Colloidal crystal order and structure revealed by tabletop extreme ultraviolet scattering and coherent diffractive imaging.

Colloidal crystals with specific electronic, optical, magnetic, vibrational properties, can be rationally designed by controlling fundamental parameters such as chemical composition, scale, periodicity and lattice symmetry. In particular, silica nanospheres -which assemble to form colloidal crystals- are ideal for this purpose, because of the ability to infiltrate their templates with semiconductors or metals. However characterization of these crystals is often limited to techniques such as grazing incidence small-angle scattering that provide only global structural information and also often require synchrotron sources. Here we demonstrate small-angle Bragg scattering from nanostructured materials using a tabletop-scale setup based on high-harmonic generation, to reveal important information about the local order of nanosphere grains, separated by grain boundaries and discontinuities. We also apply full-field quantitative ptychographic imaging to visualize the extended structure of a silica close-packed nanosphere multilayer, with thickness information encoded in the phase. These combined techniques allow us to simultaneously characterize the silica nanospheres size, their symmetry and distribution within single colloidal crystal grains, the local arrangement of nearest-neighbor grains, as well as to quantitatively determine the number of layers within the sample. Key to this advance is the good match between the high harmonic wavelength used (13.5nm) and the high transmission, high scattering efficiency, and low sample damage of the silica colloidal crystal at this wavelength. As a result, the relevant distances in the sample - namely, the interparticle distance (≈124nm) and the colloidal grains local arrangement (≈1μm) - can be investigated with Bragg coherent EUV scatterometry and ptychographic imaging within the same experiment simply by tuning the EUV spot size at the sample plane (5μm and 15μm respectively). In addition, the high spatial coherence of high harmonics light, combined with advances in imaging techniques, makes it possible to image near-periodic structures quantitatively and nondestructively, and enables the observation of the extended order of quasi-periodic colloidal crystals, with a spatial resolution better than 20nm. In the future, by harnessing the high time-resolution of tabletop high harmonics, this technique can be extended to dynamically image the three-dimensional electronic, magnetic, and transport properties of functional nanosystems.