A Finite Difference Scheme Solving the Boltzmann–Poisson System for Semiconductor Devices

Majorana, Armando; Pidatella, R. M.

doi:10.1006/jcph.2001.6929

Cited by 56 publications

(32 citation statements)

References 10 publications

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“…However, the simulation results are often noisy, and it is difficult to compute transient details (time dependent states), especially if the probability density function (pdf ) is desired. In recent years, deterministic solvers to the BP system were considered in the literature, see for example [1,2,3,4]. These methods provide accurate results which, in general, agree well with those obtained from DSMC simulations, sometimes at a comparable or even less computational time.…”

Section: Introductionmentioning

confidence: 86%

Discontinuous Galerkin methods for the Boltzmann-Poisson systems in semiconductor device simulations

Cheng¹,

Gamba²,

Majorana³

et al. 2011

AIP Conference Proceedings

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Abstract. We are interested in the deterministic computation of the transients for the Boltzmann-Poisson system describing electron transport in semiconductor devices. The main difficulty of such computation arises from the very high dimensions of the model, making it necessary to use relatively coarse meshes and hence requiring the numerical solver to be stable and to have good resolution under coarse meshes. In this paper we consider the discontinuous Galerkin (DG) method, which is a finite element method using discontinuous piecewise polynomials as basis functions and numerical fluxes based on upwinding for stability, for solving the Boltzmann-Poisson system. In many situations, the deterministic DG solver can produce accurate solutions with equal or less CPU time than the traditional DSMC (Direct Simulation Monte Carlo) solvers. Numerical simulation results on a diode and a 2D double-gate MOSFET are given.

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Section: Introductionmentioning

confidence: 86%

Discontinuous Galerkin methods for the Boltzmann-Poisson systems in semiconductor device simulations

Cheng¹,

Gamba²,

Majorana³

et al. 2011

AIP Conference Proceedings

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“…In the one-dimensional case we apply the method proposed in [13] which is based on the integral representation of the analytic solution. For two space dimensions, we perform the standard finite-difference approximation of the Laplace operator and use an iterative method [5] to solve the resulting linear system determining the electric potential at the grid points.…”

Section: Phase-space Discretizationmentioning

confidence: 99%

“…In the past, mainly stochastic approaches such as the Ensemble Monte Carlo (EMC) methods [5] were applied. Recently, deterministic solvers to the Boltzmann-Poisson system have become popular [7,[10][11][12][13][14]. Deterministic methods enable us to obtain directly the time evolution of the phase-space distribution function.…”

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confidence: 99%

Efficient time integration of the Boltzmann-Poisson system applied to semiconductor device simulation

Auer

Schürrer

2006

J Comput Electron

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This paper presents new efficient methods for performing the time integration of finite-difference WENO approximations of the Boltzmann-Poisson system applied to semiconductor device simulation. The developed methods are based on local time-step schemes for hyperbolic conservation laws which permit the use of different time increments at different positions in space. A strategy to dynamically adapt the space-time grid according to the actual stability criteria imposed by the CFL-condition is proposed. The resulting numerical schemes are used to simulate the electron transport in a n + −n −n + silicon diode and in a silicon MESFET. Several numerical tests and comparisons with computations performed with TVD Runge-Kutta type algorithms prove the efficiency of the presented time integration methods.

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“…A well-accepted model for the charge carrier transport in semiconductors is the Boltzmann equation. It represents the starting point of analytical, asymptotic, and numerical investigations carried out in recent years [9,25,20,3]. There are many differences between the semiconductor Boltzmann equation and the classical one for a perfect gas.…”

Section: Introductionmentioning

confidence: 99%

On the Cauchy problem for spatially homogeneous semiconductor Boltzmann equations: existence and uniqueness

Majorana

Marano

2005

Annali di Matematica

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The non-linear semi-classical Boltzmann equation for an electron gas in a semiconductor is investigated in the framework of Lebesgue spaces by first providing a rigorous definition of the collision operator. The case of possibly unbounded collision frequencies is treated. Global existence and uniqueness of integrable, space independent solutions to the related Cauchy problem are established. Entropy inequalities, upper bounds for moments as well as mass conservation are also obtained. Mathematics Subject Classification (2000). 76P05, 45K05, 47H07, 82D37

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A Finite Difference Scheme Solving the Boltzmann–Poisson System for Semiconductor Devices

Cited by 56 publications

References 10 publications

Discontinuous Galerkin methods for the Boltzmann-Poisson systems in semiconductor device simulations

Discontinuous Galerkin methods for the Boltzmann-Poisson systems in semiconductor device simulations

Efficient time integration of the Boltzmann-Poisson system applied to semiconductor device simulation

On the Cauchy problem for spatially homogeneous semiconductor Boltzmann equations: existence and uniqueness

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