Simulation of Nanostructure Formation in Thin Polymer Films

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Simulation of Nanostructure Formation in Thin Polymer Films Dongchoul Kim and Wei Lu Department of Mechanical Engineering, University of Michigan Ann Arbor, MI 48109, USA ABSTRACT A thin polymer film subjected to an electrostatic field may lose stability at the polymer-air interface, leading to uniform self-organized pillars emerging out of the film surface. This paper presents a three dimensional dynamic model to account for the behavior. The coupled diffusion, viscous flow, and dielectric effect are incorporated into a phase field framework. Numerical simulations reveal rich dynamics of the pattern formation process and the substrate effect. The pillar size is insensitive to the film thickness, but the distance between pillars and the growth rate are significantly affected. The study suggests an approach to control structural formation in thin films with a designed electric field. INTRODUCTION Recent experiments show that a flat interface between two dielectric media may lose stability in an electrostatic field and self-assemble into morphological patterns [1-3]. The mechanism can be explained by two competing energetics: surface energy and electrostatic energy. Linear or weakly nonlinear perturbation analyses under the lubrication approximation of a viscous flow have been performed [4-6]. These studies point out that a wavy interface reduces the electrostatic energy, but increases the interface energy. The competition determines a critical wavelength. A perturbation with a larger wavelength will grow over time. The fastest growth wavelength is related to the field strength, such that a stronger electric field leads to a smaller wavelength. While these studies provide valuable insight into the early stage evolution, it is still not clear how the instability may lead to the uniform pillar structure. The latter would require a reliable and accurate explanation of the thin film behavior in the nonlinear evolution regime. In other words, the dynamic process between an early perturbation and the late structure is crucial to understand the self-assembly behavior. For a thin film, the self-assembly process is significantly affected by the substrate. The fast growth wavelength obtained from small perturbation analysis may not have sufficient time to develop before it meets the substrate, and thus has no direct connection to the size of the late structure. The lack of kinetic route may essentially prevent the coarsening of pillars when the film breaks. When the film thickness is comparable to or smaller than the fast

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wavelength, even the early evolution is considerably affected by the substrate. A careful consideration of the problem leads us to the point that the phenomenon may have a complex nature and involve rich dynamics. Its potential application for nanofabrication relies on an effective computational approach to simulate and understand the entire self-assembly process. MODEL Consider a thin polymer film on a substrate subjected to an electrostatic field. The field is generated by two

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