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Optimal Control of the Stationary Quantum Drift-Diffusion Model

2007
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Communications in Mathematical Sciences
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In this work an optimal control problem for a stationary quantum drift diffusion (QDD) model is analyzed. This QDD model contains four space-dependent observables: The nonnegative particle density of electrons, the electrostatic potential, the quantum quasi-Fermi potential and the current density. The goal is to optimize the shape of quantum barriers in a quantum diode. Existence of optimal solutions is proved. Moreover, first-order necessary optimality conditions are derived. For the notion of

doi:10.4310/cms.2007.v5.n1.a4
fatcat:s77ikbuse5fa5pjh76xyjvkvlm