Low-dimensional approximations of multiscale epitaxial growth models for microstructure control of materials

The desire to control the microstructure of materials during growth has rec ently led to the development of multiscale models combining molecular infor mation from microscopic scales with continuum-type information at macroscop ic scales. Such multiscale models for epitaxial growth are here reduced thr ough proper orthogonal decomposition to obtain low-dimensional approximatio ns that can be useful for on-line control. The approach is illustrated in a stagnation flow microreactor by examining the effects of substrate tempera ture and inlet composition on film morphology. Numerically, this is the fir st attempt to describe the dynamics of coupled deterministic partial differ ential equations and stochastic partial differential equations (a master eq uation) with a small set of ordinary differential equations. Reduction is c arried for both the fluid phase and the film morphology at different operat ing conditions. It is found that while information generated by molecular m odels can be represented by relatively low-dimensional deterministic models , the minimum necessary reduced model dimension for description of microsca le features of epitaxial films is higher than that needed for fluid phase s pecies concentrations. Trained models obtained from model reduction can be used for nearby parameter changes. (C) 2000 Academic Press.