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Analysis of External-Field-Driven Surface Stabilization and Patterning

The ability to form, manipulate, and stabilize fine-scale materials features by controlling macroscopic forces is essential to advancing microelectronics and nanotechnology. For example, externally applied electric fields and thermal gradients drive atomic motion through the mass transport phenomena of electromigration or thermomigration, respectively, that have been considered for several decades as major sources of materials reliability problems in microelectronics. However, when tuned optimally, the same "destructive" forces can provide paradigm shifts in surface engineering and nanofabrication. Toward this end, developing a fundamental understanding and multi-physics, multi-scale mathematical models capable of predicting external-field-driven surface morphological evolution constitutes the main focus of this thesis. We have developed a surface mass transport model that accounts for electromigration and thermomigration, diffusional anisotropy, and the temperature dependence of atomic diffusivity to examine the surface morphological response of stressed electrically and thermally conducting crystalline elastic solids under the simultaneous action of an electric field and/or a temperature gradient; these solid materials include uniaxially stressed bulk crystals and coherently strained epitaxial films on substrates that may undergo stress-induced surface morphological instabilities such as the Asaro-Tiller/Grinfeld instability and the Stranski-Krastanow growth instability, respectively. Using linear stability analysis, and validated by self-consistent dynamical simulations, we have found that properly directed external fields of magnitude higher than a critical value can stabilize the planar surface morphology and derived the conditions for synergistic action of multiple external fields, as well as the criticality conditions for surface stabilization. We have also minimized the critical external field strength requirements by combining the external field action with substrate engineering techniques. Furthermore, we have investigated systematically the complex asymptotic states reached in the electromigration-driven void morphological evolution in thin films of face-centered cubic metals with-oriented film planes under the simultaneous action of a general biaxial mechanical stress. In addition, we have developed and experimentally validated a model for analyzing the current-driven dynamics of single-layer epitaxial islands on crystalline substrates. Simulations based on the model have shown that the dependence of the stable steady island migration speed on the inverse of the island size stops being linear for larger-than-critical island sizes. In this nonlinear regime, we have discovered morphological transitions, Hopf bifurcations, and necking or fingering instabilities for various surface crystallographic orientations, island misfit strains, and diffusional anisotropy parameters. Consistent with the predictions of linear stability theory, dynamical simulations show that, under certain conditions, large-size islands undergo a fingering instability which following finger growth and, depending on the substrate orientation, necking instability, leads to formation of single or multiple nanowires. The nanowires have constant widths, on the order of 10 nm, which can be tuned by controlling the externally applied electric field strength. Moreover, we have studied systematically the patterns formed due to the current-driven evolution of pairs of different-size islands driven to coalescence.
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