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

Pages: 742 - 751, Issue Special, July 2003

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Paolo Rinaldi - Dept. of Systems Science and Mathematics, Washington University, One Brookings Drive, St. Louis, MO 63130, United States (email)
Heinz Sch├Ąttler - Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899, United States (email)

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.

Keywords:  Optimal Control, FIeld of extremals, semiconductor devices, base transit time.
Mathematics Subject Classification:  Primary: 49K15,49L20; Secondary: 93B50.

Received: August 2002; Published: April 2003.