Defects in silicon: the role of vibrational entropy

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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 H 2 and H 2 ∗ 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 H 2 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.