Solving the Navier-Stokes Equation for Thermal Reflow
J. Korean Phy. Soc. 2008; 53: 2682~2687
Published online November 15, 2008 © 2008 The Korean Physical Society.

For below 32-nm pattern formation, the extreme ultraviolet (EUV) andhigh-index fluid-based immersion ArF lithography are still underdevelopment and it is questionable whether they will be ready totimely meet resolution needs of most aggressive memory designs.Extending technology, such as resist reflow technology, appears tobe a bridge option calling for serious consideration. Hence, aphysical and mechanical understanding of thermal reflow is requiredfor its better implementation and application. In this paper, resistflow is described by using a two-dimensional time-dependentNavier-Stokes equation with the mass conservation equation, which iscomposed of the flow of the resist, the variation of the viscosity,the reflow temperature and the reflow time. Due to an approximationbased on experiment results, numerical solutions of this equationare described and the simulation results of these solutions arecompared to experiment results for a contact hole pattern. In thevirtual world, these simulations can predict the phenomenon ofthermal reflow, such as the effects of temperature and pitch size onthe contact hole patterns, with the appropriate correspondencebetween these mechanical parameters and the thermal reflowparameters.
Keywords: Lithography, Lithography simulation, Finite element method, Thermal reflow process, Chemically-amplified resist
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