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.

The squeezing of polymers in narrow gaps is important for the dynamics of nanostructure fabrication by nanoimprint embossing and the operation of polymer boundary lubricants. We measured stress versus strain behavior while squeezing entangled polystyrene films to large strains. In confined conditions where films were prepared to a thickness less than the size of the bulk macromolecule, resistance to deformation was markedly reduced for both solid-glass forging and liquid-melt molding. For melt flow, we further observed a complete inversion of conventional polymer viscosity scaling with molecular weight. Our results show that squeeze flow is accelerated at small scales by an unexpected influence of film thickness in polymer materials.

This work investigates the initial stages of polymer deformation during hot embossing micro-manufacturing at processing temperatures near the glass transition temperature (Tg) of polymer films having sufficient thickness such that polymer flow is not supply limited. Several stages of polymer flow can be observed by employing stamp geometries of various widths and varying imprint conditions of time and temperature to modulate polymer viscosity. Experiments investigate conditions affecting cavity filling phenomena, including apparent polymer viscosity. Stamps with periodic ridges of height and width 4 µm and periodicity 30, 50 and 100 µm emboss trenches into polymethyl methacrylate films at Tg − 10 °C < Temboss < Tg + 20 °C. Imprint parameters of time, temperature and load are correlated with replicated polymer shape, height and imprinted area. Polymer replicates are measured by atomic force microscopy and inspected by scanning electron microscopy. Cavity size and the temperature dependence of polymer viscosity significantly influence the nature of polymer deformation in hot embossing micro-manufacturing and must be accounted for in rational process design.

This paper presents continuum simulations of viscous polymer flow during nanoimprint lithography (NIL) for embossing tools having irregular spacings and sizes. Simulations varied non-uniform embossing tool geometry to distinguish geometric quantities governing cavity filling order, polymer peak deformation, and global mold filling times. A characteristic NIL velocity predicts cavity filling order. In general, small cavities fill more quickly than large cavities, while cavity spacing modulates polymer deformation mode. Individual cavity size, not total filling volume, dominates replication time, with large differences in individual cavity size resulting in non-uniform, squeeze flow filling. High density features can be modeled as a solid indenter in squeeze flow to accurately predict polymer flow and allow for optimization of wafer-scale replication. The present simulations make it possible to design imprint templates capable of distributing pressure evenly across the mold surface and facilitating symmetric polymer flow over large areas to prevent mold deformation and non-uniform residual layer thickness.