Defect physics of theCuInSe2chalcopyrite semiconductor

We studied the defect physics in ${\mathrm{CuInSe}}_{2},$ a prototype chalcopyrite semiconductor. We showed that (i) it takes much less energy to form a Cu vacancy in ${\mathrm{CuInSe}}_{2}$ than to form cation vacancies in II-VI compounds (ii) defect formation energies vary considerably both with the Fermi energy and with the chemical potential of the atomic species, and (iii) the defect pairs such as $({2\mathrm{V}}_{\mathrm{Cu}}^{\mathrm{\ensuremath{-}}}{+\mathrm{I}\mathrm{n}}_{\mathrm{Cu}}^{2+})$ and $({2\mathrm{C}\mathrm{u}}_{\mathrm{In}}^{2\mathrm{\ensuremath{-}}}{+\mathrm{I}\mathrm{n}}_{\mathrm{Cu}}^{2+})$ have particularly low formation energies (under certain conditions, even exothermic). Using (i)--(iii), we (a) explain the existence of unusual ordered compounds ${\mathrm{CuIn}}_{5}{\mathrm{Se}}_{8},$ ${\mathrm{CuIn}}_{3}{\mathrm{Se}}_{5},$ ${\mathrm{Cu}}_{2}{\mathrm{In}}_{4}{\mathrm{Se}}_{7},$ and ${\mathrm{Cu}}_{3}{\mathrm{In}}_{5}{\mathrm{Se}}_{9}$ as a repeat of a single unit of $({2\mathrm{V}}_{\mathrm{Cu}}^{\mathrm{\ensuremath{-}}}{+\mathrm{I}\mathrm{n}}_{\mathrm{Cu}}^{2+})$ pairs for each $n=4,$ 5, 7, and 9 units, respectively, of ${\mathrm{CuInSe}}_{2};$ (b) attribute the very efficient $p$-type self-doping ability of ${\mathrm{CuInSe}}_{2}$ to the exceptionally low formation energy of the shallow defect Cu vacancies; (c) explained in terms of an electronic passivation of the ${\mathrm{In}}_{\mathrm{Cu}}^{2+}$ by ${2\mathrm{V}}_{\mathrm{Cu}}^{\mathrm{\ensuremath{-}}}$ the electrically benign character of the large defect population in ${\mathrm{CuInSe}}_{2}.$ Our calculation leads to a set of new assignment of the observed defect transition energy levels in the band gap. The calculated level positions agree rather well with available experimental data.