A numerical study of nanoscale electrohydrodynamic patterning in a liquid film

Abstract

A computational model is developed to study the manufacturing of micro/nanostructures by electrohydrodynamic (EHD) patterning processes. The computational methodology is based on the iterative coupling of the discontinuous boundary element method for electric field with the finite element method for free surface deformation. The model is capable of modeling fully nonlinear free surface deformations induced by an electric field. Geometric discontinuity resulting from the contact of the liquid film with the template is fully accounted for by introducing the short-range molecular forces. The critical voltage for liquid film instability is found by tracing the asymptote of the structural height vs. applied voltage curve, followed by a confirmation by the existence of an internal minimum of the total free energy. Computer codes are verified using the analytical solutions and available measurements. An important finding from the numerical simulations is that steady state structures can be electrohydrodynamically patterned when the applied voltage is either below or above a critical value. While linear analyses are useful, they may significantly over-predict the critical voltage, a crucial parameter for an EHD patterning process. The highly nonlinear phenomena of wetting the template above the critical voltage were considered to be unstable within the framework of linear perturbation. However, these phenomena can be very well predicted by the nonlinear boundary/finite element model enhanced by the short-range molecular forces. Finally, the computational model is flexible and may be modified with ease to analyze an EHD-patterning process for an air–polymer–polymer tri-layered system or other multiple-layered films for fabricating more complex nanostructures.