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

Abstract

The binding free energy $E_{\mathrm{b}}$ 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, $E_{\mathrm{b}}\left(T\right)$ 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 $T=0\mathrm{K}$, and electrical activities. The temperature-dependence is obtained from (Helmholtz) vibrational free energies and configurational entropies. $E_{\mathrm{b}}$ 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.