Décider, c’est sélectionner une alternative parmi l’ensemble des options possibles en accord avec nos buts. Les décisions perceptuelles, correspondant à la sélection d’une action sur la base d’une perception, résultent de l’accumulation progressive d’information sensorielle jusqu’à un seuil de décision. Aux niveaux comportemental et cérébral, ce processus est bien capturé par les modèles de décision par échantillonnage séquentiel. L’étude neurobiologique des processus de décision, guidée par l’usage de modèles computationnels, a permis d’établir un lien clair entre cette accumulation d’information sensorielle et un réseau cortical incluant le sillon intra-pariétal et le cortex dorso-latéral préfrontal. L’architecture des réseaux biologiques impliqués dans la prise de décision, la nature des algorithmes qu’ils implémentent et surtout, l’étude des relations entre structure biologique et computation est au cœur des questionnements actuels en neurosciences cognitives et constitue le fil conducteur de cette thèse. Dans un premier temps, nous nous sommes intéressés aux mécanismes neuraux et computationnels permettant l’ajustement du processus de décision perceptuelle à son contexte. Nous avons montré que l’information a priori disponible pour prédire nos choix diminue la distance au seuil de décision, régulant ainsi dynamiquement la quantité d’information sensorielle nécessaire pour sélectionner une action. Pendant la prise de décision perceptuelle, le cortex cingulaire antérieur ajuste le seuil de décision proportionnellement à la quantité d’information prédictive disponible et le cortex dorso-latéral préfrontal implémente l’accumulation progressive d’information sensorielle. Dans un deuxième temps, nous avons abordé la question de l’unicité, au travers des domaines cognitifs, des mécanismes neuro-computationnels implémentant la prise de décision. Nous avons montré qu’un modèle de décision par échantillonnage séquentiel utilisant la valeur subjective espérée de chaque option prédisait avec précision le comportement de sujets lors de choix économiques risqués. Pendant la décision, la portion médiale du cortex orbito-frontal code la différence entre les valeurs subjectives des options considérées, exprimées sur une échelle de valeur commune. Ce signal orbito-frontal médian sert d’entrée à un processus de décision par échantillonnage séquentiel implémenté dans le cortex dorso-latéral préfrontal. Pris ensemble, nos travaux précisent les contours d’une architecture fonctionnelle de la prise de décision dans le cortex préfrontal humain en établissant une cartographie des modules computationnels qu’il implémente, mais aussi en caractérisant la façon dont l’intégration fonctionnelle de ces régions cérébrales permet l’émergence de la capacité à prendre des décisions / Decision-making is the selection of an alternative according to our inner goals. Perceptual decisions, the selection of an action based on our perceptions, are made when sensory evidence accumulated over time reaches a decision threshold. This cognitive process is well accounted for by sequential sampling models of decision-making. Moreover, the model-driven neurobiological study of the decision-making process has linked the accumulation of sensory information with a parieto-prefrontal cortical network. The architecture of these cortical networks, the algorithms implemented and the mapping of elementary computations onto biological structures are the questions at the core of this thesis. First, we investigated the neural mechanisms underlying the contextual modulation of the decision-making process. We showed that predictive information on the forthcoming stimuli decreased the distance to the decision threshold, adjusting dynamically the amount of sensory information required to commit to a choice. In our study, the anterior cingulate cortex modulated the decision threshold in proportion to the amount of predictive information and the dorso-lateral prefrontal cortex accumulated sensory information. Then, we addressed the question of the unicity across cognitive domains of the neuro-computational mechanisms of decision-making. We showed that a sequential sampling model of decision-making using subjective values as its inputs precisely predicted Human economic decision-making behavior. Moreover, we showed that the medial part of the orbito-frontal cortex coded the difference between the subjective values of the options under scrutiny on a common scale. This orbito-frontal decision-related value signal drove the sequential sampling decision-making process implemented in the dorso-lateral prefrontal cortex. Taken together, our work delineates a functional architecture of Human decision-making by mapping elementary computations onto the human prefrontal cortex and by characterizing how the functional integration between these brain regions subserves the ability to make choices

Mes travaux concernent deux systèmes d’équations utilisés dans la modélisation mathématique de semi-conducteurs et de plasmas : le système d’Euler-Poisson et le système d’Euler-Maxwell. Le premier système est constitué des équations d’Euler pour la conservation de la masse et de la quantité de mouvement couplées à l’équation de Poisson pour le potentiel électrostatique. Le second système décrit le phénomène d’électro-magnétisme. C’est un système couplé, qui est constitué des équations d’Euler pour la conservation de la masse et de la quantité de mouvement et les équations de Maxwell, aussi appelées équations de Maxwell-Lorentz. Les équations de Maxwell sont dues aux lois fondamentales de la physique. Elles constituent les postulats de base de l’électromagnétisme, avec l’expression de la force électromagnétique de Lorentz. En utilisant une technique de développement asymptotique, nous étudions les limites en zéro du système d’Euler-Poisson dans les modèles unipolaire et bipolaire. Il est bien connu que la limite formelle du système d’Euler-Poisson est gouvernée par les équations de dérive-diffusion lorsque le temps de relaxation tend vers zéro. Par des estimations d’énergie aux systèmes hyperboliques symétriques, nous justifions rigoureusement cette limite lorsque les conditions initiales sont bien préparées. Le phénomène des conditions initiales mal préparées est interprété par l’apparition de couches initiales. Dans ce cas, nous faisons une analyse mathématique de ces couches initiales en ajoutant des termes de correction dans le développement asymptotique. En utilisant les techniques itératives des systèmes hyperboliques symétrisables et la technique de développement asymptotique, nous étudions la limite de relaxation en zéro du système d’Euler-Maxwell, avec des conditions initiales bien préparées ainsi que l’étude des couches initiales, dans le modèle évolutif bipolaire et unipolaire. / My work is concerned with two different systems of equations used in the mathematical modeling of semiconductors and plasmas : the Euler-Poisson system and the Euler-Maxwell system. The first is given by the Euler equations for the conservation of the mass and momentum, with a Poisson equation for the electrostatic potential. The second system describes the phenomenon of electromagnetism. It is given by the Euler equations for the conservation of the mass and momentum, with a Maxwell equations for the electric field and magnetic field which are coupled to the electron density through the Maxwell equations and act on electrons via the Lorentz force. Using an asymptotic expansion method, we study the zero relaxation limit of unipolar Euler-Poisson system and of two-fluid multidimensional Euler-Poisson equations, we prove the existence and uniqueness of profiles to the asymptotic expansion and some error estimate. By employing the classical energy estimate for symmetrizable hyperbolic equations, we justify rigorously the convergence of Euler-Poisson system with well-prepared initial data. For ill-prepared initial data, the phenomenon of initial layers occurs. In this case, we also add the correction terms in the asymptotic expansion. Using an iterative method of symmetrizable hyperbolic systems and asymptotic expansion method, we study the zero-relaxation limit of unipolar and bipolar Euler-Maxwell system. For well-prepared initial data, we construct an approximate solution by an asymptotic expansion up to any order. For ill-prepared initial data, we also construct initial layer corrections in the asymptotic expansion.

L’homme est un animal social. La majorité des décisions que nous prenons se font dans un contexte social et dépendent d’autrui, ce qui implique des calculs cérébraux complexes qui incluent tous les facteurs contextuels et environnementaux. La majorité des études ultérieures de la prise en compte d’autrui dans la décision ont utilisé des tâches de partage de récompenses entre soi et autrui. Les choix possibles amènent le décideur à considérer autrui, mais dans le but de gagner soi-même une récompense ; donc dans un contexte où les récompenses liées à soi et les récompenses liées à autrui sont confondues. Le travail présenté dans cette thèse avait pour but une meilleure compréhension des mécanismes cérébraux soutenant l’intégration d’autrui dans la prise de décision, sans que la récompense pour autrui n’interfère directement avec soi. Nous nous sommes appuyés sur le cadre théorique de la décision perceptuelle et des modèles de diffusion pour l'étude i) des modifications du processus décisionnel induites par une récompense monétaire allant à autrui et ii) de l’impact de l’effet d’audience (le fait de se sentir observé) sur la décision. Nos résultats computationnels montrent qu'une récompense pour autrui, par rapport à une récompense pour soi, et une audience, par rapport au secret, modifient le taux de dérive de la variable de décision. En magnétoencéphalographie, nos résultats indiquent que les décisions pour soi et pour autrui diffèrent pendant, mais aussi après, la prise de décision dans des zones cérébrales associées avec la transformation sensori-motrice, l'ajustement du compromis entre rapidité et justesse et avec la cognition sociale. Ainsi, le cortex temporal montre des différences de -1170 millisecondes (ms) à -1023 ms, de -993 ms à -915 ms et de -343 ms à -188 ms en amont de la réponse. Ce qui suppose une influence sur l’intégration des preuves sensorielles. Après la décision, les régions frontales ont également montré des différences entre soi et autrui, de 153 ms à 303 ms post-réponse, suggérant une différence entre soi et autrui dans l’ajustement du compris entre justesse et rapidité. Le bénéficiaire de la récompense associée à la décision modifie les paramètres décisionnels et les corrélats cérébraux de la décision perceptuelle, démontrant l’importance du contexte social dans l’implémentation de la prise de décision chez l’Homme. Ce travail appuie également l’utilité des modèles mathématiques tels que les modèles de diffusion dans la compréhension des processus décisionnels, même de ceux découlant de la cognition sociale / Humans are inherently social: most of human’s decisions are within a social context and depend on others. For more than a century, researchers explore aspects of social cognition. Aiming to understand human behavior in social contexts, neuro-economic researches showed that taking others into account involve complex brain computations that include all environmental and contextual factors. However, most of the work was made using money allocation tasks; mixing self-affecting and other-affecting rewards into the decision making process. The present work intended the understanding of the brain mechanisms underpinning the integration of others into the decision making process for decisions that include others and do not interfere with self-rewards.Taking advantage of mathematical models from the drift diffusion models framework, we conducted experiments investigating how others influence the mechanistic of perceptual decisions and their correlates in the human brain. We showed that taking rewards for others into account and being observed by others influence the drift rate of the decision variable. The drift rate is higher in audience than in secret and higher for self-rewards than for other-rewards. These results indicate that others are integrated into the accumulation process together with the evidence available for making a decision. At the brain level, we found difference between self and other decisions over the anterior temporal and centro-frontal cortices during decision making. This suggests that the beneficiary of a decision modifies sensory-motor transformation processes. In addition, self- and other-affecting difference showed difference over the medial frontal sensors after the decision making process, indicating a variation in the speed-accuracy tradeoff adjustment process

<p dir="ltr">This work introduces an innovative algorithm for co-simulating time-dependent Drift Diffusion (DD) equations with Maxwell\textquotesingle s equations to characterize semiconductor devices. Traditionally, the DD equations, derived from the Boltzmann transport equations, are used alongside Poisson\textquotesingle s equation to model electronic carriers in semiconductors. While DD equations coupled with Poisson\textquotesingle s equation underpin commercial TCAD software for micron-scale device simulation, they are limited by electrostatic assumptions and fail to capture time dependent high-frequency effects. Maxwell\textquotesingle s equations are fundamental to classical electrodynamics, enabling the prediction of electrical performance across frequency range crucial to advanced device fabrication and design. However, their integration with DD equations has not been studied thoroughly. The proposed method advances current simulation techniques by introducing a new broadband patch-based method to solve time-domain 3-D Maxwell\textquotesingle s equations and integrating it with the solution of DD equations. This technique is free of the low-frequency breakdown issues prevalent in conventional full-wave simulations. Meanwhile, it enables large-scale simulations with reduced computational complexity. This work extends the simulation to encompass the complete device, including metal contacts and interconnects. Thus, it captures the entire electromagnetic behavior, which is especially critical in electrically larger systems and high-frequency scenarios. The electromagnetic interactions of the device with its contacts and interconnects are investigated, providing insights into performance at the chip level. Validation through numerical experiments and comparison with results from commercial TCAD tools confirm the effectiveness of the proposed method. </p>

Organische Halbleiterbauelemente sind eine vielversprechende Technologie, die das Spektrum der optoelektronischen Halbleiterbauelemente erweitert und etablierte Technologien basierend auf anorganischen Halbleitermaterialien ersetzen kann. Für Display- und Beleuchtungsanwendungen werden sie z. B. als organische Leuchtdioden oder Transistoren verwendet. Eine entscheidende Eigenschaft organischer Halbleitermaterialien ist, dass die Ladungstransporteigenschaften stark von der Temperatur im Bauelement beeinflusst werden. Insbesondere nimmt die elektrische Leitfähigkeit mit der Temperatur zu, so dass Selbsterhitzungseffekte, einen großen Einfluss auf die Leistung der Bauelemente haben. Mit steigender Temperatur nimmt die elektrische Leitfähigkeit zu, was wiederum zu größeren Strömen führt. Dies führt jedoch zu noch höheren Temperaturen aufgrund von Joulescher Wärme oder Rekombinationswärme. Eine positive Rückkopplung liegt vor. Im schlimmsten Fall führt dieses Verhalten zum thermischen Durchgehen und zur Zerstörung des Bauteils. Aber auch ohne thermisches Durchgehen führen Selbsterhitzungseffekte zu interessanten nichtlinearen Phänomenen in organischen Bauelementen, wie z. B. die S-förmige Beziehung zwischen Strom und Spannung. In Regionen mit negativem differentiellen Widerstand führt eine Verringerung der Spannung über dem Bauelement zu einem Anstieg des Stroms durch das Bauelement. Diese Arbeit soll einen Beitrag zur mathematischen Modellierung, Analysis und numerischen Simulation von organischen Bauteilen leisten. Insbesondere wird das komplizierte Zusammenspiel zwischen dem Fluss von Ladungsträgern (Elektronen und Löchern) und Wärme diskutiert. Die zugrundeliegenden Modellgleichungen sind Thermistor- und Energie-Drift-Diffusion-Systeme. Die numerische Diskretisierung mit robusten hybriden Finite-Elemente-/Finite-Volumen-Methoden und Pfadverfolgungstechniken zur Erfassung der in Experimenten beobachteten S-förmigen Strom-Spannungs-Charakteristiken wird vorgestellt. / Organic semiconductor devices are a promising technology to extend the range of optoelectronic semiconductor devices and to some extent replace established technologies based on inorganic semiconductor materials. For display and lighting applications, they are used as organic light-emitting diodes (OLEDs) or transistors. One crucial property of organic semiconductor materials is that charge-transport properties are heavily influenced by the temperature in the device. In particular, the electrical conductivity increases with temperature, such that self-heating effects caused by the high electric fields and strong recombination have a potent impact on the performance of devices. With increasing temperature, the electrical conductivity rises, which in turn leads to larger currents. This, however, results in even higher temperatures due to Joule or recombination heat, leading to a feedback loop. In the worst case, this loop leads to thermal runaway and the complete destruction of the device. However, even without thermal runaway, self-heating effects give rise to interesting nonlinear phenomena in organic devices, like the S-shaped relation between current and voltage resulting in regions where a decrease in voltage across the device results in an increase in current through it, commonly denoted as regions of negative differential resistance. This thesis aims to contribute to the mathematical modeling, analysis, and numerical simulation of organic semiconductor devices. In particular, the complicated interplay between the flow of charge carriers (electrons and holes) and heat is discussed. The underlying model equations are of thermistor and energy-drift-diffusion type. Moreover, the numerical approximation using robust hybrid finite-element/finite-volume methods and path-following techniques for capturing the S-shaped current-voltage characteristics observed in experiments are discussed.

The study of neural and behavioural mechanisms of perceptual decision making is often done by experimental tasks involving the categorization of sensory stimuli. Among the key perceptual tasks that decision neuroscience researchers use are motion discrimination paradigms that include tracking and specifying the net direction of a single dot or a group of moving dots. These motion discrimination paradigms, such as the random-dot motion task, allow the measurement of the participant's perceptual decision making abilities in multiple task difficulty levels by varying the amount of noise in the sensory stimuli. Computational models of perceptual decision making, such as the drift-diffusion model, are widely used to analyze the behavioural measurements from these motion discrimination experiments. However, the standard drift-diffusion model can only analyze the average measures like reaction times or the proportion of correct decisions to explain the behavioural data. In the past decade, an emerging computational modeling approach was introduced to analyze the choice behaviour based on precise noise patterns in the sensory stimuli. These computational models that use spatiotemporal stimulus details have shown promise in the single-trial analysis of motion discrimination behaviour. In this thesis, I further develop the advanced computational models of perceptual decision making that use spatiotemporal dynamics of motion stimuli to provide detailed explanations of perceptual choice behaviour. First, I demonstrate the usefulness of equipping an extended Bayesian Model, equivalent to the extended drift-diffusion model, with trial-wise stimulus information leading to a significantly better explanation of behavioural data from a single-dot tracking experiment. Second, I show that the extended drift-diffusion model constrained by spatiotemporal stimulus details can explain the consistent biased choice behaviour in response to stochastic motion stimuli. Based on this model-based analysis, I provide evidence that the source of the observed biased choice behaviour is the presence of subtle motion information in the sensory stimuli. These results further emphasize the effectiveness of using spatiotemporal details of stochastic stimuli in detailed model-based analyses of the experimental data and provide computational interpretations of the data related to underlying mechanisms of perceptual decision making.

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No. of bitstreams: 1 nunesneto_o_dr_bauru.pdf: 4276326 bytes, checksum: e73a2086ffde0d12d2f5875fb168f8c1 (MD5) Previous issue date: 2016-04-28 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Materiais e dispositivos baseados em compostos orgânicos desempenham um importante papel em diversas áreas da aplicação tecnológica devido às suas interessantes propriedades eletro-magneto- ópticas, adicionadas às suas características mecânicas únicas, facilidade de processamento, versatilidade de síntese e baixo custo relativo. Apesar do proeminente campo de aplicação destes materiais, muitos aspectos associados à sua ciência básica são ainda pouco compreendidos. Nesse cenário destaca-se o fenômeno de Magnetoresistência Orgânica (OMAR, da sigla em inglês). Tal fenômeno encontra-se associado a variações significativas da condutividade elétrica de dispositivos orgânicos induzidas por pequenos campos magnéticos externos em temperatura ambiente e tem sido observado em diversificados materiais poliméricos e moleculares. No presente trabalho avaliou-se o fenômeno de OMAR apresentado por um Diodo Emissor de Luz baseado na molécula de Alq3. Medidas de Espectroscopia de Impedância Elétrica na presença de um Campo Magnético estático externo (EIE-CM) foram realizadas sobre o referido dispositivo para diferentes temperaturas. Métodos diferenciados de aquisição e manipulação de dados foram empregados a fim de remover a dependência temporal dos sinais tipicamente observados. Os seguintes Efeitos de Campo Magnético (MFE, da sigla em inglês) foram observados sobre a resposta elétrica do dispositivo: (i) redução de cerca de 1% na resistência, efeito praticamente constante para todo o espectro de frequência e; (ii) variações significativas na capacitância, com intensificação do efeito de Capacitância Negativa em baixas frequências. Como suporte para a interpretação dos resultados experimentais foram realizadas simulações empregando-se duas abordagens: Circuitos Equivalentes e Análise de perturbações de pequenos sinais (em inglês, Small Signal Analysis ) via soluções numéricas das equações de transporte de Boltzmann numa aproximação por Drift-Diffusion empregando-se dispositivos simplificados. As análises sugerem que os MFE evidenciados podem estar associados a um aumento da mobilidade efetiva dos portadores de carga e a uma redução na taxa de recombinação bimolecular no dispositivo. Os resultados foram interpretados em termos dos modelos atualmente aceitos para o fenômeno de OMAR. Esta tese também apresenta um estudo de processos de geração e transferência de carga em corantes Cianinas, materiais promissores para aplicações em células solares com absorção no infravermelho. Técnicas de Ressonância de Spin Eletrônico induzida por Luz foram empregadas em blendas destes corantes com o polímero MEH-PPV e com o fulereno (C60) a fim de avaliar, respectivamente, o caráter aceitador e doador de elétrons das Cianinas. / Materials and devices based on organic compounds play an important role in various technological applications, mainly due to their interesting electrical-magneto-optical properties combined with their unique mechanical properties, easy processing, versatility of synthesis and relatively low cost. Despite the prominent application field of these materials many aspects associated with their basic science are still not well understood. In this context the Organic Magnetoresistance phenomenon (OMAR) deserves to be highlighted. This phenomenon is associated with significant changes in the electrical conductivity of organic devices induced by the presence of small external magnetic fields at room temperature, being observed in various polymeric and molecular materials. In this study we have investigated the OMAR phenomenon in Alq3-based OLEDs. Electrical impedance spectroscopy technique in the presence of an external static magnetic field (EIS-MF) was employed in the experiments; distinct temperatures were considered. Differentiated methods of acquisition and data manipulation were employed to remove the typically observed signal time dependence. The following magnetic field effects (MFE) were observed on the electrical response of the device: (i) a constant reduction of around 1% in the resistance over the entire frequency spectrum and; (ii) significant changes in the capacitance followed by an intensification of the negative capacitance effect at low frequencies. Simulations employing two different approaches were carried out for the interpretation of the experimental results: (i) Equivalent Circuits and (ii) Small Signal Analysis via numerical solutions of the Boltzmann transport equations by Drift-Diffusion approach. The results suggest that the observed MFE can be associated with an increase in the effective mobility of the charge carriers and a reduction in the bimolecular recombination rate in the device. The results were interpreted in terms of the currently accepted models for the OMAR phenomenon. This thesis also presents a study about generation and charge transfer processes in cyanine dyes (near infrared absorbing compounds) which are promising materials for applications in solar cells. Light induced Electron Spin Resonance (L-ESR) technique was employed to study the presence/formation of paramagnetic centers in blends of these dyes with MEH-PPV polymer and fullerene (C60) to evaluate, respectively, the electron acceptor and donor character of cyanine dyes. / FAPESP: 2011/21830-6 / CNPq: 204432/2013-8

Previous research in InGaN/GaN light emitting diodes (LEDs) employing semi-classical drift-diffusion models has used reduced polarization constants without much physical explanantion. This paper investigates possible physical explanations for this effective polarization reduction in InGaN LEDs through the use of the simulation software SiLENSe. One major problem of current LED simulations is the assumption of perfectly discrete transitions between the quantum well (QW) and blocking layers when experiments have shown this to not be the case. The In concentration profile within InGaN multiple quantum well (MQW) devices shows much smoother and delayed transitions indicative of indium diffusion and drift during common atomic deposition techniques (e.g. molecular beam epitaxy, chemical vapor deposition). In this case the InGaN square QW approximation may not be valid in modeling the devices' true electronic behavior. A simulation of a 3QW InGaN/GaN LED heterostructure with an AlGaN electron blocking layer is discussed in this paper. Polarization coefficients were reduced to 70% and 40% empirical values to simulate polarization shielding effects. QW shapes of square (3 nm), trapezoidal, and triangular profiles were used to simulate realistic QW shapes. The J-V characteristic and electron-hole wavefunctions of each device were monitored. Polarization reduction decreased the onset voltage from 4.0 V to 3.0 V while QW size reduction decreased the onset voltage from 4.0 V to 3.5 V. The increased current density in both cases can be attributed to increased wavefunction overlap in the QWs.

This thesis deals with the device physics of organic solar cells. Organic photovoltaics (OPV) is a field of applied research which has been growing rapidly in the last decade leading to a current record value of power-conversion efficiency of 10 percent. One major reason for this boom is a potentially low-cost production of solar modules on flexible (polymer) substrate. Furthermore, new application are expected by flexible or semitransparent organic solar cells. That is why several OPV startup companies were launched in the last decade. Organic solar cells consist of hydrocarbon compounds, deposited as ultrathin layers (some tens of nm) on a substrate. Absorption of light leads to molecular excited states (excitons) which are strongly bound due to the weak interactions and low dielectric constant in a molecular solid. The excitons have to be split into positive and negative charges, which are subsequently collected at different electrodes. An effective dissociation of excitons is provided by a heterojunction of two molecules with different frontier orbital energies, such that the electron is transfered to the (electron) acceptor and the positive charge (hole) remains on the donor molecule. This junction can be realized by two distinct layers forming a planar heterojunction or by an intermixed film of donor and acceptor, resulting in a bulk heterojunction. Electrodes are attached to the absorber to collect the charges by providing an ohmic contact in the optimum case. This work focuses on the electrical processes in organic solar cells developing and employing a one-dimensional drift-diffusion model. The electrical model developed here is combined with an optical model and covers the diffusion of excitons, their separation, and the subsequent transport of charges. In contrast to inorganics, charge-carrier mobilities are low in the investigated materials and charge transport is strongly affected by energy barriers at the electrodes. The current-voltage characteristics (J-V curve) of a solar cell reflect the electrical processes in the device. Therefore, the J-V curve is selected as means of comparison between systematic series of simulation and experimental data. This mainly qualitative approach allows for an identification of dominating processes and provides microscopic explanations. One crucial issue, as already mentioned, is the contact between absorber layer and electrode. Energy barriers lead to a reduction of the power-conversion efficiency due to a decrease in the open-circuit voltage or the fill factor by S-shaped J-V curve (S-kink), which are often observed for organic solar cells. It is shown by a systematic study that the introduction of deliberate barriers for charge-carrier extraction and injection can cause such S-kinks. It is explained by simulated electrical-field profiles why also injection barriers lead to a reduction of the probability for charge-carrier extraction. A pile-up of charge carriers at an extraction barrier is confirmed by measurements of transient photocurrents. In flat heterojunction solar cells an additional reason for S-kinks is found in an imbalance of electron and hole mobilities. Due to the variety of reasons for S-kinks, methods and criteria for a distinction are proposed. These include J-V measurements at different temperatures and of samples with varied layer thicknesses. Most of the studies of this this work are based on experimental data of solar cells comprisiing the donor dye zinc phthalocyanine and the acceptor fullerene C60. It is observed that the open-circuit voltage of these devices depends on the mixing ratio of ZnPc:C60. A comparison of experimental and simulation data indicates that the reason is a changed donor-acceptor energy gap caused by a shift of the ionization potential of ZnPc. A spatial gradient in the mixing ratio of a bulk heterojunction is also investigated as a donor(acceptor)-rich mixture at the hole(electron)-collecting contact is supposed to assist charge extraction. This effect is not observed, but a reduction of charge-carrier losses at the “wrong” electrode which is seen at an increase in the open-circuit voltage. The most important intrinsic loss mechanism of a solar cell is bulk recombination which is treated at the example of ZnPc:C60 devices in the last part of this work. An examination of the dependence of the open-circuit voltage on illumination intensity shows that the dominating recombination mechanism shifts from trap-assisted to direct recombination for higher intensities. A variation of the absorption profile within the blend layer shows that the probability of charge-carrier extraction depends on the locus of charge-carrier generation. This results in a fill factor dependent on the absorption profile. The reason is an imbalance in charge-carrier mobilities which can be influenced by the mixing ratio. The work is completed by a simulation study of the influence of charge-carrier mobilities and different recombination processes on the J-V curve and an identification of a photoshunt dominating the experimental linear photocurrent-voltage characteristics in reverse bias. / Diese Dissertation beschäftigt sich mit der Physik organischer Solarzellen. Die organische Photovoltaik ist ein Forschungsgebiet, dem in den letzten zehn Jahren enorme Aufmerksamkeit zu Teil wurde. Der Grund liegt darin, dass diese neuartigen Solarzellen, deren aktueller Rekordwirkungsgrad bei 10 Prozent liegt, ein Potential für eine kostengünstige Produktion auf flexiblem (Polymer)substrat aufweisen und aufgrund ihrer Vielfältigkeit neue Anwendungsbereiche für die Photovoltaik erschließen. Organische Solarzellen bestehen aus ultradünnen (einige 10 nm) Schichten aus Kohlenwasserstoffverbindungen. Damit der photovoltaische Effekt genutzt werden kann, müssen die durch Licht angeregten Molekülzustände zu freien Ladungsträgern führen, wobei positive und negative Ladung an unterschiedlichen Kontakten extrahiert werden. Für eine effektive Trennung dieser stark gebundenden lokalisierten angeregten Zustände (Exzitonen) ist eine Grenzfläche zwischen Molekülen mit unterschiedlichen Energieniveaus der Grenzorbitale erforderlich, sodass ein Elektron auf einem Akzeptor- und eine positive Ladung auf einem Donatormolekül entstehen. Diese Grenzschicht kann als planarer Heteroübergang durch zwei getrennte Schichten oder als Volumen-Heteroübergang in einer Mischschicht realisiert werden. Die Absorberschichten werden durch Elektroden kontaktiert, wobei es für effiziente Solarzellen erforderlich ist, dass diese einen ohmschen Kontakt ausbilden, da ansonsten Verluste zu erwarten sind. Diese Arbeit behandelt im Besonderen die elektrischen Prozesse einer organischen Solarzelle. Dafür wird ein eindimensionales Drift-Diffusionsmodell entwickelt, das den Transport von Exzitonen, deren Trennung an einer Grenzfläche und die Ladungsträgerdynamik beschreibt. Abgesehen von den Exzitonen gilt als weitere Besonderheit einer organischen Solarzelle, dass sie aus amorphen, intrinsischen und sehr schlecht leitfähigen Absorberschichten besteht. Elektrische Effekte sind an der Strom-Spannungskennlinie (I-U ) sichtbar, die in dieser Arbeit als Hauptvergleichspunkt zwischen experimentellen Solarzellendaten und den Simulationsergebnissen dient. Durch einen weitgehend qualitativen Vergleich können dominierende Prozesse bestimmt und mikroskopische Erklärungen gefunden werden. Ein wichtiger Punkt ist der schon erwähnte Kontakt zwischen Absorberschicht und Elektrode. Dort auftretende Energiebarrieren führen zu einem Einbruch im Solarzellenwirkungsgrad, der sich durch eine Verringerung der Leerlaufspanung und/oder S-förmigen Kennlinien (S-Knick) bemerkbar macht. Anhand einer systematischen Studie der Grenzfläche Lochleiter/Donator wird gezeigt, dass Energiebarrieren sowohl für die Ladungsträgerextraktion als auch für die -injektion zu S-Knicken führen können. Insbesondere die Tatsache, dass Injektionsbarrieren sich auch negativ auf den Photostrom auswirken, wird anhand von simulierten Ladungsträger- und elektrischen Feldprofilen erklärt. Das Aufstauen von Ladungsträgern an Extraktionsbarrieren wird durch Messungen transienter Photoströme bestätigt. Da S-Knicke in organischen Solarzellen im Allgemeinen häufig beobachtet werden, werden weitere Methoden vorgeschlagen, die die Identifikation der Ursachen ermöglichen. Dazu zählen I-U Messungen in Abhängigkeit von Temperatur und Schichtdicken. Als eine weitere Ursache von S-Knicken werden unausgeglichene Ladungsträgerbeweglichkeiten in einer Solarzelle mit flachem Übergang identifiziert und von den Barrierefällen unterschieden. Weiterer Forschungsgegenstand dieser Arbeit sind Mischschichtsolarzellen aus dem Donator-Farbstoff Zink-Phthalozyanin ZnPc und dem Akzeptor Fulleren C60. Dort wird beobachtet, dass die Leerlaufspannung vom Mischverhältnis abhängt. Ein Vergleich von Experiment und Simulation zeigt, dass sich das Ionisationspotenzial von ZnPc und dadurch die effektive Energielücke des Mischsystems ändern. Zusätzlich zu homogenen Mischschichten werden Solarzellen untersucht, die einen Gradienten im Mischungsverhältnis aufweisen. Die Vermutung liegt nahe, dass ein hoher Donatorgehalt am Löcherkontakt und ein hoher Akzeptorgehalt nahe des Elektronenkontakts die Ladungsträgerextraktion begünstigen. Dieser Effekt ist in dem hier untersuchten System allerdings vergleichsweise irrelevant gegenüber der Tatsache, dass der Gradient das Abfließen bzw. die Rekombination von Ladungsträgern am “falschen” Kontakt reduziert und somit die Leerlaufspannung erhöht. Der wichtigste intrinsische Verlustmechanismus einer Solarzelle ist die Rekombination von Ladungsträgern. Diese wird im letzten Teil der Arbeit anhand der ZnPc:C60 Solarzelle behandelt. Messungen der Leerlaufspannung in Abhängigkeit von der Beleuchtungsintensität zeigen, dass sich der dominierende Rekombinationsprozess mit zunehmender Intensität von Störstellenrekombination zu direkter Rekombination von freien Ladungsträgern verschiebt. Eine gezielte Variation des Absorptionsprofils in der Absorberschicht zeigt, dass die Ladungsträgerextraktionswahrscheinlickeit vom Ort der Ladungsträgergeneration abhängt. Dieser Effekt wird hervorgerufen durch unausgeglichene Elektronen- und Löcherbeweglichkeiten und äußert sich im Füllfaktor. Weitere Simulationsergebnisse bezüglich des Einflusses von Ladungsträgerbeweglichkeiten und verschiedener Rekombinationsmechanismen auf die I-U Kennlinie und die experimentelle Identifikation eines Photoshunts, der den Photostrom in Rückwärtsrichtung unter Beleuchtung dominiert, runden die Arbeit ab.

The topic of this thesis is a diffusion process on a potential landscape which is given by a smooth Hamiltonian function in the regime of small noise. The work provides a new proof of the Eyring-Kramers formula for the Poincaré inequality of the associated generator of the diffusion. The Poincaré inequality characterizes the spectral gap of the generator and establishes the exponential rate of convergence towards equilibrium in the L²-distance. This result was first obtained by Bovier et. al. in 2004 relying on potential theory. The presented approach in the thesis generalizes to obtain also asymptotic sharp estimates of the constant in the logarithmic Sobolev inequality. The optimal constant in the logarithmic Sobolev inequality characterizes the convergence rate to equilibrium with respect to the relative entropy, which is a stronger distance as the L²-distance and slightly weaker than the L¹-distance. The optimal constant has here no direct spectral representation. The proof makes use of the scale separation present in the dynamics. The Eyring-Kramers formula follows as a simple corollary from the two main results of the work: The first one shows that the associated Gibbs measure restricted to a basin of attraction has a good Poincaré and logarithmic Sobolev constants providing the fast convergence of the diffusion to metastable states. The second main ingredient is a mean-difference estimate. Here a weighted transportation distance is used. It contains the main contribution to the Poincaré and logarithmic Sobolev constant, resulting from exponential long waiting times of jumps between metastable states of the diffusion.