Fabricating Microlens Arrays by Surface Wrinkling**

COMMUNICATION DOI: 10.1002/adma.200601595 Fabricating Microlens Arrays by Surface Wrinkling** By Edwin P. Chan and Alfred J. Crosby* The ability to ...
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DOI: 10.1002/adma.200601595

Fabricating Microlens Arrays by Surface Wrinkling** By Edwin P. Chan and Alfred J. Crosby* The ability to generate microlens arrays in a rapid and costeffective manner allows for the fabrication of a variety of inexpensive functional devices, such as optical refractive elements or smart surfaces that mimic the patterned surfaces in biological systems used to control solid[1–3] and liquid adhesion.[4] A variety of strategies have been adopted for fabricating microlens structures. In general, they can be broadly classified into three categories: 1) surface-tension-driven techniques consisting of melt-reflow[5–7] and ink-jet printing;[8] 2) imprinting methods;[9,10] and 3) lithographic approaches such as grayscale photolithography[11,12] or interference lithography.[13,14] While these approaches demonstrate the ability to produce microlens arrays with uniform surface profiles, the techniques are either high-cost or require long fabrication times. In this paper, we introduce an alternative and novel approach for fabricating microlens arrays that is based on the confinement of surface wrinkles.[15] We demonstrate the ability to control the size and the arrangement of the microlenses through clever control of the geometric shape and material properties of the wrinkled regions. Our approach offers several advantages over previous methodologies of microlens fabrication, including: 1) the ability to create microlens arrays rapidly; 2) ease of tuning the dimensions of the microlenses; and 3) versatility in the process that allows the formation of microlens arrays on nonplanar substrates. We demonstrate the flexibility of our approach in patterning nonplanar surfaces by patterning a hemispherical surface with an array of microlenses, thereby forming a compound lens (Fig. 1). To fabricate the microlens arrays, we modified our previously developed methodology for generating wrinkle-pattern surfaces (Fig. 2a).[15] We began by selective ultraviolet/ ozone (UVO) oxidation of a crosslinked polydimethylsiloxane (PDMS) film to convert specific regions of the PDMS surface

– [*] Prof. A. J. Crosby, E. P. Chan Polymer Science and Engineering Department University of Massachusetts 120 Governors Drive, Amherst, MA 01003 (USA) E-mail: [email protected] [**] The authors thank Steve Koback, Amy McClung, and Justin Turner of Zygo Corporation for assistance and use of their optical profiler in the characterization of the compound lens structures. We thank Andrew Smith for assisting in optical characterization of the microlens arrays and Jong-Young Lee for help with atomic force microscopy measurements. We also acknowledge NSF-MRSEC Central Facilities for use of their scanning electron microscope. Funding for this work is provided by NSF CAREER Award DMR-0349078 and 3M Non-tenured Faculty Research Award.

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Figure 1. Structure of the compound lens. a) Optical profile of the microlens structures on a polydimethylsiloxane (PDMS) hemisphere. The inset illustrates the overall dimensions of the compound lens. b) Magnified optical profile of microlens surface and c) surface profile of a single microlens measured using a stylus profiler. The dimensions of a microlens are approximately 5 lm in height and 60 lm in diameter.

into a silicate thin film. The chemical modification created the necessary elastic-moduli differences on the PDMS surface to allow us to control and define the wrinkle formation. Following the silicate formation, the surface was coated with photopolymerizable n-butyl acrylate (nBA) and then covered with a glass superstrate. The acrylate monomer swelled the PDMS surface globally, but the surface wrinkles occurred only in regions where the moduli mismatch existed—that is, in the oxidized PDMS regions. This selective UVO allowed for the control of the spatial distribution of the wrinkle patterns (Fig. 2b and c). The wrinkle patterns disappeared upon evaporation of the acrylate swelling agent; however, we stabilized these wrinkle structures through photopolymerization of the nBA. Finally, we lifted away the glass superstrate, which caused cohesive fracture of the polymerized poly(n-butyl acrylate) (PnBA) film. Due to the extreme interfacial moduli mismatch between the PnBA and silicate layers, the fracture path proceeded along the contours of the wrinkle surface. Hence, the microlens arrays were revealed upon removal of the glass superstrate (Fig. 2b).

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 gˆ

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strain compatibility at the PDMS/silicate interface, a compressive stress developed that led to an elastic instability, or wrinkling. As we demonstrate in this article, the compressive stress can be controlled by changing the oxidation time and specific shape of the oxidized region. This control of the compressivestress state allows for: 1) the creation of several forms of buckling structures that have not been previously observed and 2) alignment of these wrinkle structures on both planar and nonplanar surfaces. For a laterally semi-infinite plate supported by an elastic medium, the buckling wavelength (k0) scales with the thickness of the plate (hp) multiplied by a moduli-match ratio[16] 

Ep

…1†

12 Em

where k0 ˆ 2p hp g1=3

…2†

and the elastic constants are Ep ˆ 

1 1

t2p

 Ep

…3†

and Figure 2. a) General scheme for fabricating the microlens arrays on a planar PDMS surface based on our surface-wrinkling approach. For the compound lens, we substituted the PDMS film with a PDMS hemisphere. b) Optical microscopy image of the microlens array fabricated using our wrinkling process. The root-mean-square roughness was measured by atomic force microscopy (AFM) to be 2.15 nm. c) Diffraction pattern of the microlens illustrating the order and shape uniformity of the array structure. d) To demonstrate the lensing properties of our microlens arrays, we devised a microscope projection experiment where we projected the letters CRG onto the focal plane of the microlens array. e) Miniaturized letters were observed on every microlens when imaged through the objective lens of the microscope.

To demonstrate the lensing properties of our microlens, a projection experiment was performed on the planar microlens array (Fig. 2d). First, the microlens array was positioned on the sample stage of an optical microscope. Next, the microlens array was illuminated with white light from below through a projection template, which was simply a printed transparency with the transparent letters CRG on it. Finally, the miniaturized letters were projected onto the focal plane of the microlens array and imaged through the objective lens of the microscope. As Figure 2e shows, we observed a hexagonal array of miniaturized CRG letters on the microlens arrays. This illustrates the capability of our microlens arrays to be employed as optical elements. The buckling process for microlens formation occurred as a result of the swelling of the moduli-mismatch oxidized PDMS regions.[15] Upon exposure to the acrylate swelling agent, the PDMS expanded volumetrically. However, since the PDMS was strongly adhered to the rigid top silicate layer, it was constrained from expanding in the lateral dimensions. Due to

Adv. Mater. 2006, 18, 3238–3242

Em ˆ

1 tm E …1 ‡ tm †…3 4tm † m

…4†

E*p and E*m are the elastic moduli for the semi-infinite and elastic media, respectively (with Poisson’s ratios mp and mm). The modulus-mismatch ratio, g, is an amplification factor that essentially reflects the elastic-moduli differences between the top plate and the supporting elastic medium. In this general case, where the plate is laterally semi-infinite, the buckling patterns are randomly oriented. We refer to these isotropic buckling patterns as 2D isotropic patterns, since the patterns formed randomly as there was a lack of driving force to orient the buckling structures. Based on Equation 2, an increase in k0 can arise from either an increase in hp or E*p. Both of these properties increased with increasing oxidation times, which has been previously reported.[15] The lateral dimensions of the silicate plate laterally confined the wrinkle-formation process. We controlled the lateral dimensions by defining the diameter of the oxidized region. This process was carried out employing stencil masks to oxidize specific regions of the PDMS surface that were not protected from the UVO. This change in lateral dimensions of the silicate plate altered the morphology of the buckling patterns and manifests due to the existence of new boundaries, defined by the edges of the finite silicate plate. As previously demonstrated, the presence of a boundary, as defined by the soft (unoxidized) and stiff (oxidized PDMS) regions, aligns the buckling patterns perpendicular to that boundary.[15] However, the 1D patterns persist only over a finite distance, beyond which the buckles revert back to the 2D isotropic

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buckles. The persistence length (f) of the 1D pattern scales with the buckling wavelength of a semi-infinite plate (k0), the strain of the local region (e), and the moduli-mismatch ratio, g,[16] and is given by  f≈k0

1 ‡ 2 g1=3 2 e1=2

 …5†

The length scale f is a critical parameter in determining the morphology of the buckling structures. Prior to swelling by the acrylate monomer, the silicate plate has an initial plate diameter Di. Upon swelling, the silicate plate expands laterally to a final plate diameter (D) where D = Di(1+e). We define a dimensionless parameter, D/f, to describe the critical transitions at which various buckled structures are formed. For plate dimensions much greater than the persistence length (D/f > 1), the wrinkles persist radially inward to f, beyond which they interact with adjacent wrinkles. However, as we reduce the size of the silicate plate, the persistence length becomes commensurate with, or smaller than, the plate diameter (where D/f ≤ 1). In this instance, two types of buckled structures are observed: the microlens pattern and the dimple pattern. To demonstrate this dimensional control of the wrinkled region, we created a combinatorial library of microlens arrays on a planar PDMS substrate where we systemically varied the oxidation time as well as the size of the oxidized regions. Both parameters served to change the overall stiffness of the silicate layer and hence, dictated the morphology of the wrinkle structures formed. Given this parameter space, we observed three distinctive buckling structures (Fig. 3a). For a nearly semi-infinite case (D/f >> 1), the random 2D isotropic wrin-

kles are generated (Fig. 3a IV). Similarly, at low levels of confinement (D/f > 1), the 2D isotropic wrinkles are again observed (Fig. 3a III). A further increase in lateral confinement led to the formation of the dimpled pattern (Fig. 3a II) where D/f ∼ 1. Finally, at the greatest extent of lateral confinement generated (D/f < 1), we observed the microlens pattern (Fig. 3a I). We used Equation 5 to calculate f for all the patterns. We estimated the local strain by comparing the differences in the lateral dimensions of the oxidized regions prior to the swelling stage and after the buckling process for the entire combinatorial library of oxidized patterns. Based on the estimation of e and with our prior knowledge of g,[15] we determined f values for all the buckling structures. We have summarized the results of the critical transitions into a phase map (Fig. 3b) where we compare the normalized buckling wavelength, k/k0 with D/k0. The parameter k is the measured wavelength for the buckled structure of interest. k0 is a material-defined quantity that was measured independently from the 2D wrinkling patterns. For the 2D isotropic patterns where confinement was minimal, k approaches k0 as expected. As we decreased the silicate plate diameter, edge boundaries of the silicate plate limited the lateral expansion of the swollen PDMS film. This high degree of lateral confinement played a significant role in the wrinkle formation and led to the development of the dimple pattern and microlens structure. Both patterns were essentially 2D analogs to the 1D Euler buckling modes. Similar to the Euler buckling of a rod, the microlens pattern constitutes the lowest symmetric buckling mode, which is a half-wavelength. For the dimple pattern, we interpret the buckled structure as the next-higher-order symmetric buckling mode. In instances where microlens structures were formed, k/k0 scaled as D/2k0, as illustrated by the

Figure 3. a) Morphologies of the wrinkled structures observed. Using a combinatorial approach, we varied simultaneously the oxidation time and size of the oxidized region, Di, on a planar PDMS surface. For a nearly semi-infinite case, the random 2D wrinkled patterns were formed (IV). At low levels of confinement, we again observed the formation of 2D isotropic wrinkles (III). However, as we further decreased Di, lateral confinement played a significant role as the dimpled (II) and microlens (I) buckled structures were observed. b) A phase map summarizing the effects of silicate-layer lateral confinement on the resultant wrinkled structures formed. The plot demonstrates the role of lateral confinement, as expressed by the ratio (D/k0), on the resultant buckled structures.

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R ˆ k0

1 0  2 D B 1 e1=2 C @ 1=2 ‡  2 A k0 8e 2 D=k0

…6†

Figure 4b illustrates that we are able to predict the experimental results well by assuming a constant strain of 5 % for all the microlens samples. These results demonstrate our ability to control the curvature of the microlens structures through either the size of the oxidized region or the oxidation time of the PDMS substrate.

The versatility of our approach allowed for the fabrication of a compound lens where a microlens array decorated the surface of a PDMS hemisphere (Fig. 1a, inset). Unlike previous approaches to fabricating a compound lens,[18] our process is quite simple and rapid as fewer fabrication steps are needed. Optical profilometry (Fig. 1a and b) confirmed the successful patterning of a microlens array on the surface of the PDMS hemisphere. Stylus profilometry was used to further characterize the lenticular shape of a single microlens (Fig. 1c). For this system, the dimensions of the microlens were approximately 5 lm in height and 60 lm in width. However, as we illustrated with the planar microlens arrays, we can tune its radius of curvature simply by changing either the oxidation time or the lateral dimensions of the oxidized region, or both. In summary, this spontaneous formation of wrinkle patterns provides a simple and rapid means to pattern large surfaces with a variety of surface-relief structures that include 2D wrinkles and dimple patterns as well as microlens patterns. We demonstrated that the degree of lateral confinement as described by the ratio of the silicate plate diameter versus the persistence length (D/f) determined the type of wrinkling patterns formed. Low confinement (D/f > 1) lead to the formation of 2D isotropic wrinkles. As we increased the extent of lateral confinement, the finite boundaries played a significant role in the wrinkle formation and lead to the generation of a dimple pattern (D/f ∼ 1) as well as the microlens structure (D/f < 1). The versatility of our approach for microlens formation allows for the realization of a variety of functional devices on both planar and nonplanar surfaces, as demonstrated by the synthetic compound lens structures. Given our current material system, we are able to generate microlens structures on the micrometer length scale. However, with the appropriate selection of materials, we believe that the general concept of lateral confinement of surface wrinkles can be extended to generating buckled structures on meso- and nanoscales.

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linear relationship in Figure 3b, since their diameter was half their buckling wavelength. The radius of curvature (R) of a microlens controls many properties of the microlens arrays. We can control R by adjusting either the silicate thickness or lateral dimensions of the silicate region. As Figure 4a illustrates, R decreases with increasing oxidation time (i.e., silicate thickness), while for a given oxidation time, R increases with D. The change in R is due to changes in the buckling amplitudes. According to Cerda and Mahadevan, the amplitude of a wrinkled surface scales with the buckling wavelength and the compressive strain.[17] Based on the amplitude-scaling relationship with buckling wavelength k0 and strain e, we developed an expression that relates R to k0, D, and e

Experimental

Figure 4. Radius of curvature of the microlens structures. a) Effects of silicate plate diameter (D) and oxidation time on the changes in the radius of curvature for the microlens structures. The radius of curvature (R) was determined by approximating the geometry of the microlens as a spherical cap. b) Using Equation 3, we were able to predict the changes in curvature for different plate diameter and oxidation time.

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Buckling Process: The photocurable acrylate formulation consisted of n-butyl acrylate monomer (75 wt %), ethylene glycol dimethacrylate crosslinker (25 wt %; Sigma-Aldrich), and commercial photoinitiators Irgacure 814 and 719. Both the monomer and crosslinker were purified by filtering through alumina to remove the inhibitors and then combined with the photoinitiators to yield a clear bright-yellow liquid. Crosslinked PDMS films were prepared by mixing Dow Corning Sylgard 184 oligmer thoroughly with catalyst (10:1 by weight) and then degassing for 45 min. The degassed mixture was cast onto glass substrates and cured at 110 °C for 1 h to yield 1 mm thick planar PDMS films. Ultraviolet/ozone (Jelight UVO cleaner model 342, Jelight Company Inc., Irvine, CA) was used to oxidize the PDMS film; the distance between the PDMS film and the ultraviolet light source was kept constant at 6 mm. To wrinkle the oxidized PDMS film, we deposited the acrylate formulation onto the PDMS surface and covered it with a glass superstrate. The PDMS was allowed to swell for 1 min, after which we photopolymerized the acrylate solution for 5 min (OAI 500 W DUV, wavelength = 365 nm, intensity = 20 mJ cm–2, San Jose, CA). Following polymerization, the nowpolymerized acrylate film was removed by lifting it off the glass super-

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strate. Once the acrylate film was removed, we observed the wrinkled structures present on the PDMS surface. Compound Lens: To prepare the oxidized surface, we substituted the transmission electron microscopy (TEM) grid with a patterned photoresist. Due to curvature of the PDMS hemisphere, the TEM grid could not conformably adhere to the elastomer surface. As a result, only a limited region of the hemisphere could be selectively oxidized to form microlens structures. To obtain the high coverage of microlens array as shown in Figure 1, we spun a Shipley SPR220 photoresist (MicroChem Corp., Newton, MA) onto the hemisphere at 4000 rpm for 60 s, pre-baked it at 95 °C for 60 s, and then exposed it with ultraviolet (OAI 500 W DUV, wavelength = 365 nm, intensity = 20 mJ cm–2, San Jose, CA) for 45 s through a TEM grid. The photoresist was postexpose baked at 95 °C for 60 s and developed for 2 min, which stripped away the exposed resist. This photoresist-coated PDMS hemisphere was then oxidized using UVO for 30 min. Following cooling, the remaining photoresist was removed by exposing with ethyl lactate and rinsing with deionized water and then dried in a 50 °C vacuum oven for 30 min. Characterization of Microlens Patterns: The surface profile of the compound lens was characterized by a Zygo NewView 6000 3D optical profiler (Zygo Corporation, Middlefield, CT), using a 50× Mirau objective. The surface profiles of the microlens in both the compound lens and planar array were quantified using a stylus profiler. The height amplitudes of the microlens were obtained from the stylus profile data.

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Received: July 17, 2006 Revised: September 7, 2006 Published online: November 24, 2006

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