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Self-similar solutions for a free boundary problem in the doping of semiconductors

Published online by Cambridge University Press:  26 September 2008

L. A. Peletier  and
W. C. Troy
L. A. Peletier
Affiliation:
Mathematical Institute, Leiden University, Leiden, The Netherlands
W. C. Troy
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
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Abstract

We study the development of concentration profiles in a semi-infinite slab of semi-conductor material, in which impurities have been implanted at a high concentration. When the implant is uniform throughout the slab, no impurities can pass through the face of the slab, and the vacancy concentration at the surface is kept at its equilibrium value, it is shown that the density profiles of impurities, vacancies and host atoms may have self-similar form. The analysis is constructive and yields qualitative properties of the profiles and the front.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 2 , April 1995 , pp. 169 - 189
Copyright
Copyright © Cambridge University Press 1995

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