Photonic Crystals: 2D / 3D Approaches
Abstract
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F.Müller, S. Matthias, and A. Langner
Introduction
As explained on the growth page, the area of the etched air-pores is approximately proportional to the etch-current and can be varied during the growth by changing the intensity of the applied backside illumination. However, this process has restricted the resulting pore shapes to smooth sinusoidal or ratchet-type ones with small variations in diameter so far. As a rule of thumb, the shorter the length of the modulation the lower are the variations of the diameter, which can be realized.
Strong variations in diameter on a distance less than the lateral lattice constant as well as pore shapes with sharp edges are required for the fabrication of a simple-cubic photonic crystal of overlapping air spheres in silicon. According to S. Leonard (APL 88, 2917 (2002)), such structures would have a complete 3d photonic bandgap.
Improved process
The observed smoothing of the pore shape can be significantly reduced by increasing the applied voltage although this leads to some instability in pore growth. Both, etching current and the applied voltage have to be modulated allowing to adapt the SCR continuously and to optimize the focussing effect for the holes during the etching process. With a carefully adjusted current and voltage profile the required sharp edges and large diameter variations can be grown (Fig. 1a).
Postprocessing
To obtain the cubic symmetry and the optimum porosity further post-processing of the porous sample is required. In a homogeneous and isotropic widening step the pore diameter is increased. First, the samples are annealed at 900ºC for 150 minutes to grow a silicon oxide on the silicon surface. In a second step the oxide is removed by a hydrofluoric etching step. The widening may be repeated several times to precisely adjust the filling factor. Finally, this uniform erosion leads to interconnected pores also in the plane perpendicular to the pore axis (Fig. 1b, c). Although starting from a columnar structure, the geometry obtained is very close to cubic overlapping air spheres in silicon.
Fig. 1. Scanning electron micrographs of cleaved modulated macroporous silicon wafers a: 3 macropores are arranged in a square lattice with a pitch of 1.5 µm. b: After the isotropic widening procedure an almost simple cubic arrangement of overlapping air-spheres in silicon is obtained c: Widened structure form bird's eye view. On top the lithographically defined square lattice and on bottom the etched one.
Optical characterization
The obtained samples were characterized with a Microscope Fourier Transform Infrared Spectrometer (FTIR). Fig. 2 shows the transmittance and reflectance along the growth direction. Air and a silver mirror served as background respectively. The transmission through the photonic crystal is reduced by more than 2 orders of magnitude within the fundamental stop gap. In addition Fabry-Perot-Resonances resulting from the multiple reflection at the boundaries indicate a good quality crystal. The gray highlighted region indicates the complete 3-dimensional photonic bandgap.
Fig. 2. Reflectance and transmittance measurements of the sample of Fig. 1c along the growth direction. The obtained spectra agree well with a band structure calculation. The gray highlighted region indicates the complete photonic bandgap.
Anisotropic etching of membrane structures allows to fabricate scaffold-like photonic crystals (see Fig. 3).
They show a complete 3D photonic band gap and can reach very high air filling factors.