Phonon Mean Free Path Distribution Research Articles

Phonon vortex dynamics in graphene ribbon by solving Boltzmann transport equation with ab initio scattering rates

In this work, we study thermal phonon vortex in graphene ribbon by a discrete-ordinate solution of phonon Boltzmann equation under Callaway's dual relaxation model. The phonon scattering rates of normal and resistive processes are acquired from ab initio calculation without need of any empirical input parameters. The temperature, size and isotope effects on transition from phonon vortex transport to conventional Fourier's heat conduction in both simple and complex geometries are investigated. The physical mechanism for the evolution of phonon vortex is declared by wide phonon mean free path distribution of resistive processes. A hierarchical vortex series is obtained with primary, secondary and terniary vortexes in a complicated geometry. The present work provides an accurate and efficient multi-scale numerical framework for modeling hydrodynamic phonon transport in high-thermal-conductivity materials and also sheds light on the heat dissipation applications.

Thermal conductivity of hexagonal Si, Ge, and Si1-xGex alloys from first-principles

Hexagonal Si and Ge with a lonsdaleite crystal structure are allotropes of silicon and germanium that have recently been synthesized. These materials as well as their alloys are promising candidates for novel applications in optoelectronics. In this paper, we systematically study the phonon transport and thermal conductivity of hexagonal Si, Ge, and their alloys by using the first-principle-based Peierls-Boltzmann transport equation approach. Both three-phonon and four-phonon scatterings are taken into account in the calculations as the phonon scattering mechanisms. The thermal conductivity anisotropy of these materials is identified. While the thermal conductivity parallel to the hexagonal plane for hexagonal Si and Ge is found to be larger than that perpendicular to the hexagonal plane, alloying effectively tunes the thermal conductivity anisotropy by suppressing the thermal conductivity contributions from the middle-frequency phonons. The importance of four-phonon scatterings is assessed by comparing the results with the calculations without including four-phonon scatterings. We find that four-phonon scatterings cannot be ignored in hexagonal Si and Ge as the thermal conductivity would be overestimated by around 10% (40%) at 300 K (900) K. In addition, the phonon mean free path distribution of hexagonal Si, Ge, and their alloys is also discussed.

Monte Carlo simulation of single-crystalline PbSe nanowire thermal conductivity using first-principle phonon properties

Prior experimental studies showed that nanowires are promising structures for improving the thermoelectric performance of practical thermoelectric materials due to the strongly induced phonon-boundary scattering. However, few studies examined the impact of phonon-boundary scattering on the thermal conductivity of thermoelectric nanowires from a first-principle approach. In this work, we systematically study the role of phonon-boundary scattering with different boundary specularities on the thermal conductivity of PbSe nanowires by rigorously solving the full phonon Boltzmann transport equation without any adjustable parameters. We observe significant thermal conductivity reduction for rough PbSe nanowires with diameters less than a few hundred nanometers. The reduction reaches ∼40% for 10 nm thick, rough PbSe nanowires at room temperature. The diameter-dependent thermal conductivities are found to contain important information about the phonon mean free path distribution from a standard reconstruction algorithm. The simulation results are important for fundamental understanding of nanoscale thermal transport in thermoelectric materials and will guide the future design of thermoelectric devices to achieve better energy conversion efficiency.

Monte Carlo study of temperature-dependent non-diffusive thermal transport in Si nanowires

Non-diffusive thermal transport has gained extensive research interest recently due to its important implications on fundamental understanding of material’s phonon mean free path distributions and many nanoscale energy applications. In this work, we systematically investigate the role of boundary scattering and nanowire length on the non-diffusive thermal transport in thin silicon nanowires by rigorously solving the phonon Boltzmann transport equation (BTE) using a variance reduced Monte Carlo technique across a range of temperatures. The simulations use the complete phonon dispersion and spectral lifetime data obtained from first-principle density function theory calculations as input without any adjustable parameters. Our BTE simulation results show that the nanowire length plays an important role in determining the thermal conductivity of silicon nanowires. In addition, our simulation results suggest significant phonon confinement effect for the previously measured silicon nanowires. These findings are important for a comprehensive understanding of microscopic non-diffusive thermal transport in silicon nanowires.

Variational approach to extracting the phonon mean free path distribution from the spectral Boltzmann transport equation

The phonon Boltzmann transport equation (BTE) is a powerful tool for studying non-diffusive thermal transport. Here, we develop a new universal variational approach to solving the BTE that enables extraction of phonon mean free path (MFP) distributions from experiments exploring non-diffusive transport. By utilizing the known Fourier solution as a trial function, we present a direct approach to calculating the effective thermal conductivity from the BTE. We demonstrate this technique on the transient thermal grating (TTG) experiment, which is a useful tool for studying non-diffusive thermal transport and probing the mean free path (MFP) distribution of materials. We obtain a closed form expression for a suppression function that is materials dependent, successfully addressing the non-universality of the suppression function used in the past, while providing a general approach to studying thermal properties in the non-diffusive regime.

Measuring Phonon Mean Free Path Distributions by Probing Quasiballistic Phonon Transport in Grating Nanostructures.

Heat conduction in semiconductors and dielectrics depends upon their phonon mean free paths that describe the average travelling distance between two consecutive phonon scattering events. Nondiffusive phonon transport is being exploited to extract phonon mean free path distributions. Here, we describe an implementation of a nanoscale thermal conductivity spectroscopy technique that allows for the study of mean free path distributions in optically absorbing materials with relatively simple fabrication and a straightforward analysis scheme. We pattern 1D metallic grating of various line widths but fixed gap size on sample surfaces. The metal lines serve as both heaters and thermometers in time-domain thermoreflectance measurements and simultaneously act as wire-grid polarizers that protect the underlying substrate from direct optical excitation and heating. We demonstrate the viability of this technique by studying length-dependent thermal conductivities of silicon at various temperatures. The thermal conductivities measured with different metal line widths are analyzed using suppression functions calculated from the Boltzmann transport equation to extract the phonon mean free path distributions with no calibration required. This table-top ultrafast thermal transport spectroscopy technique enables the study of mean free path spectra in a wide range of technologically important materials.

Improved Thermoelectric Performance of Silver Nanoparticles‐Dispersed Bi2Te3 Composites Deriving from Hierarchical Two‐Phased Heterostructure

A practical and feasible bottom‐up chemistry approach is demonstrated to dramatically enhance thermoelectric properties of the Bi2Te3 matrix by means of exotically introducing silver nanoparticles (AgNPs) for constructing thermoelectric composites with the hierarchical two‐phased heterostructure. By regulating the content of AgNPs and fine‐tuning the architecture of nanostructured thermoelectric materials, more heat‐carrying phonons covering the broad phonon mean free path distribution range can be scattered. The results show that the uniformly dispersed AgNPs not only effectively suppress the growth of Bi2Te3 grains, but also introduce nanoscale precipitates and form new interfaces with the Bi2Te3 matrix, resulting in a hierarchical two‐phased heterostructure, which causes intense scattering of phonons with multiscale mean free paths, and therefore significantly reduce the lattice thermal conductivity. Meanwhile, the improved power factor is maintained due to low‐energy electron filtering and excellent electrical transport property of Ag itself. Consequently, the maximum ZT is amazingly found to be enhanced by 304% arising from the hierarchical heterostructure when the AgNPs content reaches 2.0 vol%. This study offers an easily scalable and low‐cost route to construct a wide range of multiscale hierarchically heterostructured bulk composites with significant enhancement of thermoelectric performance.

Lattice thermal conductivity of Bi, Sb, and Bi-Sb alloy from first principles

Using first principles, we calculate the lattice thermal conductivity of Bi, Sb, and Bi-Sb alloys, which are of great importance for thermoelectric and thermomagnetic cooling applications. Our calculation reveals that the ninth-neighbor harmonic and anharmonic force constants are significant; accordingly, they largely affect the lattice thermal conductivity. Several features of the thermal transport in these materials are studied: (1) the relative contributions from phonons and electrons to the total thermal conductivity as a function of temperature are estimated by comparing the calculated lattice thermal conductivity to the measured total thermal conductivity, (2) the anisotropy of the lattice thermal conductivity is calculated and compared to that of the electronic contribution in Bi, and (3) the phonon mean free path distributions, which are useful for developing nanostructures to reduce the lattice thermal conductivity, are calculated. The phonon mean free paths are found to range from 10 to 100 nm for Bi at 100 K.

Role of phonon dispersion in studying phonon mean free paths in skutterudites

Experimental thermal conductivity of bulk materials are often modeled using Debye approximation together with functional forms of relaxation time with fitting parameters. While such models can fit the temperature dependence of thermal conductivity of bulk materials, the Debye approximation leads to large error in the actual phonon mean free path, and consequently, the predictions of the thermal conductivity of the nanostructured materials using the same relaxation time are not correct even after considering additional size effect on the mean free path. We investigate phonon mean free path distribution inside fully unfilled (Co4Sb12) and fully filled (LaFe4Sb12) bulk skutterudites by fitting their thermal conductivity to analytical models which employ different phonon dispersions. We show that theoretical thermal conductivity predictions of the nanostructured samples are in agreement with the experimental data obtained for samples of different grain sizes only when the full phonon dispersion is considered.