Approach to Phonon Relaxation Time and Mean Free Path in Nonlinear Lattices

2021 ◽  
Vol 38 (4) ◽  
pp. 044401
Author(s):  
Yue Liu ◽  
Dahai He
Keyword(s):  
Relaxation Time ◽  
Free Path ◽  
Mean Free Path ◽  
Nonlinear Lattices ◽  
Phonon Relaxation Time

scholarly journals Analysis of Transport Properties of the Randomly Moving Electrons in Metals

2019 ◽  
Vol 26 (2) ◽  
pp. 147-153
Author(s):  
Villius PALENSKIS ◽  
Evaras ŽITKEVIČIUS
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Free Path ◽  
Mean Free Path ◽  
Periodic Lattice ◽  
Simple Method ◽  
Temperature Range ◽  
Average Diffusion Coefficient ◽  
Average Diffusion ◽  
Average Relaxation Time

In this critical analysis on the base of randomly moving (RM) electrons, presented the resistivity dependence on temperature for elemental metals both above and below the Debye’s temperatures. There also are presented the general relationships for estimation of the average diffusion coefficient, the average velocity, mean free path and average relaxation time of RM electrons on the Fermi surface at mentioned temperature range. It is shown that the scattering of RM electrons mainly is due to electronic defects associated with distortion of the periodic potential distribution in the periodic lattice, and accounting the exchange of the thermal energies between phonon and RM electron. The calculation results of resistivity dependence on temperature in the temperature range from 1 K to 900 K are demonstrated for Au and W and compared with the experimental data. There also is presented the simple method for determination of the basic kinetic characteristic dependences on temperature only from the resistivity dependence on temperature. It is at first time determined for Au and W the temperature dependences of the mean free path, average diffusion coefficient, average relaxation time of RM electrons from 1 K to 900 K.

Simulation of Unsteady Small Heat Source Effects in Sub-Micron Heat Conduction

2003 ◽  
Vol 125 (5) ◽  
pp. 896-903 ◽  
Author(s):  
Sreekant V. J. Narumanchi ◽  
Jayathi Y. Murthy ◽  
Cristina H. Amon
Keyword(s):  
Relaxation Time ◽  
Heat Source ◽  
Time Scales ◽  
Electric Fields ◽  
Hot Spot ◽  
Mean Free Path ◽  
Boltzmann Transport ◽  
Electron Phonon Interaction ◽  
Relaxation Time Approximation ◽  
Phonon Relaxation Time

In compact transistors, large electric fields near the drain side create hot spots whose dimensions are smaller than the phonon mean free path in the medium. In this paper, we present a study of unsteady hot spot behavior. The unsteady gray phonon Boltzmann transport equation (BTE) is solved in the relaxation time approximation using a finite volume method. Electron-phonon interaction is represented as a heat source term in the phonon BTE. The evolution of the temperature profile is governed by the interaction of four competing time scales: the phonon residence time in the hot spot and in the domain, the duration of the energy source, and the phonon relaxation time. The influence of these time scales on the temperature is investigated. Both boundary scattering and heat source localization effects are observed to have considerable impact on the thermal predictions. Comparison of BTE solutions with conventional Fourier diffusion analysis reveals significant discrepancies.

Built-in-polarization effect on relaxation time and mean free path of phonons in AlxGa1−xN/GaN heterostructure

2016 ◽  
Vol 30 (08) ◽  
pp. 1650097
Author(s):  
Sushant Kumar Sahoo ◽  
Anju Pansari ◽  
Bijaya Kumar Sahoo
Keyword(s):  
Relaxation Time ◽  
Free Path ◽  
Electron Scattering ◽  
Phonon Scattering ◽  
Mean Free Path ◽  
Polarization Field ◽  
Scattering Mechanisms ◽  
Gan Heterostructure ◽  
Debye Frequency ◽  
Phonon Velocity

In this paper, we have theoretically investigated the effect of built-in-polarization field on various phonon scattering mechanisms in Al[Formula: see text]Ga[Formula: see text]N/GaN heterostructure. The built-in-polarization field enhances the elastic constant, phonon velocity and Debye frequency of Al[Formula: see text]Ga[Formula: see text]N alloy. As a result, various phonon scattering mechanisms are modified. Important phonon scattering mechanisms such as normal scattering, Umklapp scattering, point defect scattering, dislocation scattering and phonon–electron scattering processes have been considered. The combined relaxation time due to above scattering mechanisms has also been computed as a function of phonon frequency for various Al contents at room temperature. Our result shows that built-in-polarization field suppresses scattering rates leading to enhanced combined relaxation time. Increased relaxation time implies longer phonon mean free path and enhanced optical and thermal transport properties. The result can be used to determine the effect of built-in-polarization field on optical and thermal properties of Al[Formula: see text]Ga[Formula: see text]N/GaN heterostructure and will be useful, particularly, for improvement of thermoelectric performance of Al[Formula: see text]Ga[Formula: see text]N/GaN heterostructure through polarization engineering.

scholarly journals Prediction of Spectral Phonon Mean Free Path and Thermal Conductivity with Applications to Thermoelectrics and Thermal Management: A Review

2014 ◽  
Vol 2014 ◽  
pp. 1-25 ◽  
Author(s):  
Tianli Feng ◽  
Xiulin Ruan
Keyword(s):  
Thermal Conductivity ◽  
Relaxation Time ◽  
Free Path ◽  
Thermal Management ◽  
Lattice Dynamics ◽  
Mean Free Path ◽  
Dynamics Simulation ◽  
Mode Analysis ◽  
Anharmonic Lattice ◽  
Dynamics Calculation

We give a review of the theoretical approaches for predicting spectral phonon mean free path and thermal conductivity of solids. The methods can be summarized into two categories: anharmonic lattice dynamics calculation and molecular dynamics simulation. In the anharmonic lattice dynamics calculation, the anharmonic force constants are used first to calculate the phonon scattering rates, and then the Boltzmann transport equations are solved using either standard single mode relaxation time approximation or the Iterative Scheme method for the thermal conductivity. The MD method involves the time domain or frequency domain normal mode analysis. We present the theoretical frameworks of the methods for the prediction of phonon dispersion, spectral phonon relaxation time, and thermal conductivity of pure bulk materials, layer and tube structures, nanowires, defective materials, and superlattices. Several examples of their applications in thermal management and thermoelectric materials are given. The strength and limitations of these methods are compared in several different aspects. For more efficient and accurate predictions, the improvements of those methods are still needed.

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