Figure 1 - Electrochemcial etched Macropores in p-type Silicon
Figure 1 - Electrochemcial etched Macropores in p-type Silicon
2D Photonic Crystals: If one retains a periodicity of an alternating index of refraction in the xy-plane while the
z-direction remains unmodulated, a two dimensional photonic crystal results. A break through for 2D photonic crystals
was achieved by Grüning et al. [see above] who used the well known technique of macropore formation in n-type silicon
under back side illumination [see above] and obtained for the first time a complete 2D band gap in the near-infrared
(at a wavelength of about 4.9 µm). A complete band gap in this case means that a band gap always exists independent of
the polarization and propagation of the light wave.
Figure 1 shows prestructured macropores in p-type silicon. These structures can used for designing 2D Photonic Crystals.
The use of silicon as a photonic crystal is limited by the width of the electronic band gap (1.1 eV, strong absorption
for wavelengths < 1043 nm). Therefore the use of compound semiconductors opens new possibilities due to the larger band
gap of the materials (GaP: 2.24 eV, GaAs: 1.42 eV, and InP: 1.12 eV). All these compound semiconductors are common
optoelectronical materials. Pore etching in III-V compounds, however, is in its infancy and prestructured pore arrays have
not yet been produced. However, a strong tendency to self organization (known from other pore systems, e,g porous alumina)
may be uses for producing 2D PGB material. This is shown for InP, where due to a strong interaction of pores a hexagonal
self-arranged 2D structure can be obtained - see Figure 2.
Figure 2 - Electrochemcial etched pores in n-type InP (Self-arranged 2D structure)
There are at least two degrees of freedom which can be manipulated in order to control the diameters of the pores:
doping level of the samples and electrolyte concentration. Changing the doping from 1016 to 1018
cm-3, the diameter of the pores can be decreased from 1-2 mircometer down to nearly 50-100 nm.
Simple fcc crystals, even with high dielectric contrast, do not yield a complete photonic band gap.
However, Ho et al. [Ho, K. M., Chan, C. T., and Soukoulis, C. M., 1990, "Existence of a Photonic Gap in Periodic Dielectric Structures", Phys. Rev. Lett., Vol. 65, pp. 3152-3155]
showed theoretically that photonic atoms arranged in a diamond crystal may have a
complete band gap. The first corresponding structure was fabricated by the group of Yablonovitch [Yablonovitch, E., Gmitter, T. J., Leung, K. M., 1991, "Photonic band gap structure:
The face-centered-cubic case employing nonspherical atoms", Phys. Rev. Lett., Vol. 67, pp. 2295-2301] (this crystal
is called “Yablonovite” in the literature). The Yablonovite was the first crystal which showed experimentally a
full 3D band gap in the mi-crowave range. A schematic drawing of the Yablonovite is illustrated in Fig. 3 a.).
Starting from one point at the surface three channels are drilled into the substrate.
In the group of Prof. Dr. Foell the anisotropy of macropore formation in silicon was investigated in detail.
Two main growth directions for macropores in p- and n-type silicon were found: <100> and <113>. On a {111}-surface
three equivalent <113>-macropores start to grow into the substrate. These pores can intersect and form a three
dimensional pore network in the silicon. The resulting structure is slightly different from the Yablonovite crystal;
the pores are tilted about 29° off the vertical axes whereas in the Yablonovite they have an angle of about 35° -
see Fig. 3. However, calculations from Klose and Dichtel (University of Kiel) suggest that the structure should exhibit a complete 3D band gap for an appropriate
pore diameter. Birner et al. [Birner, A., Wehrspohn, R. B., Gösele, U., and Busch, K., 2001, "Reviews - silicon-based photonic crystals“,
Adv. Materials, Vol. 13, pp. 377-388] dubbed this structure “Kielovite”, because of the strong relation to the Yablonovite.
Fig. 4 shows parts of a not yet fully or-dered “Kielovite” structure. We are currently trying to realize a
real 3D crystal by optimizing prepatterning and etching techniques similar to those of the 2D macropores arrays.
The Kielovite is a first approach to the realization of a 3D PGB material.
Figure 3 - Yabolovite vs. Kielovite structure
Figure 4 - Kielovite structure
Pores grow anisotropically in III-V compounds, too. At low current densities, pores in GaAs, GaP and InP usually grow preferentially in <111>-directions. Fig. 5 shows pores in (100)-oriented materials growing in <111>-directions. In contrast to silicon, however, the four <111>-directions directed into the sub-strate are not equivalent. Two of them are usu-ally called [111]A and the other two [111]B. The difference is that in [111]A direction the atoms are arranged as -AIII---BV-AIII---BV- ... while in [111]B directions as -BV---AIII-BV---AIII- ... , where AIII means an element from the group III and BV an element from group V of the periodic table of elements, “-” represents one chemical bond. As a consequence of the differences in chemical properties between elements from group III and V, the velocity of pore growth in [111]B is larger than in [111]A direction. The difference can be minimized, however, by choosing an appro-priate electrolyte for which the velocity of pore growth in all four directions will be nearly the same. The <111>-pore networks obtainable in III-V compounds in analogy to the <113> networks in Si, do not have a full 3D band gap. But strong nonlinear optical effects can be predicted and exploited. As with the Kielovite structure, for a real 3D PGB crystal prepatterned pore arrays are necessary. Developing a prestucturing technique for pores in III-V compound materials therefore will be an important step towards usable PBG-materials from III-V semiconductors.
Figure 5 - Pores in GaP
Pore formations in silicon
and III-V compounds offer a large potential for structuring two and three dimensional photonic
crystals. In silicon and all used III-V compounds (InP, GaAs, GaP) crystallographically oriented
pores can be used for three dimensional structuring. The “Kielovite” structure in silicon should
lead to a full 3D band gap. Self-organizing features, producing periodicities in x, y, and z-direction,
may offer additional degrees of freedom. The next steps towards first 3D PGB from these semiconductors
comprise the development of prestructured pore arrays in III-V semiconductors, optimized etching conditions,
and a stabilization of the “Kielovite” structure.