Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Semiconductor equations
SIAM Journal on Applied Mathematics
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
A finite difference scheme solving the Boltzmann-Poisson system for semiconductor devices
Journal of Computational Physics
Space-Time Discretization of Series Expansion Methods for the Boltzmann Transport Equation
SIAM Journal on Numerical Analysis
Moment Methods for the Semiconductor Boltzmann Equation on Bounded Position Domains
SIAM Journal on Numerical Analysis
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
High order numerical methods for the space non-homogeneous Boltzmann equation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A kinetic transport and reaction model and simulator for rarefied gas flow in the transition regime
Journal of Computational Physics
2D numerical simulation of the MEP energy-transport model with a finite difference scheme
Journal of Computational Physics
Implicit—Explicit Schemes for BGK Kinetic Equations
Journal of Scientific Computing
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
A deterministic solver for a hybrid quantum-classical transport model in nanoMOSFETs
Journal of Computational Physics
Journal of Computational Physics
Numerical properties of high order discrete velocity solutions to the BGK kinetic equation
Applied Numerical Mathematics
Recovering doping profiles in semiconductor devices with the Boltzmann-Poisson model
Journal of Computational Physics
Strong Stability Preserving Two-step Runge-Kutta Methods
SIAM Journal on Numerical Analysis
Hi-index | 31.49 |
In this paper we develop a deterministic high order accurate finite-difference WENO solver to the solution of the 1-D Boltzmann-Poisson system for semiconductor devices. We follow the work in Fatemi and Odeh [9] and in Majorana and Pidatella [16] to formulate the Boltzmann-Poisson system in a spherical coordinate system using the energy as one of the coordinate variables, thus reducing the computational complexity to two dimensions in phase space and dramatically simplifying the evaluations of the collision terms. The solver is accurate in time hence potentially useful for time-dependent simulations, although in this paper we only test it for steady-state devices. The high order accuracy and nonoscillatory properties of the solver allow us to use very coarse meshes to get a satisfactory resolution, thus making it feasible to develop a 2-D solver (which will be five dimensional plus time when the phase space is discretized) on today's computers. The computational results have been compared with those by a Monte Carlo simulation and excellent agreements have been found. The advantage of the current solver over a Monte Carlo solver includes its faster speed, noise-free resolution, and easiness for arbitrary moment evaluations. This solver is thus a useful benchmark to check on the physical validity of various hydrodynamic and energy transport models. Some comparisons have been included in this paper.