Conduction in non-crystalline materials: III. Localized states in a pseudogap and near extremities of conduction and valence bands

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 ⅓. 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 ⅕. 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.