Minimization of the base transit time in semiconductor devices using optimal control

Paolo Rinaldi; Heinz Schättler

doi:10.3934/proc.2003.2003.742

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2003, Volume 2003: 742-751. Doi: 10.3934/proc.2003.2003.742 open access

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Minimization of the base transit time in semiconductor devices using optimal control

Paolo Rinaldi¹ and
Heinz Schättler^2,

1.
Dept. of Systems Science and Mathematics, Washington University, One Brookings Drive, St. Louis, MO 63130
2.
Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899

Received: July 31, 2002

Published: March 2003

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Abstract

We consider the problem of determining the optimal profile of doping concentration that minimizes the base transit time in homojunction bipolar transistors. This is a well-studied problem in the electronics literature, but typically only numerical optimization is used to find solutions. In this paper we give an explicit analytic solution to the problem using the Pontryagin Maximum Principle with state-space constraints and prove its optimality using synthesis type arguments.

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Mathematics Subject Classification: Primary: 49K15,49L20; Secondary: 93B50.

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