Interaction of Misfit Dislocations with Perturbated Surface in Epitaxial Thin Film

Abstract

AbstractThe analytical method for the analysis of the stress fields arising as a result of the interaction of misfit dislocations with an undulated surface in an epitaxial thin film is considered. The boundary-value problem of the plane theory of elasticity for an infinite isotropic half-space containing an infinite row of line edge dislocations parallel to the undulated boundary is formulated assuming that the elastic properties of the film and substrate materials are approximately equal. The depth of dislocations beneath the surface is equal to the film thickness, and dislocations are spaced with the distance equal to the surface perturbation wavelength. The solution is based on Goursat–Kolosov’s complex potentials, Muskhelishvili’s representations, the boundary perturbation method, and superposition technique. Using the first-order approximation of the boundary perturbation method, the hoop stress distribution along the sine-curved surface is analyzed by varying the distance of dislocations to the unperturbed boundary.