Moment equations for electrons in semiconductors: comparison of spherical harmonics and full moments

Liotta, S.F.; Struchtrup, Henning

doi:10.1016/s0038-1101(99)00215-4

Cited by 20 publications

(9 citation statements)

References 17 publications

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“…The comparison of results obtained by the models 4MM and DDAn with results of the conventional driftdiffusion model DDAc as well as kinetically obtained results has pointed out that the new approach strongly increases the accuracy of fluid models for the description of electron transport in nonthermal plasmas. Since similar partial differential equations for electrons arise in the theoretical description of semiconductors [47][48][49], it potentially improves the theoretical description of electrons in semiconductor devices, too.…”

Section: Discussionmentioning

confidence: 99%

Derivation of Moment Equations for the Theoretical Description of Electrons in Nonthermal Plasmas

Becker¹,

Loffhagen²

2013

APM

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The derivation of moment equations for the theoretical description of electrons is of interest for modelling of gas discharge plasmas and semiconductor devices. Usually, certain artificial closure assumptions are applied in order to derive a closed system of moment equations from the electron Boltzmann equation. Here, a novel four-moment model for the description of electrons in nonthermal plasmas is derived by an expansion of the electron velocity distribution function in Legendre polynomials. The proposed system of partial differential equations is consistently closed by definition of transport coefficients that are determined by solving the electron Boltzmann equation and are then used in the fluid calculations as function of the mean electron energy. It is shown that the four-moment model can be simplified to a new drift-diffusion approximation for electrons without loss of accuracy, if the characteristic frequency of the electric field alteration in the discharge is small in comparison with the momentum dissipation frequency of the electrons. Results obtained by the proposed fluid models are compared to those of a conventional drift-diffusion approximation as well as to kinetic results using the example of low pressure argon plasmas. It is shown that the results provided by the new approaches are in good agreement with kinetic results and strongly improve the accuracy of fluid descriptions of gas discharges.

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Section: Discussionmentioning

confidence: 99%

Derivation of Moment Equations for the Theoretical Description of Electrons in Nonthermal Plasmas

Becker¹,

Loffhagen²

2013

APM

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“…In the second equality, we show an equivalent way of performing the spherical harmonic expansion in Projected Symmetric Trace-Free (PSTF) tensors in n a basis [26, [57][58][59]. The PSTF part of any index-tensor is given by [26, [61][62][63][64],…”

Section: Ii2 Covariant and Multipole Moment Decomposition Of Observablesmentioning

confidence: 99%

Consequences of using a smooth cosmic distance in a lumpy universe: I

Umeh¹

2022

Preprint

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How do we appropriately fit a model based on an idealised Friedmann-Lemaıtre Robertson-Walker (FLRW) spacetime to observations made from a single location in a lumpy Universe? We address this question for surveys that measure the imprints of the Baryon Acoustic Oscillation (BAO) in galaxy distribution and the peak apparent magnitude of the type 1A supernova (SN1A). These observables are related to the cosmological model through the Alcock-Paczynski parameters and the distance-redshift relation. Using the corresponding inhomogeneous spacetime expressions of these as observed data, we perform a parameter inference assuming that the background FLRW model is the correct model of the universe. This process allows us to estimate the best fit Hubble rate and the deceleration parameter. We find that the inferred Hubble rate from the monopole of the Alcock-Paczynski parameters is in tension with the Hubble rate determined using the distance-redshift relation. The latter gives the best fit Hubble rate for the cosmological expansion. The constraint on the Hubble rate from the Alcock-Paczynski parameters is contaminated by the environment. When the environmental contribution is restricted to modes in the Hubble flow, we find about (9-12)% discrepancy in the Hubble rate. Finally, we comment on the insufficiency of the method of cosmography in constraining the deceleration parameter. CONTENTS

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“…According to Staratton [28], the electron ic temperature has no physical mean ing, unless the distribution function is a displaced Maxwellian as described by equation (15). However, the Maxwellian d istribution is only valid near equilibriu m, and in highly doped regions, where carrier-carrier co llisions are dominant.…”

Section: About the Definition Of The Carrier Temperaturementioning

confidence: 99%

“…In addition, the so-called energy transport model (ETM) and mo ment methods [27], which are somet imes called the hydrodynamic model (HDM), have been also used to solve the BT E in the hot carrier regime. In the ETM approach the distribution function is decomposed into an even and odd parts and the collision term is expressed using a microscopic relaxation time appro ximat ion [28].…”

Section: Introductionmentioning

confidence: 99%

Yet Another Hydrodynamic Model with Correlated Parameters for Silicon Devices

El-Saba¹

2013

MSSE

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In this paper we present a complete hydrodynamic model (HDM) describing the transport of charge carriers in semiconductor devices with arbitrary band structure. The model is appended with advanced physical models fo r almost all the physical parameters of interest in modern Si Devices. These parameters are inter-related v ia the carrier energy relaxation time. An improved analytical model of the carrier heat flu x, on the basis of a fourth mo ment of the Bolt zmann transport equation (BTE), is also presented. In order to resolve the heat evacuation problems in SOI and power devices, the model is coupled with a lattice heat conservation equation. The transport of hot carriers is simu lated, according to the proposed HDM and the results are compared with the conventional data obtained using the drift-diffusion model (DDM) and MC simu lation. We show from the HD simu lation, the effect of the energy relaxat ion time value on the hot carrier transport in general and the breakdown voltage in particu lar, of both MOSFETs and bipolar devices.

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Moment equations for electrons in semiconductors: comparison of spherical harmonics and full moments

Cited by 20 publications

References 17 publications

Derivation of Moment Equations for the Theoretical Description of Electrons in Nonthermal Plasmas

Derivation of Moment Equations for the Theoretical Description of Electrons in Nonthermal Plasmas

Consequences of using a smooth cosmic distance in a lumpy universe: I

Yet Another Hydrodynamic Model with Correlated Parameters for Silicon Devices

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