Chemical trend of a Cu impurity in Zn chalcogenides

Cu is usually considered as an effective dopant to introduce shallow acceptors in Zn chalcogenides because it is on the left-hand side of Zn in the Periodic Table. Here, using first-principles calculations based on the hybrid functional with spin polarization, we show that contrary to the common expectation, Cu substituting Zn ($\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$) in bulk Zn chalcogenides actually generates rather deep acceptor levels in ZnO, ZnS, and ZnSe, i.e., 2.91, 1.03, and 0.53 eV above the valence-band maximum (VBM), respectively, except in ZnTe (0.13 eV). More interestingly, the absolute Cu impurity energy level does not follow the variation of the VBM, decreasing from ZnTe to ZnSe to ZnS to ZnO, instead, it is the highest in ZnO. The abnormal behavior of $\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$ in ZnO is attributed to the fact that, due to the very low O $2p$-orbital energy, the $\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$ defect wave function has dominantly localized the Cu $3d$-orbital component, whereas in other Zn chalcogenides, anion $p$ states are dominant. The localized Cu $3d$ state leads to the enhanced exchange energy that elevates the acceptor level, which explains why the Cu impurity level is abnormally deep in ZnO. This finding provides insight in designing shallow acceptor levels in II–VI semiconductors.

Figure 1

(a) Calculated formation energy of $\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$ as a function of the Fermi level in Zn chalcogenides under an anion-rich condition. The VBMs of $\mathrm{Zn}X$ are all set as zero, and the CBMs are represented by the dashed line with the corresponding color for the semiconductors. (b) Calculated valence-band offsets and (0/−) acceptor levels in Zn chalcogenides. By setting the VBM of ZnS as zero, the VBMs in ZnO, ZnSe, and ZnTe are at −1.17, 0.73, and 1.54 eV, respectively. (c) and (d) The structure of $\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$ in ZnO after and before ionic relaxation. The blue and red spheres represent the Cu and O atoms, respectively. The yellow isosurface represents the charge-density distribution of the $\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$ defect level.

Figure 2

(a) The single-electron energy level of $\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$ in Zn chalcogenides. The red line with a circle indicates an empty (hole) state within the spin-down channel. The energy zero is set at the VBM of ZnS. (b) The calculated atomic energy levels of $p$ and $d$ orbitals of the relevant elements in this paper with hybrid functional and spin-orbital couplings. The energy zero is the potential at infinity.

Figure 3

The total and the projected density of states of the anion $p$ orbital, Cu $3d$ orbital of the ${\mathrm{Cu}}_{\mathrm{Zn}}^0$ defect state in Zn chalcogenides. The Fermi level is set at zero at the VBMs and denoted by the brown dashed lines, and the CBMs are denoted by the purple dashed lines.