Self-Compensation-Limited Conductivity in Binary Semiconductors. III. Expected Correlations With Fundamental Parameters

The previously developed calculation of the degree of self-compensation in a binary semiconductor is used to obtain a useful correlation between the degree of self-compensation by singly ionized natural defects and the ratio of the electronic energy gap to certain generally known thermodynamic quantities. The latter quantities are related to the cohesive energy. It is shown, however, that the correlation factor given herein is more meaningful than the previously suggested ratio of the energy gap to the cohesive energy. The results are generalized to include compounds having a composition $M_a{N}_b$. One interesting conclusion is the prediction that $M$-atom vacancies will generally dominate interstitial $N$ atoms when $b<a$ and vice versa. It has previously been shown that the second ionization level of a compensating natural defect can be critical in determining the degree of self compensation, particularly in the case of the II-VI compounds. A simple model of a singly ionized vacancy is presented which suggests that size considerations should play a major role in determining the second ionization level of such a defect. It is shown that the gross electrical properties of the II-VI compounds can be completely correlated with a single parameter, the ratio of the tetrahedral covalent radii of the elements. Finally, the over-all classification scheme described above is applied to a reasonably large group of compounds. The predicted gross electrical properties of these compounds are found to be in essential agreement with what is known experimentally, with the single exception of $n$-Cd${\mathrm{F}}_2$, for which an explanation is offered.