Critical concentration for metallization of doped germanium and silicon

An elementary model for the metal-non metal transition in n-type Ge and Si is considered. The model is based on recent theoretical work on electron-hole droplets in illuminated semiconductors. The energy of the metallic phase is computed from experimentally known values of the conduction band effective masses and the background dielectric constant. The critical concentration is determined approximately by comparing the energy of the metallic phase with the energy of an isolated donor atom (a bound electron-impurity ion pair). The theoretical estimates of the critical concentration agree in order of magnitude with experiments. The trend in chemical shifts is reproduced.