Tensile-strained germanium is one of the promsing materials for Si-based photonic devices due to its quasi-direct band and compatiblility with silicon technology. The band structure of tensile-strained germanium is investigated based on the theory of van de Walle deformed potential. The carrier distributions in the conduction bands at Γ and L vallies under the strain, and the n-type doping concentratoin in germanium are analyzed. Considering the competition between radiative recombinations at Γ and L vallies and Auger recombination, as well as dislocation induced non-radiative recombination, internal quantum efficiency and optical gain for direct band transition in n-type Ge are calculated. It is shown that 74.6% internal quantum efficiency can be obtained in the 1.5% tensile-strained n-type doped Ge under carrier injection and a strong optical gain is predicted, which is comparable to those of III-V materials.