Flow‐Induced Microdomain Alignment During Block Copolymer Graphoepitaxy
Baopu Zhang, Mingchao Ma, Zehao Sun, Jaedong Jang, Alfredo Alexander‐Katz, Caroline A. Ross
TL;DR
This study explores how polymer flow during a nanofabrication process affects the alignment of tiny structures on patterned surfaces.
Contribution
The study reveals how flow processes during solvent vapor annealing influence microdomain orientation in block copolymer graphoepitaxy.
Findings
Capillary flow in the first minute of annealing planarizes the film into an incommensurate thickness.
Isotropic dewetting produces microdomains transverse to trench sidewalls, while anisotropic dewetting promotes alignment parallel to the walls.
The study demonstrates a connection between flow-induced microdomain alignment, film thickness, and trench depth.
Abstract
Block copolymer (BCP) graphoepitaxy provides a strategy for advanced nanofabrication based on self‐assembly. However, the polymer flow processes that occur due to the topography of the substrates and their effects on the self‐assembled microdomain patterns are not well understood. Here, by analyzing film thickness profiles and microdomain morphologies as a function of time during solvent vapor annealing, the time scale of the flow processes (capillary flow and dewetting) and how they determine the in‐plane orientation of cylindrical microdomains with respect to the sidewalls of trenches etched in the substrate are revealed. Capillary flow in the first minute of annealing planarizes the film into an incommensurate thickness. The film then dewets through nucleation and growth of islands and holes, which extend either isotropically or anisotropically along the trench axis, depending on…
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FIGURE 1
FIGURE 2
FIGURE 3
FIGURE 4| Time | Shallow Trench | Deep Trench | Flat Substrate |
|---|---|---|---|
| 6 min | 1.1 ± 0.5 | 6.8 ± 2.7 | 1.0 ± 0.1 |
| 30 min | 0.8 ± 0.3 | 26.5 ± 11.3 | 1.0 ± 0.1 |
- —NSF10.13039/100000001
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Taxonomy
TopicsBlock Copolymer Self-Assembly · Fluid Dynamics and Thin Films · Nanofabrication and Lithography Techniques
Introduction
1
BCP self‐assembly has long been considered a promising pathway toward high‐throughput fabrication of nanostructures for functional devices such as patterned magnetic media [1], gas sensors [2], plasmonic surfaces [3], and for rectification of patterns formed by UV lithography [4]. Among multiple strategies to obtain self‐assembled patterns with long‐range order, flow‐induced alignment, in which a BCP thin film is subjected to shear stress, is efficient in aligning microdomains parallel to the shearing direction [5, 6, 7, 8, 9, 10, 11, 12]. Graphoepitaxy, in which substrate topography guides the self‐assembly of a BCP thin film, has successfully directed the formation of arrays of spherical [13, 14], cylindrical [15, 16], and lamellar [17, 18] microdomains. Graphoepitaxy is capable of directing BCPs with a period more than an order of magnitude smaller than the topographical features (pattern multiplication) [15, 16], as well as directing the formation of non‐trivial 3D structures, including meshes and interconnected networks [19, 20, 21]. However, the polymer flow processes (capillary flow and dewetting) occurring during graphoepitaxy when a BCP film on a topographically patterned substrate is annealed, and the effects of local flow processes on microdomain orientation, are not well characterized.
An as‐spun thin film conforms to the topography of the substrate, but during annealing, capillary forces drive polymer redistribution from the raised mesas into recessed trenches to reduce surface curvature [22]. Numerous studies have reported the emergence of cylindrical microdomains oriented transverse to the trench sidewalls after both thermal annealing (TA) [23, 24] and solvent vapor annealing (SVA) [15, 25], and attributed this orientation to capillary flow. Notably, transverse alignment has been found after hours of SVA and tens of hours of TA [15, 24]. However, most studies inferred the role and kinetics of capillary flow indirectly from changes in microdomain orientation, with few directly measuring the capillary flow directly from the film profile. Fitzgerald et al. measured film thickness on mesas and trenches after different TA durations, and revealed that capillary flow was coupled with residual solvent evaporation. However, the resulting morphology consisted of out‐of‐plane oriented microdomains, rather than in‐plane, likely due to the dominant solvent evaporation process [26]. Therefore, key questions are unanswered, particularly the time scale of capillary flow during SVA and its correspondence with the emergence of transverse alignment of in‐plane cylindrical microdomains.
BCP thin films that form layers of in‐plane oriented microdomains dewet into islands and holes during annealing to achieve a film thickness with minimal energy that is commensurate with the microdomain layer spacing and wetting layers [27, 28, 29]. Two widely reported dewetting mechanisms: nucleation and growth, and spinodal dewetting, have been observed under both TA [30, 31] and SVA [32, 33]. In the early stages of dewetting, the nucleation and growth mechanism leads to randomly positioned island and hole nuclei. In contrast, spinodal dewetting forms a bicontinuous network of islands and holes. Eventually, both mechanisms produce discrete islands and holes. Dewetting occurs on significantly shorter timescales under SVA compared to TA [31, 32]. On flat substrates, islands and holes are randomly located, but dewetting can be guided by templates, and this has been utilized to generate hierarchical structures [34, 35, 36, 37, 38]. However, most studies on dewetting over templates have focused on the final microdomain morphologies, and the interplay between polymer flow, the template geometry, and morphological evolution throughout dewetting has not been described.
Here, we examine the film thickness profile and microdomain orientation of a cylindrical‐morphology BCP after various periods of SVA. Our results reveal that capillary flow dominates the early stages of annealing, planarizing the initially conformal film and leading to a preferential orientation of the microdomains transverse to the trench sidewalls. Subsequently, the planarized film dewets via a nucleation and growth mechanism to attain regions with commensurate thicknesses. The film thickness governs the shape of the islands and the resulting microdomain orientation. For isotropic island growth, the microdomains remain oriented transverse to the trench sidewalls. In contrast, anisotropic island growth parallel to the trenches causes the reorientation of the initially transverse microdomains to become aligned parallel to the trench wall. This is the first study that comprehensively reveals the time scales of capillary flow and dewetting on topographical trenches during SVA, and the temporal mapping to microdomain orientation demonstrates an intriguing dependence of flow‐induced microdomain alignment on the film thickness and trench depth.
Results
2
We used a cylinder‐forming polystyrene‐block‐polydimethylsiloxane (PS‐b‐PDMS, 11 kg mol^−1^‐b‐5 kg mol^−1^, center‐to‐center spacing L 0 ≈ 20 nm) as a model system. We spin coated the BCP solution onto substrates patterned with trenches of two different depths, 14.5 nm (‘shallow’ trenches) and 18 nm (‘deep’ trenches), both having trench widths of 125 nm and a period of 250 nm. The samples were annealed using acetone vapor for various durations. Atomic force microscopy (AFM) was used to characterize the topography of the annealed film, and hence the flow of the BCP from the mesas to the trenches, as well as the thickness of islands and holes formed by dewetting, and the microdomain morphology was revealed by reactive ion etching and scanning electron microscopy (SEM). A CF_4_ plasma removed the PDMS wetting layer, followed by an O_2_ plasma that selectively removed the PS block and converted PDMS into silicon oxide. Details are given in the Methods Section and Section S1.
Figure 1A summarizes the two key characteristics of the final microdomain arrangement—microdomain orientation and island shape—for various as‐coated film thicknesses on the two trench depths after SVA. There is a clear relationship between the microdomain orientation and the island shape. Microdomains aligned parallel to the sidewalls are consistently associated with anisotropic dewetting in which islands grow parallel to the trenches, while transverse microdomains are consistently associated with isotropic or no dewetting. To understand this relationship, we examine the evolution of the 20 nm film on both trench depths in detail. Figure 1B summarizes the key stages of capillary flow, dewetting, and microdomain alignment observed during SVA for the 20 nm film on the two trench depths. We first describe the overall evolution of the film during the three stages, and then consider each stage in detail in subsequent sections.
Summary of polymer flow processes and microdomain orientation. (A) Summary of microdomain orientations (transverse or parallel) and dewetting mechanisms (anisotropic, isotropic, or no dewetting under commensurate conditions) for various trench depths and film thicknesses, defined as the nominal thickness on a flat substrates. (B) Schematic of the evolution of the 20 nm film. The first row corresponds to shallow trenches and the second row to deep trenches. In the as‐spun film, the surface of the film is conformally curved. Between 0 and 1 min, capillary flow planarizes the film in its swelled state and induces a preferential but imperfect transverse microdomain orientation. The planar film is represented by pink, the PDMS microdomains are highlighted in red, and the PS matrix is highlighted in blue. Between 2 and 3 min, the planarized but incommensurate film undergoes dewetting to nucleate monolayer islands. On shallow trenches, nuclei draw polymer from the film on both trenches and mesas, and span across multiple trenches and mesas. In contrast, on deep trenches, nuclei draw polymer primarily from the film on the trenches, and are thus confined along the trench long axis. For both trench depths, the fraction of transverse microdomains increases. After 3 min, on shallow trenches, islands grow isotropically, and the microdomains are oriented transverse to the trenches, whereas for deep trenches, islands grow anisotropically along the trench axis, and the microdomains reorient to lie along the trenches.
During the first stage of SVA, within 1 min, capillary flow drives the polymer from the mesas into the trenches, planarizing the film in its swelled state. Simultaneously, microphase separation occurs, leading to the appearance of cylindrical PDMS microdomains transverse to the sidewalls within the trenches. For shallow trenches, the film remaining on the mesas is thick enough to exhibit perpendicular cylinders, whereas for deep trenches, the thinner residual film on the mesas does not exhibit microdomains.
During the second stage of SVA, between 2 and 3 min, dewetting is initiated. The planarized film is, in general, incommensurate with the layer thickness of the microdomains and dewets to form small islands (nuclei) composed of a monolayer of cylinders. The source of excess polymer for these islands depends on the film thickness and trench depth. For the case of the 20 nm film on shallow trenches, the film on both mesas and trenches dewets, whereas for deep trenches, only the film on the trenches dewets. Consequently, island nuclei on shallow trenches are equiaxed and span multiple mesas, whereas those on deep trenches are elongated and confined along a single mesa. During this stage, the transverse orientation of the microdomains on the trenches becomes more pronounced.
The third stage of SVA, after 3 min is the growth of islands. For the 20 nm film on shallow trenches, the equiaxed islands grow isotropically. In contrast, the elongated islands on deep trenches primarily grow along the trench axis. The final microdomain orientation becomes transverse on shallow trenches and parallel on deep trenches. The same general principles apply to the other film thicknesses shown in Figure 1A. For example, for the thinnest films (11 nm), dewetting only occurs within the trenches, leading to elongated islands/holes and parallel microdomain orientation for both trench depths. For the thickest films (24 nm) dewetting occurs isotropically, or the film is commensurate and does not dewet, and the transverse orientation persists.
Capillary Flow
2.1
To characterize the capillary flow regime, the topography of the film was measured by AFM to determine the film thickness on both mesas and trenches after deswelling. The topographical templates were also measured as a reference after scratching off a small region of the film without damaging the adjacent film. The exposed mesa provided a reference height to determine the film thickness on the mesas and trenches (Section S2) [39, 40]. We define the mesa film thickness, *d_m_ *, as the height difference between the highest point in the film profile and the mesa surface, and the trench film thickness, *d_t_ *, as the height difference between the lowest point in the film profile and the trench surface (Figure 2B). The film thickness was obtained from averaging three cross sections in the AFM scan (Figure S2). Figure 2A shows that *d_t_
- increases while *d_m_
- decreases during the first minute of annealing for both trench depths, and they remain stable between 1 and 2 min, suggesting that capillary flow occurs within the first minute of annealing.
Capillary flow. (A) The temporal variation of film thickness on trenches and mesas for both trench depths, for films nominally 20 nm thick. (B) Schematic of film profile in the deswelled and swelled state. (C) Height difference between mesa and trench. Δ0 is calculated from the measured film thicknesses and the swelling ratio based on the assumption that the swelled film is planar. Microdomains on (D) shallow trenches and (E) deep trenches after 0, 15, and 60 s of annealing. All scale bars are 100 nm.
The film thickness in the swelled state is inferred from the measured thickness distribution of the deswelled film and the time‐dependent swelling ratio SR, which was determined by in situ spectral reflectometry measurements of film thickness on a flat substrate during SVA (Section S4). In Figure 2B, the deswelled film profile is approximated by a sinusoidal function in which the peak‐to‐valley height difference is denoted as Δ and the trench depth is denoted as t. Our model describing the swelled film is described in detail in Section S3. In the swelled state, we assume that both *d_m_
- and *d_t_
- increase proportionally by a factor of SR to define the peak and valley of the sinusoidal swelled film profile. The swelled film should be planar when capillary flow is complete, leading to:
In Equation (2), t·(1−1SR)=Δ0 is the planarized film condition deduced from Equation (1). Therefore, when Δ, the peak‐to‐valley height difference in the deswelled state, equals Δ_0_, the film was planar in its swelled state. Figure 2C plots the measured Δ vs. annealing time, and the calculated Δ_0_ corresponding to deswelling a planar film based on Equation (2). Prior to 1 min, Δ > Δ_0_ for both trench depths, indicating that the swelled film is not yet planar and capillary flow is still occurring to reduce curvature. After 1 min, Δ ≈ Δ_0_, suggesting the film is planar in the swelled state, i.e., the capillary flow has planarized the swelled film.
We have assumed the same SR for films on flat substrates, on trenches, and on mesas due to the difficulty of measuring SR over topographical features using reflectometry. Zettl et al. found that SR was higher for thinner films of polystyrene‐*block‐*polybutadiene (47 kg mol^−1^, *f_PS_
- = 26%) in chloroform vapor, changing from 1.2 to 1.4 when the film thickness was decreased by more than a monolayer [41]. A similar dependence of SR in our case for film thickness approximately 10 nm would lead to a difference in swelled thickness of order 1 nm, which would have minor effects on the analysis.
Our model implies that Δ_0_ is independent of the absolute film thickness, but varies linearly with trench depth t. This is consistent with the results of Michman et al., who also reported a linear relationship between t and height difference Δ in the deswelled state after annealing polystyrene‐block‐polymethyl methacrylate (PS‐b‐PMMA) (312 kg mol^−1^, *f_PS_
- = 48%) thin films on trenches using chloroform vapor in a petri dish for 15 min [39, 40]. Their result, Δ ≈ 0.44t, corresponds to SR ≈ 1.8 based on Equation (2). Although their study did not report the SR, this inferred SR value aligns well with that reported in two studies using chloroform vapor to anneal PS and PMMA [42, 43].
We examined the microdomain morphology by SEM at various time points, shown in Figure 2D,E for shallow and deep trenches, respectively. The as‐spun film shows short‐range microdomains across both mesas and trenches. For the shallow trenches, 15 s annealing yields continuous cylinders spanning the mesas and trenches, and 60 s annealing causes the microdomains on the mesas to break down into a mixture of dots and cylinders. The dots can be described as short perpendicular cylinders, which form when the film is too thin to accommodate in‐plane cylinders [44], consistent with the redistribution of polymer from the mesas to the trenches. For deep trenches, after 15 s annealing, only faint dots are visible on the mesas, and at 60 s, no observable features remain. The thinner film on the mesas of deep trenches is consistent with Figure 2A, where *d_m_
- on deep trenches is smaller.
Island Nucleation and Growth
2.2
The planar film produced by capillary flow represents an incommensurate film thickness, which drives dewetting into islands and holes to satisfy the commensurability condition [28, 35, 45, 46]. As Figure 3A shows, at 2 min we observe island nuclei on mesas for the 20 nm film on both trench depths and for the flat substrate, with random distribution (Figure 3A–D at 2 min). The islands consist of a monolayer of in‐plane cylinders. For the shallow trenches and the flat substrate, the thinner regions between the islands consist of vertical cylinders (dots), but for the deep trenches, the mesas are mainly featureless because the film on the mesa is too thin to support microdomains.
Island nucleation and growth for 20 nm thick films. (A) Island nucleation at 2 min on shallow trenches (left), deep trenches (middle), and flat substrates (right). Temporal evolution of island and hole morphologies for (B) shallow trenches, (C) deep trenches, and (D) flat substrates. (E) Temporal evolution of film thickness on islands and holes. In the label S(D)‐H(I)‐M(T), the first label stands for shallow (S) and deep (D) trenches, the second for holes (H) and islands (I), and the third for mesas (M) and trenches (T). (F) The dimensions of islands on different substrates at 6 and 30 min. Scale bar is 100 nm for (A) and 5 µm for (B–D).
After 3 min annealing, the islands are equiaxed on shallow trenches and on a flat substrate, but they are elongated along the trench axis on deep trenches. For the shallow trenches, the film on both mesas and trenches contributes polymer volume to the island nuclei, which can thus expand across the mesas, similar to island nucleation on the flat substrate. In contrast, for deep trenches, the film on the mesas is thin, and the polymer volume that forms the island nuclei primarily comes from the film on the trenches.
These differences suggest the film thickness on the mesas, which is indirectly governed by trench depth, is a critical factor determining the dewetting mechanism by constraining the polymer flow direction. The self‐assembly results for other film thicknesses summarized in Figure 1A support our conclusion. For example, for the 16.5 nm film on the shallow trench, the mesas only have a thin wetting layer after capillary flow occurs, whereas for the 24 nm film on the deep trench, the mesas show a mix of in‐plane and out‐of‐plane cylinders. Consistent with our conclusion, the islands in the 16.5 nm film/shallow trenches are elongated, and those in the 24 nm film/deep trenches are equiaxed (Section S12, Figures S17 and S18).
To analyze island growth in the 20 nm thick films during further annealing, we measured the film thickness by AFM (Figure 3E). The notation S(D)‐H(I)‐T(M) denotes the film thickness at specific locations: in the holes (H) or islands (I), on the trenches (T) or on the mesas (M), and for shallow (S) or deep (D) trenches. Measurements at 2 min did not include the thickness of the islands due to their small size, so only four categories were recorded, but after 3 min annealing, all eight categories of sites were measured. There are two key observations. First, the film thickness clusters into discrete values: approximately 8 nm for H‐M, 16 nm for I‐M and H‐T, and 25 nm for I‐T. These thicknesses correspond to the featureless wetting layer on the mesas for H‐M, a monolayer of in‐plane cylinders for I‐M and H‐T, and a bilayer of in‐plane cylinders for I‐T (Section S5). Interestingly, the height difference Δ is similar for both islands and holes (differing by less than 2 nm, Section S3). This can be understood from the model of the swelled film profile. Rewriting Equation (2) as:
shows that adding a monolayer of cylinders (denoted as a film thickness of L 1) to both *d_m_
- and *d_t_
- does not affect Δ, and thus the planarized film condition remains satisfied. Similar Δ between islands and holes was also observed by Michman et al. [39].
Second, from 3 to 30 min annealing, the film thickness of all eight categories remains constant (Figure 3E). The constant film thickness suggests that the islands are formed in the first 2–3 min, and further annealing leads to growth of the islands and holes without changing their thickness. We note that the SR reaches equilibrium around 6 min (Figure S5), and thus the island growth may be at least partially due to continued swelling of the film and a net increase in its volume. In fact, Figure 3D shows a transition from holes at 3 min to islands at 6 min on the flat substrate, likely due to increased volume. See Section S7 for further discussion. In the following, we will focus on describing the island morphology after SR reaches equilibrium to analyze island growth behavior at fixed swelling.
The in‐plane flow direction during island growth was inferred by tracking the dimensions of islands with time. The X‐axis is transverse to the trench axis, and the Y‐axis is parallel to the trench. We measured the X and Y dimensions of more than one hundred islands using a self‐developed image analysis code (Section S6), as shown in Figure 3F. Table 1 summarizes the aspect ratios (ΔY/ΔX) of the islands over time. On shallow trenches and flat substrates, islands grow isotropically, whereas on deep trenches, growth is predominantly along the Y‐axis, and their aspect ratio increases with time. Previous work using TA concluded that polymer flowing from small to large islands through diffusion accounts for island growth [47, 48]. Assuming the same growth mechanism occurs under SVA, the polymer flow is therefore isotropic for the shallow trenches and directed along the trench axis for the deep trenches.
Microdomain Orientation
2.3
The effect of capillary flow and dewetting on microdomain orientation in 20 nm thick films was studied by measuring the microdomain orientation from SEM images using orientation mapping, as shown in Figure 4B,C (Section S8). The alignment with respect to the trench wall was quantified using the following formulae:
where N θ is the number of pixels containing cylinders with an orientation of θ. 0° and 90° indicate alignment perpendicular and parallel to the trench wall, respectively. The orientation includes a ± 7° deviation, following Ryu et al. [49]. Therefore, f ⊥ and f ∥ denote the fraction of microdomains having transverse and parallel orientation, respectively. Figure 4A shows the temporal evolution of these two fractions in the islands. At each time point, the average fraction was computed from three randomly selected spots, each containing six trenches. The data shows that f ⊥ increases for both trench depths during the first 2 min, i.e., when capillary flow occurs and prior to island nucleation and growth. After 2 min, when islands form and grow, f ⊥ becomes dominant on shallow trenches, while f ∥ becomes dominant on deep trenches. The orientation shows little further change after 12 min anneal. The orientation evolution in hole regions showed a similar dominant orientation to that in the islands (Section S10), but the orientation was less pronounced (its plateau value was approximately 0.4 vs. 0.8, Figure S12).
Microdomain orientation evolution for 20 nm thick films. (A) Temporal evolution of transverse and parallel fractions of microdomains on shallow and deep trenches in islands. Examples of orientation mapping on (B) shallow trenches and (C) deep trenches at key timepoints. Scale bar is 100 nm. (D) Kuiper's test result at 6 min (upper right) and 60 min (bottom left). The pair with the lowest α is highlighted, and the cropped orientation mapping is shown. Scale bar is 100 nm. (E) The self‐assembly behavior on a V‐shaped trench of 18 nm depth at 1, 3, and 60 min. Scale bar is 100 nm for the first row and 2 µm for the second row.
Figure 4B,C shows representative examples of microdomain orientations. At 1 min, a small fraction of the microdomains on both trench depths are transverse due to capillary flow. At 3 min, the islands on shallow trenches cross multiple mesas and trenches, and more of the microdomains are transverse. On deep trenches, islands are often confined to one mesa and its neighboring trenches, and microdomains on the trenches show a mixed orientation. At 60 min, both trench depths show ordered cylinder microdomains on the trenches with few defects. Section S9, Figures S10 and S11 show the complete data set over time.
For the deep trenches, we expect that the directional polymer flow along the trenches during island growth causes the reorientation of the cylindrical microdomains to lie parallel to the sidewalls. For the shallow trenches, the isotropic flow likely allows the initial transverse microdomain alignment established by capillary flow to persist and develop.
To test the hypothesis that microdomain orientation is not changed by isotropic island growth on shallow trenches, we compared orientation mapping at each of twelve randomly selected areas using the nonparametric two‐sample Kuiper's test, a widely applied statistical test to analyze angular distributions [50, 51]. We treated the normalized orientation mapping as a probability function, and the Kuiper's test was applied to compare their cumulative distribution functions (Section S11). The null hypothesis H 0 assumes the normalized orientation mapping of two areas to be from the same distribution, and the alternative hypothesis H 1 assumes they are from different distributions. A significance level α = 0.05 was used as a threshold to accept H 1 and reject H 0. Failure to reject H 0 would support our hypothesis that the isotropic flow during island growth has little effect on microdomain orientation, because the twelve randomly chosen areas are expected to have different flow directions during island growth, yet there is no statistically significant difference. Conversely, acceptance of H 1 would suggest that the flow significantly affects orientation.
Figure 4D shows the test results at 6 and 60 min. Each pixel in the matrix shows the significance level for the pairwise comparison between the two areas that the row and column correspond to. The upper‐right and lower‐left triangle shows the results at 6 and 60 min, respectively (complete SEM images are given in Figures S15 and S16). Diagonal elements are omitted as they represent comparing an area with itself. In all comparisons, the test result exceeds the significance threshold, often by an order of magnitude, and we thus fail to reject H 0. The pair that gave the lowest significance level (highest confidence to reject H 0) at 6 and 60 min are highlighted, and their corresponding orientation maps are shown. Note, we cropped the original image containing 6 trenches to only 3 trenches to highlight the morphology details. At 6 min, f ⊥ is comparable between the two areas, only with a few defects that have different orientations. At 60 min, both areas have highly ordered transverse microdomains with few defects. Thus, even for these two most divergent cases, the microdomain orientation is very similar. The analysis supports our hypothesis that the isotropic flow during island growth has little effect on microdomain orientation. A similar conclusion can be drawn from the results at 12 and 30 min (Figure S14).
We also found that deep trenches lead to anisotropic island growth for a 20 nm film, even for V‐shaped trenches with a 60° bend. In Figure 4E, the capillary flow, island nucleation and growth, and microdomain orientation followed similar mechanisms and time scales as those on straight trenches. This observation supports our hypothesis that microdomains are realigned by the directional polymer flow during anistropic dewetting.
These results are consistent with the hypothesis that capillary flow promotes the initial orientation of the microdomains transverse to the trench walls, and the orientation evolves in the subsequent dewetting phase. The transverse orientation develops further during isotropic island growth, but the microdomains reorient parallel to the sidewalls during anisotropic island growth. We also reproduced transverse microdomain orientations on shallow V‐shape and circular trenches, and parallel microdomain orientations on deep circular trenches (Figures S19–S21) for the same 20 nm nominal film thickness. For all cases, transverse microdomains correlate with isotropic island morphologies while parallel microdomains correlate with elongated islands along the trench axis, suggesting the generality of the proposed flow‐induced alignment during graphoepitaxy over multiple topographical patterns.
Now we apply the principles from the two model systems to understand the self‐assembly behaviors in the other cases summarized in Figure 1A. The 24 nm film on deep trenches shows isotropic dewetting and transverse microdomains (Figure S17), while the 16.5 nm film on shallow trenches shows anisotropic dewetting with parallel microdomains (Figure S18). For the 11 nm film on both trench depths, the trenches exhibit out‐of‐plane cylinders after capillary flow. With further annealing, nuclei composing of a monolayer of in‐plane cylinders are formed within the trenches. After the nucleation has completed, the trenches exhibit regions consisting of a monolayer of cylinders (islands) and regions of a wetting layer (holes), which then grow anisotropically along the trench long axis. The directed flow aligns the microdomains parallel to the trench walls (Figures S22 and S23). For the 15 nm film on deep trenches, at 1 min, the mesas are featureless, and the trenches exhibit a mixture of out‐of‐plane and in‐plane cylinders. With further annealing up to 60 min, the out‐of‐plane cylinders gradually disappear, and there is no apparent thickness non‐uniformity over the patterned area (Figure S24). Therefore, this case corresponds to a regime where the film thickness on both trenches and mesas are near the commensurability condition after capillary flow, and there is minimal dewetting. The same commensurability condition applies to the 24 nm film on shallow trenches, where mesas feature a monolayer of cylinders, and the trenches feature a double layer of cylinders after capillary flow (Figure S25). The fact that microdomains are aligned transversely under both commensurate cases supports our conclusion that isotropic island growth has little effect on microdomain alignment, and the transverse orientation originates from capillary flow. Different nominal film thicknesses lead to different film profiles after capillary flow, whose commensurability conditions over trenches and mesas define the subsequent dewetting mechanism, and thus the microdomain orientation. The self‐consistent results in Figure 1A validate the generality and robustness of the flow‐induced alignment model over a broader range of film thicknesses.
Our finding is consistent with previous observations on a variety of polymers. Zhang et al. reported in‐plane polystyrene‐block‐poly (2‐vinlypyridine) (PS‐b‐P2VP) cylinders aligned perpendicular to an island boundary (i.e., along the flow direction) during the early stage of island growth on flat substrates [52]. Liu et al. modeled capillary flow with dissipative particle dynamics simulation by applying a net force perpendicular to the trench wall on solvent molecules [21]. This induced a transverse alignment, which continued to develop after removing the force. Further, the PS‐b‐P2VP cylindrical microdomain orientation dependence on trench depth is consistent with our findings. Several other studies reported transverse cylindrical microdomains in trenches at intermediate annealing times, which gradually realigned parallel to the trench wall upon further annealing [15, 24, 25]. In those studies, one block preferentially wetting the trenches, either due to the brush layer or surface energy, promotes parallel orientation, suggesting that the initial transverse microdomains occurred due to capillary flow and subsequently reoriented. Our study was conducted without brush layers, and the transverse microdomains persisted for the 20 nm film on shallow trenches even after 300 and 600 min of annealing (Section S13). This long‐term stability of transverse microdomains without a brush layer is consistent with a previous study [53]. However, after modifying the surfaces with a PDMS brush, we observed highly ordered parallel microdomains for a 20 nm film on shallow trenches, despite it still undergoing isotropic dewetting (Figure S28). Therefore, the wetting properties between the substrate and different blocks also play an essential role in flow‐induced microdomain alignment.
Furthermore, we see an intriguing connection between capillary flow and flow alignment (shear coating) on flat substrates. A simplified scaling analysis demonstrates the stress generated by capillary flow and shear coating to be of the same order of magnitude (Section S14). Microdomains align parallel to the shearing direction, with improved alignment through repetitive shearing [5, 8]. Capillary flow can thus be viewed as applying a single shear that biases the initial microdomains toward a transverse alignment, which then develops or decays depending on the subsequent dewetting mechanism.
The anisotropic dewetting observed on deep trenches illustrates how topographical templates can direct dewetting by constraining the direction of polymer flow, which is relevant to homopolymers as well as block copolymers. Moungthai et al. investigated the dewetting of PS on hexagonal well arrays bounded by mesas. The polymer at the mesa edges first flowed into the wells under capillary forces, followed by Rayleigh instability‐induced pinch‐off into ordered droplets [54]. Ordered block copolymer droplets on topographical arrays likely form through the same mechanism [36, 37]. Templated dewetting has also been reported in studies employing chemical patterns (chemoepitaxy) where 1D chemical stripe patterns guide dewetting of both homopolymers and BCPs. Directional flow first occurs from unpatterned regions with high surface energy to patterned regions with low surface energy, defining the film profile for subsequent dewetting [55, 56]. Thus, the dewetting regime described in the present work may be relevant to a variety of templated dewetting scenarios.
Lastly, we explored how self‐assembly results changed under additional trench widths and swelling conditions to provide further practical guidelines when applying the flow‐induced microdomain alignment principles. For a 20 nm thick film, isotropic dewetting and transverse microdomains are observed on shallow trenches up to 560 nm wide, while for deep trenches anisotropic dewetting and parallel alignment along mesas are only observed in trenches up to 240 nm wide. As the trench width increases, isotropic dewetting is more readily accommodated, and the tendency for parallel orientation driven by anisotropic dewetting is suppressed (Section S16). Therefore, the trench dimension is another important factor to consider, especially when interest lies in producing parallel microdomains.
The results reported in the main text were obtained from an equilibrium SR of 1.5, and we compared the results for a 20 nm film on shallow trenches when the SR is over 2 and when the SR is 1.4. The three swelling conditions all showed isotropic dewetting and transverse microdomains (Section S17), though the timescale of the microdomain evolution varied. These results not only indicate that the flow‐induced alignment principles are general within a broad range of SR, but also suggest that SR is an effective parameter to tune alignment kinetics and island‐to‐hole area ratio.
Conclusions
3
In summary, this work studied the coupled self‐assembly and polymer flows occurring in block copolymer thin films on topographical templates under solvent vapor annealing. By comparing the microdomain evolution of 11–24 nm thick films on shallow (14.5 nm) and deep (18 nm) trenches, we verified the effect of capillary flow to initially yield a transverse alignment of in‐plane cylindrical microdomains, analogous to the effects of shear alignment. On further annealing, the dewetting mechanisms acting on the film in different trench depths determined how the initial transverse microdomains develop. Isotropic island growth exhibiting equiaxed islands has little effect on microdomain orientation, and the initial transverse microdomain orientation persists and grows. In contrast, anisotropic island growth along the trench axis, exhibiting elongated islands, replaces the transverse microdomains with parallel ones. The thickness of the polymer film on the mesas and trenches, determined by nominal film thickness and trench depth, plays an important role in the flow direction during island evolution and hence on the final microdomain orientation. The temporal mapping between polymer flow processes and corresponding microdomain orientation not only reveals the general tendency of BCP cylindrical microdomains to align parallel to the flow direction in thin films, but also provides principles to control microdomain orientation on topographically patterned surfaces, which is inspiring for both 2D pattern transfer and 3D layer‐by‐layer nanofabrication.
Materials and Methods
4
Materials
4.1
Cylinder‐forming polystyrene‐b‐polydimethylsiloxane (PS‐b‐PDMS) (*M_n_
- = 11‐b‐5 kg mol^−1^, PDI = 1.11) was purchased from Polymer Source and used without further purification. The BCP was dissolved in cyclohexane (J. T. Baker) at concentrations of 0.3, 0.35, 0.45, and 0.55 wt.%.
Trench Fabrication
4.2
Straight, V‐shaped, and circular trenches were fabricated using electron beam lithography (EBL) and reactive ion etching techniques. We first spin coated a 300 nm thick positive electron‐beam resist (CSAR AR‐P 6200.09) onto silicon substrates with a 285 ± 15 nm silicon dioxide layer (University Wafer) at 4k rpm. The resist was baked at 150°C for 60 s. Trench patterns were defined using EBL (Elionix HS‐50) with a dose of 155 µC/cm^2^. The exposed resist was developed in o‐xylene for 90 s. We transferred the trench pattern to the underlying silicon dioxide substrate through a CF_4_‐based reactive ion etching (Plasma Therm 790, 10 mTorr pressure, 15 sccm flow rate, and 200 W power). The trench depth was tuned by adjusting the etching time. Etching of 30 s resulted in a depth of 14.5 nm, and 36 s led to 18 nm depth. Residual resist was removed by sonication in acetone for 5 min, followed by O_2_ plasma ashing (10 mTorr pressure, 10 sccm gas flow, and 90 W power).
Film Preparation and Solvent Vapor Annealing
4.3
To ensure consistent film thickness across samples, we first spin coated the BCP solution (0.45 wt.%) onto a flat substrate and then measured the film thickness using a Filmetrics F20 reflectometer. The spin coating speed was adjusted accordingly to guarantee a film thickness of approximately 20 nm on flat substrates. The same spin coating recipe was immediately applied to substrates patterned with trenches. The as‐spun film was subsequently annealed in an in‐house apparatus using the reservoir method [57] in which a glass chamber was loaded with 3.5 mL of acetone. Samples were exposed to the vapor for varying durations to study the temporal evolution of microdomains. At the designated time point, we promptly took the sample out of the chamber to halt the annealing process. The swelling ratio (SR) was measured in situ using Filmetrics F20. By flowing 7 and 10 sccm N_2_ into the chamber, we controlled the equilibrium SR to be approximately 1.5 and 1.4. Without N_2_, the SR exceeded 2 around 6 min, and the film showed large scale dewetting. The annealed samples were then used for further AFM and SEM analysis. To obtain 24 nm, 16.5 nm, and 11 nm films, we used solutions of 0.55, 0.35, and 0.3 wt.%, respectively. To apply PDMS brush layer, PDMS‐OH was spin coated onto the substrate and thermal annealed at 170°C for 15 h in a vacuum oven. Afterward, the unattached PDMS was removed by rinsing in toluene.
AFM Characterization
4.4
We scratched the film using a pointed tweezer, aligning the scratch parallel to the trench long axis. We then acquired the film profile using the AC mode on an Oxford Instruments Asylum Research Cypher S AFM. The cantilever tip we used was 160 AC‐NA (f 0 = 300 kHz, k = 26 N/m, tip radius < 7 nm, NanoAndMore USA). All AFM measurements were conducted at room temperature. The AFM files were processed using the Gwyddion software (ver 2.65) (Section S2).
Electron Microscopy
4.5
We characterized the microdomain morphologies using a scanning electron microscope (Gemini 450, Zeiss). To enhance imaging contrast, we first used CF_4_ etching for 3 s to remove the PDMS wetting layer (Plasma Therm 790, 10 mTorr pressure, 10 sccm gas flow, and 50 W power), then the PS block was removed using O_2_ plasma for 6 s (Plasma Therm 790, 10 mTorr pressure, 10 sccm gas flow, and 90 W power) and the PDMS block was converted into silicon oxide simultaneously [15].
Orientation Mapping and Island Dimension Measurement
4.6
We developed an image analysis code in MATLAB 2022a to quantify the microdomain orientation and to measure the island dimension on flat substrates and shallow trenches. To map the microdomain orientation, we first rotated SEM images to align trench walls vertically and then extracted the microdomains in trenches to analyze their orientation. To measure the island dimension, we applied a low‐pass filter and binarization to capture the islands. The island dimension on deep trenches was measured using ImageJ (Sections S6 and S8).
Statistical Analysis
4.7
The orientation mappings at twelve randomly selected spots on shallow trenches were compared using the nonparametric two‐sample Kuiper's test. The orientation mapping at each spot was used as a probability function to inversely sample 50 data points for the Kuiper's test (Section S11).
Conflicts of Interest
The authors declare no conflicts of interest.
Supporting information
Supporting File: adma72555‐sup‐0001‐SuppMat.pdf.
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