SIMULATION OF n+−n−n+ DEVICES BY A HYDRODYNAMIC MODEL: SUBSONIC AND SUPERSONIC FLOWS

Anile, A. M.; Maccora, C.; Pidatella, R. M.

doi:10.1108/eb010135

Cited by 18 publications

(14 citation statements)

References 16 publications

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“…where s = 0.01µm, n 0 = n 0 (0), Regarding the boundary conditions, in principle the number of independent conditions on each boundary should be equal to the number of characteristics entering the domain. However, in the highly doped regions, one is close to thermodynamic equilibrium; therefore in that part of the device the nonlinear effects are negligible and the results should be very close to those of the model obtained by Maxwellian iteration [41]. Numerical results show that in the latter the solution is flat near the boundary.…”

Section: Numerical Resultssupporting

confidence: 53%

Extended Hydrodynamical Model of Carrier Transport in Semiconductors

Anile¹,

Russo²,

Romano³

2000

SIAM J. Appl. Math.

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A hydrodynamical model based on the theory of extended thermodynamics is presented for carrier transport in semiconductors. Closure relations for fluxes are obtained by employing the maximum entropy principle. The production terms are modeled by fitting the Monte Carlo data for homogeneously doped semiconductors. The mathematical properties of the model are studied. A suitable numerical method, which is a generalization of the Nessyahu-Tadmor scheme to the nonhomogeneous case, is provided. The validity of the constitutive relations has been assessed by comparing the numerical results with detailed Monte Carlo simulations.

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Section: Numerical Resultssupporting

confidence: 53%

Extended Hydrodynamical Model of Carrier Transport in Semiconductors

Anile¹,

Russo²,

Romano³

2000

SIAM J. Appl. Math.

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“…In this way Gardner [17] was able to show evidence for an electron shock wave in the diode. A method similar to Gardner's was used by Anile, Maccora, and Pidatella [3] in order to solve the AP model with viscosity included. Gardner's results were also recovered within their approach.…”

Section: Previous Work On Steady-state Model Integrationsmentioning

confidence: 99%

Assessment of a High Resolution Centered Scheme for the Solution of Hydrodynamical Semiconductor Equations

Anile¹,

Nikiforakis²,

Pidatella³

2001

SIAM J. Sci. Comput.

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Hydrodynamical models are suitable to describe carrier transport in submicron semiconductor devices. These models have the form of nonlinear systems of hyperbolic conservation laws with source terms, coupled with Poisson's equation. In this article we examine the suitability of a high resolution centered numerical scheme for the solution of the hyperbolic part of these extended models, in one space dimension. Because of the lack of physically significant exact analytical solutions, the method is assessed against a benchmark for the system of compressible, unsteady Euler equations with source terms, which has an exact solution; the latter is shown to be nearly identical to the numerical one. The method is then used to solve the extended hydrodynamical model (EM) based on the maximum entropy closure recently introduced by Anile, Romano, and Russo, simulating a ballistic diode n + − n − n + , which models a metal oxide semiconductor field effect transistor (MOSFET) channel. Results are presented for the reduced-and full-equation EM formulation at steady state, for an initially discontinuous electron density at the junctions. Transient results show the evolution of highly nonlinear waves emanating from the neighborhood of the junctions. Introduction.Enhanced functional integration in modern electron devices requires an accurate modeling of energy transport in semiconductors in order to describe high-field phenomena such as hot-electron propagation, impact ionization, and heat generation in the bulk material. Furthermore, when using compound semiconductors for high frequency applications, usually one deals with multivalley band structures and in these cases the transfer of carriers from one valley to the other must also be modeled. The standard drift-diffusion models cannot cope with highfield phenomena because they do not comprise energy as a dynamical variable. Also they do not incorporate dynamical transfer of carriers from one valley to the other and this renders them ill-suited for simulating time dependent high frequency phenomena. Therefore, generalizations of the drift-diffusion equations have been sought which would incorporate energy as a dynamical variable and which also could treat time dependent high frequency phenomena. Because of their mathematical similarity to the equations of compressible fluid flow, these models are called hydrodynamical models. Semiconductor hydrodynamical models are obtained from the infinite hierarchy of moment equations of the semiclassical Boltzmann transport equation (BTE) by a suitable truncation procedure. This requires making suitable assumptions on (i) choosing the appropriate moments, (ii) closing the hierarchy of moment equations by finding appropriate expressions for the N + 1 order moment in terms of the previous

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“…In order to check the validity of the stability analysis, we set k W−F = 0.1 which aims at balancing the hyperbolic and the parabolic characters of system (1), (3). In this regard, see Fig.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…For the numerical approximation, an explicit first-order finite difference method is used, consisting of a central discretization on cartesian grids of the derivatives of the fluxes plus an upwinding correction along the characteristic variables. Finite difference schemes, which can be written in conservation form, are robust in presence of discontinuous solutions, and have been widely employed for the discretization of semiconductor device equations (see, for instance, [16] for two-dimensional simulations, and [3,6,13] for one-dimensional simulations).…”

Section: Introductionmentioning

confidence: 99%

On a viscous-hydrodynamic model for semiconductors: numerical simulation and stability analysis

Ballestra

Micheletti

Sacco

et al. 2001

Computing and Visualization in Science

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We deal with a hydrodynamic model for semiconductors with a physical viscosity in the momentum/energy equations. The discretization uses a first-order finite difference scheme with upwinding based on the characteristic variables. We perform a stability analysis of the numerical method applied to a linearized incompletely parabolic system assuming vanishing viscosity in one space dimension although the analysis can be extended to the two dimensional case. A thorough numerical parametric study as a function of the heat conductivity and of the momentum viscosity is carried out in order to investigate their effect on the development of shocks in both one and two space dimensions.

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SIMULATION OF n+−n−n+ DEVICES BY A HYDRODYNAMIC MODEL: SUBSONIC AND SUPERSONIC FLOWS

Abstract: The effects of viscosity, previously neglected in electronic device stimulations, are studied using a non‐standard hydrodynamic model, following Anile and Pennisi. Results are compared with those of Gardner.

Cited by 18 publications

References 16 publications

Extended Hydrodynamical Model of Carrier Transport in Semiconductors

Extended Hydrodynamical Model of Carrier Transport in Semiconductors

Assessment of a High Resolution Centered Scheme for the Solution of Hydrodynamical Semiconductor Equations

On a viscous-hydrodynamic model for semiconductors: numerical simulation and stability analysis

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