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 root 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.