Metal—insulator transition in doped silicon

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Abstract
It is proposed, contrary to some earlier conjectures, that the insulator—metal transition in uncompensated silicon—phosphorus (Si: P), which occurs in the limit of low temperature under the influence of increasing concentration of the dopant, or change of stress, is first order, in the sense that the interval ε1 between the Fermi energy and the mobility edge jumps discontinuously from a negative to a positive value. This occurs for a small value of ε2, but before ε2 vanishes. A discontinuous transition may occur for all uncompensated extrinsic semiconductors, but not when the compensation is large. The relevance to recent measurements of Rosenbaum et al. (1980) and Thomas et al. (1981, 1982) is discussed. A main conclusion is that the conductivity due to electrons in a many-valley conduction band can drop well below [sgrave]min and may even vanish, [sgrave]min being Mott's calculated value of the minimum metallic conductivity for electrons in an impurity band. On the other hand, the electronic specific heat shows only some minor changes from the free-electron value. Metallic conductivities below about [sgrave]min/3 as observed by Rosenbaum et al., are proposed to be due to long-range fluctuations of potential, the nature of which is discussed and which may be statistical. For compensated material, however, if as the present authors believe intra-centre electron—electron interaction can for them be neglected, then Mott's previous theory needs little modification; in the authors’ view a second-order Anderson transition (Anderson 1958) occurs and a minimum metallic conductivity exists. Even for uncompensated materials, this appears to be so when the transition is induced by a magnetic field. Some possible effects of long-range interaction are considered, following the work of McMillan (1981). Its effect on the resistivity and on the specific heat is calculated.