Effect of substrate modulus difference on dislocation formation in an epitaxial film

Abstract

The effect of substrate modulus difference on dislocation formation in an epitaxial film is derived in the present study. The analysis is based on the energy approach, in which the self-energy of the dislocation and the interaction energy between the dislocation and the mismatch strain are calculated. The elastic stress field due to the interface dislocation is derived by superposition of the elastic stress fields of the film/substrate system with the following two configurations: (i) a dislocation at the interface assuming the film is also semi-infinite, and (ii) prescribed traction on the film surface which are the negative of those calculated from the first configuration at the location equivalent to the film surface in the second configuration. The results show that the critical film thickness for forming interface dislocation increases with the decrease in the shear modulus ratio of the film to the substrate.