Lumped-Parameter Modeling for Meniscus Dynamic Analysis in Immersion Flow Field

Motivated by the interest to increase production throughputs of immersion lithography machines, wafers are scanned at increasingly high velocities and accelerations, which may result in liquid loss at the receding contact line. The dynamic characteristics of the immersion fluid with free boundary play an important role for fluid management system, and are concerned in various potential immersion unit designs. To offer intuitive insights into the dynamic effects of the immersion fluid due to scan speeds, a lumped-parameter model is developed to characterize the hydrodynamics of the immersion flow process. To validate the model, meniscus behavior information under dynamic conditions is extracted experimentally and analyzed using image processing techniques. The reduced model agrees qualitatively well with the experimental data revealing that parts of the surface tension have an effect on the dynamic response of the menisci similar to that due to a pure time delay in the system.