Macroscopic Model of Formation of Vacancies in Semiconductors

Abstract
We treat the vacancy as a bubble of one atomic volume. We use empirical values of the surface tension measured for the metallic liquid phase to estimate the free energy of formation of this bubble. A small additive correction is made to account for covalent bonding in the semiconducting phase. The model is reasonable for cases where the Wigner-Seitz atomic radius is large compared with the dielectric screening length. Good agreement with experiment is found for available data for Si, Ge, and Sn.