An effective quantum potential for particle-particle interactions in three-dimensional semiconductor device simulations

Clemens Heitzinger, Christian Ringhofer

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The classical Coulomb potential and force can be calculated efficiently using fast multi-pole methods. Effective quantum potentials, however, describe the physics of electron transport in semiconductors more precisely. Such an effective quantum potential was derived previously for the interaction of an electron with a barrier for use in particle-based Monte Carlo semiconductor device simulators. The method is based on a perturbation theory around thermodynamic equilibrium and leads to an effective potential scheme in which the size of the electron depends upon its energy and which is parameter-free. Here we extend the method to electron-electron interactions and show how the effective quantum potential can be evaluated efficiently in the context of many-body problems. Finally several examples illustrate how the momentum of the electrons changes the classical potential.

Original languageEnglish (US)
Pages (from-to)401-408
Number of pages8
JournalJournal of Computational Electronics
Volume6
Issue number4
DOIs
StatePublished - Dec 2007

Fingerprint

Semiconductor Device Simulation
Particle interactions
particle interactions
Semiconductor devices
semiconductor devices
Electron
Three-dimensional
Electrons
Interaction
Electron-electron interactions
electrons
simulation
Poles
Momentum
Physics
Simulators
many body problem
Thermodynamics
Coulomb Potential
Thermodynamic Equilibrium

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Electrical and Electronic Engineering

Cite this

@article{a02acdf3af954d64a0c2c9ddb33dcf30,
title = "An effective quantum potential for particle-particle interactions in three-dimensional semiconductor device simulations",
abstract = "The classical Coulomb potential and force can be calculated efficiently using fast multi-pole methods. Effective quantum potentials, however, describe the physics of electron transport in semiconductors more precisely. Such an effective quantum potential was derived previously for the interaction of an electron with a barrier for use in particle-based Monte Carlo semiconductor device simulators. The method is based on a perturbation theory around thermodynamic equilibrium and leads to an effective potential scheme in which the size of the electron depends upon its energy and which is parameter-free. Here we extend the method to electron-electron interactions and show how the effective quantum potential can be evaluated efficiently in the context of many-body problems. Finally several examples illustrate how the momentum of the electrons changes the classical potential.",
author = "Clemens Heitzinger and Christian Ringhofer",
year = "2007",
month = "12",
doi = "10.1007/s10825-007-0148-4",
language = "English (US)",
volume = "6",
pages = "401--408",
journal = "Journal of Computational Electronics",
issn = "1569-8025",
publisher = "Springer Netherlands",
number = "4",

}

TY - JOUR

T1 - An effective quantum potential for particle-particle interactions in three-dimensional semiconductor device simulations

AU - Heitzinger, Clemens

AU - Ringhofer, Christian

PY - 2007/12

Y1 - 2007/12

N2 - The classical Coulomb potential and force can be calculated efficiently using fast multi-pole methods. Effective quantum potentials, however, describe the physics of electron transport in semiconductors more precisely. Such an effective quantum potential was derived previously for the interaction of an electron with a barrier for use in particle-based Monte Carlo semiconductor device simulators. The method is based on a perturbation theory around thermodynamic equilibrium and leads to an effective potential scheme in which the size of the electron depends upon its energy and which is parameter-free. Here we extend the method to electron-electron interactions and show how the effective quantum potential can be evaluated efficiently in the context of many-body problems. Finally several examples illustrate how the momentum of the electrons changes the classical potential.

AB - The classical Coulomb potential and force can be calculated efficiently using fast multi-pole methods. Effective quantum potentials, however, describe the physics of electron transport in semiconductors more precisely. Such an effective quantum potential was derived previously for the interaction of an electron with a barrier for use in particle-based Monte Carlo semiconductor device simulators. The method is based on a perturbation theory around thermodynamic equilibrium and leads to an effective potential scheme in which the size of the electron depends upon its energy and which is parameter-free. Here we extend the method to electron-electron interactions and show how the effective quantum potential can be evaluated efficiently in the context of many-body problems. Finally several examples illustrate how the momentum of the electrons changes the classical potential.

UR - http://www.scopus.com/inward/record.url?scp=35248864339&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35248864339&partnerID=8YFLogxK

U2 - 10.1007/s10825-007-0148-4

DO - 10.1007/s10825-007-0148-4

M3 - Article

AN - SCOPUS:35248864339

VL - 6

SP - 401

EP - 408

JO - Journal of Computational Electronics

JF - Journal of Computational Electronics

SN - 1569-8025

IS - 4

ER -