Open Access
December 2008 On/off-state design of semiconductor doping models
M. Burger, R. Pinnau, M.-T. Wolfram
Commun. Math. Sci. 6(4): 1021-1041 (December 2008).


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.


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M. Burger. R. Pinnau. M.-T. Wolfram. "On/off-state design of semiconductor doping models." Commun. Math. Sci. 6 (4) 1021 - 1041, December 2008.


Published: December 2008
First available in Project Euclid: 18 December 2008

zbMATH: 1160.49021
MathSciNet: MR2511704

Primary: 35J50 , 49J20 , 49K20

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

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 4 • December 2008
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