Interdependency between localization parameter and criterion of the coherent-potential-approximation applicability

The proof is given that the potential-well analogy (PWA) can be used together with the coherent-potential approximation (CPA) at the low impurity concentration despite the fact that the CPA does not describe correctly the immediate vicinity of the band edge. The correspondent criterion of the CPA applicability for three-dimensional systems is presented. It is demonstrated that the CPA is reliable above the mobility edge position predicted by the PWA.