Thermal transport across three-dimensional Lennard-Jones superlattices, two-dimensional heterostructures of graphene and hexagonal boron nitride (hBN), and in C60 molecular crystals is studied atomistically. The first two systems are studied as finite junctions placed between bulk leads, while the molecular crystal is studied as a bulk. Two computational methods are used: molecular dynamics (MD) simulations and harmonic lattice dynamics calculations in conjunction with the scattering boundary method (SBM). In Lennard-Jones superlattice junctions with a superlattice period of four atomic monolayers at low temperatures, those with mass-mismatched leads have a greater thermal conductance than those with mass-matched leads. We attribute this lead effect to interference between and the ballistic transport of emergent junction vibrational modes. The lead effect diminishes when the temperature is increased, when the superlattice period is increased, and when interfacial disorder is introduced, and is reversed in the harmonic limit. In graphene-hBN heterostructure junctions, the thermal conductance is dominated by acoustic phonon modes near the Brillouin zone center that have high group velocity, population, and transmission coefficient. Out-of-plane modes make their most significant contributions at low frequencies, whereas in-plane modes contribute across the frequency spectrum. Finite-length superlattice junctions between graphene and hBN leads have a lower thermal conductance than comparable junctions between two graphene leads due to lack of transmission in the hBN phonon band gap. The thermal conductances of bilayer systems differ by less that 10% from their single-layer counterparts on a per area basis, in contrast to the strong thermal conductivity reduction when moving to from single- to multi-layer graphene. We model C60 molecules using the polymer consistent force-field and compute the single molecule vibrational spectrum and heat capacity. In the face-center cubic C60 molecular crystal at a temperature of 300 K, we find three frequency peaks in the center-of-mass translations at 20, 30 and 38 cm􀀀1, agreeing with the average frequencies of the three acoustic branches of the frozen phonon model of the same system and suggesting that a phonon description of center-of-mass translations. We use both direct method and Green- Kubo MD simulations to predict the thermal conductivity of the molecular crystals at a temperature of 300 K. We find that the thermal conductivity of the molecular crystal is 20 to 50% lower than that of a reduced order model where only molecular center-ofmass translations are present, suggesting that molecular vibrations and rotations act as significant scattering sources for the center-of-mass phonons.

Phonon transport analysis in nano- and micro-porous materials is critical to their energy-related applications. Assuming diffusive phonon scattering by pore edges, the lattice thermal conductivity can be predicted by modifying the bulk phonon mean free paths with the characteristic length of the nanoporous structure, i.e., the phonon mean free path (Lambda(pore)) for the pore-edge scattering of phonons. In previous studies (Jean et al., 2014), a Monte Carlo (MC) technique have been employed to extract geometry determined Lambda(pore) for nanoporous bulk materials with selected periods and porosities. In other studies (Minnich and Chen, 2007; Machrafi and Lebon, 2015), simple expressions have been proposed to compute Lambda(pore). However, some divergence can often be found between lattice thermal conductivities predicted by phonon MC simulations and by analytical models using Lambda(pore). In this work, the effective Lambda(pore) values are extracted by matching the frequency-dependent phonon MC simulations with the analytical model for nanoporous bulk Si. The obtained Lambda(pore) values are usually smaller than their analytical expressions. These new values are further confirmed by frequency-dependent phonon MC simulations on nano porous bulk Ge. By normalizing the volumetric surface area A and Lambda(pore) with the period length p, the same curve can be used for bulk materials with aligned cubic or spherical pores up to dimensionless p.A of 1.5. Available experimental data for nanoporous Si materials are further analyzed with new Lambda(pore) values. In practice, the proposed model can be employed for the thermal analysis of various nanoporous materials and thus replace the time-consuming phonon MC simulations.

Over the last two decades, advanced fabrication techniques have enabled the fabrication of materials and devices at sub-micron length scales. For heat conduction, the conventional Fourier model for predicting energy transport has been shown to yield erroneous results on such length scales. In semiconductors and dielectrics, energy transport occurs through phonons, which are quanta of lattice vibrations. When phase coherence effects can be ignored, phonon transport may be modeled using the semi-classical phonon Boltzmann transport equation (BTE). The objective of this thesis is to develop an efficient computational method to solve the BTE, both for single-material and multi-material systems, where transport across heterogeneous interfaces is expected to play a critical role. The resulting solver will find application in the design of microelectronic circuits and thermoelectric devices. The primary source of computational difficulties in solving the phonon BTE lies in the scattering term, which redistributes phonon energies in wave-vector space. In its complete form, the scattering term is non-linear, and is non-zero only when energy and momentum conservation rules are satisfied. To reduce complexity, scattering interactions are often approximated by the single mode relaxation time (SMRT) approximation, which couples different phonon groups to each other through a thermal bath at the equilibrium temperature. The most common methods for solving the BTE in the SMRT approximation employ sequential solution techniques which solve for the spatial distribution of the phonon energy of each phonon group one after another. Coupling between phonons is treated explicitly and updated after all phonon groups have been solved individually. When the domain length is small compared to the phonon mean free path, corresponding to a high Knudsen number ([mathematical equation]), this sequential procedure works well. At low Knudsen number, however, this procedure suffers long convergence times because the coupling between phonon groups is very strong for an explicit treatment of coupling to suffice. In problems of practical interest, such as silicon-based microelectronics, for example, phonon groups have a very large spread in mean free paths, resulting in a combination of high and low Knudsen number; in these problems, it is virtually impossible to obtain solutions using sequential solution techniques. In this thesis, a new computational procedure for solving the non-gray phonon BTE under the SMRT approximation is developed. This procedure, called the coupled ordinates method (COMET), is shown to achieve significant solution acceleration over the sequential solution technique for a wide range of Knudsen numbers. Its success lies in treating phonon-phonon coupling implicitly through a direct solution of all equations in wave vector space at a particular spatial location. To increase coupling in the spatial domain, this procedure is embedded as a relaxation sweep in a geometric multigrid. Due to the heavy computational load at each spatial location, COMET exhibits excellent scaling on parallel platforms using domain decomposition. On serial platforms, COMET is shown to achieve accelerations of 60 times over the sequential procedure for Kn<1.0 for gray phonon transport problems, and accelerations of 233 times for non-gray problems. COMET is then extended to include phonon transport across heterogeneous material interfaces using the diffuse mismatch model (DMM). Here, coupling between phonon groups occurs because of reflection and transmission. Efficient algorithms, based on heuristics, are developed for interface agglomeration in creating coarse multigrid levels. COMET is tested for phonon transport problems with multiple interfaces and shown to outperform the sequential technique. Finally, the utility of COMET is demonstrated by simulating phonon transport in a nanoparticle composite of silicon and germanium. A realistic geometry constructed from x-ray CT scans is employed. This composite is typical of those which are used to reduce lattice thermal conductivity in thermoelectric materials. The effective thermal conductivity of the composite is computed for two different domain sizes over a range of temperatures. It is found that for low temperatures, the thermal conductivity increases with temperature because interface scattering dominates, and is insensitive to temperature; the increase of thermal conductivity is primarily a result of the increase in phonon population with temperature consistent with Bose-Einstein statistics. At higher temperatures, Umklapp scattering begins to take over, causing a peak in thermal conductivity and a subsequent decrease with temperature. However, unlike bulk materials, the peak is shallow, consistent with the strong role of interface scattering. The interaction of phonon mean free path with the particulate length scale is examined. The results also suggest that materials with very dissimilar cutoff frequencies would yield a thermal conductivity which is closest to the lowest possible value for the given geometry. / text

Understanding the magnitude of the temperature in AlGaN/GaN heterostructure fi eld e ffect transistors(HFETs) is a critical aspect of understanding their reliability and providing proper thermal management. At present, most models used to determine the temperature rise in these devices are based on continuum based heat conduction. However, in such devices, the heat generation region can be on the order of or smaller than the phonon mean free path of the heat carriers, and thus, such models may under predict the temperature. The aim of this work is towards building a multiscale thermal model that will allow for the prediction of heat transport from ballistic-diffusive phonon transport near the heat generation region and diffusive transport outside of this zone. First, a study was performed to determine the appropriate numerical solution to the phonon Boltzmann transport equation followed by its integration into a multiscale thermal scheme. The model, which utilizes a Discrete Ordinates Solver, was developed for both gray and non-gray phonon transport. The scheme was applied to the solution of speci fic test problems and then finally to the electrothermal modeling of AlGaN/GaN HFETs under various electrical bias conditions.

Thesis advisor: David Broido / We present fundamental studies of phonon and electron transport in semiconductors. First principles density functional theory (DFT) is combined with exact numerical solutions of the Boltzmann transport equation (BTE) for phonons and electrons to calculate various transport coefficients. The approach is used to determine the lattice thermal conductivity of three hexagonal polytypes of silicon carbide. The calculated results show excellent agreement with recent experiments. Next, using the infinite orders T-matrix approach, we calculate the effect of various neutral and charged substitution defects on the thermal conductivity of boron arsenide. Finally, we present a general coupled electron-phonon BTEs scheme designed to capture the mutual drag of the two interacting systems. By combining first principles calculations of anharmonic phonon interactions with phenomenological models of electron-phonon interactions, we apply our implementation of the coupled BTEs to calculate the thermal conductivity, mobility, Seebeck and Peltier coefficients of n-doped gallium arsenide. The measured low temperature enhancement in the Seebeck coefficient is captured using the solution of the fully coupled electron-phonon BTEs, while the uncoupled electron BTE fails to do so. This work gives insights into the fundamental nature of charge and heat transport in semiconductors and advances predictive ab initio computational approaches. We discuss possible extensions of our work. / Thesis (PhD) — Boston College, 2019. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Le graphène planaire se présente comme un des matériaux les plus prometteurs pour la nanoélectronique de demain, grâce particulièrement à sa conductivité thermique et sa mobilité électronique qui sont les plus élevées jamais mesurées dans un solide. Parmi ses allotropes, le graphène découpé en nanorubans est une des formes les plus intéressantes, notamment pour les possibilités d'ingénierie de bandes qu'il offre. Ses propriétés électroniques et vibrationnelles sont fortement influencées par la présence des bords et s’éloignent de celles du graphène planaire. A ce jour, ses propriétés thermiques et thermoélectriques ont été encore peu explorées. Dans ce travail de thèse, grâce à une modélisation atomistique du réseau cristallin, les modes de vibration caractéristiques de chaque type de ruban ont été identifiés et, dans le cadre du formalisme des fonctions de Green hors équilibre, le transport de ces modes a été simulé. On a ainsi évalué les propriétés thermiques des nanorubans en identifiant les types de rubans offrant la plus forte conductance thermique pour envisager une meilleure gestion de la chaleur dans les dispositifs du futur. Dans la direction opposée, des techniques de nanostructuration du ruban permettent de dégrader le transport des phonons et d’amplifier la figure de mérite thermoélectrique en bénéficiant simultanément d'un phénomène de transport électronique résonant. En exploitant ces techniques, un premier dispositif thermoélectrique basé sur les nanorubans de graphène a été conçu et ses performances ont été évaluées par une approche multi-échelle. La possibilité de très forte densité d’intégration du graphène fait l’intérêt d’un tel dispositif qui pourrait fournir des puissances électriques ou de refroidissement très supérieures à celles des dispositifs thermoélectriques actuels. / 2D graphene is one of the most promising materials for nanoelectronics; its thermal conductivity and electronic mobility are the highest ever measured in solids. Among its allotropes, graphene cut in nanoribbons (GNRs) is one of the most interesting structures because it offers possibilities of bandgap engineering. Electronic and vibrational properties of GNRs are strongly affected by the presence of the edges and can differ significantly from those of 2D graphene. Up to now, their thermal and thermoelectric properties have been rarely explored. In this thesis, using an atomistic model of crystal lattice, the vibrational modes associated to each type of ribbon have been identified and via the formalism of nonequilibrium Green’s functions, the transport of these modes has been simulated. We have evaluated the better ribbon structures in terms of thermal conductance for a better heat management in future devices and circuits. On the other side we have identified some particular nanostructured ribbons where the thermoelectric figure of merit is strongly amplified thanks to both the degradation of phonon conductance and the occurring of resonant electron transport. A first thermoelectric device based on such GNRs has been designed and its performance has been evaluated using a multi-scale approach. This device becomes interesting in the case of high integration density of GNRs.

Electronics industry has been developing at a tremendous rate for last five decades and currently is one of the biggest industries in the world. The key to the rapid growth of electronics industry is innovation that made possible the constant scaling of transistors with reduced cost and improved performance. Scaling transistors were simpler at the beginning, but currently as the gate length of transistors has reached few nanometers, different short channel effects have emerged and power density of transistors has also increased drastically, which made further scaling much more challenging. To study electro-thermal transport in these reduced dimensionality devices, continuum models are no longer sufficient. In this work, the electrical and thermal transport properties have been modeled by solving Boltzmann Transport Equation (BTE) for electrons and phonons, respectively, using the Monte Carlo (MC) technique. To solve BTE for the phonons, a coupled Molecular Mechanics-Monte Carlo approach is employed where phonon band-structure is obtained using the atomistic modified Valence Force Field (VFF) model and is coupled with a Monte Carlo Phonon Transport kernel which solves the BTE for phonons. The phonon-phonon scattering is modeled in relaxation time approximation (RTA) using Holland’s formalism. Diffusive boundary scattering for phonons has been modeled using the Beckmann-Kirchhoff (B-K) surface roughness scattering model taking into account the effects of phonon wavelength, incident angles and degree of surface roughness. The effect of rough surface on longitudinal acoustic (LA) and transverse acoustic (TA) phonon branches has been studied with the help of the B-K model and it has been found that, at elevated temperatures, there is less backscattering to the LA branch due to rough surface. Effort has been made then to couple the developed phonon Monte Carlo transport simulator with an electron Monte Carlo transport simulator to study the origin and effects of self-heating in a nanoscale field-effect transistor (FET). In contrast to the widely used continuum model, where Fourier heat diffusion equation is usually solved to describe the thermal transport, the simulator developed in this dissertation treats both the electrons and the phonons at the particle level. Acoustic and intervalley g and f type electron-phonon scattering mechanisms are considered and the resulting local temperature modification has been used to bridge the electron and phonon transport paths. Phonon transport at the oxide-silicon interface has been modeled using the Diffuse Mismatch (DM) model, whereas, the phonons in the oxide have been described using the Debye model and temperature and frequency dependent relaxation time. The simulator is then benchmarked and used to study the electron-phonon transport processes in a FinFET device with a gate length of 18 nm, channel width of 4 nm, and a fin height of 8 nm. Preliminary results show that there can be a current degradation of as high as ~9.56% due to self-heating effect. Also, temperature in the entire channel region could rise due to self-heating. The maximum temperature rise in the channel region is found to be ~30K.

High power Gallium Nitride (GaN) based field effect transistors are used in many high power applications from RADARs to communications. These devices dissipate a large amount of power and sustain high electric fields during operation. High power dissipation occurs in the form of heat generation through Joule heating which also results in localized hot spot formation that induces thermal stresses. In addition, because GaN is strongly piezoelectric, high electric fields result in large inverse piezoelectric stresses. Combined with residual stresses due to growth conditions, these effects are believed to lead to device degradation and reliability issues. This work focuses on studying these effects in detail through modeling of Heterostructure Field Effect Transistors (HFETs) and metal oxide semiconductor hetero-structure field effect transistor (MOSHFETs) under various operational conditions. The goal is to develop a thorough understanding of device operation in order to better predict device failure and eventually aid in device design through modeling. The first portion of this work covers the development of a continuum scale model which couples temperature and thermal stress to find peak temperatures and stresses in the device. The second portion of this work focuses on development of a micro-scale model which captures phonon-interactions at the device scale and can resolve local perturbations in phonon population due to electron-phonon interactions combined with ballistic transport. This portion also includes development of phonon relaxation times for GaN. The model provides a framework to understand the ballistic diffusive phonon transport near the hotspot in GaN transistors which leads to thermally related degradation in these devices.

Gallium nitride (GaN) has been targeted for use in high power (>30 W/mm) and high frequency (>160 GHz) application due to its wide band gap and its large break down field. One of the most significant advances in GaN devices has evolved from the AlGaN/GaN high electron mobility transistor (HEMT). As a result of the large power densities being applied to these devices there can develop intense hot spots near areas of highest electric field. The hot spot phenomenon has been linked to a decrease in device reliability through a range of degradation mechanisms. In order to minimize the effect that hot spot temperatures have on device reliability a detailed understanding of relevant transport mechanisms must be developed. This study focuses on two main aspects of phonon transport within GaN devices. The first area of focus was to establish an understanding of phonon relaxation times within bulk GaN. These relaxation times were calculated from an application of Fermi's Golden Rule and explicitly conserve energy and crystal momentum. This analysis gives insight into the details behind the macroscopic thermal conductivity parameter. Once relaxation times for GaN were established a multiscale phonon transport modeling methodology was developed that allowed the Boltzmann Transport Equation to be coupled to the energy equation. This coupling overcomes some computational limits and allows for nanoscale phenomena to be resolved within a macroscopic domain. Results of the transport modeling were focused on benchmarking the coupling method as well as calculating the temperature distribution within an operating 6 finger HEMT.

Ce travail de thèse porte sur les propriétés de transport thermique liées aux phonons dans un nouveau matériau nanostructuré constituée de couches minces de Ge:Mn de type "electron crystal - phonon glass". Ce matériau est élaboré par épitaxie par jets moléculaire au CEA/INAC à Grenoble sur des substrats spécifiques « Germanium-on-insulator (GOI) ». Il consiste en une matrice de germanium possédant une qualité cristalline parfaite dans laquelle sont inclues une importante concentration de nano-inclusions de Ge3Mn5 de forme quasi-sphérique. Révélé par les caractérisations de TEM, les nano-inclusions ont une distribution de diamètre variant de 5 à 50 nm. Il est par ailleurs possible de jouer sur les paramètres de croissance afin de modifier la dispersion de taille des inclusions ainsi que leur concentration. Cette possibilité nous a donc permit d'étudier l'influence des nano-inclusions sur le transport de chaleur de façon exhaustive autour de la température ambiante.Pour ce faire, une expérience de mesure de conductivité thermique « 3 omega » dédiée à ces échantillons et extrêmement sensible, a été fabriquée à l'institut Néel. Cette expérience nous a permis de mesurer les variations de conductivité thermique induites par la modification de la distribution en taille des nano-inclusions de Ge:Mn dans des couches minces d'une centaine de nanomètre d'épaisseur avec une erreur réduite d'environ 12%. Il a été montré que le transport thermique dans ces couches minces pouvait être réduit d'un facteur 20 comparé au germanium massif puisque des valeurs de conductivité thermique de l'ordre de 3 W.m-1.K-1 ont été mesurées. Ces valeurs ont été confirmées par des expériences SThM au CETHIL de Lyon. Les valeurs obtenues sont mêmes en dessous de la limite d'alliage pour le SiGe, ce qui n'est pas explicable par les théories actuelles. Ces faibles conductivités thermiques ainsi que la grande mobilité des porteurs dans le germanium font de ces matériaux à base de GeMn de bons candidats pour la thermoélectricité. Des simulations numériques ont été utilisées afin de mieux comprendre cette diminution spectaculaire de la conductivité thermique et d'interpréter les données expérimentales. / This PhD project is an exhaustive study on the characterization of the thermal properties of a new type semiconducting materials based on germanium. It is a germanium matrix containing nano-inclusions with the objective of creating a perfect "electron crystal - phonon glass" material. The materials are thin films of an epitaxial germanium matrix embedded with Ge:Mn nano-inclusions, grown on a Germanium-on-insulator (GOI) substrate in CEA/INAC in Grenoble. From TEM images of the thin films it has been demonstrated that both the matrix and inclusions are monocrystalline, and the nano-inclusions have generally a spherical form with a diameter distribution ranging from 5 to 50 nm. Depending on the growth parameters in molecular beam epitaxy, i.e. the Mn concentration and the annealing temperature, the geometries, mean diameters and diameter distributions of nano-inclusions in Ge:Mn can be varied. With these unique structural features, these Ge:Mn thin films are one of the most interesting models for the study of the influence of nano-inclusions on thermal transport in a crystalline matrix.The characterization of the thermal properties of the material have been done using two advanced techniques: the 3-omega method in Institut Néel, and the Scanning Thermal Microscopy (SThM) in CETHIL (Centre d'Energétique et de Thermique de Lyon) in Lyon. A highly sensitive differential 3-omega measurement setup has been developed in the work, which permits precise (error~12%) measurements of electrical conductive thin films having low thermal conductivities. Dramatically reduced thermal conductivities have been revealed for Ge:Mn thin films containing different Mn% and having different inclusion geometries at room temperature, compared to crystalline bulk Ge. A minimum value of 3.3 Wm-1K-1 was found for Ge:Mn thin film containing 10% Mn, beating the “alloy limit” of thermal conductivity set by SiGe alloys at room temperature (6-12 Wm-1K-1). The measurement results of SThM confirmed the low thermal conductivities for all Ge:Mn/GOI samples at room temperature. Numerical simulations using different models have been performed to try to interpret the experimental results and to understand the mechanisms of the influence of the nano-inclusions on the phonon transport in semiconductor materials.