In screen-printed silicon-crystalline solar cells, the contact resistance of a thin interfacial glass layer between the silicon and the silver electrode plays a limiting role for electron transport. The motivation of this project is to gain increased understanding of the transport mechanisms of the electrons across this layer, which can be exploited to provide higher performance crystalline silicon solar cells. Our methodology throughout is to formulate and analyse mathematical models for the electron transport, based on the drift diffusion equations. In the first chapter we outline the problem and provide a summary of relevant theory. In Chapter 2 we formulate a one-dimensional model for electron transport across the glass layer, that we solve both numerically and by employing asymptotic techniques. Chapter 3 extends the model presented in Chapter 2 to two dimensions. To solve the two-dimensional model numerically we devise and validate a new spectral method. The short circuiting of current through thinner regions of the glass layer enables us to find limiting asymptotic expressions for the average current density for two different canonical glass layer profiles. In Chapter 4 we include quantum mechanical effects into the one-dimensional model outlined in Chapter 2 and find that they have a negligible effect on the contact resistance of the glass layer. We model the boundary effects present at the silicon emitter-glass interface in Chapter 5. Finally, in Chapter 6 we summarise our key results, suggest possible future work, and outline the implications of our work to crystalline silicon solar cell manufacturers.

In tasks with more than one path to succeed, it is possible that participants’ strategies vary and therefore, participants should not be analyzed as a homogeneous group. This thesis investigates individual differences in a two-dimensional categorization task with redundancy (i.e., a task where any of the two dimensions by itself suffices for perfect performance). Individual differences in learned knowledge and used knowledge are considered and studied. Participants first performed a categorization task with redundancy (training phase), and afterward were asked to do categorizations in which the previously redundant knowledge becomes decisive (testing phase). Using the data from the testing phase, dimension(s) learned by each participant were determined and the response patterns of each participant in the training phase was used to determine which dimension(s) were used. The used knowledge was assessed using two separate analyses, both of which look at accuracy and response time patterns, but in different ways. Analysis 1 uses iterative decision bound modeling and RT-distance hypothesis and Analysis 2 uses the stochastic version of general recognition theory. In Analysis 1, more errors and slower response times close to a decision bound perpendicular to a dimension indicate that a participant is using that dimension. Analysis 2 goes a step further and in addition to determining which dimension(s) are used, specifies in what way they were used (i.e., identifying the strategy of each participant). Possible strategies are described heuristically (unidimensional, time efficient and conservative) and then each heuristic is translated into a drift diffusion model by the unique way that strategy is assumed to affect trial-by-trial difficulty of the task. Finally, a model selection criterion is used to pick the strategy that is used by each participant.

abstract: Semiconductor devices often face reliability issues due to their operational con- ditions causing performance degradation over time. One of the root causes of such degradation is due to point defect dynamics and time dependent changes in their chemical nature. Previously developed Unified Solver was successful in explaining the copper (Cu) metastability issues in cadmium telluride (CdTe) solar cells. The point defect formalism employed there could not be extended to chlorine or arsenic due to numerical instabilities with the dopant chemical reactions. To overcome these shortcomings, an advanced version of the Unified Solver called PVRD-FASP tool was developed. This dissertation presents details about PVRD-FASP tool, the theoretical framework for point defect chemical formalism, challenges faced with numerical al- gorithms, improvements for the user interface, application and/or validation of the tool with carefully chosen simulations, and open source availability of the tool for the scientific community. Treating point defects and charge carriers on an equal footing in the new formalism allows to incorporate chemical reaction rate term as generation-recombination(G-R) term in continuity equation. Due to the stiff differential equations involved, a reaction solver based on forward Euler method with Newton step is proposed in this work. The Jacobian required for Newton step is analytically calculated in an elegant way improving speed, stability and accuracy of the tool. A novel non-linear correction scheme is proposed and implemented to resolve charge conservation issue. The proposed formalism is validated in 0-D with time evolution of free carriers simulation and with doping limits of Cu in CdTe simulation. Excellent agreement of light JV curves calculated with PVRD-FASP and Silvaco Atlas tool for a 1-D CdTe solar cell validates reaction formalism and tool accuracy. A closer match with the Cu SIMS profiles of Cu activated CdTe samples at four different anneal recipes to the simulation results show practical applicability. A 1D simulation of full stack CdTe device with Cu activation at 350C 3min anneal recipe and light JV curve simulation demonstrates the tool capabilities in performing process and device simulations. CdTe device simulation for understanding differences between traps and recombination centers in grain boundaries demonstrate 2D capabilities. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2019

Semiconductors with an additional intermediate band (IB) have the potential to greatly improve solar cell efficiency. Their theoretical efficiency limit is over 50% higher than that of standard semiconductor solar cells at full concentration. In practice however, their efficiencies are low compared to this detailed balance limit. Part of the reason is that it has not been possible to optimize IB device geometry because no device model has existed that could capture all the effects present in IB materials (e.g., charge transport inside the IB and self-consistent optics). In this thesis I introduce my new device model for intermediate band semiconductors called Simudo. The software uses the finite element method to solve the coupled Poisson/drift-diffusion (PDD) system of equations that describe the carrier dynamics inside semiconductor (IB or not) devices, along with optical propagation. I benchmark its accuracy on standard semiconductor problems against Synopsys Sentaurus, and I find that not only does it give valid results but in fact converges to the solution with a smaller number of mesh points by having quartic rather than merely quadratic solution convergence with respect to the number of mesh points. I also demonstrate Simudo's immediate usefulness by answering the question of whether IB mobility can compensate for mismatched optical absorption processes in different regions of the device. The device model work is preceded by three introductory chapters bringing the reader up to speed on semiconductor device physics and providing them with a primer on the finite element method. The coupled PDD equations are numerically challenging to solve, and the road to development of Simudo tried a number of formulations of the problem that were not successful. In the final chapter I discuss some of these formulations and why they did not succeed.

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Une décision perceptive est un processus délibératif consistant à choisir une proposition catégorielle ou un plan d'action parmi plusieurs alternatives sur la base d'information sensorielle. Les modèles de prise décision font l'hypothèse que l'information sensorielle est accumulée au cours du temps jusqu'à un seuil décisionnel. Ces modèles ont récemment reçu un support empirique important grâce à la découverte de neurones accumulateurs dans le cerveau de singes. Toutefois, l'étude neurophysiologique de ces système d'accumulation chez l'homme est rare. Ce travail de thèse vise à mieux comprendre les mécanismes neuronaux de prise de décision chez l'homme dans des contextes de la vie réelle, beaucoup plus complexes que ceux utilisés chez le singe. / A perceptual decision is a deliberative process that aims to choose a categorical proposition or course of action from a set of alternatives on the basis of available sensory information. Models of perceptual decision-making assume that sensory information is accumulated to some threshold level, whence the decision terminates in a choice. The recent discovery of neural correlates of these theoretical predictions in the non-human primate brain has reinforced their validity. However, neurophysiological studies of perceptual decision-making mechanisms in humans are relatively scarce. This work aims at enhancing our understanding of the computations and neurophysiology underpinning such mechanisms in humans, through the study of decision-making contexts more complex than those used in monkey research.

abstract: A general continuum model for simulating the flow of ions in the salt baths that surround and fill excitable neurons is developed and presented. The ion densities and electric potential are computed using the drift-diffusion equations. In addition, a detailed model is given for handling the electrical dynamics on interior membrane boundaries, including a model for ion channels in the membranes that facilitate the transfer of ions in and out of cells. The model is applied to the triad synapse found in the outer plexiform layer of the retina in most species. Experimental evidence suggests the existence of a negative feedback pathway between horizontal cells and cone photoreceptors that modulates the flow of calcium ions into the synaptic terminals of cones. However, the underlying mechanism for this feedback is controversial and there are currently three competing hypotheses: the ephaptic hypothesis, the pH hypothesis and the GABA hypothesis. The goal of this work is to test some features of the ephaptic hypothesis using detailed simulations that employ rigorous numerical methods. The model is first applied in a simple rectangular geometry to demonstrate the effects of feedback for different extracellular gap widths. The model is then applied to a more complex and realistic geometry to demonstrate the existence of strictly electrical feedback, as predicted by the ephaptic hypothesis. Lastly, the effects of electrical feedback in regards to the behavior of the bipolar cell membrane potential is explored. Figures for the ion densities and electric potential are presented to verify key features of the model. The computed steady state IV curves for several cases are presented, which can be compared to experimental data. The results provide convincing evidence in favor of the ephaptic hypothesis since the existence of feedback that is strictly electrical in nature is shown, without any dependence on pH effects or chemical transmitters. / Dissertation/Thesis / Ph.D. Applied Mathematics 2013

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