"Phonon transport in micro- nanoscale crystalline materials can be well modeled by the Boltzmann transport equation (BTE). The complexities associated with solving the BTE have led to the development of various numerical models to simulate phonon transport. These models have been applied to predict thermal transport from the diffuse to ballistic regime. While some success using techniques such as the Monte Carlo method has been achieved, there are still a significant number of approximations related to the intricacies of phonon transport that must be more accurately modeled for better predictions of thermal transport at reduced length scales. The objective of the present work is to introduce a Statistical Phonon Transport (SPT) model for simulating thermal transport in crystalline materials from the diffuse to ballistic regime. The SPT model provides a theoretically more realistic treatment of phonon transport physics by eliminating some of the common approximations utilized by other numerical modeling techniques. The SPT model employs full anisotropic dispersion. Phonon populations are modeled without the use of scaling factors or pseudo-random number generation. Three-phonon scattering is rigorously enforced following the selection rules of energy and pseudo-momentum. The SPT model provides a flexible framework for incorporating various phonon scattering mechanisms and models. Results related to the determination of allowable three-phonon interactions are presented along with several three-phonon scattering models. Steady-state and transient thermal transport results for silicon from the diffuse to ballistic regimes are presented and compared to analytical and experimental results. Recommendations for future work related to increasing the robustness of the SPT model as well as utilizing the SPT model to predict thermal transport in practical applications are given."--Abstract.

The monograph is devoted to the investigation of physical processes that govern the phonon transport in bulk and nanoscale single-crystal samples of cubic symmetry. Special emphasis is given to the study of phonon focusing in cubic crystals and its influence on the boundary scattering and lattice thermal conductivity of bulk materials and nanostructures.

"Managing thermal energy generation and transfer within the nanoscale devices (transistors) of modern microelectronics is important as it limits speed, carrier mobility, and affects reliability. Application of Fourier’s Law of Heat Conduction to the small length and times scales associated with transistor geometries and switching frequencies doesn’t give accurate results due to the breakdown of the continuum assumption and the assumption of local thermodynamic equilibrium. Heat conduction at these length and time scales occurs via phonon transport, including both classical and quantum effects. Traditional methods for phonon transport modeling are lacking in the combination of computational efficiency, physical accuracy, and flexibility. The Statistical Phonon Transport Model (SPTM) is an engineering design tool for predicting non-equilibrium phonon transport. The goal of this work has been to enhance the models and computational algorithms of the SPTM to elevate it to have a high combination of accuracy and flexibility. Four physical models of the SPTM were enhanced. The lattice dynamics calculation of phonon dispersion relations was extended to use first and second nearest neighbor interactions, based on published interatomic force constants computed with first principles Density Functional Theory (DFT). The computation of three phonon scattering partners (that explicitly conserve energy and momentum) with the inclusion of the three optical phonon branches was applied using scattering rates computed from Fermi’s Golden Rule. The prediction of phonon drift was extended to three dimensions within the framework of the previously established methods of the SPTM. Joule heating as a result of electron-phonon scattering in nanoscale electronic devices was represented using a modal specific phonon source that can be varied in space and time. Results indicate the use of first and second nearest neighbor lattice dynamics better predicted dispersion when compared to experimental results and resulted in a higher fidelity representation of phonon group velocities and three phonon scattering partners in an anisotropic manner. Three phonon scattering improvements resulted in enhanced fidelity in the prediction of phonon modal decay rates across the wavevector space and thus better representation of non-equilibrium behavior. Comparisons to the range of phonon transport modeling approaches from literature verify that the SPTM has higher phonon fidelity than Boltzmann Transport Equation and Monte Carlo and higher length scale and time scale fidelity than Direct Atomic Simulation. Additional application of the SPTM to both a 1-d silicon nanowire transistor and a 3-d FinFET array transistor in a transient manner illustrate the design capabilities. Thus, the SPTM has been elevated to fill the gap between lower phonon fidelity Monte Carol (MC) models and high fidelity, inflexible direct quantum simulations (or Direct Atomic Simulations (DAS)) within the field of phonon transport modeling for nanoscale electronic devices. The SPTM has produced high fidelity device level non-equilibrium phonon information in a 3-d, transient manner where Joule heating occurs. This information is required due to the fact that effective lattice temperatures are not adequate to describe the local thermal conditions. Knowledge of local phonon distributions, which can’t be determined from application of Fourier’s law, is important because of effects on electron mobility, device speed, leakage, and reliability."--Abstract.

The field of low-dimensional structures has been experiencing rapid development in both theoretical and experimental research. Phonons in Low Dimensional Structures is a collection of chapters related to the properties of solid-state structures dependent on lattice vibrations. The book is divided into two parts. In the first part, research topics such as interface phonons and polaron states, carrier-phonon non-equilibrium dynamics, directional projection of elastic waves in parallel array of N elastically coupled waveguides, collective dynamics for longitudinal and transverse phonon modes, and elastic properties for bulk metallic glasses are related to semiconductor devices and metallic glasses devices. The second part of the book contains, among others, topics related to superconductor, phononic crystal carbon nanotube devices such as phonon dispersion calculations using density functional theory for a range of superconducting materials, phononic crystal-based MEMS resonators, absorption of acoustic phonons in the hyper-sound regime in fluorine-modified carbon nanotubes and single-walled nanotubes, phonon transport in carbon nanotubes, quantization of phonon thermal conductance, and phonon Anderson localization.

Thermal management becomes a significant challenge due to generating more power per unit volume in developing high-power density micro-/nano-sized electronics. The critical feature size of nano- or micro-electronics has already reached less than 10 nm. The thermal conductivity of the semiconducting, dielectric, and metallic materials used in fabricating these microelectronics can be reduced significantly at a small dimension because of increased boundary scattering of phonons and electrons, known as the heat carriers in solids. The size effects on the thermal transport property are considered one of the most fundamental problems for thermal management, which needs to be understood thoroughly for next-generation electronic devices' rational design. This work seeks to advance the understanding of how heat travels in solid materials. Utilizing precise methodologies for characterizing thermophysical properties is the most critical job. Transient thermoreflectance (TTR) and grating imaging techniques are developed to measure thermal conductivity in both lateral and horizontal directions. These techniques are employed to study materials from bulk to nanostructure, including thin-film and nanoparticles, to be characterized. A new regime of phonon transport between ballistic and diffusive transports, called hydrodynamic phonon transport, is observed with a novel method of heat pulse measurement. With thermal characterization using the TTR, four bulk materials, including glass, sapphire, GaAs, and Si are examined for interfacial thermal resistance and cross-plane thermal conductivity. Nanostructures are also tested, such as MoS2 thin-films over a wide range of thicknesses and digital alloy samples of GaAs/InAs. Cu nanoparticles' effective thermal properties are also measured, including heat capacity, density, and thermal conductivity to improve laser sintering technology in the additive manufacturing industry. Thermal characterization using the grating imaging technique, the in-plane thermal conductivity is measured in GaAs/AlAs superlattices and Cu nano-films on Si substrate, representing the bulk and layered structures, respectively. A new regime of phonon transport, hydrodynamic, is observed in graphite using optical heat pulse measurement. The measurement results reveal transient lattice cooling near the adiabatic center of a ring-shaped pump beam at temperatures between 80 and 120 K

Heat conduction in semiconductors and dielectrics involves cumulative contributions from phonons with different frequencies and mean free paths (MFPs). Knowing the phonon MFP distribution allows us to gain insight into the fundamental microscopic transport physics and has important implications for many energy applications. The key metric that quantifies the relative contributions of different phonon MFPs to thermal conductivity is termed thermal conductivity accumulation function. In this thesis, we advance a thermal conductivity spectroscopy technique based upon experimental observation of non-diffusive thermal transport using wire grid linear polarizer in conjunction with time-domain thermoreflectance (TDTR) pump-and-probe measurement setup. Consistent algorithm based on solution from the phonon Boltzmann transport equation (BTE) is also developed to approximately extract the thermal conductivity accumulation functions in materials studied. The heat flux suppression function appropriate for the experimental sample geometry relates the measured apparent thermal conductivities to the material's phonon MFP distributions. We develop a multi-dimensional thermal transport model based on the gray phonon BTE to find the suppression function relevant to our spectroscopy experiment. The simulation results reveal that the suppression function depends upon both the heater size and the heater array period. We also find that the suppression function depends significantly on the location of the temperature measurement. Residual suppression effect is observed for finite filling fractions (ratio of heater size to heater array period) due to the transport coupling in the underlying substrate induced by the neighboring heaters. Prior phonon MFP spectroscopy techniques suffer from one or several of the following limitations: (1) diffraction limited to micrometer lengthscales by focusing optics, (2) applying only to transparent materials, or (3) involving complex micro-fabrications. We explore an alternate approach here using wire grid linear polarizer in combination with TDTR measurement. The wire grid polarizer is designed with sub-wavelength gaps between neighboring heaters to prevent direct photo-excitation in the substrate while simultaneously functioning as heaters and thermometers during the measurement. The spectroscopy technique is demonstrated in crystalline silicon by studying length-dependent thermal transport across a range of lengthscales and temperatures. We utilize the calculated heat flux suppression functions and the measured size-dependent effective thermal conductivities to reconstruct the phonon MFPs in silicon and achieve reasonably good agreement with calculation results from first principle density function theory. Knowledge of phonon MFP distributions in thermoelectric materials will help design nanostructures to further reduce lattice thermal conductivity to achieve better thermoelectric performance in the next-generation thermoelectric devices. We apply the developed wire grid polarizer spectroscopy technique to study phonon MFP distributions in two thermoelectric materials: Nb0.95 Ti0.05FeSb and boron-doped nanocrystalline Si80Ge20B. We find that the dominant phonon MFPs that contribute to thermal conductivity in those two materials are in the a few tens to a few hundreds of nanometers. The measurement results also shed light on why nanostructuring is an effective approach to scattering phonons and improve the thermoelectric behavior.

Over time, technology has shrunk to smaller length scales, and as a result the heat transport in these systems has entered the nanoscale regime. With increasing computational speed and power consumption, there is a need to efficiently dissipate the heat generated for proper thermal management of computer chips. The ability to understand the physics of thermal transport in this regime is critical in order to model, engineer, and improve the performance of materials and devices. In the nanoscale regime, thermal transport is no longer diffusive, and the Fourier heat conduction equation, which we commonly utilize at the macroscale, fails to accurately predict heat flow at the nanoscale. We model the heat flow due to phonons (crystal lattice vibrations), the dominant heat carriers in semiconductors and dielectrics, by solving the Boltzmann transport equation (BTE) to develop an understanding of nondiffusive thermal transport and its dependence on the system geometry and material properties, such as the phonon mean free path. A variety of experimental heat transfer configurations have been established in order to achieve short time scales and small length scales in order to access the nondiffusive heat conduction regime. In this thesis, we develop a variational approach to solving the BTE, appropriate for different experimental configurations, such as transient thermal grating (TTG) and time-domain thermoreflectance (TDTR). We provide an efficient and general methodology to solving the BTE and gaining insight into the reduction of the effective thermal conductivity in the nondiffusive regime, known as classical size effects. We also extend the reconstruction procedure, which aims to utilize both modeling efforts as well as experimental measurements to back out the material properties such as phonon mean free path distributions, to provide further insight into the material properties relevant to transport. Furthermore, with the developed methodology, we aim to provide an analysis of experimental geometries with the inclusion of a thermal interface, to provide insight into the role the interface transmissivity plays in thermal transport in the nondiffusive regime. Lastly, we explore a variety of phonon source distributions that are achieved by heating a system, and show the important link between the system geometry and the distribution of phonons initiated by the heating. We show the exciting possibility that under certain nonthermal phonon distributions, it is possible to achieve enhanced thermal transport at the nanoscale, contrary to the current understanding of size effects only leading to reduced thermal conductivities at the nanoscale for thermal phonon distributions.

In Transport in Phonon Systems'' the principles of physical kinetics are given and the description of transport properties in a wide class of macroscopic physical systems - the phonon systems - is presented. Important problems of phonon transport such as thermal conductivity and thermal waves of second sound, dielectric losses, sound propagation and absorption, phonon echo, and phonon transport in superfluid helium II are discussed. Many of these problems are discussed for the first time and the author presents numerous original results. Not only specialists but also those wishing to enter the field of phonon physics and phonon kinetics can benefit from Transport in Phonon Systems''.

This book presents a comprehensive description of phonons and their interactions in systems with different dimensions and length scales. Internationally-recognized leaders describe theories and measurements of phonon interactions in relation to the design of materials with exotic properties such as metamaterials, nano-mechanical systems, next-generation electronic, photonic, and acoustic devices, energy harvesting, optical information storage, and applications of phonon lasers in a variety of fields. The emergence of techniques for control of semiconductor properties and geometry has enabled engineers to design structures in which functionality is derived from controlling electron behavior. As manufacturing techniques have greatly expanded the list of available materials and the range of attainable length scales, similar opportunities now exist for designing devices whose functionality is derived from controlling phonon behavior. However, progress in this area is hampered by gaps in our knowledge of phonon transport across and along arbitrary interfaces, the scattering of phonons with crystal defects, interface roughness and mass-mixing, delocalized electrons/collective electronic excitations, and solid acoustic vibrations when these occur in structures with small physical dimensions. This book provides a comprehensive description of phonons and their interactions in systems with different dimensions and length scales. Theories and measurements of phonon interactions are described in relation to the design of materials with exotic properties such as metamaterials, nano-mechanical systems, next-generation electronic, photonic, and acoustic devices, energy harvesting, optical information storage, and applications of phonon lasers in a variety of fields.