Systems tasks in nanotechnology via hierarchical multiscale modeling: Nanopattern formation in heteroepitaxy

A kinetic phase diagram for two-dimensional nanopattern formation in heteroepitaxy is generated by symbiotically employing deterministic continuum mesoscopic models and coarse-grained Monte Carlo (CGMC) simulations. The phase diagram at submonolayer film thickness is derived in the absence of thermal fluctuations via linear stability analysis of continuum mesoscopic models. The type of nanoscopic patterns, such as discs and stripes, is deduced from nonlinear analysis. The analysis provides for the first time a physical understanding and scaling laws for pattern feature size, shape, and growth times in terms of the interaction potential parameters, substrate temperature, film thickness and material properties. It is concluded that the long-ranged repulsive interaction determines the pattern wavelength, whereas the short-ranged attractive interactions control the temperature for the onset of patterns. The phase diagram is refined by including thermal fluctuations using CGMC simulations. It is shown that thermal fluctuations are responsible for the non-uniformity in pattern shapes and sizes. CGMC simulations indicate that the phase diagrams from mesoscopic equations are reasonably accurate. The role of temperature on the pattern size distributions and inter-feature distance obtained from CGMC is analyzed. It is found that entropy plays an important role in pattern selection.