Moving towards a photonic band gap for visible light

The most characteristic property of photonic crystals is the fact that they show a periodical change of the refractive index at a longitudinal scale of the wavelength in three-dimensional light. The frequent change will lead to an interaction between the crystal and light that is largely analogous to the interaction between a semiconductor and electrons. In a semiconductor electrons that have a so-called energy band gap - an English loan word - are not able to replicate, because the semiconducter material obstructs the electrical current at that energy. In a photonic crystal something similar applies for photons that have an energy (or wavelength) similar to the photonic band gap. In this case, the crystal obstructs the replication of light and so, light is being manipulated by a photonic crystal. Notwithstanding great progress in constructing increasingly smaller structures, scientists have not still been able to create a three-dimensional structure with a band gap for visible light. Researchers of the research group Soft Condensed Matter, Utrecht University, led by Alfons van Blaaderen and Marjolein Dijkstra, have now succeeded in finding a way that may lead to similar structures through the self-organization of colloids (submicron particles). Their results can be found in Nature Materials, a relatively fresh journal that have reached a high 'impact factor' of all bèta-related scientific journals within a very short time. 

Conditions for a photonic crystal with a band gap
In order to get a photonic crystal with a band gap, it has to meet with three conditions simultaneously. Firstly, the difference in the refractive index between the various materials that the crystal is composed of, must be relatively high. Besides, the materials are not allowed to absorb the light. Therefore, a theoretically suitable material such as silicon is unsuitable for visible light.
Secondly, the crystal must have the right crystal symmetry, and thirdly, the crystal grid (the organization of colloids within crystal) must be perfect. Scientists have not still succeeded in constructing sufficiently high-grade three-dimensional structures that have the required grid space of about 200 nanometers (1/5 micrometer). So, photonic crystals with a band gap for visible light still proved to be unfeasable.

An answer in the picture
Inspired by previous research on colloidal particles, in their own laboratory, for one, the researchers at Utrecht University have been developing some ideas that seem to provide for an answer. They have much experience in constructing colloidal crystals that have an extremely orderly structure and that consist of various materials with a large difference in the refractive index. They also have much expertise in computing and simulating all sorts of crystal structures on the basis of colloidal particles.
For over a decade it has been known that crystals that have a structure similar to that of diamond will open up a band gap at a clear lower contrast of refractive index than crystals that have a so-called face-centered cubic (fcc) structure.
Materials like titanium dioxide and zinc sulphide would be very useful for crystals with a diamond structure, also in the visible part of the spectrum. In 2006 academic computations showed that another specific crystal structure exists that opens up a band gap at nearly as low a contrast of refractive index as diamond. In solid-state physics this structure is known as pyrochlorine, the name of a specific mineral.

Diamond and pyrochlorine
The answer is now that, by using their judgment and combined with computer simulation, the researchers at Utrecht University have discovered conditions that enable them to create a so-called binary crystal, by using the spontaneous crystallization of two-sized ratio colloidal particles. The large balls in the binary crystal adopt the diamond structure and the small balls adopt the structure of pyrochlorine (figure 1). In this way, scientists are able to make both 'optimum' crystal structures in one go. However, it is still necessary to make another move, as the band gap just opens up in diamond and pyrochlorine and not in the binary crystal itself. Either the large balls have to be removed, which produces pyrochlorine, or the small balls have to disappear and that will produce diamond structures. A similar move can be realised by creating particles of different material, for example, organic particles (such as polystyrene) combined with titaniumdioxide. Then, the organic particles can be removed by heating, a process that the researchers in Utrecht have already been used for other crystals. Prior to this, the team has also developed the necessary particles that have a high refractive index, which are titaniumdioxide and zincsulphide.

It is not that straighforward
However, this is not the whole story. As happens more often, Murphy's law became effective during the research. It appeared from computer similation by FOM-researcher Antti-Pekka Hynninen, currently working for Princeton University, that on the conditions which created the binary structure, also two different binary crystals were being created that had almost exactly the same thermodynamic stability. But computations executed by FOM-researcher Job Thijssen and Nanoned-researcher Esther Vermolen proved that these structures are far from photonically optimal. So, another trick was needed in order to have taking place the growth of the chosen structure at the expense of the growth of the other two. Simply installing a wall with a layer of glued balls and having the structure of one of the crystal faces of the chosen crystal, appeared to provide for the best results in computer simulations (figures 2 and 3). This method, which has been developed at Utrecht University and is called colloidal epitaxy, has already been successfully applied in experimental use several times. The first experimental moves towards constructing walls of the right structure have been made, but optimizing the ideal conditions will still require much research. Particularly, the possibility to realise structures with a band gap for visible light through a, basically, cheap way, must be more than enough motivation for activating the presented way, not only in the silicon of a computerchip, but also in the laboratory. 

For more information, please contact professor dr. Alfons van Blaaderen, phone +31 (0)30 253 22 04 or dr. Marjolein Dijkstra, phone +31 (0)30 253 32 70; see also www.colloid.nl.