To design processes that effectively use polymer directed self-assembly, we would like to have a complete picture of stable and defective polymer configurations. Field-theoretic simulations are an effective way to gain knowledge about these configurations and predict defect populations: we can easily vary design parameters such as prepattern dimensions, wetting conditions and polymer composition/architecture and observe their effects on pattern formation. We previously showed that an optimized phase field model, a modification of the Ohta-Kawasaki model, is more accurate at predicting domain spacing and defect formation in bulk systems. This accuracy is achieved by a systematic mapping procedure that optimizes parameters in the model using inexpensive, low-dimensional selfconsistent field theory (SCFT) calculations. We now make two improvements to the model. First, we implement a conjugate gradient method, a more efficient numerical solver for phase field models not available to SCFT, and characterize its performance. We find that an optimized phase field model simulation requires one to two orders of magnitude less computation time than an SCFT simulation of the same system. Second, we extend our model to confined templates and demonstrate that the new model does not suffer from the nonphysical behavior found in other phase field models in the presence of confining walls.
Block copolymer self-assembly is a powerful tool for nanoscale patterning which benefits from predictive simulations. Two classes of simulations are self-consistent field theory (SCFT), which is accurate but computationally expensive, and phase field models, which are faster but historically less accurate. We refine a mapping procedure that uses results from SCFT to optimize parameters in a phase field model for diblock copolymers. We validate the performance of this optimized phase field model with regards to accuracy and computational speed in perfect and defective configurations. The optimized phase field model is significantly faster than SCFT and more accurate than previous phase field models, making it a viable design tool for directed self-assembly processes.
A major challenge in the application of block copolymer directed self-assembly (DSA) to advanced lithography is the
exploration of large design spaces, including the selection of confinement shape and size, surface chemistry to affect
wetting conditions, copolymer chain length and block fraction. To sweep such large spaces, a computational model is
ideally both fast and accurate. In this study, we investigate various incarnations of the density functional theory (DFT)
approach and evaluate their suitability to DSA applications. We introduce a new optimization scheme to capitalize on the
speed advantages of DFT, while minimizing loss of accuracy relative to the benchmark of self-consistent field theory
(SCFT). Although current DFT models afford a 100-fold reduction in computational complexity over SCFT, even the
best optimized models fail to match SCFT density profiles and make extremely poor predictions of commensurability
windows and defect energetics. These limitations suggest that SCFT will remain the gold standard for DSA simulations
in the near future.