Structure Determination in Colloidal Crystal Photonic Bandgap Structures

Structure/optical property relationships in photonic bandgap structures are evaluated by a novel combination of sample sectioning, microscopy, and image analysis. Disordered colloidal crystals of solution-derived, monosized SiO₂ particles were sectioned by focused ion beam (FIB) milling and then imaged using field emission scanning electron microscopy (FE-SEM). Pair correlation and radial distribution functions of the particulate arrangement were generated directly from a binary color scale rendering of the FE-SEM images, therein defining the level of order or disorder in the structure. These experimentally obtained spatial correlation functions were used to compute the scattering spectral properties in an analogous, although inverse (i.e., solving the inverse scattering problem), method to that used in X-ray diffraction for structure determination. Using a first-order approximation to the scattering from a disordered structure, the bandwidth and midgap values for the colloidal crystal photonic bandgap materials were within 15% of those measured. This new methodology promises to provide a simple and direct approach for quantifying the structure/optical property relationships in ordered and disordered photonic crystals directly from standard microstructural imaging techniques.