  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.
