Surface instability of thin polymer resist films with phase change effects on coating flow using numerical approximation techniques

摘要

This paper investigates the phenomena of surface instability of thin axisymmetric polymer resist films with phase change effects on coating flow. A set of Navier-Stokes equations with non-Newtonian behavior limited by a low Reynolds number provided a mathematical description of the physical systems. Long-wave perturbation analysis is proposed to derive an evolutionary equation of the Ostwald de-Waele type governing propagation of surface waves. Linear stability is studied using the normal mode. The multiple scales method is used to study the weakly nonlinear dynamics of the film flow. The amplitude of the instability is determined by a Ginzburg-Landau equation. The study reveals that the degree of the flow index n plays a vital role in stabilizing the film flow with phase change effects. The condensate film is more stable than the evaporating film with the same flow index. Furthermore, it is shown that sub-critical stability and supercritical stability are respectively possible for condensate and evaporating films.