A numerical approach to quantify self-ordering among self-organized nanostructures

The geometrical layout in two-dimensional arrays of self-organized nanostructures is usually not completely ordered, nor completely disordered. The ability to quantify a degree of order gives significant insight in nanoscale self-organization processes. We address this issue analytically. We first simulate the arrangement of nuclei in two-dimensional lattices with mixed order/disorder, as defined by a suitable order parameter. We focus on statistical properties of the local environment of the simulated nuclei. Finally, we compare this statistical analysis with results from actual experimental images. Here we test our analysis with the Ge/Si(1 1 1) model system. Our approach reveals a significant tendency towards self-ordering in this system, which is primarily attributed to Brownian nucleation and capture dynamics.