Theory of lithographically-induced self-assembly

Recent experiments show that, when a two-phase fluid confined between paral lel substrates is subject to an electric field, one phase can self-assemble into a triangular lattice of islands in another phase. We describe a theor y of the stability of the island lattice. It is well known that the total i nterface energy reduces when the island diameter increases. We show that, u nder certain conditions, the electrostatic free energy reduces when the isl and diameter decreases. The islands select the equilibrium diameter to mini mize the combined interface energy and electrostatic energy. We describe th e conditions for electrostatic field to stabilize the island lattice, and a nalyze an idealized model. The theory suggests considerable experimental co ntrol over stable island size. (C) 2001 American Institute of Physics.