Optimizing self-consistent field theory block copolymer models with X-ray metrology.

A block copolymer self-consistent field theory (SCFT) model is used for direct analysis of experimental X-ray scattering data obtained from thin films of polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA) made from directed self-assembly. In a departure from traditional approaches, which reconstruct the real space structure using simple geometric shapes, we build on recent work that has relied on physics-based models to determine shape profiles and extract thermodynamic processing information from the scattering data. More specifically, an SCFT model, coupled to a covariance matrix adaptation evolutionary strategy (CMAES), is used to find the set of simulation parameters for the model that best reproduces the scattering data. The SCFT model is detailed enough to capture the essential physics of the copolymer self-assembly, but sufficiently simple to rapidly produce structure profiles needed for interpreting the scattering data. The ability of the model to produce a matching scattering profile is assessed, and several improvements are proposed in order to more accurately recreate the experimental observations. The predicted parameters are compared to those extracted from model fits via additional experimental methods and with predicted parameters from direct particle-based simulations of the same model, which incorporate the effects of fluctuations. The Flory-Huggins interaction parameter for PS-b-PMMA is found to be in agreement with reported ranges for this material. These results serve to strengthen the case for relying on physics-based models for direct analysis of scattering and light signal based experiments.

Quantitative Three-Dimensional Characterization of Block Copolymer Directed Self-Assembly on Combined Chemical and Topographical Prepatterned Templates.

Characterization of the three-dimensional (3D) structure in directed self-assembly (DSA) of block copolymers is crucial for understanding the complex relationships between the guiding template and the resulting polymer structure so DSA could be successfully implemented for advanced lithography applications. Here, we combined scanning transmission electron microscopy (STEM) tomography and coarse-grain simulations to probe the 3D structure of P2VP-b-PS-b-P2VP assembled on prepatterned templates using solvent vapor annealing. The templates consisted of nonpreferential background and raised guiding stripes that had PS-preferential top surfaces and P2VP-preferential sidewalls. The full 3D characterization allowed us to quantify the shape of the polymer domains and the interface between domains as a function of depth in the film and template geometry and offered important insights that were not accessible with 2D metrology. Sidewall guiding was advantageous in promoting the alignment and lowering the roughness of the P2VP domains over the sidewalls, but incommensurate confinement from the increased topography could cause roughness and intermittent dislocations in domains over the background region at the bottom of the film. The 3D characterization of bridge structures between domains over the background and breaks within domains on guiding lines sheds light on possible origins of common DSA defects. The positional fluctuations of the PS/P2VP interface between domains showed a depth-dependent behavior, with high levels of fluctuations near both the free surface of the film and the substrate and lower fluctuation levels in the middle of the film. This research demonstrates how 3D characterization offers a better understanding of DSA processes, leading to better design and fabrication of directing templates.

Turning statistical physics models into materials design engines.

Despite the success statistical physics has enjoyed at predicting the properties of materials for given parameters, the inverse problem, identifying which material parameters produce given, desired properties, is only beginning to be addressed. Recently, several methods have emerged across disciplines that draw upon optimization and simulation to create computer programs that tailor material responses to specified behaviors. However, so far the methods developed either involve black-box techniques, in which the optimizer operates without explicit knowledge of the material's configuration space, or require carefully tuned algorithms with applicability limited to a narrow subclass of materials. Here we introduce a formalism that can generate optimizers automatically by extending statistical mechanics into the realm of design. The strength of this approach lies in its capability to transform statistical models that describe materials into optimizers to tailor them. By comparing against standard black-box optimization methods, we demonstrate how optimizers generated by this formalism can be faster and more effective, while remaining straightforward to implement. The scope of our approach includes possibilities for solving a variety of complex optimization and design problems concerning materials both in and out of equilibrium.

Molecular pathways for defect annihilation in directed self-assembly.

Over the last few years, the directed self-assembly of block copolymers by surface patterns has transitioned from academic curiosity to viable contender for commercial fabrication of next-generation nanocircuits by lithography. Recently, it has become apparent that kinetics, and not only thermodynamics, plays a key role for the ability of a polymeric material to self-assemble into a perfect, defect-free ordered state. Perfection, in this context, implies not more than one defect, with characteristic dimensions on the order of 5 nm, over a sample area as large as 100 cm(2). In this work, we identify the key pathways and the corresponding free energy barriers for eliminating defects, and we demonstrate that an extraordinarily large thermodynamic driving force is not necessarily sufficient for their removal. By adopting a concerted computational and experimental approach, we explain the molecular origins of these barriers and how they depend on material characteristics, and we propose strategies designed to overcome them. The validity of our conclusions for industrially relevant patterning processes is established by relying on instruments and assembly lines that are only available at state-of-the-art fabrication facilities, and, through this confluence of fundamental and applied research, we are able to discern the evolution of morphology at the smallest relevant length scales-a handful of nanometers-and present a view of defect annihilation in directed self-assembly at an unprecedented level of detail.

Simulation of Defect Reduction in Block Copolymer Thin Films by Solvent Annealing.

Solvent annealing provides an effective means to control the self-assembly of block copolymer (BCP) thin films. Multiple effects, including swelling, shrinkage, and morphological transitions, act in concert to yield ordered or disordered structures. The current understanding of these processes is limited; by relying on a theoretically informed coarse-grained model of block copolymers, a conceptual framework is presented that permits prediction and rationalization of experimentally observed behaviors. Through proper selection of several process conditions, it is shown that a narrow window of solvent pressures exists over which one can direct a BCP material to form well-ordered, defect-free structures.

Evolutionary Optimization of Directed Self-Assembly of Triblock Copolymers on Chemically Patterned Substrates.

Directed self-assembly of block copolymers on chemical patterns is of considerable interest for sublithographic patterning. The concept of pattern interpolation, in which a subset of features patterned on a substrate is multiplied through the inherent morphology of an ordered block copolymer, has enabled fabrication of extremely small, defect-free features over large areas. One of the central challenges in design of pattern interpolation strategies is that of identifying system characteristics leading to ideal, defect-free directed assembly. In this work we demonstrate how a coarse-grained many-body model of block copolymers, coupled to an evolutionary computation (EC) strategy, can be used to design and optimize substrate-copolymer combinations for use in lithographic patterning. The proposed approach is shown to be significantly more effective than traditional algorithms based on random searches, and its results are validated in the context of recent experimental observations. The coupled simulation-evolution method introduced here provides a general and efficient method for potential design of complex device-oriented structures.