The doping factor approach in solid state ionics

Abstract

The doping factor approach is a simple, sometimes a “back-of-the-envelope” method, to predict concentrations of native point defects upon doping with aliovalent dopants. The doping factor is defined as the ratio between the concentration of quasi-free electrons in the doped state and their concentration in a reference state, typically at the undoped state. In binary compounds, as long as the Boltzmann statistics hold, the neutrality equation becomes a polynomial equation for the doping factor. Once the doping factor is found, all the concentrations of the native point defects are readily determined. While other computational methods allow us to find those concentrations, it is beneficial for researchers to possess such a simple tool for calculating the resulting new concentrations. Furthermore, this method may be the only one available in cases with small deviations from stoichiometry. The method is explained and demonstrated using a simple case of magnesium oxide, as well as on intrinsic compound oxide semiconductors.