Monte Carlo and hydrodynamic simulationof a one dimensional n<sup>+</sup> ‐ n ‐ n<sup>+</sup> silicon diode

Muscato, Orazio; Pidatella, R. M.; Fischetti, Massimo V.

doi:10.1155/1998/98910

Cited by 16 publications

(15 citation statements)

References 4 publications

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“…The resulting constitutive equations for various moments have been compared with the results obtained by Monte Carlo (MC) simulations in [7,29] and are very encouraging in support of the maximum entropy ansatz. In these models the production terms are modeled by means of a fitting of the MC data for both homogeneous and inhomogeneous doped semiconductors.…”

Section: Introductionmentioning

confidence: 71%

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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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Section: Introductionmentioning

confidence: 71%

“…In both cases the relaxation times are obtained as functions of energy W from fitting to MC simulation for the same benchmark device (see [29]). The reduced model resembles strongly the so-called energy-transport models obtained from the semiclassical BTE by a Chapman-Enskog-like procedure [1].…”

Section: Semiconductor Equationsmentioning

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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“…there are more unknowns than equations. The Maximum Entropy Principle leads to a systematic way for obtaining constitutive relations on the basis of the information theory [20], as already proved successfully in the bulk case [21][22][23][24][25], and for quantum well structures [26], [27]. Actually, in a semiconductor electrons interact with phonons describing the thermal vibrations of the ions placed at the points of the crystal lattice.…”

Section: Extended Hydrodynamic Modelmentioning

confidence: 98%

Electron transport in silicon nanowires having different cross-sections

Muscato

Castiglione

2016

Communications in Applied and Industrial Mathematics

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Transport phenomena in silicon nanowires with different cross-section are investigated using an Extended Hydrodynamic model, coupled to the Schrödinger-Poisson system. The model has been formulated by closing the moment system derived from the Boltzmann equation on the basis of the maximum entropy principle of Extended Thermodynamics, obtaining explicit closure relations for the high-order fluxes and the production terms. Scattering of electrons with acoustic and non polar optical phonons have been taken into account. The bulk mobility is evaluated for square and equilateral triangle cross-sections of the wire.

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“…The MEP gives a systematic way for obtaining constitutive relations on the basis of information theory [13][14][15]. Such an approach has been used in the simulation of 2D nanoscale structures [33,34] and for simulating the 3D electron transport in sub-micrometric devices, in the case in which the lattice is considered as a thermal bath with constant temperature [35][36][37][38] or when the phonons are off-equilibrium [39][40][41][42][43][44][45]. We shall assume that the electron gas is sufficiently dilute, then the entropy density can be taken as the classical limit of the expression arising in the Fermi statistics, i.e.,…”

Section: Maximum Entropy Principle and Closure Relationsmentioning

confidence: 99%

A Hydrodynamic Model for Silicon Nanowires Based on the Maximum Entropy Principle

Muscato

Castiglione

2016

Entropy

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Silicon nanowires (SiNW) are quasi-one-dimensional structures in which the electrons are spatially confined in two directions, and they are free to move along the axis of the wire. The spatial confinement is governed by the Schrödinger-Poisson system, which must be coupled to the transport in the free motion direction. For devices with the characteristic length of a few tens of nanometers, the transport of the electrons along the axis of the wire can be considered semiclassical, and it can be dealt with by the multi-sub-band Boltzmann transport equations (MBTE). By taking the moments of the MBTE, a hydrodynamic model has been formulated, where explicit closure relations for the fluxes and production terms (i.e., the moments on the collisional operator) are obtained by means of the maximum entropy principle of extended thermodynamics, including the scattering of electrons with phonons, impurities and surface roughness scattering. Numerical results are shown for a SiNW transistor.

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Monte Carlo and hydrodynamic simulationof a one dimensional n⁺ ‐ n ‐ n⁺ silicon diode

Cited by 16 publications

References 4 publications

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

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

Electron transport in silicon nanowires having different cross-sections

A Hydrodynamic Model for Silicon Nanowires Based on the Maximum Entropy Principle

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Monte Carlo and hydrodynamic simulationof a one dimensional n+ ‐ n ‐ n+ silicon diode

Cited by 16 publications

References 4 publications

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

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

Electron transport in silicon nanowires having different cross-sections

A Hydrodynamic Model for Silicon Nanowires Based on the Maximum Entropy Principle

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Monte Carlo and hydrodynamic simulationof a one dimensional n⁺ ‐ n ‐ n⁺ silicon diode