Numerical simulation of the temperature dependence of the ionization energy of hydrogen-like impurities in semiconductors: Application to transmutation-doped Ge: Ga

Abstract

An electrostatic model describing the dependence of the thermal ionization energy of impurities on their concentration, compensation factor, and temperature is developed. The model takes into account the screening of impurity ions by holes (electrons) hopping from impurity to impurity, the change in the impurity-band width, and its displacement with respect to the edge of the valence band for acceptors (conduction band for donors). The displacement of the impurity band is due to the functional dependence of the hole (electron) affinity of the ionized acceptor (donor) on the screening of the Coulomb field of the ions. The spatial distribution of the impurity ions over the crystal was assumed to be Poisson-like, and the energy distribution was assumed to be normal (Gaussian). For the relatively low doping levels under investigation, the behavior of the density of states at the edges of the valence and conduction bands was assumed to be the same as for the undoped crystal. The results of the numerical study are in agreement with the decrease in the ionization energy that is experimentally observed for moderately compensated Ge: Ga as the temperature and the doping level are decreased. It is predicted that the temperature dependence of the thermal ionization energy has a small anomalous maximum at small compensation factors.