Na condução por saltos dispersiva, os portadores de carga são caracterizados por tempos de residência não exponenciais. Como uma conseqüência, efeitos hereditários aparecem e o problema deve ser conduzido no espaçõ de Laplace. Distribuições dielétricas conhecidas e algumas outras foram usadas como possíveis funções capazes de descrever o meio desordenado. Um estudo cuidadoso de seus espectros de freqüência foi realizado. O método de inversão de Widder truncado foi desenvolvido para possibilitar a volta do espaço de Laplace para o do tempo real. Dois tipos de problemas práticos foram abordados: condução dispersiva na qual o campo elétrico das cargas móveis pode ser desprezado e o caso de carga espacial para o qual essa aproximação não pode ser feita. Duas configurações de interesse foram escolhidas: decaimento do potencial de superfície de amostras carregadas por descarga corona e a subida do potencial no carregamento por corrente constante. / Dispersive conductive process are characterized by non-exponential residence times of the hopping carrier. As a consequence, hereditary effects appear and the problem must be conducted in the Laplace space. A bunch of known dielectric distributions functions and others were used as possible functions describing the disordered medium. A careful study of their frequency spectrum was carried out. The truncate Widder inversion was developed in order to allow returning from the Lapace to the real time space. Two kind of practical problems were studied: dispersive conduction in which the electric field of the mobile charge may be neglected and the space charge ones when that approximation cannot be made. Two configurations of interest were selected: the corona discharge potential decay and the constant current potentinal build-up.

Submitted by Cátia Araújo (catia.araujo@unipampa.edu.br) on 2017-01-25T11:32:18Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Um modelo para dispersão de poluentes na camada limite planetária com coeficientes de difusão dependentes da distância da fonte.pdf: 1813716 bytes, checksum: 2b7788e4583766741e3b5c4e7ae8da30 (MD5) / Approved for entry into archive by Cátia Araújo (catia.araujo@unipampa.edu.br) on 2017-01-25T11:33:16Z (GMT) No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Um modelo para dispersão de poluentes na camada limite planetária com coeficientes de difusão dependentes da distância da fonte.pdf: 1813716 bytes, checksum: 2b7788e4583766741e3b5c4e7ae8da30 (MD5) / Made available in DSpace on 2017-01-25T11:33:16Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Um modelo para dispersão de poluentes na camada limite planetária com coeficientes de difusão dependentes da distância da fonte.pdf: 1813716 bytes, checksum: 2b7788e4583766741e3b5c4e7ae8da30 (MD5) Previous issue date: 2013-07-15 / Este trabalho apresenta a solução da equação da difusão-advecção bidimensional estacionária para simular a dispersão de poluentes na Camada Limite Planetária. A solução é obtida através do método ADMM (Analytical Dispersion Multilayer Model) e da técnica de inversão numérica utilizando o algoritmo de Fixed Talbot. A validação da solução é comprovada, mediante os parâmetros estatísticos, através do confrontamento das concentrações calculadas a partir do modelo com as obtidas experimentalmente pelo experimento de Prairie Grass. Para a determinação das concentrações utiliza-se o perfil do vento segundo o modelo de similaridade de Monin-Obukhov e os parâmetros de turbulência com dependência da distância longitudinal da fonte e da altura vertical, considerando a componente vertical do espectro Euleriano e de acordo com o modelo sugerido por Hɸjstrup que divide os espectros em alta e baixa frequência. Para efeito comparativo utiliza-se um coeficiente de difusão para grandes tempos de difusão. Os melhores resultados foram alcançados com a utilização dos coeficientes de difusão considerando a distância longitudinal da fonte e a altura vertical. / This work presents the solution of two-dimensional advection-diffusion equation stationary to simulate the dispersion of pollutants in the Planetary Boundary Layer. The solution is obtained through the ADMM method (Analytical Multilayer Dispersion Model) and the numerical inversion technique using the algorithm Fixed Talbot. Validation of the solution is proven, statistical parameters, through the confrontation of the concentrations calculated from the model with those obtained experimentally by the Experiment of Prairie Grass. For the determination of the concentration profile of the wind the form of Monin-Obukhov similarity and turbulence parameters with longitudinal distance dependence of source and of vertical height, considering the vertical component of the Eulerian spectrum and according to the model proposed by Hɸjstrup that divides the high and low frequency spectra. To use the comparative effect diffusion coefficient for large diffusion times according. The best results were achieved with the use of diffusion coefficients considering the longitudinal distance from the source and the vertical height.

Made available in DSpace on 2016-06-02T20:06:07Z (GMT). No. of bitstreams: 1 5123.pdf: 958057 bytes, checksum: 23f5ad95404afd58fe48eeb517ef5b41 (MD5) Previous issue date: 2013-04-01 / Financiadora de Estudos e Projetos / The volatility of financial assets changes over time, indicating the specification of regime change in volatility models. Furthermore, the presence of asymmetry in the returns of the financial market has been recognized in the financial literature of recent decades. In this paper, we present some heteroscedastic models with regime change, considering that the error component of these models follows Skew Laplace distribution, as well as the process of estimating its parameters via maximum likelihood and Bayesian methods. / A volatilidade dos ativos financeiros se altera ao longo do tempo, sinalizando a especificação de mudança de regime para modelos de volatilidade. Além disso, a presença de assimetria nos retornos do mercado financeiro tem sido reconhecida na literatura financeira das últimas décadas. Neste trabalho, apresentamos alguns modelos heterocedásticos com mudança de regime, considerando que a componente do erro desses modelos segue distribuição Laplace assimétrica, bem como o processo de estimação de seus parâmetros via máxima verossimilhança e métodos bayesianos.

In this thesis, a comprehensive study of the electrical properties of carbon-hydrogen (CH) complexes in silicon (Si) and silicon-germanium (SiGe) alloys is presented. These complexes form by the reaction of residual carbon impurities with hydrogen that is introduced either by wet chemical etching or a dc hydrogen plasma. The complexes were detected and characterized by the deep level transient spectroscopy (DLTS), Laplace DLTS, and minority carrier transient spectroscopy (MCTS) technique. With this approach, properties like the activation enthalpy for carrier emission, the capture cross section, the charge state, and the thermal stability of the complexes were determined. The composition of the complexes was derived from the analysis of their depth profiles in samples with different impurity concentrations. Using these methods, eight carbon-hydrogen related defect levels (E42, E65, E75, E90, E90', E262, H50, H180) and one hydrogen related level (E150) were detected in Si, SiGe alloys and Ge. Hydrogen plasma treatment at temperatures around 373 K introduces four dominant traps in Si at about Ec-0.06 eV (E42), Ec-0.52 eV (E262), Ev+0.33 eV (H180), and Ev+0.08 eV (H50). E42 and E262 are shown to be two charge states of the same defect. The characteristic field dependence of their emission rate links E42 with the double acceptor level and E262 with the single acceptor level of a CH complex. By comparison of their properties with calculations they are assigned to the anti-bonding configuration of the CH complex (CH_1AB). H180 was previously suggested to be the donor state of the CH_1AB configuration. This hypothesis could not be confirmed. Instead, it is shown that H180 exhibits a barrier for hole capture of about 53 meV, which hinders the reliable determination of its charge state from the field dependence of the emission rate. However, its activation enthalpy is in reasonable agreement with the predicted level position of the acceptor state of the CH_T configuration of CH, where H sits on the tetrahedral interstitial (T) position next to carbon. Therefore, H180 is tentatively assigned to CH_T. H50 is reported for the first time and it appears with concentrations close to the detection limit of the DLTS technique (~1E11 cm^-3). This complicates the determination of its charge state. Nevertheless, theory predicts the acceptor level of the CH_2AB configuration at about Ev+0.07 eV, which is remarkably close to the experimental value of H50. Therefore, H50 is tentatively assigned to the acceptor level of CH_2AB. In contrast, hydrogenation of silicon by wet chemical etching introduces three dominant levels at Ec-0.11 eV (E65), Ec-0.13 eV (E75), and Ec-0.16 eV (E90). Previously, E90 was contradictorily assigned by different authors to the donor and to the acceptor state of the bond-centered configuration of the CH complex (CH_1BC). In this work, this contradiction is resolved. It is shown that two different defect levels (E90 and E90') appear in the DLTS spectra at about 90 K in samples with a low oxygen concentration (< 1E17 cm^-3). The acceptor state of the CH_1BC configuration (E90) can be observed directly after hydrogenation by wet chemical etching or a dc hydrogen plasma treatment at temperatures below 373 K. In contrast, the donor state of a CH_n complex (E90', Ec-0.14 eV), that involves more than one hydrogen atom, is formed by a reverse bias annealing of samples with a net donor concentration of Nd > 1E15 cm^-3. By comparison with theory it is concluded that n > 2. In samples with a high oxygen concentration (> 1E17 cm^-3) E65 and E75 are dominant. Both levels belong to the CH_1BC configuration disturbed by a nearby oxygen atom. The appearance of two levels is the result of two inequivalent positions of the oxygen atom in respect to the CH bond. E42, E90, E262, and H180 are also investigated in diluted SiGe alloys to analyze the influence of alloying on their electrical properties. The presence of Ge atoms in the closest environment of the defects leads to the appearance of additional defect levels close to those observed in pure Si. The relative concentration of these additional defects is in agreement with models of the proposed defect structure of E42, E90, E262, and H180. An increase of the Ge content in SiGe alloys leads to a shift of the defect levels in the band gap of SiGe. An extrapolation of this shift predicts the appearance of E90 and E262 also in pure Ge. A hydrogen related level E150 (Ec-0.31 eV) is indeed observed in hydrogenated n-type Ge. Its concentration is significantly higher after hydrogen plasma treatment than after wet chemical etching. It is shown that E150 contains a single hydrogen atom and involves an unknown impurity, most likely carbon, oxygen, or silicon. E150 represents a reasonable candidate for a CH complex in Ge. / In dieser Arbeit werden die elektrischen Eigenschaften von Kohlenstoff-Wasserstoff-Komplexen in Silizium (Si) und Silizium-Germanium-Legierungen (SiGe) studiert. Diese Komplexe bilden sich durch Reaktion von Kohlenstoff-Verunreinigungen mit Wasserstoff, welcher durch nasschemisches Ätzen oder eine Wasserstoffplasma-Behandlung eingebracht wird. Der Nachweis und die Charakterisierung der Defekte erfolgte mit den Methoden der Kapazitätstransientenspektroskopie (DLTS), Laplace DLTS und der Minoritätsladungsträgertransientenspektroskopie (MCTS). Damit wurden Eigenschaften wie die Aktivierungsenergie der Ladungsträgeremission, die Einfangquerschnitte, der Ladungszustand und die thermische Stabilität der Komplexe bestimmt. Die Zusammensetzung der Komplexe wurde durch eine Analyse der Tiefenprofile ermittelt, welche in Proben mit verschiedenen Verunreinigungskonzentrationen gemessen wurden. Mit diesen Methoden wurde acht Kohlenstoff-Wasserstoff-korrelierte Defektniveaus (E42, E65, E75, E90', E90, E262, H50, H180) in Si und SiGe und ein Wasserstoff-korreliertes Niveau in Ge nachgewiesen. Eine Wasserstoffplasma-Behandlung bei Temperaturen um 373 K erzeugt vier dominante Defektniveaus in Si bei Ec-0.06 eV (E42), Ec-0.52 eV (E262), Ev+0.33 eV (H180) und Ev+0.08 eV. Es wird gezeigt, dass E42 und E262 zwei Ladungszustände desselben Defektes sind. Die charakteristische Feldabhängigkeit der Emissionsrate zeigt, dass E42 der Doppel-Akzeptor- und E262 der Einfach-Akzeptor-Zustand eines CH-Komplexes ist. Durch Vergleich der beobachteten Eigenschaften mit theoretischen Berechnungen werden beide Niveaus der antibindenden Konfiguration des CH-Komplexes (CH_1AB) zugeordnet. Das Niveau H180 wurde in der Literatur bisher mit dem Donator-Zustand der CH_1AB-Konfiguration in Verbindung gebracht. Diese Hypothese konnte nicht bestätigt werden. Es wird gezeigt, dass H180 eine Barriere für den Löchereinfang von etwa 53 meV besitzt, was die Bestimmung des Ladungszustandes aus der Feldabhängigkeit der Emissionsrate erschwert. Die Aktivierungsenergie von H180 stimmt jedoch befriedigend mit der berechneten Aktivierungsenergie des Akzeptorzustandes der CH_T-Konfiguration überein, bei der H auf der T-Zwischengitterposition sitzt. Daher wird H180 vorläufig dem CH_T-Komplex zugeordnet. Das Niveau H50, welches zum ersten Mal hier beschrieben wird, wird nur mit sehr geringen Konzentrationen nachgewiesen. Dies erschwert die Bestimmung des Ladungszustandes. Die Aktivierungsenergie von H50 stimmt jedoch auffallend gut mit dem von der Theorie vorhergesagten Akzeptorniveau von CH_2AB (Ev+0.07 eV) überein. Daher wird H50 vorrübergehend CH_2AB zugeordnet. Das Einbringen von Wasserstoff in Silizium durch nasschemisches Ätzen führt zu drei dominanten Defektniveaus bei Ec-0.11 eV (E65), Ec-0.13 eV (E75) und Ec-0.16 eV (E90). E90 wurde bisher widersprüchlich von verschiedenen Autoren dem Donatorzustand und dem Akzeptorzustand der bindungszentrierten Konfiguration (CH_1BC) des CH-Komplexes zugeordnet. Dieser Widerspruch konnte aufgelöst werden. Es wird gezeigt, dass in Silizium mit niedrigem Sauerstoffanteil (< 1E17 cm^-3) zwei verschiedene Defektniveaus (E90 und E90') bei etwa 90 K in den DLTS-Spektren erscheinen, welche nur mit der Laplace DLTS-Technik aufgelöst werden können. Der Akzeptorzustand der CH_1BC-Konfiguration kann direkt nach nasschemischem Ätzen oder einer Wasserstoffplasma-Behandlung bei 373 K beobachtet werden. Im Gegensatz dazu wird durch eine Sperrspannungs-Temperung in Proben mit einer Donatorkonzentration von Nd > 1E15 cm^-3 der Donatorzustand eines CH_n-Komplexes (E90', Ec-0.14 eV), welcher mehr als ein Wasserstoffatom enthält, gebildet. Durch Vergleich mit theoretischen Berechnungen wird n > 2 geschlussfolgert. Die Niveaus E65 und E75 sind in Proben mit einem hohen Sauerstoffanteil (> 1E17 cm^-3) dominant. Beide Niveaus gehören zu einer durch ein O-Atom verzerrten CH_1BC-Konfiguration. Das Auftreten von zwei Niveaus wird durch zwei nicht-äquivalente Positionen des O-Atoms bezüglich der CH-Bindung erklärt. Die Eigenschaften von E42, E90, E262 und H180 wurden ebenfalls in verdünnten SiGe-Legierungen untersucht. Es wird gezeigt, dass Ge-Atome in der direkten Umgebung der Defekte zusätzliche Defektniveaus erzeugen, die in der Bandlücke nahe zu den Si-Defektniveaus liegen und von durch Ge-Atomen verzerrten Defekten stammen. Die beobachteten relativen Konzentrationen dieser Ge-korrelierten Niveaus kann mit Modellen der atomaren Struktur der Defekte erklärt werden. Eine Verschiebung der Defektniveaus proportional zum Ge-Anteil in der Legierung wurde beobachtet. Eine Extrapolation dieser Verschiebung legt den Schluss nahe, dass E90 und E262 auch in reinem Ge beobachtbar sein sollten. Tatsächlich wurde ein Wasserstoff-korrelierter Defekt E150 (Ec-0.31 eV) in n-Typ Germanium beobachtet. Die Konzentration von E150 ist nach einer Wasserstoffplasma-Behandlung wesentlich höher als nach nasschemischen Ätzen. Es wird gezeigt, dass E150 ein einzelnes Wasserstoffatom und ein noch unbekanntes Verunreinigungsatom enthält, höchstwahrscheinlich Kohlenstoff, Sauerstoff oder Silizium. Damit ist E150 ein sehr wahrscheinlicher Kandidat für einen CH-Komplex in Germanium.

Na condução por saltos dispersiva, os portadores de carga são caracterizados por tempos de residência não exponenciais. Como uma conseqüência, efeitos hereditários aparecem e o problema deve ser conduzido no espaçõ de Laplace. Distribuições dielétricas conhecidas e algumas outras foram usadas como possíveis funções capazes de descrever o meio desordenado. Um estudo cuidadoso de seus espectros de freqüência foi realizado. O método de inversão de Widder truncado foi desenvolvido para possibilitar a volta do espaço de Laplace para o do tempo real. Dois tipos de problemas práticos foram abordados: condução dispersiva na qual o campo elétrico das cargas móveis pode ser desprezado e o caso de carga espacial para o qual essa aproximação não pode ser feita. Duas configurações de interesse foram escolhidas: decaimento do potencial de superfície de amostras carregadas por descarga corona e a subida do potencial no carregamento por corrente constante. / Dispersive conductive process are characterized by non-exponential residence times of the hopping carrier. As a consequence, hereditary effects appear and the problem must be conducted in the Laplace space. A bunch of known dielectric distributions functions and others were used as possible functions describing the disordered medium. A careful study of their frequency spectrum was carried out. The truncate Widder inversion was developed in order to allow returning from the Lapace to the real time space. Two kind of practical problems were studied: dispersive conduction in which the electric field of the mobile charge may be neglected and the space charge ones when that approximation cannot be made. Two configurations of interest were selected: the corona discharge potential decay and the constant current potentinal build-up.

No estudo de imagens radiográcas, os parâmetros relacionados ao contraste objeto, SC, razão sinal ruído, SNR, e dose, estão vinculados à forma do espectro de raios X utilizado e seu conhecimento permite predizer e otimizar a qualidade da imagem. Neste trabalho foi desenvolvida uma metodologia que permite obter o espectro de tubos de raios X odontológicos de uso clínico de forma indireta. Esta metodologia é baseada na aplicação de um modelo matemático que utiliza a transformada inversa de Laplace da curva de transmissão do feixe para gerar dados sobre a distribuição espectral do mesmo. Com o auxílio de uma câmara de ionização e ltros alumínio de alta pureza, foram levantadas as curvas de transmissão de 8 tubos de raios X disponíveis comercialmente. Para a validação do método foi realizada a espectrometria direta com detector de telureto de cádmio (CdTe), cuja resposta foi determinada por simulação Monte Carlo (MC). A partir reconstrução espectral obtida, foram realizados estudos sobre os parâmetros de qualidade de imagem SNR, contraste objeto, SC, KERMA na entrada da pele. O desempenho dos tubos foi avaliado com base na relação entre SNR e KERMA na entrada da pele. Os resultados mostram que é possível determinar a distribuição espectral de tubos de raios X odontológicos com base no método proposto. A relação proposta entre SNR e KERMA na entrada da pele sugere que tubos com fótons de baixa energia possuem baixo rendimento. / In the study of radiographic images, the parameters related to the subject contrast, SC, signal to noise ratio, SNR, and dose, are linked to the shape of the X-ray spectrum used and their knowledge allows to predict and optimize the image quality. In this work we developed a methodology to obtain the spectrum of dental X-ray tubes of clinical usage in an indirety way. This methodology is based on application of a mathematical model that uses the inverse Laplace transform of the attenuation curve to generate data on the spectral distribution of the beam. With the aid of an ionization chamber and high purity aluminum lters, were raised the transmission curves of 8 X-ray tubes that are available commercially. The method validation was performed with direct spectrometry detector cadmium telluride (CdTe), whose response was determined by Monte Carlo simulation (MC). From reconstruction obtained spectral studies were carried out on the parameters of SNR image quality, contrast object, SC, KERMA entrance skin. The performance of the tubes was evaluated based on the relationship between SNR and KERMA entrance skin. The results show that it is possible to determine the spectral distribution of dental X-ray tubes based on the proposed method. The proposed relationship between SNR and KERMA entrance skin suggests that tubes with low energy photons have a low performance.

Orientador: Edmundo Capelas de Oliveira / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-24T12:52:57Z (GMT). No. of bitstreams: 1 Teodoro_GrazianeSales_M.pdf: 8150080 bytes, checksum: 07ef5ddebc25d941750b2dee59bd4022 (MD5) Previous issue date: 2014 / Resumo: O cálculo fracionário, nomenclatura utilizada para cálculo de ordem não inteira, tem se mostrado importante e, em muitos casos, imprescindível na discussão de problemas advindos de diversas áreas da ciência, como na matemática, física, engenharia, economia e em muitos outros campos. Neste contexto, abordamos a integral fracionária e as derivadas fracionárias, segundo Caputo e segundo Riemann-Liouville. Dentre as funções relacionadas ao cálculo fracionário, uma das mais importantes é a função de Mittag-Leffler, surgindo naturalmente na solução de várias equações diferenciais fracionárias com coeficientes constantes. Tendo em vista a importância dessa função, a clássica função de Mittag-Leffler e algumas de suas várias generalizações são apresentadas neste trabalho. Na aplicação resolvemos a equação diferencial associada ao problema do oscilador harmônico fracionário, utilizando a transformada de Laplace e a derivada fracionária segundo Caputo / Abstract: The fractional calculus, which is the nomenclature used to the non-integer order calculus, has important applications due to its direct involvement in problem resolution and discussion in many fields, such as mathematics, physics, engineering, economy, applied sciences and many others. In this sense, we studied the fractional integral and fractional derivates: one proposed by Caputo and the other by Riemann-Liouville. Among the fractional calculus's functions, one of most important is the Mittag-Leffler function. This function naturally occurs as the solution for fractional order differential equations with constant coeficients. Due to the importance of the Mittag-Leffler functions, various properties and generalizations are presented in this dissertation. We also presented an application in fractional calculus, in which we solved the differential equation associated the with fractional harmonic oscillator. To solve this fractional oscillator equation, we used the Laplace transform and Caputo fractional derivate / Mestrado / Matematica Aplicada / Mestra em Matemática Aplicada

In this thesis, a comprehensive study of the electrical properties of carbon-hydrogen (CH) complexes in silicon (Si) and silicon-germanium (SiGe) alloys is presented. These complexes form by the reaction of residual carbon impurities with hydrogen that is introduced either by wet chemical etching or a dc hydrogen plasma. The complexes were detected and characterized by the deep level transient spectroscopy (DLTS), Laplace DLTS, and minority carrier transient spectroscopy (MCTS) technique. With this approach, properties like the activation enthalpy for carrier emission, the capture cross section, the charge state, and the thermal stability of the complexes were determined. The composition of the complexes was derived from the analysis of their depth profiles in samples with different impurity concentrations. Using these methods, eight carbon-hydrogen related defect levels (E42, E65, E75, E90, E90', E262, H50, H180) and one hydrogen related level (E150) were detected in Si, SiGe alloys and Ge. Hydrogen plasma treatment at temperatures around 373 K introduces four dominant traps in Si at about Ec-0.06 eV (E42), Ec-0.52 eV (E262), Ev+0.33 eV (H180), and Ev+0.08 eV (H50). E42 and E262 are shown to be two charge states of the same defect. The characteristic field dependence of their emission rate links E42 with the double acceptor level and E262 with the single acceptor level of a CH complex. By comparison of their properties with calculations they are assigned to the anti-bonding configuration of the CH complex (CH_1AB). H180 was previously suggested to be the donor state of the CH_1AB configuration. This hypothesis could not be confirmed. Instead, it is shown that H180 exhibits a barrier for hole capture of about 53 meV, which hinders the reliable determination of its charge state from the field dependence of the emission rate. However, its activation enthalpy is in reasonable agreement with the predicted level position of the acceptor state of the CH_T configuration of CH, where H sits on the tetrahedral interstitial (T) position next to carbon. Therefore, H180 is tentatively assigned to CH_T. H50 is reported for the first time and it appears with concentrations close to the detection limit of the DLTS technique (~1E11 cm^-3). This complicates the determination of its charge state. Nevertheless, theory predicts the acceptor level of the CH_2AB configuration at about Ev+0.07 eV, which is remarkably close to the experimental value of H50. Therefore, H50 is tentatively assigned to the acceptor level of CH_2AB. In contrast, hydrogenation of silicon by wet chemical etching introduces three dominant levels at Ec-0.11 eV (E65), Ec-0.13 eV (E75), and Ec-0.16 eV (E90). Previously, E90 was contradictorily assigned by different authors to the donor and to the acceptor state of the bond-centered configuration of the CH complex (CH_1BC). In this work, this contradiction is resolved. It is shown that two different defect levels (E90 and E90') appear in the DLTS spectra at about 90 K in samples with a low oxygen concentration (< 1E17 cm^-3). The acceptor state of the CH_1BC configuration (E90) can be observed directly after hydrogenation by wet chemical etching or a dc hydrogen plasma treatment at temperatures below 373 K. In contrast, the donor state of a CH_n complex (E90', Ec-0.14 eV), that involves more than one hydrogen atom, is formed by a reverse bias annealing of samples with a net donor concentration of Nd > 1E15 cm^-3. By comparison with theory it is concluded that n > 2. In samples with a high oxygen concentration (> 1E17 cm^-3) E65 and E75 are dominant. Both levels belong to the CH_1BC configuration disturbed by a nearby oxygen atom. The appearance of two levels is the result of two inequivalent positions of the oxygen atom in respect to the CH bond. E42, E90, E262, and H180 are also investigated in diluted SiGe alloys to analyze the influence of alloying on their electrical properties. The presence of Ge atoms in the closest environment of the defects leads to the appearance of additional defect levels close to those observed in pure Si. The relative concentration of these additional defects is in agreement with models of the proposed defect structure of E42, E90, E262, and H180. An increase of the Ge content in SiGe alloys leads to a shift of the defect levels in the band gap of SiGe. An extrapolation of this shift predicts the appearance of E90 and E262 also in pure Ge. A hydrogen related level E150 (Ec-0.31 eV) is indeed observed in hydrogenated n-type Ge. Its concentration is significantly higher after hydrogen plasma treatment than after wet chemical etching. It is shown that E150 contains a single hydrogen atom and involves an unknown impurity, most likely carbon, oxygen, or silicon. E150 represents a reasonable candidate for a CH complex in Ge. / In dieser Arbeit werden die elektrischen Eigenschaften von Kohlenstoff-Wasserstoff-Komplexen in Silizium (Si) und Silizium-Germanium-Legierungen (SiGe) studiert. Diese Komplexe bilden sich durch Reaktion von Kohlenstoff-Verunreinigungen mit Wasserstoff, welcher durch nasschemisches Ätzen oder eine Wasserstoffplasma-Behandlung eingebracht wird. Der Nachweis und die Charakterisierung der Defekte erfolgte mit den Methoden der Kapazitätstransientenspektroskopie (DLTS), Laplace DLTS und der Minoritätsladungsträgertransientenspektroskopie (MCTS). Damit wurden Eigenschaften wie die Aktivierungsenergie der Ladungsträgeremission, die Einfangquerschnitte, der Ladungszustand und die thermische Stabilität der Komplexe bestimmt. Die Zusammensetzung der Komplexe wurde durch eine Analyse der Tiefenprofile ermittelt, welche in Proben mit verschiedenen Verunreinigungskonzentrationen gemessen wurden. Mit diesen Methoden wurde acht Kohlenstoff-Wasserstoff-korrelierte Defektniveaus (E42, E65, E75, E90', E90, E262, H50, H180) in Si und SiGe und ein Wasserstoff-korreliertes Niveau in Ge nachgewiesen. Eine Wasserstoffplasma-Behandlung bei Temperaturen um 373 K erzeugt vier dominante Defektniveaus in Si bei Ec-0.06 eV (E42), Ec-0.52 eV (E262), Ev+0.33 eV (H180) und Ev+0.08 eV. Es wird gezeigt, dass E42 und E262 zwei Ladungszustände desselben Defektes sind. Die charakteristische Feldabhängigkeit der Emissionsrate zeigt, dass E42 der Doppel-Akzeptor- und E262 der Einfach-Akzeptor-Zustand eines CH-Komplexes ist. Durch Vergleich der beobachteten Eigenschaften mit theoretischen Berechnungen werden beide Niveaus der antibindenden Konfiguration des CH-Komplexes (CH_1AB) zugeordnet. Das Niveau H180 wurde in der Literatur bisher mit dem Donator-Zustand der CH_1AB-Konfiguration in Verbindung gebracht. Diese Hypothese konnte nicht bestätigt werden. Es wird gezeigt, dass H180 eine Barriere für den Löchereinfang von etwa 53 meV besitzt, was die Bestimmung des Ladungszustandes aus der Feldabhängigkeit der Emissionsrate erschwert. Die Aktivierungsenergie von H180 stimmt jedoch befriedigend mit der berechneten Aktivierungsenergie des Akzeptorzustandes der CH_T-Konfiguration überein, bei der H auf der T-Zwischengitterposition sitzt. Daher wird H180 vorläufig dem CH_T-Komplex zugeordnet. Das Niveau H50, welches zum ersten Mal hier beschrieben wird, wird nur mit sehr geringen Konzentrationen nachgewiesen. Dies erschwert die Bestimmung des Ladungszustandes. Die Aktivierungsenergie von H50 stimmt jedoch auffallend gut mit dem von der Theorie vorhergesagten Akzeptorniveau von CH_2AB (Ev+0.07 eV) überein. Daher wird H50 vorrübergehend CH_2AB zugeordnet. Das Einbringen von Wasserstoff in Silizium durch nasschemisches Ätzen führt zu drei dominanten Defektniveaus bei Ec-0.11 eV (E65), Ec-0.13 eV (E75) und Ec-0.16 eV (E90). E90 wurde bisher widersprüchlich von verschiedenen Autoren dem Donatorzustand und dem Akzeptorzustand der bindungszentrierten Konfiguration (CH_1BC) des CH-Komplexes zugeordnet. Dieser Widerspruch konnte aufgelöst werden. Es wird gezeigt, dass in Silizium mit niedrigem Sauerstoffanteil (< 1E17 cm^-3) zwei verschiedene Defektniveaus (E90 und E90') bei etwa 90 K in den DLTS-Spektren erscheinen, welche nur mit der Laplace DLTS-Technik aufgelöst werden können. Der Akzeptorzustand der CH_1BC-Konfiguration kann direkt nach nasschemischem Ätzen oder einer Wasserstoffplasma-Behandlung bei 373 K beobachtet werden. Im Gegensatz dazu wird durch eine Sperrspannungs-Temperung in Proben mit einer Donatorkonzentration von Nd > 1E15 cm^-3 der Donatorzustand eines CH_n-Komplexes (E90', Ec-0.14 eV), welcher mehr als ein Wasserstoffatom enthält, gebildet. Durch Vergleich mit theoretischen Berechnungen wird n > 2 geschlussfolgert. Die Niveaus E65 und E75 sind in Proben mit einem hohen Sauerstoffanteil (> 1E17 cm^-3) dominant. Beide Niveaus gehören zu einer durch ein O-Atom verzerrten CH_1BC-Konfiguration. Das Auftreten von zwei Niveaus wird durch zwei nicht-äquivalente Positionen des O-Atoms bezüglich der CH-Bindung erklärt. Die Eigenschaften von E42, E90, E262 und H180 wurden ebenfalls in verdünnten SiGe-Legierungen untersucht. Es wird gezeigt, dass Ge-Atome in der direkten Umgebung der Defekte zusätzliche Defektniveaus erzeugen, die in der Bandlücke nahe zu den Si-Defektniveaus liegen und von durch Ge-Atomen verzerrten Defekten stammen. Die beobachteten relativen Konzentrationen dieser Ge-korrelierten Niveaus kann mit Modellen der atomaren Struktur der Defekte erklärt werden. Eine Verschiebung der Defektniveaus proportional zum Ge-Anteil in der Legierung wurde beobachtet. Eine Extrapolation dieser Verschiebung legt den Schluss nahe, dass E90 und E262 auch in reinem Ge beobachtbar sein sollten. Tatsächlich wurde ein Wasserstoff-korrelierter Defekt E150 (Ec-0.31 eV) in n-Typ Germanium beobachtet. Die Konzentration von E150 ist nach einer Wasserstoffplasma-Behandlung wesentlich höher als nach nasschemischen Ätzen. Es wird gezeigt, dass E150 ein einzelnes Wasserstoffatom und ein noch unbekanntes Verunreinigungsatom enthält, höchstwahrscheinlich Kohlenstoff, Sauerstoff oder Silizium. Damit ist E150 ein sehr wahrscheinlicher Kandidat für einen CH-Komplex in Germanium.

[pt] Uma técnica bem conhecida para resolver problemas dependentes do tempo é a formulação, desses problemas, no domínio da frequência por meio da transformada de Laplace ou Fourier, com as consequêntes expressões apropriadas desses resultados utilizando inversões numéricas. Embora de fácil implementação, tais inversões numéricas, são computacionalmente dispendiosas quando resultados mais exatos são desejados e suscetíveis a instabilidades num´ericas. Para problemas de tipo difusão, o algoritmo de Gaver-Stehfest parece ser satisfatório. Problemas gerais de dinâmica demandam algoritmos mais robustos, usualmente baseados em expansões em séries de Fourier tal como foi proposto inicialmente por Dubner e Abate. Algoritmos de outros tipos já são implementados em softwares matemáticos tais como Matlab e Mathematica. A livraria de Fortran possui um algoritmo proposto por Crump e aperfei¸coado por de Hoog e colegas. Mais recentemente, foi proposto resolver problemas transientes de potencial e elasticidade pelo uso de uma técnica avançada de superposição modal que é aplicado a modelos de elementos finitos e elementos de contorno baseados em equilíbrio. O método começa com a formulação no domínio da frequência a qual leva a uma matriz de rigidez efetiva, simétrica-complexa (quando amortecimento viscoso é considerado), expressa como uma série de potências de frequência com matrizes generalizadas de rigidez, amortecimento e massa. Após a solução do problema de autovalor não linear associado, obtém-se uma solução modal avançada do problema, a qual permite uma rápida solução no domínio do tempo obtendo as expressões imediatamente de qualquer resultado de interesse. O objetivo deste trabalho é comparar o desempenho computacional da técnica de superposição modal avançada com as técnicas baseadas em transformadas inversas numéricas de Laplace como aplicações a problemas generais de grande porte. A bibliografia relevante é revista e as principais diferenças conceituais desses métodos são brevemente tratados. Todos os algoritmos são implementados em Fortran com o intuito de garantir uma base comum de comparação. Alguns resultados iniciais são mostrados, conclusões mais definitivas so poderão ser obtidas após uma grande série de simulações numéricas. / [en] An established technique to solve time-dependent problems is the formulation of a complete frequency-domain analysis via Laplace or Fourier transforms, with subsequent ad hoc expression of results by numerical inversion. Although usually easy to implement, such a transform inversion is computationally intensive, if accurate results are desired, and liable to numerical instabilities. For diffusion-type problems, the Gaver-Stehfest algorithm seems well suited. General dynamics problems demand more robust algorithms usually based on Fourier series expansions, as firstly proposed by Dubner and Abate. Algorithms of either kind are already implemented in mathematical languages such as Matlab and Mathematica. The Fortran library has a Fourier-series algorithm proposed by Crump and improved by de Hoog et al. More recently, it has been proposed to solve transient problems of potential and elasticity by using an advanced mode superposition technique that applies to equilibrium-based finite element and boundary element models. One starts with a frequency-domain formulation that leads to a complex-symmetric (if viscous damping is included), effective stiffness matrix expressed as a frequency power series with generalized stiffness, dumping and mass matrices. After solution of the associated complex-symmetric, non-linear eigenvalue problem, one arrives at an advanced modal solution of the problem, which leads to the straightforward solution in the time domain and the immediate expression of any results of interest. Aim of the present research work is to compare the computational efficiency of the proposed advanced modal analysis with the techniques based on numerical inverse transforms, as applied to general, large scale problems. The relevant literature is reviewed and the main conceptual differences of the investigated methods are briefly outlined. All algorithms are implemented in Fortran so as to assure a common basis of comparison. Some initial results are displayed, as more definitive conclusions can only be expected after a large series of numerical simulations.

O principal objetivo deste trabalho é estudar as singularidades e hipersingularidades existentes nas formulações: singular - clássica - e hipersingular no Método dos Elementos de Contorno (MEC). Também é proposto um esquema residual h-adaptativo para a solução numérica do problema físico governado pela equação de Laplace. Usa-se malha poligonal, juntamente, com funções de interpolação - distribuição - de forma, dos tipos: constantes e lineares. Para controlar o erro a posteriori, é considerado o valor do resíduo, fora dos pontos de colocação. Também é testada uma técnica de quadratura numérica chamada adaptativa, específica para subelementos, no sentido de verificar se a precisão no cálculo das integrais com singularidades é melhorada. O uso de funções hierárquicas é discutido na forma de um algoritmo para atualização da matriz principal do sistema linear. / The main purpose of this work is to study the existing singularities and hypersingularities in the Boundary Element Method (BEM) with singular - classical - and hypersingular formulations. Also, an h-adaptive residual scheme for the numerical solution of the physical problem, driven by Laplace equation, is proposed. Boundary polygonal mesh, with constant and linear interpolation - distribution - shape functions together are used. To control the a posteriori error, is considered the residue value outside the collocation points. Also, a sub-element specific adaptive numerical quadrature technique, in an effort to verify if the precision when dealing with integrals possessing singularities is increased, is tested. The use of hierarchical functions is discussed, as an algorithm to update the linear system main matrix.