  Motivated by the discovery of superconductivity in boron-doped (B-doped)
diamond, we investigate the localization and superconductivity in heavily doped
semiconductors. The competition between Anderson localization and s-wave
superconductivity is investigated from the microscopic point of view. The
effect of microscopic inhomogeneity and the thermal fluctuation in
superconductivity are taken into account using the self-consistent 1-loop-order
theory with respect to superconducting fluctuation. The crossover from
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. We show that superconductor-insulator transition (SIT)
accompanies the crossover. We point out an enhancement of Cooper pairing in the
crossover regime. Further localization of the electron wave function gives rise
to incoherent Cooper pairs and the pseudogap above T_c. A global phase diagram
is drawn for host band superconductivity, impurity band superconductivity,
Anderson localization, Fermi liquid state, and pseudogap state. A theoretical
interpretation is proposed for superconductivity in the doped diamond, SiC, and
Si.
