scholarly journals Moment Equations with Maximum Entropy Closure for Carrier Transport in Semiconductor Devices: Validation in Bulk Silicon

VLSI Design ◽  
2000 ◽  
Vol 10 (4) ◽  
pp. 335-354 ◽  
Author(s):  
A. M. Anile ◽  
O. Muscato ◽  
V. Romano
Keyword(s):  
Maximum Entropy ◽  
Moment Method ◽  
Carrier Transport ◽  
Maximum Entropy Principle ◽  
Bulk Silicon ◽  
Moment Equations ◽  
Balance Equations ◽  
Entropy Principle ◽  
Closure Relations ◽  
The Moment

Balance equations based on the moment method for the transport of electrons in silicon semiconductors are presented. The energy band is assumed to be described by the Kane dispersion relation. The closure relations have been obtained by employing the maximum entropy principle.The validity of the constitutive equations for fluxes and production terms of the balance equations has been checked with a comparison to detailed Monte Carlo simulations in the case of bulk silicon.

scholarly journals Maximum Entropy Principle within A Total Energy Scheme for Hot-carrier Transport in Semiconductor Devices

VLSI Design ◽  
2001 ◽  
Vol 13 (1-4) ◽  
pp. 381-386 ◽  
Author(s):  
M. Trovato ◽  
L. Reggiani
Keyword(s):  
Maximum Entropy ◽  
Carrier Transport ◽  
Maximum Entropy Principle ◽  
Average Energy ◽  
Band Model ◽  
Hot Carrier ◽  
Hydrodynamic Calculations ◽  
Entropy Principle ◽  
The Moment ◽  
Total Average

By extending the maximum entropy principle within a scheme in total average energy we obtain a closed system of hydrodynamic equations for a full nonparabolic band model in which all the unknown constitutive functions are completely determined. The theory is validated by comparing hydrodynamic calculations with Monte Carlo simulations performed for bulk and submicron Si structures at 300 K. In the general framework of the moment theory a systematic study of small-signal response functions is provided.

scholarly journals Electron transport in silicon nanowires having different cross-sections

2016 ◽  
Vol 7 (2) ◽  
pp. 8-25 ◽  
Author(s):  
Orazio Muscato ◽  
Tina Castiglione
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Silicon Nanowires ◽  
Maximum Entropy Principle ◽  
Optical Phonons ◽  
Poisson System ◽  
Moment System ◽  
Entropy Principle ◽  
Closure Relations ◽  
The Moment

AbstractTransport 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.

On Singular Closures for the 5-Moment System in Kinetic Gas Theory

2015 ◽  
Vol 17 (2) ◽  
pp. 371-400 ◽  
Author(s):  
Roman Pascal Schaerer ◽  
Manuel Torrilhon
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Second Order ◽  
Gas Flows ◽  
Moment Equations ◽  
Moment System ◽  
Entropy Principle ◽  
Kinetic Gas Theory ◽  
Closure Theory ◽  
Non Equilibrium

AbstractMoment equations provide a flexible framework for the approximation of the Boltzmann equation in kinetic gas theory. While moments up to second order are sufficient for the description of equilibrium processes, the inclusion of higher order moments, such as the heat flux vector, extends the validity of the Euler equations to non-equilibrium gas flows in a natural way.Unfortunately, the classical closure theory proposed by Grad leads to moment equations, which suffer not only from a restricted hyperbolicity region but are also affected by non-physical sub-shocks in the continuous shock-structure problem if the shock velocity exceeds a critical value. Amore recently suggested closure theory based on the maximum entropy principle yields symmetric hyperbolic moment equations. However, if moments higher than second order are included, the computational demand of this closure can be overwhelming. Additionally, it was shown for the 5-moment system that the closing flux becomes singular on a subset of moments including the equilibrium state.Motivated by recent promising results of closed-form, singular closures based on the maximum entropy approach, we study regularized singular closures that become singular on a subset of moments when the regularizing terms are removed. In order to study some implications of singular closures, we use a recently proposed explicit closure for the 5-moment equations. We show that this closure theory results in a hyperbolic system that can mitigate the problem of sub-shocks independent of the shock wave velocity and handle strongly non-equilibrium gas flows.

scholarly journals Consistent Order Approximations in Extended Thermodynamics of Polyatomic Gases

2021 ◽  
Vol 1 (2) ◽  
pp. 12-21
Author(s):  
Sebastiano Pennisi
Keyword(s):  
Maximum Entropy ◽  
Arbitrary Number ◽  
Maximum Entropy Principle ◽  
Extended Thermodynamics ◽  
The Other ◽  
Balance Equations ◽  
Polyatomic Gases ◽  
New Model ◽  
Independent Variables ◽  
Entropy Principle

In this article the known models are considered for relativistic polyatomic gases with an arbitrary number of moments, in the framework of Extended Thermodynamics. These models have the downside of being hyperbolic only in a narrow domain around equilibrium, called "hyperbolicity zone". Here it is shown how to overcome this drawback by presenting a new model which satisfies the hyperbolicity requirement for every value of the independent variables and without restrictions. The basic idea behind this new model is that hyperbolicity is limited in previous models by the approximations made there. It is here shown that hyperbolicity isn't limited also for an approximated model if terms of the same order are consistently considered, in a new way never used before in literature. To design and complete this new model, well accepted principles are used such as the "Entropy Principle" and the "Maximum Entropy Principle". Finally, new trends are analized and these considerations may require a modification of the results published so far; as a bonus, more manageable balance equations are obtained. This allows to obtain more stringent results than those so far known. For example, we will have a single quantity (the energy e) expressed by an integral and all the other constitutive functions will be expressed in terms of it and its derivatives with respect to temperature. Another useful consequence is its easier applicability to the case of diatomic and ultrarelativistic gases which are useful, at least for testing the model in simple cases.

Maximum-entropy closure for a Galerkin model of an incompressible periodic wake

2012 ◽  
Vol 700 ◽  
pp. 187-213 ◽  
Author(s):  
Bernd R. Noack ◽  
Robert K. Niven
Keyword(s):  
Maximum Entropy ◽  
Energy Levels ◽  
Maximum Entropy Principle ◽  
Mean Amplitude ◽  
Navier Stokes ◽  
Cylinder Wake ◽  
Balance Equations ◽  
Side Constraints ◽  
Entropy Principle ◽  
Good Agreement

AbstractA statistical closure is proposed for a Galerkin model of an incompressible periodic cylinder wake. This closure employs Jaynes’ maximum entropy principle to infer the probability distribution for mode amplitudes using exact statistical balance equations as side constraints. The analysis predicts mean amplitude values and modal energy levels in good agreement with direct Navier–Stokes simulation. In addition, it provides an analytical equation for the modal energy distribution.

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