Period L0 Research Articles

Disclosing Topographical and Chemical Patterns in Confined Films of High-Molecular-Weight Block Copolymers under Controlled Solvothermal Annealing.

The microphase separation of high-molecular-weight block copolymers into nanostructured films is strongly dependent on the surface fields. Both, the chain mobility and the effective interaction parameters can lead to deviations from the bulk morphologies in the structures adjacent to the substrate. Resolving frustrated morphologies with domain period L0 above 100 nm is an experimental challenge. Here, solvothermal annealing was used to assess the contribution of elevated temperatures of the vapor Tv and of the substrate Ts on the evolution of the microphase-separated structures in thin films symmetric of polystyrene-b-poly(2vinylpyridine) block copolymer (PS-PVP) with L0 about 120 nm. Pronounced topographic mesh-like and stripe patterns develop on a time scale of min and are attributed to the perforated lamella (PL) and up-standing lamella phases. By setting Tv/Ts combinations it is possible to tune the sizes of the resulting PL patterns by almost 10%. Resolving chemical periodicity using selective metallization of the structures revealed multiplication of the topographic stripes, i.e., complex segregation of the component within the topographic pattern, presumably as a result of morphological phase transition from initial non-equilibrium spherical morphology. Reported results reveal approaches to tune the topographical and chemical periodicity of microphase separation of high-molecular-weight block copolymers under strong confinement, which is essential for exploiting these structures as functional templates.

In Situ Grazing-Incidence SAXS Investigation of Thermal-Induced Self-Assembly Process of PS-b-PMMA Films Deposited on Surface-Modified Substrate.

Directed self-assembly of block copolymers (BCPs) is widely investigated for its potential application in surface patterning. The self-assembly kinetics of BCP based on modified layers is the key to realizing structural control for obtaining highly ordered lamellar grains. In this study, morphological evolution of PS-b-PMMA films during the thermal-induced self-assembly process was investigated via the in situ grazing-incidence small-angle X-ray scattering (GISAXS) technique. In the first heating stage, reorientation of lamellar grains occurred as the temperature increased above the glass transition temperature. Then, a fast increase in the lamellar repeat period L0 was observed, which is considered as a phase separation process. Whereas the size of the lamellar grain ξ was observed to have rapidly increased in the stage wherein the temperature was held at 230 °C, the L0 was almost constant. This result indicates that the formation of ordered structure in PS-b-PMMA films was mainly determined by two periods: phase separation of block molecules followed by growth of grains in the nanodomain. In addition, it was interesting that the better-order nanodomains were obtained with thermal annealing at a faster heating rate. These findings suggest that accomplishing ordered structure control in a large area could be realized via the design of a proper heating profile.

Lattice self-consistent field calculations of confined symmetric block copolymers of various chain architectures.

The effects of chain architecture and confinement on the structure and orientation of lamellae formed by incompressible and symmetric AB-type block copolymer melts confined between two parallel and identical surfaces are investigated using self-consistent field calculations on a simple cubic lattice. Five systems of various chain architectures (linear, ring, and star) and lengths are studied, with their bulk lamellar period L0 chosen such that they have comparable L0/Rg, where Rg denotes the ideal-chain radius of gyration. For thin films of thickness D = L0 confined between two neutral surfaces, we define the rescaled volume fraction profiles of A, B, chain end, and joint segments in the parallel and perpendicular lamellae such that these profiles can be directly compared among the five systems to quantitatively reveal the interplay between the chain-end enrichment near confining surfaces and the surface-induced A-B compatibilization, and how such interplay is affected by the chain architectures (for example, the chain-crowding effects in the star block copolymers). The effects of D and surface preference for one of the blocks are also investigated.

Semicrystalline Block Copolymers in Rigid Confining Nanopores.

We have investigated PLLA crystallization in lamellae-forming PS-b-PLLA confined to straight cylindrical nanopores under weak confinement (nanopore diameter D/equilibrium PS-b-PLLA period L0 ≥ 4.8). Molten PS-b-PLLA predominantly forms concentric lamellae along the nanopores, but intertwined helices occur even for D/L0 ≈ 7.3. Quenching PS-b-PLLA melts below TG(PS) results in PLLA cold crystallization strictly confined by the vitrified PS domains. Above TG(PS), PLLA crystallization is templated by the PS-b-PLLA melt domain structure in the nanopore centers, while adsorption on the nanopore walls stabilizes the outermost cylindrical PS-b-PLLA shell. In between, the nanoscopic PS-b-PLLA melt domain structure apparently ripens to reduce frustrations transmitted from the outermost immobilized PS-b-PLLA layer. The onset of PLLA crystallization catalyzes the ripening while transient ripening states are arrested by advancing PLLA crystallization. Certain helical structure motifs persist PLLA crystallization even if PS is soft. The direction of fastest PLLA crystal growth is preferentially aligned with the nanopore axes to the same degree as for PLLA homopolymer, independent of whether PS is vitreous or soft.

Process highlights to enhance directed self-assembly contact patterning performances

We focus on the directed self-assembly (DSA) for contact hole (CH) patterning application using polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA) block copolymers (BCPs). By employing the DSA planarization process, we highlight the DSA advantages for CH shrink, repair, and multiplication, which are extremely needed to push forward the limits of currently used lithography. Meanwhile, we overcome the issue of pattern density-related defects that are encountered with the commonly used graphoepitaxy process flow. Our study also aims to evaluate the DSA performances as functions of material properties and process conditions by monitoring main key manufacturing process parameters: CD uniformity (CDU), placement error (PE), and defectivity [hole open yield (HOY)]. Concerning process, it is shown that the control of surface affinity and the optimization of self-assembly annealing conditions enable significant enhancement of CDU and PE. Regarding material properties, we show that the best BCP composition for CH patterning should be set at 70/30 of PS/PMMA total weight ratio. Moreover, it is found that increasing the PS homopolymer content from 0.2% to 1% has no impact on DSA performances. Using a C35 BCP (cylinder-forming BCP of natural period L0=35 nm), good DSA performances are achieved: CDU-3σ=1.2 nm, PE-3σ=1.2 nm, and HOY=100%. Finally, the stability of DSA process is also demonstrated through the process follow-up on both patterned and unpatterned surfaces over several weeks.

Directed Assembly of Block Copolymers in Thin to Thick Films

The extent to which lamellae-forming polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA, bulk period L0 = 48 nm) can be directed to assemble on chemically nanopatterned striped surfaces (period LS), with few defects and with domains registered to and extending vertically away from the underlying pattern, was studied as a function of film thickness, commensurability between L0 and LS, and annealing temperature. Two regimes of behavior are identified: thin film (<∼72 nm) and thick film. In the thin film regime, the range of LS/L0 over which the block copolymer could be directed to assemble into ordered linear arrays (with period L = LS) decreased with increasing film thickness. On identical chemical patterns, for example, a film thickness of 30 nm assembled at 0.89 < LS/L0 < 1.04, but a 72 nm film only assembled when LS ∼ L0. In the thin film regime, assembly is cooperative throughout the film thickness, and the behavior can be understood using thermodynamic arguments based on a phenomenological model that includes terms related to the configurational entropy of polymer chains, block–block interfacial energy, and film substrate interfacial energy. In the thick film regime, Directed Assembly occurs only for LS ∼ L0 but can occur in films as thick as 620 nm. In this regime, we present evidence that nucleation and growth of grains occurs independently at the free surface of the film and near the chemically patterned surface. Upon further annealing, the directed orientation and near perfect ordering nucleated on the chemical pattern eventually dominates the structure across the entire film. The thickness through which the directed structure may be realized increases with increasing annealing temperature and time such that under certain conditions (L0 = LS, annealing temperature = 230 °C) PS-b-PMMA films as thick as 620 nm (domain aspect ratio ≈25) exhibited very low levels of defectivity.

Chemical Patterns for Directed Self-Assembly of Lamellae-Forming Block Copolymers with Density Multiplication of Features

Lamellae-forming polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) films, with bulk period L0, were directed to assemble on lithographically nanopatterned surfaces. The chemical pattern was comprised of “guiding” stripes of cross-linked polystyrene (X-PS) or poly(methyl methacrylate) (X-PMMA) mats, with width W, and interspatial “background” regions of a random copolymer brush of styrene and methyl methacrylate (P(S-r-MMA)). The fraction of styrene (f) in the brush was varied to control the chemistry of the background regions. The period of the pattern was Ls. After assembly, the density of the features (domains) in the block copolymer film was an integer multiple (n) of the density of features of the chemical pattern, where n = Ls/L0. The quality of the assembled PS-b-PMMA films into patterns of dense lines as a function of n, W/L0, and f was analyzed with top-down scanning electron microscopy. The most effective background chemistry for directed assembly with density multiplication corresponded to...

Nonbulk Complex Structures in Thin Films of Symmetric Block Copolymers on Chemically Nanopatterned Surfaces

Thin films of symmetric polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) with a bulk lamellar period of Lo were equilibrated on chemically nanopatterned surfaces that had alternating PS and PMMA preferential wetting stripes. The chemical patterns had a period of LS, and the width of the PMMA wetting stripes was W. We identified a set of four morphologies, two of which are fully three-dimensional. On chemical patterns with LS = 2Lo, as W/L0 increased from 0 to 1, block copolymers formed morphologies including bulk-like structures, nominally, parallel lamellae and vertical lamellae, and two bulk-deviate complex morphologies. On chemical patterns with W/L0 = 0.5, as the commensurability factor, δ = LS/L0, increased from 0.87 to 3.05, block copolymers formed complex three-dimensional structures. At the substrate, the block copolymer had a wetting layer reflecting the chemical pattern. At the free surface, the block copolymer formed lamellar-like structures with period L0 along the direction of the underlying chemically patterned stripes when δ was close to an integer, and fingerprint-like structures when δ was not close to an integer. Morphologies obtained by numerical simulations of a coarse grained model of block copolymers compare favorably with our experimental results and help explain the origin of the observed behavior.

Confinement-Induced Morphologies of Cylinder-Forming Asymmetric Diblock Copolymers

Self-assembly of cylinder-forming diblock copolymers confined in cylindrical nanopores is studied systematically using a simulated annealing method. The diblock copolymers form hexagonally packed cylinders in the bulk with a period L0, whereas novel structures spontaneously form when the copolymers are confined inside cylindrical pores. It is discovered that the sequence of structures is controlled by the ratio between the pore diameter (D) and L0, as well as the selectivity of the pores. For selective small pores (D/L0 < 2.7), the following structural sequence occurs as the pore size is increased: a string of spheres, a single cylinder, a straight band, a twisted band or stacked disks, a single helix, a set of degenerate structures (includes single helix, stacked toroids and double helices), and double helices. For larger pores (D/L0 > 2.7), the outer ring of the minority block-domain forms helices or stacked toroids, while the inner structure repeat the sequence of structures observed in smaller pores. For neutral pores, cylinders oriented parallel and nearly perpendicular to the cylindrical pore are observed besides helical or toroidal structures. These morphologies are consistent with available experiments and theoretical studies. Mechanisms of the morphological transitions can be understood based on the degree of commensurability between the pore diameter and bulk period of the copolymer L0, parametrized by the ratio D/L0. The effect of the cylindrical pore length on final morphologies is investigated. The chain conformations as a function of morphologies are calculated and analyzed. A mechanism for the formation of helices is proposed based on a packing model, which gives a reasonable description of the radius and pitch of the observed helices.

Morphology Transition of Block Copolymers under Curved Confinement

AbstractThe morphology transitions in AB diblock and ABA triblock copolymers confined between flat and curved surfaces were investigated by MC simulations. Upon variation of the extent of frustration between thickness d and bulk lamellae period L0, parallel and vertical or distorted vertical lamellar structures appear in both flat and curved confinements. With increasing curvature, the compatibility of d and L0 becomes more perturbed so that perfectly parallel lamellae are formed with increasing difficulty. Owing to the smaller L0 of ABA as compared to AB, the transformation frequency of the incompatible region of d/L0(ABA) is more notable for ABA and the corresponding transformation period is larger than that of AB.magnified image

Morphology of Symmetric Diblock Copolymers Confined Between Two Stripe‐Patterned Surfaces – Tilted Lamellae and More

AbstractSummary: We report the first Monte Carlo simulations on the thin‐film morphology of symmetric diblock copolymers confined between either symmetrically or antisymmetrically stripe‐patterned surfaces. Under suitable surface configurations (where the lamellae can comply with the surface patterns and can have a period close to the bulk lamellar period L0), tilted lamellae are observed for film thicknesses D ≥ 2L0; the checkerboard morphology is obtained for smaller film thicknesses. The A‐B interfaces in the tilted lamellae are basically perpendicular to the surfaces in their immediate vicinity, and exhibit undulations away from them. In some cases, the severe frustration imposed by the two patterned surfaces leads to irregular or unexpected morphologies, which represent locally stable states. The efficient sampling of our expanded grand‐canonical Monte Carlo technique enables us to observe more than one locally stable morphologies and the flipping between them during a single simulation run.Tilted lamellae between symmetrically patterned surfaces (perpendicular to z) with a surface pattern period of 1.5L0 and a film thickness of 2.67L0. L0 is the bulk lamellar period and the black curves mark the A‐B interfaces.imageTilted lamellae between symmetrically patterned surfaces (perpendicular to z) with a surface pattern period of 1.5L0 and a film thickness of 2.67L0. L0 is the bulk lamellar period and the black curves mark the A‐B interfaces.

Phase Turbulence in the Complex Ginzburg-Landau Equation via Kuramoto?Sivashinsky Phase Dynamics

We study the Complex Ginzburg-Landau initial value problem for a complex field u ∈ C, with α,β∈R. We consider the Benjamin–Feir linear instability region We show that for all and for all initial data u 0 sufficiently close to 1 (up to a global phase factor e iφ 0 ,φ0∈R) in the appropriate space, there exists a unique (spatially) periodic solution of space period L 0 . These solutions are small even perturbations of the traveling wave solution, and s,η have bounded norms in various L p and Sobolev spaces. We prove that apart from corrections whenever the initial data satisfy this condition, and that in the linear instability range the dynamics is essentially determined by the motion of the phase alone, and so exhibits ‘phase turbulence’. Indeed, we prove that the phase η satisfies the Kuramoto–Sivashinsky equation for times while the amplitude 1+α2 s is essentially constant.

Influence of the Talbot effect on the loss permutations of Fabry — Perot resonator modes

The loss permutations of Fabry — Perot resonator modes caused by the harmonic spatial perturbation of the radiation phase on one of the mirrors are studied numerically. The periods and amplitudes of perturbations are found at which the second or third mode in the eigenvalue modulus becomes the first mode. It is shown that in the case of perturbations with the period l0, at which the Talbot length is equal to the double resonator length, the permutations are caused by an increase in the losses of the fundamental mode. It is also shown that the perturbation amplitudes with the period l0, which equalise losses of the modes, depend linearly on the inverse Fresnel number F-1.

Morphology of Ultrathin Supported Diblock Copolymer Films: Theory and Experiment

An analysis of the morphological behavior of substrate-supported diblock copolymer films for thicknesses t below the equilibrium period L0 of the copolymer is presented. Substrate-supported films generally exhibit dissimilar interactions between the copolymer block components and the free and substrate surfaces. Accordingly, in this study, self-consistent-field calculations that incorporate asymmetric surface energetics were used to assess equilibrium film morphologies. Phase diagrams were constructed as a function of film thickness, surface interaction energies, the segmental interaction, and the chain length. In conjunction, experiments were conducted on a series of polystyrene-b-poly(n-alkyl methacrylate) copolymer films supported by silicon substrates. These employed a novel atomic force microscopy technique that allowed for the precise tracking of morphology as a function of film thickness. Comparison of the experimental results and calculations revealed several common trends. In particular, hybrid m...

Symmetric diblock copolymer thin films confined between homogeneous and patterned surfaces: Simulations and theory

We have investigated the ability of a simple phenomenological theory to describe the behavior of symmetric diblock copolymer thin films confined between two hard surfaces. Prior knowledge of the morphology in the confined films is crucial for applying this theory to predict the phase diagram of such systems. Taking advantage of our observations in Monte Carlo simulations, we use the theory to construct phase diagrams for thin films confined between patterned-homogeneous surfaces, and obtain good agreement with our results of simulations. Two conditions are essential for obtaining long-range ordered perpendicular lamellae: a lower stripe-patterned surface with the surface pattern period Ls comparable to the bulk lamellar period L0, and an upper neutral or weakly preferential surface. We have also examined the undulation of perpendicular lamellae between two hard surfaces. For the cases of two homogeneous (preferential) surfaces and patterned-preferential surfaces, our calculations using the phenomenological theory indicate that the amplitudes of the undulation are on the same order of magnitude as observed in our Monte Carlo simulations, and are one order of magnitude larger than previously reported. The theory, however, is unable to capture the shape of the undulation. For the case of patterned-neutral surfaces, we find that an earlier analysis is unable to yield the undulations that would stabilize the perpendicular lamellar morphology. We have addressed this issue and obtained undulations that are consistent with our observations from Monte Carlo simulations.

Monte Carlo Simulations of Diblock Copolymer Thin Films Confined between Chemically Heterogeneous Hard Surfaces

Thin films of symmetric diblock copolymers confined between two hard, flat and parallel surfaces have been investigated by means of Monte Carlo simulations on a simple cubic lattice. The upper surface is homogeneous, either neutral or preferential to one of the two blocks, and the lower surface is stripe-patterned, with all the stripes having the same width Ls/2 and alternatively preferring A and B blocks with the same strength of preference. We studied the effects of surface configuration (including surface type, surface pattern period, and surface separation) on the morphology of confined diblock copolymer thin films. Our results show that two conditions are essential for obtaining macroscopically ordered (over micrometers) perpendicular lamellae in the confined films (with film thickness no less than the bulk lamellar period L0): a stripe-patterned substrate with pattern period Ls comparable to L0, which directs the ordering of perpendicular lamellae over a macroscopic scale, and a neutral or weakly preferential hard surface on the top of the confined films, which stabilizes the perpendicular lamellae. When the perpendicular lamellae complying with the lower surface pattern form throughout the entire film, undulations of the A−B interfaces in the perpendicular lamellae are observed if the upper surface is not truly neutral, which could have adverse effects for nanolithography.

Monte Carlo simulations of diblock copolymer thin films confined between two homogeneous surfaces

Thin films of symmetric diblock copolymers confined between two hard, flat and homogeneous surfaces have been investigated by means of Monte Carlo simulations on a simple cubic lattice. For such simulations, the match between bulk lamellar period L0 and the simulation box size is crucial to obtain meaningful results. The simulations have been performed in an expanded grand-canonical ensemble, where the chemical potential and the temperature of the confined films are specified and the density is allowed to fluctuate. The dependence of morphology, density, and chain conformation in the confined films on the type of surfaces, surface separation, and the strength of surface-block interactions has been studied systematically. Our results are consistent with experimental findings.

Self-consistent field theory of diblock copolymer melts at patterned surfaces

Self-consistent field theory is used to investigate the density profile of diblock copolymer melts in a thin film confined between two surfaces, one of which carries a chemically active pattern. The temperature is slowly lowered through the critical point in order to obtain well organized structures. For strong surface interactions, the lamellae for symmetric diblock copolymers comply with the surface pattern. Their orientation depends on the ratio of natural bulk period L0 to surface period L. For L0⩽L, the lamellae tilt at an angle θ=arcsin L0/L with respect to the surface. For L0⩾L, the diblocks are distorted close to the surface and the necessary relaxation off the surface induces parallel oriented lamellae with respect to the surface for films thicker than 2 lamellar periods. Very thin films still support the perpendicular orientation.

Plastic Deformation of Polypropylene. III. Small-Angle X-Ray Scattering in the Neck Region

The small-angle x-ray scattering (SAXS) pattern of polypropylene (PP) drawn at various temperatures (Td = 20°, 100°, and 135°C) was investigated in a range of very closely spaced draw ratio (λ) values through the neck region. In the zone before the neck starts (λ = 1.05–1.1) the uniform diffraction ring due to microspherulitic material with a long period L0 changes into a four-point diagram superposed onto an elliptical halo. At the beginning of the neck (λ = 1.3–2.5) two meridional maxima arising from a new fibrous structure with a limiting long period LT appear. Irrespective of whether L0&amp;gt;LT or L0&amp;lt;LT the transition between L0 and LT is discontinuous. The four-point pattern reminiscent of the spherulitic structure remains observable up to the end of the neck. In the same manner as in the case of PE, stacks of lamellae exhibiting the most favorable orientation for chain tilt and slip start being plastically deformed and finally break into folded-chain blocks which are incorporated into microfibrils. The fracture occurs in a thin destruction zone which separates the new microfibrils from the not yet transformed stack of original lamellae. Because of the morphological inhomogeneity of the spherulitic sample, the destruction zones and, hence, the starting points of the microfibrils are rather randomly scattered in the neck region and do not merge into one single layer extending over the whole cross section of the sample.