Mechanism of the generation of donor–acceptor pairs in heavily doped $n$-ZrNiSn with the Ga acceptor impurity

The nature of the mechanism of the simultaneous generation of donor–acceptor pairs under heavy doping of $n$-ZrNiSn intermetallic semiconductor with the Ga acceptor impurity is established. Such spatial arrangement in the crystal lattice of ZrNiSn$_{1-x}$Ga$_{x}$ is found when the rate of movement of the Fermi level $\varepsilon_{\mathrm F}$ found from calculations of the density distribution of electron states coincides with that experimentally established from dependences $\ln\rho(1/T)$. It is shown that when the Ga impurity atom $(4s^{2}4p^{1})$ occupies the 4$b$ sites of Sn atoms $(5s^{2}5p^{2})$, structural defects of both acceptor nature and donor nature in the form of vacancies in the 4$b$ site are simultaneously generated. The results are discussed in the scope of the Shklovskii–Efros model of a heavily doped and compensated semiconductor.