On epitaxial thin film growth and control of nanoscale materials

Abstract. We describe a continuum model for epitaxial film growth, consider its stability properties and suggest control strategies. The used model for YBCO thin film growth has been suggested by Ortiz, Repetto, and Si, based upon phenomenological considerations of Zangwill. We consider stability properties of the continuous film solution and of its numerical approximation. In particular, we investigate the impact on stability by the so-called transition function. Using the sensitivity equation approach we show how parameter identification and open loop control problems can be tackled. Finally, a feedback control law allows to design thin films with prescribed growth properties.