Effects of P, As, and Sb heavy doping on band gap narrowing of germanium as light-emitting materials

The n-type tensile-strained Ge can be used as high-efficient light-emitting materials. To reveal the influence of n-type doping on the electronic structure of Ge, we have computed the electronic structure of P, As and Sb doped Ge using first-principles calculation and band unfolding technique. We find that these n-type doping can induce both indirect and direct band gap narrowing, which well reproduce experimental observation that red-shifts occur in photoluminescence spectra of Ge with n-type doping. We reveal that the indirect band gap narrowing is mainly caused by impurity state, while the direct band gap narrowing is a result of lattice distortion induced by the dopant atom. Moreover, we find that it can use E_g^{\Gamma}-E_g^L to explain the voltage increase was needed to reach the same current densities of light emission through the different samples with increasing doping concentrations.