Gurdaman S. Khaira

Molecular pathways for defect annihilation in directed self-assembly

Significance A molecular model is used to calculate the free energy of formation of ordered and disordered copolymer morphologies. We rely on advanced methodologies to identify the minimum free energy pathways that connect such states of the material. Our predictions for defect formation and annealing are compared with experimental observations. Our results provide a detailed molecular view of isolated block copolymer defects, which measure approximately 5 nm and represent isolated events in large areas. They are true “needles in the hay stack” that can only be studied by concerted molecular simulations and dedicated access to production-level fabrication tools. We show that defect annealing is an activated process, where defects are eliminated by operating near the order−disorder transition. 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 cm2. 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.

Evolutionary pattern design for copolymer directed self-assembly

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.

Turning statistical physics models into materials design engines

Significance A fundamental tenet of science is that the properties of a material are intimately linked to the nature of the constituent components. Although there are powerful methods to predict such properties for given components, a key challenge for materials design is the inverse process: identifying the required components and their structural configuration for given target properties. This paper presents a new approach to this challenge. A formalism is introduced that generates algorithms for materials design both under equilibrium and under nonequilibrium conditions and operates without the need for user input beyond a design goal. This formalism is broadly applicable, fast, and robust, and it provides a powerful tool for materials optimization as well as discovery. 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.

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.

Physical verification and manufacturing of contact/via layers using grapho-epitaxy DSA processes

This paper extends the state of the art by describing the practical material’s challenges, as well as approaches to minimize their impact in the manufacture of contact/via layers using a grapho-epitaxy directed self assembly (DSA) process. Three full designs have been analyzed from the point of view of layout constructs. A construct is an atomic and repetitive section of the layout which can be analyzed in isolation. Results indicate that DSA’s main benefit is its ability to be resilient to the shape of the guiding pattern across process window. The results suggest that directed self assembly can still be guaranteed even with high distortion of the guiding patterns when the guiding patterns have been designed properly for the target process. Focusing on a 14nm process based on 193i lithography, we present evidence of the need of DSA compliance methods and mask synthesis tools which consider pattern dependencies of adjacent structures a few microns away. Finally, an outlook as to the guidelines and challenges to DSA copolymer mixtures and process are discussed highlighting the benefits of mixtures of homo polymer and diblock copolymer to reduce the number of defects of arbitrarily placed hole configurations.