The effect of lattice-mismatch induced stress upon the crystallographic structure, strain, strain relaxation, and the generation of different types of defects in heteroepitaxially grown SrTiO ₃ films on CeO ₂ buffered sapphire is examined. Depending on the thickness of the SrTiO ₃ layer, characteristic changes in the structural perfection of the layers, their crystallographic orientation with respect to the substrate system, and their strain is observed. For thin films misfit dislocations partially compensate the stress in the SrTiO ₃ layer, whereas cracks develop in thicker SrTiO ₃ films. The cracks are orientated along two predominant crystallographic orientations of the sapphire. The structural modifications and the formation of misfit defects and cracks are explained in a model based on lattice misfit induced stress, on the one hand, and energy considerations taking into account the stress release due to crack formation and the energy necessary for the formation of new surfaces at the crack, on the other hand. The impact of lattice misfit is discussed in two steps, i.e., intrinsic and thermal induced misfits during heteroepitaxial film growth at a given temperature and the subsequent cooling of the sample, respectively. The comparison of the theoretical predictions and the experimental observations demonstrate that intrinsic mismatch and thermal mismatch have to be considered in order to explain strain dependent effects in complex heteroepitaxial layer systems such as induced ferroelectricity of SrTiO ₃ on sapphire.