Critical epitaxial film thickness for forming interface dislocations

The system of an epitaxial film on a semi-infinite substrate of a different material is considered and the critical thickness of the film to form misfit interface dislocations is derived in the present study. The energy approach is used to predict the critical thickness and both the self-energy of the dislocation and the interaction energy between the dislocation and the mismatch strain are analyzed. The elastic stress field due to the interface dislocation is required in analyzing the energies and both the superposition principle and Fourier integral are adopted to derive this elastic stress field. The predicted stress fields in the system satisfy both the free surface condition at the film surface and the continuity condition at the interface. The predicted critical film thickness for forming interface dislocation decreases with the increase in the shear modulus ratio of the film to the substrate.