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Template-Directed Growth of (100)-Oriented Colloidal Crystals Yadong Yin,† Zhi-Yuan Li, and Younan Xia* Department of Materials Science and Engineering and Department of Chemistry, University of Washington, Seattle, Washington 98195-1700 Received September 23, 2002. In Final Form: October 31, 2002 This paper describes a simple and convenient procedure that allowed for the fabrication of large colloidal crystals with their (100) planes oriented parallel to the surfaces of supporting substrates. Such crystals were grown by templating against two-dimensional (2D) regular arrays of square pyramidal pits or V-shaped grooves etched in the surfaces of Si(100) substrates. The capability and feasibility of this approach have been demonstrated by crystallizing spherical colloids (>250 nm in diameter) into (100)-oriented crystals over areas as large as several square centimeters. We further demonstrated that inverse opals with (100) crystallographic orientation could be fabricated by templating liquid precursors (such as a UV-curable prepolymer) against these colloidal crystals. In addition to silicon templates whose fabrication involved extensive use of cleanroom facilities, multiple copies of polymer templates having similar functions were also generated by replica molding, a process that could be performed in any ordinary laboratory. We believe that the ability to control the crystallographic orientation of colloidal crystals will greatly enrich our studies on their properties. In particular, the availability of large colloidal crystals with specific crystallographic orientations should allow us to systematically investigate their photonic band structures in an effort to elucidate their structure-property relationship.
Introduction Monodispersed spherical colloids can spontaneously form three-dimensionally periodic lattices (or colloidal crystals) as a direct consequence of various types of thermodynamic driving forces.1 These long-range ordered structures have been recognized as a unique model system to explore fundamental phenomena of condensed matter physics that include, for example, phase transition,2 nucleation,3 and diffusion.4 These crystalline lattices also provide a good opportunity to systematically investigate the influences of morphological parameters (e.g., grain size, crystal orientation) on the properties of a solid material.5 More recently, colloidal crystals have become a subject of intensive research, because of their photonic applications as optical filters,6 switches,7 sensors,8 and waveguiding structures.9 In all these optical devices, the functionality of colloidal crystals not only depends on the constituent colloidal particles, but also on the long-range order exhibited by their periodic lattices. As a matter of fact, recent studies on the peculiar optical properties of these materials have now evolved into a new, exciting field of research that is often referred to as photonic band * Corresponding author. E-mail:
[email protected]. † Department of Materials Science and Engineering. (1) (a) P. Pieranski, Contemp. Phys. 1983, 24, 25. (b) Dinsmore, A. D.; Crocker, J. C.; Yodh, A. G. Curr. Opin. Colloid Interface 1998, 3, 5. (c) Gast, A. P.; Russel, W. B. Physics Today 1998, December, 24. (d) From Dynamics to Devices: Directed Self-Assembly of Colloidal Materials (Grier, D. G., Ed.), a special issue of MRS Bull. (1998, 23, 21). (e) Xia, Y.; Gates, B.; Yin, Y.; Lu, Y. Adv. Mater. 2000, 12, 693. (2) Murray, C. A.; Grier, D. G. Am. Sci. 1995, 83, 238. (3) Skjeltorp, A. P.; Meakin, P. Nature 1988, 335, 424. (4) Simon, R.; Palberg, T.; Leiderer, P. J. Chem. Phys. 1993, 99, 3030. (5) (a) Robbins, M. O.; Kremer, K.; Grest, G. S. J. Chem. Phys. 1988, 88, 3286. (b) Palberg, T.; Mo¨nch, W.; Schwarz, J.; Leiderer, P. J. Chem. Phys. 1995, 102, 5082. (6) Weissman, J. M.; Sunkara, H. B.; Tse, A. S.; Asher, S. A. Science 1996, 274, 959. (7) Pan, G.; Kesavamoorthy, R.; Asher, S. A. Phys. Rev. Lett. 1997, 78, 3860. (8) Holtz, J. H.; Asher, S. A. Nature 1997, 389, 829. (9) Lee, W.; Pruzinsky, S. A.; Braun, P. V. Adv. Mater. 2002, 14, 271.
gap (PBG) crystals.10 It has been shown that such a photonic material may exhibit a frequency band in which electromagnetic waves are forbidden to exist, irrespective of their directions of propagation in three-dimensional (3D) space.11 This feature can be used to localize electromagnetic waves to specific areas, to inhibit spontaneous emission, and to waveguide the propagation of electromagnetic waves along specific directions, as well as at restricted frequencies.12 Thanks to many years of efforts from various groups, long-range ordered colloidal crystals can now be fabricated from monodispersed spherical colloids using a number of approaches that involved, for example, self-assembly with the aid of gravitational forces,13 repulsive electrostatic interactions,14 and attractive capillary forces.15 Our group has also demonstrated a confined self-assembly method by which colloidal crystals with controllable thickness could be conveniently produced with sizes as large as several square centimeters.16 When flat surfaces were used as the substrates, colloidal crystals prepared using these methods usually displayed a face-center-cubic (fcc) struc(10) See, for example, a special issue of Adv. Mater. (2001, 13, 369450). (11) Joannopoulos, J. D.; Meade, R. D.; Winn, J. N. Photonic Crystals: Molding Flow of Light; Princeton University Press: New Jersey, 1995. (12) See, for example, a special issue of J. Lightwave Technol. (1999, 17, 1931-2411). (13) (a) Davis, K. E.; Russel, W. B.; Glantschnig, W. J. Science 1989, 245, 507. (b) Pusey, P. N.; van Megen, W. Nature 1986, 320, 340. (c) Mayoral, R.; Requena, J.; Moya, J. S.; Lo´pez, C.; Cintas, A.; Miguez, H.; Meseguer, F.; Va`zquez, L.; Holgado, M.; Blanco, A. Adv. Mater. 1997, 9, 257. (14) (a) Carlson, Roger J.; Asher, S. A. Appl. Spectrosc. 1984, 38, 297. (b) Ise, N. Angew. Chem., Int. Ed. Engl. 1986, 25, 323. (c) Sunkara, H. B.; Jethmalani, J. M.; Ford, W. T. Chem. Mater. 1994, 6, 362. (15) (a) Denkov, N. D.; Velev, O. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura, H.; Nagayama, K. Langmuir 1992, 8, 3183. (b) Dushkin, C. D.; Nagayama, K.; Miwa, T.; Kralchevsky, P. A. Langmuir 1993, 9, 3695. (c) Lazarov, G. S.; Denkov, N. D.; Velev, O. D.; Kralchevsky, P. A.; Nagayama, K. J. Chem. Soc., Faraday Trans. 1994, 90, 2077. (d) Dimitrov, A. S.; Nagayama, K. Langmuir 1996, 12, 1303. (e) Jiang, P.; Bertone, J. F.; Hwang, K. S.; Colvin, V. L. Chem. Mater. 1999, 11, 2132. (16) (a) Park, S. H.; Qin, D.; Xia, Y. Adv. Mater. 1998, 10, 1028. (b) Gates, B.; Qin, D.; Xia, Y. Adv. Mater. 1999, 11, 466.
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ture, with their (111) planes oriented parallel to the support. Due to this restriction, almost all optical measurements on colloidal crystals have been limited to the [111] direction of an fcc lattice, or the L-point of its reciprocal lattice.17 To the best of our knowledge, optical measurements along crystallographic directions other than [111] have only been accomplished by two groups. In one approach, Zhang et al. spent a few weeks growing silica colloidal crystals of several millimeters in dimensions by using the conventional sedimentation method.18 They claimed that they were able to record transmission spectra along various directions by changing the angle between the incident light and the normal to (111) planes. No experimental detail was provided regarding the determination of the single crystallinity of their crystal, as well as the exact orientation of their crystal relative to incident light in a 3D coordinate system. In another demonstration, Lo´pez et al. fabricated thin slabs of colloidal crystals having specific facets by cutting a colloidal crystal (embedded in polymer matrix) along appropriate planes.19 Reflectance spectra were recorded from facets bounded by {111}, {110}, and {100} planes. Despite these advances, it still remains a contemporary challenge in the area of colloidal crystals to accomplish a convenient and reproducible control over the crystallographic orientation of a crystal. A number of methods have been demonstrated to control the growth habit of colloidal crystals by applying an external electrical,20 magnetic,21 or optical field.22 Crystallization against solid surfaces patterned with relief structures has also been examined as a promising strategy to control crystallographic orientation. It has been demonstrated that appropriate arrays of relief structures on solid substrates could serve as templates to dictate the nucleation and growth of colloidal crystals with their specific planes oriented parallel to the substrates. For example, van Blaaderen and Wiltzius et al. demonstrated a mesoscale epitaxial process by growing (100)- and (110)-oriented colloidal crystals on nanolithographically patterned photoresist surfaces through sedimentation.23 Yodh and coworkers combined entropic depletion and surfaces imprinted with relief structures to generate colloidal crystals with (100) or (110) orientation.24 Similar methods based on surface templating have also been employed by several other groups for controlling the spatial orientation of colloidal crystals obtained by convective self-assembly.25 These templating processes can be considered as a mesoscopic equivalent of epitaxial growth, a process that has been extensively explored at the atomic and molecular scales to generate thin films characterized by well-defined crystallographic orientations.26 The capability of these (17) See, for example, Tarhan, I. I.; Watson, G. H. Phys. Rev. Lett. 1996, 76, 315. (18) Mei, D.; Liu, H.; Cheng, B.; Li, Z.; Zhang, D. Phys. Rev. B 1998, 58, 35. (19) Fenollosa, R.; Ibisate, M.; Rubio, S.; Lo´pez, C.; Meseguer, F.; Sanchez-Dehesa, J. Proc. SPIE 2002, 4655, 34. (20) (a) Yeh, S. R.; Shraiman, B. I. Nature 1997, 386, 57. (b) Hayward, R. C.; Saville, D. A.; Aksay, I. A. Nature 2000, 404, 57. (21) Grzybowski, B. A.; Stone, H. A.; Whitesides, G. M. Nature 2000, 405, 1033. (22) (a) Burns, M. M.; Fournier, J. M.; Golovchenko, J. A. Science 1990, 249, 749. (b) Wei, Q. H.; Bechinger, C.; Rudhardt, D.; Leiderer, P. Phys. Rev. Lett. 1998, 81, 2602. (23) (a) van Blaaderen, A.; Ruel, R.; Wiltzius, P. Nature 1997, 385, 321. (b) van Blaaderen, A.; Wiltzius, P. Adv. Mater. 1997, 9, 833. (24) Lin, K.-H.; Crocker, J. C.; Prasad, V.; Schofield, A.; Weitz, D. A.; Lubensky, T. C.; Yodh, A. G. Phys. Rev. Lett. 2000, 85, 1770. (25) (a) Burmeister, F.; Schafle, C.; Keilhofer, B.; Bechinge, C.; Boneberg, J.; Leiderer, P. Adv. Mater. 1998, 10, 495. (b) Ye, Y.-H.; Badilescu, S.; Truong, V.-V.; Rochon, P.; Natansohn, A. Appl. Phys. Lett. 2001, 79, 872. (c) Yi, D. K.; Seo, E.-M.; Kim, D.-Y. Appl. Phys. Lett. 2002, 80, 225. (26) See, for example, Cho, A. Y. MRS Bull. 1995, April, 21.
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mesoscopic epitaxial methods have been, however, limited to spherical colloids with diameters larger than ∼1 µm, since the feature size of templates had to be kept on the same scale as the dimensions of colloids. In the setting of an ordinary research laboratory, there still exist experimental barriers to apply conventional photolithographic methods to generate submicrometer-sized structures. Advanced nanolithographic techniques (such as deep-UV photolithography or electron beam writing) are often required to fabricate templates necessary for the crystallization of colloids with diameters smaller than 0.5 µm. The high cost or slow speed associated with these methods makes them only available to a relatively small group of chemists and materials scientists. Ozin et al. overcame this difficulty by introducing a new class of templates whose relief structures were characterized by tapered dimensions. Typical examples include the square pyramidal pits or V-shaped grooves anisotropically etched in Si(100) substrates.27 These patterned surfaces have been employed as templates to fabricate relatively small colloidal crystals with their (100) planes oriented parallel to the silicon substrates. In a related study, we further extended the use of these templates to assemble spherical colloids into aggregates with the well-controlled, square pyramidal shape.28 More recently, we demonstrated that the same type of templates could be adopted to generate large colloidal crystals with their (100) planes oriented parallel to the supporting substrates.29 The major advantage of this method is that the feature size of templates could be many times larger than the diameter of spherical colloids to be crystallized. This paper provides a more detailed description of this templating method, together with some discussions on the optical measurements and potential applications related to (100)-oriented colloidal crystals. Experimental Section Materials and Substrates. Monodispersed polystyrene (PS) beads (aqueous dispersions) were purchased from Duke Scientific (Palo Alto, CA) or Polysciences (Warrington, PA). Mylar films of ∼21 µm in thickness were purchased from Fralock of Lockwood Industries (Canoga Park, CA). Poly(dimethylsiloxane) (PDMS) elastomer kits (Sylgard 184) were obtained from Dow Corning (Midland, MI). Silicon substrates with (100) orientation and flat glass substrates (Micro slides #2947) were obtained from Silicon Sense (Nashua, NH) and Corning Glass Works (Corning, NY), respectively. Both silicon and glass substrates were cleaned by immersing in a stabilized piranha solution (NanoStrip 2X, Cyantek Corp., Frement, CA) and rinsed with deionized (DI) water (E-Pure, Barnstead, Dubuque, IA). These substrates were finally dried by blowing with a stream of filtered nitrogen gas. Caution: piranha solution reacts violently with organic chemicals and should be handled with extreme care! The ultraviolet-curable precursor to polyurethane (PU) was purchased from Norland Products (NOA 73, New Brunswick, NJ). Fabrication of Templates. The pyramidal cavities and V-shaped grooves were prepared in the surfaces of Si(100) wafers using conventional, contact-mode photolithography, followed by anisotropic wet etching.30 In a typical procedure, the silicon substrate was first coated with thin films of titanium/tungsten alloy (TiW, 15 nm) and gold (100 nm) using a MRC 822 Sputtersphere (System Control Technology, Livermore, CA). A uniform thin film of positive photoresist (AZ-1512, Clariant Corp., Somerville, NJ) was spin-coated (at 3000 rpm) onto the surface of gold and soft-baked on a hotplate at 105 °C for 3 min. This (27) (a) Yang, S. M.; Ozin, G. A. Chem. Commun. 2000, 2507. (b) Ozin, G. A.; Yang, M. Y. Adv. Funct. Mater. 2001, 11, 95. (28) Yin, Y.; Lu, Y.; Gates, B.; Xia, Y. J. Am. Chem. Soc. 2001, 123, 8718. (29) Yin, Y.; Xia, Y. Adv. Mater. 2002, 14, 605. (30) Madou, M. J. Fundamentals of microfabrication: the science of miniaturization, 2nd ed.; CRC Press: New York, 2001.
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substrate was then mounted for contact proximity photolithography using a 3 in. Quintel aligner (Mountain View, CA). Chrome masks containing appropriate test patterns were used: a 2D array of square holes for the formation of pyramidal pits and an array of parallel lines for V-shaped grooves. The photoresist was exposed to the UV light and developed under gentle agitation in the AZ-351 developer (Clariant Corp., 1:4 dilution with 18 MΩ water). The gold unprotected by photoresist was etched in a solution containing 1 g of I2, 4 g of KI, and 40 mL of H2O. The underlying TiW alloy was removed using a 30% H2O2 aqueous solution. The patterned silicon substrate was rinsed with 18 MΩ water and dried in a stream of filtered nitrogen gas. The patterned microstructures of gold were subsequently used as masks for the anisotropic wet etching of silicon. The etching solution was prepared by dissolving 125 g of KOH in a mixture containing 400 mL of H2O and 100 mL of 2-propanol. The etching was usually performed at 80 °C for about 18 min, with magnetic stirring constantly applied at ∼300 rpm. To further reduce the width of ridges between adjacent cavities or grooves, the silicon substrates were subjected to an isotropic etching process that involved the use of a mixture of HNO3 (69.8 wt %) and HF (49 wt %) with a volume ratio of 100:1. The lift-off of gold films from the substrates could be used as a reference point to determine whether the silicon underneath the gold mask had been completely undercut and sharp ridges had been achieved. Finally, the substrates were washed with DI water and dipped in I2/KI and then H2O2 solutions to remove any residual Au and TiW. Replica molding (REM) was used to fabricate multiple copies of templates in polymers.31 The silicon substrates containing pyramidal pits or V-shaped grooves could directly serve as masters for REM. In a typical procedure, UV-curable prepolymer (NOA 73) was applied (in the form of thin film) to the surface of an etched silicon substrate and then cured by exposing to a broadband UV light source (λmax ) 350 nm). After peeling off the cross-linked polyurethane film from the silicon master, a polymer replica was obtained whose surface had been patterned with relief structures complementary to those on the silicon master. The backside (without patterns) of this thin film was then adhered to a flat glass substrate using a drop of NOA 73 as the glue. After curing with UV light, this polymer replica supported on a glass substrate could be used as template in the controlled growth of colloidal crystal. We have also tried to fabricate polymer templates by molding against PDMS stamps cast from silicon masters. Replica molding that involves the use of an elastomeric (rather than rigid) material such as PDMS allows for the easy separation between the replica and the master. As a result, multiple copies of polymer templates exhibiting surface morphology essentially the same as that on the silicon master could be conveniently fabricated. In a typical procedure, the original silicon template was placed in a plastic Petri dish. A 10:l (v:v) mixture of PDMS prepolymer and curing agent was poured onto the silicon substrate. The PDMS was then cured at room temperature for ∼6 h, followed by additional curing at 60 °C for ∼30 min. After cooling to room temperature, the PDMS block was carefully peeled off from the silicon master. This PDMS block was subsequently used in another step of replica molding to generate PU replicas with relief structures similar to those on the original silicon master. In this case, the patterned side of this PDMS stamp was pushed into a thin layer of PU precursor supported a glass slide. After curing with UV irradiation, the PDMS stamp was peeled off, leaving behind a patterned PU film on the glass slide. Fabrication of Fluidic Cells. The spherical colloids were crystallized in a fluidic cell that was constructed from two parallel substrates:32 the top substrate was a flat glass slide and a silicon substrate (or polymer replica supported on glass slide) whose surface had been patterned with relief structures served as the bottom one. Figure 1A provides a schematic design for this fluidic cell. A hole 3 mm in diameter was generated in the top glass substrate by drilling with a diamond-coated tool. A glass tube (6 mm in diameter) was then attached to this hole using an epoxy (31) (a) Xia, Y.; Kim, E.; Zhao, X.-M.; Rogers, J. A.; Prentiss, M.; Whitesides, G. M. Science 1996, 273, 347. (b) Xia, Y.; McCleland, J. J.; Gupta, R.; Qin, D.; Zhao, X.-M.; Shon, L. L.; Celotta, R.; Whitesides, G. M. Adv. Mater. 1997, 9, 147. (32) Lu, Y.; Yin, Y.; Gates, B.; Xia, Y. Langmuir 2001, 17, 6344.
Yin et al.
Figure 1. (A) A schematic illustration of the flow cell used to crystallize monodispersed, spherical colloids into 3D periodic lattices. (B) Step-by-step formation of a (100)-oriented, ccp lattice by templating spherical colloids against a 2D array of square pyramidal pits. To generate (100) oriented crystals over relatively large area, it is generally required that the pitch (P) of the pyramidal pits equals n times the diameter (D) of the colloids, with n being an integer. adhesive. The surface of the top glass substrate was treated with oxygen plasma (PDC-001, Harrick Scientific Corp., NY) for a few minutes to enhance its wettability by water. The cell was assembled together by sandwiching a rectangular gasket (cut from Mylar film) between the top and bottom substrates and tightened with several binder clips. Template-Directed Growth of Colloidal Crystals. After an aqueous dispersion of PS beads was injected into the glass tube through a syringe, the opening of this glass tube was sealed with Parafilm (American National Can, Chicago, IL) to prevent the solvent from evaporating through this opening. The packing cell was then placed on an ultrasonic cleaner (Branson 1510, Greco Brothers Inc., Providence, RI) to allow the spherical colloids to crystallize into a long-range ordered 3D lattice. Once the crystal had reached the desired area or size, the excess dispersion of spherical colloids in the glass tube was removed using a syringe. Finally, the sample was dried by slowly evaporating the solvent at room temperature. Fabrication of Inverse Opals. Colloidal crystals have been directly used as templates to generate macroporous materials known as inverse opals.33 The void spaces among the particles could be conveniently filled with a liquid precursor, such as the UV-curable organic prepolymer or sol-gel precursor. After solidifying the liquid precursor, the colloidal particles could be removed by selective chemical etching to leave behind a 3D macroporous membrane consisting of a highly ordered architecture of interconnected spherical pores. Both PS beads and silica colloids have been explored as templates. In the present work, several drops of the liquid precursor to PU (NOA 73) were applied along the lower edge of the packing cell to fill the void (33) Gates, B.; Yin, Y.; Xia, Y. Chem. Mater. 1999, 11, 2827.
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spaces among colloidal particles via capillary action. The prepolymer was then cured by exposure to a broadband UV light source. The colloidal particles in the crystalline array changed very little in their positions during the templating process, because they were tightly confined by the packing cell. Finally, the PS particles were selectively dissolved by immersing the film in a toluene bath for approximately 2 h. The spherical pores generated in the membrane had almost the same dimension as that of the particles serving as templates. Instrumentation. The scanning electron microscopy (SEM) images were obtained using two field emission microscopes (FSEM) (JEOL-6300F, Peabody, MA; and Siron, FEI Co., Hillsboro, OR) or an environmental microscope (ESEM) (Electroscan 2020, Wilmington, MA). Both FSEMs were operated with an accelerating voltage of 5 kV. The ESEM was operated with an accelerating voltage of 20 kV and a pressure of ∼5 Torr. Except the silicon templates, all samples prepared for SEM studies were coated with thin layers of gold (∼40 nm in thickness) before imaging. The optical characterizations were performed on a miniature fiber optic spectrometer (S2000, Ocean Optics Inc., Dunedin, FL).
Results and Discussion The key component of this approach is a template whose surface has been patterned with tapered relief structures. Anisotropic etching of single crystalline Si(100) substrates represents one of the simplest methods for generating such a template. When a Si(100) wafer is immersed in a solution containing chemicals such as potassium hydroxide (KOH), the atoms on (100) planes will be etched away more quickly than those on other planes. The etching rate of (111) planes will be relatively slow, leading to the formation of tapered features. If the etching mask contains square (or circular) holes, square pyramidal pits will be generated in the surface of a Si(100) wafer.30 We have demonstrated the use of these pits as a physical template to assemble spherical colloids into uniform, square pyramidal aggregates.28 When the diameter of spherical colloids is much smaller than the dimensions of the pyramidal pits, these particles will nucleate and grow into small, pyramid-shaped crystals, with their (100) planes oriented parallel to the surface of silicon (see Figure 1B for a schematic illustration). In this template-dictated process, the atomic scale symmetry of the Si(100) single crystals could be faithfully transferred into the mesoscale crystals constructed from spherical colloids. Figure 2A shows the SEM image of a Si(100) substrate whose surface had been patterned with a 2D array of discrete pyramidal pits. This silicon wafer has been overetched to reduce the width of the ridges (tr, see Figure 1B) between adjacent cavities from ∼2 µm to less than ∼250 nm. Because the gold mask tended to be detached from the ridges at this point, it was very difficult to further reduce the width of these ridges by anisotropic etching for longer periods of time. These patterned substrates will be limited in use as templates to grow (100)-oriented crystals over large areas. Although all crystals inside the pyramid pits have a (100)-orientation due to geometric confinement, crystals nucleated on the top surface of this template (i.e., the flat regions between adjacent cavities) will prefer to grow along the (111) orientation. Since it is energetically more favorable, the growth along [111] direction will eventually dominate the growth of colloidal crystals once they have been released from the physical confinement applied by the pyramidal pits. As a result, the width of ridges has to be reduced to a value much smaller than the diameter of spherical colloids in order to obtain pure, (100)oriented crystals with relatively large domain sizes. We solved this problem by adding an isotropic wet etching (in HNO3/HF solution) step to the anisotropic etching process.
Figure 2. SEM images of 2D arrays of square pyramidal pits that were patterned in the surfaces of Si(100) wafers using photolithography, followed by (A) anisotropic chemical etching and (B) anisotropic and then isotropic chemical etching. Note that isotropic etching could further reduce the width of ridges from ∼250 nm (A) to less than ∼10 nm (B).
Because all planes have approximately the same etching rate in this wet etchant, silicon atoms belonged to different facets of the pyramidal cavities can be evenly etched to roughly retain the original shape of the pyramidal cavities. In comparison with anisotropic etching, the isotropic etching process was sufficiently mild that it was possible to further undercut silicon ridges without lifting off the gold mask. As shown in Figure 2B, we were able to routinely generate arrays of pyramidal pits with extremely sharp ridges (
