Characterization of photonic colloidal crystals in real and reciprocal space

Abstract

In this thesis, we present experimental work on the characterization of photonic colloidal crystals in real and reciprocal space. Photonic crystals are structures in which the refractive index varies periodically in space on the length scale of the wavelength of light. Self-assembly of colloidal particles is a promising route towards three-dimensional (3-D) photonic crystals. However, fabrication of photonic band-gap materials remains challenging, so calculations that predict their optical properties are indispensable. Our photonic band-structure calculations on binary Laves phases have led to a proposed route towards photonic colloidal crystals with a band gap in the visible region. Furthermore, contrary to results in literature, we found that there is no photonic band gap for inverse BCT crystals. Finally, optical spectra of colloidal crystals were analyzed using band-structure calculations.

Self-assembled photonic crystals are fabricated in multiple steps. Each of these steps can significantly affect the 3-D structure of the resulting crystal. X-rays are an excellent probe of the internal structure of photonic crystals, even if the refractive-index contrast is large. In Chapter 3, we demonstrate that an angular resolution of 0.002 mrad is achievable at a third-generation synchrotron using compound refractive optics. As a result, the position and the width of Bragg reflections in 2D diffraction patterns can be resolved, even for lattice spacings larger than a micrometer (corresponding to approximately 0.1 mrad). X-ray diffraction patterns and electron-microscopy images are used in Chapter 4 to determine the orientation of hexagonal layers in convective-assembly colloidal crystals. Quantitative analysis revealed that, in our samples, the layers were not exactly hexagonal and the stacking sequence was that of face-centered cubic (FCC) crystals, though stacking faults may have been present.

In Chapter 5, binary colloidal crystals of organic spheres (polystyrene, PMMA) and/or inorganic spheres (silica) are introduced as promising templates for strongly photonic crystals. To prevent melting of the template, we used atomic layer deposition (ALD) to infiltrate polystyrene and PMMA templates with alumina, after which chemical vapor deposition (CVD) was used to further enhance the refractive-index contrast. Binary colloidal crystals of silica spheres can be infiltrated by CVD directly, but they often have a layer of colloidal fluid on top. Preliminary etching experiments demonstrated that it may be possible to etch silica templates with plasmas or with adhesive tape. As described in Chapter 6, sedimentation of colloidal silica spheres in an external, high-frequency electric field lead to mm-scale BCT crystals with up to 25 layers. In addition, electric fields were used as an external control to switch between BCT and close-packed (CP) crystal structures within seconds. We also developed two procedures to invert BCT crystals without loss of structure - colloidal particles were immobilized by diffusion-polymerization or photo-induced polymerization of the surrounding solvent. Some BCT crystals were even infiltrated with silicon using CVD. We demonstrate in Chapter 7 that X-ray diffraction can be used to determine the 3-D structure of such photonic colloidal crystals at the various stages of their fabrication. Excellent agreement was found with confocal and electron-microscopy images.