Abstract
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.
Highlights
In recent years, increasing attention has been focused on seeking novel structures and materials with desired thermal properties, especially thermal conductivity
Analytical models of spectral phonon properties are advantageous in their clear physical insights, but they usually contain empirical fitting parameters, and this limitation has motivated the development of numerical methods based on first principles and molecular dynamics that can predict these spectral properties from their atomic structure, without fitting Journal of Nanomaterials parameters and with greater accuracy
The results reveal typical features of phonon relaxation time in bulk materials: (a) acoustic phonons generally have much higher relaxation times than optical phonons, (b) for acoustic modes, the relaxation times always decrease with increasing frequency except for the high-frequency ranges which often show opposite trend, such phenomenon is found in other materials such as argon [67, 102], silicon [143], and germanium [151], (c) the value of α in frequency dependence relation τ ∼ ω−α of the acoustic phonon often deviates from 2 and ranges from 0.5 to 4, (d) τ of optical mode has weak frequency dependence, and (e) increasing temperature typically shortens the phonon relaxation time and mean free path
Summary
In recent years, increasing attention has been focused on seeking novel structures and materials with desired thermal properties, especially thermal conductivity. Analytical models have been used by Balandin and Wang to estimate frequency-dependent phonon group velocity and various phonon scattering rates including phonon-phonon, phononimpurity, and phonon-boundary scattering processes They used this approach to observe the strong modification of acoustic phonon group velocity and enhanced phonon scattering rate due to boundary scattering in semiconductor quantum wells, so as to successfully explain their significantly reduced lattice thermal conductivity [2].
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