Electronic Structure of Copper Impurities in ZnO

We have measured the near infrared absorption, Zeeman effect, and electron spin resonance of ${\mathrm{Cu}}^{2+}$ ions introduced as a substitutional impurity into single-crystal ZnO. From the $g$ values of the lowest ${\Gamma }_6$ component of the $T_2$ state (the ground state), $g_{\mathrm{II}}=0.74\mathrm{}$ and $g_{\perp }=1.531\mathrm{}$, and from the $g$ values of the ${\Gamma }_4{\Gamma }_5$ component of the $E$ state, $g_{\mathrm{II}}=1.63\mathrm{}$ and $g_{\perp }=0\mathrm{}$, we have determined the wave functions of ${\mathrm{Cu}}^{2+}$ in terms of an LCAO MO model in which overlap only with the first nearest neighbor oxygen ions is considered. These wave functions indicate that the copper $3d$ ($t_2$) hole spends about 40% of its time in the oxygen orbitals, and that the copper $t_2$ orbitals are expanded radially with respect to the $e$ orbitals. Corroboration for the radial expansion of the $t_2$ orbitals is obtained from an analysis of the hyperfine splitting. It is concluded from our model that the large values of the hyperfine constants, $\mathrm{}\left|A\right|=195\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $\mathrm{}\left|B\right|=231\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, are due to the contribution from the orbital motion of the $t_2$ hole.