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Flow-Controlled Vertical Deposition Method for the Fabrication of Photonic Crystals Zuocheng Zhou and X. S. Zhao* Department of Chemical and Environmental Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 Received September 10, 2003. In Final Form: November 8, 2003
Introduction Photonic crystals are an emerging family of optical materials that manipulate the behavior of photons in much the same way as crystalline semiconductors do for electrons.1,2 Thus, they are envisioned to play a vital role in tomorrow’s photonic technology. Presently, one of the challenges in photonic technology is fabrication of threedimensional (3D) photonic crystals with a complete photonic band gap at the wavelength scale of visible light. Lithography and micromachining have proven successful.3-5 However, these conventional techniques have trouble producing thick 3D structures. Recently, self-assembly has been explored and demonstrated as a simple and inexpensive approach to the fabrication of 3D photonic crystals.6 In this method, the growth of highly ordered colloidal arrays in large domains without the presence of defects is extremely important. Up to now, a number of techniques such as gravitational sedimentation,7,8 vertical deposition (VD),9-12 membrane filtration,13,14 emulsion crystallization,15 and the Langmuir-Blogett (LB) method16,17 have been demonstrated to grow colloidal crystals for photonic applications. Among * Corresponding author. E-mail:
[email protected]. Phone: 65-68744727. Fax: 65-67791936. (1) Yablonovitch, E. Phys. Rev. Lett. 1987, 58, 2059-2062. (2) John, S. Phys. Rev. Lett. 1987, 58, 2486-2489. (3) Lin, S. Y.; Fleming, J. G.; Hetherington, D. L.; Smith, B. K.; Biswas, R.; Ho, K. M.; Sigalas, M. M.; Zubrzycki, W.; Kurtz, S. R.; Bur, J. Nature 1998, 394, 251-253. (4) Noda, S.; Tomoda, K.; Yamamoto, N.; Chutinan, A. Science 2000, 289, 604-606. (5) Aoki, K.; Miyazaki, H. T.; Hirayama, H.; Inoshita, K.; Baba, T.; Sakoda, K.; Shinya, N.; Aoyagi, Y. Nature Mater. 2003, 2, 117-121. (6) Special issue. Adv. Mater. 2001, 13, 369. (7) (a) van Blaaderen, A.; Ruel, R.; Wiltzius, P. Nature 1997, 385, 321-324. (b) Braun, P. V.; Zehner, R. W.; White, C. A.; Weldon, M. K.; Kloc, C.; Patel, S. S.; Wiltzius, P. Adv. Mater. 2001, 13, 721-724. (8) (a) Mı´guez, H.; Chomski, E.; Garcı´a-Santamarı´a, F.; Ibisate, M.; John, S.; Lo´pez, C.; Meseguer, F.; Mondia, J. P.; Ozin, G. A.; Toader, O.; van Driel, H. M. Adv. Mater. 2001, 13, 1634-1637. (b) Blanco, A.; Chomski, E.; Grabtchak, S.; Ibisate, M.; John, S.; Leonard, S. W.; Lo´pez, C.; Meseguer, F.; Mı´guez, H.; Mondia, J. P.; Ozin, G. A.; Toader, O.; van Driel, H. M. Nature 2000, 405, 437-439. (9) Vlasov, Y. A.; Bo, X.-Z.; Sturm, J. C.; Norris, D. J. Nature 2001, 414, 289-293. (10) (a) Jiang, P.; Hwang, K. S.; Mittleman, D. M.; Bertone, J. F.; Colvin, V. L. J. Am. Chem. Soc. 1999, 121, 11630-11637. (b) Jiang, P.; Bertone, J. F.; Hwang, K. S.; Colvin, V. L. Chem. Mater. 1999, 11, 21322140. (11) Egen, M.; Voss, R.; Griesebock, B.; Zentel, R. Chem. Mater. 2003, 15, 3786-3792. (12) Gu, Z.-Z.; Fujishima, A.; Sato, O. Chem. Mater. 2002, 14, 760765. (13) (a) Velev, O. D.; Jede, T. A.; Lobo, R. F.; Lenhoff, A. M. Nature 1997, 389, 447-448. (b) Velev, O. D.; Tessier, P. M.; Lenhoff, A. M.; Kaler, E. W. Nature 1999, 401, 548. (14) (a) Park, S. H.; Xia, Y. Adv. Mater. 1998, 10, 1045-1048. (b) Gates, B.; Qin, D.; Xia, Y. Adv. Mater. 1999, 11, 466-469. (15) (a) Velev, O. D.; Nagayama, K. Langmuir 1997, 13, 1856-1859. (b) Velev, O. D.; Lenhoff, A. M.; Kaler, E. W. Science 2000, 287, 22402243.
them, the VD method has gained a great deal of attention. In this method, a substrate is placed vertically in a colloidal suspension. With the evaporation of the solvent, the liquid surface moves down and a thin layer of colloidal particles forms on the substrate. Although this method has been proven workable for the growth of colloidal crystals, there are a number of problems such as lack of uniformity of the deposited film along the solvent-evaporation direction and inefficiency in the assembly of large colloidal spheres. In the past few years, some improvements on the method have been described.9,12 Vlasov and co-workers9 introduced a temperature gradient to allow convective flow to minimize particle sedimentation. Gu et al.12 described a device for the fabrication of opal films by lifting the substrate out of the colloidal suspension. In this paper, we describe another improved VD method, named the flowcontrolled VD (FCVD) method, which is based on the LB technique. By controlling the dropping velocity of the liquid surface, concentration of the suspension, and particle size of the spherical colloids, we have been able to fabricate colloidal spheres of up to a 1.5-µm size into uniform 3D arrays in large domains with a controllable and uniform thickness. Experimental Section Polystyrene (PS) spheres with diameters ranging from 0.5 to 1.5 µm and a standard deviation of less than 5% were prepared by using the emulsifier-free emulsion polymerization technique.18 The FCVD method is schematically illustrated in Figure S1 (see Supporting Information). A plastic vessel containing a colloidal suspension with a cap was connected with a microtube. The inner diameters of the container and the tube were 90 and 1 mm, respectively. A glass microslide (Marienfeld) was vertically attached to the inside wall of the container. The slide was soaked in concentrated H2SO4 overnight, and rinsed with water and finally with ethanol before use. The volume fraction of the suspension was determined by mixing a certain amount of PS spheres in 200 mL of ethanol (a value of 1.05 g/mL was taken as the density of the PS spheres). The suspension was withdrawn from the container by using a variable-flow peristaltic minipump (Fisher Scientific Pte., Ltd.). The flow rates of the pump (Q) were varied between 0.2445 and 0.009 mL/min, which led to the liquid surface dropping velocities (VP) ranging from 0.64 to 0.0236 µm/ s. The temperature of the container was maintained at 30 °C by using a heating tape. The evaporation rate of the solvent (je) was measured under the same experimental conditions, which was about 0.031 µm/s. The numbers of the layers of the resultant films were determined with a JEOL JSM-5600LV scanning electron microscope (SEM). Optical transmission spectra were measured on a Shimadzu UV-3101PC UV-visible-near-infrared spectrophotometer.
Results and Discussion In the traditional LB technique, a monolayer is first formed on the liquid surface of a colloidal suspension, followed by deposition on the surface of a solid substrate during withdrawal of the substrate. Multilayer films of polymer spheres have been recently fabricated at elevated temperatures using the LB method.16,17 On the other hand, the VD method describes that colloidal spheres are (16) (a) Im, S. H.; Lim, Y. T.; Suh, D. J.; Park, O. O. Adv. Mater. 2002, 14, 1367-1369. (b) Im, S. H.; Kim, M. H.; Park, O. O. Chem. Mater. 2003, 15, 1797-1802. (17) (a) Griesebock, B.; Egen, M.; Zentel, R. Chem. Mater. 2002, 14, 4023-4025. (b) Gildenberg, L. M.; Wagner, J.; Stumpe, J.; Paulke, B.R.; Go¨rnitz, E. Langmuir 2002, 18, 3319-3323. (18) Shim, S.-E.; Cha, Y.-J.; Byun, J.-M.; Choe, S. J. Appl. Polym. Sci. 1999, 71, 2259-2269.
10.1021/la035686y CCC: $27.50 © 2004 American Chemical Society Published on Web 12/25/2003
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Figure 1. SEM image of PS colloidal crystals fabricated by using the FCVD method, showing a uniform thickness in large domains. The diameter of the microspheres was 1.5 µm.
dispersed evenly in a solvent and an ordered structure forms with the withdrawal of a solid substrate because of the formation of a liquid meniscus. In the VD process, the concentration of the colloidal suspension increases with the evaporation of the solvent, resulting in variable thicknesses of the resultant colloidal arrays along the evaporation direction. In addition, the VD method requires a relatively long period of time because of slow solvent evaporation, which results in sedimentation of the colloidal particles, leading to inefficiency of self-assembly, particularly for large particles. Improvements have been reported by some research groups such as the dipping method described by Gu et al.12 and Dimitrov and Nagayama.19a However, our FCVD method has a number of advantages over the previously reported improved VD methods (Figure S1, Supporting Information). First, in the FCVD method the relative motion between the colloidal suspension and the substrate is manipulated by decreasing the liquid surface with the help of a peristaltic pump, not involving any complex facilities. Second, because the substrate is fixed in the colloidal suspension, the shaking problem during lift-up of the substrate can be avoided. Third, in the dipping method the lift-up speed of the substrate is solely controlled by the motor. However, in our FCVD method, the dropping velocity of the liquid surface (Vs; here the evaporation of the solvent can be ignored as the vessel is capped) is determined by the pumping flow rate (Q) and the cross-sectional area of the container (S), namely, Vs ) Q/S. As a result, by using a common peristaltic pump the dropping velocity of the liquid surface can be easily controlled. For example, the smallest velocity that can be achieved in the FCVD method is 0.0236 µm/s, while it is 0.1 µm/s in the dipping method.12 Finally, because the peristaltic pump can maintain a constant flow rate over a wide range, the liquid surface dropping velocity can be controlled precisely. Figure 1 shows the SEM images of 3D colloidal crystals fabricated from PS spheres of 1.5 µm using the FCVD method. It can be seen that the thickness of the film is uniform over large domains, while it is impossible to fabricate photonic crystals from such large particles by using the conventional VD method. Because a fast liquid surface dropping velocity can be achieved by using the FCVD method, the concentration gradient of the colloidal (19) (a) Dimitrov, A. S.; Nagayama, K. Langmuir 1996, 12, 13031311. (b) Dimitrov, A. S.; Nagayama, K. Chem. Phys. Lett. 1995, 243, 462-468.
Figure 2. SEM images of photonic crystals fabricated by using the FCVD method with PS spheres of (A) 0.56, (B) 0.67, (C) 1.0, and (D) 1.5 µm. (E) Number of layers versus inverse particle diameter. Volume fraction φ ) 1%; pump flow velocity VP ) 0.26 µm/s. (F) Optical transmission curves of the photonic crystals fabricated by using PS spheres with diameters of (a) 0.56, (b) 0.67, and (c) 1.0 µm.
particles due to sedimentation can be substantially minimized. In addition to the PS-ethanol system, our experimental results have shown that the FCVD method is workable for the PS-water system and for the fabrication of photonic crystals from colloidal spheres larger than 1.5 µm. The cross-sectional SEM images of colloidal crystals fabricated from PS spheres of different sizes are shown in Figure 2A-D. The number of particle layers against the inverse particle diameter (d) is plotted in Figure 2E. It can be seen that the number of particle layers decreases with an increase in the diameter of the spheres. In other words, the product of the diameter and the number of layers, namely, the thickness of the film, is a constant. Figure 2F shows the optical transmission curves of the photonic crystals fabricated with PS spheres of 0.56, 0.67, and 1.0 µm (because of the limitation of the wavelength range of the spectrophotometer, the transmission spectrum of the sample fabricated with 1.5-µm PS spheres was not measured). It can be seen from Figure 2F that the photonic crystals display band gaps at different wavelengths, which are dependent on the colloidal sphere sizes, confirming the highly ordered 3D lattices. In the study of the self-assembly of colloidal spheres into two-dimensional (2D) arrays on a solid substrate using the LB technique, Dimitrov and Nagayama19 derived a mathematic model to describe the formation of 2D arrays:
k)
jeφ βL 0.605 dVW(1 - φ)
(1)
where k is the layer number, β is a constant depending on particle-particle and particle-substrate interactions, L is the evaporation length, d is the particle diameter, φ is the particle volume fraction of the colloidal suspension, and VW is the withdrawal velocity of the substrate, which is equal to the growth rate of the k-layer array, VC, under the experimental conditions described by the authors.19
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Figure 3. Number of colloid layers versus the volume fraction. Particle diameter d ) 0.56 µm; pump flow velocity VP ) 0.26 µm/s.
By optimization of the model, the authors were able to fabricate a monolayer film. Here, we use eq 1 to understand the observed relationship between the thickness of colloidal arrays and colloid diameters. However, under our experimental conditions, VW in eq 1 is replaced by the dropping velocity of the liquid surface Vs. It can be seen from Figure 2E that our experimental data are in good agreement with eq 1 in the whole range of the particle sizes studied in this work. We further investigated the relationship of the layer numbers with the particle volume fraction. Figure S2 (see Supporting Information) shows the side view of the SEM images of the particle films formed with different volume fractions. It is seen that, when a volume fraction of 0.2% was used, an incomplete monolayer formed (Figure S2A). In the volume-fraction range of 0.5-3%, fairly good films of increased thickness with increasing volume fraction were obtained (Figure S2B-D), which agrees very well with eq 1 (see Figure 3). Simply by adjusting the flow rate of the peristaltic pump, we were able to control the number of colloidal particle layers as revealed by the SEM images shown in Figure S3 (see Supporting Information). In the conventional VD method, the evaporation velocity je and the array growth velocity Vc are assumed to be identical because the liquid dropping velocity is solely determined by solvent evaporation.10b However, under our experimental conditions, not only the evaporation of solvent but also the pump flow velocity induces the decrease in the liquid surface. As a result, eq 1 should be rewritten as
k)
jeφ βL 0.605 d(VP + je)(1 - φ)
(2)
Equation 2 shows that increasing the ratios of VP/je will result in a decrease in k. This is supported by our experimental data shown in Figure S3 (see Supporting Information). As can be seen by increasing the pump flow velocity, the number of layers was decreased. Thus, maintaining an appropriate ratio of VP/je is important for the formation of photonic crystals of a given number of layers. These data also show that, by controlling the pump flow velocity, the thickness of the photonic crystals can be controlled.
Figure 4. Number of colloidal layers versus inverse pump flow velocity. Volume fraction φ ) 1%; particle diameter d ) 0.56 µm.
As can be seen from Figure 4, the plot of the layer number against the reverse pump flow velocity is no longer linear. It is understood that, when VP is much larger than je, the curves becomes linear, which means the effect of je on the liquid surface dropping velocity of the colloidal suspension can be ignored. When VP is comparable to je, the latter must be considered, which leads to the departure of the curve. All parameters in eq 2 can be experimentally determined except for the evaporation length L. The substitution of parameters d, Vs, φ, β, k, and je into eq 2 allowed us to obtain L, which was in the range of 2200-2500 µm. If one considers experimental errors, an average L value of 2350 µm can be taken. This value is much larger than that obtained by Jiang et al.,10b which was about 300 µm. We believe that the inconsistency of the L values observed by different research groups is due to the use of different colloid-solvent systems, as well as the different experimental conditions. Conclusions We have developed a simple and effective method, named FCVD, for the self-assembly of colloidal spheres by precise control of the liquid surface dropping velocity of a colloidal suspension. With this method, we have successfully fabricated photonic crystals in large domains and of controllable and uniform thickness. In addition, the FCVD method allows the minimization of particle sedimentation and the concentration gradient. Furthermore, it is believed that the FCVD method can be used in other applications such as the LB film technology. The experimental data observed in this study can be understood using a model developed by Dimitrov and Nagayama.19 Acknowledgment. We thank A*STAR and ARF of NUS for financial support. Supporting Information Available: Illustration of the FCVD method and SEM images of colloidal crystals fabricated under different particle volume fractions and pump flow velocities. This material is available free of charge via the Internet at http://pubs.acs.org. LA035686Y
