Electronic quasichemical formalism: Application to arsenic deactivation in silicon

A statistical mechanical formalism is developed to simultaneously treat chemical and electronic disorder. The method is based on a quasichemical approximation with an arbitrary number of chemical components and defects, and an arbitrary cluster size. The chemical potentials of the atomic constituents are explicitly included so that both open and closed systems can be treated. For the electronic subsystem, bandlike excitations can be treated separately, and Fermi-Dirac statistics are employed. The formalism is applied to the problem of electrical deactivation in heavily arsenic-doped silicon, using ab initio total energies. Our results are in good agreement with the observed experimental behavior. The deactivation can be explained by equilibrium densities of arsenic clustering about a single vacancy. Clusters containing more than one vacancy and second-neighbor arsenic pairs relaxed to threefold coordination but not accompanied by a vacancy are present, but in equilibrium do not dominate the deactivation. Because of the rarity of four arsenic atoms surrounding a single silicon atom in randomly solidified material, for which the deactivating clusters can form in one step, vacancy clusters containing only two or three arsenic atoms and pairs of threefold-coordinated arsenic atoms not accompanied by Vacancies may dominate the initial deactivation, prior to the rearrangement of atoms needed to achieve full equilibrium. At low arsenic concentrations, activated arsenic represents the equilibrium state for temperatures at which equilibrium can occur. An explanation of the experimentally observed transient reactivation is proposed.