On the Change of Activation Energy with Impurity Concentration in Semiconductors

The existing theories of change in activation energy with impurity concentration are discussed and their limitations pointed out. The Ionization energy of a pair of impurities in a dielectric medium is calculated as a function of impurity separation Assuming a random distribution of impurities, an averaging process is employed to calculate the mean change in activation energy with concentration. This approximation should be poor for high impurity densities but good for low densities. Specific calculations have been made for the case of phosphorus impurities in silicon and satisfactory agreement is obtained with experimental results