We present a new approach to the design of semiconductor devices, which leads to fast optimization methods
whose numerical effort is of the same order as a single forward simulation of the underlying model, the stationary
drift-diffusion system. The design goal we investigate is to increase the outflow current on a contact for fixed applied
voltage, the natural design variable is the doping profile.
By reinterpreting 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. This property allows to construct efficient iterative optimization algorithms, which avoid to solve the fully coupled drift-diffusion system, but only need solves of the continuity equations and their adjoints. The efficiency and success of the new approach is demonstrated in several numerical examples.
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