Article pubs.acs.org/Macromolecules
Orientational Preference in Multilayer Block Copolymer Nanomeshes with Respect to Layer-to-Layer Commensurability Corinne L. Carpenter,† Samuel Nicaise,§ Patrick Lauren Theofanis,∥ David Shykind,∥ Karl K. Berggren,§ Kris T. Delaney,‡ and Glenn H. Fredrickson*,†,‡ †
Department of Chemical Engineering and ‡Materials Research Laboratory, University of California, Santa Barbara, Santa Barbara, California 93106, United States § Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States ∥ Intel Corporation, Hillsboro, Oregon 97124, United States S Supporting Information *
ABSTRACT: We present a combination of self-consistent field theory simulations and experimental results to explore the mechanism behind the orientational preference of second-layer cylinders in nanomeshes formed by two consecutive steps of the self-assembly of block copolymers (BCPs). Incommensurability of the top-layer cylinder spacing with that of the bottom-layer features is found to dictate orientation preference, and this mismatch can be controlled by either the film height or the nanomesh spacing ratio via the molecular weight of the polymers used. When the space available within the film does not accommodate the hexagonal packing of the parallel orientation, the system will favor orthogonal alignment of the second-layer cylinders. This behavior is robust: it is consistently observed in many experimental systems and verified here by the comparison of free energies of both states obtained from simulations. We also discuss the impact of substrate selectivity and air−polymer interface selectivity on these energies and therefore their effect on the orientational selection.
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BACKGROUND AND PREVIOUS RESEARCH The directed self-assembly (DSA) of block copolymers has proven to be a highly versatile tool for supplementing existing processing techniques for patterning applications in the electronics industry, especially as a precursor to metallic features such as nanowires.1,2 Through combinations of topographical features, chemoepitaxial patterning, and substrate selectivity, DSA can be used to create uniform features,5−7 create isolated features such as those used in circuit design,8−10 or increase pattern density through pitch multiplication at a fraction of the cost of multiple passes of traditional lithography.3,4 Through the use of multiple DSA steps, it is possible to create more complicated three-dimensional morphologies via stacked layers.11−13 Our study focuses on the formation of nanomeshes from two separately deposited cylinder monolayers, with the configuration of the first layer preserved by an etch process in between the coating steps. These nanomesh configurations have a variety of interesting properties, but one of the most attractive for manufacturing and patterning applications is the orthogonality of the second-layer alignment. It is well documented that lamellar and cylindrical domains will align orthogonal to surfaces with neutral selectivity in thin films14,15 and trenches.16−18 Similar orientational preferences have been © XXXX American Chemical Society
observed in lamellae on corrugated or faceted substrates, where the behavior can be attributed to the alleviation of chain stretching.19−23 The analogous behavior has been observed in cylindrical morphologies,24−26 but the orthogonal orientation of cylinders above substrate features has not yet been satisfactorily explained. A previous study into the orthogonal assembly of nanomeshes displayed the aforementioned alignment in its experimental results, which included multiple morphologies, dimensions, and pitches.27 The experimental systems were varied and their exploration thorough, but their accompanying simulations were relatively sparse and focused primarily on trench-like and truncated systems or systems in which the film thickness was less than would be required to accommodate the assembly of a monolayer of cylinders above the first-layer features. The study used a film thickness of L0, the equilibrium spacing of cylindrical domains in a monolayer. The unphysically thin films used in simulations led to the conclusion that only extremely shallow topographical features (relative to the film height) and weak substrate interactions would produce Received: June 16, 2017 Revised: September 29, 2017
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DOI: 10.1021/acs.macromol.7b01290 Macromolecules XXXX, XXX, XXX−XXX
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Figure 1. A two-dimensional cross section of the substrate for a simulation cell with four half-cylinder features. The film height is fixed at 6.1Rg unless otherwise stated, while the height, width, and spacing of the cylinders are scaled by the spacing ratio, n. The top pattern of the mesh was fabricated by repeating the above process, though with slightly different conditions as reported here. For some cases of SD16, the spinning speed was increased to 2500 rpm, and the solution concentration was decreased to 0.28 wt %. For the smallest BCP line pattern, a film of 10.7 kg mol−1 (SD10) (PS-bPDMS) was spun from a 0.5 wt % solution in cyclohexane at 2500 rpm. SD10 films were solvent annealed overnight in acetone. After etching the second layer with the same approach as the first, the remaining patterns were composed of in-plane cylinders of oxidized PDMS, and the patterns were imaged with scanning electron microscopy (SEM) at an accelerating voltage of 5 kV with a working distance of around 7 mm in order to obtain the 1280 × 960 pixel images. Simulation Setup. We study second-layer self-assembly using selfconsistent field-theoretic (SCFT) simulations28,29 of cylinder-forming diblock copolymers (minority-block volume fraction fA = 0.3 and Flory−Huggins interaction parameter χABN = 25).30,31 We use 3D simulation cells that are laterally periodic, while we use a densitymasking method with optional chemical selectivity to confine the thin film between a topographically rough substrate and a flat top surface.32 The reference length for the simulations is the unperturbed radius of gyration (Rg) of the block copolymer, which for the polymer modeled here is approximately 7.1 nm. The top surface of the system is attractive to the minority component (χA−TN = −10) in order to mimic the chemical characteristics of a PS-b-PDMS thin film that exhibits a PDMS wetting layer at the air−polymer interface. In this notation, “A” refers to the cylinder-forming minority block of the polymer (PDMS), and system characteristics will be described as they relate to this component. For example, the top surface will be referred to as “attractive” as a convenient shorthand for “attractive to the minority block, and neutral to the majority block, of the diblock copolymer”. The lower density mask of the system is topographically patterned with uniform (position-independent) chemical selectivity of interaction strength, χA−SN, mimicking the experimentally prepared substrate for second deposition obtained from a postetched first deposition. Precise chemical selectivities of the substrate are difficult to establish due to the complex etch chemistry and presence of topographical features. Here we assume the substrate to have weakto-neutral interactions with the minority A block (χA−SN = −5, 0, and 5) and neutral interactions with the majority B block (χB−SN = 0). Because of the periodic nature of the cells, it was convenient to use complete, square repeat units of the nanomesh at the prescribed spacing ration, chosen here to range from 1 to 3 in increments of 0.5. In order to accomplish this, the length of each system was set equal to the center-to-center distance for the desired number of cylinders in the second layer (e.g., Lx = Ly = n·4.1Rg where n is the number of cylinders required and 4.1Rg is the center-to-center distance for cylinders), and the four half-cylindrical features on the substrate were sized to fit accordingly as shown in Figure 1. Finally, the system height was set to a “commensurate” depth of 6.1Rg (4.1Rg to accommodate the cylinders and 2Rg to accommodate the feature height), which allows the cylinders to form above the substrate features; this corresponds to a film thickness of approximately 43 nm. In later simulations, the film thickness was swept over a range from 4.1Rg to 8.1R g , ±2R g from the commensurate film thickness. These impressively large simulations were conducted on NVIDIA Tesla M2075 GPUs.33 By seeding SCFT with cylinder monolayers in two
orthogonal alignment and the creation of a nanomesh. Furthermore, the prior study did not examine relative free energies of candidate structures and does not preclude the possibility of trapping in metastable states. As we will argue, these simulation shortcomings lead to incorrect conclusions and miss the most significant influences on orientational selection. Here we present explicit energetic calculations for the parallel and orthogonal states and use the difference to determine their relative stability and concentrations at equilibrium. By examining these free energy differences at a variety of conditions, we propose a widely applicable mechanism for the reliable control of interlayer orientation in BCP nanomeshes formed by a double-DSA process. These conclusions are fully corroborated by the available experimental evidence.
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METHODS
In this section, we explore the formation of orthogonally aligned DSA nanomeshes created with block copolymers with different degrees of polymerization and varied film thicknesses. The first-layer features are created from diblocks with a higher degree of polymerization, and therefore larger feature-to-feature distances, than the second layer, as this was previously found to yield more desirable configurations.27 This leads to one of the most important characteristics of the nanomesh configurations: the “spacing ratio”, used here as the number of cylinders in the top layer per cylinder in the bottom layer. It can also be calculated by dividing the feature-to-feature in-plane spacing of the first layer by that of the second layer. Experimental Setup. Samples of silicon (approximately 1.5 in. by 1.5 in.) were cut from a ⟨100⟩ wafer, which was subsequently coated with a hydroxy-terminated polymer brush of poly(dimethylsiloxane) (0.8 kg mol−1 from Polymer Source, Inc. Quebec, Canada). The spin solution was 1 wt % in toluene, filtered through a 0.2 μm Anodisc membrane, and spun at 2000 rpm for 60 s. The wafers were annealed in a nitrogen environment at 170 °C overnight (approximately 15 h) and cooled for 2 min to ambient temperature. Nonattached polymer was removed by soaking the wafers in a toluene bath for 15 min, rinsing with toluene, and blowing dry with N2. The bottom pattern of the mesh was fabricated by spin-coating a block copolymer (BCP) film, solvent annealing to promote formation of in-plane cylindrical microdomains of polydimethylsiloxane (PDMS), and etching of the polystyrene (PS) matrix. For larger pitches of lines, a film of 45.5 kg mol−1 poly(styrene-b-dimethylsiloxane) (SD45) (PS-b-PDMS) with 30 wt % PDMS was spun from a 1.6 wt % solution in propylene glycol monomethyl ether acetate (PGMEA) at 2000 rpm. The films were solvent vapor annealed for roughly 6 h in a lidded glass dish with a liquid reservoir of toluene and heptane (3:1 ratio) in the bottom. For smaller pitches of lines, a film of 16 kg mol−1 poly(styrene-b-dimethylsiloxane) (SD16) (PS-b-PDMS) was spun from a 0.5 wt % solution in cyclohexane at 2000 rpm. These films were solvent vapor annealed for greater than 5 h in a lidded glass dish with a liquid reservoir of acetone in the bottom. The BCP morphologies were then quenched with the removal of the lid, allowing solvent desorption from the film. The line patterns were revealed and fixed by etching the surface-wetting PDMS layer and bulk of PS with reactive ion plasma etching. B
DOI: 10.1021/acs.macromol.7b01290 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules orientations, we were able to determine their equilibrium configurations and compare their free energies. Initializing our simulations from seeds is necessary because it is extremely difficult to converge to a defect-free configuration from disorder without some form of guidance. For the purposes of this study, we will focus simply on the sign of this free energy difference: negative favors parallel orientation at equilibrium, while positive will favor orthogonal orientation. It should be noted that there is a third possible orientation in which cylinders stand perpendicular to the substrate, but it was not observed in our experimental results.
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RESULTS Incommensurability Leads to Orthogonal Alignment. In this section we will provide theoretical and experimental evidence that the formation of orthogonally aligned DSA nanomeshes is dominated by the commensurability of the second-layer cylinders with the spacing and size of the first layer features and the height of the film. The previously specified ranges of spacing ratios and weak substrate interactions were examined, and the resulting extensive free-energy differences between parallel and orthogonal orientation with respect to substrate half cylinders are collected in Table 1. Table 1. Intensive Free Energy Differences (in 0.001kT/ Chain) between the Parallel and Orthogonal Orientations of PS-b-PDMS Second-Layer Films at a Commensurate Height of 6.1Rga
Figure 2. SCFT simulation images of a system with a spacing ratio of 1.5 and weakly repulsive substrate interactions (χA−SN = 5). The substrate and first-layer features are indicated in blue, while the minority-block densities are shown in red. The free energy difference between the parallel and orthogonal states is 10.0kT.
spacing ratio XPDMS−SN
1
1.5
2
2.5
3
−5 0 5
−7.89 −2.64 3.67
2.42 1.29 2.04
−1.73 −0.87 −1.73
1.46 0.94 0.61
−6.30 −3.61 −1.02
versus desired space within the film by “draping” the upper cylinders over the half-cylinders on the substrate, causing undulations along their length. Although this bending is not present in the bulk hexagonal phase, it results in lower free energy than the frustration of the parallel orientation observed in incommensurate systems. When the spacing mismatch does not occur, as in systems with integer spacing ratios and a commensurate film height, the system can assemble into the parallel configuration with a minimum of distortion, resulting in a lower free energy and making it the preferred state at equilibrium. This clean, unfrustrated assembly can be seen in Figure 3a, with the unfavored orthogonal candidate in Figure 3c. In the commensurate system (with a spacing ratio of 2), cylinders can form above and between the half-cylinders, and the minor features on the substrate are identical in every trench. By contrast, cylinders aligned orthogonal to the existing features must drape over each half-cylinder, resulting in energetically unfavorable bending and splitting of the halfcylinders on the substrate. The orthogonal configuration exhibits the same behaviors as in the incommensurate systems but is no longer a lower-energy alternative to the parallel configuration. The main factor controlling whether the second layer will favor parallel or orthogonal orientation appears to be the degree of commensurability in the parallel configuration and its ability to assemble regular, strain-free repeat units between each feature. Experimental observations, as shown in Figure 4, verify this observation, as systems with in-plane commensurability form parallel configurations, while those without it align orthogonal to the first-layer topographical features.
a Positive (bold) indicates that the orthogonal configuration is lower in free energy and therefore more frequently observed at equilibrium conditions, while negative (italic) indicates the same for the parallel orientation.
It is immediately evident from these data that the spacing ratio of the mesh is the primary controlling influence on orientation preference given commensurate film thicknesses and for weak substrate interactions. Systems with in-plane incommensurability (or those with a noninteger spacing ratio) display a clear preference for orthogonal alignment, while commensurate systems strongly tend toward parallel alignment. Figure 2 provides an example of the switch from a frustrated parallel configuration (Figure 2a) to a more relaxed orthogonal configuration (Figure 2c) obtained from SCFT simulations. In incommensurate systems, cylinders oriented parallel to the substrate features (as in Figure 2a) are unable to position in consistent locations above the topographic pattern. This frustration leads to some cylinders becoming centered above the trenches, while others are situated off-center, as shown in Figure 2b. A single simulation cell captures the full repeat unit of this morphology, but the individual trenches exhibit alternating behavior. Such a pattern has a relatively high free energy because, due to incompressibility, PS-block chain stretching must be increased for polymer chains anchored in cylinders above the trenches. This parallel configuration could be slightly less unfavorable were the top surface of the film allowed to undulate. However, our simulations are restricted to a flat air surface corresponding to a high surface tension case. The orthogonal orientation (shown in Figure 2c) of the top layer of cylinders alleviates the mismatch between the available C
DOI: 10.1021/acs.macromol.7b01290 Macromolecules XXXX, XXX, XXX−XXX
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The importance of commensurability continues to dominate assembly behavior when the film thickness is also altered, although it changes from simple in-plane commensurability to fully three-dimensional behavior. Figure 5 clearly shows a film
Figure 5. A system with a first layer of SD45 and a second layer of SD16, with feature-to-feature distances of 33 and 18 nm, respectively. This results in a spacing ratio of 1.83. The black (white) arrows indicate the local direction of the first (second)-layer features. The morphologies in the regions are (from left to right) a bilayer of cylinders orthogonal to the substrate (first-layer) cylinders, monolayer cylinders parallel to the substrate pattern, disordered, and orthogonal alignment. The greatest film thickness is found in the region with double-layered cylinders (far left), with thinner films associated with orthogonal alignment (far right), disordered (center right), and monolayer parallel (center left) cylinders accordingly.
Figure 3. A system with a spacing ratio of 2 and weakly repulsive substrate interactions (χA−SN = 5). The substrate and first-layer features are indicated in blue, while the minority-block densities are shown in red. The free energy difference between the parallel and orthogonal states is −15.1kT.
in which multiple morphologies are observed within a single system prepared with a spacing ratio of 1.83. By viewing the system at a slight angle, we were able to determine that the regions corresponded to thickness variations within the secondlayer film. This observation demonstrates a clear film thickness dependence to the relative orientation of the two layers, as this system has uniform feature spacing in the first layer and would be expected to adhere strictly to a single orientational preference based on the spacing ratio alone. Fluctuations in the film thickness result in a multitextured film morphology, resembling grains delineated by grain boundaries in a polycrystalline material. The controlling influence of commensurability can also be seen in systems with an integer spacing ratio and a film thickness that does not correspond to the commensurate height for a monolayer of cylinders. It is possible to stabilize orthogonal orientation in a system with an integer spacing ratio but incommensurate height, and this can be observed experimentally as shown in Figure 6. Figure 6a displays the orthogonal alignment of the second layer cylinders in nanomeshes with a noninteger spacing ratio of 1.83 and commensurate film height. This orientation persists across the sample in all regions of equal film thickness. In contrast, Figure 6b displays orthogonal orientation of secondlayer features, but at an integer spacing ratio of 2 and a reduced film height. The cylinders here do not lay on top of the substrate features; instead, they align orthogonally between the features with no interconnect between trenches. This leads to decorrelated features that, while oriented in the desired direction, are not aligned across trenches and are problematic for patterning applications because of their unpredictable
Figure 4. Orthogonal (a) and parallel (b) alignment in systems with commensurate film thickness. The first layer of each system is SD45, while the second layer is SD16.
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Figure 7. A system with a spacing ratio of 2, weakly repulsive surface interactions (χA−SN = 5), and a film thickness of 4.1Rg, or roughly twothirds of the commensurate value. The parallel configuration is 37kT higher in free energy than its orthogonal counterpart. The substrate and first-layer features are indicated in blue, while the minority-block densities are shown in red.
6b. The interplay between film thickness and spacing ratio in selectively stabilizing the orthogonal orientation is revealed by a comprehensive set of SCFT simulations that are summarized in Figure 8. As Figure 8 illustrates, the stability of the orthogonal orientation requires a specific combination of film thickness, spacing ratio, and substrate selectivity. In particular, films with a commensurate thickness will exhibit the orthogonal orientation at mismatched spacing ratio regardless of substrate selectivity (within the range examined here). The assembly of orthogonally aligned cylinders in shallower systems, on the other hand, is highly sensitive to substrate selectivity, with the weakly repulsive substrates resulting in stability at more spacing ratios than the weakly attractive substrates. One set of systems present in Table 1 but notably not yet addressed are those with a perfect match in length scales (e.g., one top-layer cylinder per half-cylinder on the substrate as shown in Figure 9). The free energy differences presented in Table 1 show that in 1:1 systems with neutral substrate− diblock interactions there is a relatively small energetic preference for the parallel orientation (5.76 kT lower in free energy than the orthogonal morphology). Thus, we anticipate that at equilibrium such systems will exhibit heavily intermixed areas of orthogonal and parallel alignment. Our simple commensurability argument suggests that parallel alignment should emerge at weak substrate interactions, but interestingly this is not always the case for perfectly matched systems. Although in the 1:1 configuration the parallel configuration is almost identical across the three substrate selectivities, the interactions between the substrate and the partial cylinders lying in the trenches introduce a sufficient energetic difference to give rise to different orientational preferences. When the substrate is weakly attractive to the minority component, the interfacial area of the substrate with the half-cylinders at the bottom of the system reduces the free energy and reinforces the stability of the parallel configuration, leading to a free energy difference of −17.2kT. However, if the substrate switches to
Figure 6. Orthogonal alignment in systems with (a) noninteger spacing ratio and commensurate height and (b) integer spacing ratio and incommensurate height. The first layer of each system is SD45, while the second layers are SD16 and SD12, respectively.
placement. Theoretical support for this conjecture is provided in Figure 7, reporting SCFT simulations conducted at an integer spacing ratio of 2, but at an incommensurate (shallower) film thickness of 4.1Rg. The decrease in film height causes clear distortions in both orientations. Each trench in the parallel configuration (Figure 7a) still forms a full repeat unit, but the top-layer cylinders are forced to lie between the features rather than above them. With insufficient space to assemble two complete cylinders in the trench, one of the pair attaches to the topographical features. The decreased height of the film prevents this displaced cylinder from sitting directly on top of the bottom-layer cylinders, so it lies off-center. This introduces additional chain stretching that the system attempts to accommodate by structuring of the wetting layer at the air interface and forming features with a depleted stripe between them. Because the top surface is attractive to the minority block, these depleted regions are energetically unfavorable, especially when combined with the frustrated cylinders. The orthogonal orientation under the same conditions avoids the issue of depleted stripes and the severe frustration in alternating cylinders. Even with its high degree of domain bending, the orthogonal orientation is energetically favorable at this reduced thickness. An experimental system displaying this behavior can be found in Figure E
DOI: 10.1021/acs.macromol.7b01290 Macromolecules XXXX, XXX, XXX−XXX
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Figure 8. Stable phase in second layer copolymer films of varying spacing ratio and height with varying substrate selectivities (weakly attractive, neutral, and weakly repulsive from left to right). The film height is measured from the base of the half-cylinder substrate features. Green squares indicate the locations of stable orthogonal configurations, and red circles indicate locations where parallel or defective conditions are more stable. For full quantitative data, please refer to the Supporting Information.
accordingly less sensitive to the unfavorable interactions with the substrate and favor nanomesh formation under such conditions. In summary, our simulations have demonstrated that across a range of spacing ratios, film thicknesses, and substrate interactions the primary controlling feature in the preference of a nanomesh for orthogonal orientation is the commensurability of the upper layer cylinders, which encompasses both height and spacing ratio, while the substrate interactions are secondary factors. Selectivity of Air Interface. In the simulation results presented thus far, the air−polymer interface was attractive to the minority component (χA−TN = −10); this enforced a wetting layer at the air interface in a manner corresponding to the behavior of the PS-b-PDMS diblock used in the experimental systems. Another diblock of interest in DSA, PS-b-PMMA, lacks this large selectivity and the accompanying wetting layer at the top of the system. By simply switching off the attractiveness of the top system (χA−TN = 0, where A now refers to polystyrene, the more etch-resistant component), we explored the free energies of the parallel and orthogonal morphologies at the same film height previously found to be commensurate with a monolayer of cylinders in the presence of a selective air interface (6.1Rg). The resulting energy differences are presented in Table 2. By comparing these energies with those found in Table 1, it is clear that the selectivity of the air−polymer interface (and therefore the two relevant chemistries) plays only a small role in the relative stability of the parallel and orthogonal
Figure 9. A system with a neutral substrate and a spacing ratio of 1. The morphologies for the corresponding configurations with weakly attractive and repulsive substrates are visually indistinguishable and are therefore not shown here. The substrate and first-layer features are indicated in blue, while the minority-block densities are shown in red. The parallel system is 5.76kT lower in free energy than the orthogonal system.
Table 2. Intensive Free Energy Differences (in 0.001kT/ Chain) between the Parallel and Orthogonal Orientations in PS-b-PMMA Systemsa spacing ratio
weakly repulsive, the opposite occurs: the contact area between the half-cylinders and the substrate incurs an energetic penalty, increasing the free energy of the parallel orientation. The orthogonal configuration experiences corresponding increases in free energy, but this increase is smaller because of the reduced surface area at the substrate interface. The partial cylinders on the substrate break apart rather than drape continuously over the first-layer features, meaning their contact area is roughly half that of the parallel case. They are
XPMMA−SN
1
1.5
2
2.5
3
−5 0 5
−5.89 −5.54 0.46
−0.01 5.02 1.70
−6.98 −4.65 −2.33
2.58 1.24 0.94
−6.13 −3.50 −0.93
a Positive (bold) indicates that the orthogonal configuration is lower in free energy and therefore more frequently observed at equilibrium conditions, while negative (italic) indicates the same for the parallel orientation.
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DOI: 10.1021/acs.macromol.7b01290 Macromolecules XXXX, XXX, XXX−XXX
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For the sake of completeness, we report on SCFT simulations conducted for films mimicking PS-b-PDMS with strongly selective substrates (χPDMS−SN = ± 15). Both cases proved to be unfavorable for the orthogonal morphology. Systems with substrates that were strongly attractive to the minority cylinder-forming component of the diblock (χPDMS−SN = −15) consistently exhibited wetting behavior between the features on the substrate, forming horizontal structures, as shown in Figure 11. If these systems were to be used for pattern
morphologies. The only notable difference is in the system with a substrate with a weak preference for the minority component and a spacing ratio of 1.5, which has almost no preference for either orientation. The competing morphologies are shown in Figure 10.
Figure 10. PS-b-PMMA candidate alignments for a spacing ratio of 1.5 and a weakly attractive substrate (XPMMA−SN = −5). The top surface is neutral (XPMMA−TN = 0), unlike PS-b-PDMS systems where it is attractive to PDMS. The substrate and first-layer features are indicated in blue, while the minority-block densities are shown in red. The energy difference between the parallel and orthogonal systems is only 0.04kT.
This lack of preference appears to be the result of the additional interface between the substrate and the horizontal features at the base of the system. The additional surface area with the minority-attractive substrate seems to balance the entropic stretching penalty due to the mismatch of the hexagonally packed cylinders, so that the energy penalty is nearly equal to that of the slight bending in the orthogonal morphology. Systems with larger spacing ratios return to the commensurability-dependent behavior discussed earlier. In summary, on the basis of our computational analysis of the role of top/air interface selectivity, it appears that the creation of self-assembled nanomeshes is possible for a range of block copolymer chemistries with the same prescription, i.e., spacing ratio for controlling orientation. Large Substrate Selectivity. In previous sections, we have addressed the energetic effects of neutral or weakly selective substrates under a variety of conditions. With the exception of a few notable situations discussed above, these interactions have little influence on the orientational preference of nanomeshes.
Figure 11. A system with a spacing ratio of 2 and a strongly attractive substrate (XPDMS−SN = −5). The substrate and first-layer features are indicated in blue, while the minority-block densities are shown in red.
transfer, these structures could interfere, as they will survive the selective etch process along with the cylinders and make further patterning steps extremely difficult. The other scenario, that of a substrate strongly repulsive to the minority component (χPDMS−SN = 15), is also unfavorable for the formation of the orthogonal morphology. When the wetting layer on the substrate becomes energetically unfavorable, the orthogonal configuration is destabilized relative to the parallel configuration (with its reduced interfacial area). This has no visible impact on the system configurations but results in free energies of the parallel configurations lower than their G
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orthogonal counterparts. As this holds for all systems studied, the exact values are not shown here. Fortunately, none of the experimental systems display the morphological behavior associated with either of the strongly selective substrates. The etch after the first step of DSA appears to create a nonselective or weakly preferential substrate, allowing for good assembly of the target morphologies. As long as the substrate is not strongly selective toward one of the polymer components, the exact nature of the selectivity appears not to be an important consideration in the stability of the orthogonal orientation in the DSA of nanomeshes.
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CONCLUSIONS
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ASSOCIATED CONTENT
REFERENCES
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The preference for the orthogonal orientation of cylinders above topographically patterned substrates is primarily dependent on the lateral commensurability of the diblock with the first-layer features and the film thickness. At film heights commensurate with a monolayer of cylinders, noninteger inplane spacing ratios result in orthogonal orientations, while integer spacing ratios only do so at a reduced film thickness. The substrate selectivity has little influence if it is sufficiently weak. Substrates that are strongly selective toward either component disrupt the formation of nanomeshes. The air− polymer interfacial selectivity was further shown to have little effect on the formation of nanomeshes. The two-step DSA process, initially presented by Tavakkoli et al.27 and further explored here, is a low-cost method for the creation of nanomeshes at a variety of conditions. Our SCFT simulations, coupled with the experimental results presented here and elsewhere,27 suggest that the mechanism behind the orthogonal orientation is sufficiently robust to allow for the patterning of grids with tunable spacing ratios, expanding the potential applications of this technique and enhancing the use of DSA in the manufacture of advanced semiconductors.
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b01290.
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Article
Quantitative data for Figure 8 (PDF)
AUTHOR INFORMATION
Corresponding Author
*E-mail
[email protected] (G.H.F.). ORCID
Corinne L. Carpenter: 0000-0001-9462-7020 Samuel Nicaise: 0000-0003-3329-9099 Glenn H. Fredrickson: 0000-0002-6716-9017 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We are pleased to acknowledge financial support from Intel Corporation and computing resources provided by the Center for Scientific Computing at the CNSI and MRL: an NSF MRSEC (DMR-1121053) and NSF CNS-0960316. S.M.N. acknowledges support by the National Science Foundation (CMMI-1246740). H
DOI: 10.1021/acs.macromol.7b01290 Macromolecules XXXX, XXX, XXX−XXX
Article
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DOI: 10.1021/acs.macromol.7b01290 Macromolecules XXXX, XXX, XXX−XXX
