Computational studies of the electronic structure of copper-doped ZnO quantum dots

Copper-doped ZnO quantum dots (QDs) have attracted substantial interest. The electronic structure and optical and magnetic properties of Cu³⁺(d⁸)-, Cu²⁺(d⁹)-, and Cu⁺(d¹⁰)-doped ZnO QDs with sizes up to 1.5 nm are investigated using the GGA+U approximation, with the +U corrections applied to d (Zn), p(O), and d(Cu) orbitals. Taking +Us parameters, as optimized in previous bulk calculations, we obtain the correct band structure of ZnO QDs. Both the description of electronic structure and thermodynamic charge state transitions of Cu in ZnO QDs agree with the results of bulk calculations due to the strong localization of Cu defect energy levels. Atomic displacements around Cu are induced by strong Jahn-Teller distortion and affect Kohn-Sham energies and thermodynamic transition levels. The average bond length of Cu-O and the defect structure are crucial factors influencing the electronic properties of Cu in ZnO QDs. The analysis of the optical properties of Cu in ZnO QDs is reported. The GGA+U results, compared with the available experimental data, support Dingle's model [Phys. Rev. Lett. 23, 579 (1969)], in which the structured green luminescence observed in bulk and nanocrystals originates from the [(Cu⁺, hole) → Cu²⁺] transition. We also examine the magnetic interaction between the copper pair for two charge states: 0 and +2, and four positions relative to the center of QDs. Ferromagnetic interaction between ions is obtained for every investigated configuration. The magnitude of ferromagnetism increases for positive charge defects due to the strong hybridization of the d(Cu) and p(O) states.