Valence-Band Electronic Structures of Cu⁺-Doped ZnS, Alloyed Cu–In–Zn–S, and Ternary CuInS₂ Nanocrystals: A Unified Description of Photoluminescence across Compositions

Abstract

Copper-doped and copper-based colloidal semiconductor nanocrystals have attracted broad attention as phosphors in many contexts, but fundamental aspects of their electronic structures that give rise to their photoluminescence are not understood. Here, we report a detailed systematic investigation of the electronic structures of Cu+-doped ZnS, alloyed Cu–In–Zn–S, and CuInS2 nanocrystals (NCs) using density functional theory. These calculations demonstrate a continuous evolution in electronic structure from lightly doped to ternary compositions. As an impurity, Cu+ introduces isolated midgap d orbitals above the valence-band edge, with large Cu(3d)–S(3p) covalency. As the Cu+ content is increased in Cu–In–Zn–S alloys, these orbitals evolve to become the CuInS2 valence band in the ternary limit. The calculations further describe the highest occupied molecular orbital (HOMO) as localized and Cu(3d)-based for all compositions from Cu+-doped ZnS to stoichiometric CuInS2. The calculations predict that the Cu(3d)-based HOMOs can only delocalize over ca. 2 or 3 adjacent Cu+ ions but not more, reflecting weak Cu+–Cu+ electronic coupling, attributable in large measure to the directionality of the d orbitals. HOMO localization is also sensitive to the local Cu+ environment, Cu+–Cu+ geometric connectivity, and electrostatics. We conclude that the Cu(3d)-based HOMO of chalcopyrite CuInS2 makes localization likely even in defect-free CuInS2 NCs, placing this material in stark contrast with structurally analogous II–VI semiconductor NCs that have anion p-orbital-based HOMOs and show facile HOMO delocalization. The strong tendency for HOMO localization in both Cu+-doped II–VI and Cu+-based chalcopyrite NCs has significant implications for interpretation of the photophysical properties of such materials.