Abstract
A “smooth” quantum hydrodynamic (QHD) model for semiconductor devices is derived by a Chapman-Enskog expansion of the Wigner-Boltzmann equation which can handle in a mathematically rigorous way the discontinuities in the classical potential energy which occur at heterojunction barriers in quantum semiconductor devices. A dispersive quantum contribution to the heat flux term in the QHD model is introduced.
Highlights
This investigation is concerned with the derivation of a quantum hydrodynamic (QHD) model in the presence of discontinuities in the classical potential energy which occur at heterojunction barriers in quantum semiconductor devices
In the quantum case the first two conservation laws (1) and (2) can be derived directly from a nonlinear Schr6dinger equation. In this case one obtains an explicit formula for the internal energy density w in terms of n, depending on the form of interaction potential used in the Hamiltonian of the Schr6dinger equation [2]
We introduce the notation f / M(F) Fdp, M) (F) pjFdp, f Mk(F p:pFdp, (6)
Summary
A "smooth" quantum hydrodynamic (QHD) model for semiconductor devices is derived by a Chapman-Enskog expansion of the Wigner-Boltzmann equation which can handle in a mathematically rigorous way the discontinuities in the classical potential energy which occur at heterojunction barriers in quantum semiconductor devices. A dispersive quantum contribution to the heat flux term in the QHD model is introduced
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