Off-diagonal disorder and the metal-insulator transition in impurity bands in semiconductors

The role of disorder in the metal-insulator transition in impurity bands in semiconductors is examined by means of a random, one-body, tight-binding Hamiltonian with pure off-diagonal disorder. A homomorphic cluster coherent potential approximation is used to calculate the average Green's function and the $L\left(E\right)\mathrm{}$ criterion is employed to study the localization of electron states. An Anderson transition is found to take place as the impurity concentration reaches a critical value given approximately by $n_c^{\frac{1}{3}}{\alpha }_B^{*}\approx 0.16$.