Dispersion relation of 3D photonic crystals based on macroporous silicon
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Dispersion relation of 3D photonic crystals based on macroporous silicon J. Schilling, F. Müller, R.B. Wehrspohn, U. Gösele, K. Busch1 Max-Planck Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany 1 Institut für Theorie der Kondensierten Materie, Universität Karlsruhe, P.O. Box 6980,76128 Karlsruhe, Germany ABSTRACT Extended 3D photonic crystals based on macroporous silicon are prepared by applying a periodic variation of the illumination during photoelectrochemical etching. If the lateral pore arrangement is 2D hexagonal, the resulting structure exhibits a simple 3D hexagonal symmetry. The dispersion relation along the pore axis is investigated by optical transmission measurements. Photonic band gaps originating from the pore diameter modulation are observed and the group velocities of the photonic bands are determined by analyzing the Fabry-Perot resonances. Furthermore, angular resolved transmission measurements show a spectral region of omnidirectional total reflectivity. INTRODUCTION 2D macroporous silicon photonic crystals have been extensively studied in the last seven years since the the pioneering work of Lehmann and Grüning [1,2]. A recent review is given by Schilling et al. [3]. The concept to obtain 3D photonic crystal by pore diameter modulation has already been predicted seven years ago [4], but just recently we have shown the first realizations of these 3D photonic crystals [5]. In the following we are going to analyze the optical properties in detail. FABRICATION OF THE 3D PHOTONIC CRYSTALS The fabrication of 2D macroporous silicon photonic crystal is described in Refs. 1-4. The pattern and the pitch of the 2D pore array are defined by lithographic prestructuring. The pore radius is determined by the etch current and can therefore be controlled by the backside illumination. Increasing the illumination of the sample causes a higher hole generation rate. This results in an increased total current density j leading to a higher porosity and a larger radius of the pores. To achieve a periodic variation of the pore diameter with pore depth, the illumination intensity and thus the etch current is varied periodically during pore growth. Figure 1 shows examples of resulting structures. The macropores are initially arranged in a 2D hexagonal lattice with a pitch of a = 1.5 µm (figure 1e). The etch parameters are: cHF = 4 wt%; T = 17°C; U = 1.5 V. The illumination of the wafer backside was modulated applying zig-zag profiles with different periods. Shorter modulation periods of the illumination lead to shorter periods of the pore diameter modulation. Although the measured etch current exactly follows the intended zigzag profile, the etched pore profiles show a slightly smoother shape. Especially for the shortest shown modulation period the minima and maxima of the zig-zag current profile are smeared out and the amplitude of the pore diameter modulation is reduced.
L6.8.1
a)
lz = 3.6 µm
b)
1,5µm
lz = 2.6 µm
lz
c)
lz = 1.7 µm
d)
lz = 0.8 µm
1.5 µm
e)
f)
Figure 1. a)-d) SEM-image
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