Modeling and control of thin film morphology using unsteady processing parameters: Problem formulation and initial results

Thin film deposition is an industrially-important process to which control theory has not historically been applied. The need for control is growing as the size of integrated circuits shrinks, requiring increasingly tighter tolerances in thin film manufacture. In this work we formulate a lattice model of film growth as a control system and take the process parameters as inputs. In the evolution equation, nonlinear functions of the process parameters multiply linear vector fields, yielding a structure similar to a bilinear system. The process conditions in some deposition methods are inherently unsteady, which produces films with altered morphology. We use the model developed in this study to analyze the effects of fast periodic forcing on thin film evolution. With the method of averaging we develop new effective transition rates which may produce film properties unattainable with constant inputs. These effective rates are the convex hull of the set of rates associated with constant inputs. We present conditions on the convex hull for which the finite-time and infinite-time reachability sets cannot be expanded with fast periodic forcing. An example in which this forcing increases the reachability set and produces more desirable morphology is also presented