X-RAY MASK MEMBRANE MOTION IN NARROW-GAP LITHOGRAPHY - HYDRODYNAMIC MODEL AND EXPERIMENT

The viscosity of the gas in the proximity gap between x-ray mask and s ilicon wafer causes damping of any membrane motion. As x ray is extend ed to future integrated circuit generations, this effect becomes incre asingly significant, because the gap must be rapidly scaled down to pe rmit resolution of finer lithographic features. Damping is much greate r at a reduced gap. Damping can be beneficial in reducing unwanted flu ctuations in the gap due to vibration, convection, or ambient sound. T he longer settling time following gap adjustment, however, can be detr imental to the throughput of x-ray steppers. This article introduces s imple hydrodynamic models, formulas, and numerical algorithms to calcu late membrane response to adjustments in gap setting. It applies the a nalysis to a variety of mask formats, including advanced ''pedestal'' design. Time constants of several seconds are shown to result from gap setting < 10 mum, which may be needed for 0.12 mum proximity x-ray li thography.