An efficient hybrid 2D/3D thin film discrete dislocation dynamics

Crystalline thin fi lms are increasingly used in semiconductor devices, ferroelectric and ferromagnetic devices, biomedical components, fuel cells, solar cells, and wear-resistant coatings. Given their widespread use, understanding the unique mechanisms that control their properties is critical. This has proven challenging because the properties of thin fi lms do not obey bulk scaling laws. In particular, dislocations that naturally arise during thin fi lm deposition result in deleterious effects at the device application level. Substantial research has been devoted to attempting to understand how dislocation structures evolve and how they affect device properties. However, current dislocation simulation methods are only able to model highly idealized systems accurately. The methods that do exist are either analytical, which can only be used for a small number of dislocations under specialized loading and geometries; two-dimensional (2D), which are incapable of capturing realistic three-dimensional (3D) dislocation interactions; or fully 3D, which are too computationally intensive to model high dislocation densities and their resultant deformations that are observed in some real applications. In this article, we propose a novel method to exploit the quasi-two-dimensional nature of 3D dislocation loops in a thin fi lm to model their behaviors. For most fi lm confi gurations, simulation performance can be enhanced by implementing a hybrid 2D/3D model without losing signifi cant fi delity. In this technique, misfi ts stress fi elds are modeled by superposing multiple 2D models. Threads are modeled with a more traditional 3D implementation as they move through the misfi t stress fi eld. Combining the 2D and 3D analyses, leads to a sizeable reduction in the computational costs. Therefore, using this innovative technique, much higher strains and/or dislocation densities could be studied. Although admittedly this method is not capable of investigating all possible interactions within a dislocation structure in a thin fi lm, it captures all signifi cant dislocation structures and interactions that govern mechanical properties of the fi lm. In this article, the accuracy of this new method is examined by comparison with a fully 3D discrete dislocation dynamics model. The resulting dislocation structures, as well as the stress contours, of the two models are comparable. This demonstrates that the hybrid 2D/3D method can accurately predict behaviors similar to the 3D discrete dislocation dynamics models in a fraction of the time.