Numerical simulation of the smooth quantum hydrodynamic model for semiconductor devices

Carl Gardner; Christian Ringhofer

doi:10.1016/S0045-7825(99)00180-2

Numerical simulation of the smooth quantum hydrodynamic model for semiconductor devices

Carl Gardner, Christian Ringhofer

CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	393-401
Number of pages	9
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	181
Issue number	4
DOIs	https://doi.org/10.1016/S0045-7825(99)00180-2
State	Published - Jan 21 2000

Keywords

Electron tunneling
Numerical simulations
Quantum hydrodynamic model
Semiconductor devices

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
Physics and Astronomy(all)
Computer Science Applications

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10.1016/S0045-7825(99)00180-2

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AU - Ringhofer, Christian

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AB - 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.

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KW - Numerical simulations

KW - Quantum hydrodynamic model

KW - Semiconductor devices

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