Limitations on length scales for electrostatically induced submicrometer pillars and holes

Thin leaky and perfect dielectric films can be driven electrically to form well-ordered patterns, typically of pillar arrays. While the technique appears to promise nanometer scale features, this paper begins to examine some of the limitations. The process, sometimes referred to as lithographically induced self-assembly, begins by spin coating a polymer onto a silicon wafer generating an initially featureless film and then overlaying a mask, which may be patterned, leaving a small gap. This configuration is heated above the glass transition temperature of the polymer, upon which flow ensues with a characteristic wavelength set by a combination of electrical forces and surface tension. The authors recently examined the initial stages of this process under pattern-free masks by deriving a generalized linear stability analysis not restricted to the lubrication approximation (J. Chem. Phys. 2003, 118, 3790). Herein comparison of this model with experimental data from the literature finds good agreement over a wide range of conditions including applied voltages and oxide layers on the mask and substrate. A significant discrepancy at the highest fields may be due to dielectric breakdown, suggesting that the minimum feature size may be limited. Viscous effects may also limit the effectiveness of large decreases in surface tension or large increases in electric field, leading to lower limits for the feature size. Long-range ordering seems to decrease as surface tension decreases and the potential increases, indicating that smaller pillars come with decreased quality. In the absence of an electric field, consideration of the viscosity-dependent time scale suggests an explanation for the apparent conflict between observations by Schäffer et al. (Nature 2000, 403, 874) and those of Chou and Zhuang (J. Vac. Sci. Technol., B 1999, 17, 3197).