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Cette thèse se concentre sur l'étude de l'impact de divers défauts de réseau, c'est-à-dire de dislocations, de parois entre phases inversées, de décalages de mailles et de gaps, sur la conductivité thermique de nano-fils par simulation de dynamique moléculaire et les calculs de fonctions de Green atomiques. Tout d'abord, nous calculons la conductivité thermique de nano-fils de silicium orientés <110> incluant une dislocation spirale par la dynamique moléculaire de non-équilibre. Nous constatons qu'avec l'inclusion d'une dislocation, le taux de diffusion phonon-phonon est amélioré de façon significative en raison de l'existence du champ de déformation induit. Ce processus de diffusion anharmonique augmente avec le vecteur de Burger. Par conséquent, la conductivité thermique de nano-fils disloqués est largement réduite et le pourcentage de réduction est proportionnel à la grandeur du vecteur de Burger. Deuxièmement, le concept de nano-fils de super-réseau anti-phase est proposé et leur conductivité thermique est étudiée avec la dynamique moléculaire d'équilibre. On constate que la frontière anti-phase peut diffuser fortement les phonons et réduire la vitesse de groupe des phonons. Le jeu entre le transport cohérent de phonons et la diffusion de surface conduit à une conductivité thermique minimale à une période de longueur spécifique. La combinaison de la diffusion des phonons à l'interface et la diffusion de surface des nanofils réduit la conductivité thermique de SiC de deux ordres de grandeur, ce qui est d'un grand intérêt pour les applications en thermoélectricité. Troisièmement, nous démontrons que le transport des phonons peut être entravé en grande partie dans un nano-fil de Si avec une structure en zig-zag périodique. Une conductivité thermique plus faible est observée du fait d'un pur effet géométrique, qui produit une disparition complète des directions principales de polarisation de phonon à une période de longueur spécifique. La conductivité thermique minimale et la longueur de période correspondante sont dépendantes du diamètre. L'avantage de cette structure est qu'elle supprime en grande partie le transport thermique sans détériorer le transport d'électrons. Enfin, la transition entre la conduction de la chaleur et le rayonnement de champ proche dans un système de chaîne de clusters de SiO2 est étudiée avec la méthode des fonctions de Green. Trois régions de variation de la conductance dans ce domaine de largeur de gap sont identifiées, plus particulièrement, la région liée à la conduction où les électrons des deux corps sont mis en commun au milieu du gap, la région de champ proche prédominée par des interactions de charges de surface, et la région de champ proche prédominée par des interactions dipôle-dipôle de volume. Cette étude fournit finalement une description de la transition entre le rayonnement et la conduction de la chaleur dans les gaps de dimensions inférieures à quelques nanomètres. / This thesis is focused on the investigation of the impact of various lattice defects, i.e., screw dislocations, anti-phase boundaries, twinning boundaries, and vacuum gaps, on the thermal conductivity of nanowires by molecular dynamic simulations and Green's function calculations. We firstly calculated the thermal conductivity of <110> Si nanowires with a screw dislocation in the center through non-equilibrium molecular dynamics.We find that with the inclusion of a dislocation, the phonon-phonon scattering rate is enhanced dramatically due to the dislocation-induced strain field. This anharmonic scattering process increases with the Burger's vector. As a result, the thermal conductivity of dislocated nanowires is largely reduced and the reduction percentage is proportional to the magnitude of Burger's vector. Secondly, the concept of anti-phase superlattice nanowire is proposed and its thermal conductivity is investigated with equilibrium molecular dynamics. It is found that the anti-phase boundary can strongly scatter phonons and reduce the phonon group velocity. The interplay between phonon coherent transport and boundary scattering results in a minimum thermal conductivity at a specific period length. The combination of anti-phase boundary scattering and nanowire surface scattering reduces the thermal conductivity of SiC by two orders of magnitude, which is of great interest for potential thermoelectric applications. Thirdly, we demonstrate that phonon transport can be hindered to a large extent in a Si nanowire with periodically distributed twinning boundaries. A minimum thermal conductivity is observed due to a pure geometrical effect, which produces a thorough disappearance of favored phonon polarization directions at a specific period length. The minimum thermal conductivity and the corresponding period length are diameter dependent. The advantage of this structure is that it largely suppresses the thermal transport without deteriorating the electron transport. Finally, the transition from heat conduction to near field radiation in a SiO2 cluster chain system is investigated with the phonon Green's function. Three conductance variation regions within the studied distances are identified, more specifically, the heat conduction region with shared electrons in the middle of a gap, the near field region predominated by surface charge interactions, and the near field region predominated by volume dipole-dipole interactions. This study finally provides a description of the transition between radiation and heat conduction in gaps smaller than a few nanometers.

Le but de cette thèse est de décrire l'impact des fluctuations thermiques quantiques sur les spectres XANES et RMN du solide, à l'aide d'une étude conjointe expérimentale et théorique. Ce projet comporte deux volets. D'une part, il s'agit d'acquérir des données expérimentales de très bonne qualité, afin d'observer et comprendre l'influence des vibrations quantiques dans les oxydes d'éléments légers. D'autre part, un modèle théorique est mis en place afin de reproduire les effets observés expérimentalement et décrire leur origine d'un point de vue fondamental. L'approche théorique développée est fondée sur la théorie de la fonctionnelle de la densité. Dans le cadre de l'approximation de Born-Oppenheimer et de l'approximation quasi-harmonique, les fluctuations thermiques de nature quantiques sont modélisées en générant des configurations atomiques obéissant à la statistique quantique à température finie. Les spectres XANES et paramètres RMN sont, par la suite, calculés dans ces configurations et les résultats moyens sont comparés aux données spectroscopiques à température finie. Cette approche a été validée par une étude menée dans une série d'oxydes d'éléments légers, où les résultats se sont avérés être en excellent accord avec les données expérimentales originales que nous avons enregistrées. En outre, il est montré que les fluctuations quantiques des noyaux ne jouent pas le même rôle selon la symétrie locale du site atomique sondé. / In this thesis the impact of quantum thermal fluctuations on XANES and solid-state NMR spectra is described using an experimental and theoretical joint study. This project has two components. First, high-quality experimental data are acquired in order to observe and understand the influence of quantum vibrations in light-elements oxides. Second, a theoretical model is set up to reproduce the effects observed experimentally and describe their origin from a fundamental point of view. The developed theoretical approach is based on the density-functional theory. Within the Born-Oppenheimer and quasiharmonic approximations, the quantum thermal fluctuations of nuclei are modeled by generating atomic configurations obeying quantum statistics at finite temperature. The XANES spectra and NMR parameters are subsequently calculated in these configurations and the average results are compared with spectroscopic data at finite temperature. This approach has been validated by a joint theoretical-experimental study conducted in a series of light-element oxides, where the results were found to be in excellent agreement with the original experimental data. In addition, it is shown that the impact of the quantum fluctuations of the nuclei is influenced by the local symmetry of the probed atomic site.

Les boîtes quantiques (BQ) semi-conductrices possèdent une structure électronique discrète qui en fait une excellente source de photons uniques et indiscernables. Elles sont ainsi devenues un système très attractif pour des futures applications en information quantique, grâce à la possibilité de les intégrer dans des nano-dispositifs permettant un couplage efficace lumière-matière. Cependant, les BQs constituent par nature un système ouvert en interagissant fortement avec l'environnement solide, une des conséquences étant la destruction partielle de la cohérence des photons émis. Dans ce travail, nous avons choisi d'utiliser une BQ comme sonde très sensible de ces interactions. Des expériences d'interférences à deux photons, de type Hong-Ou-Mandel, sous excitation résonante et en fonction de la température, nous ont permis d’étudier l'interaction entre une BQ et les phonons acoustiques de la matrice cristalline environnante. En combinant nos résultats expérimentaux et un modèle théorique microscopique, nous avons identifié deux processus distincts responsables de la perte d’indiscernabilité : le premier dû aux transitions réelles par absorption-émission de phonons, le deuxième à cause de transitions virtuelles, processus du deuxième ordre, dues à la présence d’états excités de plus haute énergie dans la boîte. Nous avons par ailleurs étudié des échantillons dopés permettant d’appliquer un champ électrique sur le plan de BQ, mettant en évidence que le contrôle de l’état de charge d’une BQ permet sont excitation résonante systématique. / Developments in quantum information processes require the use of solid state qubits that would emit on demand single and indistinguishable photons. Semiconductor quantum dots (QDs) show an atom-like spectrum which makes them attractive in this regard. However, a single QD constitutes an open quantum system coupled to its surrounding solid-state environment, the phonon bath and the fluctuating electrostatic environment. This has important consequences on the coherence properties of the electronic system and the QD is a probe to study these fundamental interactions. Using Fourier spectroscopy and temperature-dependent resonant HOM experiments we show that these two mechanisms occur on very different time scales: spectral diffusion is a slow dephasing process acting on microseconds, while phonon interaction takes place in less than one ns. Then, the loss of ndistinguishability in HOM measurements is only related to dephasing induced by the coupling to the phonon bath. The TPI visibility is preserved around 85 % at low temperature, followed by a rapid loss of coherence. To fully understand the experimental results we developed a mircroscopic model for the electron-phonon interaction which allow to obtain analytic expressions for the dephasing rates. Below 10K the relaxation of the vibrational lattice is the dominant contribution to the loss of TPI visibility. This process corresponds to real phonon transitions resulting in a broad phonon sideband in the QD emission spectra. Above 10K, virtual phonon transitions to higher lying excited states become the dominant dephasing mechanism, leading to broadening of the zero phonon line and a corresponding rapid decay in the visibility.

Le transport thermique dans les nanostructures semi-conductrices est un sujet de recherche très actuel, couvrant de larges domaines applicatifs dont l’auto-échauffement des composants nanoélectroniques et la conversion d’énergie par effet thermoélectrique. La modélisation du transport thermique à l’échelle nanométrique est complexe car la longueur des dispositifs devient du même ordre de grandeur que le libre parcours moyen des porteurs de chaleurs (phonons). L’hypothèse de pseudo-équilibre local n’est plus pertinente, de plus des effets de confinements peuvent aussi apparaitre. Il faut donc développer des outils de modélisation spécifiques.Pour prendre en compte les effets de confinement, j'ai calculé les relations de dispersions des phonons dans les nanostructures. Pour cela, j’ai mis en œuvre une méthode atomistique semi-empirique nommée ABCM (« Adiabadic Bond Charge Model »). J’ai pu ainsi calculer, dans l'ensemble de la zone de Brillouin (« Full Band »), la dispersion des phonons dans du silicium et du germanium en phase Zinc-Blende et aussi en phase Wurtzite.En outre, afin d’évaluer la résistance thermique d’interface, une extension originale du modèle « Acoustic Mismatch Model », entièrement « full-band », a été développée. Grâce à l’approche « Full-Band » la dépendance à l’orientation relative des cristaux de chaque côté de l’interface a été étudiée. Les effets d’orientations sur la transmission ont aussi été étudiés dans des nanofils polyphasés nouvellement synthétisés dans le laboratoire.En parallèle, pour étudier le transport des phonons, j'ai développé un simulateur Monte Carlo particulaire qui utilise les dispersions « Full-Band » calculées en ABCM. Ce type de simulateur est très polyvalent et permet de décrire l’ensemble des régimes de transports (du balistique au diffusif). De plus, comme il utilise une dispersion « Full-Band » les effets de confinement peuvent aussi être inclus. Ce simulateur m’a permis d’étudier les effets d’un changement d’orientation des plans cristallographiques du cristal sur la conductivité thermiques dans des nanofils de silicium et de germanium. J’ai ainsi évalué l’anisotropie du flux thermique dans ces nanostructures. / The heat transfer in semiconducting nanostructures is a current research topic, covering a wide range of applications including self-heating in nanoelectronic devices and energy conversion via thermoelectric effect. The modeling of heat transport at the nanometer scale is complex as the device length is in the same order of magnitude than the mean free path of heat carriers (phonons). The local pseudo-equilibrium assumption is no longer relevant, moreover confinement effects can also appear. Therefore development of specific modeling tools is highly desirable.To take into account the confinement effects, I have calculated the phonon dispersion relations in nanostructures. For this, I have implemented an atomistic semi-empirical method called ABCM (Adiabadic Bond Charge Model). I have calculated, in the entire Brillouin zone (Full Band approach), the dispersion relationship of phonons in both Silicon and Germanium for both Zinc-Blende and Wurtzite phases.In addition, to evaluate the thermal interface resistance, an original extension of the Acoustic Mismatch Model, completely full band, was developed. Within this approach, the dependence on the relative orientation of crystals has been studied in polytype nanowires that were recently synthesized in the laboratory.In parallel, to study the transport of phonons, I developed a particle Monte Carlo simulator that uses Full-Band dispersions calculated via ABCM. This kind of simulator is very versatile and can describe all transport regimes (from ballistic to diffusive one). Moreover, as it uses a "Full-Band" dispersion confinement effects can also be included. This simulator allowed me to study the effects of a change in orientation of the crystallographic planes on the thermal conductivity in both silicon and germanium nanowires. I have thus evaluated the anisotropy of the heat fluxes in these nanostructures.

Le transistor est la brique élémentaire des circuits intégrés présents dans tous les appareils électroniques. Années après années l’industrie de la microélectronique a amélioré les performances des circuits intégrés (rapidité, consommation énergétique) en réduisant les dimensions du transistor. De nos jours, en plus de la réduction de la taille du transistor d’autres techniques permettent de soutenir cette croissance: ce sont les « booster » technologiques. Les contraintes mécaniques ou encore le remplacement du Silicium par d’autres matériaux tels que germanium (Ge) et les matériaux semi-conducteurs de type III-V sont des exemples de booster technologiques. Grâce à la modélisation numérique, cette thèse propose d’étudier les effets de booster technologiques sur les performances électriques de la future génération de transistors. / The transistor is the elementary brick of Integrated circuits found in all electronic devices. Years after years the microelectronic industry has enhanced the performances of integrated circuits (speed and energy consumption) by downscaling the transistor. Nowadays besides the transistor’s downscaling, other techniques have been considered to maintain this growth: they are called technological boosters. Mechanical strain or new material, such as germanium (Ge) and III-V semiconductors, to replace Silicon are example of technological boosters. By the means of numerical quantum simulations and modeling, this these work propose a study of the effect of technological boosters on the electric performances of the next generation of transistors.

It is well established that rarefied flows cannot be properly described by traditional hydrodynamics, namely the Navier-Stokes equations for gas flows, and the Fourier’s law for heat transfer. Considering the significant advancement in miniaturization of electronic devices, where dimensions become comparable with the mean free path of the flow, the It is well established that rarefied flows cannot be properly described by traditional hydrodynamics, namely the Navier-Stokes equations for gas flows, and the Fourier's law for heat transfer. Considering the significant advancement in miniaturization of electronic devices, where dimensions become comparable with the mean free path of the flow, the study of rarefied flows is extremely important. This dissertation includes two main parts. First, we look into the heat transport in solids when the mean free path for phonons are comparable with the length scale of the flow. A set of macroscopic moment equations for heat transport in solids are derived to extend the validity of Fourier's law beyond the hydrodynamics regime. These equations are derived such that they remain valid at room temperature, where the MEMS devices usually work. The system of moment equations for heat transport is then employed to model the thermal grating experiment, recently conducted on a silicon wafer. It turns out that at room temperature, where the experiment was conducted, phonons with high mean free path significantly contribute to the heat transport. These low frequency phonons are not considered in the classical theory, which leads to failure of the Fourier's law in describing the thermal grating experiment. In contrast, the system of moment equations successfully predict the deviation from the classical theory in the experiment, and suggest the importance of considering both low and high frequency phonons at room temperature to capture the experimental results. In the second part of this study, we look into the gas-surface interactions for conventional gas dynamics when the gas flow is rarefied. An extension to the well-known Maxwell boundary conditions for gas-surface interactions are obtained by considering velocity dependency in the reflection kernel from the surface. This extension improves the Maxwell boundary conditions by providing an extra free parameter that can be fitted to the experimental data for thermal transpiration effect in non-equilibrium flows. The velocity dependent Maxwell boundary conditions are derived for the Direct Simulation Monte Carlo (DSMC) method and the regularized 13-moment (R13) equations for conventional gas dynamics. Then, a thermal cavity is considered to test and study the effect of these boundary conditions on the flow formation in the slip and early transition regime. It turns out that using velocity dependent boundary conditions allows us to change the size and direction of the thermal transpiration force, which leads to marked changes in the balance of transpiration forces and thermal stresses in the flow. / Graduate

Thesis advisor: David A. Broido / A theory is presented for describing the lattice thermal conductivities of graphene and single-walled carbon nanotubes. A phonon Boltzmann transport equation approach is employed to describe anharmonic phonon-phonon, crystal boundary, and isotopic impurity scattering. Full quantum mechanical phonon scattering is employed and an exact solution for the linearized Boltzmann transport equation is determined for each system without use of common relaxation time and long-wavelength approximations. The failures of these approximations in describing the thermal transport properties of nanotubes is discussed. An efficient symmetry based dynamical scheme is developed for carbon nanotubes and selection rules for phonon-phonon scattering in both graphene and nanotubes are introduced. The selection rule for scattering in single-walled carbon nanotubes allows for calculations of the thermal conductivities of large-diameter and chiral nanotubes that could not be previously studied due to computational limitations. Also due to this selection rule, no acoustic-only umklapp scattering can occur, thus, acoustic-optic scattering must be included in order to have thermal resistance from three-phonon processes. The graphene selection rule severely restricts phonon-phonon scattering of out-of-plane modes. This restriction leads to large contributions to the total thermal conductivity of graphene from the acoustic, out-of-plane modes which have been previously neglected. Empirical potentials used to model interactions in carbon-based materials are optimized to better describe the lattice dynamics of graphene-derived systems. These potentials are then used to generate the interatomic force constants needed to make calculations of the thermal conductivities of graphene and carbon nanotubes. Calculations of the thermal conductivities of single-walled carbon nanotubes and graphene for different temperatures and lengths are presented. The thermal conductivities of SWCNTs saturate in the diffusive regime when the effects of higher-order scattering processes are estimated and correctly reproduce the ballistic limit for short-length nanotubes at low temperatures. The effects of isotopic impurity scattering on the thermal conductivities of graphene and SWCNTs are explored. Isotopic impurities have little effect in the low (high) temperature regime where boundary (umklapp) scattering dominates the behavior of the thermal conductivities. In the intermediate temperature regime, modest reductions in the thermal conductivities, 15-20%, occur due to impurities. The thermal conductivities of a wide-range of SWCNTs are explored. The thermal conductivities of successively larger-diameter, one-dimensional nanotubes approach the thermal conductivity of two-dimensional graphene. / Thesis (PhD) — Boston College, 2010. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Yung Lit Hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves p. [122]-124). / Text in English; abstracts in English and Chinese. / Yung Lit Hung. / Abstract --- p.i / Acknowledgements --- p.ii / List of Figures --- p.v / List of Tables --- p.vii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Dissipative two-state system --- p.3 / Chapter 2.1 --- Introduction --- p.3 / Chapter 2.2 --- A two-state system viewed as a spin --- p.4 / Chapter 2.3 --- Rotation of spin operators --- p.5 / Chapter 2.4 --- Dissipative two state system --- p.7 / Chapter 2.5 --- The model in consideration --- p.8 / Chapter 2.5.1 --- gk= 0 --- p.8 / Chapter 2.5.2 --- Δ0 = 0 --- p.8 / Chapter 2.5.3 --- dispersionless phonon case with constant coupling --- p.10 / Chapter 3 --- Linearized spin-wave approximation and mean-field method --- p.13 / Chapter 3.1 --- Holstein Primakoff Transformation --- p.13 / Chapter 3.2 --- Application of linearized spin-wave approxmation to our system --- p.14 / Chapter 3.3 --- Mean-field method --- p.24 / Chapter 4 --- Variational method for optical phonons with constant coupling --- p.35 / Chapter 4.1 --- Introduction --- p.35 / Chapter 4.2 --- Variational Principle --- p.35 / Chapter 4.3 --- Variational Principle applied to optical phonon case --- p.36 / Chapter 4.4 --- Results --- p.41 / Chapter 4.5 --- Conclusion --- p.54 / Chapter 5 --- Variational method for acoustic phonons with ohmic dissipation --- p.56 / Chapter 5.1 --- Introduction --- p.56 / Chapter 5.2 --- Variational Principle applied to acoustic phonon case --- p.57 / Chapter 5.3 --- μk= 0 case --- p.59 / Chapter 5.4 --- Search for any μk≠ 0 solution --- p.60 / Chapter 5.5 --- Results --- p.62 / Chapter 5.6 --- Conclusion --- p.70 / Chapter 6 --- Coupled Cluster Method --- p.72 / Chapter 6.1 --- Introduction --- p.72 / Chapter 6.2 --- Coupled Cluster Method --- p.73 / Chapter 6.2.1 --- Zeroth Level --- p.74 / Chapter 6.2.2 --- First Level --- p.74 / Chapter 6.2.3 --- The bra-state --- p.75 / Chapter 6.3 --- Coupled cluster method applied to our system --- p.76 / Chapter 6.4 --- Coupled cluster method applied to optical phonon case --- p.78 / Chapter 6.4.1 --- First Level --- p.79 / Chapter 6.4.2 --- Second Level --- p.81 / Chapter 6.5 --- Coupled cluster method applied to acoustic phonon case --- p.90 / Chapter 6.5.1 --- First Level --- p.90 / Chapter 6.5.2 --- Second Level --- p.92 / Chapter 6.6 --- Conclusion --- p.98 / Chapter 7 --- Spin system interacting with a photon field --- p.99 / Chapter 7.1 --- Rotation wave approximation --- p.100 / Chapter 7.2 --- Spin system interacting with an optical field --- p.101 / Chapter 7.3 --- Heisenberg equation of motion --- p.102 / Chapter 7.4 --- Brogoliubov transformation approach --- p.104 / Chapter 7.5 --- Conclusion --- p.106 / Chapter A --- Supplementary calculations --- p.107 / Chapter A.1 --- First level calculation for optical photon --- p.107 / Chapter A.2 --- Second level calculation for optical photon --- p.111 / Chapter A.3 --- First level calculation for acoustic photon --- p.114 / Chapter A.4 --- Second level calculation for acoustic photon --- p.118 / Bibliography --- p.121

In this thesis, I explore dissipative quantum dynamics of several prototypical model systems via various approaches, ranging from approximate to numerically exact schemes. In particular, in the realm of the approximate I explore the accuracy of Padé–resummed master equations and the fewest switches surface hopping (FSSH) algorithm for the spin–boson model, and non-crossing approximations (NCA) for the Anderson–Holstein model. Next, I develop new and exact Monte Carlo approaches and test them on the spin–boson model. I propose well–defined criteria for assessing the accuracy of Padé-resummed quantum master equations, which correctly demarcate the regions of parameter space where the Padé approximation is reliable. I continue the investigation of spin–boson dynamics by benchmark comparisons of the semiclassical FSSH algorithm to exact dynamics over a wide range of parameters. Despite small deviations from golden-rule scaling in the Marcus regime, standard surface hopping algorithm is found to be accurate over a large portion of parameter space. The inclusion of decoherence corrections via the augmented FSSH algorithm improves the accuracy of dynamical behavior compared to exact simulations, but the effects are generally not dramatic for the cases I consider. Next, I introduce new methods for numerically exact real-time simulation based on real-time diagrammatic Quantum Monte Carlo (dQMC) and the inchworm algorithm. These methods optimally recycle Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. In the context of the spin–boson model, I formulate the inchworm expansion in two distinct ways: the first with respect to an expansion in the system–bath coupling and the second as an expansion in the diabatic coupling. In addition, a cumulant version of the inchworm Monte Carlo method is motivated by the latter expansion, which allows for further suppression of the growth of the sign error. I provide a comprehensive comparison of the performance of the inchworm Monte Carlo algorithms to other exact methodologies as well as a discussion of the relative advantages and disadvantages of each. Finally, I investigate the dynamical interplay between the electron–electron interaction and the electron–phonon coupling within the Anderson–Holstein model via two complementary NCAs: the first is constructed around the weak-coupling limit and the second around the polaron limit. The influence of phonons on spectral and transport properties is explored in equilibrium, for non-equilibrium steady state and for transient dynamics after a quench. I find the two NCAs disagree in nontrivial ways, indicating that more reliable approaches to the problem are needed. The complementary frameworks used here pave the way for numerically exact methods based on inchworm dQMC algorithms capable of treating open systems simultaneously coupled to multiple fermionic and bosonic baths.