Variation of impurity−to−band activation energies with impurity density

A theory of the variation of conduction electron density with the temperature for various impurity concentrations is presented. In addition to previously noted effects of condcution band edge lowering and screening of the impurity potential by the conduction electrons, the influence of a finite energy transfer integral and spatial fluctuation in the potential are included. The results show that for ND≳1017 cm−3 in silicon one must not view the activation as occurring between a single impurity level and a well−defined conduction band edge, but must include the broadening of the impurity level and tailing of the conduction−band density of states. Calculations for the shallow donors P, Sb, and As in Si are found to be in satisfactory agreement with experiment.