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

TL;DR

This study uses density functional theory with +U corrections to analyze the optical properties of Co-doped ZnO, clarifying ionization channels, internal transitions, and their effects on the band gap, aligning theory with experimental observations.

Contribution

The paper provides a detailed theoretical analysis of Co ionization and internal transitions in ZnO using GGA+U, including calculated transition energies and the impact on the band gap, which was not previously well understood.

Findings

Two ionization channels involve electron excitation from Co states to the conduction band.

The third ionization channel requires over 4 eV, not contributing below the band gap.

Theoretical band gap increase with Co concentration matches experimental data.

Abstract

Previous luminescence and absorption experiments in Co-doped ZnO revealed two ionization and one intrashell transition of $d(\textrm{Co}^{2+})$ 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 $\textrm{Co}^{2+}$ 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 $\textrm{Co}^{2+}$ 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 $\textrm{Co}^{3+}$ 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 $+U(\textrm{Co})$ 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 $d(\textrm{Co})$ electrons, and by large lattice relaxations around Co ions. In turn, over $\sim 1$~eV changes of $\textrm{Co}^{2+}$ levels induced by the internal transition are mainly caused by the occupation-dependent $U(\textrm{Co})$ corrections.