Temperature and sample dependence of the binding free energies of complexes in crystals: The case of acceptor-oxygen complexes in Si

The binding free energy Eb of a complex {A,B} in a crystal varies not only with temperature but also the concentrations of the constituent species A and B in the sample. Except at very low temperatures, Eb(T) is a linear function of T with a slope determined by the configurational entropy and free energy terms. This is quantitatively illustrated for acceptor-oxygen complexes in Si. First principles calculations establish their structures, vibrational spectra, binding energies at T=0K, and electrical activities. The temperature-dependence is obtained from (Helmholtz) vibrational free energies and configurational entropies. Eb varies much more with temperature for complexes involving species that are present in low concentrations than in high concentrations. The implications of these predictions are discussed.