Modeling And Simulation Of Driven Nanopatterning Of Bulk Material And Thin Film Surfaces

Material nanostructures such as nanowires, quantum dots, and nanorings have a wide variety of applications in electronic and photonic devices among numerous others. Assembling uniformly arranged and consistently sized nanostructure patterns on solid material surfaces is a major challenge for nanotechnology. This dissertation focuses on developing predictive models capable of simulation and analysis of such nanopattern formation on bulk material and strained thin film surfaces. Single-layer atomic clusters (islands) of sizes larger than a critical size on crystalline conducting substrates undergo morphological instabilities when driven by an externally applied electric field or thermal gradient. We have conducted a systematic and comprehensive study of epitaxial single-layer island dynamics under electromigration conditions, which has revealed that in homoepitaxial islands of larger-than-critical size, an externally applied electric field triggers fingering and necking instabilities on the edge of the migrating islands. These instabilities, when properly controlled, result in parent island breakup into organized regular or complex patterns such as arrays of parallel nanowires, single-layer nanorings, and nanodisc distributions. In all cases, we have explained the onset of morphological instability based on linear stability analysis and characterized the post-instability dynamics and the resulting stable nanopatterns. We have also analyzed the formation of quantum dots and nanorings resulting from stress-driven atomic diffusion on strained thin film surfaces. Epitaxially depositing germanium thin films, beyond a critical thickness, on an ordered pit-patterned silicon substrate leads to self-assembly of ordered germanium quantum dots inside the pits. In order to describe Ge film surface morphological response, we have developed an atomistically-informed, 3D continuum-scale kinetic model. Self-consistent dynamical simulations based on our model and supported by linear and nonlinear morphological stability theories show formation of complex nanostructures on the epitaxial film surface, including nanorings at the rims of pits, a single quantum dot and/or concentric nanorings at the center of a pit, as well as regular arrays of quantum dots inside pyramidal pits. Our findings are consistent with experimental observations reported in the literature and reveal that the types, shapes, and dimensions of the formed nanostructure patterns can be controlled precisely by properly tuning materials, processing, or geometrical parameters.