Oxide-Based Photonic Crystals from Biological Templates

Michael H. Bartl, Jeremy W. Galusha, Matthew R. Jorgensen

Department of Chemistry and Department of Physics

University of Utah, Salt Lake City, UT 84112

9.1 Introduction

The ability to organize crystalline and amorphous metal oxide compounds into periodically ordered three-dimensional structures has led to a range of novel functional materials. Today, periodically ordered metal oxide frameworks with periodicities spanning several orders of magnitude from the microscale (several Ångstroms) to the mesoscale (2 to 50 nanometers) and to the macroscale are available [1-6]. Regardless of the framework feature size, it is the combination of inherent metal oxide properties with three-dimensional structure organization that gives periodically ordered composites their unique functionalities and has led to a broad field of new applications. While micro- and mesostructured metal oxides organized by small molecules [7, 8] and supramolecular self-assembly chemistry [5, 9, 10], respectively, are useful in sorption, separation and catalysis [2, 3, 8], as low-k dielectrics [11], and for various optical, optoelectronic, and energy applications [10, 12-14], macrostructured metal oxides with periodic feature sizes from a few hundred nanometers to several micrometers [6, 15-17] are prime candidates for so-called photonic crystals [18, 19].

Photonic crystals, originally proposed by John [20] and Yablonovich [21] in 1987, are an emerging type of optical materials with the potential to manipulate light in revolutionary new ways. The defining characteristic of photonic crystals is a periodic variation of the dielectric constant (or refractive index) with periodicities on the order of the photon-wavelength of interest. Due to this periodic variation of the dielectric constant, the behavior of light in photonic crystals is governed by band structure concepts—similar to how electrons are affected in crystalline atomic crystals [19]. This unique, non-classical behavior has the potential to lead to fundamentally new optical principles based on light localization,[20, 22, 23] making photonic band structure materials particularly interesting for next-generation all-optical information processing and advanced energy technologies [24].

Interestingly, millions of years before we “invented” photonic band structure materials, nature had already made use of these optical concepts for creating spectacular structural colors in many insects, birds, and marine animals. In particular, the strikingly colorful world of insects is in large part the result of optical interference produced by the interaction of light with precisely ordered, periodic biopolymeric structures, incorporated into their wings and exoskeletons [25-33]. These biological systems have evolved to create astonishingly complex photonic architectures—structures that are still far out of our synthetic reach [34-36]. While biological photonic crystals present exciting structural alternatives to our current limited photonic engineering capabilities, unfortunately, they do not possess the high photo- and heat-stability required for most advanced applications. In addition, biological photonic structures are composed of electrically insulating, low-dielectric biopolymers, which strongly limits their device integration. These problems can be overcome, by converting biopolymeric photonic structures into inorganic, high-dielectric compounds by biotemplating methods [35, 37-43].

In this chapter we will describe and compare different approaches for creating three-dimensional photonic crystals. Particular focus will be on oxide-based photonic crystals with complex lattice structures created using replication routes from various biological photonic templates.

We will cover three main topics, beginning with a brief introduction of photonic crystals, emphasizing the non-classical optical properties of these band structure materials. We will review the most important top-down and bottom-up fabrication methods for engineering three-dimensional photonic crystals operating in the infrared and visible part of the electromagnetic spectrum and also discuss current limitations of these approaches.

Next, we will introduce biological systems that employ photonic band structure concepts to create a wide variety of structural colors, spanning the entire visible range. A new structure evaluation method based on sequential focused ion beam milling and scanning electron microscopy imaging will be discussed. This method enables a high-resolution three-dimensional reconstruction of photonic architectures and gives unprecedented insights into the structure-optical properties relationship of biological complex photonic crystal lattices.

Then, we will discuss the potential of biological photonic crystal architectures as biotemplates for conversion into oxide-based high-dielectric replicas. We will briefly introduce and compare different biotemplating methods, including atomic layer deposition, conformal evaporation films by rotation, and sol-gel chemistry. The structural and optical properties of oxide-based photonic crystals obtained from these three methods will be addressed. Special focus will be directed toward sol-gel biotemplating methods that have recently resulted in the fabrication of a photonic crystal with a complete band gap at visible frequencies. We will finish our chapter with some conclusions and a brief outlook on the potential and promise of oxide-based three-dimensional photonic crystals for novel optical phenomena at visible frequencies.

9.2 Engineered Photonic Crystals

9.2.1 Characteristics of Photonic Band Structure Materials

In the following section we will give a brief introduction into characteristics and properties of photonic crystals. It is, however, beyond the scope of this chapter to provide a detailed discussion of the physics of photonic crystals and the foundation of photonic band structure properties and we refer the interested reader to the excellent literature available; see, for example [18, 19, 23, 24] and references therein.

Photonic band structure materials, also known as photonic crystals, are periodically ordered dielectric composite structures with periodicities ranging from a few hundred nanometers to several micrometers [18, 19]. The fascination with these materials stems from their ability to strongly affect the propagation of light in non-classical ways, making them interesting candidates for next-generation optoelectronic applications and all-optical information processing [24]. The non-classical properties of photonic crystals are the direct result of their periodic variation of the dielectric constant. Photons with wavelengths comparable to the variation-periodicity of a given photonic crystal are strongly affected by Bragg diffraction events—similar to how electrons are affected in atomic crystals. As a consequence, many concepts of solid state physics can be applied to describe the properties of photonic crystals, leading to direction and frequency-dependent photonic band structure diagrams with allowed optical bands and so-called photonic bandgaps (Fig 1).

Fig. 1 Calculated photonic band structure diagram for a photonic crystal consisting of dielectric spheres with a refractive index of 3.6 arranged in a diamond structure. Adapted from [50]

While photonic crystal can be designed with periodicities in one, two, or three dimensions, of particular interest are three-dimensional photonic crystals, since they can have a complete (or omnidirectional) photonic bandgap—a frequency range for which propagation of light is strictly forbidden [19-21]. Photonic bandgaps are the basis for several new optical concepts such as control of spontaneous emission in bulk materials, slow-light enhanced photocatalysis, low-threshold light amplification and quantum information processing [22-24, 44-48].

Motivated by the range of new and exciting optical phenomena predicted for photonic bandgap materials, numerous efforts have been undertaken to fabricate photonic crystals with complete bandgaps in the microwave, infrared and visible regions of the electromagnetic spectrum. In general, the band structure properties of a photonic crystal are determined by its lattice morphology and the refractive index contrast of its dielectric building blocks. Along with possessing a high transparency in the wavelength range of interest, the two different (high and low) dielectric materials building up the photonic crystal lattice should also have strongly differing refractive indices; for example, air and silicon (for photonic crystals operating in the infrared) or air and titanium dioxide (for photonic crystals operating in the visible). In addition to having a high refractive index contrast, it is also of great importance that these dielectric building blocks are arranged in an optimal lattice structure. While every periodically ordered structure results in a direction-dependent energy dispersion of photonic states, only a few selected lattices also give rise to the formation of complete photonic bandgaps [45, 49-55]. Among them the diamond crystal structure is the clear “champion” [52]. Moreover, the diamond crystal structure has been shown to be rather insensitive to deviations from the ideal lattice configuration, resulting in a variety of so-called diamond-based (or diamond-like) morphologies that allow a complete bandgap to open for refractive index ratios as low as 2.1 [50, 52, 53].

Fig. 2 Diamond structure models. a) Dielectric spheres arranged in the diamond lattice. b) Dielectric rods connecting nearest-neighbor sites in the diamond lattice. Adapted from [52]

To date, tremendous progress in photonic structure engineering has been made in the microwave and infrared regimes. Using top-down microfabrication and bottom-up colloidal self-assembly techniques, various three-dimensional photonic crystal structures have been synthesized with complete bandgaps at infrared frequencies [56-64]. In contrast to the successes in the infrared regime, complete photonic bandgaps at visible frequencies have proven elusive due mainly to difficulties of creating efficient three-dimensional photonic lattices with feature sizes in the hundred-nanometer range. In the following section we will briefly review fabrication strategies for photonic crystals operating in the infrared and visible regime. We will discuss advantages and limitations of different top-down and bottom-up fabrication techniques focusing on attainable feature sizes, crystal lattices and high-dielectric compounds.

9.2.2 Photonic Crystals Operating in the Infrared

The fabrication of photonic band gap crystals operating at infrared frequencies has benefited tremendously from powerful microprocessing techniques that have been optimized in the semiconductor industry during the last 50 years. These techniques can generally be classified into direct and indirect methods. In the former, a desired photonic crystal structure is formed directly out of a high-dielectric semiconductor compound. For example, Lin and co-workers used a comprehensive multi-level stacking process consisting of a repeated deposition, lithographic patterning, and etching to successfully fabricate dielectric woodpile (a diamond-based lattice structure) photonic crystals with bandgaps in the infrared regime [58]. Subsequently, Noda et al. developed a wafer-fusion based method to create woodpile structures made out of GaAs with a complete bandgap at near infrared wavelengths [59], whereas Johnson, Joannopoulos and co-workers designed and fabricated a nine-layer photonic crystal with a wide (up to 25 percent gap-to-mid-gap ratio) bandgap out of silicon by sequential layer-by-layer scanning-electron-beam lithography [61].

A common disadvantage of these direct methods is that fabrication of high-quality three-dimensional photonic crystals is very time consuming, expensive and is generally limited to only a few layers. Indirect methods, on the other hand, use a template structure created out of inexpensive polymers. This structure serves as a sacrificial mold for templating high-index compounds such as silicon or germanium. Successfully applied methods to create such polymeric photonic crystal template structures, including the highly efficient diamond-based woodpile lattices, are multi-beam holography, multi-photon lithography, and direct laser writing methods [64-66]. An interesting alternative to these light-patterning routes is the direct ink writing method originally developed by Lewis and co-workers [67, 68]. In this technique, a cylindrical filament approximately 1 micrometer in diameter is formed by deposition of a fluidic polyelectrolyte/water ink into an alcohol-rich reservoir. Braun, Lewis and coworkers demonstrated that this filament can then be patterned in a layer-by-layer sequence to build a woodpile structure with photonic crystal feature sizes in the near infrared [57, 69].

All of these polymeric templates can then be converted into high-dielectric photonic crystals made out of silicon or germanium. Since the polymeric templates would not withstand the high deposition temperatures required for typical semiconductor deposition techniques such as chemical vapor deposition, they are first protected by a metal oxide (silica or alumina) coating formed by atomic layer deposition. For example, Ozin and coworkers showed that depending on the amount of metal oxide deposition (complete backfilling or deposition of a thin coating) it is possible to create high-dielectric photonic crystals in the form of a positive replica or an inverse of the original template structure [64, 70]. While a silicon double-inversion procedure produced a woodpile photonic crystal with a complete (up to 9 percent wide) bandgap in the infrared [70], Hermatschweiler et al. showed a silicon inverse woodpile photonic crystals with a more than 14 percent wide complete bandgap centered at a wavelength of around 2.5 micrometer can be fabricated by a silicon single-inversion method [64]. Braun, Lewis and co-workers used a similar—although independently developed—technique to convert direct ink-writing-created woodpile templates into germanium photonic crystals with wide (up to 25 percent) complete bandgaps centered at a wavelength of around 6 micrometers (Fig. 3) [57].

Fig. 3 Scanning electron microscopy images of an inverse germanium woodpile structure fabricated by direct ink writing and a combination of atomic layer deposition and chemical vapor deposition. Adapted from [57]

An interesting—fast, simple, and low-cost—alternative to these rather labor-intensive routes is colloidal self-assembly [71-73]. In this bottom-up photonic crystal fabrication technique monodisperse microspheres are deposited onto planar substrates by self- or directed assembly in close-packed face-centered-cubic or hexagonally-close-packed colloidal crystals (also called artificial opals, since these colloidal crystals closely resemble the microstructure of natural opal gemstones). Similar to the indirect methods described above, these colloidal crystals are then used as templates and are infiltrated with an infrared-transparent high-dielectric component. After selective removal of the opal template a so-called inverse opal photonic crystal (a close-packed face-centered-cubic lattice of air spheres in a high dielectric material) is obtained [45]. While inverse opal photonic crystals are less effective (i.e. less efficient in affecting and controlling the propagation of light) than diamond-based lattices, it was shown that formation of a complete photonic bandgap is possible provided that the high dielectric material has a refractive of 3 or higher versus air as the low dielectric component [49]. Using polycrystalline silicon as the high dielectric component (with a refractive index of 3.2 to 3.4) John and co-workers [56] and Norris and co-workers [62] successfully fabricated inverse opal photonic crystals with a complete bandgap in the near infrared.

9.2.3 Photonic Crystals Operating at Visible Frequencies

Compared to the enormous progress achieved in fabricating photonic crystals operating in the infrared, photonic structure engineering in the visible is far less advanced—due mainly to the difficulties in shaping visible-light transparent, high-dielectric materials into efficient morphologies with periodicities at visible wavelengths. Unlike infrared photonic crystals with complete bandgaps of up to 20-30 percent gap-to-mid-gap ratios [57-63], enabled by infrared-transparent materials with refractive indices of 3.2 and higher, the lack of visible-light-transparent dielectrics with comparable refractive indices embosses an enormous challenge for achieving complete bandgaps at visible wavelengths. The best compounds for photonic crystals in the visible are cadmium chalcogenides and oxide semiconductors such as zinc oxide and titanium dioxide (titania) with refractive indices in the range of 2.0-2.6. Calculations show the lowered refractive index ratio as compared to infrared compounds not only reduces the width of potential complete bandgaps to below 10 percent, but also limits photonic crystal morphologies with potentially complete bandgaps at visible frequencies to pyrochlore and diamond-based crystal lattices [50-52].

Unfortunately, successful synthesis of such lattices with feature sizes at visible length scales is extremely challenging. On the one hand, typical microfabrication methods used to create diamond-based photonic crystal structures in the infrared rely on lithographic/holographic or direct-writing methods and are therefore very difficult to successfully implement at the small length scales required for three-dimensional structures with bandgaps in the visible. Subramania and co-workers showed that this obstacle could be overcome by electron beam direct-writing of a titania woodpile structure with lattice parameters in the visible [74, 75]. However, creating large-scale structures with this technique has proven extremely challenging, limiting the fabricated photonic crystals to 9 alternating layers. On the other hand, bottom up supramolecular self-assembly of polymeric building blocks into diamond-based lattices is limited to features sizes less than 150 nanometers due to the increasingly slowed assembly kinetics of the required ultra-high molecular weight monomers, restricting this technique to fabrication of photonic crystals operating in the ultraviolet regime [76].

A fabrication technique that readily bridges the feature-size gap between microfabrication and supramolecular assembly is colloidal self-assembly of submicrometer spheres [71-73]. Indeed, colloidal crystals can be formed with periodicities spanning the entire visible range and can be converted into inverse opals by infiltration with visible-light-transparent dielectric compounds [6, 15, 17, 77-79]. This approach has been used to create inverse opal photonic crystals composed of high-dielectric metal oxide compounds using various infiltration techniques. For example, successful procedures were reported by Stein and co-workers [6, 80] and Vos and co-workers [17, 81], who used alkoxide-condensation in air to create titania, zirconia and alumina inverse opals and Pine and co-workers [77, 79], who showed that titania and silica inverse opals can also be prepared by infiltration of opals with ultrafine colloidal particles of the oxides. Recently, Bartl and co-workers developed a new titania sol-gel precursor and combined it with a lift-off/turn-over infiltration/processing technique to fabricate planar titania inverse opals with an open surface and defined thickness (Fig. 4) [15].

Another powerful method to infiltrate polymeric templates is low-temperature atomic layer deposition [82]. For example, King et al. used this method to fabricate titanium dioxide inverse structures from various self-assembled and holographically-prepared templates with highly controlled filling fractions and excellent quality [83-85].