View source for Modeling and Control of Thin Film Morphology Using Unsteady Processing Parameters: Problem Formulation and Initial Results

{{HTDB paper
| authors = Martha A. Gallivan, David G. Goodwin and Richard M. Murray
| title = Modeling and Control of Thin Film Morphology Using Unsteady Processing Parameters: Problem Formulation and Initial Results
| source = Submitted, 2001 Conference on Decision and Control
| year = 2001
| type =  Conference 
  Paper
| funding = NSF, AFOSR
| url = http://www.cds.caltech.edu/~murray/preprints/ggm01-cdc.pdf
| abstract = 
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 the manufacture of thin films. Our contributions in this study are two-fold: we formulate a model of thin film
growth as a control system and we examine the effects of fast periodic forcing.
<p>
We choose a lattice formulation of crystal growth as our physical model, which captures atomic length scale effects at a time scale compatible with film growth. We focus on the control of film morphology, or surface height profile. Although the system
dimension is high, the structure is simple: the dynamics and the output are linear in the state. We consider the process conditions as inputs, which alter the transition rate
functions. In the evolution equation, each of these nonlinear functions is multiplied by a linear vector field, yielding a system with a structure similar to a bilinear system.
<p>
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. We show that 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.
| flags = 
| tag = ggm01-cdc
| id = 2001c
}}