A nearly universal critical conductivity for semiconductor-metal alloys

Classical ionized impurity scattering is employed to calculate the conductivity at and in the vicinity of the critical point. The result sigma(iis)(x = x(c),T) = Asqrt[T], closely given by e(2)/Planck's over 2pilambda(dB) with the de Broglie wavelength lambda(dB) = h/(2m(*)kT)(1/2) in the nondegenerate regime epsilon(F)<x(c), T) might also explain the linear scaling behavior sigma(x, T)-Asqrt[T] = sigma(0)(x/x(0)-1).

Resolution of the scaling exponent puzzle for weakly compensated crystalline silicon and germanium metal-insulator systems

Using a classical theory for ionized impurity scattering, it is demonstrated that in the degenerate regime the conductivity scales as sqrt[epsilon(F)] where the Fermi energy is measured with respect to the mobility edge. The approach, a special case of alloy theory, explains the conductivity scaling exponent s = 1 / 2 observed for weakly compensated, doped crystalline Si and Ge. The results explain the breadth of scaling range and suggest how to obtain a consistent picture of the scaling of the mobility, diffusion coefficient, and Hall coefficient.