Roughening and smoothing behavior of Al/Zr multilayers grown on flat and saw-tooth substrates

Diffraction gratings with high efficiency and high groove density are required for EUV and soft x-ray spectroscopy techniques (such as Resonant Inelastic X-ray Scattering, RIXS) designed for state-of-the-art spectral resolution and throughput. A multilayer coated blazed grating (MBG) fabricated by deposition of a multilayer on a saw-tooth substrate could address these challenges. In order to obtain high diffraction efficiency one should provide perfect triangular grooves on a substrate and perfect replication of the groove profile during the multilayer deposition. However, multilayers trend to smooth out the corrugated surface of the substrates, resulting in the main limiting factor for efficiency of ultra-dense MBGs. Understanding of the growth of multilayers on saw-tooth substrates is a key for further grating improvement. In this work we investigate growth behavior of Al/Zr multilayers on saw-tooth substrates with a groove density of 10,000 lines/mm. We apply existing growth models to describe an evolution of Power Spectral Density functions of a grating surface during the multilayer deposition, and identify a main smoothing mechanism. We found that growth of flat multilayers is well modeled with surface diffusion caused by surface curvature as a main relaxation mechanism, while growth of the multilayer on saw-tooth substrates obeys different kinetics. Limitations of the linear approach and possible model improvements by accounting for an additional component of the surface diffusion flux, caused by a gradient of adatom concentration on a corrugated surface are discussed.