Neste trabalho utilizamos o método k.p na aproximação de função envelope, que é uma ferramenta muito útil para a solução de problemas relacionados a heteroestruturas em geral. Apresentamos a análise de heteroestruturas semicondutoras com confinamento espacial nas três direções de crescimentos {Quantum Dots}, utilizando o Hamiltoniano de Kane (8x8) em sua forma generalizada para descrever os estados do elétrons na banda de condução e na banda valência. Fazendo uso dessa ferramenta foram realizadas simulações de estruturas de banda em sistemas quase zero-dimensionais de InAs em matrizes de GaAs, em vários formatos e dimensões e sob diferentes estados de tensionamento. Um estudo sistemático de como as propriedades geométricas e as dimensões de um dado sistema podem influenciar os estados eletrônicos do mesmo foi também realizado, onde puderam ser confirmadas a presença de estados localizados e a sensibilidade do comportamento dos estados eletrônicos a estas propriedades. Pudemos observar um deslocamento para o vermelho no espectro de fotoluminescência com o aumento das dimensões do sistemas estudados. Foram ainda realizados cálculos de {Quantum Dots} de InN em matriz de GaN, que permitem explorar outras regiões do espectro eletromagnético e observamos o comportamento dos mesmos sob estados de tensionamentos diferentes. Com base nos autoestados do sistema foram calculados espectros de fotoluminescência para as heteroestruturas aqui estudadas, permitindo uma comparação direta com resultados experimentais. Como pode-se verificar o strain exerce importância primordial na determinação dos estados eletrônicos dos sistemas estudados e na presença do hidrostático pode-se verificar mudanças apreciáveis na resposta óptica do material, onde pode ser observado um deslocamento para o azul quando levado em consideração a presença de um hidrostático. / In this work, we use the k.p method in the approximation of the envelope function, that is a very useful tool, to the solution of heterostructure related problems. We present a semiconductor heterostructure analysis with confinement on the three directions (Quantum Dots), using the Kane Hamiltonian (8x8) on its generalized form to describe electron eigenstates on the conduction and valence bands. Using this tool, we have made band structure simulations in quasi zero-dimensional systems of InAs in GaAs matrices, in diverse shapes and dimensions and on different tension states. A systematic study of how the geometrical properties and dimensions of a given system could influence the electronic states was also done. There can be confirmed the presence of localized states and the sensitivity of the electronic states to these properties.We could observe a deviation to the red on the photoluminescence spectrum with the increase of the system dimensions. There were also made calculations on InN dots in a GaN matrix, which allow to explore other electromagnetic spectral regions and we have studied their behavior under different tension states. From the system eigenvalues, we calculated the photoluminescence spectra from the heterostructures studied here, allowing a direct comparison with experimental results. It can be verified that the strain is is extremely important on the determination of the electronic states of the studied systems in the presence of an hydrostatic strain. We could observe important modifications on the optical responseof the material, where there is a deviation to the blue when it is considered the presence of the hydrostatic strain.

Devido à inconfiabilidade do modelo EM-X?, no cálculo da energia total, consideramos uma correção na densidade de carga \"muffin-tin\". Com esta correção podemos ajustar a energia total, a partir de parâmetros definidos na teoria. O objetivo deste trabalho é o estudo da curva da energia total associada ao estado excitado do sistema GaAs: AsGa, quando o átomo substitucional de As se desloca na direção . Partindo de cálculos de primeiros princípios (LARGE UNIT CELL APPROACH), reproduzimos a curva da energia total do estado fundamental. A partir dos parâmetros encontrados na correção não \"muffin-tin\" da densidade de carga, calculamos a curva do estado excitado utilizando o conceito de estado de transição de Slater. Nossos resultados mostraram que o efeito Jahn-TeIler não ocorre para defeitos tipo antisítio. Vimos também que a curva do comportamento dos autovalores com o deslocamento do átomo substitucional, está de acordo com cálculos recentes encontrados na literatura. / Since total energy calculations within the Multiple Scattering-X? model are not reliable, a non \"muffin-tin\" correction to the charge density has been considered. With this correction the total energy can be adjusted through parameters defined in the theory. The aim of this work is to study the total energy curve of the excited state of the GaAs: AsGa system when the arsenic substitutional atom is displaced in the direction. As a first step, the ground-state total energy curve obtained from first-principles calculations (LARGE UNIT CELL APPROACH) was reproduced. From the parameters found for the non \"muffin-tin\" charge density corrections, we have calculated the excited-state total energy curve by using the Slater transition-state concept. Our results show that the Jahn-Teller effect is not expected to occur for antisite-like defects. Moreover, the obtained behavior of the eigenvalues with displacement of the substitutional atom is in fairly good agreement with recent theoretical calculations found in the literature.

Quantum Monte Carlo (QMC) methods are a class of stochastic techniques that can be used to compute the properties of electronic systems accurately from first principles. This thesis is mainly concerned with the development of trial wave functions for QMC. An extension of the backflow transformation to inhomogeneous electronic systems is presented and applied to atoms, molecules and extended systems. The backflow transformation I have developed typically retrieves an additional 50% of the remaining correlation energy at the variational Monte Carlo level, and 30% at the diffusion Monte Carlo level; the number of parameters required to achieve a given fraction of the correlation energy does not appear to increase with system size. The expense incurred by the use of backflow transformations is investigated, and it is found to scale favourably with system size. Additionally, I propose a single wave function form for studying the electron-hole system which includes pairing effects and is capable of describing all of the relevant phases of this system. The effectiveness of this general wave function is demonstrated by applying it to a particular transition between two phases of the symmetric electron-hole bilayer, and it is found that using a single wave function form gives a more accurate physical description of the system than using a different wave function to describe each phase. Both of these developments are new, and they provide a powerful set of tools for designing accurate wave functions. Backflow transformations are particularly important for systems with repulsive interactions, while pairing wave functions are important for attractive interactions. It is possible to combine backflow and pairing to further increase the accuracy of the wave function. The wave function technology that I have developed should therefore be useful across a very wide range of problems.

Le tellurure de mercure et de cadmium (HgCdTe ou MCT) est un matériau reconnu pour la physique de la matière condensée, dont l'histoire, datant aujourd'hui de plus de cinquante ans, constitue un excellent exemple des progrès remarquables réalisés dans la recherche sur les semi-conducteurs et les semi-métaux. Notre travail est principalement motivé par l’intérêt fondamental que suscitent ces systèmes, mais notre recherche peut également avoir un impact pratique (indirect) sur la médecine, la surveillance ou la détection de l’environnement ainsi que sur les systèmes de sécurité. Cela peut aider à améliorer les performances des photodétecteurs dans la limite des grandes longueurs d'onde ou à faciliter la fabrication de dispositifs émettant de la lumière.La présente thèse de doctorat vise principalement à combler certaines des lacunes de notre compréhension de la structure de bande électronique des hétérostructures 2D et quasi-2D basées sur les matériaux HgTe/HgCdTe et InAs/InSb, qui peuvent être transformés en phase topologiquement isolante à l'aide des paramètres de croissance. Pour explorer leurs propriétés, la technique expérimentale de base, la magnéto-spectroscopie infrarouge et THz fonctionnant dans un large éventail de champs magnétiques, est combinée à des mesures complémentaires de magnéto-transport. Cette combinaison de méthodes expérimentales nous permet d’obtenir de précieuses informations sur les états électroniques non seulement à l’énergie de Fermi, mais également dans son voisinage relativement large. Diverses hétérostructures ont été étudiées avec des caractéristiques globales et/ou spécifiques déterminées principalement par les paramètres de croissance.La réponse magnéto-optique observée, due aux excitations intra-bande (résonance cyclotron) et interbandes (entre les niveaux de Landau) peut être interprétée dans le contexte d'études antérieures sur des échantillons 3D, des puits quantiques et des super-réseaux, mais également en rapport aux attentes théoriques. Ici, nous visons à obtenir une explication quantitative des données expérimentales recueillies, mais également à développer un modèle théorique fiable. Ce dernier comprend le réglage précis des paramètres de structure de bande présents dans le modèle établi de Kane, mais surtout, l'identification de termes supplémentaires pertinents (d'ordre élevé) nécessaires pour parvenir à un accord quantitatif avec nos expériences. On peut s’attendre à ce que les corrections dues à ces termes supplémentaires affectent davantage les sous-bandes de valence, généralement caractérisées par des masses effectives relativement importantes et, par conséquent, par une grande densité d’états ou, lorsque le champ magnétique est appliqué, par un espacement assez étroit (et mélange important) des niveaux de Landau. / Mercury cadmium telluride (HgCdTe or MCT) is a time-honored material for condensed matter physics, whose history  nowadays more than fifty years long  may serve as an excellent example of remarkable progress made in research on semiconductors and semimetals. The ternary compound HgCdTe implies two important aspects, which largely contributed to its undoubted success in solid-states physics.The present PhD thesis primarily aims at filling some of existing gaps in our understanding of the electronic band structure in 2D and quasi-2D heterostructures based on HgTe/HgCdTe and InAs/InSb materials, which both may be tuned into topologically insulating phase using particular structural parameter. To explore their properties, the primal experimental technique, infrared and THz magneto-spectroscopy operating in a broad of magnetic fields, is combined with complementary magneto-transport measurements. This combination of experimental methods allows us to get valuable insights into electronic states not only at the Fermi energy, but also in relatively broad vicinity.The observed magneto-optical response - due to intraband (cyclotron resonance) and interband inter-Landau level excitations - may be interpreted in the context of previous studies performed on bulk samples , quantum wells and superlattices, but also compared with theoretical expectations. Here we aim at achieving the quantitative explanation of the collected experimental data, but also further developing a reliable theoretical model. The latter includes the fine-tuning of the band structure parameters present in the established Kane model, but even more importantly, identifying additional relevant (high-order) terms and finding their particular strengths, needed to achieve quantitative agreement with our experiments. One may expect that corrections due to these additional terms will more affect the valence subbands, which are in general characterized by relatively large effective masses. Consequently, valence subbands have larger density of states compared to conduction band or, when the magnetic field is applied, rather narrow spacing (and possibly large mixing) of Landau levels.

Mn5Ge3 suscite de l'intérêt pour des applications dans le domaine de l'électronique de spin car il a une température de Curie élevée (≈300 K) et il peut croître épitaxialement sur des substrats Ge(111) permettant ainsi d'injecter directement dans le semi-conducteur Ge un courant polarisé en spin.Nous avons étudié par photoémission résolue en angle et en spin (ARPES, SARPES), utilisant le rayonnement synchrotron, des films minces de Mn5Ge3(001), obtenus par croissance sur la surface reconstruites Ge(111)-c(2x8).Les résultats ARPES, obtenus dans les plans GALM et GAHK, sont en accord avec des simulations faites sur la base de calculs de structure de bandes faisant appel à la théorie de la fonctionnelle de la densité.Les mesures SARPES faites en plusieurs points du plan GALM sont aussi bien reproduites par ces simulations.D'une façon globale, nos résultats apportent une validation remarquable de la description des propriétés électroniques de Mn5Ge3 par le modèle de bandes. Seule l'intensité spectrale au niveau de Fermi n'est pas bien expliquée par la simulation. Cette différence est attribuée à la nature tridimensionnelle de l'échantillon et à des effets de corrélation. / Mn5Ge3 attracts strong interest for spintronics applications because it has a high Curie-temperature (≈300 K) and it can be grown epitaxially on Ge(111) substrates, permitting direct injection of a spin-polarized current into the Ge semiconductor.Mn5Ge3(001) thin films grown on Ge(111)-c(2x8) reconstructed surface were studied by angle- and spin- resolved photoemission (ARPES, SARPES) using synchrotron radiation. ARPES results, obtained in the GALM and GAHK planes, are in agreement with simulations done with the help of band structure calculations based on the density functional theory, taking into account lifetime broadening and broadening caused by correlation effects.SARPES measurements done at several k-points of the GALM plane are also well acounted for by these simulations.Overall our results provide a remarkable validation of the band structure model for a proper description of the electronic properties of Mn5Ge3. Only the spectral intensity at the Fermi level is not well explained by the simulation. This departure is attributed to the 3D nature of the sample and to correlation effects.

Devido à inconfiabilidade do modelo EM-X?, no cálculo da energia total, consideramos uma correção na densidade de carga \"muffin-tin\". Com esta correção podemos ajustar a energia total, a partir de parâmetros definidos na teoria. O objetivo deste trabalho é o estudo da curva da energia total associada ao estado excitado do sistema GaAs: AsGa, quando o átomo substitucional de As se desloca na direção . Partindo de cálculos de primeiros princípios (LARGE UNIT CELL APPROACH), reproduzimos a curva da energia total do estado fundamental. A partir dos parâmetros encontrados na correção não \"muffin-tin\" da densidade de carga, calculamos a curva do estado excitado utilizando o conceito de estado de transição de Slater. Nossos resultados mostraram que o efeito Jahn-TeIler não ocorre para defeitos tipo antisítio. Vimos também que a curva do comportamento dos autovalores com o deslocamento do átomo substitucional, está de acordo com cálculos recentes encontrados na literatura. / Since total energy calculations within the Multiple Scattering-X? model are not reliable, a non \"muffin-tin\" correction to the charge density has been considered. With this correction the total energy can be adjusted through parameters defined in the theory. The aim of this work is to study the total energy curve of the excited state of the GaAs: AsGa system when the arsenic substitutional atom is displaced in the direction. As a first step, the ground-state total energy curve obtained from first-principles calculations (LARGE UNIT CELL APPROACH) was reproduced. From the parameters found for the non \"muffin-tin\" charge density corrections, we have calculated the excited-state total energy curve by using the Slater transition-state concept. Our results show that the Jahn-Teller effect is not expected to occur for antisite-like defects. Moreover, the obtained behavior of the eigenvalues with displacement of the substitutional atom is in fairly good agreement with recent theoretical calculations found in the literature.

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-06-06T19:33:29Z No. of bitstreams: 1 EdvanMoreira.pdf: 4583939 bytes, checksum: 5ab3a481fd56c037eec7e3edec77e8b9 (MD5) / Made available in DSpace on 2017-06-06T19:33:29Z (GMT). No. of bitstreams: 1 EdvanMoreira.pdf: 4583939 bytes, checksum: 5ab3a481fd56c037eec7e3edec77e8b9 (MD5) Previous issue date: 2008-03-31 / Fundação de Amparo à Pesquisa e ao Desenvolvimento Científico e Tecnológico do Maranhão (FAPEMA) / From its discovery, the nanotubes of carbon are seen as material’s highly promising for a lot of applications. The combination of nanotubes of carbon with other molecules is the most general form of modifying their properties. New methods to control and to tune these properties are necessary for the developing of their potentials applications. The functionalization has been proposed as one of the processes capable to modify the optical properties of the nanotubes of carbon, through chemical reaction ”it is arrested”another molecule in the surface of the nanotube. However, another more elegant form of functionalization is through the encapsulation of molecules inside the nanotube. Recently, the encapsulation of the molecule of the beta-carotene experimentally in nanotubes of carbon was accomplished and changes were verified in the absorption spectrum. In this work we performed simulations of molecular dynamics using field of similar universal force to test the encapsulation of the beta-carotene, and calculations of Electronic Structure to verify charge transference. The obtained results of the molecular dynamics confirm that the encapsulation of the -carotene happens in the three cases studied experimentally by Yanagi and collaborators. / Desde sua descoberta, os nanotubos de carbono são vistos como um material altamente promissor para muitas aplicações. A combinação de nanotubos de carbono com outra molécula é a forma mais geral de se modificar suas propriedades. Novos métodos para controlar e sintonizar estas propriedades são necessários afim de se desenvolver suas potenciais aplicações. A funcionalização tem sido proposta como um dos processos capaz de se modificar as propriedades ópticas dos nanotubos de carbono, através de reação química ”prende-se”a outra molécula na superfície do nanotubo. Entretanto, uma outra forma mais elegante de funcionalização se dá através do encapsulamento de moléculas no interior do nanotubo. Recentemente, foi realizado experimentalmente o encapsulamento da molécula do beta-caroteno em nanotubos de carbono e foram constatadas mudanças no espectro de absorção. Neste trabalho realizamos simulações de dinâmica molecular usando campo de força universal afim de verificar se o encapsulamento do beta-caroteno ocorre, e cálculos de Estrutura Eletrônica para verificar se há ou não transferências de carga no sistema. Os resultados obtidos da dinâmica molecular confirmam que o encapsulamento do beta-caroteno ocorre nos 3 casos reportados experimentalmente por Yanagi e colaboradores.

Os resultados apresentados neste trabalho estão sistematizados em três partes. Em uma primeira etapa, efetuamos um estudo sistemático do comportamento da estrutura eletrônica em super-redes de deltas em função do período da super-rede e em função da concentração planar de dopantes. Uma nova abordagem, que se baseia no método celular e na solução autoconsistente das equações de Schroedinger e de Poisson, foi desenvolvida e aplicada para super-redes com dopagem planar tipo n em GaAs e em silício. Em ambos os casos, foi observada a transição de um comportamento eletrônico de caráter bi- para tridimensional conforme o período da super- rede diminui. No caso de super-redes de deltas de Si em GaAs foi empreendido o cálculo da energia de corte nos espectros de fotoluminescência de excitação. Uma boa concordância com as medidas experimentais foi obtida. O estudo da estrutura eletrônica para o caso de super-rede de deltas de Sb em Si foi pioneiro. Isto tornou os resultados de nossa investigação teórica de importância fundamental para experimentais e teóricos atuando na 6rea. A concordância entre nossas previsões teóricas e dados experimentais da literatura demonstram a consistência e o poder da abordagem desenvolvida. Em uma segunda etapa, foi efetuado o estudo da distribuição espacial do campo elétrico interno em heteroestruturas contendo camadas tipo \"bulk\", compostas por GaAs e (A1Ga)As. Uma nova abordagem foi desenvolvida para a execuqi3o de cálculos dos perfis de potencial eletrostático e de campo elétrico, sem assumir a ionização total dos dopantes e a não-degenerescência do material. Nosso método transforma a equação de Poisson em uma equação integral que deve ser resolvida autoconsistentemente. Os exemplos numéricos demonstram a aplicabilidade de nossa abordagem a sistemas reais. Perfis do campo elétrico calculados são usados para interpretar os espectros de fotorefletância. Em uma terceira etapa, a teoria geral da fotorefletância de heteroestruturas semicondutoras foi desenvolvida neste trabalho para tornar a interpretação de espectros de fotorefletância precisa e de aplicação eficiente. Um novo metodo de cdculo do coeficiente de reflexgo na presenga de inomogeneidade espacial da funggo dieletrica no interior de cada camada fmeceu um novo patamar de cornpreens20 dos espectros de fotorefletiincia. Este metodo e baseado na construgiio de uma matriz de transferhcia que iraclui as inomogeneidades no interior da camada de um mod0 integral. Portanto, para descrever uma camada de heteroestrutura e preciso ter apenas uma ma& de transferencia. 0s resultados de simulag6es numericas de espectros da fotoreflethcia estilo em uma concordhcia bastante boa com aqueles obtidos atravb de medidas opticas. A eficiencia de nosso metodo o torna aplicavel a simulag6es tip0 \"on-line\". 0s resultados dos metodos anteriores sgo reproduzidos como casos limites de nossa abordagem geral. / The results presented in this work can be displayed along the following three lines. In the first we performed a systematical study of the electronic structure behavior in delta superlattices as a function of superlattice period and sheet doping concentration. A new approach, based on the cellular method and on the selfconsistent solution of Schroedinger and Poisson equations, was developed and applied to superlattices with n-type delta doping in GaAs and silicon. In both cases, a transition from bi- to three- dimensional electronic behavior with the decrease of superlattice period was observed. For Si delta-doping superlattices in GaAs we performed calculations of the energy threshold in the photoluminescence excitation spectra. A good agreement with experimentally measured values was observed. Our investigation of the electronic structure of Sb delta-doping superlattices in Si was a pioneer theoretical study. Due to thls fact, the results of our work are of great importance for experimentalists and theoreticians acting in this area. The agreement between our theoretical predictions and the available experimental data demonstrates the consistency and the power of the developed approach. Along the second line we studied electric field spatial distribution inside of heterosinctures containing bulk layers of GaAs and (A1Ga)As. A new approach was developed to calculate the electrostatic potential and electric field profiles, providing the possibility to take .into account the incomplete ionization of impurities and the degeneracy of the materials. Our method transforms the Poisson equation into an integral equation, which must be solved selfconsistently. Numerical examples show the way to apply our approach to real systems. Internal electric field proiiles, calculated by means of our method are used to interpret photoreflectance spectra. In the third line, a general theory of photoreflectance for semiconductor heterostructures was developed in this work to make the interpretation of fotoreflectance spectra more precise and straightfornard. A new method to calculate the reflection coefficient in the presence of weak spatial inhomogenities of the dielectrical function inside each layer, provided us with a new degree of comprehension of the photoreflectance spectra. This method is based on the construction of a transfer matrix which includes the inhomogenities inside the layer in an integral way. This explains why we need only one matrix to describe one layer of the heterostructure. Results of our numerical simulations are in very good agreement with data of optical measurements. The efficiency of our method makes it suitable for on-line simulations. The results of previous methods emerge from our general approach as limit cases.

Dans cette thèse nous avons réalisé une étude théorique concernant les mécanismes de formation et les propriétés de transport électronique de fils de section atomique d’Au et de Pt.Pour cela, nous avons utilisé un Hamiltonien de Liaisons Fortes donnant accès aux propriétés électroniques et à l’énergie totale. Lors de nos simulations de traction de nanofils cristallins en Dynamique Moléculaire nous avons observé la formation de structures assimilables `a des nanotubes dont la chiralité évolue au cours de la déformation. En poursuivant la traction, nous avons observé la formation de structures planes (ou rubans) dans le cas de l’Au et du Pt. Ces rubans permettent de former des fils de section atomique pour l’Au mais pas pour le Pt, la différence étant liée aux propriétés mécaniques des éléments. Les calculs réalisés sur les propriétés de transport ont mis en évidence des effets d’interférence destructive induits par la géométrie du système. / In this thesis we study the formation mechanisms and the electronic transport propertiesof Au and Pt atomic wires. We have used a Tight Binding Hamiltonian giving access to theelectronic structure and to the total energy. By performing traction simulations of cristallinenanowires by Molecular Dynamics we observe the formation of structures similar to nanotubeswhose chirality evolve during the deformation. Following the traction process we observe theformation of planar structures (or ribbons) for both Au and Pt. These ribbons give rise to theformation of wires of atomic section for Au but not for Pt, the different behavior is related withthe different elastic properties of the two elements. Our preliminary results on the electronictransport properties show interference effects induced by the geometry which can cancel out theconductance.

Le dioxyde d'uranium (UO2) est le combustible nucléaire le plus largement utilisé dans les réacteurs nucléaires à travers le monde. En conditions d’exploitation, UO2 est soumis au flux de neutrons et subit des réactions en chaîne de fission nucléaire, ce qui crée un grand nombre de produits de fission et des défauts ponctuels. L'étude du comportement des produits de fission et des défauts ponctuels est importante pour comprendre les propriétés du combustible sous irradiation. Nous effectuons des calculs de structure électronique basés sur la théorie de la fonctionnelle de la densité (DFT) pour modéliser les dégâts d’irradiation à l'échelle atomique. La méthode DFT+U est utilisé pour décrire les fortes corrélations des électron 4f du cérium et des électrons 5f de l’uranium dans les matériaux étudiés (UO2, CeO2 et (U, Ce)O2). (U, Ce)O2 est étudié car il est considéré comme un matériau modèle peu radioactif d'oxydes d’actinides mixtes comme (U, Pu)O2 qui est le combustible d'oxydes mixtes (MOX) utilisé dans les réacteurs à eau légère et les réacteurs à neutrons rapides. Le dioxyde de cérium (CeO2) est étudié pour des données de référence de (U, Ce)O2. Nous effectuons une étude DFT+U des défauts ponctuels et des produits de fission gazeux (Xe et Kr) dans CeO2 et comparons nos résultats à ceux déjà existants pour l’UO2. Nous étudions les propriétés en volume, ainsi que le comportement des défauts pour (U, Ce)O2, et comparons nos résultats à ceux de (U, Pu)O2. En outre, pour l'étude des défauts dans UO2, des améliorations méthodologiques sont explorées considérant l'effet de couplage spin-orbite et l’effet de taille finie de la supercellule de modélisation. / Uranium dioxide (UO2) is the most widely used nuclear fuel in existing nuclear reactors around the world. While in service for energy supply, UO2 is submitted to the neutron flux and undergoes nuclear fission chain reactions, which create large number of fission products and point defects. The study of the behavior of the fission products and point defects is important to understand the fuel properties under irradiation. We conduct electronic structure calculations based on the density functional theory (DFT) to model this radiation damage at the atomic scale. The DFT+U method is used to describe the strong correlation of the 4f electrons of cerium and 5f electrons of uranium in the materials studied (UO2, CeO2 and (U, Ce)O2). (U, Ce)O2 is studied because it is considered as a low radioactive model material of mixed actinide oxides such as the MOX fuel (U, Pu)O2 used in light water reactors and fast neutron reactors. Cerium dioxide (CeO2) is studied to provide reference data of (U, Ce)O2. We perform a DFT+U study of point defects and gaseous fission products (Xe and Kr) in CeO2 and compare our results to the existing ones of UO2We study the bulk properties as well as the behavior of defects for (U, Ce)O2, and compare our results to the ones of (U, Pu)O2. Furthermore, for the study of defects in UO2, methodological improvements are explored considering the spin-orbit coupling effect and the finite-size effect of the simulation supercell.