Conduction in non-crystalline materials

Abstract If the distance between atoms in a crystalline lattice is increased, an energy gap appears, which in a divalent material will separate occupied from unoccupied states of an electron. In a non-crystalline substance, a minimum is expected in the density of states (a ?pseudogap?). An approximate theoretical estimate is given of the depth of the minimum at which the one-electron states become localized so that ?σE(0)? vanishes; this turns out to be such that N(E F)/N(E F)free is about ?. The result depends rather sensitively on the parameters used; the value deduced from the experiments of Hensel and Franck (1966, 1968) on the resistivity of mercury at high temperatures gives for this ratio a value of ?. It is shown also that the localized states at the extremities of a valence or conduction band are of negligible importance if the wave functions are s-like on the atoms or ions, but may be of importance if they are not. A discussion is given of the electrical behaviour of chalcogenide glasses, amorphous germanium and of some liquid semiconductors based on these ideas.