Impact of polymer film thickness and cavity size on polymer flow during embossing: toward process design rules for nanoimprint lithography

This paper presents continuum simulations of polymer flow during nanoimprint lithography (NIL). The simulations capture the underlying physics of polymer flow from the nanometer to millimeter length scale and examine geometry and thermophysical process quantities affecting cavity filling. Variations in embossing tool geometry and polymer film thickness during viscous flow distinguish different flow driving mechanisms. Three parameters can predict polymer deformation mode: cavity width to polymer thickness ratio, polymer supply ratio and capillary number. The ratio of cavity width to initial polymer film thickness determines vertically or laterally dominant deformation. The ratio of indenter width to residual film thickness measures polymer supply beneath the indenter which determines Stokes or squeeze flow. The local geometry ratios can predict a fill time based on laminar flow between plates, Stokes flow, or squeeze flow. A characteristic NIL capillary number based on geometry-dependent fill time distinguishes between capillary- or viscous-driven flows. The three parameters predict filling modes observed in published studies of NIL deformation over nanometer to millimeter length scales. The work seeks to establish process design rules for NIL and to provide tools for the rational design of NIL master templates, resist polymers and process parameters.