Two-dimensional numerical simulation of thin film flow on a rotating disk*

The flow of a thin liquid film on a solid surface is the phenomenon encountered commonly in industries, particularly in the manufacturing of semiconductors. Numerical simulation of the film flow, however, is challenging due to multi-phase effects and especially the large difference in length scales between film domain size and film height. In this study, to evaluate the development process of photolithography, we use a finite-volume based solver for the two-dimensional simulation of liquid film flow over a rotating disk. Governing equations are averaged over the height of the film, which results in a set of equations for evolving film height as well as radial and tangential velocities. In our work, to simulate the development process, development liquid is injected over a rotating wafer through a nozzle that moves independently from the wafer. The impinging region is modeled using prescribed height and momentum source term, whose values are determined using a simple analytical approach. Our numerical results show excellent agreement with three-dimensional VOF simulations and experiments.