A hierarchy of hydrodynamic models for silicon carbide semiconductors

Muscato, Orazio; Stefano, Vincenza Di

doi:10.1515/caim-2017-0013

Cited by 1 publication

(1 citation statement)

References 27 publications

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“…The variables T The number of the unknowns present in the evolution equations is greater than the number of the equations, therefore one needs constitutive equations for the extravariables. A physically well sound method to get these constitutive equations is based on the exploitation of MEP [30][31][32][33][34][35]. This principle states that the occupation number can be approximated by that which maximizes the total entropy under the constraints that it reproduces the moments which have been chosen to describe the phonon state.…”

Section: Macroscopic Modelsmentioning

confidence: 99%

Exploitation of the Maximum Entropy Principle in the Study of Thermal Conductivity of Silicon, Germanium and Graphene

Mascali¹

2022

Energies

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In this paper, we review the application of a recent formula for the lattice thermal conductivity to silicon and germanium, which are two of the most commonly used materials in electronic devices, and to graphene, one the most promising new materials. The formula, which is based on a hierarchy of macroscopic models that generalize the Cattaneo equation, is capable of reproducing the results achieved by means of the well-known Callaway formula. In semiconductors, energy transport is largely due to acoustic phonons, therefore one can choose suitable moments of their occupation numbers as variables of the models. Equations determining the time evolution of these state variables are derived from the Boltzmann–Peierls transport equation by integration, while the maximum entropy principle (MEP) is used to obtain closure relations for the extra variables. All relevant phonon scattering mechanisms are taken into account. We present numerical results regarding the steady-state and dynamical thermal conductivities of silicon, germanium, and graphene, showing their main characteristics and how these are affected by the various scatterings. The results are in good qualitative and quantitative agreement with those in the literature, confirming that MEP is a valid method for developing macroscopic models of charge and energy transport in semiconductor materials.

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Section: Macroscopic Modelsmentioning

confidence: 99%

Exploitation of the Maximum Entropy Principle in the Study of Thermal Conductivity of Silicon, Germanium and Graphene

Mascali¹

2022

Energies

View full text Add to dashboard Cite

show abstract

A hierarchy of hydrodynamic models for silicon carbide semiconductors

Cited by 1 publication

References 27 publications

Exploitation of the Maximum Entropy Principle in the Study of Thermal Conductivity of Silicon, Germanium and Graphene

Exploitation of the Maximum Entropy Principle in the Study of Thermal Conductivity of Silicon, Germanium and Graphene

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