Dislocations and Internal Stresses in Thin Films: A Discrete-Continuum Simulation

The plasticity of thin films and layers is of considerable technological interest. For instance, the relaxation of internal stresses in semiconducting epitaxial layers has been the object of many studies [1, 2]. This relaxation is usually treated via the concept of critical thickness, the latter being defined as the maximum layer thickness below which dislocations cannot spontaneously move and relax the internal stresses. The various internal stresses present in epitaxial layers (e.g. the misfit and elastic incompatibility stresses at the film/substrate interface and the image force in a free-standing film) can be computed within a continuum frame. However, the way they influence the motion of a dislocation has not yet been computed, even in a approximate manner. An useful approximation that allows treating the boundary condition at the surface of a free-standing film consists of making use of the concept of image dislocation. Then, the critical stress for moving a dislocation in a free-standing film is the same as that of a capped layer of thickness twice that of the film. To date, models and dislocation dynamics (DD) simulations are available that involve several levels of approximation for the treatment of the dislocation/interface and dislocation/surface interactions [3–7]. For reasons that are not clearly understood, however, these models predict critical thicknesses that are systematically larger than the expected ones. The comparison with experiment is, in addition, made difficult because stresses have to be artificially introduced to replace the internal stresses and approximations have to be done to treat the image stresses. In the present work it is shown that it is now possible to fully account for the contribution of the various sources of internal stresses to the critical stress for the motion of a threading dislocation. This is performed numerically with the help of a hybrid code that combines a DD code for the treatment of the dislocation dynamics and a Finite Element (FE) code for the treatment of the boundary conditions. In what follows, several applications of this discrete-continuum model (DCM) to the study of dislocation motion in epitaxial layers are presented. The motion of a dislocation in a thin film is considered, including the image force and successively adding a misfit stress and an elastic incompatibility stress at the film/substrate interface.