Theory and simulation of nanoscale self-assembly on substrates

Experimental evidence has accumulated in the recent decade that nanoscale patterns can self-assemble on substrates. A two-component monolayer grown on a substrate surface may separate into distinct phases, forming periodic stripes, triangular lattice of dots, or other regular patterns. These phases may have a size scale of 1-100 nm and are stable against annealing. The phenomenon poses intriguing scientific problems and receives wide attention for its potential application in nanofabrication. This paper reviews the current understanding of the self-assembly mechanism, a theoretic framework that we have developed recently to model the phenomenon, and the numerical approach for efficient and accurate computation. Simulations of self-assembly and templated self-assembly have revealed remarkably rich dynamics in the formation and evolution of nanoscale patterns. Diverse patterns have been demonstrated by tuning material anisotropy, surface chemistry, and substrate strain field. These studies suggest a significant degree of capability and flexibility to design and guide a self-assembly process.