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Quantum hydrodynamic equations and quantum-hierarchy decoupling scheme.

F A Buot1, Y Jiang, A I Fedoseyev

  • 1CFD Research Corporation (CFDRC), Cummings Research Park, 215 Wynn Drive, Huntsville, Alabama 35805, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 7, 2003
PubMed
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This study simplifies quantum transport simulations by developing a quantum hierarchy and decoupling scheme. This approach accurately captures quantum effects in semiconductor devices without restrictive assumptions.

Area of Science:

  • Quantum mechanics
  • Semiconductor device physics
  • Computational physics

Background:

  • Quantum transport simulations are complex and computationally intensive.
  • Existing quantum hydrodynamic (QHD) models rely on approximations limiting their applicability.

Purpose of the Study:

  • To develop a simplified yet accurate method for quantum transport simulations.
  • To derive quantum hydrodynamic and drift-diffusion equations from first principles.
  • To incorporate nonequilibrium quantum corrections for advanced device modeling.

Main Methods:

  • Utilized Hermite polynomial expansion to reduce degrees of freedom.
  • Developed a general quantum-hierarchy decoupling scheme.
  • Renormalized lower-order equations with effective potentials and quantum corrections.

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Main Results:

  • Derived a quantum hierarchy in real space.
  • Established a rigorous decoupling procedure for QHD and drift-diffusion equations.
  • Achieved quantum corrections to order Planck's over h(2) valid at all temperatures.

Conclusions:

  • The proposed method offers a more general and accurate approach to quantum transport.
  • It overcomes limitations of existing QHD formulations, especially for abrupt heterojunctions.
  • The approach is crucial for modeling nonlinear quantum phenomena in devices like resonant tunneling structures.