Modeling acoustic agitation for enhanced development of PMMA resists

Abstract

Although acoustic agitation is known to en- hance the development rate of LIGA resists, the operative physical mechanism is not well understood. Analytical and numerical models presented here suggest that the ob- served enhancement results from steady acoustic stream- ing and associated polymer fragment transport induced by the high frequency sound waves. The computed steady flow within the feature is torroidal with downflow along the feature walls and upflow in the center. The numerically calculated enhancement of fragment transport is shown to be well approximated by a closed-form expression based on a pair of asymptotic formulas for weak and strong agitation. These transport models are combined with a model of PMMA dissolution kinetics and used to predict development rates for a range of LIGA feature sizes. The results are in good agreement with experimental data from