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.