Remote processes

2020 ◽  
pp. 632-648
Author(s):  
Sandip Tiwari
Keyword(s):  
Electron Transport ◽  
Transport Equation ◽  
Short Range ◽  
Phonon Scattering ◽  
Boltzmann Transport Equation ◽  
Local Effect ◽  
Seebeck Effect ◽  
Boltzmann Transport ◽  
Coulomb Interactions ◽  
High Permittivity

This chapter discusses remote processes that influence electron transport and manifest themselves in a variety of properties of interest. Coulomb and phonon-based interactions have appeared in many discussions in the text. Coulomb interactions can be short range or long range, but phonons have been treated as a local effect. At the nanoscale, the remote aspects of these interactions can become significant. An off-equilibrium distribution of phonons, in the limit of low scattering, will lead to the breakdown of the local description of phonon-electron coupling. Phonons can drag electrons, and electrons can drag phonons. Soft phonons—high permittivity—can cause stronger electron-electron interactions. So, plasmon scattering can become significant. Remote phonon scattering too becomes important. These and other such changes are discussed, together with phonon drag’s consequences for the Seebeck effect, as illustrated through the coupled Boltzmann transport equation. The importance of the zT coefficient for characterizing thermoelectric capabilities is stressed.

Prediction of Non-Equilibrium Heat Conduction Using Parallel Computation of the Phonon Boltzmann Transport Equation

2014 ◽  
Author(s):  
Syed A. Ali ◽  
Gautham Kollu ◽  
Sandip Mazumder ◽  
P. Sadayappan
Keyword(s):  
Heat Conduction ◽  
Transport Equation ◽  
Parallel Computation ◽  
Large Scale ◽  
Phonon Scattering ◽  
Boltzmann Transport Equation ◽  
Computational Time ◽  
Spectral Space ◽  
Boltzmann Transport ◽  
Non Equilibrium

Non-equilibrium heat conduction, as occurring in modern-day sub-micron semiconductor devices, can be predicted effectively using the Boltzmann Transport Equation (BTE) for phonons. In this article, strategies and algorithms for large-scale parallel computation of the phonon BTE are presented. An unstructured finite volume method for spatial discretization is coupled with the control angle discrete ordinates method for angular discretization. The single-time relaxation approximation is used to treat phonon-phonon scattering. Both dispersion and polarization of the phonons are accounted for. Three different parallelization strategies are explored: (a) band-based, (b) direction-based, and (c) hybrid band/cell-based. Subsequent to validation studies in which silicon thin-film thermal conductivity was successfully predicted, transient simulations of non-equilibrium thermal transport were conducted in a three-dimensional device-like silicon structure, discretized using 604,054 tetrahedral cells. The angular space was discretized using 400 angles, and the spectral space was discretized into 40 spectral intervals (bands). This resulted in ∼9.7×109 unknowns, which are approximately 3 orders of magnitude larger than previously reported computations in this area. Studies showed that direction-based and hybrid band/cell-based parallelization strategies resulted in similar total computational time. However, the parallel efficiency of the hybrid band/cell-based strategy — about 88% — was found to be superior to that of the direction-based strategy, and is recommended as the preferred strategy for even larger scale computations.

Size and edge roughness dependence of thermal conductivity for vacancy-defective graphene ribbons

2015 ◽  
Vol 17 (14) ◽  
pp. 8822-8827 ◽  
Author(s):  
Guofeng Xie ◽  
Yulu Shen
Keyword(s):  
Thermal Conductivity ◽  
Transport Equation ◽  
Phonon Scattering ◽  
Boltzmann Transport Equation ◽  
Boundary Scattering ◽  
Boltzmann Transport ◽  
Single Vacancy ◽  
Edge Roughness ◽  
Defective Graphene

By incorporating the phonon–phonon scattering, phonon-boundary scattering and phonon-vacancy scattering into the linearized Boltzmann transport equation, we theoretically investigate the effects of size and edge roughness on thermal conductivity of single vacancy-defective graphene ribbons.

Lattice Boltzmann Modeling of Ultrafast Laser Heating on Metal Film

2013 ◽  
Author(s):  
Dadong Wang ◽  
Yanbao Ma
Keyword(s):  
Transport Equation ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Laser Heating ◽  
Metal Film ◽  
Phonon Scattering ◽  
Boltzmann Transport Equation ◽  
Ultrafast Laser ◽  
Boltzmann Transport ◽  
Boltzmann Method

Lattice Boltzmann method based on Boltzmann transport equation is developed to simulate the nanoscale heat transport in metal film. The Boltzmann transport equation is applicable to describe both electron and phonon scattering processes: the absorption of photon energy by electrons and the subsequent heating of metal lattice (phonons) through electron-phonon collisions. We show that the Boltzmann transport equation can give rise to the well-known two-temperature model. To validate our numerical tool, ultrafast laser heating on metal film is analyzed by lattice Boltzmann method and finite difference method based on two-step model separately, and exactly the same results are obtained. The predicted transient reflectivity changes agree with picosecond laser heating experiments data also.

scholarly journals Calculation of the effective thermal conductivity of a superlattice based on the Boltzmann transport equation using first-principle calculations

2020 ◽  
Vol 22 (3) ◽  
pp. 190-196
Author(s):  
K. K. Abgaryan ◽  
I. S. Kolbin
Keyword(s):  
Experimental Data ◽  
Thermal Conductivity ◽  
Transport Equation ◽  
Thermal Conductivity Coefficient ◽  
Phonon Scattering ◽  
Boltzmann Transport Equation ◽  
First Principle ◽  
Boltzmann Transport ◽  
First Principle Calculations ◽  
Molecular Dynamics Methods

In this work, we calculate the effective thermal conductivity coefficient for a binary semiconductor heterostructure using the GaAs/AlAs superlattice as an example. Different periods of layers and different ambient temperatures are considered. At the scale under consideration, the use of models based on the Fourier law is very limited, since they do not take into account the quantum-mechanical properties of materials, which gives a strong discrepancy with experimental data. On the other hand, the use of molecular dynamics methods allows us to obtain accurate solutions, but they are significantly more demanding on computing resources and also require solving a non-trivial problem of potential selection. When considering nanostructures, good results were shown by methods based on the solution of the Boltzmann transport equation for phonons; they allow one to obtain a fairly accurate solution, while having less computational complexity than molecular dynamics methods. To calculate the thermal conductivity coefficient, a modal suppression model is used that approximates the solution of the Boltzmann transport equation for phonons. The dispersion parameters and phonon scattering parameters are obtained from first-principle calculations. The work takes into account 2-phonon (associated with isotopic disorder and barriers) and 3-phonon scattering processes. To increase the accuracy of calculations, the non-digital profile of the distribution of materials among the layers of the superlattice is taken into account. The obtained results are compared with experimental data showing good agreement.

Solving Nongray Boltzmann Transport Equation in Gallium Nitride

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Ajit K. Vallabhaneni ◽  
Liang Chen ◽  
Man P. Gupta ◽  
Satish Kumar
Keyword(s):  
Gallium Nitride ◽  
Transport Equation ◽  
Thermal Transport ◽  
Hot Spot ◽  
Boltzmann Transport Equation ◽  
Significant Loss ◽  
Computational Time ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Fourier Model

Several studies have validated that diffusive Fourier model is inadequate to model thermal transport at submicron length scales. Hence, Boltzmann transport equation (BTE) is being utilized to improve thermal predictions in electronic devices, where ballistic effects dominate. In this work, we investigated the steady-state thermal transport in a gallium nitride (GaN) film using the BTE. The phonon properties of GaN for BTE simulations are calculated from first principles—density functional theory (DFT). Despite parallelization, solving the BTE is quite expensive and requires significant computational resources. Here, we propose two methods to accelerate the process of solving the BTE without significant loss of accuracy in temperature prediction. The first one is to use the Fourier model away from the hot-spot in the device where ballistic effects can be neglected and then couple it with a BTE model for the region close to hot-spot. The second method is to accelerate the BTE model itself by using an adaptive model which is faster to solve as BTE for phonon modes with low Knudsen number is replaced with a Fourier like equation. Both these methods involve choosing a cutoff parameter based on the phonon mean free path (mfp). For a GaN-based device considered in the present work, the first method decreases the computational time by about 70%, whereas the adaptive method reduces it by 60% compared to the case where full BTE is solved across the entire domain. Using both the methods together reduces the overall computational time by more than 85%. The methods proposed here are general and can be used for any material. These approaches are quite valuable for multiscale thermal modeling in solving device level problems at a faster pace without a significant loss of accuracy.

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