The free-carrier concentration in Si-doped AlxGa1-xAs has been calculated by grand-canonical-ensemble statistics without any fitting parameters. Our results are quantitatively in agreement with various experimental data in the temperature range 77—300 K, which indicates that the physical picture of the ground state of DX center (DX-) is of an electronic bipolaron due to the interaction between excess electrons and lattice. When exposed to light, one bipolaron can turn into a polaron, meantime release one electron to the conduction band accompanied by lattice relaxations. Our calculations also prove that DX0 is unstable at thermal equilibrium, which further confirms our bipolaron mechanism.