1,721,046 research outputs found
Monte Carlo Simulation of Coarse Grain Polymeric Systems
No full textWe introduce a particle-based Monte Carlo formalism for the study of polymeric melts, where the interaction energy is given by a local density functional, as is done in traditional field-theoretic models. The method enables Monte Carlo simulations in arbitrary ensembles and direct calculation of free energies. We present results for the phase diagram and the critical point of a binary homopolymer blend. For a symmetric diblock copolymer, we compute the distribution of local stress in lamellae and locate the order-disorder transition
Defect Removal in the Course of Directed Self-Assembly is Facilitated in the Vicinity of the Order-Disorder Transition
No full textThe stability of prototypical defect morphologies in thin films of symmetric diblock copolymers on chemically patterned substrates is investigated by self-consistent field theory. The excess free energy of defects and barriers of defect-removal mechanisms are obtained by computing the minimum free-energy path. Distinct defect-removal mechanisms are illustrated demonstrating that (i) defects will become unstable at a characteristic value of incompatibility chi N- above the order-disorder transition and (ii) the kinetics is accelerated at weak segregation. Numerical findings are placed in the context of physical mechanisms, and implications for directed self-assembly are discussed
Simulations of theoretically informed coarse grain models of polymeric systems
No full textSimulations of theoretically informed coarse grain models, where the interaction energy is given by a functional of the local density, are discussed in the context of polymeric melts. Two different implementations are presented by addressing two examples. The first relies on a grid-based representation of non-bonded interactions and focuses on the concept of density multiplication in block copolymer lithography. Monte Carlo simulations are used in a high-throughput manner to explore the parameter space, and to identify morphologies amenable to lithographic fabrication. In the second example, which focuses on the order disorder transition of block copolymers, the constraints imposed by a grid are removed, thereby enabling simulations in arbitrary ensembles and direct calculation of local stresses and free energies
Morphology of multi-component polymer systems: single chain in mean field simulation studies
No full textRecent work exploring phase separation and self-assembly in multicomponent polymer fluids using a particle-based self-consistent field simulation method is reviewed. The computational method is placed in the context of classical molecular dynamics and Monte Carlo simulations as well as field-theoretic approaches. Its potential is illustrated by applications ranging from spinodal decomposition in symmetric polymer blends and the ordering of diblock copolymers in the bulk to more complex phenomena such as solvent evaporation from thin polymer films and the fabrication of three-dimensional bicontinuous diblock copolymer morphologies via reconstruction on patterned substrates
Free Energy of Defects in Ordered Assemblies of Block Copolymer Domains
No full textWe investigate commonly occurring defects in block copolymer thin films asembled on chemically nanopatterned substrates. and predict their probability of occurence by computing their free energies. A theoretically informed 3D coarse. grain model is used to describe the system. These defects substrate increases and when partial defects occur close to the top surface of the flim. The results presented defects. here reveal an extraordinarily large thermodynamic driving force for the elimination of defects. When the characteristics of the substrate are commensurate with the morphology of the block copolymer, the probability of creating a defect is extremely small and well below the specifications of the semiconductor industry for fabrication of features having characteristic dimensions on the scale of nanometers. We also investigate how the occurrence of defect change's when imperfections arise in the underlysing patterns and find that, while defects continue to be remarkably unstable, stretched patterns are more permissive than compressed patterns
Dimensions and shapes of block copolymer domains assembled on lithographically defined chemically patterned substrates
No full textThin films of a nearly symmetric lamellae-forming diblock copolymer of poly(styrene-b-methyl methacrylate) (PS-b-PMMA) having a bulk repeat period, L-O, were directed to assemble vertically away from chemically nanopatterned striped substrates (having a periodicity L-S) that consisted of alternating stripes that were preferentially wet by the two blocks of the copolymer. The relative widths of the adjacent stripes were systematically varied such that the normalized line width of the chemical surface pattern, defined as the width of the stripe that was wet by the styrene block of the block copolymer, W, divided by the constant chemical surface pattern period, L-s had values between 0.30 and 0.65. On chemical surface patterns with L-S approximate to L-O the diblock copolymer domains formed defect-free perpendicular arrays if the normalized line width W/L-S, was between 0.36 and 0.63. On chemical surface patterns with L-S not equal L-O, the range of W/L-S capable of inducing defect free arrays decreased as the difference between L-S and L-O increased. Single-chain-in-mean-field (SCMF) simulations provided information on the dimensions and shapes of the block copolymer domains. The SCMF simulations indicated that the widths of the lamellae at half film thickness were 0.47L(S) independent of W/L-S and the angle of the interface between the vertically oriented domains remained within 11 degrees of the substrate normal over the range of experimentally relevant values of W/L-S
Directed copolymer assembly on chemical substrate patterns: A phenomenological and single-chain-in-mean-field simulations study of the influence of roughness in the substrate pattern
No full textThe directed assembly of lamella-forming copolymer systems on substrates chemically patterned with rough stripes has been studied using a Helfrich-type, phenomenological theory and Single-Chain-in-Mean-Field (SCMF) simulations. The stripe period matches that of the lamellar spacing in the bulk. The effect of the line edge roughness (LER) of the substrate pattern on the microphase-separated morphology was investigated considering two generic types of substrate LER with a single characteristic wavelength imposed on the edges of the stripes: undulation and peristaltic LER. In both cases, the domain interfaces are pinned to the rough stripe boundary at the substrate and, thus, are deformed. We study how this deformation decays as a function of the distance from the substrate. The simple theory and the SCMF simulations demonstrate that one of the basic factors determining the decay of the roughness transferred into the self-assembled morphology is the characteristic LER wavelength of the substrate pattern; i.e., the distance over which the roughness propagates away from the substrate increases with wavelength. However, both approaches reveal that, for a quantitative understanding of the consequences of substrate LER, it is important to consider the interplay of the pattern wavelength with the other characteristic length scales of the system, such as the film thickness and the bulk lamellar spacing. For instance, in thin films, the induced deformation of the lamellar interface decays slower with distance from the patterned surface than in thicker films. It is shown that the phenomenological theory can capture many of the same qualitative results as the SCMF simulations for copolymer assembly on substrate patterns with LER, but, at the same time, is limited by an incomplete description of the constraints on the polymer chain conformations imposed by the substrate
Remediation of Line Edge Roughness in Chemical Nanopatterns by the Directed Assembly of Overlying Block Copolymer Films
No full textBlock copolymer Structures have been directed to assemble oil chemically patterned surfaces with the domain interfaces oriented perpendicular to the substrate. Such methods have been pursued for lithographic applications to achieve long-range order in the assembled structures and, potentially more important, provide nanometer-level control over the interfaces between Structures. The chemically striped surfaces used for the directed assembly of lamellae are patterned by top-down lithographic techniques and thus often have rough edges between the regions of different chemistry. Here we quantitatively characterize, using experiments and molecular-level simulations, the propagation of line edge roughness from the chemically patterned surfaces into the interfaces between domains of block copolymer lamellae as a function of the wavelength, amplitude, and geometry of the roughness. Two geometries of surface pattern roughness are considered with oscillatory neighboring interfaces that are either in-phase or out-of-phase. Block copolymer lamellae of poly(styrene-b/ock-methyl methacrylate) effectively self-corrected surface patterns with small wavelength in-phase and out-of-phase roughness such that little or no memory of the Substrate pattern roughness could be observed at the top surface of a 40 nm thin film. Larger wavelength in-phase roughness, and to a lesser extent larger wavelength out-of-phase roughness, propagated farther from the surface pattern such that the domain interfaces between block copolymer lamellae maintained the roughness throughout the film. These self-healing capabilities of block copolymers will be essential for lithographic applications with tight tolerances on line edge roughness and line width control, e.g., in patterning transistor gates
Directed Assembly of Non-equilibrium ABA Triblock Copolymer Morphologies on Nanopatterned Substrates
No full textThe majority of past work on directed assembly of block copolymers on chemically nanopatterned surfaces (or chemical patterns) has focused on AB diblock copolymers, and the resulting morphologies have generally corresponded to equilibrium states. Here we report a study on directed assembly of ABA triblock copolymers. Directed assembly of thin films of symmetric poly(methyl methacrylate-b-styrene-b-methyl methacrylate) (PMMA-b-PS-b-PMMA) triblock copolymers is shown to be capable of achieving a high degree of perfection, registration, and accuracy on striped patterns having periods, L-s,L- commensurate with the bulk period of the copolymer, L-o. When L-s is incommensurate with L-o, the triblock copolymer domains can reach dimensions up to 55% larger or 13% smaller than L-o. The range over which triblock copolymers tolerate departures from a commensurate L-s is significantly larger than that accessible with the corresponding diblock copolymer material on analogous directed assembly systems. The assembly kinetics of the triblock copolymer is approximately 3 orders of magnitude slower than observed in the diblock system. Theoretically informed simulations are used to interpret our experimental observations; a thermodynamic analysis reveals that triblocks can form highly ordered, non-equilibrium metastable structures that do not arise in the diblock
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