Several recent developments have made it possible to begin exploring in formal ways the trajectory space of epitaxial growth during molecular beam epitaxy. This paper reviews the fundamentals of trajectory morphing an...
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Several recent developments have made it possible to begin exploring in formal ways the trajectory space of epitaxial growth during molecular beam epitaxy. This paper reviews the fundamentals of trajectory morphing and presents results showing that trajectory morphing may be used to explore the trajectory space of an epitaxial thin film growth system. We have derived a simplified growth model, suitable for use in morphing, and this is also presented. are reviewed.
Builds on the previous work by the authors (1998) by defining local versions of cross-positivity for vector fields, especially as related to shifted cones. The paper also furthers the development of a stability theory...
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Builds on the previous work by the authors (1998) by defining local versions of cross-positivity for vector fields, especially as related to shifted cones. The paper also furthers the development of a stability theory by introducing preliminary concepts of directed stability. The motivation is to apply this theory to analyzing the control of certain directionally constrained models, such as those found in materials processing.
In this paper nonlinear trajectory morphing is introduced. We show how it can explore the trajectory space of a nonlinear system. A trajectory tracking projection operator is defined for practical implementation of mo...
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In the molecular-beam epitaxy (MBE) process precise control over thickness, composition, and doping profiles are critical for end device performance. This paper addresses the problem of accurately controlling the flux...
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In the molecular-beam epitaxy (MBE) process precise control over thickness, composition, and doping profiles are critical for end device performance. This paper addresses the problem of accurately controlling the flux sources (effusion cells) used in MBE. We present a nonlinear compensator based on exact input-output linearization via feedback to control the flux of an effusion cell. The unmeasured states, necessary for implementation of the controller, are estimated by a Kalman-Bucy observer. We present simulations of the composite observer/nonlinearcontroller system, showing successful flux command following and elimination of shutter induced flux transients.
This paper introduces the concept of cross-positivity for vector fields and explores ramifications of cross-positivity relative to solutions of ordinary differential equations. The motivation is to understand the dyna...
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