Simulating Surface-Mediated Self Assembly Patterns by a Stabilized Fourier Spectral Method

抄録

Atoms on solid surfaces may self-assemble into ordered nanophases. The phase field method in combination with semi-implicit Fourier spectral method provides an ideal tool to simulate this dynamic process. The appearance of surface stress term in the evolving kinetic equations, however, may lead to divergence of simulation if standard spectral method is used. A stabilized scheme is proposed in this paper and a second-order approach is given to perform long time simulation with rather large time step. The scheme is used to simulate the self-assembly of binary epilayers with different average concentrations on a solid substrate. The results indicate that the self-assembly patterns are influenced by the average concentration, which agrees well with the experimental results. Based on the validated scheme, simulations of self-assembly guided by closed pre-patterns are performed. It is found that the closed pre-patterns can guide to form isolated closed loops after long time of evolution. This procedure provides a possible strategy to fabricate microelectronic devices and circuits.