Form of the quantum potential for use in hydrodynamic equations for semiconductor device modeling

D. K. Ferry, Jing Rong Zhou

Research output: Contribution to journalArticle

86 Citations (Scopus)

Abstract

We solve a form of the Bloch equation for the density matrix in a manner that identifies a ''quantum'' correction to the classical potential. This correction is given by the difference between the Bohm self-potential and a form of the Wigner potential that have both been used in previous simulations of semiconductor devices. The net potential appearing in the density is then a nonlocally smoothed average of the total semiclassical potential, which itself is composed of the classical potential and the quantum correction. However, the effective potential, which appears in hydrodynamic equations for device modeling, is shown to be the difference between this nonlocally smoothed potential and the local value of the potential. The various definitions that have appeared in the literature for the quantum potential and the effective potential are compared and it is demonstrated how a connection exists among these various definitions.

Original languageEnglish (US)
Pages (from-to)7944-7950
Number of pages7
JournalPhysical Review B
Volume48
Issue number11
DOIs
StatePublished - 1993

Fingerprint

Semiconductor device models
hydrodynamic equations
Semiconductor devices
semiconductor devices
Hydrodynamics

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Form of the quantum potential for use in hydrodynamic equations for semiconductor device modeling. / Ferry, D. K.; Zhou, Jing Rong.

In: Physical Review B, Vol. 48, No. 11, 1993, p. 7944-7950.

Research output: Contribution to journalArticle

Ferry, D. K. ; Zhou, Jing Rong. / Form of the quantum potential for use in hydrodynamic equations for semiconductor device modeling. In: Physical Review B. 1993 ; Vol. 48, No. 11. pp. 7944-7950.
@article{73031dba16c843e6bd182e344e1cbf13,
title = "Form of the quantum potential for use in hydrodynamic equations for semiconductor device modeling",
abstract = "We solve a form of the Bloch equation for the density matrix in a manner that identifies a ''quantum'' correction to the classical potential. This correction is given by the difference between the Bohm self-potential and a form of the Wigner potential that have both been used in previous simulations of semiconductor devices. The net potential appearing in the density is then a nonlocally smoothed average of the total semiclassical potential, which itself is composed of the classical potential and the quantum correction. However, the effective potential, which appears in hydrodynamic equations for device modeling, is shown to be the difference between this nonlocally smoothed potential and the local value of the potential. The various definitions that have appeared in the literature for the quantum potential and the effective potential are compared and it is demonstrated how a connection exists among these various definitions.",
author = "Ferry, {D. K.} and Zhou, {Jing Rong}",
year = "1993",
doi = "10.1103/PhysRevB.48.7944",
language = "English (US)",
volume = "48",
pages = "7944--7950",
journal = "Physical Review B-Condensed Matter",
issn = "0163-1829",
publisher = "American Institute of Physics Publising LLC",
number = "11",

}

TY - JOUR

T1 - Form of the quantum potential for use in hydrodynamic equations for semiconductor device modeling

AU - Ferry, D. K.

AU - Zhou, Jing Rong

PY - 1993

Y1 - 1993

N2 - We solve a form of the Bloch equation for the density matrix in a manner that identifies a ''quantum'' correction to the classical potential. This correction is given by the difference between the Bohm self-potential and a form of the Wigner potential that have both been used in previous simulations of semiconductor devices. The net potential appearing in the density is then a nonlocally smoothed average of the total semiclassical potential, which itself is composed of the classical potential and the quantum correction. However, the effective potential, which appears in hydrodynamic equations for device modeling, is shown to be the difference between this nonlocally smoothed potential and the local value of the potential. The various definitions that have appeared in the literature for the quantum potential and the effective potential are compared and it is demonstrated how a connection exists among these various definitions.

AB - We solve a form of the Bloch equation for the density matrix in a manner that identifies a ''quantum'' correction to the classical potential. This correction is given by the difference between the Bohm self-potential and a form of the Wigner potential that have both been used in previous simulations of semiconductor devices. The net potential appearing in the density is then a nonlocally smoothed average of the total semiclassical potential, which itself is composed of the classical potential and the quantum correction. However, the effective potential, which appears in hydrodynamic equations for device modeling, is shown to be the difference between this nonlocally smoothed potential and the local value of the potential. The various definitions that have appeared in the literature for the quantum potential and the effective potential are compared and it is demonstrated how a connection exists among these various definitions.

UR - http://www.scopus.com/inward/record.url?scp=0000996833&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000996833&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.48.7944

DO - 10.1103/PhysRevB.48.7944

M3 - Article

VL - 48

SP - 7944

EP - 7950

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 11

ER -