Valence band ordering and magneto-optical properties of free and bound excitons in ZnO

The Zeeman splitting of free and bound excitons is analysed theoretically for both Gamma(7) and Gamma(9), symmetries of the upper valence band. The Zeeman splitting of the Gamma(7) (Gamma(9)) holes in magnetic field parallel to the hexagonal c axes of the crystal is found to be smaller (larger) than the Zeeman splitting of the electrons. The magnetic-field dependence of the bound exciton optical transition energies measured in the Faraday geometry with right and left circular polarized light can be well described with Gamma(7) as well as with Gamma(9) holes. However, the fitting of the experimental dependence of the Zeeman splitting on the angle between magnetic field and c axis proves the Gamma(7) symmetry of the holes involved in all low temperature transitions and thus of the upper valence band in bulk ZnO. The determined parameters are in excellent agreement with known experimental data on the fine structure of the free exciton ground state in ZnO. The hole g-factors determined for excitons bound to an ionized and neutral impurity centers are close to each other and to the g-factor calculated for the Gamma(7) hole in the free exciton ground state. This points to a donor character of the neutral impurity centers. This conclusion is confirmed by temperature dependent magneto-transmission and magneto-luminescence measurements.