${\Gamma }_7$ valence band symmetry related hole fine splitting of bound excitons in ZnO observed in magneto-optical studies

The symmetry ordering of the valence bands in ZnO is derived from high-resolution magneto-optical measurements of bound excitons. We report on the experimental observation of a hole state related fine splitting for bound excitons in the Voigt configuration. This splitting is related to a nonzero Landé $g$ value $g_{\perp }$ for hole states from the $A$ valence band. Based on theoretical considerations, the symmetry of the uppermost valence band is doubtlessly identified as ${\mathbf{\Gamma }}_{\mathbf{7}}$. This attribution is confirmed by polarization and angular resolved magnetophotoluminescence spectroscopy.

Figure 1

(Color online) Level scheme and splitting of donor bound exciton states under the influence of external magnetic fields. Holes originating from valence bands with different symmetry representations lead to variations in the hole $g$ values as expressed by the size of the Zeeman splitting.

Figure 2

(Color online) Photoluminescence spectra of the $I_{6a}$, $I_7$, and $I_8$ bound exciton lines at 2 K for different magnetic fields, orientations and angles. (a) Faraday configuration $\left(\mathit{B}\Vert \mathit{c}\Vert \mathit{k}\right)$, (b) angles $\theta =0,15,30,45,60,75,90$ between $\mathit{B}$ and $\mathit{c}$ with $B=5\text{T}$, and (c) Voigt configuration $\left(\mathit{B}\perp \mathit{c}\parallel \mathit{k}\right)$. The dark (blue) and light (red) lines (a) indicate the right ${\sigma }^{+}$ and left ${\sigma }^{-}$ polarized light, respectively.

Figure 3

(Color online) Zeeman splitting of the $I_{6a}$ bound exciton line at 2 K. (a) Faraday configuration $\left(\mathit{B}\Vert \mathit{c}\Vert \mathit{k}\right)$, (b) various angles $\theta$ between $\mathit{B}$ and $\mathit{c}$ with $B=5\text{T}$, and (c) Voigt configuration $\left(\mathit{B}\perp \mathit{c}\parallel \mathit{k}\right)$. Solid (blue) and open (red) triangles (a) indicate the peak position for ${\sigma }^{+}$ and ${\sigma }^{-}$ polarized light, respectively. Solid black dots show the peak energies in the unpolarized measurements. Outer (green) and inner (orange) lines (c) represent theoretical fits for $\mathit{E}\perp \mathit{B}$ and $\mathit{E}\parallel \mathit{B}$, respectively.

Figure 4

(Color online) Photoluminescence spectra of the $I_4$ bound exciton line at 2 K for magnetic fields of 0–6 T recorded in the Voigt configuration $\left(\mathit{B}\perp \mathit{c}\right)$. Dark (green) and light (orange) lines represent linear polarized measurements in the $\mathit{E}\perp \mathit{B}$ and $\mathit{E}\parallel \mathit{B}$ orientation, respectively.