Letter pubs.acs.org/NanoLett
Directed Assembly of Lamellae Forming Block Copolymer Thin Films near the Order−Disorder Transition Sangwon Kim,† Paul F. Nealey,‡ and Frank S. Bates*,† †
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States Institute for Molecular Engineering, University of Chicago, Illinois 60637, United States
‡
S Supporting Information *
ABSTRACT: The impact of thin film confinement on the ordering of lamellae was investigated using symmetric poly(styrene-b-[isoprene-ran-epoxyisoprene]) diblock copolymers bound by nonpreferential wetting interfaces. The order−disorder transition temperature (TODT) and the occurrence of composition fluctuations in the disordered state are not significantly affected by two-dimensional confinement. Directed self-assembly using chemical patterning is demonstrated near TODT. These results establish the minimum feature size attainable using directed self-assembly of a given diblock copolymer system. KEYWORDS: Block copolymer, thin film, directed self-assembly, fluctuation, lithography
I
mixing, as the ODT is approached, may set stricter limits on this strategy. Practical lithographic processes also must afford a high level of integration with current manufacturing processes, placing constraints on allowable process steps, material architectures, and specific alignment of the nanostructures with the underlying substrate. We recently demonstrated that poly(A[B-ran-C]) diblock copolymers comprised of appropriately tailored homopolymer (A) and random copolymer [B-ran-C] blocks characterized by χBC > χAB ≈ χAC can produce segregated nanodomain structures endowed with equivalent interfacial energies at free and substrate surfaces.6 This “decoupling” of the bulk and interfacial thermodynamic properties results in the spontaneous alignment of the morphology (e.g., lamellae) in a perpendicular arrangement when cast into thin films. The molecularly engineered block chemistry enables simple thermal annealing to achieve desirable architectures for pattern transfer, obviating the need for more complex processing steps such as solvent annealing7 or application of top-coats.8−10 Overall, these demands place stringent restrictions on the design of new lithographic materials. This Letter addresses fundamental issues related to the limitations set by fluctuation effects as χN → (χN)ODT in thin films of lamellae forming poly(styrene-b-[isoprene-ran-epoxyisoprene]) diblock copolymers that intrinsically form perpendicular through-film structures by thermal annealing. Composition fluctuations have been shown to influence the structure11 and dynamics12 of symmetric diblock copolymers in the vicinity of the ODT, transforming the continuous (secondorder) lamella-disorder transition anticipated by mean-field
n 2007, the International Technology Roadmap for Semiconductors (ITRS) first listed directed self-assembly as a potential solution to the impending resolution limitations associated with optical lithography in the production of large scale integrated microelectronic devices. Block copolymers are a particularly promising class of materials for attaining patterns with sub-20 nm half-pitch dimensions. Several methods for aligning the domains of thin-film block copolymers have been demonstrated, and chemical patterning1,2 and graphoepitaxy3,4 are attracting the most attention for nanolithography in various applications. Thermodynamic incompatibility between polymer blocks induces local segregation leading to predictable nanodomain geometries with bulk and thin-film features that scale as L0 ∼ Nδ, where L0 and N correspond to the domain periodicity and the degree of polymerization, respectively, and 0.5 ≤ δ ≤ 1. Thus smaller domain features dictate the use of lower molecular weight block copolymers. However, reducing the block copolymer molecular weight drives the material toward the order−disorder transition (ODT), ultimately resulting in a homogeneous state devoid of the desired nanoscale structure. Mean-field theory anticipates the ODT for symmetric (equal volume fractions of each block), lamellaeforming diblock copolymers at (χN)ODT = 10.5, where χ, the Flory−Huggins segment−segment interaction parameter, is proportional to the relative thermodynamic incompatibility of the two blocks.5 Increasing χ (i.e., enhancing the chemical dissimilarity between blocks) reduces the lower limit on N driving down the smallest achievable domain dimensions, a strategy actively pursued today. In principle, the highest resolution for a given pair of polymers is achieved by simultaneously increasing χ and reducing N under the constraints set by (χN)ODT. Fluctuation effects, which impact the magnitude and N dependence of (χN)ODT, and interfacial © 2013 American Chemical Society
Received: September 28, 2013 Revised: November 27, 2013 Published: December 11, 2013 148
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theory into a weakly first-order phase transition.13 Unfortunately there is no rigorous way to treat the effects of composition fluctuations analytically outside the limit of very high molecular weights (N > 109).13 A practical approach to modeling the ODT for a specific set of diblock copolymers (e.g., PEP-PEE,14 PI-PLA,11 or PtBS-PMMA15) is to apply the mean-field prediction (χN)ODT = 10.5 self-consistently in interpreting rheological and small-angle scattering data obtained as a function of N and temperature (T), leading to an effective segment−segment interaction parameter, usually taking the form χeff = α + βT−1, where α and β are system specific constants. (Although this procedure does not lead to an unambiguous assignment of χ(T) as discussed by Mauer et al.,16 it provides a practical predictive approach to modeling the ODT for a specific block copolymer system). Three states of self-assembly can be identified within this conceptual framework:11 (i) ordered lamellae when χeffN > 10.5, (ii) a spatially homogeneous state when χeffN < (χeffN)t, and (iii) a disordered but fluctuating state when (χeffN)t < χeffN < 10.5. Small-angle (X-ray and neutron) scattering15,17,18 and rheological experiments12,14 indicate that composition fluctuations first appear in the disordered state at the transition point (χeffN)t ≈ 8−9. Symmetric ( f S = 0.49 ± 0.02) and relatively monodisperse (Mw/Mn ≤ 1.06) poly(styrene-b-isoprene) (SI) diblock copolymers of three different molecular weights (SIxx where xx refers to the molecular weight in kg/mol) were synthesized using anionic polymerization and subsequently partially epoxidized (xn = 78−80% of the unsaturated groups in the poly(isoprene) (PI) blocks were functionalized as described earlier6) resulting in specimens denoted SIxxE (Table 1; also
Figure 1. Reduced frequency (aTω) plot for dynamic storage modulus (G′) for SI14E; the data have been shifted as shown in the Supporting Information. Nonterminal behavior is observed for T < 85 °C while for T > 95 °C this material displays a terminal viscoelastic response, indicative of order and disorder, respectively. The inset shows the temperature dependence of G′(ω = 1 rad/s) obtained while heating at 0.5 °C/min leading to TODT = 91 °C.
SE14E displays terminal viscoelastic behavior in the low frequency limit (G′ ∼ ω2) consistent with a state of disorder while below 85 °C a nonterminal response indicates an ordered morphology. We have assigned TODT = 91 °C to this material based on the onset of a precipitous drop in G′(ω = 1 rad/s) at this temperature (inset of Figure 1). Using the same criteria we have established that SI21E and SI10E are ordered and disordered, respectively, over the range of temperatures accessed in this study (60 °C ≤ T ≤ 160 °C) as anticipated based on the associated molecular weights (Supporting Information Figure S7). Interestingly, T ODT is almost unaffected by epoxidation as evidenced by TODT = 86 °C for SI14 (Supporting Information Figure S6). Thin films of SI10E, SI14E, and SI21E were prepared above poly(styrene-ran-methyl methacrylate) random copolymer brushes (labeled SMyy, where yy denotes the mole % of styrene) by spin-casting from toluene followed by annealing under vacuum for 3−6 h at temperatures listed in Table 1. As described in our preliminary report,6 partial epoxidation of the poly(isoprene) blocks results in presumably equal surface energies between blocks when xn ≅ 75% leading to perpendicular alignment of lamellae when thin films are supported on a suitable brush. SMyy brushes with compositions 28% ≤ yy ≤ 57% act as nonpreferential substrates as demonstrated by the thickness independence of perpendicular ordering of SI21E above these brushes (Supporting Information Figure S9). Apparently the mechanism that “decouples” the free surface and bulk thermodynamics allows for nearly equal interfacial energies at the brush interface as well. Figure 2 exhibits top-down SEM images (upper panels) of thin-films (⟨L⟩/L0 = 1.5 − 2.0, where ⟨L⟩ is the average film thickness and L0 is the lamellar period) of SI21E annealed at 105 °C (panel a) and SI10E annealed at 80 °C (panel b) on nonpreferential brushes. Perpendicular ordering of lamellar domains is evident for SI21E, corroborated by a cross-sectional SEM image acquired at a tilt angle of 45° (panel c in Figure 2). In contrast, the SEM image from the SI10E thin film is devoid of structural features at length scales commensurate with L0 (see Table 1). Figure 3 shows how the annealing temperature influences the state of ordering in ⟨L⟩/L0 = 0.8−1.5 thick films
Table 1. Molecular Characterization of Symmetric Poly(styrene-b-isoprene) Block Copolymers with Partial Epoxidation (%) Na
xn (%)
L0 (nm)
SI21E SI14E
259 158
78 78
19.1 14.6
SI10E
111
80
11.6d
TODT (°C) e
>160 91 TODT) and (ii) (T < TODT). The associated thin-film SEM images (Figure 3) are strikingly similar to the well-documented bulk morphologies that characterize symmetric diblock copolymers near the ODT,20 that is, ordered lamellae and a disordered bicontinuous state, respectively. Recently, we have shown that the fundamental length scale q* = 2π/L0 and the local composition profile are invariant above and below the bulk order−disorder transition,11 that is, between states (ii) and (iii) at TODT. The results presented here unexpectedly show that this threedimensional behavior appears to persist as the geometry of the system is reduced to the two-dimensional limit, leaving TODT unaffected within experimental error. This finding is of fundamental interest and has practical implications on the applications of block copolymers to device manufacturing. Spatial confinement has nontrivial effects on various physical phenomena, including phase transformations in metal alloys21 and liquid crystals,22 sphere packing in block copolymers,23,24 the critical temperature for phase separation in mixtures,25−27 and numerous macromolecular properties.28−30 Reducing the space dimension also generally enhances the effects of fluctuations.31 The TODT of thin-film cylinder- and sphereforming block copolymers has been estimated based on the transitions to the isotropic liquid phase from the nematic and the hexatic phases, respectively.32−34 These studies have produced conflicting results in the thin-film TODT with respect to the bulk, depending on the morphology and the underlying topography. The influence on TODT of thin-film confinement of
Figure 2. Top-down SEM images taken from thin films (⟨L⟩/L0 = 1.5−2.0) of (a) SI21E and (b) SI10E on nonpreferential brushes. Fourier transforms of the images (insets) are consistent with states of perpendicularly aligned lamellae and a lack of microstructure (homogeneity), respectively. (c) A cross-sectional view of SI21E taken at a tilt angle of 45° shows that the lamellar domains propagate through the entire film. Scale bars correspond to 100 nm.
of SI14E above and below the bulk TODT. At 70 and 80 °C, the domains clearly display translational order, while at 100 and 120 °C the films display segregated domains that lack lateral correlations beyond several domain periods. Cross-section SEM confirms that the morphologies evident at 80 and 100 °C span the thickness of the film. Remarkably, the order−disorder transition in the 2D limit, that is, ⟨L⟩/L0 → 1, is identical within 10 °C to the bulk (3D) result. The effective Flory−Huggins interaction parameter for partially epoxidized poly(styrene-b-isoprene) diblock copolymers has been estimated as a function of xn and temperature (Kelvin) based on the binary interaction model6 ⎡ ⎛ xn ⎞ ⎛ xn ⎞2 ⎤ ⎟ + 3.39⎜ ⎟ ⎥ χeff = (28.6 T−1 − 0.02)⎢1 − 2.3⎜ ⎝ 100 ⎠ ⎝ 100 ⎠ ⎦ ⎣ (1)
Figure 3. Top-down SEM images (a−d) obtained from thin films (⟨L⟩/L0 = 0.8−1.5) of SI14E above nonpreferential polymer brush SM45 following annealing at the indicated temperatures. Fourier transforms (insets) indicate ordered and disordered states of nanoscale structure below and above TODT = 91 °C, respectively. Cross-sectional views at a tilt angle of 45° (b2 and c2) demonstrate that the domains propagate through the entire films. These SEM images were taken after a small degree of plasma etching. Scale bars correspond to 100 nm. 150
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Figure 4. (a) Schematic illustrating the process for chemical pattern fabrication. (b) Top-down SEM images of directed self-assembly of SI21E (⟨L⟩/ L0 = 1.5, 105 °C) and SI14E (⟨L⟩/L0 = 2.0, 80 °C). Arrows identify defects in the aligned lamellae. Scale bars correspond to 100 nm. For SI14E, a small degree of plasma etching was applied before SEM imaging.
namic driving force for lamellar alignment. Defects in assembly (e.g., dislocations) are apparent (indicated by white arrows) in these images. Defect formation is induced by various factors, such as the commensurability in the periodicity between the chemical pattern and the block copolymer,2 the effective composition of the backfill brush,41,42 and the relative line width of the chemical patterns.39,43 Despite the minor defects observed with SI21E and SI14E, attributable to these factors, the significant degree of alignment of these block copolymers indicates that this type of directed self-assembly remains viable in the limit χeffN → (χeffN)ODT. In this molecularly engineered polymer system, directed assembly of through film perpendicularly oriented features by simple thermal annealing is therefore feasible at a resolution below 10 nm. Thermal fluctuations intrinsically favor a random arrangement of domains, as suggested by Mishra et al.,44 who observed the disruption of aligned cylinders of thin-film block copolymers (i.e., the loss of the translational and orientational order) as the annealing temperature approached the bulk TODT. The directed self-assembly of SI14E (which is at the verge of disorder; (χeffN) = 1.04(χeffN)ODT at 80 °C based on eq 1 with TODT = 91 °C) over a large region (Figure 4b) demonstrates the effect of the directional field exerted by the chemical patterns. Preferential interaction of the SM94 guiding stripes with the poly(styrene) block of SIxxE is expected to enhance the degree of “order” in the system by raising χeffN.45,46 This suggests that lamellae alignment on the patterned substrate may persist at temperatures even beyond TODT, analogous to the effects of shearing in bulk specimens due to the suppression of
lamellar diblock copolymers also has been explored using simulations and experiments,35−37 but not in the ideal limit of two neutral surfaces and ⟨L⟩/L0 → 1, where we might have anticipated disruption of periodic translational order at all values of χeffN > (χeffN)ODT due to a Peierls instability.38 Apparently this does not happen although we believe this point warrants further investigation from the perspective of critical phenomena. Directed self-assembly of SI21E and SI14E was achieved using lithographically defined chemical patterns that possess selective affinities to the block constituents. The polymer chemistry and physics, materials and processes, and boundary conditions and design rules that have been established for other block polymer systems were applied here without attempting to optimize the conditions. The procedure for fabricating the chemical patterns is illustrated in Figure 4a.39 E-beam exposure and development generates stripe patterns of photoresists (zep520), and subsequent oxygen plasma treatment transfers the pattern in the photoresist to the underlying mat (SM94) (Supporting Information Figure S10). Backfilling and grafting a brush (SM25) in the interspatial regions leads to a precise chemical pattern consisting of preferential wetting guiding stripes for one block (i.e., poly(styrene) block) and background regions that are weakly preferential wetting for the other block. Stripe periodicities close to integer multiples of L0 (39.0 nm ≈ 2 × 19.1 nm; 44.1 nm ≈ 3 × 14.6 nm) were chosen to achieve assembly with density multiplication.40 Figure 4b shows the directed assembly of SI21E (105 °C) and SI14E (80 °C) guided by the chemical patterns, which provide a thermody151
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composition fluctuations,47 and consistent with previous findings dealing with thin films of sphere forming diblock copolymer.48
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ASSOCIATED CONTENT
S Supporting Information *
Bulk and thin film sample preparation, table of molecular characterization of SIxx, SEC, SAXS, and rheology data for SIxx and SIxxE, and top-down SEM images of SIxxE. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Financial support for this work was provided by the National Science Foundation (NSF) sponsored Nanoscale Science and Engineering Center (NSEC) at the University of Wisconsin− Madison (Grant DMR-0832760). Cross-linked mat and graft brush materials have been generously provided by Chris Thode (Nealey group) and Eungnak Han (Gopalan group). The authors thank Lei Wan (HGST, Western Digital Company) for conducting the e-beam exposure as part of chemical pattern fabrication and for helpful discussion on directed self-assembly. Parts of this work were carried out in the Characterization Facility, University of Minnesota, which receives partial support from the NSF through the MRSEC program.
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REFERENCES
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