Abstract
AbstractWe discuss recent progress in the mathematical modeling of semiconductor devices. The central result of this paper is a combined quantum-classical model that self-consistently couples van Roosbroeck’s drift-diffusion system for classical charge transport with a Lindblad-type quantum master equation. The coupling is shown to obey fundamental principles of non-equilibrium thermodynamics. The appealing thermodynamic properties are shown to arise from the underlying mathematical structure of a damped Hamitlonian system, which is an isothermal version of socalled GENERIC systems. The evolution is governed by a Hamiltonian part and a gradient part involving a Poisson operator and an Onsager operator as geoemtric structures, respectively. Both parts are driven by the conjugate forces given in terms of the derivatives of a suitable free energy.
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Kantner, M., Mielke, A., Mittnenzweig, M., Rotundo, N. (2019). Mathematical Modeling of Semiconductors: From Quantum Mechanics to Devices. In: Hintermüller, M., Rodrigues, J. (eds) Topics in Applied Analysis and Optimisation. CIM Series in Mathematical Sciences. Springer, Cham. https://doi.org/10.1007/978-3-030-33116-0_11
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DOI: https://doi.org/10.1007/978-3-030-33116-0_11
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-33115-3
Online ISBN: 978-3-030-33116-0
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