Self-compensation in semiconductors

The problem of self-compensation of charged dopants is analyzed. Special emphasis is given to dopants in binary oxides. It is shown that one can determine the degree of self-compensation from the properties of the host material and dopant concentration alone. It is further shown that for a native p-type semiconductor, donors are compensated, mostly, by native ionic defects. On the other hand, doping with acceptors allows us to increase significantly the hole concentration, i.e., self-compensation is low under high doping levels. For a native n-type semiconductor the opposite is true, namely, extrinsic acceptors are mainly compensated by native ionic defects. It is shown that the changes in concentration of all the charged defects are simply related by a single factor, the doping factor f, or its power $f^k$ where k depends solely on the defect’s charge. Quantitative calculations of f and defect concentrations are presented for ${\mathrm{Cu}}_2\mathrm{O},$ which was used as a model material. It is found that for p-type ${\mathrm{Cu}}_2\mathrm{O}$ doping with donors results in f within the range of $1–10,$ depending on the dopant concentration and $P\left({\mathrm{O}}_2\right).\mathrm{}$ This means that the hole concentration decreases and the electron concentration increases at most by a factor of 10. Therefore one does not expect to obtain a changeover from p- to n-type cuprous oxide by doping, under equilibrium conditions. Most of the donors are compensated by negative ionic defects. Self-compensation in the presence of amphoteric defects and Fermi level stabilization are discussed, using the former formalism.