Entropy of ionization and temperature variation of ionization levels of defects in semiconductors

We make simple estimates of the entropy of ionization of Coulombic, isoelectronic, and vacancy-type defects in semiconductors by considering the effect of localized and free-carrier charge distributions upon the lattice modes. The empirical values of these entropies are observed as the temperature variation of the corresponding ionization levels. We predict a crossing of vacancy donor and acceptor levels in Si and Ge, which is supported by quenching and diffusion experiments. We also conclude that some of the deep Coulombic defects, such as the Au acceptor in Si, are most likely a complex of the Coulombic center with some isoelectronic or vacancy defect, such as Au interstitial with Si vacancy, rather than a simple substitutional impurity as previously assumed.