Electrostatically induced submicron patterning of thin perfect and leaky dielectric films: A generalized linear stability analysis

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Abstract
Thin leaky and perfect dielectric films can be driven electrically to form well-ordered patterns typically of pillar arrays. The process, sometimes referred to as lithographically induced self-assembly, begins by spin coating a polymer onto a silicon wafer to generate an initially featureless film. A small gap, filled with air or another polymeric/organic liquid, is left between the first film and a second wafer called the mask, which may be patterned. This configuration is heated above the glass transition temperature of the polymer, upon which flow ensues in response to destabilizing electrical forces. The authors examined the initial stages of pillar formation under a pattern free mask by performing a linear stability analysis under the lubrication approximation [J. Non-Newtonian Fluid Mech. 102, 233 (2002)] and found the quest for smaller pillars to be assisted by the presence of free charge as described by the leaky dielectric. In practice, however, the lubrication approximation may not strictly apply in the situations of greatest interest. Contrasting the linear stability analysis with and without the lubrication approximation shows that the approximation fails where surface tension is small and electric fields are large, typical of experiments with a polymer/organic liquid instead of air in the gap—precisely the conditions that generate the smallest pillar arrays. This general linear stability analysis predicts conditions where pillars/holes pack more tightly, have smaller diameters, greater aspect ratios, and larger growth exponents for both perfect and leaky dielectric films, in which the smallest features reach deep into the submicron length scales. The analysis also highlights two approaches to smaller pillars by either making the polymer film conducting or choosing polymers with high dielectric contrast, with the former being more universally applicable.