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Modeling pattern dependencies in the micron-scale embossing of polymeric layers

We describe a highly computationally efficient method for calculating the topography of a thermoplastic polymeric layer embossed with an arbitrarily patterned stamp. The approach represents the layer at the time of embossing as a linear-elastic material, an approximation that is argued to be acceptable for the embossing of thermoplastics in their rubbery regime. We extend the modeling approach to represent the embossing of layers with thicknesses comparable to the characteristic dimensions of the pattern on the stamp. We present preliminary experimental data for the embossing of such layers, and show promising agreement between simulated and measured topographies. Where the thickness of the embossed layer is larger than the characteristic dimensions of the pattern being embossed, the stamp-layer contact pressure exhibits peaks at the edges of regions of contact, and material fills stamp cavities with a single central peak. In contrast, when the layer thickness is smaller than the characteristic dimensions of the features being embossed, contact pressures are minimal at the edges of contact regions, and material penetrates cavities with separate peaks at their edges. These two apparently distinct modes of behavior, and mixtures of them, are well described by the simple and general model presented here.