Upwind finite difference solution of Boltzmann equation applied to electron transport in semiconductor devices

Journal Article · Fri Oct 01 04:00:00 EDT 1993 · Journal of Computational Physics; (United States)

DOI:https://doi.org/10.1006/jcph.1993.1176· OSTI ID:7270753

Fatemi, E ^[1]; Odeh, F ^[2]

---

1. Institute for Mathematics and Its Applications, Minneapolis, MN (United States)
2. IBM T.J. Watson Research Center, Yorktown Heights, NY (United States)

The authors present a new numerical method for solving the Boltzmann-Poisson system which describes charge transport in semiconductor devices. The Boltzmann equation is reduced from three dimensions in velocity space to two by taking the electric field parallel to the z axis, which implies invariance of the probability density function under rotation around the z axis. We develop a finite difference discretization of the Boltzmann equation in one spatial dimension and two-dimensional velocity space, coupled to the Poisson equation. The system of equations obtained by taking the first five moments of the Boltzmann equation coupled to the Poisson equation is known as the hydrodynamic model in semiconductor modeling. A comparison of the numerical results from our method and the hydrodynamic model is given. Also a numerical investigation is done with respect to the heat conduction, viscosity, and momentum relaxation terms in the hydrodynamic model. 16 refs., 9 figs.

• OSTI ID: 7270753
• Journal Information: Journal of Computational Physics; (United States), Journal Name: Journal of Computational Physics; (United States) Vol. 108:2; ISSN 0021-9991; ISSN JCTPAH
• Country of Publication: United States
• Language: English

Related Subjects

664300* -- Atomic & Molecular Physics-- Collision Phenomena-- (1992-)
74 ATOMIC AND MOLECULAR PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
BOLTZMANN EQUATION
CALCULATION METHODS
COMPUTERIZED SIMULATION
DIFFERENTIAL EQUATIONS
ELECTRON TRANSFER
EQUATIONS
FINITE DIFFERENCE METHOD
ITERATIVE METHODS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
SIMULATION