Influence of distorted electric field distribution on microstructure formation in the electrohydrodynamic patterning process

Electrohydrodynamic (EHD) patterning is a process for electrically duplicating a micrometer- or submicrometer-scale pattern of a template onto a thin polymer film on a substrate by applying an electric potential between the template and substrate as an electrode pair. Simulations of the electrohydrodynamic patterning process that have been reported have been based on a linear and analytical formulation assuming an ideal template shape and process setup for mathematical simplification. However, the EHD process, involving coupling of electrostatic and hydrodynamic fields, tends to be strongly nonlinear in practice. Consequently, even a small deviation (represented by nonuniformity in the height of template microstructures or nonuniform gap between template and polymer film, for example) can lead to deviation of the duplicated pattern from the pattern expected under ideal process conditions. This article presents a numerical method for simulating this electrically induced microstructuring process based on nonlinear EHD theory and arbitrary Lagrangian-Eulerian (ALE) finite element formulation. The dynamic evolution of the microstructure obtained for nonuniform height of the template pattern and a nonuniform gap between the template and polymer film shows that a small deviation tends to lead to considerable distortion in the electrical field during growth of the polymer pattern, resulting in irregularity in the duplicated microstructures. The numerical analysis also demonstrates how the polymer structure irregularity can be alleviated by reduced electric potential and reduced average gap between the template and polymer surface.