The prediction of the promising properties of PXs by Yablonovitch in 1987 was the seed that gave rise to a large and ever increasing number of theoretical and experimental work. Following the track of semiconductor theory, the main goal was the calculation of the photonic band structures for different crystal symmetries and topologies in order to find the optimum conditions to maximise the magnitude of the gaps. This task, which is still in progress, was especially important since it allowed the scientific community to lay the first stones on the path to reach a full PBG (1).
Concerning 3D systems, the most suitable symmetry for full gap appearance was found to be a diamond lattice of holes in a dielectric background, provided the filling factor is properly chosen (2). In this sort of symmetry, a threshold value of 4 for the dielectric constant contrast is needed to open a full gap. However, for other symmetries higher contrasts are needed. For instance a full PBG for an “air sphere” compact face centred cubic (fcc) structure (3), can be achieved provided a contrast of dielectric constant of 8 is reached. In 1991 Yablonovitch (4) and co-workers made the first prototype that showed a full PBG (in the microwave region). This was a modified diamond structure, in which the dielectric constant contrast was e1/e2» 13. It was carried out by drilling holes in a bulk material along three well chosen directions, with a typical length scale of the order of mm. The empty volume (i.e. filling fraction) was 76%. Later, many 2D and 3D PX operating at different regions of the EM spectrum have been devised and fabricated. Nevertheless, the realisation of PXs with desired dimensions is sometimes a difficult task (5,6). A paradigmatic example is the construction of a three-dimensional photonic crystal with a full gap at visible wavelengths. Interest springs from one of the main potential technological applications of PXs: the control of the spontaneous emission in lucent photonic systems through the photonic density of states (7,8). The figure shows the electronic and the photonic bands of a hybrid semiconductor-PBG device. In the bulk semiconductor, electronic transitions between conduction and valence bands result in photon emission. However, the process completely changes when the semiconductor, as in the figure, is coupled to a PBG material. Here the photonic gap is tuned to the electronic one and, because there are no photons available to couple to electronic decay, the emission is inhibited. In 1D systems hybrid lucent-PBG devices have already been developed. This is solved by the fabrication of a distributed Bragg reflector in which a defect is created and a light emitting diode implemented. In this field of semiconductor microcavities, new phenomena, as high efficiency lasers and strong photon-exciton coupling effects (9) have been found.
|FIG. 1. Coupling between electron and photon states. When the PBG matches the emission band of a semiconductor no states are available for the emitted photon and electron radiative decay is inhibited.|
As mentioned, a vast effort has been devoted in the last few years to the fabrication of 2D (10-15) and 3D (16) PBG materials with periodicity in the submicron scale. The most extended method is the micromachining of a bulk material by lithographic methods. However, obtaining a 3D PBG material with full gap in the visible and infrared region is still an unconquered target.
One of the reasons is that the empty volume needed to get a full gap is so large (about 74%) that the mechanical stability of the structure is very poor. On the other hand the material thus obtained is full of defects as a result of the etching: the specific area is extremely large and surface defects plague the system. Recently, materials based on self-organised structures have revealed as a real possibility to obtain robust PBG materials with gaps in the visible and IR region of the EM spectrum. Thus, inverted opals have made it possible to realize a full photonic band gap first
in Silicon and then in the visible with stibnite.
1- See for example: 1993. ‘Photonic band Gaps and Localization’ edited by C.M. Sokoulis (Plenum. New York. Also, 1993. J. Opt. Soc. Am. B 10, 208-248. Finally, 1996 ‘Photonic Band Gap Materials’, edited by C.M. Sokoulis NATO ASI Series E 315 (Kluwer Dordrecht)).
2- K.M. Ho, C.T. Chan, and C.M. Soukoulis. 1990. Phys. Rev. Lett. 65, 3152.
3- H.S. Sözüer, J.W. Haus, and R. Inguva. 1993. Phys. Rev. B 45, 13962.
4- E. Yablonovitch. 1991. Phys. Rev. Lett. 67, 2295.
5- S. Fan, P.R. Villeneuve, R.D. Meade, and J.D. Joannopoulos. 1994. Appl. Phys. Lett. 65, 1466.
6- J.D. Joannopoulos, P.R. Villeneuve, and S. Fan. 1997. Nature 386, 143.
7- T. Quang, M. Woldeyohannes, S. John, and G.S. Agarwal. 1997. Phys. Rev. Lett. 79, 5238.
8- S. Fan, P.R. Villeneuve, J.D. Joannopoulos. and E.F. Schubert. 1997. Phys Rev. Lett. 78, 3294.
9- C. Weisbuch, M. Nishioka, M.A. Ishikawa,.and Y. Arakawa. 1992. Phys. Rev. Lett. 69, 3314.
10- T. Krauss, R. De La Rue, and S. Band. 1996. Nature 383, 699.
11- J.R. Wendt, G.A. Vawter, P.L. Gourley, T.M. Brennan, and B.E. Hammons. 1993. J. Vac. Sci. & Tech. B 11, 2637.
12- U. Grüning, V. Lehmann, S. Ottow, and K. Busch. 1996. Appl. Phys. Lett. 68, 747.
13- H.B. Lin, R.J. Tonucci, and A.J. Campillo. 1996. Appl, Phys, Lett. 68, 2927.
14- A. Rosenberg, R.J. Tonucci, and A. Bolden. 1996. Appl. Phys. Lett. 69, 2638.
15- K. Inoue, M. Wada, K. Sakoda, M. Hayashi, T. Fukushima, and A. Yamanaka. 1996. Phys. Rev. B, 53, 1010.
16- C.C. Cheng, and A. Scherer. 1995. J. Vac. Sci. & Tech. B 13, 2696