Studies on the spin Hamiltonian parameters and the defect structures for the two interstitial tetragonal Cu2+ centers in the ZnO nanocrystals

The spin Hamiltonian parameters (g factors and hyperfine structure constants) are theoretically studied for the two interstitial Cu2+ centers I and II in the ZnO nanocrystals from the perturbation formulas of these parameters for a tetragonally elongated octahedral 3d9 cluster. The ligand spin–orbit coupling and orbital contributions are involved from the cluster approach in view of moderate covalency. The two Cu2+ centers demonstrate slight tetragonal elongation distortions (denoted by the relative elongation parameters ρ ≈ 3.4% and 3.2% for centers I and II, respectively) due to the Jahn–Teller effect. The calculated spin Hamiltonian parameters and three optical transition bands are in good agreement with the observed values. The differences in EPR and optical spectra for both centers can be ascribed to the weaker covalency (higher N), stronger tetragonal elongation distortion (larger ρ) and slightly larger core polarization constant κ as well as almost identical crystal-fields (nearly the same Dq) for center I as compared to center II. The above delicate discrepancies in spectroscopic behaviors may be attributed to the tiny differences in local structures and electronic states for Cu2+ at dissimilar parts of the ZnO nanocrystals.