Stabilization of Ternary Compounds via Ordered Arrays of Defect Pairs

Abstract

First-principles calculations show that the defect pair $({2V}_{\mathrm{Cu}}^{\ensuremath{-}}+{\mathrm{In}}_{\mathrm{Cu}}^{+})$ in CuInS${\mathrm{e}}_{2}$ has an unusually low formation energy, due both to the relative ease of forming Cu vacancies $({V}_{\mathrm{Cu}})$ and to the attractive interactions between ${V}_{\mathrm{Cu}}^{\ensuremath{-}}$ and ${\mathrm{In}}_{\mathrm{Cu}}^{2+}$. The defect pair is predicted to be electrically inactive. This explains the surprising electrical tolerance of CuInS${\mathrm{e}}_{2}$ to its huge $(\ensuremath{\sim}1%)$ concentration of native defects. An attractive interaction among the defect pairs is further predicted to lead to a crystallographic ordering of the pairs, explaining the observed, but hitherto surprising, structures CuI${\mathrm{n}}_{5}$S${\mathrm{e}}_{8}$, CuI${\mathrm{n}}_{3}$S${\mathrm{e}}_{5}$, C${\mathrm{u}}_{2}$I${\mathrm{n}}_{4}$S${\mathrm{e}}_{7}$, etc.