Legitimate domain of a Newtonian behavior for thermal nanoimprint lithography

• Imprint of a simple line into a polymeric layer is modeled with no-slip boundary condition and constant viscosity.
• The legitimate domain of the newtonian behviour is expressed for a thermoplastic polymer.
• Usual non-dimensional analysis is performed to express the output forces and maximum shear rate for thermal NIL.
• Numerical simulations based on the natural element method allow to compute a master curve for a given geometry.

Nanoimprint lithography is an efficient way to reproduce nanostructures down to 20 nm in sub-micrometer polymeric films. To optimize this process, simulation using a Newtonian behavior is a cheap and efficient way to predict the polymer flow in micro and nano size cavities. This behavior is nevertheless limited to flows with shear rates below a critical value that can be determined with standard rheology measurements. We have investigated the validity domain of this behavior to simulate thermal NIL. This domain of validity is composed of two uncoupled functions, one for the material properties and the mean pressure applied to the pattern, and one for the geometry considered. The latter function has been determined with numerical simulations using the natural element method. It is demonstrated that knowing the mean applied pressure, the critical shear rate, and the viscosity of the material we are able to determine, depending on stamp geometry, if shear-thinning may or may not occur during an imprinting process.

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