Advances in microelectronics and nanotechnology have generated tremendous interest in the non-Fourier regimes of heat conduction, where the conventional theories based on local equilibrium no longer apply. The non-Fourier regimes include small length scales, where the medium can no longer be treated using bulk properties due to ballistic transport, and short time scales, on the order of the relaxation time of heat carriers, such as in short pulse laser heating. One of the objectives of this thesis is to clarify some misunderstandings in hyperbolic heat equation (HHE), commonly thought as a remedy of Fourier's law at small time scales. The HHE is analyzed from the stand point of statistical mechanics with an emphasis on the consequences of assumptions applied to the Boltzmann transport equation (BTE) when deriving the HHE. In addition, some misperceptions of the HHE, caused by a few experiments and confusion with other physical phenomena, are clarified. It is concluded that HHE should not be interpreted as a more general equation governing heat transport because of several fundamental limitations. The other objective of this thesis is to introduce radiation entropy to the equation of phonon radiative transport (EPRT) for understanding the heat transfer mechanism on a fundamental level which can be applied to both diffusion and ballistic heat conduction in dielectric solids. The entropy generation due to phonon transport is examined along with the definition of a phonon brightness temperature, which is direction and frequency dependent. A better understanding of non-Fourier heat conduction will help researchers and engineers to choose appropriate theories or models in analyzing thermal transport in nanodevices.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Optical frequency combs have resulted in significant advances in optical frequency metrology and found wide application to precise physical measurements and molecular fingerprinting. A direct analogue of frequency combs in the phononic or acoustic domain has not been reported to date. This thesis describes a series of results to provide the first clear evidence for the generation of phononic frequency combs in the domain of micromechanical resonators. These results are supported by a theoretical framework which was originally developed to predict the existence of such features of combs in physical systems described by Fermi-Pasta-Ulam dynamics. The phononic frequency combs is mediated by nonlinear coupling between a primary driven mode and one or more parametrically excited internal modes. We provide experimental evidence for the formation of such phononic frequency combs in systems comprising of 2 or more coupled modes, with results qualitatively consistent with previous numerical studies based on Fermi-Pasta-Ulam dynamics. Additionally, externally pumped comb processes are also reported. Through systematic experiments at different drive frequencies and amplitudes, we portray the well-connected processes of phononic frequency comb formation and define attributes to control their concomitant features. Further, the interplay between these new nonlinear resonances and the well-established Duffing phenomenon is also discussed. While the experimental verification of the existence of phononic frequency combs is of scientific interest, several potential engineering applications exist including the unique capability to track resonant frequency of a micromechanical resonator without the requirement for an external feedback loop to sustain oscillations at the resonant frequency. The initial experimental results also demonstrate that good short-term frequency stability may be obtained for such micromechanical resonators operated under ambient conditions.

This thesis presents work done on the calculation of the effects of anharmonic nuclear motion on the properties of solid materials from first principles. Such anharmonic effects can be significant in many cases. A vibrational self-consistent field (VSCF) method is used as the basis for these calculations, which is then improved and applied to a variety of solid state systems. Firstly, work done to improve the efficiency of the VSCF method is presented. The standard VSCF method involves using density functional theory (DFT) to map the Born-Oppenheimer (BO) energy surface that the nuclei move in, a computationally expensive process. It is shown that the accurate forces available in plane-wave basis DFT can be used to help map the BO surface more accurately and reduce the computational cost. This improved VSCF+f method is tested on molecular and solid hydrogen, as well as lithium and zirconium, and is found to give a speed-up of up to 40%. The VSCF method is then applied to two different systems of physical interest. It is first applied to the case of the neutral vacancy in diamond, in order to resolve a known discrepancy between harmonic ab initio calculations and experiment -- the former predict a static Jahn-Teller distortion, whilst the latter leads to a dynamic Jahn-Teller effect. By including anharmonic corrections to the energy and nuclear wavefunction, we show that the inclusion of these effects results in agreement between first-principles calculations and experiment for the first time. Lastly, the VSCF method is applied to barium titanate, a prototypical ferroelectric material which undergoes a series of phase transitions from around 400 K downwards. The nature of these phase transitions is still unclear, and understanding them is an active area of research. We describe the physics of the phase transitions of barium titanate, including both anharmonicity and the effect of polarisation caused by long wavelength vibrations, to help understand the important physics from first principles.

The polaron problem is studied, on an infinite lattice, using the continuous-time path-integral quantum Monte Carlo scheme The method is based on the Feynman technique to analytically integrate out the phonon degrees of freedom. The transformed problem is that of a single electron with retarded self-interaction in imaginary time. The Metropolis algorithm is used to sample an ensemble of electron trajectories with twisted (rather than periodic) boundary conditions in imaginary time, which allows dynamic properties of the system to by measured directly. The method is numerically "exact", in the sense that there are no systematic errors due to finite system size, trotter decomposition or finite temperature The implementation of the algorithm in continuous imaginary time dramatically increases computational efficiency compared with the traditional discrete imaginary time algorithms.

Ce travail de thèse a pour objectif d'étudier et de mieux comprendre les relations structure-propriétés de céramiques transparentes Yb:CaF2 obtenues par voie humide, en particulier sur le plan des propriétés thermiques. Dans un premier temps nous présentons les atouts des céramiques transparentes Yb:CaF2 dans le cadre d'une application en laser de puissance. Le procédé de fabrication par voie humide des céramiques est ensuite décrit au cours d'une seconde partie. Les résultats d'analyses et caractérisations diverses ayant eu lieu à différentes étapes de la synthèse des céramiques sont présentés, menant à une optimisation du procédé de fabrication. Un troisième chapitre est ensuite consacré à une étude expérimentale des propriétés thermiques de nos céramiques, qui montre en particulier une grande similitude avec les propriétés des monocristaux. Cette étude est complétée par un volet de modélisation décrit dans un quatrième chapitre. Deux modèles prédictifs de conductivité thermique sont explorés et comparés, et permettent d'apporter une explication théorique aux tendances observées expérimentalement. L'hypothèse selon laquelle l'impact des joints de grains sur la diminution de la conductivité thermique est négligeable devant celui du dopage est notamment confirmée. Enfin, dans une cinquième et dernière partie, plusieurs pistes sont explorées afin d'apporter une explication à l'échauffement supérieur des céramiques par rapport aux monocristaux observé en conditions laser. / This PHD work is aiming at getting a better understanding of the structure-properties relationships of Yb:CaF2 transparent ceramics obtained with a wet-route fabrication process, with a special focus on thermal properties. At first, we introduce the assets of Yb:CaF2 transparent ceramics in the frame of high-power laser applications. The wet-route fabrication process is then described in a second chapter. The results of several analysis and characterizations performed along different steps of the ceramics synthesis are also presented, leading to an optimized fabrication process. The third chapter then focuses on an experimental study of the thermal properties of our ceramics, which shows in particular an important similarity with single crystals properties. This study is complemented with a modelization work described in chapter four. Two predictive models of thermal conductivity are investigated and compared. They bring a theoretical explanation to the tendencies experimentally observed. We thereby confirm the hypothesis according to which the grain boundaries impact on thermal conductivity is negligible with respect to that of the doping element introduction. Finally, in the fifth and last chapter, several hypothesis are investigated in order to bring an explanation to the ceramics overheating observed in laser conditions, which is superior to single crystals.

Monte Carlo based statistical approach to solve Boltzmann Transport Equation (BTE) has become a norm to investigate heat transport in semiconductors at sub-micron regime, owing mainly to its ability to characterize realistically sized device geometries qualitatively. One of the primary issues with this technique is that the approach predominantly uses empirically fitted phonon dispersion relations as input to determine the properties of phonons so as to predict the thermal conductivity of specified material geometry. The empirically fitted dispersion relations assume harmonic approximation thereby failing to account for thermal expansion, interaction of lattice waves, effect of strain on spring stiffness, and accurate phonon-phonon interaction. To circumvent this problem, in this work, a coupled molecular mechanics-Monte Carlo (MM-MC) platform has been developed and used to solve the phonon Boltzmann Transport Equation (BTE) for the calculation of thermal conductivity of several novel and emerging nanostructures. The use of the quasi-anharmonic MM approach (as implemented in the open source NEMO 3-D software toolkit) not only allows one to capture the true atomicity of the underlying lattice but also enables the simulation of realistically-sized structures containing millions of atoms. As compared to the approach using an empirically fitted phonon dispersion relation, here, a 17% increase in the thermal conductivity for a silicon nanowire due to the incorporation of atomistic corrections in the LA (longitudinal acoustic) branch alone has been reported. The atomistically derived thermal conductivity as calculated from the MM-MC framework is then used in the modular design and analysis of (i) a silicon nanowire based thermoelectric cooler (TEC) unit, and (ii) a GaN/InN based nanostructured light emitting device (LED). It is demonstrated that the use of empirically fitted phonon bandstructure parameters overestimates the temperature difference between the hot and the cold sides and the overall cooling efficiency of the system, thereby, demanding the use of the BTE derived thermal conductivity in the calculation of thermal conductivity. In case of the light-emitting device, the microscopically derived material parameters, as compared to their bulk and fitted counterparts, yielded ~3% correction (increase) in optical efficiency. A non-deterministic approach adopted in this work, therefore, provides satisfactory results in what concerns phonons transport in both ballistic and diffusive regimes to understand and/predict the heat transport phenomena in nanostructures.

Orientador: Carlos Rettori / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-17T05:10:39Z (GMT). No. of bitstreams: 1 Garcia_FernandoAssis_D.pdf: 2669059 bytes, checksum: 122a24668135bef8b9e2ee683190a28a (MD5) Previous issue date: 2010 / Resumo: Esta tese aborda o problema geral dos efeitos de campos cristalino e rattling modes em compostos do tipo skutterudite. Emprega, predominantemente, a técnica de ressonância de spin eletrônico (ESR, ou EPR na literatura clássica) a fim de sondar a simetria local dos estados eletrônicos associados a íons de terras raras nestes compostos e investigar as inomogeneidades decorrentes da dinâmica (rattling modes) destes íons. Desenvolvemos o nosso estudo predominantemente sob o sistema Ce1-xRxFe4P12 (R = Gd, Dy, Er, Yb), usualmente descrito como um semicondutor com gap G ¿ 0.15 eV. Nossos resultados apontam que a correta determinação dos efeitos de campo cristalino requer uma nova abordagem no estudo de compostos com simetria Th. O grupo pontual Th é um dos cinco grupos pontuais cúbicos (O, Oh, T, Th, Td) e é obtido pelo produto T x sh, onde T descreve a simetria de um tetraedro regular. Desta maneira, Th não possui as operações 6C4 e 3C¿2 e precisamos utilizar um novo parâmetro de sexta ordem para descrever todos os invariantes da simetria do grupo pontual Th Este novo parâmetro causa uma mistura na simetria do estado fundamental de sistemas cúbicos que dá origem a fenômenos não triviais discutidos na tese. Resultado igualmente importante é que, a partir do estudo deste novo parâmetro, fomos capazes de mapear a inomogeneidade de campo cristalino decorrente da dinâmica dos íons de terra rara. Desta maneira, a técnica de ESR foi utilizada pela primeira vez no estudo da dinâmica de íons em sistemas do tipo gaiola. Os estudos em sistemas S (L = 0) mostraram ainda que os efeitos desta dinâmica nos espectros de ESR não depende da presença deste parâmetro, sendo algo mais geral. Esta tese examina estes dois importantes aspectos relacionados a estrutura cristalina da família das skutterudites e discute estes resultados no contexto das possíveis aplicações destes compostos na construção de dispositivos termoelétricos e também no estudo de fenômenos fortemente correlacionados / Abstract: This thesis addresses the general problem of crystall field effects and rattling modes in skut- terudite compounds. It employs, predominantly, the electron spin resonance technique (ESR or EPR, in the classical literature) aiming to probe the local point symmetry of the electronic states associated to the rare earth ions and the inohomogenities implied by their dynamics (rattling modes). Our study was mainly directed to the Ce 1-xRxFe4P12 (R = Gd, Dy, Er, Yb) compounds, usually described as a small gap semiconductor (G ¿ 0.15 eV). Our results pointed that the correct determination of the crystall field effects requires a new approach in the case of compounds with Th symmetry. The point group Th is one the five cubic point groups (O, 0h, T, Th, Td) being generated by the product T x sh, where T describes the full symmetry of a regular tetrahedron. In this sense, Th lacks the symmetry operations 6C4 e 3C¿2 and we need a new sixth order parameter, to describe all the invariants of point group T^ symmetry. This new parameter gives rise to a mix of the ground state symmetry of cubic systems, implying in non trivial phenomena discussed in this these. Interesting enough, following these results, we were able to map the crystall field ino-homogenities due to the dynamics of the rare earth ion within the skutterudite cage. In this sense, the ESR techinique was introduced as a probe to the guest ion dynamics in cage systems. Investigation of S systems (L = 0) showed that the effects of this dynamics in our experiment does not require the presence of this new sixth order parameter, being associated to a more general role of the rattling modes. We examine these two important aspects related to crystal structure of the skutterudite family and discuss the results in the context of possible applications of these compounds in the construction of thermoelectric devices and also in the study of strongly correlated phenomena / Doutorado / Física da Matéria Condensada / Doutor em Ciências

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Estudamos as estruturas e as propriedades dinÃmicas de um cristal clÃssico bidimensional (2D) em bicamadas de partÃculas dipolares magnÃticas carregadas em um arranjo no qual os dipolos sÃo perpendiculares Ãs camadas e com mesma densidade de partÃculas em cada camada. A energia do sistema à devido à interaÃÃo carga - carga (interaÃÃo coulom- biana) e a interaÃÃo dipolo - dipolo. Devido ao fato dessas interaÃÃes serem de longo alcance, usamos o mÃtodo da soma de Ewald para obter uma expressÃo para a energia envolvendo somas que convergem rapidamente. Comparando as energias de possÃveis geometrias do cristal, determinamos o diagrama de fase do sistema em funÃÃo do parÃmetro η (que està relacionado com a distÃncia entre as camadas de dipolos magnÃticos carregados e a densidade de partÃculas) e da intensidade relativa das interaÃÃes elÃtrica e magnÃtica. Mudando a intensidade relativa da interacÃo dipolo - dipolo com respeito à interaÃÃo elÃtrica, podemos encontrar seis diferentes estruturas cristalinas estÃveis em funÃÃo de η. Uma caracterÃstica interessante desse sistema à a possibilidade de permanecer em arranjos nos quais as camadas sÃo ou nÃo deslocadas uma em relaÃÃo a outra, apenas variando a interaÃÃo magnÃtica entre os dipolos, por exemplo, atravÃs de um campo magnÃtico externo. As transiÃÃes entre as estruturas cristalinas podem ser contÃnuas e descontÃnuas. No intuito de investigar a estabilidade das configuraÃÃes de mÃnima energia, calculamos o espectro dos fÃnons do sistema usando a aproximaÃÃo harmÃnica. Para isto, recorremos novamente a tÃcnica de Ewald para obter somas que convergem rapidamente. A anÃlise da relaÃÃo de dispersÃo (fÃnons) revela caracterÃsticas do sistema que sÃo de grande utilidade no estudo da transiÃÃo sÃlido-lÃquido (fusÃo). / We study the structural and dynamical properties of a two-dimensional (2D) classical bi-layer crystal of charged magnetic dipolar particles in a setup where the dipoles are oriented perpendicular to the layers and equal density of charged dipolar particles in each layer. The energy of the system is due to the charge - charge interaction (Coulomb interaction) and the dipole - dipole interaction. Due to the long-range nature of the interactions, we use the Ewald summation method to obtain an expression for the energy involving rapidly convergent sums. By comparing the energies of a number of possible crystal geometries, we determine the phase diagram of the system as a function of the parameter η (which is related to the separation between the layers of charged magnetic dipoles and the particle density) and the relative intensity of the magnetic and electrical interactions. By changing the relative intensity of the dipole - dipole interaction with respect to electrical one, we are able to find six diferent stable crystalline structures as a function of η. An interesting feature of the present model system is the possibility to tune between the matched and staggered arrangements by varying the magnetic interaction between the dipoles, e.g. through an external magnetic field. The phase boundaries of the crystalline structures consist of both continuous and discontinuous transitions. In order to investigate the stability of the minimum energy arrangements we also calculate the phonon spectra of the system within the harmonic approximation. In this case, we resort again on the Ewald technique to obtain the rapidly convergent sums. The analysis of the phonon spectra reveals interesting features which are useful in the study of melting.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-05-25T20:26:17Z No. of bitstreams: 1 diegoferreiracarneiro.pdf: 6578490 bytes, checksum: b8b30b289f5b6f707ae31c8a290081dc (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-05-26T13:10:20Z (GMT) No. of bitstreams: 1 diegoferreiracarneiro.pdf: 6578490 bytes, checksum: b8b30b289f5b6f707ae31c8a290081dc (MD5) / Made available in DSpace on 2017-05-26T13:10:20Z (GMT). No. of bitstreams: 1 diegoferreiracarneiro.pdf: 6578490 bytes, checksum: b8b30b289f5b6f707ae31c8a290081dc (MD5) Previous issue date: 2016-02-26 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho é estudado o tunelamento ressonante numa heteroestrutura de dupla barreira (HDB) considerando a interação elétron-fônon na presença de um campo magnético paralelo à corrente de tunelamento. O dispositivo é uma heteroestrutura na escala nanométrica composta por GaAs/AlGaAs. Este é controlado por um potencial externo (bias) e quando os elétrons decaem do estado excitado dentro do poço para o fundamental emitem fônons ópticos primários (LO1). Tais fônons decaem num par de longitudinais ópticos secundários (LO2) e transversais acústicos (TA), podendo ser representado por LO1 →LO2 +TA. Os fônons TA produzidos formam um feixe coerente na faixa do terahertz(THz), definindo assim o saser. O sistema pode ser representado pelo hamiltoniano tight-binding que leva em consideração a interação entre elétrons, fônons e elétron-fônon. A fim de calcular a transmitância e a corrente eletrônica fora do equilíbrio, para uma temperatura finita, utilizaram-se funções de Green retardadas no formalismo de Keldysh. Resolvemos um sistema de equações cinéticas que descreve a dinâmica dos elétrons e fônons no saser. Os fônons TA têm um tempo de vida muito grande e um livre caminho médio que poderia passar de um centímetro. No limite de baixas temperaturas e campos magnéticos fracos, nossos resultados coincidem com os obtidos anteriormente. No formalismo de Keldysh consideramos os níveis de Landau que, além dos fônons LO1, abrem novos canais para fluxo de elétrons no dispositivo. Obtemos os resultados para magnetotunelamento ressonante que estão de acordo com as observações experimentais e estudos teóricos com outros formalismos. / In this work we study the resonant tunneling through a double barrier heterostructure considering the electron-phonon interaction in the presence of a magnetic field parallel to the tunneling current. The device studied here is a heterostructure at the nanoscale composed of GaAs/AlGaAs. It is controlled by an external potential. For a given bias electrons decay from the excited state in the well to the ground state by emitting primary optical phonons (LO1). That phonons decay into a pair of longitudinal optical (LO2) and transverse acoustic (TA), being represented by LO1 →LO2 +TA. The TA phonons form a coherent beam produced in the terahertz range (THz), defining the saser. The system was described by a thight-binding Hamiltonian that includes the electrons, the phonons and the electron-phonon interaction. In order to calculate the transmittance and electron current out of equilibrium at finite temperature, Keldysh Green functions were used. We solve a system of kinetic equations that describes the dynamics of electrons and phonons in the saser. The phonons TA have a very long lifetime and a mean free path that could reach more than one centimeter. In the limit of low temperatures and low magnetic fields our results coincide with those obtained previously In this Keldysh formalism we consider Landau levels that, besides the LO1 phonons, opens new channels for the flow of electrons in the device. We obtain the results for resonant magnetotunneling according to the experimental observations and other theoretical studies.