Metal — Insulator Transition in Doped Semiconductors

Heavily doped semiconductors exhibit, as the concentration of impurities is changed, the phenomenon of metal-insulator transition. Mott1-4 pointed out that Coulomb repulsion, if large enough in comparison with the transfer matrix element, inhibits electronic propagation in a half-filled band. Subsequently, Hubbard5 introduced a simple periodic model incorporating this competition between the transfer matrix element V (which facilitates propagation) and the on-site Coulomb repulsion U (which opposes propagation).