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Numerical studies of one-electron hydrogenic impurity states in doped semiconductors. II. Fully compensated systems.

We report the results of a numerical study of one-electron hydrogenic impurity states in fully compensated semiconductors. The wave functions are linear combinations of 1s orbitals centered on the N impurity sites. Diagonal Coulomb interactions, overlap, and two- and three-center integrals are taken into account, as are Coulomb interactions with the N compensating impurities. Screening effects are introduced through an exponential cutoff in the interactions. Calculations are carried out for arrays of 664 and 1008 donor impurities distributed at random on a diamond lattice. Data are presented for the densities of states and the localization indices. A criterion for Anderson localization is established, and a lower limit is given for the critical density. Comparisons are made with the corresponding results for uncompensated arrays. The relevance of our findings to experimental studies of the metal-insulator transition is briefly discussed.