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Download as PDFModeling and Theoretical Design Methods for Self-assembly of Block Copolymers
Block copolymer self-assembly on nanolithographically-defined templates has great potential in fabricating patterned media and devices at the nanometer scale. Current experimental work requires first that the templates be written lithographically and then that the block copolymer morphology around the template be observed and categorized. An alternative approach to the problem of finding the correct template to get the desired morphology of block copolymers can be achieved through self-consistent field theory modeling (SCFT) [1] . By reducing the problem of polymer interactions with the substrate to density and field interactions, the theory allows for quick computational exploration of phase diagrams for two-dimensional unit cell templates. Large cell templates and three-dimensional unit cell templates can be modeled as well but at a cost of larger computation time. However, these simulations can be used to predict or confirm proposed three-dimensional structures that are hard to observe using conventional planar microscopy methods, as seen in Figure 1 [2] . In the theory, topographical constraints are modeled as hard potential barriers to the polymer, and chemical surface affinity effects are modeled as attractive potential fields, as schematically represented in Figure 2. The traditional approach with the theory is to impose an initially randomly configured system of copolymers to a predefined template and have the system evolve through pseudo-dynamical relaxation schemes to reach saddle points in the system energy space, thus allowing for both metastable states and the thermodynamic equilibrium state to be observed. Combining SCFT with surface energy analysis calculations of the observed equilibrium morphologies, one can develop a simple theory of where ordered structure transitions occur based on geometric commensurability conditions. Eventually, the theory should allow for taking desired block copolymer morphologies as the simulation input and determining what the minimum required template is to achieve that morphology.
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- Figure 1: SCFT results of 3D structures obtained by different topological boundary conditions. (a) Double layer of hexagonal spheres in a hexagonal lattice template and (b) cylinders assembled on a trench template.
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- Figure 2: Schematic view of field constraints used in simulations. The color-coding corresponds to regions with different field constraints.
- R. A. Mickiewicz, J. K. W. Yang, A. F. Hannon, Y. S. Jung, A. Alexander-Katz, K. K. Berggren, and C. A. Ross, “Enhancing the potential of block copolymer lithography with polymer self-consistent field theory simulations,” Macromolecules, vol. 43, no. 19, pp. 8290–8295, 2010. [↩]
- J. G. Son, A. F. Hannon, K. W. Gotrik, A. Alexander-Katz, and C. A. Ross, “Hierarchical nanostructures by sequential self-assembly of styrene-dimethylsiloxane block copolymers of different periods,” Adv. Mater. vol. 23, pp. 634-639, 2011. [↩]