Kinetics of pattern formation in symmetric diblock copolymer melts

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.

Symmetric Diblock Copolymers in Cylindrical Confinement: A Way to Chiral Morphologies?

We investigate the confinement-induced formation and stability of helix morphologies in lamella-forming AB diblock copolymers via large-scale, particle-based, single-chain-in-mean-field simulations. Such helix structures are rarely observed in bulk or thin films. Structure formation is induced by quenching incompatibility, χN, from a disordered morphology. If the surfaces of the cylindrical confinement do not prefer one component over the other, we observe that stacked lamellae, with their normals along the cylinder axis, are the preferred morphology. Kinetically, this morphology initially forms close to the cylinder surface, whereas the spontaneous, spinodal microphase separation in the cylinder's interior gives rise to a microemulsion-like morphology, riddled with defects and no directional order. Subsequently, the ordered morphology on the cylinder surface progresses inward, pervading the entire volume. In case that the cylindrical pore is only partially filled, the additional confinement along the cylinder axis generally gives rise to incommensurability between the equilibrium spacing of stacked lamellae and the cylinder height. To accommodate this mismatch, the lamella normals will tilt away from the cylinder axis and generate helices of lamellae on the surface of the cylinder. Again, this order progresses from the cylinder surface inward, generating a chiral morphology. Because the spacing between the internal AB interfaces decreases upon approaching the helix center, the concomitant stress results in a decrease in the number of lamellae and the formation of unique dislocation defects. This type of chiral defect morphology is reproducibly formed by the kinetics of structure formation in partly filled cylindrical pores with nonpreferential surfaces and may find applications in photonic applications.

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.

Temperature and initial composition dependence of pattern formation and dynamic behavior in phase separation under deep-quenched conditions

Phase separation of SCN-H2O ([CH2CN]2-H2O) transparent solutions is simulated in two dimensions and the effects of quenching temperature and initial composition on the pattern formation and dynamic behavior of the second phase are examined via Minkowski functionals. The simulation is based on model H where the molar free energy of the SCN-H2O solution is obtained by the CALPHAD approach. We find that the composition and temperature do not affect the exponent in the domain growth law, where the average domain size with time yields R(t)-t n . However, they influence the pattern formation and dynamic behavior of the second phase in phase separation. Lower temperature leads to a finer bicontinuous structure in spinodal decomposition and promotes the nucleation rate, which accelerates the phase separation and results in more liquid droplets with smaller size. As the initial composition diverges from the critical value, the spatial patterns change gradually from bicontinuous into a droplet-like structure. When the initial composition is closer to the critical value, for spinodal decomposition, the diffusion-driven growth lasts for a longer time and the average domain size of liquid droplets is larger. For nucleation-driven growth, in contrast, the single phase separates more quickly and the average size of liquid droplets is smaller.

Numerical algorithms for solving self-consistent field theory reversely for block copolymer systems

Besides dictating the equilibrium phase diagram, the rugged free-energy landscape of AB block copolymers gives rise to a multitude of non-equilibrium phenomena. Self-consistent field theory (SCFT) can be employed to calculate the mean-field free energy, F [ ϕ A t a r g e t ] , of a non-equilibrium unstable state that is characterized by a given spatial density distribution, ϕ A t a r g e t , in the incompressible system. Such a free-energy functional is the basis of describing the structure formation by dynamic SCFT techniques or the identification of minimum free-energy paths via the string method. The crucial step consists in computing the external potential fields that generate the given density distribution in the corresponding system of non-interacting copolymers, i.e., the potential-to-density relation employed in equilibrium SCFT calculations has to be inverted (reverse SCFT calculation). We describe, generalize, and evaluate the computational efficiency of two different numerical algorithms for this reverse SCFT calculation-the Debye-function algorithm based on the structure factor and the field-theoretic umbrella-potential (FUP) algorithm. In contrast to the Debye-function algorithm, the FUP algorithm only yields the exact mean-field values of the given target densities in the limit of a strong umbrella potential, and we devise a two-step variant of the FUP algorithm that significantly mitigates this issue. For Gaussian copolymers, the Debye-function algorithm is more efficient for highly unstable states that are far away from the equilibrium, whereas the improved FUP algorithm outperforms the Debye-function algorithm closer to metastable states and is easily transferred to more complex molecular architectures.