Influence of Disorder on Semiconductor-Metal Transition in Insb

TLDR: In this paper, Anderson et al. pointed out a role of disorder and predicted the metal non-metal transition to occur when the Fermi level, EF, crosses the mobility edge, EC, from the extended to the localized states.

Abstract: A large variety of semiconductors undergo a non-metal metal transition Mott transition when the concentration of impurities is increased to a critical value N given by: $$ N_c^{1/3} \cdot {a_B} \simeq 0.25 $$ (1) where aB is the effective Bohr radius of the impurity center. Another approach to the metal non-metal transition (MNM) due to Anderson points out a role of disorder and predicts the MNM transition to occur when the Fermi level, EF, crosses the mobility edge, EC, from the extended to the localized states. The central problem in the theory of the MNM transition in disordered systems is to understand the interplay between the effects of correlation and disorder [1]. In addition there have been many attempts to include the nature of disorder in considerations of the MNM transition. Castner et al. [2] have demonstrated for silicon the relation between the type of donor impurity and the tendency to the electron delocalization. Prom the other point of view the effect of increasing the dopant concentration is to increase the number of donor pairs and clusters. They form low energy tails of the density of states significantly increasing the binding energy of electrons [3]. Fritzsche [4] pointed out the role of compensation in the increase of NC. At given donor concentration, ND, with increasing compensation, K = NA/ND (NA is an acceptor concentration) several effects occur i/the total concentration of scattering centers increases, ii/the impurity potential becomes less screened, iii/EF is lowered and IV/the randomness of the donor potential increases leading to the enhancement of the impurity band-width.