Mathematical modeling of semiconductors: from quantum mechanics to devices

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Item Type:	Conference or Workshop Item
Title:	Mathematical modeling of semiconductors: from quantum mechanics to devices
Creators Name:	Kantner, M., Mielke, A., Mittnenzweig, M. and Rotundo, N.
Abstract:	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 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.
Source:	CIM Series in Mathematical Sciences (CIMSMS)
Series Name:	CIM Series in Mathematical Sciences (CIMSMS)
Title of Book:	Topics in applied analysis and optimisation : partial differential equations, stochastic and numerical analysis
ISSN:	2364-950X
ISBN:	978-3-030-33115-3
Publisher:	Springer
Page Range:	269-293
Date:	28 November 2019
Official Publication:	https://doi.org/10.1007/978-3-030-33116-0_11

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