Electrostatic models of insulator-metal and metal-insulator concentration phase transitions in Ge and Si crystals doped by hydrogen-like impurities

Two electrostatic models have been developed that allow calculation of the critical concentration of hydrogen-like impurities in three-dimensional crystalline semiconductors corresponding to the insulator-metal and metal-insulator transition in the zero temperature limit. The insulator-metal transition manifests itself as a divergence of the static permittivity observed in lightly compensated semiconductors as the concentration of polarizable impurities increases to the critical level. The metal-insulator transition is signaled by the divergence of the dc electrical resistivity in heavily doped semiconductors as the compensation of the majority impurity increases (or its concentration decreases). The critical impurity concentration corresponds to the coincidence of the percolation level for the majority carriers with the Fermi level. The results of the calculations made with these models fit the experimental data obtained for n-and p-type silicon and germanium within a broad range of their doping levels and impurity compensation.