Co在ZnO中的光学性质计算：内跃迁和电离跃迁
Calculated optical properties of Co in ZnO: internal and ionization transitions
摘要：
先前在Co掺杂ZnO中的发光和吸收实验揭示了$d(\textrm{Co}^{2+})$电子的两个电离和一个壳层内跃迁。这些光学性质的分析范围内的广义梯度近似的密度泛函理论。两个电离通道涉及从两个$\textrm{Co}^{2+}$间隙态（$t_{2\uparrow}$三重态和$e_{2\downarrow}$二重态）到导带的电子激发。第三种可能的电离通道，其中电子从价带被激发到$\textrm{Co}^{2+}$能级，需要超过4 eV的能量，并且不能导致低于ZnO带隙的吸收，与早期的建议相反。我们还考虑了两个复合通道，直接复合和两步过程，其中光电子被$\textrm{Co}^{3+}$捕获，然后通过内部跃迁复合。最后，所观察到的带隙随Co浓度的增加被理论很好地再现。通过对Zn、O和Co的相关轨道进行$+U$修正，实现了对ZnO：Co的精确描述。$+U(\textrm{Co})$值通过线性响应方法计算，并通过将计算的跃迁能与光学数据拟合独立获得。相应的值，3.4和3.0~eV，吻合良好。电离的钴诱导大的能隙能级的位移，由不同的库仑耦合之间的$d(\textrm{Co})$电子，并通过大的晶格弛豫Co离子。反过来，在$\sim 1$ ~eV范围内，由内跃迁引起的$\textrm{Co}^{2+}$能级的变化主要是由占位效应相关的$U(\textrm{Co})$修正引起的。
英文摘要：
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.
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