Magíster en Ciencias de la Ingeniería, Mención Eléctrica / Ingeniero Civil Eléctrico / Las simulaciones computacionales son un importante recurso para ayudar en el diseño y a entender el funcionamiento de dispositivos semiconductores de una forma rápida y económica, por lo que se han desarrollado diversas herramientas de simulación, tanto comerciales como libres. No obstante, diversos centros de investigación y universidades han optado por desarrollar programas propios, lo que les permite tener continuidad en el desarrollo, control y mayor entendimiento de los fenómenos simulados. Bajo esta misma idea, el presente trabajo tiene como objetivo desarrollar herramientas de simulación para materiales y dispositivos semiconductores, centrado principalmente en el problema en dos dimensiones, y que tenga la flexibilidad suficiente para propósitos prácticos de diseño y educacionales, sirviendo además como un punto de partida para trabajos futuros. Para cumplir el objetivo mencionado, se implementaron dos modelos clásicos de simulación: Arrastre-Difusión o DD (Drift-Diffusion) y Monte Carlo o MC (que resuelve la ecuacion de transporte de Boltzmann). Dichos modelos tienen diferentes grados de precisión, capacidades y costos computacionales, cubriendo así un gran rango de dispositivos y necesidades. Para ambos, se utilizó una malla no estructurada de Voronoi, para cuya generación se presenta un algoritmo basado en la triangulación de Delaunay, lo que permite la descripción de diversas topologías. Ambos modelos fueron incluidos en un mismo programa escrito en MATLAB, con una interfaz basada en archivos de texto de alto nivel que permite el uso casi indistinto entre uno u otro, característica que le da otorga una mayor flexibilidad y simpleza. La realización de distintas pruebas numéricas y comparaciones con la literatura y otras referencias, permitieron verificar el apropiado funcionamiento de los métodos y mostrar distintas características de éstos. En particular, para DD se constató la superioridad Newton-Raphson (NRM) sobre Gummel, y de el esquema de estabilización de Schaffeter-Gummel (SG) sobre Aguas Arriba. Para MC, se desarrollaron distintas técnicas para que el método fuese coherente con la malla no estructurada y topologías generalizadas. Además, se compararon DD y MC, mostrando sus diferencias en congruencia con la literatura. El modelo de DD implementado es resuelto usando Volumenes Finitos y el método de NRM, que otorga buenas características de convergencia. Para la estabilización, se utilizó la discretización de SG. Modelos básicos de movilidad, heterojunturas y condiciones de borde, fueron incluidos para extender la versatilidad del método y establecer ideas para futuras mejoras. El método de Monte Carlo implementado en esta instancia, incluye fuentes básicas de dispersión y utiliza bandas analíticas esféricas o elípticas con no-parabolicidad para electrones. En cambio, para huecos, sólo simples modelos parabólicos e isotrópicos fueron considerados. Finalmente, fueron señaladas las limitaciones más relevantes del programa y los posibles modelos para paliarlas. Esto, junto con el resto del trabajo, se espera que se constituyan como bases para futuros desarrollos y mejoras.

This dissertation computationally and analytically investigates ways to model solar cells when the lateral motion of charge carriers and light are relevant. We focus on back-contact perovskite solar cells, and assessing the experimental technique of scanning photocurrent microscopy as a means to investigate them. Solar cells are three-dimensional objects frequently modelled as being one-dimensional. However, for more complex designs of solar cell or if the cell is only point-illuminated, one-dimensional modelling is insufficient. In the first study, some conditions for reducing the complexity of two-dimensional drift-diffusion simulations are investigated for a back-contact perovskite cell. Analytic expressions for the relationship in both the low extraction velocity and high extraction velocity regimes are demonstrated, and the conditions where these approximations break down are investigated. These findings are then applied a point-excited film with an extended electrode, a problem encountered during scanning photocurrent microscopy. We show the current recorded in this case should decay exponentially with the distance between excitation and electrode, with a decay constant that can be related to device parameters. The characteristic equilibration time for the system to reach this current is demonstrated to increase linearly with distance. Between this gradient and the exponent, information about the diffusion and recombination mechanics can be extracted from a variety of systems. Photon recycling is the process in whereby photogenerated carriers recombine to generate light that is absorbed again within the solar cell. In the second section, we apply the findings of the first section to show that experimental results published elsewhere are best explained by photon recycling in methylammonium lead iodide perovskite back-contact solar cells. However we do not have an established theoretical model for long-ranged lateral optical transport in these solar cells. Three models are developed: a bimolecular model for unscattered, coherent transport; a photon diffusion model for frequently scattered, noncoherent light; and a monomolecular, assisted-diffusion model. The modal nature of coherent optical transport is considered and modifications to previous one-dimensional theories are made. The nature of the photon diffusion model is discussed, as are theoretical shortcomings. All three models are then solved numerically and compared to experimental results. The low-scattering photon diffusion models correspond well to the experiment. The third investigation involves the performance of different architectures of back-contact perovskite cells. These cells potentially offer increased current due to less shadowing by front electrodes. We compare them to each other and to traditional vertical structures. It is found that, in terms of internal transport, the back-contact solar cells give less efficient performance than the vertical design. The best of the back-contact cells investigated is a flat interdigitated design. The increase in efficiency from optical factors would have to exceed 10% for the overall efficiency of back-contact cells to be higher than vertical devices. We also develop a model of photon recycling appropriate for short-ranged, bulk 2D transport and demonstrate that in perovskites, it produces little change in power conversion efficiency (and small changes in short-circuit voltage) when compared with the standard drift-diffusion equations with the second-order recombination constant is adjusted.

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To make a High Voltage Direct Current (HVDC) transmission more energy efficient, the voltage of the system has to be increased. To allow for that the components of the system must be constructed to handle the increases AC and DC stresses that this leads to. One key component in such a transmission is the HVDC converter transformer. The insulation system of the transformer usually consists of oil and oil-impregnated pressboard. Modeling of the electric DC field in the insulation system is currently done with the ion drift diffusion model, which takes into account the transport and generation of charges in the oil and the pressboard. The model is however lacking a description of how charges are being injected from the electrodes and the oil-pressboard interfaces. The task of this thesis work was to develop and implement a model for this which improves the result of the ion drift diffusion model. A theoretical study of ion injection was first carried out and proceeding from this, a model for the ion injection was formulated. By using experimental data from 5 different test geometries, the injection model could be validated and appropriate parameter values of the model could be determined. By using COMSOL Multiphysics®, the ion drift diffusion model with the injection model could be simulated for the different test geometries. The ion injection gave a substantial improvement of the ion drift diffusion model. The positive injection from electrodes into oil was found to be in the range 0.3-0.6 while the negative injection was 0.3 lower. Determination of the parameters for the injection from oil-pressboard interfaces proved to be difficult, but setting the parameters in the range 0.01-1 allowed for a good agreement with the experimental data. Here, a fit could be obtained for multiple assumptions about the set of active injection parameters. Finally it is recommended that the investigation of the ion injection continues in order to further improve the model and more accurately determine the parameters of it. Suggestions on how this work could be carried out are given in the end.

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Ce travail de thèse se concentre sur l'étude des modèles de type drift-diffusion. Des approches sont développées pour la modélisation de la Microscopie à sonde de Kelvin, des cellules solaires à base de matériaux pérovskites (PSCs), des cellules solaires tandem de type pérovskite/silicium et des îlots quantiques lll-V/GaP. Tout d'abord, l'approche de la modélisation de la sonde de Kelvin est examinée pour la surface de TiOx et l'absorbeur pérovskite MAPbI3 Ensuite, des mesures avec sonde de Kelvin et des simulations sont proposées pour des jonctions diffuses à base de silicium et pour des PSCs à base de TiOx mésa poreux. Les variations du potentiel interne sont étudiées ouvrant la voie à une amélioration supplémentaire des dispositifs. L'influence de l'état de surface des couches wo. sur des mesures à sonde de Kelvin est étudiée théoriquement. Différents facteurs à l'origine des pertes de tension de circuit ouvert (Voc) des PSCs sont discutés. L'effet anormal d'hystérésis dans les PSCs est également simulé, en tenant compte des étals de pièges d'interface et des ions mobiles. En outre, le design de cellules solaires tandem 2T pérovskite/silicium est étudié en détails. Une jonction tunnel à base de silicium entre les deux sous-cellules supérieure et inférieure est proposée pour assurer le bon fonctionnement des cellules en série. L'influence du profil de dopage dans la jonction tunnel est discutée. Au final, le transport des porteurs dans les îlots quantiques III-V/GaP est étudié dans le cadre plus général de l'intégration d'émetteurs lll-V sur silicium. Les caractéristiques électroluminescentes et électriques de ces structures sont simulées dans une approximation cylindrique. / This PhD work focuses on optoelectronic device simulations based on drift-diffusion models. Approaches are developed for the modelling of Kelvin Probe Force Microscopy (KPFM), perovskite-based solar cells (PSCs), perovskite/silicon tandem solar cells and lll-V/GaP quantum dots (ODs). Firstly, a new approach for the modelling of KPFM is applied to TiOx slabs and to the MAPbI3 perovskite absorber. Secondly, KPFM measurements and simulations are proposed for silicon-based diffused junctions and mesoporous TiOx based PSCs. The built-in potential is investigated, and this study paves the way toward fu rther device improvements. In addition, the influence of the surface of WO. slabs on KPFM measurements is studied theoretically. Various facto rs influencing open circuit voltage (Voe) losses in PSCs are discussed. The abnormal hysteresis effect in the PSCs is simulated as well, considering interface trap states and mobile ions. The design of two-terminal perovskite/silicon tandem solar cells is studied in detail. A siliconbased tunnel junction between the top and the bottom subcells is proposed for serial current matching. The influence of the doping profile in the tunnel junction is discussed. At the end of the manuscript, the carrier transport in III-V/GaP QDs is investigated, for the integration of III-V emitters on silicon. The electroluminescence and electrical characteristics of these III -V light emitting devices are simulated by using a cylindrical approximation.

Diese Arbeit beschäftigt sich mit der Entwicklung und Implementierung eines Algorithmus zur Berechnung des diffusiven elektronischen Transportes durch Kohlenstoffnanoröhrchen-Feldeffekttransistoren (CNTFETs) unter Verwendung des Drift-Diffusions-Modells. Als Grundlage dient ein bekannter, eindimensionaler Algorithmus für klassische Halbleiter, durch welchen das elektrostatische Potential im stationären Zustand berechnet werden kann. Dieser Algorithmus wird erweitert, um die geometrischen und physikalischen Besonderheiten von CNTFETs, insbesondere die Quasi-Eindimensionalität, zu berücksichtigen. Wichtige Kenngrößen des CNTFETs werden berechnet und deren Abhängigkeit von den Bauteilparametern wird untersucht.:1. Einleitung 2. Theoretische Betrachtungen 2.1. Kohlenstoffnanoröhrchen 2.1.1. Graphen als Baustein für CNTs 2.1.2. Eigenschaften von CNTs 2.2. Drift-Diffusions-Modell 2.2.1. Drift-Diffusions-Gleichungen 2.2.2. Kontinuitätsgleichungen 2.2.3. Poisson-Gleichung 3. Implementierung 3.1. Modell für klassische Halbleiter 3.1.1. Herleitung der dimensionslosen Bewegungsgleichungen 3.1.2. Umformung der Drift-Diffusions-Gleichungen 3.1.3. Iterative Lösung des Gleichungssystems 3.2. Anwendung des Modells auf Kohlenstoffnanoröhrchen 3.2.1. Betrachtetes Modell 3.2.2. Separationsansatz und Poisson-Gleichung 3.2.3. Anpassung der Drift-Diffusions-Gleichungen 3.2.4. Gate-Spannung 3.2.5. Intrinsische Ladungsträgerdichte und Ladungsträgerrandbedingungen 3.2.6. Dielektrizität 3.3. Numerik 3.3.1. Berechnung der Ladungsträgerdichten 3.3.2. Lösung der Poisson-Gleichung 3.3.3. Iterative Veränderung von Parameterwerten 3.3.4. Überprüfung der Konvergenz des Gitters 4. Auswertung 4.1. Literaturmodelle 4.2. Ergebnisse 4.2.1. Potentialverlauf 4.2.2. Potentialplateau 4.2.3. Abschirmlänge 4.2.4. Stromfluss 4.2.5. Rechenzeit 5. Zusammenfassung Anhang A. Herleitung der Drift-Diffusions-Gleichungen aus der Boltzmann-Transportgleichung B. Herleitung der eindimensionalen Poisson-Gleichung aus dem Separationsansatz

This dissertation is focused on the research efforts to develop the growth, processing, and modeling technologies for GaN-based Heterojunction Field Effect Transistors (HFETs). The interest in investigating GaN HFETs is motivated by the advantageous material properties of nitride semiconductor such as large band gap, large breakdown voltage, and high saturation velocity, which make it very promising for the high power and microwave applications. Although enormous progress has been made on GaN transistors in the past decades, the technologies for nitride transistors are still not mature, especially concerning the reliability and stability of the device. In order to improve the device performance, we first optimized the growth and fabrication procedures for the conventional AlGaN barrier HFET, on which high carrier mobility and sheet density were achieved. Second, the AlInN barrier HFET was successfully processed, with which we obtained improved I-V characteristics compared with conventional structure. The lattice-matched AlInN barrier is beneficial in the removal of strain, which leads to better carrier transport characteristics. Furthermore, new device structures have been examined, including recess-gate HFET with n+ GaN cap layer and gate-on-insulator HFET, among which the insertion of gate dielectrics helps to leverage both DC and microwave performances. In order to depict the microwave behavior of the HFET, small signal modeling approaches were used to extract the extrinsic and intrinsic parameters of the device. An 18-element equivalent circuit model for GaN HFET has been proposed, from which various extraction methods have been tested. Combining the advantages from the cold-FET measurements and hot-FET optimizations, a hybrid extraction method has been developed, in which the parasitic capacitances were attained from the cold pinch-off measurements while the rest of the parameters from the optimization routine. Small simulation error can be achieved by this method over various bias conditions, demonstrating its capability for the circuit level design applications for GaN HFET. Device physics modeling, on the other hand, can help us to reveal the underlying physics for the device to operate. With the development of quantum drift-diffusion modeling, the self-consistent solution to the Schrödinger-Poisson equations and carrier transport equations were fulfilled. Lots of useful information such as band diagram, potential profile, and carrier distribution can be retrieved. The calculated results were validated with experiments, especially on the AlInN layer structures after considering the influence from the parasitic Ga-rich layer on top of the spacer. Two dimensional cross-section simulation shows that the peak of electrical field locates at the gate edge towards the drain, and of different kinds of structures the device with gate field-plate was found to efficiently reduce the possibility of breakdown failure.