Langmuir 2003, 19, 3479-3485
3479
Optical Properties of Colloidal Photonic Crystals Confined in Rectangular Microchannels Herna´n Mı´guez,†,‡ San Ming Yang,† and Geoffrey A. Ozin*,† Materials Chemistry Research Group, Lash Miller Chemical Laboratories, Department of Chemistry, University of Toronto, 80 Saint George Street, M5S 3H6 Toronto, Ontario, Canada, and Fibre Radio Group, ITACA Research Institute, Edificio I-4, Camino de Vera s/n, Universidad Polite´ cnica de Valencia, 46022 Valencia, Spain Received December 17, 2002 Herein we report experimental and theoretical analysis of the optical properties of planarized selfassembled colloidal photonic crystals confined within rectangular microchannels. A detailed mapping of the optical features, performed by microspectroscopy, is presented, providing evidence that spherical colloids confined in microchannels crystallize as single-domain colloidal crystal several hundreds of microns long with a very low concentration of intrinsic defects. A study of defective colloidal crystals is also made to illustrate this point. The effect of the different parameters affecting the reflection properties of these structures, such as crystal size, orientation, and nature of the substrate, is also analyzed. We show that the well-defined geometry and dimensions of the channels serve to template colloidal crystals with precise size, shape, and orientation, which imply accurate control of their photonic crystal properties.
I. Introduction There exists a major interest in developing new optical materials and structures to manipulate visible and nearinfrared (NIR) light, which could ultimately allow a substitution of electrons by photons as the main information carriers in current technology. In recent years, a novel class of materials, known as photonic crystals,1,2 has opened up new ways to mold the flow of light that eventually could yield new applications in photonics.3 The interaction of these periodic dielectric lattices with radiation results in a suppression of the photon density of states (DOS) for a certain frequency range along a determined direction of the crystal. These forbidden regions, whose frequency depends on the propagation direction, are known as stop bands and are identified as gaps in a particular crystalline direction in the photon dispersion relationship. Among the different structures that have been considered as good candidates for three-dimensional (3D) visible and NIR photonic crystals, ordered spherical colloids are increasingly attracting the attention of the fundamental and applied optics research communities.4 A wide variety of techniques such as sedimentation,5,6 electrophoresis,7 template-directed crystallization,8 convection forces,9 or confinement between two parallel plates10 have been employed in order to crystallize microspheres in threedimensional structures. In most cases, the photonic crystal * Corresponding author. † University of Toronto. ‡ Universidad Polite ´ cnica de Valencia. (1) John, S. Phys. Rev. Lett. 1987, 58, 2486. (2) Yablonovitch, E. Phys. Rev. Lett. 1987, 58, 2059. (3) Joannopoulos, J. D.; Villeneuve, P. R.; Fan, S. Nature 1997, 386, 143. (4) For a recent review on this topic, see: Colvin, V. L. Mater. Res. Soc. Bull. 2001, 26, 637. (5) Mı´guez, H.; Lo´pez, C.; Meseguer, F.; Blanco, A.; Va´zquez, L.; Mayoral, R.; Ocan˜a, M.; Forne´s, V.; Mifsud, A. Appl. Phys. Lett. 1997, 71, 1148. (6) Vlasov, Yu. A.; Astratov, V. N.; Karimov, O. Z.; Kaplyanskii, A. A.; Bogomolov, V. N.; Prokofiev, A. V. Phys. Rev. B 1997, 55, R13357. (7) Holgado, M.; Garcı´a-Santamarı´a, F.; Blanco, A.; Ibisate, M.; Cintas, A.; Mı´guez, H.; Serna, C. J.; Molpeceres, C.; Requena, J.; Mifsud, A.; Meseguer, F.; Lo´pez, C. Langmuir 1999, 15, 4701. (8) van Blaaderen, A.; Ruel, R.; Wiltzius, P. Nature 1997, 385, 321. (9) Bertone, J. F.; Jiang, P.; Hwang, K. S.; Mittleman, D. M.; Colvin, V. L. Phys. Rev. Lett. 1999, 83, 300. (10) Park, S. H.; Qin, D.; Xia, Y. Adv. Mater. 1998, 10, 1028.
behavior of so-built materials has been confirmed by optical analysis. At the same time, important progress toward the integration of microsphere-based photonic crystals into optical microcircuits has been done. Colloidal crystallization carried out within confined spaces of micrometer size and precise geometry has proved to be a valid route to control size, shape, and orientation of the resulting lattice.11-14 These conclusions are supported by structural characterization studies performed by electron microscopy. However, no optical analysis of these confined systems has been reported so far. Here we show an optical study of geometrically confined silica colloidal crystals. We have analyzed the optical reflectance of the photonic structure grown inside rectangular microchannels of different depths and grown on top of different types of substrates. A microspectroscopy technique allowed us to collect the optical features coming from very small regions of the confined crystals. We obtained a detailed characterization of the regularity of the optical properties achievable by confinement by performing an optical mapping along the colloidal crystal microchannels. The optical study shows that confined colloidal microspheres present extraordinarily long range order, the spatial coherence being kept for distances of the order of hundreds of microns in channels of a few tens of microns in width (aspect ratio ∼ 100). A comparative analysis has been made between confined and freestanding colloidal crystals, the latter being grown using standard sedimentation techniques. The effect on the optical properties of the decreasing number of intrinsic defects present in confined crystals is explicitly demonstrated. Moreover, long-range order is observed regardless of the microsphere size, which enables tailoring of the lattice constant and therefore the optical properties of confined colloidal crystals. Important effects of the finite crystal size and the nature of the substrate are observed and are analyzed theoretically employing a scalar wave (11) Kim, E.; Xia, Y.; Whitesides, G. M. Adv. Mater. 1996, 8, 245. (12) Yang, P.; Deng, T.; Zhao, D.; Feng, P.; Pine, D.; Chmelka, B.; Whitesides, G. M.; Stucky, G. D. Science 1998, 282, 2244. (13) Yang, S. M.; Ozin, G. A. Chem. Commun. 2000, 2507; Adv. Func. Mater. 2001, 11, 95. (14) Yang, P.; Rizvi, A. H.; Messer, B.; Chmelka, B.; Whitesides, G. M.; Stucky, G. D. Adv. Mater. 2001, 13, 427.
10.1021/la027014y CCC: $25.00 © 2003 American Chemical Society Published on Web 03/12/2003
3480
Langmuir, Vol. 19, No. 8, 2003
Mı´guez et al.
Figure 1. SEM images of different kinds of confined colloidal crystals: (a) low-magnification micrograph showing an array of colloidal crystals confined in rectangular microchannels; (b) top view, (c) cross section, and (d) lateral surface of a confined colloidal crystal.
approximation, a good agreement between theory and experiment being found. II. Sample Preparation and Structural Characterization Although full descriptions of the micromold preparation and the colloidal crystallization process have been presented elsewhere,15 we will briefly describe here the main characteristics of this method and focus on the description of the final structural features of the confined lattices. First, an array of rectangular walls was patterned on top of a glass substrate by soft-lithography.16 The walls were made of either epoxy-glass, pure glass, or pure polymer. Their width and separation were varied between 15 and 25 microns, the height being in the range between 4 and 8 microns. Silica microspheres of different diameters (200-1000 nm) were crystallized within these microchannels by using directed evaporation induced self-assembly (DEISA). A scanning electron microscopy (SEM) image of colloidal crystals confined in an array of microchannels is shown in Figure 1a, in which it can be seen that the crystallization takes place only within the channels and not on top of their walls, indicating that capillary forces are strongly driving this process. The top surface of the colloidal lattice shows a long-range order hexagonal close-packed arrangement of microspheres, as shown in Figure 1b. The spatial coherence of microspheres along the microchannel is maintained for hundreds of microns, in many cases millimeters. Some randomly distributed vacancies are observed. Regarding the 3D arrangement, by cleaving the samples or removing the walls of the microchannel template, it was possible to study the ordering along other directions of the so-built colloidal crystal. Transversal and longitudinal cleavage of the microchannel arrays allowed us to observe the cross section and the lateral surfaces of the confined crystal, respectively. SEM images of both kinds of cleavage are shown in Figure 1c,d. The comparison of the SEM images with models of 3D arrangements of spheres in a rectangular channel indicates that the microspheres crystallize in a face-centered (15) Yang, S. M.; Mı´guez, H.; Ozin, G. A. Adv. Func. Mater. 2002, 12, 425. (16) Xia, Y.; Whitesides, G. M. Angew. Chem., Int. Ed. 1998, 37, 550.
Figure 2. Diagram showing the two vectors used to describe the surface orientation relative to the microchannel walls. cubic (fcc) lattice, rather than in hexagonal or random packing arrangements. This tendency toward fcc ordering has been previously observed in colloidal crystals obtained by other selfassembly techniques.9,17 Furthermore, the surface relief pattern of rectangular microchannels seems to impose a determined orientation to the 3D crystals grown within. To see this, let us analyze in more detail the external surface. This presents a closepacked hexagonal arrangement of spheres and possesses a 6-fold symmetry. A cell for this two-dimensional (2D) lattice is plotted in the diagram shown in Figure 2, and we have drawn two nonorthogonal vectors a and b that will be used as a basis to describe the orientation of the surface relative to the channel walls. A closer look at the SEM images of the top external plane of the confined crystal, like that shown in Figure 1b, indicates that the [11] direction of the hexagonal surface, in the basis shown in Figure 2, is always oriented perpendicular to the microchannel walls. This well-defined orientation of the external surface implies, in turn, a well-defined orientation of the confined 3D crystal. By building a model of a 3D fcc lattice confined in a rectangular box, we conclude that such observed orientation of the external surface relative to the lateral walls implies that the [11-2] crystalline direction of the 3D structure is perpendicular to these walls, the [1-10] direction being parallel to them. These results are in good agreement with the crystalline faces observed (17) Mı´guez, H.; Meseguer, F.; Lo´pez, C.; Mifsud, A.; Moya, J. S.; Va´zquez, L. Langmuir 1997, 13, 6009.
Optical Properties of Colloidal Photonic Crystals
Figure 3. Model of the confined structure made of colloidal spherical particles in a rectangular box based on the information obtained from the SEM analysis. From top to bottom, the top external surface (a), the transversal section (b), and the longitudinal section (c) of the modeled confined colloidal crystal are shown. In each case, the main crystalline directions with respect to the channel walls are indicated. in the SEM images of cross sections and lateral cleaved edges shown in Figure 1. For comparison, the computer models employed for this study are shown in Figure 3. The crystal axes, perpendicular or parallel to the channel walls or bottom, are also indicated. As opposed to other crystallization processes in which the geometry of the mold is the main factor determining the orientation of the lattice,8,13,18 in this case the orientation seems to be the result of a more complex process in which capillary, convection, and gravitational forces must be taken into account, as well as particle-particle and particle-wall interactions. In particular, our observations support the hypothesis that the particles tend to create a high-density crystalline surface in contact with the flat channel walls and substrate, which would explain why the formation of an oriented fcc structure in the channel is favored. Therefore, crystallization in confined spaces is strongly biased by the wall-particle interaction. Besides, the absence of particles deposited on the top of the confining channel walls indicates that the capillary forces are also playing an important role. Further analysis of the ordering process is currently being performed. Control over the orientation might enable the observation of fundamental properties related to the propagation of polarized light through the structure,19 as well as enhance the range of applications that depend sensitively on this orientation.20
III. Microspectroscopy Optical Analysis of Confined Colloidal Crystals An accurate optical test requires the analysis of the individual colloidal crystal microchannels. To do so, we have studied our samples employing an optical microspectroscopy technique.21 A diagram of the experimental setup is shown in Figure 4. An optical microscope is attached to a spectrometer and a silicon array charge coupled device (CCD) detector. A quartz lamp is used as a light source. A ×10 magnification objective is used to irradiate the sample and collect the reflected light. To have a well-defined propagation direction in the crystal, the angle of the cone of light impinging the sample has (18) Yin, Y. D. Xia, Adv. Mater. 2002, 14, 605. (19) Ochiai, T.; Sa´nchez-Dehesa, J. Phys. Rev. B 2001, 64, 245113. (20) Shkunov, M. N.; Vardeny, Z. V.; DeLong, M. C.; Polson, R. C.; Zakhidov, A. A.; Baughman, R. H. Adv. Func. Mater. 2002, 12, 21. (21) Mı´guez, H.; Yang, S. M.; Ozin, G. A. Appl. Phys. Lett. 2002, 81, 2493.
Langmuir, Vol. 19, No. 8, 2003 3481
been reduced by using a mask in front of the objective that lowers its numerical aperture from NA ) 0.25 to NA ) 0.05. This allows an accurate optical analysis since the uncertainty of the propagation direction is largely diminished from 0° ( 14° to 0° ( 3° with respect to the normal to the analyzed sample surface. In addition, a square confocal pinhole was used to spatially filter the image created by the microscope objective and discriminate the information coming from a specific region of the colloidal crystal. An example of the masking effect of the variable size pinhole is shown in the inset of Figure 5b, being in this case the window size enlarged up to 70 µm × 70 µm for the sake of clarity. This allows one to study the variation of the optical features along the full length of a microchannel by mapping different sites. Figure 5a,b shows optical micrographs of an array of colloidal crystals grown within epoxy-glass walls built on top of a glass substrate. In this case, the diameter of the microspheres employed is φ ) 320 ( 10 nm. The width of both the wall and the colloidal crystal is 25 µm, the thickness of the crystal being 7.8 µm. Pictures have been taken in both transmission and reflection modes. The sample was irradiated with white light incident at a normal angle with respect to the (111) planes of the confined crystal. The colored pattern displayed by the structure is the result of the partial suppression of the density of states for a certain band of frequencies due to the modulation of dielectric constant along the [111] direction. Optical reflectance spectra were collected every 20 µm along a several hundreds of microns length of the channels using the setup described above. Measurements were done using a spatial filter to select the reflectance coming from areas of the sample of 20 µm × 20 µm. The spectral analysis of the reflected light along a single colloidal crystal microchannel made of spheres of φ ) 320 ( 10 nm is shown in Figure 6a. In this case, the width and depth of the crystal are 25 and 4 µm, respectively. The confining walls are made of epoxy-glass built on top of a silicon wafer. The primary maximum observed in each spectrum corresponds to the lowest energy stop band that opens at the L-point of the first Brillouin zone, while the lower intensity fringes detected on both sides of the main peak stem from the finite size of the crystal, which was measured by SEM to be 20 close-packed sphere layers (N ) 20) and will be analyzed in detailed later. The observation of this oscillation of the reflectance intensity is consistent with previously reported experimental results on polycrystalline22 and thin film colloidal crystals.9 Regarding the optical quality, it can be seen that the optical features of the crystal are maintained along the microchannels for extremely long distances compared to the microchannel width, no significant change being observed in the intensity, width, and position of both the main reflectance peak and side fringes. This indicates that the crystal thickness is uniform along the channel and that there is a low occurrence of defects such as cracks or disorder, which would largely broaden the peak width and remove or alter the fine structure of secondary minima.23 In Figure 6b, the position and width of the reflectance maximum at each observed site are plotted versus the distance of the site to the first optically tested part of the microchannel, the total length shown being 540 microns in this case. We estimate the width of the stop band or pseudogap at the L-point as the spectral (22) Vlasov, Y. A.; Deutsch, M.; Norris, D. J. Appl. Phys. Lett. 2000, 76, 1627. (23) Vlasov, Yu. A.; Astratov, V. N.; Baryshev, A. V.; Kaplyanskii, A. A.; Karimov, O. Z.; Limonov, M. F. Phys. Rev. E 2000, 61, 5784.
3482
Langmuir, Vol. 19, No. 8, 2003
Mı´guez et al.
Figure 4. Experimental setup used to perform the microspectroscopy analysis of the confined crystals (after ref 21).
Figure 5. Optical micrographs of an array of confined colloidal crystals built on a glass substrate. Pictures have been taken in transmission (a) and reflection (b) mode when light impinges normally to the (111) planes of the confined fcc lattice (microsphere diameter φ ) 320 ( 10 nm). The inset in (b) shows the effect of the spatial filter used to analyze selectively different regions of the channel.
separation between the two minima labeled as m ) 1 in Figure 6a. The small fluctuation of these parameters is evidence of the long-range order existing in the microchannel-confined colloidal crystals. These fluctuations are very likely due to variations in the lattice constant caused by random fluctuations of the microchannel width and/or the presence of randomly distributed vacancies that induce a relaxation of the crystal. Similar characteristics can be seen in the optical microanalysis of colloidal crystals confined within surface relief patterns built on different types of substrates. Figure 7 shows spatially resolved reflectance spectra measured along a colloidal crystal microchannel made of the same microspheres as in the case of Figure 6 but built on top of a glass substrate instead of silicon. One of the main applications of these lattices is as templates to form inverted colloidal crystals.24-26 In such structures, a full photonic band gap opens up between the (24) 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.
8th and 9th bands of the fcc structure provided a high enough dielectric constant and a correct filling fraction are achieved.27 However, these higher energy bands are extremely sensitive to defects,28 which may cause the gap to close even for a very low concentration of them. In this sense, the properties herein presented indicate that colloidal crystal confinement might be a way to grow lattices with a low number of defects and, consequently, with more robust photonic gaps. The high optical quality of confined crystals is emphasized when compared to photonic colloidal crystals prepared by some other standard techniques. For comparison, a similar microspectroscopy analysis was performed for colloidal crystals made by natural sedimentation of an aqueous suspension of (25) Miguez, H.; Chomski, E.; Garcia-Santamaria, F.; Ibisate, M.; John, S.; Lopez, C.; Meseguer, F.; Mondia, J. P.; Ozin, G. A.; Toader, O.; van Driel, H. M. Adv. Mater. 2001, 13, 1624. (26) Vlasov, Y. A.; Bo, X. Z.; Sturm, J. C.; Norris, D. J. Nature 2001, 414, 289. (27) Busch, K.; John, S. Phys. Rev. E 1998, 58, 3896. (28) Li, Z. Y.; Zhang, Z. Q. Phys. Rev. B 2000, 62, 1516.
Optical Properties of Colloidal Photonic Crystals
Figure 6. (a) Spatially resolved reflectance spectra of a single colloidal crystal microchannel confined within glass walls built on top of a silicon wafer. Each spectrum corresponds to an area of the confined crystal of dimensions 20 µm × 20 µm, selected using a spatial filter. Spectra are taken every 20 microns along the channel and are shifted for the sake of clarity. (b) Fluctuation of the position and the width of the main optical reflectance peak shown in (a).
Figure 7. (a) Spatially resolved microspectroscopy mapping similar to the one shown in Figure 6, but in this case for a single colloidal crystal microchannel confined within glass walls built on top of a glass slide. Spectra are taken every 20 microns along the channel and are shifted for the sake of clarity. (b) Fluctuation of the position and the width of the main optical reflectance peak.
silica microspheres on a flat substrate, a widely employed nondirected self-assembly technique. This leads to polycrystalline samples presenting a thickness of thousands of sphere layers. The optical mapping of the so-obtained colloidal crystal along an arbitrarily selected 20 µm × 240 µm stripe of its surface is shown in Figure 8, each spectrum being obtained under exactly the same conditions as those used for the study of microchannels. Unlike confined colloidal crystals, a strong fluctuation of the position, width, and intensity of the reflectance peak can be clearly seen. This is a consequence of the high concentration of intrinsic defects such as vacancies, dislocations, stacking faults, and disordered regions present in this type of crystals. Such irregularities cannot be detected using optical analysis tools that probe large areas of the sample, which provide an average of these local optical features.5,6 Thus, microspectroscopy proves to be a powerful tool to test the uniformity of the optical properties at a length scale of a few microns.
Langmuir, Vol. 19, No. 8, 2003 3483
Figure 8. Spatially resolved reflectance spectra of a freestanding, polycrystalline, silica colloidal crystal obtained by sedimentation on a flat substrate. Each spectrum corresponds to an area of the crystal of dimensions 20 µm × 20 µm, selected using a spatial filter. Spectra are taken every 20 microns along an arbitrarily selected 20 microns × 220 microns stripe and are shifted for the sake of clarity.
Figure 9. Reflectance spectra of a 20 µm × 20 µm area of a confined colloidal crystal made of spheres of diameter φ ) 320 ( 10 nm and built on top of (a) a glass slide and (b) a silicon wafer. Crystal thicknesses are 20 and 15 close-packed sphere layers, respectively. In both cases, the thinner line corresponds to the theoretical spectrum calculated using a scalar wave approximation.
IV. Analysis of the Optical Properties: Effect of the Substrate and the Crystal Size Large differences are observed for the shape of the reflectance spectra depending on the nature of the substrate chosen to support the confined crystals. Panels a and b of Figure 9 show experimental spectra (thick lines) extracted from Figures 6a and 7a, respectively. Crystal thickness, in sphere layers, is N ) 20 in Figure 9a and N ) 15 in Figure 9b, and the confining walls are epoxy-glass in both cases. The most striking difference between the two spectra is the large asymmetry present in the spectrum shown in Figure 9a, which does not exist in the one presented in Figure 9b. To study the origin of this difference between silicon- and glass-supported confined crystals, reflectance spectra were calculated using analytical expressions derived from a scalar wave approximation
3484
Langmuir, Vol. 19, No. 8, 2003
Mı´guez et al.
between the channel depth L and the interplanar distance in the [111] direction perpendicular to the substrate, as can be seen in Figure 1.
N)
Figure 10. (a) Three normalized reflectance spectra corresponding to confined colloidal crystal microchannels made of different silica microsphere diameters, namely, φ ) 320 ( 10 nm, φ ) 550 ( 15 nm, and φ ) 970 ( 35 nm. In all three cases, the microchannel width and depth were the same. (b) Reflectance spectra corresponding to confined crystals presenting a thickness of (1) 9 and (2) 16 sphere layers. For the sake of comparison, the ordinate axis is presented in nondimensional units, φ/λ, where φ is the sphere diameter. (c) Gap to midgap ratio ∆λ/λc versus crystal thickness, expressed in number of (111) sphere layers. Values obtained for samples grown on top of silicon ([) and on glass (O) are shown. Dotted and dashed lines show the evolution of ∆λ/λc calculated for both silicon and glass substrates, respectively. A horizontal line is drawn at ∆λ/λc ) 5.2%, corresponding to the value expected for an infinite crystal.
(SWA),29,30 in which both the finite size of the crystal and the refractive index of the substrate are taken into account. For the sake of comparison, results of the calculations31 are plotted (thin lines) in Figure 9a,b along with the experimental data. Theoretical results accurately reproduce the experiment, both qualitatively and quantitatively. One of the conclusions extracted from this model is that the large difference observed between the shapes of the spectra is due to the nature of the substrate. The reflection properties of substrate-supported thin photonic crystal slabs are strongly affected by the coupling of the propagating light to the continuum distribution of available light states of the substrate. Due to the finite photonic crystal size, there is a nonzero transmittance for photon states with energies within the photonic pseudogap, represented by exponentially decaying evanescent waves. Figure 10a shows microspectroscopy spectra obtained from confined crystals made of spheres of different average diameter, namely, (1) 970 nm, (2) 550 nm, and (3) 315 nm. In all cases the optical quality is similar, the structure of fine side fringes being observable in all cases. By confinement, the crystal size is entirely determined by the ratio (29) Shung, K. W. K.; Tsai, Y. C. Phys. Rev. B 1993, 48, 11265. (30) Mittleman, D. M.; Bertone, J. F.; Jiang, P.; Hwang, K. S.; Colvin, V. L. J. Chem. Phys. 1999, 111, 345. (31) For these calculations, we consider a value of the refractive index of n ) 1.425 for the amorphous silica microspheres and the presence of water (9% filling fraction), bonded to the sphere surface, as indicated by thermogravimetric measurements: Garcı´a-Santamarı´a, F.; Ibisate, M.; Mı´guez, H.; Meseguer, F.; Lo´pez, C. Langmuir 2002, 18, 1942. Concerning the substrates, refractive indexes have been considered to be n ) 1.5 for glass and n ) 3.796 + 0.013i for silicon: Aspnes, D. E.; Studna, A. A. Phys. Rev. B 1983, 27, 985.
L ) d(111)
L
x
2 φ 3
(1)
This geometric control presents no restrictions affecting the sphere size and therefore implies a major improvement when compared to other planarization methods previously reported in the literature, which are limited to a narrow range of microsphere sizes and depend on many parameters not always easy to determine.9 The accurate control of the colloidal crystal size achieved through confinement allows one to study in detail its effect on the optical properties. In Figure 10b, we show the reflectance spectra measured for two colloidal crystals confined within microchannels of the same depth (L ) 7 µm) but made of spheres of different average diameter, namely, (1) 970 nm and (2) 550 nm. The number of (111) planes parallel to the substrate was measured by SEM and found to be (1) N ) 9 and (2) N ) 16 sphere layers, respectively, in excellent agreement with values from formula 1. For the sake of comparison, the coordinate axis is presented in nondimensional units, φ/λ, where φ is the sphere diameter. It can be clearly seen in Figure 10b that the width of the main reflectance peak increases as the crystal thickness decreases, as does the spectral separation between secondary minima. To illustrate in more detail the variation of the reflectance properties with the crystal thickness, the experimental pseudogap to midgap ratio (∆λm)1/λc), estimated as the ratio between the main reflectance peak width as defined above (∆λm)1) and its maximum position (λc), is plotted in Figure 10c for several different confined crystals versus the number of (111) sphere layers measured by SEM. The variation of ∆λm)1/λc as a function of crystal size expected from the scalar wave approximation for a glass (long dashed line) and a silicon (short dashed line) substrate is also shown, both the trend and the actual experimental values being in good agreement with this model. It can be seen that the differences between both ∆λm)1/λc curves diminish as N increases, since the effect of the substrate on the reflectance becomes less pronounced. The dotted horizontal line in Figure 10c indicates the value of ∆λm)1/λc ) 5.2% expected for an infinite crystal, from photonic band structure calculations, toward which both curves tend asymptotically. Using the SWA, we estimate that crystals with thicknesses larger than 200 (111) sphere layers present pseudogap-to-midgap ratios that differ by less than 1% from this value. No experimental data have so far been reported for defect-free, large colloidal photonic crystals that could be regarded as bulk materials. V. Spectroscopy of Different Crystalline Directions It is clear from the SEM characterization presented in section II that control over the orientation is achieved by confinement. However, to obtain optical evidence of this control is not an easy task since it requires both tilting the substrate on which the confined crystals are built and focusing light on areas of either 4 µm (depth) × 25 µm (width), in the case of light propagating along the channel, or 4 µm (depth) × ∞ µm (length), in the case of light propagating perpendicular to the lateral surfaces. By using an optical microspectroscopy technique, we analyzed the
Optical Properties of Colloidal Photonic Crystals
Langmuir, Vol. 19, No. 8, 2003 3485
Figure 11. (a) Optical reflectance obtained from the top and the lateral free crystalline faces of a colloidal crystal channel built on top of a silicon wafer and made of spheres of φ ) 870 ( 30 nm. (b) Photonic band structure of a face-centered cubic crystal made of spheres along some principal directions of the crystal relevant to our study.
reflectance along these three main crystalline directions in a colloidal crystal microchannel in which the confining walls have been removed in order to measure the lateral surface, as in Figure 1d. Besides, the samples were transversally cleaved, as in Figure 1c, to allow us to collect the light reflected by the cross section and obtain information about the optical propagation along the channel. In Figure 11a, we show the optical reflectance spectra obtained when light impinges normal to the top and the lateral surfaces of a 870 ( 30 nm diameter sphere colloidal crystal channel. The top spectrum was measured using white light impinging perpendicularly to the (111) planes (see Figure 1b and Figure 4). The bottom spectrum was obtained tilting the planar substrate 70° with respect to its normal, until the free lateral surface of the sample was perpendicular to the probing light beam (see Figure 1d). This propagation direction is parallel to the [11-1] crystalline direction. In fact, the observed reflectance maximum is at the same wavelength position in both spectra, since for both the [111] and [11-1] directions the corresponding first lowest photonic pseudogap opens up at the same wavelength. A similar reflectance spectrum was obtained for all the different regions tested along the lateral surface. The photonic band structure along the Γ-L and the Γ-K direction is plotted in Figure 11b. On the other hand, no peak or oscillatory pattern was observed in the specular reflectance coming from the transversal cross section of the samples. The absence of a reflection peak coming from the cross sections of the channels is in good agreement with the degeneracy of the lowest photonic bands at the K-point of the first Brillouin zone, as can be seen in Figure 11b. These results strongly support the hypothesis, also suggested by the SEM analysis, that crystallization within rectangular microchannels tends to form a well-oriented colloidal crystal in which all the
free external surfaces belong to the {111} family and the crystalline direction along the microchannel groove is [1-10]. That implies the cross section of a confined colloidal crystal does not inherit the rectangular shape of the confining microchannel, but its transversal section is a nonrectangular parallelogram whose sides form angles of 70° and 110° between them, the angle between crystalline planes belonging to the {111} family. In addition, it shows the optical frequency filtering effect occurring in different directions of the structure, which could be put into practice in actual planarized self-assembled colloidal crystal-based microphotonic devices. VI. Conclusion We have shown here results for the optical properties of planarized face-centered cubic colloidal crystal photonic crystals confined in geometrically and spatially welldefined microchannels. By using an optical microspectroscopy technique, we have analyzed the optical quality of such photonic crystals. In addition, we have studied the effect of the crystal size and the substrate on the stop bands and the optical propagation along different crystalline directions. Geometrically confined microphotonic crystals of optical quality, such as those shown here, may allow reduction to practice of planarized optically integrated photonic crystal devices and chips. Acknowledgment. G.A.O. is a Canada Research Chair in Materials Chemistry. Financial support for this work was generously provided by the Natural Sciences and Engineering Research Council of Canada and the University of Toronto. H.M. thanks Generalitat Valenciana for financial support (grant CTDIA/2002/29). LA027014Y
