M Kaveh and N F Mott 1982 J. Phys. C: Solid State Phys. 15 L697 doi:10.1088/0022-3719/15/22/003
M Kaveh and N F Mott
Show affiliationsThe authors show that for an uncompensated semiconductor such as Si:P the metal-insulator transition occurs for -KFl>1 and the decrease of the conductivity sigma near the transition can be accounted for by perturbation theory. A universal dependence of sigma as a function of electron density n is given. sigma decreases with decreasing n due to formation of wavefunctions decaying with distance as a power law, causing a decrease of the diffusion constant. Electron correlation has only a small effect on sigma far above the metal-insulator transition. However, as n decreases and tends to nc, electron correlations cause a sharper decrease of sigma . For uncompensated samples transport is in a conduction band, the density of states deviates only slightly from a free-electron-like behaviour, whereas sigma drops below sigma B, the Boltzmann value of the conductivity, due to a reduction of the diffusion constant. A discontinuous transition to an impurity band occurs when the conductivity in the conduction band is about 0.03 sigma B and thus somewhat below Mott's value sigma min=0.03 e2/h(cross)a, which is correct for compensated samples. Conductivities much below sigma min for any sample must be due to long-range fluctuations or inhomogeneities. For uncompensated Si:P the authors argue for a minimum metallic conductivity of about 1/3 sigma min.
72.60.+g Mixed conductivity and conductivity transitions
71.45.Gm Exchange, correlation, dielectric and magnetic response functions, plasmons
71.55.Cn Elemental semiconductors
71.23.-k Electronic structure of disordered solids
71.30.+h Metal-insulator transitions and other electronic transitions
Issue 22 (10 August 1982)
M Kaveh and N F Mott 1982 J. Phys. C: Solid State Phys. 15 L697
B L Altshuler et al 1982 J. Phys. C: Solid State Phys. 15 7367
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