Dynamic model reduction for control of molecular beam epitaxy

One important component in the development of many smart structures and microdevices is the growth of thin firms. The control of the growth processes, therefore, is of interest. In the design of a control system for molecular beam epitaxy (MBE), it is important to have simple mathematical models that describe the different growth morphologies that a growing film may exhibit and incorporate atomic-scale information. Of the three types of models currently being considered (atomistic, continuum, and bulk), bulk models have the most interest to control. Still, due to the complexity of such models, however, a model reduction must be carried out to make real-time control possible. A model reduction routine based on a new version of the nonlinear Galerkin methods is proposed and explained for three different bulk models. A total reduction of one-third the number differential equations is obtained.