In the pursuit of enhancing the electronic properties of transparent p-type semiconductors, this work uses density functional theory to study the effects of doping tin monoxide with nitrogen, antimony, yttrium and lanthanum. An overview of the theoretical concepts and a detailed description of the methods employed are given, including a discussion about the correction scheme for charged defects proposed by Freysoldt and others [Freysoldt 2009]. Analysis of the formation energies of the defects points out that nitrogen substitutes an oxygen atom and does not provide charge carriers. On the other hand, antimony, yttrium, and lanthanum substitute a tin atom and donate n-type carriers. Study of the band structure and density of states indicates that yttrium and lanthanum improves the hole mobility. Present results are in good agreement with available experimental works and help to improve the understanding on how to engineer transparent p-type materials with higher hole mobilities.

Suspensões coloidais de microesferas de poliestireno carregadas proporcionam um sistema experimental excelente para estudar muitos problemas em física da matéria condensada. Sob condições apropriadas as partículas nessas suspensões podem se auto-organizar em um cristal com ordem de longo alcance, o chamado cristal coloidal. Neste trabalho apresentamos resultados de simulações por Dinâmica Molecular relacionados a defeitos pontuais, vacâncias e interstícios, em um cristal coloidal 2D. Calculamos a energia de formação e a interação destes defeitos pontuais, mostrando que um interstício é mais provável de ser criado do que uma vacância e que a interação entre os defeitos (vacância-vacância e interstício-interstício) é atrativa. Em conjunto esses resultados apontaram que os defeitos pontuais podem afetar o mecanismo de fusão do cristal coloidal 2D. Com relação à dinâmica dos defeitos, o foco foi sobre as vacâncias. Calculamos as entalpias de migração deste defeito de uma forma original, baseada na troca de topologias. Concluímos que a vacância não difunde de acordo com um único mecanismo, mas sim um misto de dois comportamentos, são eles: relação de Arrhenius corrigida e relação de potência com a temperatura. Calculamos também as entalpias e entropias relativas de formação das topologias da vacância, o que possibilitou identificar as topologias mais estáveis. Acreditamos que esses resultados serão importantes para trabalhos experimentais envolvendo interfaces e superfícies sólidas. / Colloidal suspensions of charged polystyrene microspheres provide an excellent experimental system to study many problems in condensed matter physics. Under appropriate conditions the particles in these suspensions organize themselves in a long-range-ordered crystal, the so-called colloidal crystal. In this thesis we report Molecular Dynamics simulations on point defects, vacancies and interstitials, in a 2D colloidal crystal. We have calculated the formation energy and interaction of these point defects, as well as the energy barriers between the various topological configurations that the defects may adopt while in thermal equilibrium. It is shown that the interstitials are more likely to be formed than the vacancies, and the interaction between defects (vacancy-vacancy and interstitial-interstitial) is attractive. Taken together, these results indicate that point defects may affect the melting process of a 2D colloidal crystal. With regard to the dynamics of the defects, emphasis was placed on the vacancies. The enthalpy for migration of a vacancy was calculated on the basis of exchanges between topologies. We concluded that the vacancy does not diffuse according to a single mechanism, but rather through a mixture of two processes: one is a modified Arrhenius mechanism and the other is represented by a power-law dependence on the temperature. We also calculated the relative enthalpies and entropies associated with the formation of the different topologies of vacancies, which allowed identification of the most stable topologies. We believe these results may have important bearing on experimental works involving interfaces and solid surfaces.

Suspensões coloidais de microesferas de poliestireno carregadas proporcionam um sistema experimental excelente para estudar muitos problemas em física da matéria condensada. Sob condições apropriadas as partículas nessas suspensões podem se auto-organizar em um cristal com ordem de longo alcance, o chamado cristal coloidal. Neste trabalho apresentamos resultados de simulações por Dinâmica Molecular relacionados a defeitos pontuais, vacâncias e interstícios, em um cristal coloidal 2D. Calculamos a energia de formação e a interação destes defeitos pontuais, mostrando que um interstício é mais provável de ser criado do que uma vacância e que a interação entre os defeitos (vacância-vacância e interstício-interstício) é atrativa. Em conjunto esses resultados apontaram que os defeitos pontuais podem afetar o mecanismo de fusão do cristal coloidal 2D. Com relação à dinâmica dos defeitos, o foco foi sobre as vacâncias. Calculamos as entalpias de migração deste defeito de uma forma original, baseada na troca de topologias. Concluímos que a vacância não difunde de acordo com um único mecanismo, mas sim um misto de dois comportamentos, são eles: relação de Arrhenius corrigida e relação de potência com a temperatura. Calculamos também as entalpias e entropias relativas de formação das topologias da vacância, o que possibilitou identificar as topologias mais estáveis. Acreditamos que esses resultados serão importantes para trabalhos experimentais envolvendo interfaces e superfícies sólidas. / Colloidal suspensions of charged polystyrene microspheres provide an excellent experimental system to study many problems in condensed matter physics. Under appropriate conditions the particles in these suspensions organize themselves in a long-range-ordered crystal, the so-called colloidal crystal. In this thesis we report Molecular Dynamics simulations on point defects, vacancies and interstitials, in a 2D colloidal crystal. We have calculated the formation energy and interaction of these point defects, as well as the energy barriers between the various topological configurations that the defects may adopt while in thermal equilibrium. It is shown that the interstitials are more likely to be formed than the vacancies, and the interaction between defects (vacancy-vacancy and interstitial-interstitial) is attractive. Taken together, these results indicate that point defects may affect the melting process of a 2D colloidal crystal. With regard to the dynamics of the defects, emphasis was placed on the vacancies. The enthalpy for migration of a vacancy was calculated on the basis of exchanges between topologies. We concluded that the vacancy does not diffuse according to a single mechanism, but rather through a mixture of two processes: one is a modified Arrhenius mechanism and the other is represented by a power-law dependence on the temperature. We also calculated the relative enthalpies and entropies associated with the formation of the different topologies of vacancies, which allowed identification of the most stable topologies. We believe these results may have important bearing on experimental works involving interfaces and solid surfaces.

In this thesis point defects in semiconductors are studied by electronic structure calculations. Results are presented for the stability and equilibrium concentrations of native defects in GaP, InP, InAs, and InSb, for the entire range of doping conditions and stoichiometry. The native defects are also studied on the (110) surfaces of InP, InAs, and InSb. Comparing the relative stability at the surface and in the bulk, it is concluded that the defects have a tendency to migrate to the surface. It is found that the cation vacancy is not stable, but decomposes into an anion antisite-anion vacancy complex. The surface charge accumulation in InAs is explained by complementary intrinsic doping by native defects and extrinsic doping by residual hydrogen. A technical investigation of the supercell treatment of defects is performed, testing existing correction schemes and suggesting a more reliable alternative. It is shown that the defect level of [2VCu-IIICu] in the solarcell-material CuIn1-xGaxSe2 leads to a smaller band gap of the ordered defect γ-phase, which possibly explains why the maximal efficiency for CuIn1-xGaxSe2 has been found for x=0.3 and not for x=0.6, as expected from the band gap of the α-phase. It is found that Zn diffuses via the kick-out mechanism in InP and GaP with activation energies of 1.60 eV and 2.49 eV, respectively. Explanations are found for the tendency of Zn to accumulate at pn-junctions in InP and to why a relatively low fraction of Zn is found on substitutional sites in InP. Finally, it is shown that the equilibrium solubility of dopants in semiconductors can be increased significantly by strategic alloying. This is shown to be due to the local stress in the material, and the solubility in an alloy can in fact be much higher than in either of the constituting elements. The equilibrium solubility of Zn in Ga0.9In0.1P is for example five orders of magnitude larger than in GaP or InP.

To assist technology advancements, it is important to continue the search for new materials. The stability of a crystal structures is closely connected to its formation energy. By calculating the formation energies of theoretical crystal structures it is possible to find new stable materials. However, the number of possible structures are so many that traditional methods relying on quantum mechanics, such as Density Functional Theory (DFT), require too much computational time to be viable in such a project. A presented alternative to such calculations is machine learning. Machine learning is an umbrella term for algorithms that can use information gained from one set of data to predict properties of new, similar data. Feature vector representations (descriptors) are used to present data in an appropriate manner to the machine. Thus far, no combination of machine learning method and feature vector representation has been established as general and accurate enough to be of practical use for accelerating the phase diagram calculations necessary for predicting material stability. It is important that the method predicts all types of structures equally well, regardless of stability, composition, or geometrical structure. In this thesis, the performances of different feature vector representations were compared to each other. The machine learning method used was primarily Kernel Ridge Regression, implemented in Python. The training and validation were performed on two different datasets and subsets of these. The representation which consistently yielded the lowest cross-validated error was a representation using the Voronoi tessellation of the structure by Ward et. al. [Phys. Rev. B 96, 024104 (2017)]. Following up was an experimental representation called the SLATM representation presented by Huang and von Lilienfeld [arXiv:1707.04146], which is partially based on the Radial Distribution Function. The Voronoi representation achieved an MAE of 0.16 eV/atom at 3534 training set size for one of the sets, and 0.28 eV/atom at 10086 training set size for the other set. The effect of separating linear and non-linear energy contributions was evaluated using the sinusoidal and Coulomb representations. The result was that separating these improved the error for small training set sizes, but the effect diminishes as the training set size increases. The results from this thesis implicate that further work is still required for machine learning to be used effectively in the search for new materials.

We present a self-consistent calculation of the mono vacancy formation energy for seven simple metals Li, Na, K, Rb, Cs (all bcc), Al (fcc) and Mg (hcp) using both model and ab initio pseudopotential used in earlier unified studies. The local model pseudopotential calculations show small variations with respect to different exchange-correlation functions and the results are in fair agreement with other similar calculations and the available experimental data. The comparisons show that reliable model (pseudo) potential for simple metals can indeed be obtained for explaining a host of properties. Also, considering the importance of third order term in ab initio calculations, the results of our second order calculation appear fairly reasonable and are comparable with other first principle calculations. The perturbation series being an oscillating one, we hope to improve the calculational results using suitable series convergence acceleration method in the next part of our study.

Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / Bi12GeO20 (BGO) belongs to the family of sillenite crystals BMO, where M = Ge, Si, Ti. These compounds exhibit remarkable photorefractive e ect and therefore are used in the development of information and image storage technologies, holography, ampli cation of luminous signals and dynamic interferometry. One of the strategies used to enhance the properties of interest of these sillenites is doping. The defects can create photorefractive centers in the matrix, introducing energy levels within the gap, in uencing the electronic and optical properties of the selenites. Experimental work reported a curious behavior when using transition metal ions (TMI) as dopants. Most of the TMIs, including Cr ions, are allocated at the high symmetry site Ge4+, with the exception of Cu2+ which enters into the matrix at the low symmetry site of Bi3+. This is a surprising fact due to the di erence between ionic radii and charge states of the dopants and the substitution ion Ge4+. In this work the LAPW method, based on the DFT theory and implemented in the WIEN2k program, was used to study the electronic, structural and energetic properties of pure BGO and doped BGO with chromium ions. In the study of doped cases, Cr ions were inserted at the substitutional sites of Ge4+ and Bi3+ The calculations were performed for neutral and charged systems. The approximations for correlation and exchange e ects were made through GGA-PBE and mBJ potentials. Were performed calculations of lattice parameter optimization, relaxation of atomic positions, state density, Bader charge and formation energies of defects. It was possible to nd the lattice parameter, and the band gap energy os the BGO pure, to analyse the way how the neighbourhood of the substitutional site behaves with the presence of the defect and nd the states that populate the valence and conduction bands of the studies cases. These data were taking into account to measure the ions valence. The results of the modeling showed that Cr prefers to accommodate in the BGO matrix with Cr3+/4+ valences. The preferential accommodation site of Cr3+ is Bi3+, which didn't meet with what has been reported experimentally in the literature. / O Bi12GeO20 (BGO) pertence a fam lia de cristais silenitas do tipo BMO, onde M = Ge, Si, Ti. Tais compostos apresentam um not avel efeito fotorrefrativo e por isso s~ao utilizados no desenvolvimento de tecnologias de armazenamento de informa c~oes e imagens, hologra a, amplia c~ao de sinais luminosos e interferometria din^amica. Uma das estrat egias utilizadas para potencializar as propriedades de interesse dessas silenitas e a dopagem. Os defeitos podem criar centros fotorrefrativos na matriz, introduzindo n veis de energias dentro do gap e in uenciar nas propriedades eletr^onicas e opticas das silenitas. Trabalhos experimentais relataram um comportamento curioso ao se utilizar ons de metais de transi c~ao (TMI) como dopantes. A maior parte dos TMIs, incluindo os ons de Cr, s~ao alocados no s tio de alta simetria Ge4+, com exce c~ao do Cu2+ que se insere na matriz no s tio de baixa simetria do Bi3+. Esse e um fato surpreendente devido a diferen ca entre raios i^onicos e estados de carga dos dopantes e do on substitucional Ge4+. Neste trabalho foi utilizado o m etodo LAPW, baseado na teoria DFT e implementado no programa WIEN2k, para estudar as propriedades eletr^onicas, estruturais e energ eticas do BGO puro e dopado com ons de cromo. No estudo de casos dopados, os ons de Cr foram inseridos nos s tios substitucionais Ge4+ e Bi3+. Os c alculos foram executados para sistemas neutros e carregados. As aproxima c~oes para os efeitos de correla c~ao e troca foram feitas atrav es do funcional GGA-PBE e do potencial mBJ. Foram realizados c alculos de otimiza c~ao de par^ametro de rede, relaxa c~ao de posi c~oes at^omicas, densidade de estados, carga de Bader e energias de forma c~ao de defeito. Foi poss vel encontrar o par^ametro de rede, a energia de gap do BGO puro, analisar a forma como a vizinhan ca do s tio substitucional se comporta com a presen ca do defeito e encontrar os estados que populam as bandas de val^encia e condu c~ao dos casos estudados. Esses dados foram levados em conta para aferir a val^encia dos ons. Os resultados das modelagens mostraram que o Cr prefere se acomodar na matriz do BGO com val^encias Cr3+/4+. O s tio de acomoda c~ao preferencial do Cr3+ e o Bi3+, o que vai de encontro ao que foi relatado experimentalmente na literatura. / São Cristóvão, SE

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work represents a theoretical study, based on density functional theory (DFT), on structural, electronic and optical properties of magnesium tetraborate (MBO, MgB 4 O 7 ) compound and of antisite Bi M O 4 defect in Bi 12 MO 20 (BMO, M=Ge, Si, Ti) compounds. All calculations have been realized by linear augmented plane wave (LAPW) method implemented in Wien2k computer code. The relaxation of atomic positions and lattice parameters has been performed using LDA (MBO) and PBE-GGA (BMO) exchange- correlation (XC) functional. Electronic structure, optical properties and chemical bonds were investigated using the semi-local XC potential of Tran and Blaha (TB-mBJ), which significantly improved the band gap description and optical properties of studied systems. The thesis is divided in two parts. The first refers to study of magnesium tetraborate in pure form. Electronic structure calculations predicted a 9.58 eV band gap value, quite close to the value determined in the similar compounds. The electronic structure around the band gap is found to be dominated by the O 2p-states and 2p-states of the boron ion with trigonal coordination with neighbouring O‘s. Optical properties were analysed in terms of complex dielectric tensor which imaginary part is directly proportional to the optical absorption spectra. The latter is found to exhibit two prominent peaks. The lower energy peak originates from electron transitions within the trigonal B−O 3 structural group. Refractive index, reflectivity, extinction coefficient and energy loss were analysed in ultraviolet range (up to 40 eV) and all calculated optical properties are found to be anisotropic. The second part presents a theoretical study upon the antisite defect Bi M O 4 in sillenites compounds, which consists of wrong occupation of the M site by the Bi ion. Calculations were performed firstly for the pure compounds. The crystal structure has been computatio- nally optimized and the band gaps found to be 3.39 eV, 3.35 eV and 3.37 eV for the BGO, BSO and BTO respectively. These values are in very good agreement with experimental data. Defects were investigated in q=-1,0,1 charge states. Electronic structure calculations demonstrated that the antisite defect introduces an energy band inside the gap formed by O 2p- and 6s- states of Bi M ion. This band occupation is directly related to the defect charge state. The neutral defect presents a semi populated band, the positively defect adonor band and the negatively defect an acceptor band. The Bader analysis confirmed that the electron added or removed from the host system is always localised in the area of the defect. The analysis of the defect formation energies demonstrated that the neutral defect is energetically favourable, and thus dominates the lowest thermal state of the sillenites (also called colour state). On the other hand, the charged defects are predominant in the so-called transparent thermal state of the sillenites. From the results, it was possible to associate the presence of the antisite defect with important properties observed in the BMO crystals, such as: (1) explanation of the charge mobility required to produce the photorefractive effect; (2) reversible transitions between the thermal states and (3) photocromic effect in sillenites. / Nesse trabalho foi realizado um estudo te´orico, baseado na Teoria do Funcional da Densidade (DFT), das propriedades estruturais, eletrˆonicas e ´opticas do tetraborato de magn´esio (MgB 4 O 7 ) e um estudo do defeito tipo antiss´ıtio Bi M O 4 em cristais do estruturas silenitas Bi 12 MO 20 (BMO, onde M=Ge, Si e Ti). As otimiza¸c˜oes das posi¸c˜oes atˆomicas e parˆametros de rede foram realizadas para todos os sistemas utilizando o funcional LDA e GGA-PBE para o MgB 4 O 7 e BMO’s, respecti- vamente. As estruturas eletrˆonicas e propriedades ´opticas do sistemas estudados foram calculadas utilizando o m´etodo LAPW implementado no c´odigo computacional WIEN2k. Os efeitos de correla¸c˜ao e troca, das estruturas eletrˆonicas e ´opticas, foram simulados pelo recentemente desenvolvido potencial TB-mBJ, que foi mostrado ser adequado para tratamento de sistemas que possuem gap. Essa tese foi dividida em duas partes. A primeira parte refere-se ao estudo do tetraborato de magn´esio puro. Os c´alculos da estrutura eletrˆonica resultaram em um valor do gap de 9,58 eV, bem pr´oximo ao esperado (comparando a compostos similares). O topo da banda de valˆencia ´e dominado por estados 2p dos oxigˆenios, enquanto o fundo da banda de condu¸c˜ao consiste predominantemente de estados 2p do boro de coordena¸c˜ao trigonal com os oxigˆenios vizinhos (BO 3 ). As caracter´ısticas propriedades ´opticas foram calculadas a partir do tensor diel´etrico complexo, cuja parte imagin´aria ´e diretamente proporcional ao espectro de absor¸c˜ao ´optica verificou-se que a borda de absor¸c˜ao ´optica ´e originada por poss´ıveis transi¸c˜oes eletrˆonicas entre os ´ıons que formam a estrutura trigonal BO 3 . O espectro de absor¸c˜ao tamb´em indicou um car´ater anisotr´opico para o composto. O ´ındice de refra¸c˜ao, coeficiente de extin¸c˜ao, refletividade e a perda de energia de el´etrons foram calculados na regi˜ao ultravioleta at´e 40 eV. A segunda parte refere-se ao estudo do defeito tipo antiss´ıtio em silenitas. Os cristais foram estudados nas formas puras e com a presen¸ca de um ´atomo de Bi ocupando o s´ıtio do ´atomo M (Bi M O 4 ). Os defeitos foram investigados nos estados de carga q=−1, 0, +1. Os band gaps dos BMO’s puros foram determinados com os valores de 3,39 eV para BGO, 3,35 eV para BSO e 3,37 eV para o BTO. Atrav´es das an´alises das densidades de estados eletrˆonicos foi confirmado que o defeito antiss´ıtio introduz uma banda de energia situada dentro do intervalo de energias proibidas,bandgap, formada por estados 2p dos oxigˆenios e 6s do defeito Bi M . A popula¸c˜ao eletrˆonica dessa banda est´a diretamente relacionada ao estado de carga. O defeito neutro (Bi 0 M ) introduz uma banda semi populada, o defeito carregado negativamente (Bi −1 M ) uma banda doadora e o defeito carregado positivamente (Bi +1 M ) uma banda aceitadora. A an´alise das liga¸c˜oes qu´ımicas confirmou que a adi¸c˜ao (ou retirada) de um el´etron do sistema sempre ocorre na banda associada ao defeito. A an´alise da energia de forma¸c˜ao de defeito constatou que o defeito neutro ´e o energeticamente favor´avel, dominando assim o estado de menor energia (tamb´em chamado de estado colorido). A partir dos resultados, tamb´em foi poss´ıvel associar a presen¸ca do defeito antiss´ıtio como geradora de importantes propriedades observadas nos cristais BMO’s, tais como: a mobilidade de carga que ocasiona o efeito fotorrefrativo; a compreens˜ao das transi¸c˜oes revers´ıveis entre estados t´ermicos e o efeito fotocrˆomico.

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