Coherence and structural design of free-standing gratings for atom-wave optics

Improvements in electron-beam writing techniques have allowed us to compensate for electron-beam system drift, making feasible tile exposure of 800 x 800 mu m gratings with period as small as 0.14 mu m. Placement errors due to drift, calibration errors, and nonplanar substrates are measured with verniers. Gratings patterned with interferometric photolithography provide an absolute reference for a measure of stage nonlinearity (runout.) Simulation of fracture formation in silicon nitride films has given us a tool for the prediction of structures that will fail during fabrication, and a way of evaluating stress relief patterns in arbitrary structures. We have used two sets of simple patterns to identify tile critical stress intensity factors in thin, free-standing films of nonstoichiometric silicon nitride.