Unusual nonlinear strain dependence of valence-band splitting in ZnO

Using first-principles band structure calculations, we investigate the crystal-field and spin-orbit splittings at the valence-band edge of ZnO and their dependence on the strain. Different from other conventional semiconductors, the variation of the valence-band splitting of ZnO shows a strong nonlinear dependence on the strain and the slope of the crystal-field splitting as a function of strain can even change sign. Our analysis shows that this unusual behavior in ZnO is due to the strong coupling between Zn $3d$ states and oxygen $2p$ states. A mapping of the valence-band ordering in ZnO under different strain levels is provided that will be useful in designing ZnO-based optoelectronic devices.