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Mathematical Modeling of Semiconductors: From Quantum Mechanics to Devices

  • Markus KantnerEmail author
  • Alexander Mielke
  • Markus Mittnenzweig
  • Nella Rotundo
Conference paper
Part of the CIM Series in Mathematical Sciences book series (CIMSMS)

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Markus Kantner
    • 1
    Email author
  • Alexander Mielke
    • 2
  • Markus Mittnenzweig
    • 2
  • Nella Rotundo
    • 2
  1. 1.Weierstrass Institute for Applied Analysis and Stochastics (WIAS)Mohrenstr. 39, 10117 BerlinGermany
  2. 2.WIAS and Humboldt University of Berlin, Department of MathematicsRudower Chaussee 25, 12489 BerlinGermany

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