A typical electronic or photonic device may consist of several materials each one potentially meeting at an interface or terminating with a free-surface boundary. As modern device dimensions reach deeper into the nanoscale regime, interfaces and boundaries become increasingly influential to both electrical and thermal energy transport. While a large majority of the device community focuses on the former, we focus here on the latter issue of thermal transport which is of great importance in implementing nanoscale devices as well as developing solutions for on-chip heat removal and waste heat scavenging. In this document we will discuss how modern performance enhancing techniques (strain, nanostructuring, alloying, etc.) affect thermal transport at boundaries and across interfaces through the avenue of three case studies. We use first-principles Density Functional Perturbation Theory to obtain the phonon spectrum of the materials of interest and then use the dispersion data as input to a phonon Boltzmann Transport model. First, we investigate the combined effects of strain and boundary scattering on the in-plane and cross-plane thermal conductivity of thin-film silicon and germanium. Second, we review a recently developed model for cross-dimensional (2D-3D) phonon transport and apply it to 3D-2D-3D stacked interfaces involving graphene and molybdenum disulfide 2D-layers. Third, we combine relevant models from earlier Chapters to study extrinsic effects, such as line edge roughness and substrate effects, on in-plane and through-plane thermal transport in 1H-phase transition metal dichalcogenide (TMD) alloys. Through these investigations we show that: (1) biaxial strain in Si and Ge thin-films can modulate cross-plane conductivity due to strong boundary scattering, (2) the thermal boundary conductance between 2D-3D materials can be enhanced in the presence of an encapsulating layer, and (3) the thermal conductivity of 1H-phase TMDs can be reduced by an order of magnitude through the combination of nanostructuring, alloying, and substrate effects.

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.

Over the last decade, substantial attention has been paid to novel nanostructures based on two-dimensional (2D) materials. Among the hundreds of 2D materials that have been successfully synthesized in recent years, graphene, boron nitride, and molybdenum disulfide are the ones that have been intensively studied. It has been demonstrated that these materials exhibit thermal conductivities significantly higher than those of bulk samples of the same material. However, little is known about the physics of phonons in these materials, especially when tensile strain is applied. Properties of these materials are still not well understood, and modelling approaches are still needed to support engineering design of these novel nanostructures. In this thesis, I use state-of-the-art atomistic simulation techniques in combination with statistical thermodynamics formulations to obtain the phonon properties (lifetime, group velocity, and heat capacity) and thermal conductivities of unstrained and strained samples of graphene, boron nitride, molybdenum disulfide, and also superlattices of graphene and boron nitride. Special emphasis is given to the role of the acoustic phonon modes and the thermal response of these materials to the application of tensile strain. I apply spectral analysis to a set of molecular dynamics trajectories to estimate phonon lifetimes, harmonic lattice dynamics to estimate phonon group velocities, and Bose-Einstein statistics to estimate phonon heat capacities. These phonon properties are used to predict the thermal conductivity by means of a mode-dependent equation from kinetic theory. In the superlattices, I study the variation of the frequency dependence of the phonon properties with the periodicity and interface configuration (zigzag and armchair) for superlattices with period lengths within the coherent regime. The results showed that the thermal conductivity decreases significantly from the shortest period length to the second period length, 13% across the interfaces and 16% along the interfaces. For greater periods, the conductivity across the interfaces continues decreasing at a smaller rate of 11 W/mK per period length increase, driven by changes in the phonon group velocities (coherent effects). In contrast, the conductivity along the interfaces slightly recovers at a rate of 2 W/mK per period, driven by changes in the phonon relaxation times (diffusive effects).

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.

The main objective of this thesis is to study phonon thermal transport in two-dimensional (2D) materials using first-principles density functional theory (DFT) calculations and the full solution of the Boltzmann transport equation (BTE). A wide range of 2D materials including graphene, 2D structures of group-VA, and recently emerged NX (X=P, As, Sb) compound monolayers are considered. Special attention is given to a mode-by-mode study of the thermal tunability via strain and functionalization. First, this thesis investigated the sensitivity of the DFT-calculated intrinsic thermal conductivity and phonon properties of 2D materials to the choice of exchange-correlation (XC) and pseudopotential (PP). It was found that the choice of the XC-PP combination results in significant discrepancies among predicted thermal conductivities of graphene at room temperature, in the range of 5442-8677 Wm^(-1)K^(-1). The LDA-NC and PBE-PAW combinations predicted the thermal conductivities in best agreement with available experimental data. This sensitivity analysis was an essential first step towards using DFT to engineer the phonon thermal transport in 2D systems. Next, DFT was used to systematically investigate the strain-dependent lattice thermal conductivity of -arsenene and -phosphorene, 2D monolayers of group-VA. The results showed that the thermal conductivity in both monolayers exhibits an up-and-down behavior when biaxial tensile strain is applied in the range from 0% to 9%. An interplay between phonon group velocities, heat capacities, and relaxation times, is found to be responsible for this behaviour. Finally, this project investigated the thermal conductivity of nitrogen functionalized - NX (X=P, As, Sb) monolayers. The results showed that the room-temperature thermal conductivities of -NP, -NAs, and -NSb are about 1.1, 5.5, and 34.0 times higher than those of their single-element -P, -As, and -Sb monolayers, respectively. The phonon transport analysis revealed that higher phonon group velocities, as well as higher phonon lifetimes were responsible for such an enhancement in the thermal conductivities of - NX compounds compared to single-element group-VA monolayers. Also, it was found that -NP has the minimum thermal conductivity among -NX monolayers, while it has the minimum average atomic mass. This thesis provides valuable insight into phonon physics and thermal transport in novel 2D materials using advanced DFT calculations.

This dissertation examines the effects of surface disorder on phonon dynamics through two different but complementary approaches. First, we use a phonon Monte Carlo (PMC) simulation with random, rough surfaces. PMC is an excellent tool for studying nanostructures of experimentally relevant sizes. We detail our PMC method, including improvements over previous PMC simulations. We investigate why rough silicon nanowires have measured thermal conductivities about two orders of magnitude lower than predicted and comparable to amorphous materials. We show that it can be largely explained through scattering from rough surfaces; extreme roughness causes a qualitative change in how phonons interact with boundaries. During this project, we uncovered the utility of the geometric mean free path (GMFP), which is a concept developed in the study of chaotic billiards. The GMFP is the average distance a particle travels between surface scattering events (in the absence of other scattering mechanisms), and we show that the thermal conductivities obtained from our PMC simulations are a function of the GMFP. Second, we study two-dimensional elastic nanoribbons using finite-difference methods. Elastic materials make good model systems for studying lattice dynamics because elastic materials capture wave behavior, and, in the long-wavelength limit, phonons behave like elastic waves. Our elastic-medium finite-difference time-domain (FDTD) simulation allows us to efficiently model relatively large structures while still treating phonons as waves. We develop a technique to calculate the thermal conductivity of elastic nanoribbons by coupling our FDTD simulation with the Green-Kubo formula. We also employ a time-independent finite-difference (TIFD) method to solve for and study individual modes of our system. We find that rough surfaces can have an outsize impact on phonon dynamics. Surfaces do not simply scatter phonons; rough surfaces can also trap energy and cause all modes throughout the system to localize. The energy trapping and localization coincide with reduced thermal conductivity. We also investigate the effects of Rayleigh waves, a nonbulk mode often ignored in phonon transport simulations. We use TIFD methods to search for signs of wave chaos in nanoribbons. We find an interesting connection between the GMFP and thermal conductivity, which points the way towards future work.