Two formulations of semiconductor transport equations based on spherical harmonic expansion of the Boltzmann transport equation

Author

Tang, Ting-wei ; Gan, Haitao

Author_Institution

Dept. of Electr. & Comput. Eng., Massachusetts Univ., Amherst, MA, USA

Volume

47

Issue

9

fYear

2000

fDate

9/1/2000 12:00:00 AM

Firstpage

1726

Lastpage

1732

Abstract

Two different formulations of semiconductor transport models based on the spherical harmonic expansion of the Boltzmann transport equation are presented. In the one-dimensional (1-D) case, macroscopic transport coefficients are defined through Legendre components of the distribution function. Although either formulation is permissible, the modeling of transport coefficients in one of the formulations is more tractable than the other. The validity of the Einstein and other relations are also examined. The two different transport formulations are then applied to the hydrodynamic simulation of an n⁺-n-n⁺ structure and results are compared with the Monte Carlo simulation data

Keywords

Boltzmann equation; Monte Carlo methods; semiconductors; Boltzmann transport equation; Einstein relation; Legendre components; Monte Carlo simulation; distribution function; hydrodynamic simulation; n⁺-n-n⁺ structure; one-dimensional model; semiconductor; spherical harmonic expansion; transport coefficient; Boltzmann equation; Current density; Differential equations; Distribution functions; Electrons; Gallium nitride; High definition video; Hydrodynamics; Integral equations; Polynomials;

fLanguage

English

Journal_Title

Electron Devices, IEEE Transactions on

Publisher

ieee

ISSN

0018-9383

Type

jour

DOI

10.1109/16.861583

Filename

861583