Hydrodynamic modeling of electron transport in silicon quantum wires

Muscato, Orazio; Castiglione, Tina; Coco, Armando

doi:10.1088/1742-6596/906/1/012010

Cited by 4 publications

(3 citation statements)

References 28 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

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“…Macroscopic models can be derived from the kinetic one [ 17 , 19 , 30 ] by taking suitable moments of the distribution functions as state variables. Here, we present in some detail only the evolution equations of the phonon variables, and refer the interested reader to [ 17 ] for a complete treatment of the problem.…”

Section: A Macroscopic Model and The Definition Of The Second Local Temperaturementioning

confidence: 99%

About the Definition of the Local Equilibrium Lattice Temperature in Suspended Monolayer Graphene

Coco

Mascali²,

Romano

2021

Entropy

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The definition of temperature in non-equilibrium situations is among the most controversial questions in thermodynamics and statistical physics. In this paper, by considering two numerical experiments simulating charge and phonon transport in graphene, two different definitions of local lattice temperature are investigated: one based on the properties of the phonon–phonon collision operator, and the other based on energy Lagrange multipliers. The results indicate that the first one can be interpreted as a measure of how fast the system is trying to approach the local equilibrium, while the second one as the local equilibrium lattice temperature. We also provide the explicit expression of the macroscopic entropy density for the system of phonons, by which we theoretically explain the approach of the system toward equilibrium and characterize the nature of the equilibria, in the spatially homogeneous case.

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“…A new finite-difference method with an improved accuracy was proposed by the author and Russo in [18,20,17] for elliptic equations and extended to thermo-poroelastic Cauchy-Navier equations for elastic deformation [15], Euler equations for gas dynamics [11,19], electron transport in semiconductors [44,45], fluid flow in porous media for water-rock interaction [16,14]. In this approach, the ghost point values are eventually coupled each other, resulting in a bigger linear system with non-eliminated boundary conditions, solved by a multigrid approach suitably designed for ghost-point methods.…”

Section: Introductionmentioning

confidence: 99%

A multigrid ghost-point level-set method for incompressible Navier-Stokes equations on moving domains with curved boundaries

Coco

2019

Preprint

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In this paper we present a numerical approach to solve the Navier-Stokes equations on moving domains with second-order accuracy. The space discretization is based on the ghost-point method, which falls under the category of unfitted boundary methods, since the mesh does not adapt to the moving boundary. The equations are advanced in time by using Crank-Nicholson. The momentum and continuity equations are solved simultaneously for the velocity and the pressure by adopting a proper multigrid approach. To avoid the checkerboard instability for the pressure, a staggered grid is adopted, where velocities are defined at the sides of the cell and the pressure is defined at the centre. The lack of uniqueness for the pressure is circumvented by the inclusion of an additional scalar unknown, representing the average divergence of the velocity, and an additional equation to set the average pressure to zero. Several tests are performed to simulate the motion of an incompressible fluid around a moving object, as well as the lid-driven cavity tests around steady objects. The object is implicitly defined by a level-set approach, that allows a natural computation of geometrical properties such as distance from the boundary, normal directions and curvature. Different shapes are tested: circle, ellipse and flower. Numerical results show the second order accuracy for the velocity and the divergence (that decays to zero with second order) and the efficiency of the multigrid, that is comparable with the tests available in literature for rectangular domains without objects, showing that the presence of a complex-shaped object does not degrade the performance.

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Hydrodynamic modeling of electron transport in silicon quantum wires

Cited by 4 publications

References 28 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

About the Definition of the Local Equilibrium Lattice Temperature in Suspended Monolayer Graphene

A multigrid ghost-point level-set method for incompressible Navier-Stokes equations on moving domains with curved boundaries

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