Proximity lithography membrane mask aeroelasticity

Proximity lithography places a thin membrane mask into close proximity (5-100 micron) to a wafer for exposure to radiation and pattern placement. Efficient production practices require that the wafer be positioned relative to the mask as quickly as possible. The positioning maneuvers involve both a lateral motion and a closing of the mask-to-wafer gap. Gap closing requires forcing the exposure chamber gas (usually air or helium, possibly at a mild vacuum) between the mask and wafer out through the edges of the gap in a squeeze film process that can substantially deflect and damage the membrane mask. Moving laterally, i.e. stepping, would be more efficient if it were performed at the close proximity gap. The buildup of hydrodynamic pressures while stepping at gap can deform and possibly damage the mask. This paper discusses methods to model, measure and control aeroelastic effects due to gap closing and lateral stepping at gap. The analysis considers an aeroelastic model based on coupling Reynolds' hydrodynamic lubrication theory with membrane mechanics. A principal result of the analysis is the prediction that it is possible to step at gap and produce minimal aeroelastic out-of-plane deflections, if the wedge angle is zero, and both the membrane and mask have a flat profile. The aeroelastic models are confirmed with experiments that measure out-of-plane stepping of a membrane versus wedge angle, gap and speed. Non-flat mask profiles, such as buttes and mesas raise additional aeroelastic issues are also examined.