Frequency shifts of the E₂^high Raman mode due to residual stress in epitaxial ZnO thin films

To investigate the stress effect on the E₂^high Raman vibration mode, we grew heteroepitaxial ZnO films on c-plane sapphire with different strain states by changing the film thicknesses between 5 and 100 nm. To determine the relationship between the observed frequency of the E ₂^high mode with the biaxial residual stress of the ZnO thin films, the out-of-plane strain of films were measured with x-ray diffraction from which the residual stress was calculated. The biaxial residual stress and E₂^high frequency were related linearly by a factor of ∼170 MPa/cm^-1, which is in agreement with reported values from high pressure investigations of bulk ZnO.