Coupling of wrinkle patterns to microsphere-array lithographic patterns

Abstract

We report a method to modulate spontaneously formed microwrinkle patterns on a metal-capped elastomer surface by introducing lithographic patterns (structures) on the original surface as spatial triggers for directed wrinkling. The lithographic patterns are designed to have approximately the same lateral length scales as the characteristic wavelength of the microwrinkles by utilizing self-assembled two-dimensional microsphere arrays with hexagonal packing as a lithographic mask. When the lateral periodicity of the lithographic pattern is close to the wavelength of wrinkles, a novel directional order originating from the hexagonal packing of microspheres is induced. Otherwise, the wrinkle crests tend to form along the small ridges of the lithographic structure. The compression direction-dependent and reversible ordering of wrinkle patterns by compressive strain is also found for patterns with directional order.

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Introduction

Various spontaneous processes have been extensively investigated as methods for patterning a surface at the micrometre, or submicrometre, length scales because such procedures are more cost-effective and technologically simple than those of conventional lithography. For example: phase separation in thin films of block copolymers produces chemically distinct regions;¹ dewetting of liquid polymer films produces dot patterns, network structures, and hierarchical assemblies;^2,3 self-assembly of transiently passivated water microdroplets on volatile polymer solutions leaves honeycomb-like structures after evaporation of solvents and water,^4–9 and mechanical instability of thin films due to in-plane stress induces wrinkles with stripe patterns on elastic/viscoelastic materials after surface hardening by metal depositions or plasma treatments.^10–16

Although most spontaneously formed patterns have characteristic lateral length scales (the periodicities of dots, domains and stripes), they largely include spatial fluctuations of the characteristic length scale, the random distribution of ordering orientation, and topological defects of the patterns.¹⁷ Such uncertainties become obstacles to technological applications that require precision. Thus, combinations of lithographic and self-organized methods are required for more efficient use of both methods.^18,19 For example, a spatially ordered pattern produced by lithography might trigger spontaneous patterns which can be better controlled, where the mechanism is analogous to the forced oscillation system with temporally ordered pacemaker stimuli.

In this study, we propose a method to reduce such uncertainties in the above-mentioned microwrinkle system and, thus, to induce artificial order by introducing, prior to wrinkle formation, surface lithographic patterns, the lateral length scales of which are close to the average wavelength of the resultant wrinkles. Although the effects of lithographic patterns with much larger length scales than those of wrinkles have been reported,^10–13 it remains to be established how wrinkle patterns couple to lithographic patterns with approximately the same lateral length scales. The pattern typical of microwrinkles, which are formed on a Pt-deposited polydimethylsiloxane (PDMS) elastomer without lithographic patterns under the condition of 2D isotropic residual stress, is a randomly packed mosaic of stripe domains (Fig. 1a), each of which has a specific orientation. The randomness arises from the uncontrollable initial surface heterogeneities, such as density distribution and roughness, because they modulate surface stress states locally, and subsequently trigger out-of-plane deformation. The introduced lithographic patterns are periodic surface heterogeneities, such as topographic and modulation patterns, that modulate the 2D local stress state in regular fashion. Thus, the resultant wrinkle pattern is modulated and, in particular, shows a novel directional order when the lateral length scales of the lithographic and microwrinkle patterns are similar (Fig. 1b).

Fig. 1 Atomic force microscopy images of (a) a typical microwrinkle pattern formed on a Pt-sputtered PDMS substrate due to isotropic residual stress,¹⁶ and (b) a microwrinkle pattern coupled to the lithographic pattern originating from a 2D array of microspheres with ϕ = 1.03 µm. The stripe orientation is restricted by the hexagonal order of the lithographic pattern in (b).

Experimental

The fabrication process for the microwrinkle structure coupled to the lithographic pattern is shown schematically in Fig. 2, which consists of (1) preparation of the 2D array of polystyrene (PS) microspheres from a water suspension, (2) transfer of the array to a bare PDMS surface by adhesion, (3) oxygen plasma treatment on the PDMS surface with the mask of the array, (4) removal of the microsphere array, and (5) Pt deposition onto the PDMS surface with a lithographic pattern. Here, microsphere-array lithography,^20–23 a surface structuring method using a 2D array of microspheres as a lithographic or etching mask, was used to fabricate an ordered pattern on the PDMS surface because it is easy to prepare a 2D array of microspheres having a high packing density and large hexagonal domains.^24,25 It should be noted that the present method does not include conventional lithographic techniques, such as electron beam lithography, which produce the micropatterns directly. Although we can use such costly techniques for arbitrary patterns, microsphere lithography serves well to demonstrate the coupling between microwrinkles and small periodic surface heterogeneities. The details of the fabrication process are described in the results and discussion section.

Fig. 2 Schematic of the experimental procedure for fabrication of microwrinkle structures coupled to lithographic patterns of a 2D microsphere array.

Results and discussion

Preparation of surfaces with lithographic patterns

Three types of 2D arrays of polystyrene microspheres having diameters ϕ of 1.03, 1.59 and 3.06 µm (Duke Scientific Corp., NIST traceable) were prepared separately on flat glass substrates. Due to water evaporation and capillary forces, the particles suspended in water formed 2D arrays by self-assembly. Moving the substrate horizontally at rates from 1.0–3.0 µm s⁻¹ controlled the speed of array formation.^24,25 The total area of the array was 1 cm². A slab of the PDMS elastomer (Dow Corning, Silpot 184) with a flat surface was carefully placed on the microsphere array to generate contact between them. After 1 min, the PDMS elastomer with microspheres was peeled off. Figs. 3a–3c show optical microscopy images of 2D microsphere arrays transferred onto the bare PDMS substrate (Olympus, BX60). The side views obtained by scanning electron microscopy (FE-SEM, Hitachi, S-5200) in Figs. 3d–3f show that the spheres were in contact with the PDMS and became deformed probably due to adhesive forces. Most parts of the microsphere array on the original glass could be transferred to the PDMS elastomer surface by this simple method. The circular areas covered by deformed spheres were protected against subsequent oxygen plasma treatment. The diameter d of the protected circular area was expressed approximately as d ≈ 0.7ϕ.

Fig. 3 Images observed for each step of the fabrication process. (a)–(c) Optical microscopy images and (d)–(f) SEM images of the side view of 2D microsphere arrays transferred to PDMS substrates. (g)–(i) AFM images (10² µm²) of the lithographic pattern produced by oxygen plasma treatment after removing the microspheres and (j)–(l) cross-sectional profiles indicated by the white lines in (g)–(i). (m)–(o) AFM images (10² µm²) and (p)–(r) optical microscopy images with large areas of microwrinkle patterns coupled to lithographic patterns. The left, middle and right columns indicate the results using polystyrene microspheres having diameters ϕ of 1.03, 1.59 and 3.06 µm, respectively.

The oxygen plasma treatment was applied weakly to the PDMS elastomer with the microsphere array using a plasma cleaner (South Bay Technology, PC2000) at 24 Pa and 10 W for 10 s. Under these conditions, the PDMS surface exposed to oxygen plasma was slightly oxidized and, thus, hardened. After removing the microspheres, by rinsing the sample with benzene, the surface was observed by atomic force microscopy (AFM, Veeco, Explorer TMX2100; all AFM images throughout this study were subjected to a first-order plane fit to compensate for sample tilt). The AFM image shows that, independent of ϕ, ring-like ridges with a height of 30–50 nm and width of 400–500 nm along the circular areas were formed, and the relative height of the exposed areas to those protected by spheres during plasma treatment was approximately 10 nm (Figs. 3g–3l). We assume the following scenario for the formation of the topography: (1) the exposed area expanded laterally and vertically during plasma treatment; (2) simultaneously, the area became oxidized and hardened by cross-linking between polymer chains; (3) during/after plasma treatment, the exposed hardened area pushed on the unexposed soft area, due to residual stress, leading to ridge formation around the boundary of the exposed and unexposed areas, which may account for one of the buckling phenomena, and the vertical expansion of the exposed area remained, leading to the height difference between the exposed and unexposed areas. The detail of this structure formation is under investigation and will be reported elsewhere because the focus of this study was wrinkle formation on the prepared lithographic pattern.

Formation of modulated wrinkles

The deposition of Pt with a thickness of approximately 6 nm was then conducted using an ion sputter (metal coating) apparatus (E-1030, Hitachi) with a current of 5 mA, a pressure of 10 Pa, a distance of 34 mm between samples and the Pt target, and a deposition time of 180 s. During deposition, the PDMS surface heated (ca. 100 °C) and expanded due to the collision energy of active species. Thus, a hard layer of Pt was formed on the expanded area. As the temperature decreased after deposition the wrinkle patterns formed.^10–13,16 When Pt deposition on bare PDMS elastomer surface without a lithographic pattern was performed under the above conditions, the spatial wavelength of wrinkles was ca. 0.80 µm (Fig. 1a). To determine how plasma treatment affected the wrinkling behavior of the PDMS surface, Pt was deposited on oxidized PDMS without microsphere patterns, and the resultant wrinkles showed a slightly larger spatial wavelength of 0.96 µm. The results indirectly indicate that the effective thickness h and/or modulus of the effective hard layer E_h for the wrinkling phenomenon increased due to the oxidized and hardened surface, because it is known theoretically that the critical wavelength λ is proportional to h (E_h/E_s)^1/3, where E_s is the modulus of the soft underlayer.^15,26

Figs. 3m–3r show that the wrinkles were markedly modulated by lithographic patterns of microspheres and different types of order were induced depending on ϕ (compare Figs. 3m–3r with Fig. 1a). In the case of large ϕ ( = 3.06 µm), wrinkle crests with λ = 0.7–0.9 µm appeared along ring-like ridges, the inner parts of the rings rose slightly, and branches of the wrinkle crests radiated randomly from the ring to fill the oxidized outer area. Although some rings were not encompassed by the wrinkle crests, the most characteristic feature in this case was that the wrinkles coupled directly with the topography of the lithographic pattern. However, in the case of medium ϕ ( = 1.59 µm), the outlines of the ring-like ridges became obscure, wrinkles with clear sinusoidal shapes became difficult to recognize, each circular area was anisotropically deformed, and the circular areas appeared to be connected to each other between the nearest neighbors at their highest points. In the case of small ϕ ( = 1.03 µm), direct coupling of wrinkles with the topography of the lithographic pattern was hardly observed. Most straight wrinkle troughs ride over multiple circular areas in a straight line along one of the three directions of the hexagonal lattice of the lithographic pattern. In other words, the most characteristic feature in this case is that the wrinkles coupled to the directional order of the periodic lithographic pattern. The magnified AFM image in the case of ϕ = 1.03 µm shown in Fig. 1b clearly indicates that the orientation of the wrinkles was restricted to the three directions that correspond to the hexagonal order of the microspheres.

The results can be qualitatively understood through the magnitude relationship between d, (ϕ − d), and λ. When d ≳ 2λ, the wrinkle formed along the ring-like ridge, i.e., the ring-like ridge rose in height and broadened. However, when the curvature radius of the ring became comparable to λ, i.e., d ≲ 2λ, such a curved wrinkle formed along the ring-like ridge became energetically unfavorable due to larger distortional deformation. As a result, a valley formed along a straight line passing through the center, which was originally lower than the ring-like ridge of a circular area. If (ϕ − d) ≳ λ, the ring-like wrinkle did not overlap the neighboring rings. However, when (ϕ − d) ≲ λ, formation of a wrinkle on a circular area was mechanically affected by the neighboring wrinkles. The effect of the mutual mechanical interaction/interference resulted in the alignments of neighboring wrinkles to minimize surface deformation. Considering the relationship d ≈ 0.7ϕ, in the present experiments, wrinkles with the characteristic length couple with the local topography (ring-like ridge) for larger ϕ and couple with the non-local 2D periodicity (hexagonal lattice) for smaller ϕ. While the experimental results are not outlined here, this qualitative relationship holds for different λ.

Orientation-restricted arrangement of wrinkles by uniaxial compression

In a previous study,¹⁶ it was reported that wrinkles with a complex stripe pattern were reversibly aligned by compression. Thus, the responses of modulated wrinkle patterns with directional order (ϕ = 1.03 µm) to uniaxial compressive strain in two different directions with respect to the hexagonal lattice direction were also investigated. The sample was placed in a small vice and subjected to 10% strain. When one of the main axes coincided approximately with the perpendicular direction of strain (commensurate configuration), the stripes were almost aligned (Fig. 4a). In other cases (incommensurate configuration), the stripes hardly aligned in the precise strain direction but in two different orientations coinciding with two of three axes of the underlying hexagonal lattice. This result indicates that the orientation of wrinkles was restricted by the specific lithographic pattern even under strain. Moreover, the stripe rearrangement processes were reversible at room temperature. In other words, the original pattern was memorized, as expected from previous studies.^16,27 Thus, the property of restricted switching of the local surface profile may be utilized for some applications as a stable mobile element.

Fig. 4 AFM images (5 × 5 µm²) of the microwrinkle pattern coupled to the lithographic pattern originating from a 2D array of microspheres with ϕ = 1.03 µm under uniaxial lateral compression of 10% strain in configurations (a) commensurate and (b) incommensurate to the strain direction. The arrows indicate the direction of strain. The triangles express configurations of the three main axes originating from the 2D hexagonal particle array.

Conclusions

In summary, we have demonstrated two types of coupling between spontaneously formed wrinkles and periodic structures due to lithography which could be controlled by the magnitude relationship between the lateral characteristic length scales: (1) the original ring-like relief (ridge) of the lithographic pattern was simply emphasized by the wrinkles when the periodicity of the lithographic pattern (ϕ) was much larger than the intrinsic wavelength of the wrinkle (λ), and (2) the directional order of the lithographic pattern coupled with the wrinkles when ϕ was comparable to λ. The present results suggest that the different types of uncertainty, which are intrinsic for patterns formed through spontaneous processes, i.e., fluctuation in the characteristic length scale, randomness in the ordering orientation, and topological defects, can be controlled by choosing the lateral scale of the artificial spatial triggers (the pattern of surface heterogeneity).

We believe that the present method to control the surface profile offers a versatile way to utilize wrinkles, for example, to achieve a desired optical effect, to provide a nano-microarray for the spatial storing of small objects with chemical/physical information, or to prepare a controlled substrate for tissue growth. In particular, the combination of the modulated wrinkle patterns and application of external stress, which reversibly controls the wrinkle orientation, may ultimately prove to be a way of fabricating a mobile surface element for nanomechanical devices. For example, if the orientation of a local wrinkle can be altered between the multiple directions that are determined by the designed surface heterogeneity, the element may become a gate or router for microfluidic channels.

Acknowledgements

We thank K. Ito, RIKEN, for experimental support.

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