Defect annihilation in chemo-epitaxial directed self-assembly: Computer simulation and Self-Consistent Field Theory
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Defect annihilation in chemo-epitaxial directed self-assembly: Computer simulation and Self-Consistent Field Theory Marcus Müller1, Weihua Li1,2, Juan Carlos Orozco Rey1, and Ulrich Welling1 1 Institut für Theoretische Physik, Georg-August Universität, 37073 Göttingen, Germany 2 Department of Macromolecular Science, Fudan University, Shanghai, China ABSTRACT Except at the order-disorder transition, defects in lamella-forming block copolymers have a free energy of several hundreds kBT where kBT denotes the thermal energy scale. Thus, they cannot be conceived as equilibrium fluctuations around a perfectly ordered state. Instead, defects, which are observed in experiments, are formed in the course of self-assembly. Their behavior is dictated by the kinetics of structure formation, in particular, the kinetic pathways of defect motion and annihilation. Computational modeling can contribute to optimize materials parameters such as film thickness, interaction between copolymer blocks and substrate, geometry of confinement, in order to avoid the formation of defects in the early stages of structure formation or facilitate defect annihilation. Computations also provide fundamental insights into the universal physical mechanisms of directing the self-assembly, addressing the equilibrium structure and thermodynamics as well as the kinetics of self-assembly. We present computer simulation of highly coarse-grained particle-based models and selfconsistent field calculations that allow us to access the long time and large length scales associated with self-assembly. These calculations provide information about the free-energy landscape and mechanisms of defect annihilation in thin films. Additionally, opportunities for directing the kinetics of self-assembly by temporal changes of thermodynamic conditions are discussed. INTRODUCTION Block copolymers are linear, flexible macromolecules that are comprised of two chemically distinct block joined at their ends. The connectivity of the two blocks prevents macroscopic phase separation of the blocks; instead a spatially modulated phase is formed. The characteristic length scale is set by the spatial extent Reo of the macromolecule and ranges from 10-100nm. If both blocks occupy roughly equal volume fractions, a stripe pattern or lamellar microphase is formed [1]. Defects are localized, metastable structures that deviate from the periodic bulk morphology. Typical examples in stripe pattern formed by symmetric block copolymer materials are dislocation and disclinations [2,3,4,5]. The integration of block copolymer lithography into semiconductor fabrication poses extreme demands on the areal density of defects. In principle, block copolymer materials are well suited to satisfy this requirement because, at intermediate segregation χN, the excess free energy of a defect, ∆Fd, typically exceeds 30 kBT, where kBT denotes the thermal energy scale [6]. This large value of free energy results from the fractal Gaussian structure of a polymer. Since a single polymer does not densely fill space, the
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