Parallel finite element method to solve the 3D Poisson equation and its application to abrupt heterojunction bipolar transistors

García‐Loureiro, Antonio J.; Pena, Tomás F.; López-González, J.M.; Prat, L.

doi:10.1002/1097-0207(20001020)49:5<639::aid-nme968>3.0.co;2-p

Cited by 11 publications

(5 citation statements)

References 12 publications

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“…In this work, we report on the development of a parallel 3D finite element MC simulator based on tetrahedral elements to solve Poisson equation [8,9] combined with an ensemble MC for bulk Si (Fig. 1).…”

supporting

confidence: 66%

Tetrahedral elements in self-consistent parallel 3D Monte Carlo simulations of MOSFETs

et al. 2008

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Novel thin-body architectures with complex geometry are becoming of large interest because they are expected to deliver the ITRS prescribed on-current when semiconductor transistors are scaled into nanometer dimensions. We report on the development of a 3D parallel Monte Carlo simulator coupled to a finite element solver for the Poisson equation in order to correctly describe the complex domains of advanced FinFET transistors. We study issues such as charge assignment, field calculation, treatment of contacts and parallelisation approach which have to be taken into account when using tetrahedral elements. The applicability of the simulator is demonstrated by modelling a 10 nm gate length double gate MOSFET with a body thickness of 6.1 nm.

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supporting

confidence: 66%

Tetrahedral elements in self-consistent parallel 3D Monte Carlo simulations of MOSFETs

et al. 2008

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“…This procedure could have been attempted here, but, again, to preserve the simplicity of our exposition, we opted for a serial algorithm to resolve the one-dimensional PB differential equation. Of course, the combination of the Newton-Raphson technique and a parallelization strategy would enhance significantly the power of the FEM and ease the treatment of more challenging two-and three-dimensional problems [28].…”

Section: Some Illustrative Resultsmentioning

confidence: 99%

The essentials of the finite element method to solve differential equations: an illustrative case in physics

Chávez-Páez,

González-Tovar,

Guerrero-García

et al. 2024

Phys. Scr.

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Here we review the basic steps of the modern and accurate finite element method in its application to solve ordinary differential equations in physics. To exemplify this well-in-vogue numerical technique, we have chosen the second-order Poisson-Boltzmann equation, which is a classic equation of colloid science. Aiming to formulate a viable, but didactic, implementation of the finite element technique, we have combined a linear basis of functions, the Galerkin weighted residuals method, the Swartz-Wendroff approximation and the Picard iteration algorithm. In summary, the finite element method transforms a differential equation into a simpler system of algebraic equations for the coefficients of the approximate solution in terms of a set of basis functions. We describe the full computational realisation of the finite element procedure and, also, we examine the corresponding Poisson-Boltzmann numerical predictions for various representative conditions.

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“…To solve this system of equations we can use a standard ILUT preconditioner combined with an FGMRES solver [13,14].…”

Section: Finite Element Discretisation Of the Poisson Equationmentioning

confidence: 99%

Reduction of the self-forces in Monte Carlo simulations of semiconductor devices on unstructured meshes

Aldegunde

Seoane

García‐Loureiro

et al. 2010

Computer Physics Communications

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Parallel finite element method to solve the 3D Poisson equation and its application to abrupt heterojunction bipolar transistors

Cited by 11 publications

References 12 publications

Tetrahedral elements in self-consistent parallel 3D Monte Carlo simulations of MOSFETs

Tetrahedral elements in self-consistent parallel 3D Monte Carlo simulations of MOSFETs

The essentials of the finite element method to solve differential equations: an illustrative case in physics

Reduction of the self-forces in Monte Carlo simulations of semiconductor devices on unstructured meshes

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