Colloidal Photonic Crystals
Raji Shankar - Final Wiki Entry for APPHY 225, Fall 2008
Final Project: Colloidal Photonic Crystals
Photonic crystals are periodic optical structures with features on the nanoscale. The periodicity of refractive index in these materials leads to a photonic bandgap similar to the energy bandgap produced by the periodic structure of a semiconductor. Photons of wavelengths corresponding to the bandgap cannot propagate through the photonic crystal. For the crystal to have what is called a complete photonic bandgap for a given wavelength range, photons of any arbitrary polarization, direction, and source must be prohibited from propagating through the photonic crystal . Typical photonic crystals (figure 1) have periodicity in two directions, relying on total internal reflection for confinement in the third direction.
A three-dimensional photonic crystal with periodicity in refractive index in all three dimensions would allow for a complete bandgap to be achieved . However, these three-dimensional photonic crystals are much more difficult to fabricate than their two-dimensional cousins, which are usually fabricated through lithography. Instead of using top-down methods such as lithography, colloidal photonic crystals are 3D photonic crystals which are fabricated through self-assembly processes driven by pressure and temperature. Due to the ease of the self-assembly process, colloidal photonic crystals are one of the most actively pursued methods for 3D photonic crystal fabrication .
Opals--Natural Photonic Crystals
The beautiful iridescence of opals is a manifestation of the fact that opals are natural 3D photonic crystals (Figure 2). Opals are composed of a periodic structure of close-packed silica spheres, with the sphere sizes on the order of hundreds of nanometers. This results in diffracted light on the order of the sphere size, resulting in the brilliant reds, greens, blues, and other colors we see on the opal's surface .
Such opals can be created synthetically, by using gravity, centrifugation, or filtration to sediment colloids from solution . The colloids then form a face-centered cubic (fcc) close-packed lattice spontaneously. However, a fcc packing of spherical colloids such as an opal does not result in a complete photonic bandgap. Figure 3 shows the photonic band diagram of an fcc lattice of sphere. No bandgap is present [1,6].
The inverse of such an opal structure, the so-called "inverse opal", can possess a complete photonic bandgap (Figure 4), due to higher index contrast between the sphere voids and interstitial regions. The colloids are used as a template to form an interstitial network when a higher index material is deposited around the colloids. The colloids are then dissolved using a wet chemical etch or thermal decomposition, leaving a high index material with periodically spaced spherical voids (Figure 5).
This simple method of making inverse opals often leads to irregular and polycrystalline photonic crystals with structural defects that can ruin the photonic bandgap. These structural defects include stacking faults, dislocations, and point defects, which can lead to the bandgap being filled with localized photonic states. Vlasov et al. came up with an alternate method in 2001 that resulted in single-crystalline photonic crystals with very few local defects . Instead of using sedimentation, they used the strong capillary forces present at a meniscus between a substrate and a colloidal sol to form an array of colloids. Solvent evaporation was used to sweep the meniscus across a vertical placed substrate, resulting in the deposition of thin planar opals. This process competes with sedimentation, so preferably smaller colloids should be used (< 4 um). However, for bandgaps located at application-rich wavelengths of 1.3 or 1.5 um, larger colloids are needed. To get around this, the authors added a convective flow to the sol to minimize any sedimentation and also to provide a continuous stream of colloids to the meniscus. Using this process on a Si wafer immersed vertically in an ethanolic solution of silica colloids, a fcc opal with very low defect density and very large single-crystalline region was obtained (Figure 6). Then, using this template, Si was added to the interstitial regions using low-pressure chemical vapor deposition, and wet etching was used to remove the silica colloids, resulting in the inverse opal photonic crystal with low defect density. The measured bandgap corresponded to that theoretically predicted for this structure .
The bandgaps of inverse opals can be improved by sintering the synthetic opal before it is infiltrated by the high index material. This consists of bonding the colloids with a tubelike connection, which results in an inverse opal with somewhat smaller filling ratio of the high index material (Figure 7). This effect is due to the enhanced connectivity of the air-filled portions .
Colloidal crystals in the form of inverse opals have been an important means by which to achieve three-dimensional photonic crystals. Their self-assembled nature makes these three-dimensional photonic crystals much easier to fabricate than woodpile structures or other three-dimensional photonic crystal designs. Methods have been developed to decrease the density of defects that occur in the self-assembly process, making achievement of a complete photonic bandgap possible. These colloidal photonic crystals can also be patterned for use in devices, which can lead to some interesting applications in all Si integrated photonic circuits.
 J. Joannopoulos et al. Photonic Crystals: Molding the Flow of Light. Princeton, NJ: Princeton University Press, 2008.
 Y. Akahane et al. "High-Q photonic crystal nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
 V.L. Colvin. "From Opals to Optics: Colloidal Photonic Crystals." MRS Bulletin, August 2001.
 V. A. Vlasov et al. "On-chip natural assembly of silicon photonic bandgap crystals," Nature 414, 289-293 (2001).
 K. Busch and S. John. "Photonic band gap formation in certain self-organizing systems," Physical Review E 58, 3896-3908 (1998).