Screening of impurities in semiconductors: Muonium in germanium, silicon, and diamond

Abstract

With the use of the density-functional formalism and the pseudopotential description of the electronic structure of a semiconductor, a new simple theory is derived for calculating the ground-state impurity level for deep donors. It is shown that within well-defined approximations the wave function of the impurity level can be determined self-consistently from a set of equations involving the dielectric function and the pseudopotential of the host lattice. The model, which is further simplified by the replacement of the potential by its spherical average around the impurity, is applied to muonium in diamond, Si, and Ge, and it is shown that the muon zero-point motion is essentially important in calculating the hyperfine frequency. The calculated results are in a qualitative agreement with the experiments.