Numerical simulation of the smooth quantum hydrodynamic model for semiconductor devices

Carl Gardner, Christian Ringhofer

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


An extension of the classical hydrodynamic model for semiconductor devices to include quantum transport effects is reviewed. This "smooth" quantum hydrodynamic (QHD) model is derived specifically to handle in a mathematically rigorous way the discontinuities in the classical potential energy which occur at heterojunction barriers in quantum semiconductor devices. A conservative upwind discretization of the one-dimensional (1D) steady-state smooth QHD equations is outlined. Smooth QHD model simulations of the resonant tunneling diode are presented which exhibit enhanced negative differential resistance when compared with simulations using the original O(ℏ2) QHD model.

Original languageEnglish (US)
Pages (from-to)393-401
Number of pages9
JournalComputer Methods in Applied Mechanics and Engineering
Issue number4
StatePublished - Jan 21 2000


  • Electron tunneling
  • Numerical simulations
  • Quantum hydrodynamic model
  • Semiconductor devices

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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