Solving the Navier-Stokes Equation for Thermal Reflow

Abstract

For below 32-nm pattern formation, the extreme ultraviolet (EUV) and high-index fluid-based immersion ArF lithography are still under development and it is questionable whether they will be ready to timely meet resolution needs of most aggressive memory designs. Extending technology, such as resist reflow technology, appears to be a bridge option calling for serious consideration. Hence, a physical and mechanical understanding of thermal reflow is required for its better implementation and application. In this paper, resist flow is described by using a two-dimensional time-dependent Navier-Stokes equation with the mass conservation equation, which is composed of the flow of the resist, the variation of the viscosity, the reflow temperature and the reflow time. Due to an approximation based on experiment results, numerical solutions of this equation are described and the simulation results of these solutions are compared to experiment results for a contact hole pattern. In the virtual world, these simulations can predict the phenomenon of thermal reflow, such as the effects of temperature and pitch size on the contact hole patterns, with the appropriate correspondence between these mechanical parameters and the thermal reflow parameters.