Diblock copolymers are known to spontaneously order into a variety of interesting morphologies, including cylinders, spheres, and lamellae with characteristic lattice repeat periods on the order of 10−100 nm.1 In thin films, these ordered structures have been used as templates for patterning via selective etching or deposition in a process known as block copolymer lithography,2 to create a variety of functional nanoscale devices, including nanowires,3, 4 magnetic storage media,5–9 FLASH memory devices,10 increased capacitance gate devices,11, 12 and photonic crystals.13 Many of the proposed applications for this technology, for example, single domain magnetic storage media,5–7, 14 will require exacting control over the placement of individual block copolymer domains that are registered with the underlying substrate. We have recently developed directed self-assembly of lamellae forming diblock copolymers on chemically nanopatterned substrates as a method that is capable of satisfying the following essential attributes of the lithographic process: the ability to achieve patterning perfection,15, 16 registration of the diblock copolymer domains with the underlying substrate,15 and generation of nonregular device-oriented structures.17 Here, we investigate the mechanistic processes and time scales required to achieve defect-free directed assembly in block copolymer thin films using experiments and simulations.
The current study is concerned with how lamellar domains form from the as-cast state in diblock copolymer thin films annealed on chemical nanopatterned stripes that have repeat periods that are commensurate with the bulk lamellar period of the block copolymer and the mechanisms by which defects in the domain structures are removed. Studies by Sakamoto and Hashimoto on the nucleation and formation of lamellar domains in bulk samples of symmetric poly (styrene-b-isoprene) found that after quenching this polymer from a disordered state, perforated lamellae formed almost instantaneously before coalescing into full lamellae after a brief incubation period.18–20 Mayes et al., using X-ray and neutron reflectivity studies on poly(styrene-b-methyl methacrylate) (PS-b-PMMA, weight fraction styrene fPS = 0.52) on silicon substrates, found that in thin films that ultimately formed well-ordered lamellae oriented parallel to the substrate, the styrene blocks of the nearly symmetric diblock copolymer formed channels that perforated adjacent lamellae to promote diffusion of the diblock copolymer chains between lamellar domains. Eventually, these perforations closed off as the lamellar domains reached their equilibrium thicknesses.21
Others have investigated the defect annihilation mechanisms of diblock copolymer thin films and have successfully quantified their time-dependent domain behavior. Harrison et al. investigated the orientational and translational ordering of block copolymers that formed spheres and cylinders oriented parallel to the substrate in uniform thin films and found that the correlation length of the block copolymer domains increased with time1/4.22–24 They also found that defects in the domain structures were removed via a mechanism in which dislocation pairs with opposite Burgers vectors met and annihilated, indicating that defect annihilation was ultimately limited by the ability of those of defects to diffuse and meet in the thin film. Similar studies quantified the evolution of order in cylindrical block copolymer domains oriented perpendicular to the substrate and found the time1/4 relationship held for the correlation lengths in those films as well.25
Previously, it was noted that many applications of block copolymer lithography will require exacting control over the placement of individual block copolymer domains. This has resulted in the development of numerous methods aimed at imparting order on self-assembled diblock copolymer systems.15–17, 26–35 Segalman et al. have looked at the complex interplay between the thermodynamics of domain formation and the kinetics of defect annihilation in one of these methods, graphoepitaxy. In graphoepitaxy, the preferential wetting of one of the blocks of the block copolymer on a topographically patterned substrate is used to induce long range order in the block copolymer domains. Segalman et al. found that defects in the hexagonal ordering of a single layer of spheres could be equilibrium structures using this technique.36–38 In some experiments, the block copolymer components did not have a sufficiently large value of χNmin, where χ is the thermodynamic interaction parameter of the block copolymer and Nmin is the degree of polymerization of the minority component, to form a truly bcc spherical phase and instead formed a hexatic phase, with low long-range order. Experiments in which the temperature was lowered, thus increasing χNmin, found that the diffusion of block copolymer defects took place at a rate that was not sufficient to induce long-range translational order in their films. These results led them to the important conclusion that the complex interplay between block copolymer diffusion and thermodynamics may render some forms of templated self-assembly incapable of inducing truly long-range translational order in block copolymer domains, given the equilibrium nature of those defects.
In this paper, we investigate the time-dependent behavior of lamellar domains in thin diblock copolymer films (∼1 LO thick) on chemically nanopatterned substrates, and study the effects of the interfacial energy between the chemically nanopatterned substrate and the block copolymer, and the commensurability of the substrate pattern period, LS, and the block copolymer repeat period, LO, on the domain ordering. One effect of the interfacial energy contrast, or the strength of the interaction between the chemically nanopatterned substrates and one of the blocks of the block copolymer, is that the block copolymer domains ordered to perfection over large areas, in registration with the underlying chemical surface patterns at much shorter annealing times, as the interfacial energy contrast of the chemical surface patterns was increased. Furthermore, on chemical surface patterns that had an interfacial energy contrast that was high enough not only to suppress the formation of defects, but also to stretch and compress the domains to length scales that were not commensurate with the bulk lamellar period of the block copolymer, the degree of commensurability between the substrate pattern period, LS, and the bulk lamellar period, LO, had a large effect on the observed degree of domain ordering and substrate registration for a given time. The mechanism by which defect-free assembly is achieved occurs in the following manner. Initially, the symmetric poly (styrene-b-methyl methacrylate) block copolymer forms hexagonally close-packed styrene domains at the free interface. These defect structures then coalesce to form linear styrene domains on the chemically patterned stripes that are not fully registered with the underlying chemical surface pattern. Defects in the linear domains are then removed by breaking linear domain structures and forming new linear domain structures with improved substrate registration. Insight into the three-dimensional structures of the block copolymer domains and the mechanism by which defect-free directed assembly is achieved was gained from single chain in mean field (SCMF) simulations.
Unless otherwise noted, all chemicals were used as received. Poly(styrene-b-methyl methacrylate) (Mn = 50-b-54 kg/mol, LO = 48 nm, and PDI = 1.04) was purchased from Polymer Source Inc. of Dorval, Quebec. Styrene, methyl methacrylate, toluene, and chlorobenzene were purchased from Aldrich Chemical Co. of Milwaukee, WI. Sulfuric acid, hydrogen peroxide, isopropyl alcohol, and methyl isobutyl ketone were purchased from Fischer Scientific. Photoresist grade poly (methyl methacrylate) (Mn = 950 kg/mol, 6 wt % in chlorobenzene) was purchased from Microchem Corp. of Newton MA and was diluted to 1.2 wt % using chlorobenzene. Silicon Wafers were purchased from MONTCO Silicon Technologies Inc.
A hydroxy-terminated random copolymer of poly- (styrene-r-methyl methacrylate) with a styrene weight fraction of 58% and hydroxy-terminated polystyrene were synthesized using a TEMPO-based 2,2,6,6-tetramethylpiperidin-1-yl oxide initiator as reported extensively in the literature.39–41 Prior to polymerization, styrene and methyl methacrylate monomers were degassed. Polymerizations were then performed for 3 days under argon at 100 °C. The resulting polymers were dissolved in toluene and precipitated in hexane, before drying overnight under vacuum at ∼30 mTorr. Silicon wafers were cleaned using a piranha solution (7:3 (v/v) H2O2:H2SO4, 100 °C, 30 min). (Caution: piranha reacts violently with organic compounds and should not be stored in closed containers.) The hydroxy-terminated random copolymers were dissolved in 1.5 wt % solutions in toluene and spin coated on the cleaned silicon wafers at 6000 rpm, resulting in films that were ∼40-nm thick. A 4-nm thick layer of random copolymer or polystyrene was then grafted to the silicon substrate by annealing the coated silicon wafers under vacuum for 48 h at ∼160 °C.16, 42 This 4-nm layer of polymer is henceforth referred to as a brush. The wafers were then slowly quenched to ∼80 °C and repeatedly sonicated in toluene to remove ungrafted portions of the polymer film. The resulting brushes were characterized by their wettability (water contact angle) and thickness (ellipsometry), presented in Table 1.
Table 1. Characteristics of Grafted Brushes used to Direct the Self-Assembly of Diblock Copolymer Domains
PS-r-PMMA Neutral Brush
Molecular weights and polysdispersity indices are presented in polystyrene equivalents.
The silicon substrates with brushes were spin-coated with a 50-nm layer of poly(methyl methacrylate) photoresist. The photoresist-covered samples were then baked in air at 130 °C for 2 min and patterned using extreme ultraviolet lithography (EUVL) as described previously in the literature.43 The gratings used in these experiments generated patterns consisting of lines and spaces having periods, LS ranging from 40 to 60 nm in increments of 2.5 nm. After exposure, the films were developed in a 1:3 development mixture of methyl isobutyl ketone and isopropyl alcohol for 30 s and rinsed extensively with isopropyl alcohol before drying in a stream of nitrogen. The topographic pattern in the photoresist was then transferred to a chemical surface pattern, using a brief oxygen plasma etch to incorporate highly polar, oxygen containing moieties in areas of the polymer brush that were not protected by the photoresist and left the areas of the polymer brush protected by the photoresist unmodified.44 The remaining photoresist was then removed via repeated sonication in chlorobenzene, yielding a chemically nanopatterned substrate. The samples were then coated with a 42-nm diblock copolymer film and annealed under vacuum at 190 °C for up to 170 h. The domain structures of the film were imaged in plan-view using a field emission scanning electron microscope (SEM) (LEO-1550 VP). Contrast in the SEM arises because the electron beam damages and removes the PMMA domains of the block copolymer.45 This results in a height difference between the PS and PMMA domains. The PS domains appear bright and the PMMA domains appear dark in the SEM images. Samples were not reannealed after an initial SEM analysis.
Quantitative information about the repeat period of the block copolymer domains was gathered from an analysis of the power spectra of two-dimensional fast Fourier transforms (2D-FFT) of SEM images. 2D-FFTs of images that were 512 × 512 pixels were interpolated to a 1023 × 1023 pixels grid. The intensities of the FFT power spectra were then averaged azimuthally over 512 rings around the 1023 × 1023 pixels grid to yield the average intensity of the FFT in q-space (q = 2π/L). First, second, and third order peaks in these spectra were used to analyze the block copolymer domain behavior.
Single chain in mean field (SCMF) simulations were performed as described previously in the literature.46 The simulations used χN = 36.7 where χ is the Flory-Huggins interaction parameter of the block copolymer and N is the degree of polymerization. Comparing the bulk lamellar spacing, LO = 1.79Re, measured in units of the end-to-end distance, Re, with the experimental result, 48 nm, we identified the length scale. The geometry 1.2Re × 17Re × 17Re with periodic boundary conditions in the two lateral directions was used in the SCMF simulations. The patterned substrate and the film surface were modeled as hard walls. The top surface did not prefer any component, while the substrate consisted of 10 stripes with widths LS/LO = 0.95 that consist of two equal portions attracting PS and PMMA segments. In the SCMF simulations, we consider the kinetics of a large ensemble of independent chains in external fields, which depend on the instantaneous density distribution. We used the chain density ρpolyRe3 = 128 and each diblock chain was discretized into 15 + 17 effective segments, that is fPS = 15/32 ≈ 0.47 The single chain dynamics is characterized by a self-diffusion coefficient of DPMMA = 3.3(3) × 10−5Re2/MCS where in each Monte Carlo step (MCS), we attempt to randomly displace each segment once on average. The attempt frequency was 100 times higher for PS segments to account for their higher mobility. Comparing the time to diffuse a distance LO, we obtain a crude mapping between the time scales of the experiment and the simulation. A value of DPMMA ≈ 1 nm2/s maps 1 s onto 40 MCS.47 Since SCMF simulations cannot describe entanglements that will considerably slow down the ordering kinetics, we expect that this mapping provides only an estimate for the order of magnitude of the timescale. SCMF simulations with slithering-snake MC moves that mimic the dynamics in a very tightly entangled melt46 resulted in a substantially slower ordering kinetics.
A schematic diagram summarizing the experimental procedure used to achieve directed self-assembly of lamellar domains in block copolymer thin films on chemically nanopatterned substrates is presented in Figure 1. Polymer brushes consisting of hydroxy terminated random copolymers of poly (styrene-r-methyl methacrylate) that are initially 58% styrene (termed: “neutral brushes”) or hydroxy-terminated polymers that are initially pure polystyrene (termed: “polystyrene brushes”) were grafted to a silicon substrate. These brush layers were then chemically patterned with stripes that had periods of 40 nm ≤ LS ≤ 60 nm such that one stripe was preferentially wet by the poly-(methyl methacrylate) block of the block copolymer. The alternating stripes were either neutral to wetting by either block of the block copolymer or strongly preferentially wet by the styrene block of the block copolymer. These patterned substrates were then coated with 42-nm thick films of symmetric PS-b-PMMA that had a molecular weight of 104 kg/mol, styrene fraction of 0.48, and a bulk lamellar repeat period, LO, of 48 nm (as determined by an FFT analysis of this block copolymer annealed on an unpatterned neutral brush). Films were then annealed for up to 170 h at 190 °C, quenched slowly to room temperature, and analyzed in plan-view using field-emission scanning electron microscopy (SEM).
The first morphology observed on the chemically nanopatterned substrates, which appeared after 3 h of annealing, was what appeared in plan view as hexagonally close-packed arrays of styrene domains in a matrix of methyl methacrylate. Figure 2 shows plan-view SEM images of PS-b-PMMA films on chemically nanopatterned neutral and polystyrene brushes with pattern periods, LS, of 42.5, 47.5, and 52.5 nm that were annealed for 3 h and corresponding 2D-FFTs of those images as insets. (When imaging PS-b-PMMA with SEM, the bright domains are styrene and the dark domains are methyl methacrylate. In all SEM images presented in this paper, the chemically nanopatterned stripes run from left to right in the micrographs.) On chemical surface patterns consisting of stripes in periodicities that were commensurate with the bulk lamellar period of the block copolymer, the styrene domains of the block copolymer exhibited long-range hexagonal ordering with six first order Bragg peaks appearing in the 2D-FFTs. Only a narrow range of substrate pattern periods, 45 nm ≤ LS ≤ 50 nm, exhibited long-range hexagonal ordering on chemically nanopatterned neutral brushes, as shown by the appearance of a circular ring in the 2D-FFTs for the LS = 42.5 nm and LS = 52.5 nm chemically nanopatterned neutral brushes in Figure 2. Increasing the interfacial energy contrast of the chemical surface patterns with the blocks of the block copolymer resulted in an increased range of substrate pattern periods that exhibited long range hexagonal ordering of the styrene domains, to 42.5 nm ≤ LS ≤ 52.5 nm. This can be seen in the 2D-FFTs presented in Figure 2 with six high intensity Bragg peaks appearing for the block copolymer domains annealed on patterned polystyrene brushes with LS = 42.5 nm and LS = 52.5 nm.48
The effects of interfacial energy contrast and substrate pattern period/block copolymer lamellar period commensurability on the long range hexagonal ordering of the hexagonally close-packed styrene domains is captured in the azimuthally averaged 2D-FFT power spectra presented in Figure 2. On chemically nanopatterned neutral brushes, for all values of LS, the azimuthally averaged power spectra display high-intensity, broad peaks at qO = 0.131 nm−1, which corresponds to the bulk lamellar period of the block copolymer. Additionally, on chemical surface patterns with repeat periods from LS = 45 to LS = 55 nm, another peak in the azimuthally averaged power spectra, at q-values that correspond to the substrate pattern period also appeared, indicating that the hexagonally close-packed styrene domains preferentially aligned with the same period as the underlying chemical surface patterns even if the spots did not exhibit long-range hexagonal ordering. The improvement in the long range hexagonal ordering of the styrene domains, induced by higher interfacial energy contrast, is also apparent in the azimuthally averaged 2D-FFT power spectra of those domains on chemically nanopatterned polystyrene brushes. Here, the spectra still display broad peaks at qO = 0.131 nm−1; however, peaks corresponding to the preferential alignment of the hexagonally close-packed styrene domains in periodicities that matched the periodicities of the underlying chemical surface patterns are far more pronounced than on the patterned neutral brushes. Moreover, the azimuthally averaged power spectra of 2D-FFTs of SEM images of the block copolymer domains annealed on the LS = 57.5 nm and LS = 60 nm patterned polystyrene brushes exhibited peaks corresponding to the alignment of the hexagonally close-packed styrene domains with the same periodicity as the underlying chemical surface pattern. These peaks were not present in the azimuthally averaged power spectra of the block copolymer domains annealed on the neutral brushes.
On patterned polystyrene brushes, at all chemical surface pattern periods, the hexagonally close-packed styrene domains aligned with the same pattern period as the underlying chemical surface pattern. Figure 3 presents a graph that displays the spacing of rows of hexagonally close-packed styrene domains, LROW, as determined from the highest intensity peak in the 2D-FFT power spectra in the direction perpendicular to the chemical surface pattern averaged over 9 pixels in the center of the 2D-FFT normalized to the lithographically defined substrate pattern period, LS. For both the patterned neutral and patterned polystyrene brushes, the hexagonally close-packed styrene domains preferentially aligned with the same pattern period as the underlying chemical surface pattern with LROW/LS = 1.00 ± 0.03. The one exception was the LS = 60 nm patterned neutral brushes where the hexagonally close-packed styrene domains did not exhibit any preferential alignment with respect to the chemically nanopatterned substrate.
In addition to calculating the spacing between rows of hexagonally close-packed styrene domains, the distance to the nearest neighbor of two styrene domains along the same chemically nanopatterned line, DNN, can also be calculated from the power spectra of the 2D-FFTs from peaks in the direction parallel to the chemical surface pattern. For a very narrow range of substrate pattern periods, from LS = 42.5 to LS = 52.5 nm, the distance to a nearest neighbor along a chemically patterned line, as determined from a second order peak in the 2D-FFT power spectra, was less than the bulk repeat period of the block copolymer with DNN = 44 nm (this peak is not apparent in the 2D-FFTs presented in Figure 2 because of the thresholding of those images). This spacing, and the range of substrate pattern periods over which it was observed, was independent of the chemistry of the patterned polymer brush.
At longer annealing times, the hexagonally close-packed styrene domains coalesced to form linear domains that were aligned with the underlying chemical surface pattern. This is captured in an SEM image presented in Figure 4, which shows coexisting linear and hexagonally close-packed domains with LS = LO on a chemically nanopatterned neutral brush. Defects in the domains with respect to the chemical surface pattern, such as s-1/2 disclinations (outlined in a white box) and dislocations (outlined in dashed boxes), formed directly from hexagonally close-packed domains. It cannot be determined if the styrene domains that are aligned with the chemical surface pattern are registered with the surface pattern and form lamellae oriented perpendicular to the substrate or whether the styrene domains are not registered with the chemical surface pattern and form structures that are more similar to cylinders oriented parallel to the substrate.
A series of plan view SEM images in Figure 5 shows defects that formed in the linear domains on chemically nanopatterned neutral brushes with LS = 47.5 nm, as those defects coarsened and disappeared with increasing annealing times. Initially, the hexagonally close-packed styrene domains coalesced to form linear domains that were primarily registered with the underlying chemical surface pattern in some regions of the chemically nanopatterned substrates, but also had a high defect density in other regions. As annealing times were increased, the defect density in the self-assembled films decreased after 12 h of annealing until perfectly aligned linear domains were observed after 36 h of annealing.
On chemically nanopatterned substrates with a high interfacial energy contrast, the time required to achieve perfectly aligned domains was reduced. Figure 5(b) shows plan-view SEM images of PS-b-PMMA films on chemically nanopatterned polystyrene brushes with LS = 47.5 nm annealed for 3 and 6 h. Already, after the short annealing time of only 6 h, the linear domains formed perfect arrays that were aligned with the underlying chemical surface pattern.
The commensurability of the chemical surface pattern period with the bulk lamellar period of the block copolymer also altered the time required to achieve perfectly aligned block copolymer domains. Figure 6 presents a series of plan-view SEM images that show the behavior the PS-b-PMMA domains on chemically nanopatterned polystyrene brushes with a pattern period of LS = 55 nm at various times. After 3 h of annealing, poorly ordered hexagonally close-packed domains formed on the chemical surface pattern. The hexagonally close-packed domains then coalesced to form linear domains that were not registered with the underlying chemically nanopatterned substrate after 6 h of annealing. Annealing for 36 h resulted in a slight improvement of the ordering of the linear domains with respect to the chemically nanopatterned substrate. It is also worth noting that after 36 h, some of the linear domains pinched and formed what appear in plan-view to be domains that are reminiscent of cylindrical domains oriented perpendicular to the substrate, as shown in the high magnification inset in Figure 6(c). After 72 h of annealing, the linear domains began to exhibit some registration with the underlying chemically nanopatterned substrate, whereas most of the remaining, unaligned linear domains exhibited a pinched morphology. When the films were annealed for 140 h, the areas of defect-free domain ordering covered a larger aerial projection of the chemically nanopatterned substrate with pinched linear domains and dislocation defects in the remaining, unregistered regions. Finally, after 170 h of annealing, the block copolymer domains were almost completely registered with the underlying chemical surface pattern with only one dislocation and one dislocation pair of defects appearing in the self-assembled film.
The azimuthally averaged power-spectra of 2D-FFTs of the images shown in Figure 6 are presented in Figure 7 and capture the various stages of substrate registration in the block copolymer domains. At 3 h, as shown previously, a broad peak corresponding to qO = 0.131 nm−1 and a narrow peak at qS = 0.114 nm−1, the substrate pattern period in q-space, appear as the hexagonally close-packed styrene domains aligned on the chemical surface patterns. After 6 h, the block copolymers coalesced to give linear domains with strong first and second order Bragg peaks at qO and 2qO; however, there were no peaks corresponding to qS. Increasing the annealing time to 36 h introduced the appearance of a third Bragg peak at 3qO. After 72 h, the time at which the block copolymer domains first exhibited directed assembly from the chemical surface pattern in the SEM images, three peaks at qS, 2qS, and 3qS appeared. These peaks increased in intensity until they were the dominant peak in the azimuthally averaged power spectra after 140 h. Eventually, those peaks narrowed into well-defined peaks, indicating that the block copolymer domains had been directed to assemble with the same pattern period as the underlying chemically nanopatterned substrate after 170 h.
The results presented in Figures 5 and 6 provide a succinct visual summary of our observations of the effect of the substrate pattern period and block copolymer lamellar period commensurability on the kinetics of block copolymer domain ordering. As the incommensurability of the bulk lamellar period of the block copolymer and the substrate pattern period increased, the time required to achieve perfectly ordered domains on chemically nanopatterned substrates increased. Plots of the azimuthally averaged power spectra of the 2D-FFTs at different times capture the various stages of block copolymer alignment on the chemically nanopatterned polystyrene brushes at various times and LS–LO commensurabilities. Figure 8 shows these plots for PS-b-PMMA thin films annealed on chemically nanopatterned polystyrene brushes for 3, 6, 72, and 170 h. After the hexagonally close-packed styrene domains coalesced into linear domains after 6 h, only the substrate pattern with LS = 47.5 nm shows registration of the block copolymer domains with respect to the lithographically defined chemically nanopatterned substrate. This is manifest in the narrow peak localized at qS = 0.132 nm−1. On chemical surface patterns with LS = 50 and 45 nm, the peaks in the azimuthally averaged power spectra appeared at qS = 0.126 nm−1 and qS = 0.140 nm−1 respectively, but also exhibited very broad bases, which is indicative of a large number of unaligned linear domains. For LS > 50 nm, the peaks in the azimuthally averaged power spectra were broad and located at multiples of qO, indicating that the block copolymer domains were not aligned with the chemically patterned substrate. Increasing the annealing time to 72 h yielded sufficiently ordered block copolymer domains on the LS = 45–52.5 nm chemical surface patterns to result in narrow peaks corresponding to multiples of qS in the azimuthally averaged power spectra, indicating that the defects in these films had been removed. For LS ≥ 55 nm, the azimuthally averaged power spectra display both broad peaks corresponding to multiples of qO and start to exhibit narrow peaks corresponding to multiples of qS, indicating that the block copolymer domains have started to align with the chemically patterned substrate. After 170 h of annealing, the transition to fully aligned linear domains was observed on the LS = 55 nm patterns, which now had only well-defined peaks at multiples of qS. Even after this long annealing time, the domains on the LS ≥ 57.5 nm chemical surface pattern were only starting to align with the underlying chemical surface pattern.
It is difficult to gather information about block copolymer structures in three dimensions experimentally, whereas simulations offer an attractive method for gaining insight into the full structure of these films. Self-consistent field theoretical calculations49 have been previously employed to successfully predict block copolymer self-assembly in the bulk,50 under confinement51 and in mixtures with homopolymers on chemically nanopatterned substrates.17 Figure 9 presents a series of images that capture the kinetic behavior of nearly symmetric block copolymers annealed on high interfacial energy contrast chemical surface patterns with LS ≈ LO. In these images, the PMMA blocks of the block copolymer have been removed. PS domains are represented in yellow, the interfaces between PS and PMMA are represented in blue, and the patterned substrate is black. In the bottom left of each image, the top 75% of the film has been removed to reveal the behavior of the block copolymer at the substrate. Initially, in panel (a), the block copolymer domains align at the chemical substrate pattern (surface-directed ordering) even as the block copolymer film at the free surface still appears to be in a disordered state. The block copolymer domains at the free surface then begin to form structures (panel (b,c)) that are reminiscent of the hexagonally close-packed styrene domains presented in Figure 2, although they do not display any long range hexagonal ordering. Eventually (panel (d–f)), these styrene domains coalesce to give linear structures that are registered with the underlying chemical surface pattern in some regions, but also display a high defect density in many regions of the film. As the simulation time further progresses (panel (g)), the structures break at the free surface and form new linear structures until perfectly registered domains are formed throughout the film (panel (h)). Using the crude mapping of the single chain dynamics, the time to achieve perfect order is about a factor 40 shorter in the SCMF simulations than in the experiment, which can partially be traced back to (i) the slightly thinner film thickness compared with the experiment, (ii) the smaller system size and (iii) most notably, the neglect of entanglement effects in the SCMF simulations.
The experimental and simulations results presented here offer important insight into the nature of the mechanism of directed self-assembly and the time scales required to achieve defect free block copolymer domain structures on chemically nanopatterned substrates. This study elucidates three important findings. First, lamellar domains of block copolymers annealed on chemically striped surface patterns form defect-free domain structures through a series of complex mechanistic steps. Second, both the interfacial energy of the chemical surface pattern and the block copolymer repeat period-substrate pattern period commensurability affect the time scales required to form defect-free block copolymer domains. Finally, the mechanism by which those defects are removed is categorically different from previously documented defect annihilation mechanisms observed in block copolymer thin films on topographically patterned and chemically uniform substrates.
The results indicate that the hexagonally close-packed styrene domains observed at short annealing times are likely different from perforated lamellae or nonequilibrium cylindrical structures previously observed in other systems.18–21, 52, 53 Other studies have investigated the transition structures of block copolymers that form in thin films or bulk systems during thermal annealing or have alternatively investigated the transient morphologies of lamellar block copolymers during solvent annealing, and observed hexagonally close-packed cylinders or perforated lamellae that have projections that could display well-ordered hexagonally close-packed domains. Contrastingly, the SCMF simulations suggest that the substrate interactions direct the near-substrate ordering in the initial stage. In the present study, the hexagonally close-packed styrene domains likely form at short annealing times in response to the directed assembly within a few nanometers of the chemically nanopatterned substrate. The appearance of hexagonally close-packed spots of styrene in a matrix of methyl methacrylate is attributed to the fact that the styrene block of the block copolymer is the minority block (volume fraction polystyrene, fPS = 0.48). These spots form such that they align with the same pattern period as the underlying chemical surface pattern.
The results of the SCMF simulations also offer insight into the nature of the linear block copolymer structures that form after the hexagonally close-packed spots coalesce. These structures give the appearance of lamellae that form in registration with the underlying chemical surface pattern. The simulations results indicate that these initial linear structures are often offset from the chemical surface pattern by LS/2 and do not necessarily propagate throughout the thickness of the film. These structures therefore may be more similar to cylinders oriented parallel to the free surface of the film than lamellae oriented perpendicular to the substrate.
The mechanism by which defects in the block copolymer domains are removed is categorically different from previously reported diffusion-annihilation mechanisms. SCMF simulations indicate that the block copolymer thin films initially form an ordered layer at the substrate that is registered with the underlying chemical surface pattern. As the annealing time is increased, the order slowly propagates upward to the free surface. The unregistered linear domains near the free surface break and reform new conformations of linear domains until defects are removed. There are two important implications of this mechanism. First, defects at the free surface cannot be assumed to be equilibrium structures, or indicative of the three dimensional structure of the films. Second, the kinetics of defect annihilation are governed primarily by the thermodynamics of the block copolymer/substrate interaction instead of the diffusion of defects to annihilate as observed previously.23 This second effect is seen in the longer annealing times required to achieve defect-free block copolymer domains on chemical surface patterns with a lower interfacial energy contrast or a period that is incommensurate with the block copolymer repeat period.
Since most of the data presented in this paper corresponds to domains annealed on chemical surface patterns with LS > LO, the possibility that we are observing tilted lamellar domains must be considered.54 In a previous study in which tilted domains were observed, defect structures at the junction of grains of lamellae that were tilted in opposite directions were also seen to form in the self-assembled domain structures.15 In the present study, no such defect structures were observed, indicating that the lamellae are truly registered with the underlying chemical surface pattern.
These results have both technological and fundamental importance for block copolymer lithography. Technologically, this study provides insight into the mechanism and processing times required to achieve defect-free assembly on chemically nanopatterned substrates, which will be important for applications of block copolymer lithography in nanomanufacturing. Furthermore, the observed mechanism for removing defects explains why defect-free arrays of block copolymer domains can be formed over arbitrarily large areas on chemically nanopatterned substrates, since defects do not need to diffuse to be removed.
The authors thank Dr. M.F. Montague and Prof. C. J. Hawker for their provision and characterization of the hydroxy-terminated initiator. This research was supported by the Semiconductor Research Corp. (SRC) (2002-MJ-985), the National Science Foundation through the Nanoscale Science and Engineering Center (DMR-0425880), and the Camille Dreyfus Teacher-Scholar Award. The authors thank the John von Neumann-Institute for Computing, Jülich, Germany, for central processing unit time on the IBM p690-cluster. This work is based in part upon research conducted at the Synchrotron Radiation Center, University of Wisconsin-Madison, which is supported by the NSF under award no. DMR-0084402. MPS acknowledges a fellowship from the SRC.