Rare-earth defects and defect-related luminescence in ZnS

Structure and energetics of rare-earth (RE) defects and luminescence of RE and related defects in zincblende zinc sulfide (ZnS) are investigated using hybrid density-functional defect calculations. We find that europium (Eu) is stable predominantly as the divalent Eu$^{2+}$ ion in bulk ZnS. The trivalent Eu$^{3+}$ is structurally and electronically stable, but energetically unfavorable compared to Eu$^{2+}$ due to the presence of low-energy native defects and Eu$^{2+}$-related defect complexes. Other RE dopants, dysprosium (Dy) and erbium (Er), are stable only as Dy$^{3+}$ and Er$^{3+}$, respectively. These results provide an explanation why it is difficult to realize Eu$^{3+}$ in bulk ZnS. A non-negligible Eu$^{3+}$/Eu$^{2+}$ ratio might be achieved with Li co-doping under S-rich (and probably non-equilibrium) synthesis conditions. Optically, Eu-related defects can act as carrier traps for band-to-defect transitions and emit light in the visible range. To assist with experimental optical characterization of the RE defects, we include band-to-defect luminescence involving native defects (Zn vacancies) and/or non-RE impurities (Cu, Cl, and Al) that may also be present in Eu-doped ZnS samples, and assign luminescence centers often observed in experiments to specific defect configurations.