The metal-insulator transition in extrinsic semiconductors

Abstract

The main purpose of this article is to describe the electrical and magnetic properties of extrinsic semiconductors when the concentration of donors varies, particularly for concentrations near that for which a metal-insulator transition takes place. Since the donor centres are distributed at random in space, the combined effects of correlation and Anderson localization have to be considered. As an introduction, in § 1 we give an outline of our present understanding of the transition in some crystalline materials, particularly V₂O₃. For this the metallic phase, a highly correlated electron gas, is discussed, as is also the question of a discontinuous change in the number of current carriers. In § 2 we discuss Si : P and similar materials. For uncompensated samples, the material near the transition is to be described by overlapping Hubbard bands, and the metal-insulator transition occurs when the states at the Fermi energy show Anderson localization. Just on the insulator side of the transition conduction is by variable-range hopping for uncompensated as for compensated materials, and a variation of log (resistivity) as T ^−1/4 is observed. The existence or otherwise of moments in the metallic phase is discussed, as is also the magnetoresistance, Hall effect and Knight shift. In § 3 the transition is described for narrow-band semiconductors, particularly La_1−x Sr _x VO₃. In § 4 some compounds of rare earths are treated, including Sm_1−x Nd _x Se.