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 nextgeneration 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.directed self-assembly | copolymer | defect | minimum free energy path | string method O ver the last decade, the directed self-assembly (DSA) of block copolymers has rapidly evolved from mere intellectual curiosity (1-4) to a potentially crucial step in the commercial fabrication of next-generation electronic circuits. Indeed, the characteristic length scale of ordered self-assembled copolymer domains is in the range of 5-50 nm. Furthermore, their size and shape can be manipulated through simple processing steps, thereby making them attractive for the production of semiconductor devices, nanofluidic devices, or high-density storage media (5, 6). The general idea behind copolymer DSA is that a surface patternchemical or topographic-can be used to guide the assembly of a polymeric material into an ordered, device-like structure that is free of defects. In so-called "density multiplication" patterning strategies (7,8), the spacing or pitch of the surface features can be much larger than the characteristic dimensions of the copolymer of interest. One can thus prepare coarse surface patterns, which are easier to create, and rely on the copolymer to self-assemble into features whose density is considerably larger. Fig. 1 shows a schematic representation of the process for obtaining a lamellar morphology on a stripe-patterned substrate under a one-to-three (or 3X) density multiplication strategy. Patterned stripes interact preferentially with one of the blocks and guide the assembly of thin copolymer films into ordered lam...

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.

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.omputer programs that can design material properties have led to exciting, new directions for materials science (1-3). Computational methods have been used to predict crystal (4) and protein (5, 6) structures, yielding the toughest crystals known to mankind (4) and de novo protein configurations unseen in nature (5). Applied to polymers, Monte Carlo methods (7-9) and evolutionary algorithms (10, 11) have paved the way toward optimizing directed self-assembly. Similar methods have been used to identify the crystal structures of patchy, colloidal particles (12). For far-from-equilibrium systems like jammed, metastable aggregates of particles (3), simulation-based optimization has been successfully used to design bulk properties like stiffness (13) and packing density (14) by way of tuning complicated microscale features like particle shape.However, despite these successes, most of the existing methods work only for narrowly defined classes of materials: Optimization techniques that prove successful at designing one class of materials may struggle or fail on other systems. Thus, designing new materials can require a large investment in trial and error at the level of the algorithm itself, even if, for given parameters, the material's behavior can be simulated easily.In black-box approaches, the algorithm tunes the material by adjusting control parameters without considering the likelihood of finding the material in microscale configurations. Instead, the optimizer operates in some auxiliary space, defined outside the physical model, and remains ignorant of the statistics in the physical configuration space. On the other hand, for the overwhelming majority of materials, an accurate description of m...

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.

Directed assembly of block polymers is rapidly becoming a viable strategy for lithographic patterning of nanoscopic features. One of the key attributes of directed assembly is that an underlying chemical or topographic substrate pattern used to direct assembly need not exhibit a direct correspondence with the sought after block polymer morphology, and past work has largely relied on trial-and-error approaches to design appropriate patterns. In this work, a computational evolutionary strategy is proposed to solve this optimization problem. By combining the Cahn-Hilliard equation, which is used to find the equilibrium morphology, and the covariance-matrix evolutionary strategy, which is used to optimize the combined outcome of particular substrate-copolymer combinations, we arrive at an efficient method for design of substrates leading to non-trivial, desirable outcomes.