Quantitative analysis of delocalization in the vicinity of the metal–insulator transition in doped semiconductors

A temperature-induced crossover from hopping to metallic conductivity is observed for barely insulating samples of Ge:As and Ge:Sb with impurity concentration N just below the critical value Nc0. The values of the correlation length ξ are obtained on both sides of the transition. A method is developed for determination of a ‘delocalization temperature’ Td , which separates the hopping and metallic conductivity. It is shown that the dependence of Td on N for various semiconductors can be reduced to a universal curve using normalization of the T -scale by the mean energy of the Coulomb interaction W = (e2/κ0)N c0 . The metal–insulator transition (MIT) is defined by the vanishing of the dc conductivity at zero temperature [1]: the value of σ(0) ≡ σ(T → 0) when plotted as a function of the impurity concentration N , is equal to zero on the insulating side of the MIT and remains finite on the metallic side, obeying scaling behaviour in the vicinity of the transition [2]: