrate the importance of extending first-principles calculations of defects in semiconductors to include free energy contributions.