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Modeling and Control of Thin Film Morphology Using Unsteady Processing Parameters: Problem Formulation and Initial Results 
Abstract 
Thin film deposition is an industriallyim … Thin film deposition is an industriallyimportant 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 twofold: 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 finitetime and infinitetime 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. re desirable morphology is also presented. +


Authors  Martha A. Gallivan, David G. Goodwin and Richard M. Murray + 
ID  2001c + 
Source  Submitted, 2001 Conference on Decision and Control + 
Tag  ggm01cdc + 
Title  Modeling and Control of Thin Film Morphology Using Unsteady Processing Parameters: Problem Formulation and Initial Results + 
Type  Conference Paper + 
Categories  Papers 
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15 May 2016 06:19:19 + 
URL This property is a special property in this wiki.

http://www.cds.caltech.edu/~murray/preprints/ggm01cdc.pdf + 
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Modeling and Control of Thin Film Morphology Using Unsteady Processing Parameters: Problem Formulation and Initial Results +  Title 
