Thermal Ionization of Impurity Levels in Semi-Conductors

Abstract

The probability of ionization of an impurity level by thermal agitation in a semi-conductor is estimated by the use of a simple Debye model. It is found that the probability of ionization by one phonon decreases exponentially with the depth of the impurity level below the conduction band, approaching zero as the energy separation becomes equal to $k{\theta }_D$. The probability of ionization by more than one quantum is also estimated by the use of an Einstein model. It appears that the probabilities so calculated may play an important role in determining the frequency dependence of the rectification efficiency in crystal rectifiers.