A self-consistent iterative scheme for one-dimensional steady state transistor calculations

Gummel, H.K.

doi:10.1109/t-ed.1964.15364

Cited by 1,063 publications

(371 citation statements)

References 17 publications

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“…Instead, a fixed 17 time step ∆t = 10 −9 is imposed. In the time integration Gummel iteration [25] is adopted. The solution procedure is as follows.…”

Section: Methodsmentioning

confidence: 99%

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The complete flux scheme—Error analysis and application to plasma simulation

Liu

Dijk

Boonkkamp

et al. 2013

Journal of Computational and Applied Mathematics

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“…Instead, a fixed 17 time step ∆t = 10 −9 is imposed. In the time integration Gummel iteration [25] is adopted. The solution procedure is as follows.…”

Section: Methodsmentioning

confidence: 99%

“…Here we used the Taylor expansion for 1/2 − W (P ) and the upper bound for z (3) (x j ) given by (25). For the remainder terms because of the similarity we only present the estimation of I 1 + I 2 , which is given by…”

Section: Consistencymentioning

confidence: 99%

The complete flux scheme—Error analysis and application to plasma simulation

Liu

Dijk

Boonkkamp

et al. 2013

Journal of Computational and Applied Mathematics

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“…In the numerical solution of this coupled nonlinear system, the iterative method of Gummel [2] is normally used to decouple the system. The result of this decoupling is that in each iteration the Poisson equation (1.1a) and the two continuity equations (1.1b), (1.1c) are solved sequentially.…”

Section: The Semiconductor Device Equationsmentioning

confidence: 99%

A parameter-uniform Schwarz method for a singularly perturbed reaction–diffusion problem with an interior layer

Miller

O’Riordan

Шишкин

et al. 2000

Applied Numerical Mathematics

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In this paper we consider numerical methods for a singularly perturbed reaction-diffusion problem with a discontinuous source term. We show that such a problem arises naturally in the context of models of simple semiconductor devices. We construct a numerical method consisting of a standard finite difference operator and a non-standard piecewise-uniform mesh. The mesh is fitted to the boundary and interior layers that occur in the solution of the problem. We show by extensive computations that, for this problem, this method is parameteruniform in the maximum norm, in the sense that the numerical solutions converge in the maximum norm uniformly with respect to the singular perturbation parameter. The semiconductor device equationsThe stationary behaviour of semiconductor devices can be described by the nonlinear system of second-order elliptic equations of van Roosbroeck [6]. In one dimension, for example, a simple p-n diode Ω = (0, 1) with two Ohmic contacts, an anode at x = 0 and a cathode at x = 1, is governed by the equationson Ω with appropriate boundary conditions at x = 0 and x = 1. Here ψ is the electrostatic potential, η and ρ are the electron and hole concentrations in the Slotboom variables, D denotes the doping function * Corresponding author.0168-9274/00/$ -see front matter © 2000 IMACS. Published by Elsevier Science B.V. All rights reserved PII: S 0168-9274(99 )00 1 40 -3

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“…We have developed a 3D 'atomistic' drift-diffusion simulator based on the decoupled Gummel procedure [16]. The solution of Poisson's equation uses a parallelized black/red Newton SOR solver, while a parallelized BiCGSTAB solver with polynomial preconditioning has been implemented for the solution of the electron current continuity equation.…”

Section: Classical Atomistic Simulationsmentioning

confidence: 99%

Statistical 3D ‘atomistic’ simulation of decanano MOSFETs

Asenov

Slavcheva

Brown

et al. 2000

Superlattices and Microstructures

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A 3D statistical 'atomistic' simulation technique has been developed to study the effect of the random dopant induced parameter fluctuations in aggressively scaled MOSFETs. Efficient implementation of the 'atomistic' simulation approach has been used to investigate the threshold voltage standard deviation and lowering in the case of uniformly doped MOSFETs, and in fluctuation-resistant architectures utilising epitaxial-layers and delta-doping. The effect of the random doping in the polysilicon gate on the threshold voltage fluctuations has also been thoroughly investigated. The influence of a single-charge trapping on the channel conductivity in decanano MOSFETs is studied in the 'atomistic' framework as well. Quantum effects are taken into consideration in our 'atomistic' simulations using the density gradient formalism.

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A self-consistent iterative scheme for one-dimensional steady state transistor calculations

Cited by 1,063 publications

References 17 publications

The complete flux scheme—Error analysis and application to plasma simulation

The complete flux scheme—Error analysis and application to plasma simulation

A parameter-uniform Schwarz method for a singularly perturbed reaction–diffusion problem with an interior layer

Statistical 3D ‘atomistic’ simulation of decanano MOSFETs

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