Self-Compensation Limited Conductivity in Binary Semiconductors. I. Theory

The techniques of Kroger and Vink and Brebrick are extended to allow a calculation of the minimum extent of self-compensation by simple vacancies or interstitial atoms in heavily doped binary semiconductors. The resulting equations are applied to a series of compounds, and it is found that the degree of self-compensation by singly ionizable vacancies varies from essentially complete in KCl (all but ∼${10}^{-9\mathrm{}}$ of the impurities compensated) to practically none in GaAs (only ≲${10}^{-3\mathrm{}}$ of the impurities compensated). The II-VI compounds occupy an intermediate position with about ∼99 and 99.9% self-compensation in CdTe and ZnTe, respectively. These theoretical conductivity limitations are not sufficient to account for the experimental limitations found in, for example, $n$-ZnTe or $p$-CdS. The above results are extended to include multiply ionizable vacancies, the ionization levels of which fall within the bandgap. It is found that essentially complete self-compensation by a combination of singly and doubly ionized vacancies will occur in the higher bandgap II-VI compounds. As a consequence, for example, the Fermi level in ZnTe cannot be pushed closer to the bottom of the conduction band than half the energy separation between the second ionization level of the acceptor vacancy and the bottom of the conduction band. Some specific implications of the above calculations with respect to CdTe and GaAs are discussed. Finally, certain solubility effects (of impurities) related to stoichiometry and the above calculations are discussed.