Calculated optical properties of Co in ZnO: internal and ionization transitions

Abstract

Previous luminescence and absorption experiments in Co-doped ZnO revealed two ionization and one intrashell transition of $d({\text{Co}}^{2+})$ electrons. Those optical properties are analyzed within the generalized gradient approximation to the density functional theory. The two ionization channels involve electron excitations from the two ${\text{Co}}^{2+}$ gap states, the $t_{2\uparrow }$ triplet and the $e_{2\downarrow }$ doublet, to the conduction band. The third possible ionization channel, in which an electron is excited from the valence band to the ${\text{Co}}^{2+}$ level, requires energy in excess of 4~eV, and cannot lead to absorption below the ZnO band gap, contrary to earlier suggestions. We also consider two recombination channels, the direct recombination and a two-step process, in which a photoelectron is captured by ${\text{Co}}^{3+}$ and then recombines via the internal transition. Finally, the observed increase the band gap with the Co concentration is well reproduced by theory. The accurate description of ZnO:Co is achieved after including $+U$ corrections to the relevant orbitals of Zn, O, and Co. The $+U(\text{Co})$ value was calculated by the linear response approach, and independently was obtained by fitting the calculated transition energies to the optical data. The respective values, 3.4 and 3.0~eV, agree well. Ionization of Co induces large energy shifts of the gap levels, driven by the varying Coulomb coupling between the $d(\text{Co})$ electrons, and by large lattice relaxations around Co ions. In turn, over $\sim 1$~eV changes of ${\text{Co}}^{2+}$ levels induced by the internal transition are mainly caused by the occupation-dependent $U(\text{Co})$ corrections.

arXiv comment10 pages, 7 figures

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• Theory of the $sp-d$ coupling of transition metal impurities with free carriers in ZnO