Superconductivity in compensated and uncompensated semiconductors

We investigate the localization and superconductivity in heavily doped semiconductors. The crossover from the superconductivity in the host band to that in the impurity band is described on the basis of the disordered three-dimensional attractive Hubbard model for binary alloys. The microscopic inhomogeneity and the thermal superconducting fluctuation are taken into account using the self-consistent 1-loop order theory. The superconductor-insulator transition accompanies the crossover from the host band to the impurity band. We point out an enhancement of the critical temperature T_c around the crossover. Further localization of electron wave functions leads to the localization of Cooper pairs and induces the pseudogap. We find that both the doping compensation by additional donors and the carrier increase by additional acceptors suppress the superconductivity. A theoretical interpretation is proposed for the superconductivity in the boron-doped diamond, SiC, and Si.