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 the exposure of 800×800 µ m gratings with period as small as 0.14 µ 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 the critical stress intensity factors in thin, free-standing films of nonstoichiometric silicon nitride.