Effect of Potential Correction on the Ground States of P and S+ Impurities in Silicon: Application of the Cavity Model

Abstract

The discrepancies between the observed and the calculated ground state energies of P and S⁺ impurities in silicon are discussed on the basis of a cavity model which roughly accounts for the spatial dependence of the inverse dielectric function in the vicinity of the impurity. Applying simple effective mass theory (without reference to the KOHN—LUTTINGER semi-empirical correction method), it is shown that the model yields energy levels (and also the wave function at the P donor nucleus) in fair agreement with the experiments, if the effective cavity radius r₀ is assumed to resemble the WIGNER-SEITZ radius r_s rather than the nearest neighbour distance r_d of the Si host lattice. The result depends critically on the assumption that the effective mass m* related to the bottom of the conduction band, may be used even for levels as deep as S⁺. Application of the cavity model in connection with the free electron mass m₀ , gives rise to an almost zero cavity radius which appears to be inconsistent with various estimates yielding r_s ≲ r₀ ≲ r_d. It is concluded that the effective mass theory rather than a free electron mass equation will be the appropriate starting point for a more refined treatment of the S⁺ spectrum and that of related defects. The paper contains a discussion of various relevant aspects of the problem as well as a review of some different attempts to account for the discrepancies.