Recent discoveries have shown that surface pattern formation in the heteroeptitaxial growth of bimetallic thin films can greatly influence the properties of novel bimetallic catalytic materials and other thin-films technologies. In particular, for catalytic applications, nano-scale surface morphology has been shown to influence the reactivity and specificity of bimetallic catalysts and, thus, a method to control surface morphology effectively at nanoscopic length scales would provide a means to “tune” the reactive properties of a material for different applications. Currently, the only available technologies for directly influencing and controlling nano-scale pattern features involve “top-down” manufacturing approaches, such as lithography techniques, which are limited to feature sizes in the range of 30 nm. However, heteroepitaxial surface patterns form with characteristic lengths as small as approximately 1 nm. Self-assembly, the autonomous arrangement of molecules into nano-scale patterns due to intermolecular forces, has the potential provide a “bottom-up” approach to control surface pattern morphologies at various length scales ranging from about 1 nm to several μm.
While the benefits of scalable “bottom-up” manufacturing over current “top-down” manufacturing are clear, practical implementation of controlled self-assembly has been hindered by the inherent nonlinearity and stochasticity of self-assembly dynamics. Model-based control techniques provide an efficient theoretical framework for overcoming these obstacles and, with the recent development of models that accurately capture the physics of pattern formation during self-assembly, they have become a viable option for designing and implementing strategies for controlling surface morphologies through self-assembly. Our ultimate goal is to create an efficient model-based control scheme harnessing self-assembly dynamics for controlling nano-scale surface morphologies. However, before such a control scheme can be implemented, a careful analysis of the controllability and sensitivity of a pattern with respect to a very limited set of manipulated variables (MVs) must be performed.
In this work, we present an analysis of a continuum model describing heteroepitaxial self-assembly of Pb on Cu(111) (Chatterjee and Vlachos, 2007; Abukhdeir, et al, 2011) where various metrics for quantifying patterns are studied in response to changes in a limited set of MV. The focus of our study is the controllability and sensitivity of the surface morphology of Pb patterns based on manipulation of a limited number of MVs that can be adjusted at the macroscopic scale, such as surface temperature, (sub-monolayer) Pb coverage, and Pb/Pb interaction strength, since, in a manufacturing setting, these will be the only MVs available to control the surface. In particular, this presentation will discuss how the surface morphology in several stable pattern regimes is affected by changes in the MVs, what the most effective metrics for quantifying surface patterns are, and to what degree the densities of several classes of defects can be minimized based on the imperfect information provided by these metrics. The implications of these findings on model-based control strategies for controlling surface morphologies will also be discussed.
Chatterjee, A. & Vlachos, D. G. Systems tasks in nanotechnology via hierarchical multiscale modeling: Nanopattern formation in heteroepitaxy. Chem. Eng. Sci., 2007
Abukhdeir, N. M., Vlachos, D. G., Katsoulakis, M. & Plexousakis, M. Long-time integration methods for mesoscopic models of pattern-forming systems. J. Comp. Phys., 2011