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

Directed Self-Assembly by Sparsely Prepatterned Substrates with Self-Responsive Polymer Brushes

The guiding pattern in the chemoepitaxially directed self-assembly (DSA) of block copolymers is often fabricated by periodically functionalizing homogeneously random copolymer brushes tethered on a substrate. The prepatterned copolymer brushes constitute a soft penetrable surface, and their two components can in principle locally segregate in response to the overlying self-assembly process of block copolymers. To reveal how the self-responsive behavior of the copolymer brushes affects the directing effect, we develop a dissipative particle dynamics model to explicitly include the prepatterned polymer brushes and implement it to simulate the DSA of a cylinder-forming diblock copolymer melt on the sparse pattern of polymer brushes. Through large-scale dynamic simulations, we identify the windows of the content of the random copolymer, the film thickness, and the diameter of the patterned spot, for the formation of perfectly ordered hexagonal patterns composed of perpendicular cylinders. Our dynamic simulations reveal that the random copolymer brushes grafted on the unpatterned area exhibit a remarkable self-responsive ability with respect to the self-assembly of the diblock copolymers overlying them, which may widen the effective window of the content of the random copolymer. Within the processing windows of these key parameters, defect-free patterns are successfully achieved both in simulations and in experiments with sizes as large as a few micrometers for 4-fold density multiplications. This work demonstrates that highly efficient computer simulations based on an effective model can provide helpful guidance for experiments to optimize the critical parameters and even may promote the application of DSA.

Numerical Simulations of Directed Self-Assembly in Diblock Copolymer Films using Zone Annealing and Pattern Templating

Bulk fabrication of surface patterns with sub-20 nm feature sizes is immensely desirable for many existing and emerging technologies. Directed self-assembly (DSA) of block copolymers (BCPs) has been a recently demonstrated approach to achieve such feature resolution over large-scale areas with minimal defect populations. However, much work remains to understand and optimize DSA methods in order to move this field forward. This paper presents large-scale numerical simulations of zone annealing and chemo-epitaxy processing of BCP films to achieve long-range orientational order. The simulations utilize a Time-Dependent Ginzburg-Landau model and parallel processing to elucidate relationships between the magnitude and velocity of a moving thermal gradient and the resulting BCP domain orientations and defect densities. Additional simulations have been conducted to study to what degree orientational order can be further improved by combining zone annealing and chemo-epitaxy techniques. It is found that these two DSA methods do synergistically enhance long-range order with a particular relationship between thermal gradient velocity and chemical template spacing.

Proposal for a Domain Wall Nano-Oscillator driven by Non-uniform Spin Currents

We propose a new mechanism and a related device concept for a robust, magnetic field tunable radio-frequency (rf) oscillator using the self oscillation of a magnetic domain wall subject to a uniform static magnetic field and a spatially non-uniform vertical dc spin current. The self oscillation of the domain wall is created as it translates periodically between two unstable positions, one being in the region where both the dc spin current and the magnetic field are present, and the other, being where only the magnetic field is present. The vertical dc spin current pushes it away from one unstable position while the magnetic field pushes it away from the other. We show that such oscillations are stable under noise and can exhibit a quality factor of over 1000. A domain wall under dynamic translation, not only being a source for rich physics, is also a promising candidate for advancements in nanoelectronics with the actively researched racetrack memory architecture, digital and analog switching paradigms as candidate examples. Devising a stable rf oscillator using a domain wall is hence another step towards the realization of an all domain wall logic scheme.

Fabrication of nanopatterns using block copolymer and controlling surface morphology

This paper reports an approach for patterning substrates on the nanoscale using a block copolymer, polystyrene-b-polymethylmethacrylate (PS-b-PMMA), which forms cylindrical microdomains. The morphology of the polymer surface was strongly dependent on the thickness of the polymer layer. Spin coating the polymer solution onto the substrate followed by baking resulted in the self-assembly of the components of the polymer. Exposure to ultraviolet radiation degraded the PMMA chain, which could be removed by rinsing in acetic acid to give patterned holes. However, the small size of the hole limits the applications of the template. This problem was solved by sonicating the sample in different solutions in a series of steps to produce a fingerprint pattern or patterns containing PS cylindrical domains having large interstitial spaces with an average of >30 nm. The morphology of the polymer film surface was examined by atomic force microscopy (AFM) and scanning electron microscopy (SEM).

Block copolymer nanolithography: translation of molecular level control to nanoscale patterns

The self-asembly of block copolymers is a promising platform for the "bottom-up" fabrication of nanostructured materials and devices. This review covers some of the advances made in this field from the laboratory setting to applications where block copolymers are in use.

Directed Block Copolymer Assembly versus Electron Beam Lithography for Bit-Patterned Media with Areal Density of 1 Terabit/inch(2) and Beyond

The directed self-assembly of block copolymer (BCP) offers a new route to perfect nanolithographic patterning at sub-50 nm length scale with molecular scale precision. We have explored the feasibility of using the BCP approach versus the conventional electron beam (e-beam) lithography to create highly dense dot patterns for bit-patterned media (BPM) applications. Cylinder-forming poly(styrene-b-methyl methacrylate) (PS-b-PMMA) directly self-assembled on a chemically prepatterned substrate. The nearly perfect hexagonal arrays of perpendicularly oriented cylindrical pores at a density of approximately 1 Terabit per square inch (Tb/in.(2)) are achieved over an arbitrarily large area. Considerable gains in the BCP process are observed relative to the conventional e-beam lithography in terms of the dot size variation, the placement accuracy, the pattern uniformity, and the exposure latitude. The maximum dimensional latitude in the cylinder-forming BCP patterns and the maximum skew angle that the BCP can tolerate have been investigated for the first time. The dimensional latitude restricts the formation of more than one lattice configuration in certain ranges. More defects in BCP patterns are observed when using low molecular weight BCP materials or on non-hexagonal prepatterns due to the dimensional latitude restriction. Finally, the limitations and challenges in the BCP approach that are associated with BPM applications will be briefly discussed.

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

The 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.

Guided self-assembly of diblock copolymer thin films on chemically patterned substrates

We study the guided self-assembly of symmetric/asymmetric diblock copolymer (BCP) films on heterogeneous substrates with chemically patterned surface by using a coarse-grained phase-separation model. During the procedure, the free energy employed for the BCP films was modeled by the Ginzburg-Landau free energy with nonlocal interaction, and the flat, chemically patterned surface was considered as a heterogeneous surface with short-range interaction with the BCP molecules. The resulting Cahn-Hilliard equation was solved by means of an efficient semi-implicit Fourier-spectral algorithm. Effects of pattern scale, surface chemical potential, and BCP asymmetry on the self-assembly process were explored in detail and compared with those without chemically patterned substrate surfaces. It was found that the morphology of both symmetric and asymmetric BCP films is strongly influenced by the commensurability between the unconstrained natural period lambda* of the bulk BCP and the artificial pattern period. Simulation shows that patterned surface with period close to lambda* leads to highly ordered morphology after self-assembly for both symmetric and asymmetric BCP films, and it also dramatically accelerates the guided self-assembly process. The present simulation is in a very good agreement with the recent experimental observation in BCP nanolithography. Finally, the present study also expects an innovative nanomanufacturing method to produce highly ordered nanodots based on the guided self-assembly of asymmetric BCP films on chemically patterned substrates.

Symmetric diblock copolymers in nanopores: Monte Carlo simulations and strong-stretching theory

We have performed lattice Monte Carlo simulations to study the self-assembled morphology of symmetric diblock copolymers in nanopores. The pore diameter and surface preference are systematically varied to examine their effects on the chain conformations, structures of various morphologies, and their phase transition. Various ensemble-averaged profiles and quantities are used to provide detailed information about the system. The simulation results are also compared with the predictions of a strong-stretching theory commonly used in the literature. Such comparisons reveal the deficiencies of this theory in describing the morphologies under cylindrical confinement, and call for further theoretical studies using more accurate formalisms.

Phase behavior of symmetric ternary block copolymer-homopolymer blends in thin films and on chemically patterned surfaces

The phase diagram of symmetric ternary blends of diblock copolymers and homopolymers in thin films was determined as a function of increasing volume fraction of homopolymer (phi(H)) and was similar to that for these materials in the bulk. Blends with compositions in the lamellar region of the diagram (phi(H)< or =0.4) could be directed to assemble into ordered lamellar arrays on chemically striped surfaces if the characteristic blend dimension (L(B)) and the period of the stripes (L(S)) were commensurate such that L(S)=L(B)+/-0.10L(B). Blends with compositions in the microemulsion region of the diagram (phi(H) approximately 0.6) assembled into defect-free lamellar phases on patterned surfaces with L(S)> or =L(B), but formed coexisting lamellar (with period L(S)) and homopolymer-rich phases when L(S)<L(B).

Fabrication of complex three-dimensional nanostructures from self-assembling block copolymer materials on two-dimensional chemically patterned templates with mismatched symmetry

A study is presented of the self-assembly of a lamella-forming blend of a diblock copolymer and its respective homopolymers on periodically patterned substrates consisting of square arrays of spots, that preferentially attract one component, as a function of pattern dimensions and film thickness. The blend morphology follows the pattern at the substrate and forms a single quadratically perforated lamella (QPL). At intermediate film thicknesses necks connect this QPL to the film surface, resulting in a bicontinuous morphology. The necks do not register with the underlying square lattice but exhibit a substantial amount of hexagonal short-range order. For thicker films we observe bicontinuous morphologies consisting of parallel lamellae with disordered perforations. These results demonstrate a promising strategy for the fabrication of complex interfacial nanostructures from two-dimensional chemically patterned templates.

Wetting-driven structure ordering of a copolymer/homopolymer/nanoparticle mixture in the presence of a modulated potential

We investigate pattern formation on a solid substrate of a diblock copolymer-homopolymer mixture containing doping wettable nanoparticles with a preferential attraction for one component of the copolymers, using a three-order-parameter model. The presence of doping nanoparticles under the surface-interaction modulation breaks the isotropy in the process of microphase-separation and macrophase-separation. This leads to the formation of orientational microphase and macrophase structures due to the interplay between the phase separation and wetting particle ordering under a modulated potential at the late stage. Simulations suggest that the microphase morphology and macrophase morphology can be changed through adjustment of the wetting strength, the amplitude as well as the period of the modulated potential. It provides some important insights for changing microphase and macrophase structures in polymer blends by wetting-driven spinodal decomposition.

Directed Assembly of Block Copolymer Blends into Nonregular Device-Oriented Structures

Self-assembly is an effective strategy for the creation of periodic structures at the nanoscale. However, because microelectronic devices use free-form design principles, the insertion point of self-assembling materials into existing nanomanufacturing processes is unclear. We directed ternary blends of diblock copolymers and homopolymers that naturally form periodic arrays to assemble into nonregular device-oriented structures on chemically nanopatterned substrates. Redistribution of homopolymer facilitates the defect-free assembly in locations where the domain dimensions deviate substantially from those formed in the bulk. The ability to pattern nonregular structures using self-assembling materials creates new opportunities for nanoscale manufacturing.

Surface-induced phase transitions in ultrathin films of block copolymers

We study theoretically the lamellar-disorder-lamellar phase transitions of AB diblock and tetrablock copolymers confined in symmetric slitlike pores where the planar surface discriminatingly adsorbs A segments but repels B segments, mimicking the hydrophobic/hydrophilic effects that have been recently utilized for the fabrication of environmentally responsive "smart" materials. The effects of film thickness, polymer volume fraction, and backbone structure on the surface morphology have been investigated using a polymer density-functional theory. The surface-induced phase transition is manifested itself in a discontinuous switch of microdomains or a jump in the surface density dictated by the competition of surface adsorption and self-aggregation of the block copolymers. The surface-induced first-order phase transition is starkly different from the thickness-induced symmetric-asymmetric or horizontal-vertical transitions in thin films of copolymer melts reported earlier.

Orientational order transition of the striped microphase structure of a copolymer-homopolymer mixture under oscillatory particles

Based on the three-order-parameter model, we investigate the orientational order transition of striped patterns in microphase structures of diblock copolymer-homopolymer mixtures in the presence of periodic oscillatory particles. Under suitable conditions, although the macrophase separation of a system is almost isotropic, the microphase separation of the system will be significantly perturbed by the oscillatory field, and composition fluctuations are suppressed anisotropically. The isotropy of the microphase will be broken up. By changing the oscillatory amplitude and frequency, we observe the orientational order transition of a striped microphase structure from the isotropic state to a state parallel to the oscillatory direction, and from the parallel state to a state perpendicular to the oscillatory direction. We examine, in detail, the microstructure and orientational order parameter as well as the domain size in the process of orientational order transition under the oscillatory field. We study also how the microphase structure changes with the composition ratio of homopolymers and copolymers in mixtures. The results suggest that our model system may provide a simple way to realize orientational order transition of soft materials.

Long-range ordered structures in diblock copolymer melts induced by combined external fields

The structure of diblock copolymer melts under a single external electric or shear field, as well as under combined orthogonal external fields was investigated using a cell dynamic system. The phase structure was determined by coupling the effects of the external fields with the original structure of the bulk free of external fields. The single electric or shear field generated long-range cylinders in asymmetric A4mB6m diblock copolymers and distorted lamellae in symmetric A5mB5m diblock copolymers. Successive orthogonal shear followed by an electric external field generated long-range lamellae in symmetrical A5mB5m systems. However, the simultaneous orthogonal electric and shear fields could more easily form long-range lamellae than the sequential orthogonal fields. The dynamical processes in diblock copolymer melts under orthogonal fields have been also examined.

Epitaxial self-assembly of block copolymers on lithographically defined nanopatterned substrates

Parallel processes for patterning densely packed nanometre-scale structures are critical for many diverse areas of nanotechnology. Thin films of diblock copolymers can self-assemble into ordered periodic structures at the molecular scale (approximately 5 to 50 nm), and have been used as templates to fabricate quantum dots, nanowires, magnetic storage media, nanopores and silicon capacitors. Unfortunately, perfect periodic domain ordering can only be achieved over micrometre-scale areas at best and defects exist at the edges of grain boundaries. These limitations preclude the use of block-copolymer lithography for many advanced applications. Graphoepitaxy, in-plane electric fields, temperature gradients, and directional solidification have also been demonstrated to induce orientation or long-range order with varying degrees of success. Here we demonstrate the integration of thin films of block copolymer with advanced lithographic techniques to induce epitaxial self-assembly of domains. The resulting patterns are defect-free, are oriented and registered with the underlying substrate and can be created over arbitrarily large areas. These structures are determined by the size and quality of the lithographically defined surface pattern rather than by the inherent limitations of the self-assembly process. Our results illustrate how hybrid strategies to nanofabrication allow for molecular level control in existing manufacturing processes.