Simulation of semiconductor devices using a Galerkin/spherical harmonic expansion approach to solving the coupled Poisson-Boltzmann system

Rahmat, K.; White, Jacob K.; Antoniadis, D.A.

doi:10.1109/43.541439

Cited by 30 publications

(34 citation statements)

References 15 publications

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“…For the bulk case, Hennacy et al presented higher-order expansions [36,37]. In the case of one-dimensional devices Rahmat et al demonstrated a third-order expansion [38]. Later expansions of arbitrary order were reported for such devices in [29].…”

mentioning

confidence: 96%

“…Later expansions of arbitrary order were reported for such devices in [29]. Box integration for the derivation of the discrete system of equations was introduced and exact current continuity achieved [27,33,38]. Without stabilization simulation of realistic semiconductor devices is not possible.…”

mentioning

confidence: 99%

“…The H-transform was developed to stabilize the equations [27]. An upwind discretization have been proposed in [38]. Later a stabilization was introduced [29], which is based on the maximum entropy dissipation scheme [23].…”

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confidence: 99%

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A fully coupled scheme for a Boltzmann-Poisson equation solver based on a spherical harmonics expansion

Hong

Jungemann

2009

J Comput Electron

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The numerical properties of a deterministic Boltzmann equation solver based on a spherical harmonics expansion of the distribution function are analyzed and improved. A fully coupled discretization scheme of the Boltzmann and Poisson equations is proposed, where stable equations are obtained based on the H-transformation. It is explicitly shown that the resultant Jacobian matrix for the zeroth order component has property M for a first order expansion, which improves the stability even of higher order expansions. The detailed dependence of the free-streaming operator and the scattering operator on the electrostatic potential is exactly considered in the Newton-Raphson scheme. Therefore, convergence enhancement is achieved compared with previous Gummel-type approaches. This scheme is readily applicable to small-signal and noise analysis. As numerical examples, simulation results are shown for a silicon n + nn + structure including a magnetic field, an SOI NMOSFET and a SiGe HBT.

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confidence: 96%

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A fully coupled scheme for a Boltzmann-Poisson equation solver based on a spherical harmonics expansion

Hong

Jungemann

2009

J Comput Electron

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“…The SHE equations are easily obtained by inserting the expansion (3) into the BTE (1) and balancing the terms of the same order in P n (cos θ). To generate a closed set of equations, all coefficients of order higher than the first are set to be zero, see Rahmat et al (1996) (a closure inspired by the Grad moment method, see Grad, 1958). But for the aims of this paper it is preferable to perform a change of variables and write down a set of two coupled equations in the unknowns…”

Section: Basic Equationsmentioning

confidence: 99%

An asymptotic solution for the SHE equations describing the charge transport in semiconductors

Liotta

2001

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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“…This has a long history and so many scientists have contributed to this art that we can cite only a few pioneering papers [3][4][5][6]. The biggest disadvantage of this method is the high memory requirement if a 2D real space is considered.…”

Section: Direct Solution Of the Bementioning

confidence: 99%

Numerical Modeling of Noise and Transport in SOI Devices

Meinerzhagen

Pham²,

Hong³

et al. 2011

ECS Trans.

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Accurate numerical modeling for SOI devices of technical interest has always been challenging concerning the accuracy of the physical models as well as concerning the convergence properties of the numerical algorithms. For partially depleted devices the most important underlying reason is the necessity of a precise modeling of low impact ionization and diffusion currents in order to get reasonable results for the kink effect and noise. On the other hand in fully depleted devices the DIBL effect at smaller channel lengths can only be sufficiently suppressed using thin Silicon films. Therefore a precise modeling of size quantization based on the Schrödinger Equation is typically needed for fully depleted devices. Today even more challenges exist due to the application of strain, hetero junctions and non standard interface and channel orientations. In this paper it is demonstrated that most of these challenges can be adequately addressed today.

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Simulation of semiconductor devices using a Galerkin/spherical harmonic expansion approach to solving the coupled Poisson-Boltzmann system

Cited by 30 publications

References 15 publications

A fully coupled scheme for a Boltzmann-Poisson equation solver based on a spherical harmonics expansion

A fully coupled scheme for a Boltzmann-Poisson equation solver based on a spherical harmonics expansion

An asymptotic solution for the SHE equations describing the charge transport in semiconductors

Numerical Modeling of Noise and Transport in SOI Devices

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