Communications in Mathematical Sciences

On/off-state design of semiconductor doping models

M. Burger, R. Pinnau, and M.-T. Wolfram

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We consider the multi-objective optimal dopant profiling of semiconductor devices. The two objectives are to gain a higher on-state current while the off-state current is kept small. This design question is treated as a constrained optimization problem, where the constraints are given by the stationary drift-diffusion model for the on-state and the linearized drift-diffusion model for the off-state. Using the doping profile as a state variable and the electrostatic potential as the new design variable, we obtain a simpler optimization problem, whose Karush-Kuhn-Tucker conditions partially decouple. Based on this observation we can construct a very efficient iterative optimization algorithm, which avoids solving the fully coupled drift-diffusion system. Due to the simple structure of the adjoint equations, this algorithm can be easily included into existing semiconductor simulation tools. The efficiency and success of this multi-objective design approach is underlined by various numerical examples.

Article information

Commun. Math. Sci., Volume 6, Number 4 (2008), 1021-1041.

First available in Project Euclid: 18 December 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J50: Variational methods for elliptic systems 49J20: Optimal control problems involving partial differential equations 49K20: Problems involving partial differential equations

Semiconductor design drift-diffusion model Gummel iteration optimal control multi-objective dopant profiling


Burger, M.; Pinnau, R.; Wolfram, M.-T. On/off-state design of semiconductor doping models. Commun. Math. Sci. 6 (2008), no. 4, 1021--1041.

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