Linear stability analysis of thin leaky dielectric films subjected to electric fields

An intriguing process, known as lithographically induced self-assembly (LISA), is initiated by positioning a template parallel to a flat silicon wafer-coated with a thin polymeric film and then raising the temperature above the glass transition/melting temperature of the film. Electric fields exert a force on charges induced at the polymer–air interface, placing the film in tension. The static equilibrium that results is unstable to disturbances with wavelengths for which the electrostatic force overcomes the surface tension. Flow ensues, generating a pattern in the film with periodicity reflecting the characteristic length of the instability.Though the initiation of the process as outlined above is generally accepted, the forces guiding the evolution of the film into the remarkably periodic microstructures observed are not. Our goal here is to create a sound understanding of the mechanism through quantitative modeling to facilitate the conversion of these microstructures into nano-structures. Given the apparent importance of conductivity in the film we adopt the “leaky dielectric model”, which also allows for re-distribution of charges on the interfaces, and undertake a linear stability analysis to explore the effects of various process parameters, particularly the conductivity and the film thickness. The linear stability analysis with the leaky dielectric model for the polymer film yields growth exponents and characteristic wavenumbers much larger than that for the perfect dielectric model. The differences are striking in that the slightest conductivity increases the growth exponent by a factor of 2–20 and decreases the fastest growing wavelength by a factor of 2–4.