Grants and Contracts Details
The research proposed herein focuses on morphological instabilities that occur during the growth of multicomponent crystals. Such instabilities are not of mere academic importance. Indeed, most relevant materials in nanotechnologies (semi-conductors, nano-electro-mechanical systems, etc.) are made of alloys or compounds, and understanding the chemical interactions between their various constituents is instrumental in controlling their behavior during processing (and subsequently the performance of the devices of which they are part). Moreover, these instabilities can be either detrimental (e.g., in multilayered structures) or beneficial (e.g., for the formation of quantum wires and dots in selfassembling materials) depending on the technological context, but in no case irrelevant. Finally, in addition to the almost exclusive focus on single-species crystals, emphasis in the engineering and applied mathematics literature has been placed on stress-driven surface-diffUsion-mediated instabilities and nearequilibrium kinetics. Comparatively, little attention has been devoted to the role of anisotropy in the evolution of steps on a vicinal surface and to grov,'th situations in which large departures away ITom local equilibrium characterize the boundary conditions at these steps, and, importantly, the possibility of chemically driven instabilities during step flow or island dynamics has barely been touched upon. Finally, little is known about the effect of electric fields (resulting ITom heating the substrate upon which deposition occurs with an electric current) on instabilities such as step bunching during growth or evaporation and, a fortiori, about the interplay between chemical kinetics and electromigration. Our goal here is to (i) develop a mathematically rigorous and thermodynamically consistent theory of multi component crystal growth that accounts for the interplay between chemistry and electromigration away ITom any equilibrium or geometric assumptions, (ii) use the above framework to investigate chemically and electrically driven instabilities, and (iii) develop numerical tools (based on level-set methods) to simulate the resulting nonlinear coupled partial differential equations.
|Effective start/end date||5/1/05 → 5/1/08|
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