  Microscopy with extreme ultraviolet (EUV) radiation holds promise for
high-resolution imaging with excellent material contrast, due to the short
wavelength and numerous element-specific absorption edges available in this
spectral range. At the same time, EUV radiation has significantly larger
penetration depths than electrons. It thus enables a nano-scale view into
complex three-dimensional structures that are important for material science,
semiconductor metrology, and next-generation nano-devices. Here, we present
high-resolution and material-specific microscopy at 13.5 nm wavelength. We
combine a highly stable, high photon-flux, table-top EUV source with an
interferometrically stabilized ptychography setup. By utilizing structured EUV
illumination, we overcome the limitations of conventional EUV focusing optics
and demonstrate high-resolution microscopy at a half-pitch lateral resolution
of 16 nm. Moreover, we propose mixed-state orthogonal probe relaxation
ptychography, enabling robust phase-contrast imaging over wide fields of view
and long acquisition times. In this way, the complex transmission of an
integrated circuit is precisely reconstructed, allowing for the classification
of the material composition of mesoscopic semiconductor systems.
