Photonic crystals (PC) promise to revolutionize our ability to manipulate light. Yet two decades after their inception, this promise has yielded few practical results. In large part, this is because there has been no cheap, reliable way of fabricating the crystals. The focus of this discussion is to shed light on the current methods that are being developed, and evaluate their potential usefulness.
Initial attempts to fabricate photonic crystals in the late 1980s and early 1990s relied heavily on their scaling properties, namely that a crystal with twice the lattice constant has a band gap at twice the wavelength. Consequently, when E. Yablonovitch sought to verify his seminal 1987 prediction of a complete 3D photonic band gap (PBG) [1], he chose his lattice constant in millimeters, rather than nanometers. This meant that he was not constrained to difficult and expensive micro-fabrication techniques. Instead, Yablonovitch ultimately constructed his design (aptly named Yablonovite) by simply drilling a series of holes in a block of material with a dielectric constant near that of silicon (ε = 12).
While Yablonovitch's design was lauded as the first successful creation of a photonic crystal exhibiting a 3D PBG, this band gap existed only across an obscure spectrum of microwave frequencies. His experiment functioned primarily as a proof of concept - though PC theory guaranteed that the basic design would function equally well for any lattice constant, fabrication techniques imposed a lower bound on the size of the lattice constant.
As interest in PCs grew, other methods of photonic crystal fabrication were rapidly developed. Perhaps the most popular among these is the so called layer-by-layer lithography method. Used as early as 1994, this technique exploits the enormous amount of research and capital already expended on developing lithographic techniques for Si and GaAs to systematically build PCs one layer at a time. The basic idea is to etch a cross section of the PC pattern onto a substrate, backfill the etched holes with SiO2, then deposit another layer of substrate. This process is repeated for each desired cross section of the PC pattern. After a sufficient number of layers (usually a minimum of 10 in order to exhibit the desired band gap), the silica is dissolved, leaving a photonic crystal that can have a PBG close to the visible regime.
The etching itself is accomplished through e-beam lithography. E-beam lithography uses a focused beam of electrons to "drill"" holes in a given substrate. The advantage of this process is that since each hole must be drilled sequentially, it is effortless to intentionally introduce defects into the design by simply omitting to etch a particular hole on a particular level. However, there are two major disadvantages to e-beam lithography: prohibitive costs and slow writing speeds.
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| Fig. 1: Layer by layer lithography technique. |
An alternative lithographic technique, x-ray interference lithography, avoids these pitfalls. Interference lithography uses the interference pattern created by several high-frequency beams (typically 4-6) to imprint the desired pattern onto a photosensitive resin. After a particular layer is completed, the resin is exposed to UV light which hardens it. Then, the next layer is deposited and the process is repeated.
Not only is this method drastically cheaper than e-beam lithography (~ 10% of the cost), but it is also incredibly rapid, since the entire pattern is being imprinted simultaneously. Furthermore, due to the small wavelength, the resolution of the etched pattern is superb.
There are two problems with x-ray lithography. The first is the difficulty in calculating the appropriate beam parameters in order to generate the correct interference pattern. In recent years, this limitation has largely been overcome and several common crystalline patterns have been implemented [2]. The second problem arises from the uniformity of the interference pattern, which makes introducing defects particularly difficult. While theoretically the appropriate combination of phases from a sufficient number of beams should be able to create an arbitrary phase pattern, in reality this is highly impractical.
Colloidal self-assembly relies on the fact that under certain conditions, sub-micron mono-dispersed spheres tend to arrange themselves via sedimentation into face-centered cubic lattices (fcc). The resulting structure, commonly referred to as a synthetic opal, acts as a mold into which a semi-conductor material may infiltrate. After this process is complete, the "mold" is removed, leaving a lattice of air-filled spheres surrounded by a high-dielectric medium. Altogether, this process is quick, efficient, and cheap. Unfortunately, it is also riddled with unintended defects.
To an extent, these defects are mitigated by the nature of fcc lattices. Fcc lattices have the largest PBG of any crystalline structure due to their nearly spherical Brillouin zones. So while in the case of colloidal self-assembly the band gap is lessened by structural defects, it nevertheless persists.
Some progress has been made in reducing the number of defects to an acceptable level [4], but in general, most researchers employ the lithographic techniques described above for photonic crystal synthesis.
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| Fig. 2: Colloidal Self-Assembly. |
New techniques have been developed which attempt to leverage the strengths of several previous methods. Specifically, a group of researchers from the University of Twente have proposed creating a periodic crystal pattern using interference lithography techniques, and then using e-beam lithography to introduce localized defects [3]. This method easily permits the introduction of defects and is rapid as well.
Researchers are also experimenting with a process known as the "femtosecond laser-driven microexplosion method" [5]. This technique relies on a system of optics similar to an optical trapping setup in order introduce a high powered burst of laser light at a specific point in a photosensitive resin. The index of the resin changes as a result of the laser exposure. If the laser is periodically moved to a new location in the resin, a three dimensional photonic crystal is created. This technique allows an unprecented level of control over crystal design in three dimensions, but the sequential nature of the fabrication limits the eventual lattice size.
© 2007 R. Timp. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059 (1987).
[2] C. K. Ullal et al., "Photonic Crystals Through Holographic Lithography: Simple Cubic, Diamond-Like, and Gyroid-Like Structures," Appl. Phys. Lett. 84, 5434 (2004).
[3] L. Vogelaar, "Large Area Photonic Crystal Slabs for Visible Light with Waveguiding Defect Structures: Fabrication with Focused Ion Beam Assisted Laser Interference Lithography," Adv. Mat. 13, 1551 (2001).
[4] Y. A. Vlasov, X.-Z. Bo, J.C. Sturm, and D. J. Norris, "On-chip Natural Assembly of Silicon Photonic Bandgap Crystals," Nature 414, 289 (2001).
[5] Guangyong Zhou, Michael James Ventura, Min Gu, "Photonic Bandgap Properties of Void-Based Body Centered Cubic Photonic Crystals in Polymer," Opt. Soc. Am. 13, 4390 (2005).