Deterministic kinetic solvers for charged particle transport in semiconductor devices

M. J. Cáceres; J. A. Carrillo; I. M. Gamba; A. Majorana; C. W. Shu

doi:10.1007/978-0-8176-4554-0_7

Deterministic kinetic solvers for charged particle transport in semiconductor devices

M. J. Cáceres, J. A. Carrillo, I. M. Gamba, A. Majorana, C. W. Shu

Department of Mathematics

Research output: Chapter in Book › Chapter › Research › peer-review

11 Citations (Scopus)

Abstract

© 2007, Birkhäuser Boston. Statistical models [F91], [L00], [MRS90], [To93] are used to describe electron transport in semiconductors at a mesoscopic level. The basic model is given by the Boltzmann transport equation (BTE) for semiconductors in the semiclassical approximation: (Formula Presented.) where f represents the electron probability density function (pdf) in phase space k at the physical location x and time t. ħ and e are physical constants; the Planck constant divided by 2π and the positive electric charge, respectively. The energy-band function ε is given by the Kane non-parabolic band model, which is a non-negative continuous function of the form (Formula Presented.) where m* is the effective mass and α is the non-parabolicity factor. In this way we observe that setting α = 0 in Equation (7.1.2) the model is reduced to the widely used parabolic approximation.

Original language	English
Title of host publication	Modeling and Simulation in Science, Engineering and Technology
Pages	151-171
Number of pages	20
ISBN (Electronic)	2164-3725
DOIs	https://doi.org/10.1007/978-0-8176-4554-0_7
Publication status	Published - 1 Jan 2007

Keywords

Boltzmann transport equation (BTE)
Weighted essentially non-oscillatory (WENO) schemes
direct simulation Monte Carlo (DSMC)
metal oxide semiconductor field effect transistor (MOSFET)
metal semiconductor field effect transistor (MESFET)
semiconductor device simulation

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title = "Deterministic kinetic solvers for charged particle transport in semiconductor devices",

abstract = "{\textcopyright} 2007, Birkh{\"a}user Boston. Statistical models [F91], [L00], [MRS90], [To93] are used to describe electron transport in semiconductors at a mesoscopic level. The basic model is given by the Boltzmann transport equation (BTE) for semiconductors in the semiclassical approximation: (Formula Presented.) where f represents the electron probability density function (pdf) in phase space k at the physical location x and time t. ħ and e are physical constants; the Planck constant divided by 2π and the positive electric charge, respectively. The energy-band function ε is given by the Kane non-parabolic band model, which is a non-negative continuous function of the form (Formula Presented.) where m* is the effective mass and α is the non-parabolicity factor. In this way we observe that setting α = 0 in Equation (7.1.2) the model is reduced to the widely used parabolic approximation.",

keywords = "Boltzmann transport equation (BTE), Weighted essentially non-oscillatory (WENO) schemes, direct simulation Monte Carlo (DSMC), metal oxide semiconductor field effect transistor (MOSFET), metal semiconductor field effect transistor (MESFET), semiconductor device simulation",

author = "C{\'a}ceres, {M. J.} and Carrillo, {J. A.} and Gamba, {I. M.} and A. Majorana and Shu, {C. W.}",

year = "2007",

month = jan,

day = "1",

doi = "10.1007/978-0-8176-4554-0_7",

language = "English",

isbn = "2164-3679",

pages = "151--171",

booktitle = "Modeling and Simulation in Science, Engineering and Technology",

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TY - CHAP

T1 - Deterministic kinetic solvers for charged particle transport in semiconductor devices

AU - Cáceres, M. J.

AU - Carrillo, J. A.

AU - Gamba, I. M.

AU - Majorana, A.

AU - Shu, C. W.

PY - 2007/1/1

Y1 - 2007/1/1

N2 - © 2007, Birkhäuser Boston. Statistical models [F91], [L00], [MRS90], [To93] are used to describe electron transport in semiconductors at a mesoscopic level. The basic model is given by the Boltzmann transport equation (BTE) for semiconductors in the semiclassical approximation: (Formula Presented.) where f represents the electron probability density function (pdf) in phase space k at the physical location x and time t. ħ and e are physical constants; the Planck constant divided by 2π and the positive electric charge, respectively. The energy-band function ε is given by the Kane non-parabolic band model, which is a non-negative continuous function of the form (Formula Presented.) where m* is the effective mass and α is the non-parabolicity factor. In this way we observe that setting α = 0 in Equation (7.1.2) the model is reduced to the widely used parabolic approximation.

AB - © 2007, Birkhäuser Boston. Statistical models [F91], [L00], [MRS90], [To93] are used to describe electron transport in semiconductors at a mesoscopic level. The basic model is given by the Boltzmann transport equation (BTE) for semiconductors in the semiclassical approximation: (Formula Presented.) where f represents the electron probability density function (pdf) in phase space k at the physical location x and time t. ħ and e are physical constants; the Planck constant divided by 2π and the positive electric charge, respectively. The energy-band function ε is given by the Kane non-parabolic band model, which is a non-negative continuous function of the form (Formula Presented.) where m* is the effective mass and α is the non-parabolicity factor. In this way we observe that setting α = 0 in Equation (7.1.2) the model is reduced to the widely used parabolic approximation.

KW - Boltzmann transport equation (BTE)

KW - Weighted essentially non-oscillatory (WENO) schemes

KW - direct simulation Monte Carlo (DSMC)

KW - metal oxide semiconductor field effect transistor (MOSFET)

KW - metal semiconductor field effect transistor (MESFET)

KW - semiconductor device simulation

U2 - 10.1007/978-0-8176-4554-0_7

DO - 10.1007/978-0-8176-4554-0_7

M3 - Chapter

SN - 2164-3679

SP - 151

EP - 171

BT - Modeling and Simulation in Science, Engineering and Technology

ER -