  Undesired unintentional doping and doping limits in semiconductors are
typically caused by compensating defects with low formation energies. Since the
formation energy of a charged defect depends linearly on the Fermi level,
doping limits can be especially pronounced in wide bandgap semiconductors where
the Fermi level can vary substantially. Introduction of non-equilibrium carrier
concentrations during growth or processing alters the chemical potentials of
band carriers and thus provides the possibility of modifying populations of
charged defects in ways impossible at thermal equilibrium. Herein we
demonstrate that, for an ergodic system with excess carriers, the rates of
carrier capture and emission involving a defect charge transition level
rigorously determine the admixture of electron and hole quasi-Fermi levels
determining the formation energy of non-zero charge states of that defect type.
To catalog the range of possible responses to excess carriers, we investigate
the behavior of a single donor-like defect as functions of extrinsic doping and
energy of the charge transition level. The technologically most important
finding is that excess carriers will increase the formation energy of
compensating defects for most values of the charge transition level in the
bandgap. Thus, it may be possible to overcome limitations on doping imposed by
native defects. Cases also exist in wide bandgap semiconductors in which the
concentration of defects with the same charge polarity as the majority dopant
is either left unchanged or actually increases. The causes of these various
behaviors are rationalized in terms of the capture and emission rates and
guidelines for carrying out experimental tests of this model are given.
