Flow Control by Electrohydrodynamic or Thermocapillary Actuation for Enhancing Pattern Fidelity in Nanofilms *

During the past decade, the pursuit of large area, contact-free and relatively low cost film patterning techniques has introduced several novel methods ideally suited to fabrication of optical micro-components. Especially noteworthy are those methods that rely on the projection of very large electric or thermal gradient field distributions onto the surface of molten nanofilms. These projected fields deform a slender featureless liquid film into 3D shapes which are then rapidly solidified in situ. Approaches described in the literature have exclusively relied on the “forward problem”, whereby intuition of the desired final shape helps guide application of suitable electric or thermal boundary conditions used to solve the highly nonlinear film evolution equation. For optical applications, however, such 3D patterning requires highly accurate solution of the “inverse problem” to elicit those optimal boundary conditions which yield the desired shape within a given time interval. We have tackled the inverse problem by formulation of an optimization routine incorporating external field distributions arising from variations in topography, temperature or voltage applied to the confining or supporting substrates. Using target shapes representative of microlens arrays or other optical components, we demonstrate numerically different strategies available for pattern optimization subject to spatiotemporal actuation.