SELF-ASSEMBLY OF A SILICON PBG MATERIAL WITH A COMPLETE 3D GAP AT 1.5 mm
Here is the synthesis and characterization of face centered cubic (fcc) PBG material, consisting of close packed 870 nm diameter air spheres in pure silicon. We infer that this silicon PBG material has a complete three-dimensional PBG centered at 1.5 microns, the wavelength of choice for fibre optic telecommunication systems. Unlike the three-dimensional photonic crystals consisting of only two unit cells in the vertical direction and fabricated by a complex lithographic procedure [1, 2], the self-assembly synthetic approach is simple, inexpensive, accurate, and well-suited for making single crystal, inverse opal structures of 100-1000 unit cells linear dimension in all directions. Furthermore, various three-dimensional defect network architectures may be imprinted into our system during the initial stage of template synthesis. Silicon PBG materials, made in this straightforward manner, also permit integration with existing silicon-based microelectronics.
Synthesis begins with the highly controlled formation of a weakly sintered fcc lattice of mondisperse silica, which then acts as a template for silicon infiltration. The choice of large spheres ensures that the final structure will have a complete PBG in a frequency range below the optical absorption edge of bulk silicon. The
synthesis is performed in a suspension of smaller, monodisperse silica particles (0.5 mm), that act as seeds for further growth. This leads to a homogeneous increase of the sphere size. Once the large spheres are made, they are settled in an aqueous solution of ethylene glycol (typically 50% concentration). The resulting opal is a close-packed fcc lattice of silica spheres with a typical single domain size of 0.1 mm. A further sintering process leads to the formation of small necks between the silica spheres. This provides mechanical stability to the template, helps to control the opal void volume for subsequent synthesis , and provides the connected network topology for removal of the template by an acid etching. This network topology is also favourable for optical waveguiding effects that play an important role in PBG formation .
Silicon is grown inside the voids of the opal template by means of chemical vapour deposition (CVD) using disilane (Si2H6) gas as a precursor [4, 5]. The temperature is varied from 250 °C for low infilling samples to 350 °C for high infilling ones. Theory predicts that the maximum PBG is obtained with a 90% infilling of the opal voids in the form of a uniform, thick, wetting layer on the silica surfaces. The reaction time was typically 24 hours and the disilane pressure was about 200 torr. After growth of silicon, the samples are heated to 500 °C in order to improve the semiconductor crystallization and to allow diffusion of silicon inside the void structure. The silica template is subsequently removed using a fluoride-based etching procedures designed to minimize the dissolution of the macroporous silicon backbone. Thermal reductive-elimination of surface hydride is employed to control the ultimate hydrogen content of the silicon layer.
|Figure 1. SEM and AFM images of opal infiltrated with silicon. (a) Shows a SEM image of an internal  face of the silicon infiltrated opal. It reveals a thick, uniform layer of silicon surrounding the well-ordered silica spheres (shown in light blue), indicating a high degree of infiltration. (b) Shows an AFM image of a local area of the infiltrated opal surface, highlighting the smoothness of the silicon coating. The surface roughness was estimated to be 2 nm. The growth of the silicon-wetting layer is quite homogeneous and is independent of the local characteristics of the opal template.|
Microscope Raman spectroscopy was used to ascertain the sample quality. The silicon phonon peak observed in our samples was narrow and centred at 515 cm-1, consistent with the presence of micro-crystalline silicon. Scanning electron microscopy (SEM) and atomic force microscopy (AFM) were used to characterize the semiconductor growth (see Figure 1). An SEM image of the corresponding inverse silicon opal taken after etching the infiltrated structure is shown in Figure 2.
|Figure 2. SEM images of internal facets of silicon inverse opal. (a)  facet. (b)  facet. The images reveal an interconnected network of air spheres surrounded by thin silicon shells, inheriting the fcc order of the opal template. The adjacent air spheres are connected via windows, which result from the sintering process.|
Unlike earlier studies of inverse opal structures made of TiO2, graphitic carbon, CdSe and CdS, our silicon inverse opal simultaneously satisfies the two essential criteria for complete PBG formation. Firstly, the refractive index of silicon is 3.5, well above the theoretically determined threshold (of 2.8) for a PBG in a fcc lattice of air spheres. Secondly, the optical absorption edge of the silicon backbone occurs at a frequency well above the frequency range of the PBG, thereby allowing coherent localization of light within the material, with minimal absorptive losses. This is an essential feature for PBG device applications. The photonic band structure of a silicon inverse opal, with 88% infiltration
of silicon into the available volume of the opal template voids, is shown in Figure 3. The hatched region highlights a complete PBG with a gap to midgap ratio of 5.1%.
|Figure 3. Band structure of silicon inverse opal with an 88% degree of silicon infiltration into the available volume of the opal template voids. The complete PBG is shown by the crosshatched region, with a gap to midgap ratio of 5.1%. The calculations were performed using the plane-wave expansion method using a basis of 2662 plane waves.|
The optical properties of the inverse opal were characterized by measuring the reflectivity spectrum and comparing the spectral positions of the observed peaks with predictions from band structure.
The lattice constant of the photonic crystal, which is preserved after infiltration and inversion, was independently determined from reflectivity measurements of the bare opal at normal incidence (the L point of the fcc Brillouin zone). By fitting the spectral positions of the first stop band edges to those predicted by band structure calculations (using 1.45 as a refractive index for silica), we obtained a (cubic) lattice constant of 1.23 mm.
|Figure 4. The measured reflectivity spectrum from the inverse silicon opal, exhibits a broad peak with a center wavelength of 2.5 microns followed by a series of three peaks in the near-IR regime. Shaded regions at 2.5 microns and 1.5 microns show the calculated positions of the first stop band and the complete PBG, respectively. Since the lattice constant and the degree of infiltration were independently determined, no extra fitting parameters were used. A microscope coupled to the spectrometer was used to locate a single crystal domain with a high surface quality and hence reflectivity. The microscope produced a spot size of approximately 20 x 20 microns2 and an incident cone of wave vectors with an angular bandwidth spanning 15-35° from normal incidence.|
For the inverse opal, we find excellent agreement (see Figure 4) with the positions of the band edges of the first stop band centered on 2.5 mm. We also find excellent agreement between the positions of the peaks in the reflectivity spectrum and the center of the stop band at 1.5 mm, which is highly sensitive to the degree of infiltration. Based on this agreement between the measured spectrum and the calculated band structure, we infer the presence of a complete photonic band gap centered at 1.5 mm, with a gap to midgap ratio of 5.1%.
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