Self-Assembling Photonic Crystals?
Various materials have dominated different human history periods. Some of them are even named by them: the Stone Age, Bronze Age, Iron Age… For example, in 5000 BC chisels made of copper (bronze is an alloy consisting primarily of copper) enabled the construction of Egyptian pyramids and sparked the growth of 1st great civilizations. From this perspective, the last century could be referred to as the Silicon Age. The “king” of this period, the silicon atom, is dressed with the electron cloud described by 1s2 2s2 2p6 3s2 3p2. Among these electrons, the outer four valence electrons, located at the 3s and 3p-orbital, are the most important for its “social” activities. These valence electrons can form a tetrahedral lattice crystal unit (Figure 1) characterized by a specific electronic band gap structure, displaying semiconducting electric behavior. This property is extremely useful, and due to its electronic semiconductors are at the heart of classical computers. The microelectronic revolution of the 20th century is based on sensitive control of electric currents in semiconductors, enabled by their band gap structure. The switching of logic functions relies on the number of electrons and holes below and above the band gap separating the valence and conducting band. Here the electronic band gap corresponds to a forbidden zone of energies that electrons cannot occupy. Among various semiconducting material, doped silicon is most commonly used. In addition to the band gap property, its main advantages with respect to competing materials were its natural abundance, optical transparency, and widespread use. In the 1980s first artificial photonic crystals appeared [1,2]. Crystal structures enabling sensitive manipulation of light beams have been demonstrated. Prototype photonic materials displayed periodic structures on a micrometer scale and possessed a photonic band gap. The latter is characterized by a window of optical wavelengths that cannot propagate through the otherwise optically transparent material. For example, the 1st photonic crystal was made by drilling a closely spaced array of sub micrometer sized cylindrical holes. These holes play a similar role as atoms in semiconductors. The band gap structure depends on the crystal symmetry and geometric parameters determining the crystal lattice. The parameters are tailored to yield the band gap in the visible wavelength regime. Again, as in the case of electric semiconductors, the tetrahedral geometry enabled desired properties, suggesting that this structure is outstanding for making a photonic band gap material. The general aim is to reproduce in photonic crystals analogous phenomena seen in electronic semiconductors. They should function as “semiconductors for light”. The key to this in the band gap structure, which is dictated by geometry. Note that the behavior of i) electrons and ii) light beams in i) electronic semiconductors and ii) photonic materials is governed by different basic equations: i) Schrodinger equation and ii) Maxwell equations, respectively.
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