A Germanium Inverse Woodpile Structure with a Large Photonic Band Gap

The fabrication of 3D structures with a large complete photonic bandgap (PBG) has been an important goal, since the concept was introduced two decades ago. Many proposed structures exhibit PBGs with theoretical relative widths below 5%, often too narrow for practical applications, since structural inhomogeneties may reduce the size, or even close, PBGs by introducing unwanted modes into the band structure. In this letter, we report the simulation, assembly, and optical properties of the first Ge inverse woodpile structure with a 25% wide PBG. This structure is created by direct-write assembly of a polymeric template followed by sequential deposition of a sacrificial oxide bilayer and Ge. The photonic response is maximized by tuning the Ge filling fraction in accordance with theoretical predictions. Upon removal of the template and sacrificial layers, the reflectance spectrum acquired from the resulting Ge inverse woodpile structure shows a large reflectance peak in the mid-IR indicative of a PBG. 3D periodic structures with a diamond symmetry offer a promising approach for creating PBG materials. Among the diamond or diamondlike lattices that have been fabricated to date, the woodpile structure introduced by Ho et al. remains the most popular. This structure is composed of dielectric rods stacked in a periodic array such that their contact points form a diamondlike lattice. A great advantage of the woodpile architecture over other structures is that it can be readily fabricated by standard lithographic techniques. However, the production of high quality, three-dimensional lattices is expensive. Hence, the study of these crystals has been rather limited. Alternate strategies, such as direct laser and ink writing, have been introduced to create inexpensive polymeric woodpile templates, and very recently, in two simultaneous publications, we and Ozin et al. demonstrated their conversion to high-refractive-index, photonic crystals. Until our recent efforts, all woodpile structures have been composed of solid dielectric rods in an air matrix, even though it is known that inverse symmetries consisting of air rods in a high-refractive-index matrix offer significant advantages. Not only are their PBGs wider, but lower dielectric filling fractions are required to maximize the gap width. Such low filling fractions are advantageous, since the PBG occurs at higher frequencies for a given lattice parameter. In this Communication, we report the first realization and characterization of a Ge inverse woodpile structure with a theoretical PBG width as large as 25%. As proposed in the literature, the woodpile structure with the largest PBG consists of interpenetrating air rods in a high-refractive-index material. In the case of Ge (n= 4.1), a 31% wide PBG can be obtained at the optimal filling fraction. However, this structure cannot be realized experimentally via templating routes, since conformal growth of high-refractive-index material leads to the formation of isolated pores that limit the Ge filling fraction. For cylindrical rods, this threshold value occurs when the outer radius equals 0.306 a, where a is the lattice parameter. Yet, even in the presence of these isolated pores, the inverse woodpile structure can display a large (25% wide) PBG. Figure 1a shows the band structure and density of states of an inverse Ge photonic crystal made of interpenetrated hollow cylinders with internal and external radii of ri = 0.25 a and re = 0.306 a, respectively. These values, corresponding to a Ge filling fraction of 0.16, yield a gap centered at a/k=0.565, where k is the wavelength. Figure 1b shows how the internal radius of the rods and, therefore, the filling fraction, can be C O M M U N IC A IO N