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 misf it interface dislocations is derived in the present study. The energy appro ach is used to predict the critical thickness and both the self-energy of t he dislocation and the interaction energy between the dislocation and the m ismatch strain are analyzed. The elastic stress field due to the interface dislocation is required in analyzing the energies and both the superpositio n principle and Fourier integral are adopted to derive this elastic stress field. The predicted stress fields in the system satisfy both the free surf ace condition at the film surface and the continuity condition at the inter face. The predicted critical film thickness for forming interface dislocati on decreases with the increase in the shear modulus ratio of the film to th e substrate. (C) 2001 Elsevier Science B.V. All rights reserved.