The dominant effect of non-centrosymmetric displacement on the crystal-field energy splitting in the strained a-plane ZnO epi-films on r-plane sapphires

The polarization-dependent photoluminescence (PL) of the a-plane ZnO (a-ZnO) films grown on r-plane sapphire substrates shows that the crystal-field energy splitting (Delta(CF)) becomes larger with increasing film thickness from 24 nm to 291 nm. In the use of the nonlinear fitting of the stress-strain tensor to the X-ray diffraction data, we found crystal symmetry breaking from wurtzite to monoclinic in these films and determined the corresponding lattice constants and the relaxed lattice constants. With the available lattice variables, we further used the tight-binding method to calculate the band energies and compared with the PL spectra. The results confirm that the crystal deformation and the non-centrosymmetric displacement had opposite effects on the Delta(CF) at the Gamma point and the displacement induced by the strain is the dominant effect on Delta(CF).