Thermodynamics and Kinetics of Defect Motion and Annihilation in the Self-Assembly of Lamellar Diblock Copolymers

Droplet-like Defect Annihilation Mechanisms in Hexagonal Cylinder-Forming Block Copolymers

The annihilation of typical individual defects in hexagonal cylinder-forming block copolymers is investigated using the self-consistent field theory (SCFT) in conjunction with the string method. Usually, defect removal in two-dimensional hexagonal patterns involves reorganizing the cylindrical domains. Unlike atoms in solid crystals, the self-assembled cylindrical domains of block copolymers are "soft". Thus, the kinetic motions of the cylindrical domains resemble liquid droplets. Dislocations in hexagonal patterns are eliminated via creating and removing cylindrical domains. Our results show that new cylindrical domains are created via either a nucleation-like process or a fission-like process, whereas excessive domains are eliminated via a fusion-like or evaporation-like process. For weakly segregated block copolymers, the nucleation-like and evaporation-like processes are preferred.

Field-theoretic simulations beyond δ-interactions: Overcoming the inverse potential problem in auxiliary field models

Modern field-theoretic simulations of complex fluids and polymers are constructed around a particle-to-field transformation that brings an inverse potential u^-1 in the model equations. This has restricted the application of the framework to systems characterized by relatively simple pairwise interatomic interactions; for example, excluded volume effects are treated through the use of δ-function interactions. In this study, we first review available nonbonded pair interactions in field-theoretic models and propose a classification. Then, we outline the inverse potential problem and present an alternative approach on the basis of a saddle-point approximation, enabling the use of a richer set of pair interaction functions. We test our approach by using as an example the Morse potential, which finds extensive applications in particle-based simulations, and we calibrate u^-1 with results from a molecular dynamics simulation. The u^-1 thus obtained is consistent with the field-theoretic model equations, and when used in stand-alone self-consistent field simulations, it produces the correct fluid structure starting from a random initial state of the density field.

Solvent Vapor Annealing, Defect Analysis, and Optimization of Self-Assembly of Block Copolymers Using Machine Learning Approaches

Self-assembly of block copolymers (BCPs) is an alternative patterning technique that promises high resolution and density multiplication with lower costs. The defectivity of the resulting nanopatterns remains too high for many applications in microelectronics and is exacerbated by small variations of processing parameters, such as film thickness, and fluctuations of solvent vapor pressure and temperature, among others. In this work, a solvent vapor annealing (SVA) flow-controlled system is combined with design of experiments (DOE) and machine learning (ML) approaches. The SVA flow-controlled system enables precise optimization of the conditions of self-assembly of the high Flory-Huggins interaction parameter (χ) hexagonal dot-array forming BCP, poly(styrene-b-dimethylsiloxane) (PS-b-PDMS). The defects within the resulting patterns at various length scales are then characterized and quantified. The results show that the defectivity of the resulting nanopatterned surfaces is highly dependent upon very small variations of the initial film thicknesses of the BCP, as well as the degree of swelling under the SVA conditions. These parameters also significantly contribute to the quality of the resulting pattern with respect to grain coarsening, as well as the formation of different macroscale phases (single and double layers and wetting layers). The results of qualitative and quantitative defect analyses are then compiled into a single figure of merit (FOM) and are mapped across the experimental parameter space using ML approaches, which enable the identification of the narrow region of optimum conditions for SVA for a given BCP. The result of these analyses is a faster and less resource intensive route toward the production of low-defectivity BCP dot arrays via rational determination of the ideal combination of processing factors. The DOE and machine learning-enabled approach is generalizable to the scale-up of self-assembly-based nanopatterning for applications in electronic microfabrication.

Understanding Kinetics of Defect Annihilation in Chemoepitaxy-Directed Self-Assembly

Directed self-assembly (DSA) of block copolymers (BCP) has attracted considerable interest from the semiconductor industry because it can achieve semiconductor-relevant structures with a relatively simple process and low cost. However, the self-assembling structures can become kinetically trapped into defective states, which greatly impedes the implementation of DSA in high-volume manufacturing. Understanding the kinetics of defect annihilation is crucial to optimizing the process and eventually eliminating defects in DSA. Such kinetic experiments, however, are not commonly available in academic laboratories. To address this challenge, we perform a kinetic study of chemoepitaxy DSA in a 300 mm wafer fab, where the complete defectivity information at various annealing conditions can be readily captured. Through extensive statistical analysis, we reveal the statistical model of defect annihilation in DSA for the first time. The annihilation kinetics can be well described by a power law model, indicating that all dislocations can be removed by sufficiently long annealing time. We further develop image analysis algorithms to analyze the distribution of dislocation size and configurations and discover that the distribution stays relatively constant over time. The defect distribution is determined by the role of the guiding stripe, which is found to stabilize the defects. Although this study is based on polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA), we anticipate that these findings can be readily applied to other BCP platforms as well.

Lithographically Defined Cross-Linkable Top Coats for Nanomanufacturing with High-χ Block Copolymers

The directed self-assembly (DSA) of block copolymers (BCPs) is a powerful method for the manufacture of high-resolution features. Critical issues remain to be addressed for successful implementation of DSA, such as dewetting and controlled orientation of BCP domains through physicochemical manipulations at the BCP interfaces, and the spatial positioning and registration of the BCP features. Here, we introduce novel top-coat (TC) materials designed to undergo cross-linking reactions triggered by thermal or photoactivation processes. The cross-linked TC layer with adjusted composition induces a mechanical confinement of the BCP layer, suppressing its dewetting while promoting perpendicular orientation of BCP domains. The selection of areas of interest with perpendicular features is performed directly on the patternable TC layer via a lithography step and leverages attractive integration pathways for the generation of locally controlled BCP patterns and nanostructured BCP multilayers.

Thermodynamics and ordering kinetics in asymmetric PS-b-PMMA block copolymer thin films

The ordering kinetics of standing cylinder-forming polystyrene-block-poly(methyl methacrylate) block copolymers (molecular weight: 39 kg mol^-1) close to the order-disorder transition is experimentally investigated following the temporal evolution of the correlation length at different annealing temperatures. The growth exponent of the grain-coarsening process is determined to be 1/2, signature of a curvature-driven ordering mechanism. The measured activation enthalpy and the resulting Meyer-Neldel temperature for this specific copolymer along with the data already known for PS-b-PMMA block copolymers in strong segregation limit allow investigation of the interplay between the ordering kinetics and the thermodynamic driving force during the grain coarsening. These findings unveil various phenomena concomitantly occurring during the thermally activated ordering kinetics at segmental, single chain, and collective levels.

Role of Defects in Achieving Highly Asymmetric Lamellar Self-Assembly in Block Copolymer/Homopolymer Blends

Lamellar structure is a prominent state in soft condensed matter. Swelling lamellar layers to highly asymmetric structures by a second component is a facile, cost-effective strategy to impart materials with adaptive size and tunable properties. One key question that remains unsolved is how defects form and affect the asymmetric lamellar order. This study unravels the role of defects by swelling a miktoarm block copolymer with a homopolymer. Ordered lamellae first lose translational order by a significant increase in the number of dislocations and then lose orientational order by the generation of disclinations. The homopolymers are not uniformly distributed in defective lamellae and primarily segregate in the vicinity of disclination cores. The free energy of defects is mainly contributed by molecular splay and significantly alleviated by an increased radius of local curvature. This study provides direct evidence to reveal the role of defects and lamellar order in block copolymer/homopolymer blends and also sheds light on understanding analogous structural transitions in other soft systems, including lyotropic liquid crystals, phospholipid membranes, and polymer nanocomposites.

Strategies for Increasing the Rate of Defect Annihilation in the Directed Self-Assembly of High-χ Block Copolymers

Directed self-assembly (DSA) of high-χ block copolymer thin films is a promising approach for nanofabrication of features with length scale below 10 nm. Recent work has highlighted that kinetics are of crucial importance in determining whether a block copolymer film can self-assemble into a defect-free ordered state. In this work, different strategies for improving the rate of defect annihilation in the DSA of a silicon-containing, high-χ block copolymer film were explored. Chemo-epitaxial DSA of poly(4-methoxystyrene-block-4-trimethylsilylstyrene) with 5× density multiplication was implemented on 300 mm wafers by using production level nanofabrication tools, and the influence of different processes and material parameters on dislocation defect density was studied. It was observed that only at sufficiently low χN can the block copolymer assemble into well-aligned patterns within a practical time frame. In addition, there is a clear correlation between the rate of the lamellar grain coarsening in unguided self-assembly and the rate of dislocation annihilation in DSA. For a fixed chemical pattern, the density of kinetically trapped dislocation defects can be predicted by measuring the correlation length of the unguided self-assembly under the same process conditions. This learning enables more efficient screening of block copolymers and annealing conditions by rapid analysis of block copolymer films that were allowed to self-assemble into unguided (commonly termed fingerprint) patterns.

Direct Imaging of Interfacial Fluctuations in Confined Block Copolymer with in Situ Slow-Scan-Disabled Atomic Force Microscopy

Using environmentally controlled, high-speed atomic force microscopy (AFM), we examine dynamic fluctuations of topographically confined poly(styrene-block-methyl methacrylate) (PS-b-PMMA) cylinders. During thermal annealing, fluctuations drive perturbations of the block copolymer (BCP) interface between polymer domains, leading to pattern roughness. Whereas previous investigations have examined roughness in room-temperature and kinetically quenched samples, we directly visualize the dynamics of PS/PMMA interfaces in real space and time at in situ temperatures above the glass transition temperature, T_g. Imaging under these experimentally challenging thermal annealing conditions is critical to understanding the inherent connection between thermal fluctuations and BCP pattern assembly. Through the use of slow-scan-disabled AFM, we dramatically improve the imaging time resolution for tracking polymer dynamics. Fluctuations increase in intensity with temperature and, at high temperatures, become spatially coherent across their confining potential. Additionally, we observe that topographic confinement suppresses fluctuations and correlations in the proximity of the guiding field. In situ imaging at annealing temperatures represents a significant step in capturing the dynamics of chain mobility at BCP interfaces.

Hybrid line-dot nanopatterns from directed self-assembly of diblock copolymers by trenches

We demonstrate that the directed self-assembly of AB diblock copolymers by periodic trenches can be used to fabricate large-scale ordered hybrid line-dot nanopatterns in addition to a defect-free dot nanopattern. The formation of line or dot nanopatterns in thin films with proper surface affinities is controlled by the film thickness, which is modulated by a topographic pattern consisting of steps and trenches. Two kinds of line-dot nanopatterns are achieved with cylinder-forming and sphere-forming copolymers, respectively. One kind of hybrid nanopatterns is composed of perpendicularly standing cylinders (dots) on the steps and parallel monolayer cylinders (lines) within the trenches, while the dots of the other kind are replaced by monolayer spheres on the steps. The thermodynamic stability region of target hybrid nanopatterns is identified by constructing two-dimensional phase diagrams with respect to two control parameters of step height and film thickness using self-consistent field theory. Furthermore, a process window of the line-dot nanopatterns is estimated using cell dynamics simulations based on time-dependent Ginzburg-Landau theory, confirming their feasibility in kinetics.

Defect Annihilation Pathways in Directed Assembly of Lamellar Block Copolymer Thin Films

Defects in highly ordered self-assembled block copolymers represent an important roadblock toward the adoption of these materials in a wide range of applications. This work examines the pathways for annihilation of defects in symmetric diblock copolymers in the context of directed assembly using patterned substrates. Past theoretical and computational studies of such systems have predicted minimum free energy pathways that are characteristic of an activated process. However, they have been limited to adjacent dislocations with opposite Burgers vectors. By relying on a combination of advanced sampling techniques and particle-based simulations, this work considers the long-range interaction between dislocation pairs, both on homogeneous and nanopatterned substrates. As illustrated here, these interactions are central to understanding the defect structures that are most commonly found in applications and in experimental studies of directed self-assembly. More specifically, it is shown that, for dislocation dipoles separated by several lamellae, multiple consecutive free energy barriers lead to effective kinetic barriers that are an order of magnitude larger than those originally reported in the literature for tightly bound dislocation pairs. It is also shown that annihilation pathways depend strongly on both the separation between dislocations and their relative position with respect to the substrate guiding stripes used to direct the assembly.

Straight motion of half-integer topological defects in thin Fe-N magnetic films with stripe domains

In thin magnetic films with perpendicular magnetic anisotropy, a periodic “up-down” stripe-domain structure can be originated at remanence, on a mesoscopic scale (~100 nm) comparable with film thickness, by the competition between short-range exchange coupling and long-range dipolar interaction. However, translational order is perturbed because magnetic edge dislocations are spontaneously nucleated. Such topological defects play an important role in magnetic films since they promote the in-plane magnetization reversal of stripes and, in superconductor/ferromagnet hybrids, the creation of superconducting vortex clusters. Combining magnetic force microscopy experiments and micromagnetic simulations, we investigated the motion of two classes of magnetic edge dislocations, randomly distributed in an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{N}}}_{2}^{+}$$\end{document}N2+-implanted Fe film. They were found to move in opposite directions along straight trajectories parallel to the stripes axis, when driven by a moderate dc magnetic field. Using the approximate Thiele equation, analytical expressions for the forces acting on such magnetic defects and a microscopic explanation for the direction of their motion could be obtained. Straight trajectories are related to the presence of a periodic stripe domain pattern, which imposes the gyrotropic force to vanish even if a nonzero, half-integer topological charge is carried by the defects in some layers across the film thickness.

Real-Time Atomic Force Microscopy Imaging of Block Copolymer Directed Self Assembly

The kinetics of directed self-assembly of symmetric PS-b-PMMA diblock copolymer on chemically patterned templates were measured during in situ thermal annealing. Although these chemical guide patterns lead to well-aligned, defect-free lamellar patterns at thermodynamic equilibrium, in practice, challenges remain in understanding and optimizing the kinetic evolution for technological applications. High-speed, environmentally controlled atomic force microscopy imaging was used to track pattern evolution on the time scale of individual microdomain connections in real space and time, allowing the direct visualization of defect healing mechanisms. When we apply this highly general technique to films on chemically patterned substrates, we find that pattern alignment is mediated by a metastable nonbulk morphology unique to these samples, referred to as the "stitch" morphology. We observe diverse and anisotropic mechanisms for the conversion from this morphology to equilibrium lamellar stripes. Directed self-assembly on chemical templates is observed to follow exponential kinetics with an apparent energetic barrier of 360 ± 80 kJ/mol from 210-230 °C, a significant enhancement when compared with ordering rates on unpatterned substrates. Ultimately, from local imaging, we find that the presence of a chemical guiding field causes morphological ordering and lamellar alignment to occur irreversibly.

Minimum free-energy paths for the self-organization of polymer brushes

A methodology to calculate minimum free-energy paths based on the combination of a molecular theory and the improved string method is introduced and applied to study the self-organization of polymer brushes under poor solvent conditions. Polymer brushes in a poor solvent cannot undergo macroscopic phase separation due to the physical constraint imposed by the grafting points; therefore, they microphase separate forming aggregates. Under some conditions, the theory predicts that the homogeneous brush and the aggregates can exist as two different minima of the free energy. The theoretical methodology introduced in this work allows us to predict the minimum free-energy path connecting these two minima as well as the morphology of the system along the path. It is shown that the transition between the homogeneous brush and the aggregates may involve a free-energy barrier or be barrierless depending on the relative stability of the two morphologies and the chain length and grafting density of the polymer. In the case where a free-energy barrier exists, one of the morphologies is a metastable structure and, therefore, the properties of the brush as the quality of the solvent is cycled are expected to display hysteresis. The theory is also applied to study the adhesion/deadhesion transition between two opposing surfaces modified by identical polymer brushes and it is shown that this process may also require surpassing a free-energy barrier.

Non-native three-dimensional block copolymer morphologies

Self-assembly is a powerful paradigm, wherein molecules spontaneously form ordered phases exhibiting well-defined nanoscale periodicity and shapes. However, the inherent energy-minimization aspect of self-assembly yields a very limited set of morphologies, such as lamellae or hexagonally packed cylinders. Here, we show how soft self-assembling materials-block copolymer thin films-can be manipulated to form a diverse library of previously unreported morphologies. In this iterative assembly process, each polymer layer acts as both a structural component of the final morphology and a template for directing the order of subsequent layers. Specifically, block copolymer films are immobilized on surfaces, and template successive layers through subtle surface topography. This strategy generates an enormous variety of three-dimensional morphologies that are absent in the native block copolymer phase diagram.