Thesis advisor: David A. Broido / Using density functional perturbation theory and a full solution of the linearized phonon Boltzmann transport equation (BTE), a parameter-free theory of semiconductor thermal properties is developed. The approximations and shortcomings of previous approaches to thermal conductivity calculations are investigated. The use of empirical interatomic potentials in the BTE approach is shown to give poor agreement with measured values of thermal conductivity. By using the adiabatic bond charge model, the importance of accurate descriptions of phonon dispersions is highlighted. The extremely limited capacity of previous theoretical techniques in the realm of thermal conductivity prediction is highlighted; this is due to a dependence on adjustable parameters. Density functional perturbation theory is coupled with an iterative solution to the full Boltzmann transport equation creating a theoretical construct where thermal conductivity prediction becomes possible. Validation of the approach is demonstrated through the calculation of a range of thermal properties for a set of polar and non-polar semiconductors which are compared with measured values. The agreement between theory and measurement is very good, confirming the promise of the theoretical approach. Due to the significant computational effort required by the parameter-free calculations, new forms for room temperature relaxation time approximations are derived. The resulting forms produce thermal conductivity values in very good agreement with the ab initio data across a wide temperature range. It is therefore shown that accurate relaxation time approximations can be developed, fixing the adjustable parameters to the ab initio theory avoiding any comparison with measured data. This approach improves the accuracy of phonon relaxation times compared with previous models. / Thesis (PhD) — Boston College, 2009. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

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Density functional theory (DFT) is a widely used quantum mechanical method for the simulation of the electronic structure of atoms, molecules, and solids. The only part that needs to be approximated is the exchange-correlation energy as a functional of the electron density. After many-year development, there is a huge variety of exchange-correlation functionals. According to the ingredients, an exchange-correlation functional can be classified as a semi-local functional or beyond. A semi-local functional can be nonempirical or empirical and only uses locality information, such as electron density, gradient of the density, Laplacian of the density, and kinetic energy density. Unlike a non-local functional that uses non-locality information, a semi-local functional is computationally efficient and can be applied to large systems. The meta-generalized gradient approximation (meta-GGA), which is the highest-level semi-local functional, has the potential to give a good description for condensed matter physics and quantum chemistry. We built the self-consistent revised Tao-Perdew-Staroverov-Scuseria (revTPSS) meta-GGA into the band-structure program BAND to test the performances of some self-consistent semi-local functionals on lattice constant with a 58-solid test set. The self-consistent effect of revTPSS was also discussed. The vibration of a crystal has a contribution to the ground state energy of a system, which is the zero-point energy at zero temperature. It has anharmonicity at the equilibrium geometry. The standard DFT doesn’t consider the zero-point energy of a crystal. We used density functional perturbation theory (DFPT), which is a powerful and flexible theoretical technique within the density functional framework, to study the zero-point energy and make a correction to the lattice constant. The method was compared to a traditional zero-point anharmonic expansion method that is based on the Debye and Dugdale-MacDonald approximations. We also tested some new meta-GGA functionals (revTPSS, regularized revTPSS, and meta-GGA made simple) on a big molecular test set - GMTKN30 - that is composed of 30 smaller test sets and covers a large cross section of chemically relevant properties. The performances of these new meta-GGAs were compared with some other popular functionals or meta-GGAs. / acase@tulane.edu

Cette thèse traite des problématiques fondamentales liées aux phonons dans le cadre des cellules solaires à porteurs chauds. Ce concept appartient aux technologies photo-voltaïques dites de troisième génération, et vise à l’extraction des porteurs de chargesphotogénérés non-encore à l’équilibre thermique avec le réseau cristallin, conduisant àun rendement théorique maximum de l’ordre de la limite thermodynamique. Un des enjeuxmajeurs est ainsi le ralentissement du refroidissement des porteurs, refroidissement qui setraduit principalement par l’émission de phonon LO via l’interactions électron-phonon.En plus de l’idée d’écranter ce dernier processus, une approche consiste à concevoir unmatériau absorbeur dans lequel le phonon LO présente un temps de vie intrinsèque pluslong qu’il ne l’est dans les matériaux classiques, favorisant ainsi sa réabsorption par lesporteurs. Dans une première partie, et utilisant la théorie de la fonctionnelle densité per-turbée, la décoposition du phonon LO est étudiée en terme d'états finaux disponibles. Suit une discussion sur le calcul du temps de vie de ces phonons, et sur la possibilité d’atteindre les critères phononiques définis comme suffisants. Dans une deuxième partie, une étude de l’interaction électron-phonon est menée dans les super-réseaux. La constante de couplage est reliée au champ électriquemacroscopique induit par le phonon LO, de sorte à pourvoir précisément rendre compte deson anisotropie. Il apparaît que la dimensionalité des populations électroniques et phononiques est différemment affectée. Cette étude appelle à développer l’analyse de ce type de structure dans le cadre des cellules à porteurs chauds. / This thesis deals with fundamental issues related to phonons in hot-carrier solar cells, athird generation photovoltaic technology. This concept aims at extracting photogeneratedcharge carriers before their reach a thermal equilibrium with the lattice, and exhibits a the-oretical efficiency close to thermodynamic limit. One of the main issue is to hinder carriercooling, which occurs through LO-phonon emission. In addition to the idea of screeningthe electron-phonon interaction, one approach consists in designing an absorber in which theLO-phonon has an intrinsic lifetime longer than what it is in conventional materials, en-hancing the rate of its reabsorption by the carriers. The LO-phonon decay and lifetimeis first investigated in semiconductors within density functional perturbation theory. Spe-cific criteria for relevant absorbing materials choosing, from a phonon point of view, arederived. A full study of the LO-phonon lifetime is performed on a singular material, andthe possibility to achieve the sufficient phononic requierements is discussed. Secondly, theabove-mentioned electron-phonon interaction is modelled in superlattices. The couplingstrength is related to the LO-phonon induced macroscopic electric field, which allows tostudy the directional dependence of the phonon emission. The latter reveals to differentlyaffect the dimensionality of the electronic and phononic interacting populations. Thisstudy calls for development of these structure in the framewok of hot-carrier solar cells.

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