Low-Dimensional Approximations of Multiscale Epitaxial Growth Models for Microstructure Control of Materials

The desire to control the microstructure of materials during growth has recently led to the development of multiscale models combining molecular information from microscopic scales with continuum-type information at macroscopic scales. Such multiscale models for epitaxial growth are here reduced through proper orthogonal decomposition to obtain low-dimensional approximations that can be useful for on-line control. The approach is illustrated in a stagnation flow microreactor by examining the effects of substrate temperature and inlet composition on film morphology. Numerically, this is the first attempt to describe the dynamics of coupled deterministic partial differential equations and stochastic partial differential equations (a master equation) with a small set of ordinary differential equations. Reduction is carried for both the fluid phase and the film morphology at different operating conditions. It is found that while information generated by molecular models can be represented by relatively low-dimensional deterministic models, the minimum necessary reduced model dimension for description of microscale features of epitaxial films is higher than that needed for fluid phase species concentrations. Trained models obtained from model reduction can be used for nearby parameter changes.