Advanced electron beam lithography strategies for fabrication of high-precision VLS x-ray gratings

We present advanced electron beam lithography (EBL) strategies for the fabrication of high-precision variable-line-spacing (VLS) x-ray gratings with sub-nanometer pitch control on large, curved silicon substrates up to 140 × 30 × 10 mm3. Our approach employs a novel non-linear dose mapping methodology, combining dynamic field scaling and multi-pass writing techniques with HSQ resist to enable precise control over pitch. The resulting grayscale lithography resist patterns are transformed into blazed grating profiles via through-mask oxidation, which leverages different silicon oxidation rates for accurate topography transfer. The implementation of newly developed dose gradient shapes dramatically improves data handling efficiency and promotes stable, reliable exposures. We validate our methods experimentally through laser goniometer measurements, which confirm a third order polynomial line density agreement between designed and fabricated pitches across the optical area of 120 × 20 mm2. Unlike mechanical ruling, where throughput decreases with increasing line density, our EBL approach maintains constant throughput regardless of the grating line density, providing unique flexibility not limited to single lines but also allows for complex freeform x-ray optics in the future. This work thus demonstrates the scalable fabrication of high-quality x-ray VLS gratings, advancing the prospects for next-generation optical components at synchrotrons and free-electron lasers.