A thermomechanical description of the mold filling process in roll-to-roll nanoimprinting lithography

Abstract

We derive the constitutive equations for a viscoelastic fluid that is undergoing a continuous mold filling process at the nanoscale within the context of a thermomechanical framework. The governing equations are obtained by substituting the constitutive equations into the appropriate balance laws. From the general characteristics inherent to the roll-to-roll nanoimprinting lithography processes, we derive suitable initial, boundary and simplifications of the governing equations. Since the general problem is nonlinear and appears to be intractable both analytically and numerically with the analytical and computational tools available currently, we simplify the problem by assuming the displacement gradient and its time rate to be small, resulting in an integro-differential problem with dynamic boundary conditions. To numerically obtain the evolution of the free surface of the fluid within the mold during filling, we propose a numerical scheme based on the Marker and Cell method for the simplified problem. We present and discuss a representative sample of the results from the numerical simulations of the nondimensional equation by considering changes to key process and transport parameters that affect mold filling.

Keywords

• Roll-to-roll nanoimprinting lithography
• Mold filling
• Multiscale modeling
• Thermomechanical approach
• Linearized viscoelastic fluid