Su-Mi Hur

Spectral collocation methods for polymer brushes

We provide an in-depth study of pseudo-spectral numerical methods associated with modeling the self-assembly of molten mixed polymer brushes in the framework of self-consistent field theory (SCFT). SCFT of molten polymer brushes has proved numerically challenging in the past because of sharp features that arise in the self-consistent pressure field at the grafting surface due to the chain end tethering constraint. We show that this pressure anomaly can be reduced by smearing the grafting points over a narrow zone normal to the surface in an incompressible model, and/or by switching to a compressible model for the molten brush. In both cases, we use results obtained from a source (delta function) distribution of grafting points as a reference. At the grafting surface, we consider both Neumann and Dirichlet conditions, where the latter is paired with a masking method to mimic a confining surface. When only the density profiles and relative free energies of two comparison phases are of interest, either source or smeared distributions of grafting points can be used, but a smeared distribution of grafting points exhibits faster convergence with respect to the number of chain contour steps. Absolute free energies converge only within the smeared model. In addition, when a sine basis is used with the masking method and a smeared distribution, fewer iterations are necessary to converge the SCFT fields for the compressible model. The numerical methods described here and investigated in one-dimension will provide an enabling platform for computationally more demanding three-dimensional SCFT studies of a broad range of mixed polymer brush systems.

The hole shrink problem: Theoretical studies of directed self-assembly in cylindrical confinement

We use self-consistent field theory (SCFT) to study the self-assembly of cylinder-forming diblock copolymers confined in a cylindrical prepattern. This situation arises in contact holes -the hole shrink problem- where the goal is to produce a cylindrical hole with reduced dimensions relative to a guiding prepattern. In this study, we focus on systems with a critical dimension (CD) ranging from 50nm to 100nm and which consequently lead to the formation of a single cylinder in the middle of the hole. We found that different morphologies arise from the self-assembly process and are strongly governed by the prepattern dimensions, wetting conditions as well as the polymer molecular weight. We also considered blends of diblock copolymers and homopolymers and determined optimal blending configurations that not only favor the formation of the desired cylindrical morphology but also extend the processing window relative to the pure diblock case.

Self-consistent field simulations of self- and directed-assembly in a mixed polymer brush

While self-assembling block copolymer thin films have attracted attention as a promising high resolution lithographic tool, the self assembly of mixed polymer brushes for lithography is relatively unexplored. Here we study the directed self-assembly of a mixed polymer brush using self-consistent field theory (SCFT) simulations. Using the model equations and numerical methods introduced and verified in our previous study, the bulk phase behavior of a mixed melt brush is studied in depth through full three dimensional calculations. We assume that the mixed A/B polymer chains, which are of the same length, are exposed to a neutral top surface and are uniformly grafted at a high density. We identify phase-separated morphologies and calculate a phase diagram for the mixed brush under melt conditions as a function of the segregation force and composition. The observed lateral microphase separation is similar to that in block copolymer thin films, but the phase separation occurs at a smaller segregation force and the transition between cylindrical and spherical morphologies are quite different than the first-order phase transition in block copolymers. We demonstrate that lateral confinement can induce long-range, in-plane order in mixed brushes and suggest promising directed self-assembly methods for the application of self-assembled mixed polymer brushes in next-generation information storage and electronic devices.

Self-consistent field theory of directed self-assembly in laterally confined lamellae-forming diblock copolymers

We use Self-Consistent Field Theory (SCFT) to study the directed self-assembly of laterally confined diblock copolymers. In this study, we focus on systems where the self-assembled lamellae are oriented parallel to the selective sidewalls of the channel. While well-ordered, perfect lamellae are observed both experimentally and numerically, undesirable defective structures also emerge. We therefore investigate the energetics of two isolated defects, dislocations and disclinations, for various chain lengths and channel dimensions and establish conditions that favor the formation of defects. We also determine the energy barrier and the transition path between the defective and perfect state using the string method.

Self-assembly in a mixed polymer brush with inhomogeneous grafting density composition

While theoretical and numerical studies have shown the possibility of obtaining long-range ordering from the self-assembly of A–B binary mixed brushes similar to diblock copolymer thin films, such ordered patterns are not currently obtainable experimentally. In addition, most experimental observations of mixed brushes show relatively short range order with many defective structures. One explanation for poor microdomain ordering in experimental mixed brushes is a strong correlation between the spatial distribution of the grafting points and the self-assembly. To investigate this relationship in detail, we use self-consistent field theory (SCFT) simulations to study the phase-separated morphologies of melt mixed brushes with spatially varying grafting density compositions. Variations in the grafting density composition are implemented by modulating the grafting chain end distribution function to locally control the ratio of A and B chains attached to the surface, while maintaining uniform total grafting density. Three different types of grafting density composition variations are investigated: a linear ramping of the grafting density composition, deterministic sinusoidal variations, and random fluctuations with various correlation lengths and strengths. The resulting patterns in the micro-phase separated brush are seen to depend sensitively on both the wavelengths and amplitudes of the imposed grafting density fluctuations.

Field-based simulations of directed self-assembly in a mixed brush system

Self-assembling block copolymer thin films have attracted considerable attention as a promising high resolution lithographic tool due to the 10 nm scale of microdomain ordering and their facility for modulation of size and pattern. However, for block copolymer lithography to be a viable solution for advanced nano-lithographic technologies, several critical requirements need to be satisfied. Our research has focused on developing complementary mixed polymer brush lithography tools satisfying the required criteria, by means of Self-Consistent Field Theory (SCFT) simulations. Specifically, we have concentrated on graphoepitaxial techniques that are widely tested and considered a particularly promising method for controlling the microdomain ordering.