Mathematical modeling of semiconductors: From quantum mechanics to devices

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Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik

We 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 so-called 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.

Semiconductor modeling, drift-diffusion system, open quantum system,, Lindblad operator, reaction-diffusion systems, detailed balance condition, gradient structure, thermodynamically consistent coupling
Kantner, M., Mielke, A., Mittnenzweig, M., & Rotundo, N. (2019). Mathematical modeling of semiconductors: From quantum mechanics to devices (Vol. 2575). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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