Article pubs.acs.org/Macromolecules
Symmetric Diblock Copolymers Confined by Two Nanopatterned Surfaces Abelardo Ramírez-Hernández, Guoliang Liu, Paul F. Nealey, and Juan J. de Pablo* Department of Chemical and Biological Engineering, University of WisconsinMadison, Madison, Wisconsin 53706, United States ABSTRACT: Using Monte Carlo simulations of a coarsegrained model, we explore the equilibrium morphologies of symmetric diblock copolymers between two chemically patterned surfaces. The chemical patterns on the surfaces consist of periodic stripes of width W with a periodicity Ls. The stripes on the two chemical patterns are oriented orthogonally. By systematically varying the width of the stripes, the interaction strength between the patterns and block copolymers, and the thickness of the block copolymer films, we investigate complex three-dimensional morphologies that are not available in the bulk and that could be useful in a wide array of applications. The results of simulations are shown to be in quantitative agreement with experimental observations.
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INTRODUCTION The self-assembly of soft materials provides a means to create well-defined morphologies with applications in nanoscale science and engineering.1,2 In particular, recent reports have shown that self-assembly of copolymers can be used in advanced technologies found in the microelectronics and high-density memory device industries.2,3 Traditional patterning methods such as photolithography and electron beam lithography are well suited for fabrication of well-defined two-dimensional features. However, the creation of three-dimensional structures requires repeated photoresist patterning and pattern transfer processes.4 The use of selfassembling soft materials such as supramolecules, colloids or block copolymers promises to enable fabrication of complex three-dimensional structures with fewer steps.5,6 Block copolymer melts have the ability to self-assemble into a variety of periodic structures whose scales range from 5 to 100 nm.7−9 The complexity of these structures depends on the architecture (linear, branched, etc.) and composition of the macromolecules. Furthermore, by using blends of homopolymers and block copolymers, one can increase the variety of morphologies available for use in various technologies. One disadvantage of these materials can be defect formation, which impedes the long-range order necessary in many applications. This problem can be avoided through the use of external fields. In that regard, a particular promising nanofabrication approach relies on the directed assembly of block copolymer thin films, where chemically patterned surfaces act as external fields that direct the assembly of the block copolymers on the nanoscale.10−12 These chemical patterns provide the thermodynamic forces needed to achieve the assembly with registration, perfection, resolution and improved quality.10−12 In the context of high-density storage media, it has been demonstrated that © 2012 American Chemical Society
this approach can lead to defect-free arrays of copolymer domains at densities of 1 terabit per square inch.3 The directed assembly of block copolymers has been used to fabricate periodic structures, including spherical, cylindrical, and lamellar morphologies13−15 and nonperiodic structures such as bends, jogs, and T-junctions.16−19 While most of these features are inherently two-dimensional, it has been demonstrated that it is possible to create a variety of complex three-dimensional structures under specific chemical patterning conditions.20,21 It has also been shown that block copolymers can be used to localize nanoparticles in specific positions dictated by the block copolymer morphologies.22,23 Work to date has largely focused on the use of only one patterned surface; therefore, it is of interest to explore the possible structures created when block copolymers are confined by two patterned surfaces. The interplay between the entropic penalty due the one-dimensional confinement and the energetic contributions of both patterns attempting to induce, locally, a specific symmetry, opens the possibility for creation of complex three-dimensional structures, even in the simple case of an AB diblock copolymer. Several theoretical approaches, ranging from lattice Monte Carlo simulations to self-consistent field theory (SCFT) calculations and Landau−Ginzburg descriptions, have been used to explore the morphologies that arise when one patterned surface is used to induce order in block copolymers. Wang et al.24−26 used a lattice model to explore the influence of the patterned surface on the morphologies of symmetric block copolymer thin films by Monte Carlo simulations. In those studies, the conditions for long-range order of perpendicular Received: December 8, 2011 Revised: January 31, 2012 Published: February 22, 2012 2588
dx.doi.org/10.1021/ma2026594 | Macromolecules 2012, 45, 2588−2596
Macromolecules
Article
by ri(s). The bonded interactions, / b, acting along the chains are given by
lamellae were indentified, obtaining good agreement with experimental data. Petera et al.27,28 performed 2D SCFT calculations to investigate the ordering of diblock copolymer thin films in the presence of one chemically patterned surface and one homogeneous surface; the studies were perfomed both above and below the order−disorder transition (ODT). They found a dependence of the orientation of the lamellae on the ratio of the natural bulk period to the pattern period, and observed that for strong surface interactions the lamellae comply with the surface pattern. Tsori et al.29,30 used a phenomenological Landau−Ginzburg free energy approach to investigate the effect of a chemically patterned surface on the morphology of symmetric diblock copolymer thin films. It was found that periodically patterned surfaces could induce a tilt of the lamellae in order to match the surface periodicity, and also identified the conditions required to obtain lamellae in other orientations. These past studies have improved our understanding of surface-induced ordering and its propagation in thin block copolymer melts. However, few reports considered the influence of two patterned surfaces confining block copolymer thin films. In particular, in ref 31, Tsori and Andelman used a Landau−Ginzburg free energy functional to investigate the morphology of diblock copolymers between two patterned surfaces in the weak segregation limit, above the ODT transition. Wang33 performed lattice Monte Carlo simulations of symmetric diblock copolymers confined between stripe patterned surfaces. Both studies revealed that by using two patterned surfaces interesting morphologies could emerge as a result of the confinement and the pattern’s properties.31−33 Here we also focus on the specific case where the assembly of a symmetric AB block copolymer is directed by two patterned surfaces. The patterns on both surfaces are identical but have different relative orientations. Our study builds on that presented in ref 31, where a more coarse-grained approach was employed. We perform a screening of the different morphologies that arise as a function of the size of confinement, the strength of the copolymer interaction with the patterned surface, and the geometric properties of the patterns. We resort to Monte Carlo simulations with a recently introduced theoretically informed coarse-grained model of block copolymers, which has been successfully used to predict the structures created in the directed assembly of these materials.3,21,34−38 The results of simulations are compared to experimental data for diblocks between lithographically nanopatterned surfaces.
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/b 3 = kBT 2
n N−1
∑ ∑ i=1 s=1
N−1 R e2
[ri(s + 1) − ri(s)]2 (1)
= (N − 1)b is the mean squared end-to-end distance of an where ideal chain and kB is the Boltzmann constant. The nonbonded interactions, / nb, are expressed as a functional of the local densities of the beads and take into account the repulsion between unlike monomers and the finite compressibility of the melt. Explicitly, it is given by Re2
/nb = kBT
2
5̅
∫V
⎤ dr ⎡ κN χN φAφB + (φA + φB − 1)2 ⎥ 3⎢ ⎣ ⎦ 2 Re
(2)
where ϕγ(r) is the local dimensionless density of beads of type γ (=A,B) and N̅ = (ρ0Re3/N)2, with ρo being the bead number density. The repulsion between unlike monomers is represented by the first term in eq 2 and its strength is given by the Flory−Huggins parameter χ. The second term is based on Helfand’s quadratic approximation46 and it gives a finite compressibility to the melt. The parameter κ is related to the inverse isothermal compressibility of the melt.43 In the presence of chemical patterns used to direct the assembly of block copolymer thin films, the chains are confined by two impenetrable hard surfaces located in the planes z = 0 and z = Lz. In this work, we consider two chemically patterned confining surfaces. The chemical pattern on each is represented by a one-body potential,
