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Mathematical Modeling of Semiconductors: From Quantum Mechanics to Devices

  • 2019
  • OriginalPaper
  • Chapter
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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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Title
Mathematical Modeling of Semiconductors: From Quantum Mechanics to Devices
Authors
Markus Kantner
Alexander Mielke
Markus Mittnenzweig
Nella Rotundo
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-030-33116-0_11

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