Nano-epitaxy modeling and design: from atomistic simulations to continuum methods
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The dissertation starts from the understanding of dislocation dissipation mechanism due to the image force acting on the dislocation. This work implements a screw dislocation in solids with free surfaces by a novel finite element model, and then image forces of dislocations embedded in various shaped GaN nanorods are calculated. As surface stress could dramatically influence the behavior of nanostructures, this work has developed a novel analytical framework to solve the stress field of solids with dislocations and surface stress. It is successfully implemented in this framework for the case of isotropic circular nanowires (2D) and the analytical result of the image force has been derived afterwards. Based on the finite element analysis and the analytical framework, this work has a semi-analytical solution to the image force of isotropic nanorods (3D) with surface stress. The influences of the geometrical parameter and surface stress are illustrated and compared with the original finite element result. In continuation, this work has extended the semi-analytical approach to the case of anisotropic GaN nanorods. It is used to analyze image forces on different dislocations in GaN nanorods oriented along polar (c-axis) and non-polar (a, m-axis) directions. This work could contribute to a wide range of nanostructure design and fabrication for dislocation-free devices.