Hubbard model for disordered systems: Application to the specific heat of the phosphorus-doped silicon

A self-consistent many-body theory of disordered systems, described by the Hubbard Hamiltonian with random transfer integrals, is developed. The random nature of the system is taken into account by the Matsubara-Toyozawa theory of impurities in semiconductors. By considering the hydrogenlike impurity states, the electronic specific heat of uncompensated phosphorus-doped silicon is calculated and compared with experimental results. It is found that it agrees well with experiment in the entire semiconductor-to-dilute-metallic region.