Interface instability and nanostructure patterning

Recent experimental findings show that a flat interface between two dielectric media may lose stability in an electrostatic field. The instability grows over time and leads to morphological patterns with quite uniform feature sizes. An understanding of the phenomenon may lead to novel approaches for nanofabrication. This paper presents a three-dimensional dynamic model to account for the behavior. The coupled viscous flow, diffusion, surface energy and dielectric effect are incorporated into a phase field framework. The semi-implicit Fourier spectral method and the preconditioned biconjugate-gradient method are proposed, which leads to high efficiency and numerical stability. The computational study reveals a complete picture of the self-assembly process, especially the critical nonlinear evolution regime that links the early perturbation and late structure. The simulations unveil rich dynamics and show that the final structure is not solely determined by energetics: the kinetic process can play an important role. Tuning the electric field can produce a variety of patterns.