Comparison of theory with quenching experiments for the entropy and enthalpy of vacancy formation in Si and Ge

In the preceding paper the authors have argued that the entropy of ionization of a vacancy in a semiconductor should be closely approximated by the entropy of the forbidden band gap; $\ensuremath{\Delta}{S}_{c\ensuremath{\nu}}=\ensuremath{\Delta}{S}_{I}({V}^{+})=\ensuremath{\Delta}{S}_{I}({V}^{\ensuremath{-}})$. Here this hypothesis is combined with the hypothesis that the entropy of formation of the neutral vacancy, $\ensuremath{\Delta}S({V}^{x})$, is only the entropy of its Jahn-Teller distortion. Thus $\ensuremath{\Delta}{S}_{I}({V}^{\ifmmode\pm\else\textpm\fi{}})\ensuremath{\gg}\ensuremath{\Delta}S({V}^{x})=k\mathrm{ln}3$ for Si and Ge. Empirical values for the enthalpy of ionization at low temperature, $\ensuremath{\Delta}{H}_{I}({V}^{\ifmmode\pm\else\textpm\fi{}})$, are combined with the values for $\ensuremath{\Delta}H({V}^{x})$ predicted by the macroscopic theory of Phillips and Van Vechten in order to predict the result of quenching experiments taking proper account of the charge states of the vacancies. Agreement with the experiments of Logan, Hiraki, and Elstner and Kamprath is quite satisfactory.