Valence-band-ordering of a strain-free bulk ZnO single crystal identified by four-wave-mixing spectroscopy technique

Spectroscopic and temporal four-wave-mixing (FWM) measurements are carried out on a strain-free bulk ZnO single crystal, in order to clarify the valence-band-ordering. Under the collinearly polarized lights with the electric-field component parallel to the c-axis, which can excite dipole-allowed Γ ₁-excitons, the FWM signal appears only in the energies corresponding to the B-exciton. Under the cross-linear polarization configuration exciting both Γ _5- and Γ ₁-excitons, the FWM signal arising from the two-photon-coherence is absent in the energies corresponding to A-exciton. Both the results indicate that Γ ₁-exciton state belongs exclusively to B-exciton, meaning that the valence-band ordering is Γ ₉ - Γ ₇ - Γ 7 in order of decreasing electron energy for the present strain-free ZnO single crystal.