Photon Management Structures for Absorption Enhancement in Intermediate Band Solar Cells and Crystalline Silicon Solar Cells

El objetivo de la tesis es investigar los beneficios que el atrapamiento de la luz mediante fenómenos difractivos puede suponer para las células solares de silicio cristalino y las de banda intermedia. Ambos tipos de células adolecen de una insuficiente absorción de fotones en alguna región del espectro solar. Las células solares de banda intermedia son teóricamente capaces de alcanzar eficiencias mucho mayores que los dispositivos convencionales (con una sola banda energética prohibida), pero los prototipos actuales se resienten de una absorción muy débil de los fotones con energías menores que la banda prohibida. Del mismo modo, las células solares de silicio cristalino absorben débilmente en el infrarrojo cercano debido al carácter indirecto de su banda prohibida. Se ha prestado mucha atención a este problema durante las últimas décadas, de modo que todas las células solares de silicio cristalino comerciales incorporan alguna forma de atrapamiento de luz. Por razones de economía, en la industria se persigue el uso de obleas cada vez más delgadas, con lo que el atrapamiento de la luz adquiere más importancia. Por tanto aumenta el interés en las estructuras difractivas, ya que podrían suponer una mejora sobre el estado del arte. Se comienza desarrollando un método de cálculo con el que simular células solares equipadas con redes de difracción. En este método, la red de difracción se analiza en el ámbito de la óptica física, mediante análisis riguroso con ondas acopladas (rigorous coupled wave analysis), y el sustrato de la célula solar, ópticamente grueso, se analiza en los términos de la óptica geométrica. El método se ha implementado en ordenador y se ha visto que es eficiente y da resultados en buen acuerdo con métodos diferentes descritos por otros autores. Utilizando el formalismo matricial así derivado, se calcula el límite teórico superior para el aumento de la absorción en células solares mediante el uso de redes de difracción. Este límite se compara con el llamado límite lambertiano del atrapamiento de la luz y con el límite absoluto en sustratos gruesos. Se encuentra que las redes biperiódicas (con geometría hexagonal o rectangular) pueden producir un atrapamiento mucho mejor que las redes uniperiódicas. El límite superior depende mucho del periodo de la red. Para periodos grandes, las redes son en teoría capaces de alcanzar el máximo atrapamiento, pero sólo si las eficiencias de difracción tienen una forma peculiar que parece inalcanzable con las herramientas actuales de diseño. Para periodos similares a la longitud de onda de la luz incidente, las redes de difracción pueden proporcionar atrapamiento por debajo del máximo teórico pero por encima del límite Lambertiano, sin imponer requisitos irrealizables a la forma de las eficiencias de difracción y en un margen de longitudes de onda razonablemente amplio. El método de cálculo desarrollado se usa también para diseñar y optimizar redes de difracción para el atrapamiento de la luz en células solares. La red propuesta consiste en un red hexagonal de pozos cilíndricos excavados en la cara posterior del sustrato absorbente de la célula solar. La red se encapsula en una capa dieléctrica y se cubre con un espejo posterior. Se simula esta estructura para una célula solar de silicio y para una de banda intermedia y puntos cuánticos. Numéricamente, se determinan los valores óptimos del periodo de la red y de la profundidad y las dimensiones laterales de los pozos para ambos tipos de células. Los valores se explican utilizando conceptos físicos sencillos, lo que nos permite extraer conclusiones generales que se pueden aplicar a células de otras tecnologías. Las texturas con redes de difracción se fabrican en sustratos de silicio cristalino mediante litografía por nanoimpresión y ataque con iones reactivos. De los cálculos precedentes, se conoce el periodo óptimo de la red que se toma como una constante de diseño. Los sustratos se procesan para obtener estructuras precursoras de células solares sobre las que se realizan medidas ópticas. Las medidas de reflexión en función de la longitud de onda confirman que las redes cuadradas biperiódicas consiguen mejor atrapamiento que las uniperiódicas. Las estructuras fabricadas se simulan con la herramienta de cálculo descrita en los párrafos precedentes y se obtiene un buen acuerdo entre la medida y los resultados de la simulación. Ésta revela que una fracción significativa de los fotones incidentes son absorbidos en el reflector posterior de aluminio, y por tanto desaprovechados, y que este efecto empeora por la rugosidad del espejo. Se desarrolla un método alternativo para crear la capa dieléctrica que consigue que el reflector se deposite sobre una superficie plana, encontrándose que en las muestras preparadas de esta manera la absorción parásita en el espejo es menor. La siguiente tarea descrita en la tesis es el estudio de la absorción de fotones en puntos cuánticos semiconductores. Con la aproximación de masa efectiva, se calculan los niveles de energía de los estados confinados en puntos cuánticos de InAs/GaAs. Se emplea un método de una y de cuatro bandas para el cálculo de la función de onda de electrones y huecos, respectivamente; en el último caso se utiliza un hamiltoniano empírico. La regla de oro de Fermi permite obtener la intensidad de las transiciones ópticas entre los estados confinados. Se investiga el efecto de las dimensiones del punto cuántico en los niveles de energía y la intensidad de las transiciones y se obtiene que, al disminuir la anchura del punto cuántico respecto a su valor en los prototipos actuales, se puede conseguir una transición más intensa entre el nivel intermedio fundamental y la banda de conducción. Tomando como datos de partida los niveles de energía y las intensidades de las transiciones calculados como se ha explicado, se desarrolla un modelo de equilibrio o balance detallado realista para células solares de puntos cuánticos. Con el modelo se calculan las diferentes corrientes debidas a transiciones ópticas entre los numerosos niveles intermedios y las bandas de conducción y de valencia bajo ciertas condiciones. Se distingue de modelos de equilibrio detallado previos, usados para calcular límites de eficiencia, en que se adoptan suposiciones realistas sobre la absorción de fotones para cada transición. Con este modelo se reproducen datos publicados de eficiencias cuánticas experimentales a diferentes temperaturas con un acuerdo muy bueno. Se muestra que el conocido fenómeno del escape térmico de los puntos cuánticos es de naturaleza fotónica; se debe a los fotones térmicos, que inducen transiciones entre los estados excitados que se encuentran escalonados en energía entre el estado intermedio fundamental y la banda de conducción. En el capítulo final, este modelo realista de equilibrio detallado se combina con el método de simulación de redes de difracción para predecir el efecto que tendría incorporar una red de difracción en una célula solar de banda intermedia y puntos cuánticos. Se ha de optimizar cuidadosamente el periodo de la red para equilibrar el aumento de las diferentes transiciones intermedias, que tienen lugar en serie. Debido a que la absorción en los puntos cuánticos es extremadamente débil, se deduce que el atrapamiento de la luz, por sí solo, no es suficiente para conseguir corrientes apreciables a partir de fotones con energía menor que la banda prohibida en las células con puntos cuánticos. Se requiere una combinación del atrapamiento de la luz con un incremento de la densidad de puntos cuánticos. En el límite radiativo y sin atrapamiento de la luz, se necesitaría que el número de puntos cuánticos de una célula solar se multiplicara por 1000 para superar la eficiencia de una célula de referencia con una sola banda prohibida. En cambio, una célula con red de difracción precisaría un incremento del número de puntos en un factor 10 a 100, dependiendo del nivel de la absorción parásita en el reflector posterior. Abstract The purpose of this thesis is to investigate the benefits that diffractive light trapping can offer to quantum dot intermediate band solar cells and crystalline silicon solar cells. Both solar cell technologies suffer from incomplete photon absorption in some part of the solar spectrum. Quantum dot intermediate band solar cells are theoretically capable of achieving much higher efficiencies than conventional single-gap devices. Present prototypes suffer from extremely weak absorption of subbandgap photons in the quantum dots. This problem has received little attention so far, yet it is a serious barrier to the technology approaching its theoretical efficiency limit. Crystalline silicon solar cells absorb weakly in the near infrared due to their indirect bandgap. This problem has received much attention over recent decades, and all commercial crystalline silicon solar cells employ some form of light trapping. With the industry moving toward thinner and thinner wafers, light trapping is becoming of greater importance and diffractive structures may offer an improvement over the state-of-the-art. We begin by constructing a computational method with which to simulate solar cells equipped with diffraction grating textures. The method employs a wave-optical treatment of the diffraction grating, via rigorous coupled wave analysis, with a geometric-optical treatment of the thick solar cell bulk. These are combined using a steady-state matrix formalism. The method has been implemented computationally, and is found to be efficient and to give results in good agreement with alternative methods from other authors. The theoretical upper limit to absorption enhancement in solar cells using diffractions gratings is calculated using the matrix formalism derived in the previous task. This limit is compared to the so-called Lambertian limit for light trapping with isotropic scatterers, and to the absolute upper limit to light trapping in bulk absorbers. It is found that bi-periodic gratings (square or hexagonal geometry) are capable of offering much better light trapping than uni-periodic line gratings. The upper limit depends strongly on the grating period. For large periods, diffraction gratings are theoretically able to offer light trapping at the absolute upper limit, but only if the scattering efficiencies have a particular form, which is deemed to be beyond present design capabilities. For periods similar to the incident wavelength, diffraction gratings can offer light trapping below the absolute limit but above the Lambertian limit without placing unrealistic demands on the exact form of the scattering efficiencies. This is possible for a reasonably broad wavelength range. The computational method is used to design and optimise diffraction gratings for light trapping in solar cells. The proposed diffraction grating consists of a hexagonal lattice of cylindrical wells etched into the rear of the bulk solar cell absorber. This is encapsulated in a dielectric buffer layer, and capped with a rear reflector. Simulations are made of this grating profile applied to a crystalline silicon solar cell and to a quantum dot intermediate band solar cell. The grating period, well depth, and lateral well dimensions are optimised numerically for both solar cell types. This yields the optimum parameters to be used in fabrication of grating equipped solar cells. The optimum parameters are explained using simple physical concepts, allowing us to make more general statements that can be applied to other solar cell technologies. Diffraction grating textures are fabricated on crystalline silicon substrates using nano-imprint lithography and reactive ion etching. The optimum grating period from the previous task has been used as a design parameter. The substrates have been processed into solar cell precursors for optical measurements. Reflection spectroscopy measurements confirm that bi-periodic square gratings offer better absorption enhancement than uni-periodic line gratings. The fabricated structures have been simulated with the previously developed computation tool, with good agreement between measurement and simulation results. The simulations reveal that a significant amount of the incident photons are absorbed parasitically in the rear reflector, and that this is exacerbated by the non-planarity of the rear reflector. An alternative method of depositing the dielectric buffer layer was developed, which leaves a planar surface onto which the reflector is deposited. It was found that samples prepared in this way suffered less from parasitic reflector absorption. The next task described in the thesis is the study of photon absorption in semiconductor quantum dots. The bound-state energy levels of in InAs/GaAs quantum dots is calculated using the effective mass approximation. A one- and four- band method is applied to the calculation of electron and hole wavefunctions respectively, with an empirical Hamiltonian being employed in the latter case. The strength of optical transitions between the bound states is calculated using the Fermi golden rule. The effect of the quantum dot dimensions on the energy levels and transition strengths is investigated. It is found that a strong direct transition between the ground intermediate state and the conduction band can be promoted by decreasing the quantum dot width from its value in present prototypes. This has the added benefit of reducing the ladder of excited states between the ground state and the conduction band, which may help to reduce thermal escape of electrons from quantum dots: an undesirable phenomenon from the point of view of the open circuit voltage of an intermediate band solar cell. A realistic detailed balance model is developed for quantum dot solar cells, which uses as input the energy levels and transition strengths calculated in the previous task. The model calculates the transition currents between the many intermediate levels and the valence and conduction bands under a given set of conditions. It is distinct from previous idealised detailed balance models, which are used to calculate limiting efficiencies, since it makes realistic assumptions about photon absorption by each transition. The model is used to reproduce published experimental quantum efficiency results at different temperatures, with quite good agreement. The much-studied phenomenon of thermal escape from quantum dots is found to be photonic; it is due to thermal photons, which induce transitions between the ladder of excited states between the ground intermediate state and the conduction band. In the final chapter, the realistic detailed balance model is combined with the diffraction grating simulation method to predict the effect of incorporating a diffraction grating into a quantum dot intermediate band solar cell. Careful optimisation of the grating period is made to balance the enhancement given to the different intermediate transitions, which occur in series. Due to the extremely weak absorption in the quantum dots, it is found that light trapping alone is not sufficient to achieve high subbandgap currents in quantum dot solar cells. Instead, a combination of light trapping and increased quantum dot density is required. Within the radiative limit, a quantum dot solar cell with no light trapping requires a 1000 fold increase in the number of quantum dots to supersede the efficiency of a single-gap reference cell. A quantum dot solar cell equipped with a diffraction grating requires between a 10 and 100 fold increase in the number of quantum dots, depending on the level of parasitic absorption in the rear reflector.

Radio propagation modeling and measurements for ZigBee based indoor wireless sensor networks

The deployment of nodes in Wireless Sensor Networks (WSNs) arises as one of the biggest challenges of this field, which involves in distributing a large number of embedded systems to fulfill a specific application. The connectivity of WSNs is difficult to estimate due to the irregularity of the physical environment and affects the WSN designers? decision on deploying sensor nodes. Therefore, in this paper, a new method is proposed to enhance the efficiency and accuracy on ZigBee propagation simulation in indoor environments. The method consists of two steps: automatic 3D indoor reconstruction and 3D ray-tracing based radio simulation. The automatic 3D indoor reconstruction employs unattended image classification algorithm and image vectorization algorithm to build the environment database accurately, which also significantly reduces time and efforts spent on non-radio propagation issue. The 3D ray tracing is developed by using kd-tree space division algorithm and a modified polar sweep algorithm, which accelerates the searching of rays over the entire space. Signal propagation model is proposed for the ray tracing engine by considering both the materials of obstacles and the impact of positions along the ray path of radio. Three different WSN deployments are realized in the indoor environment of an office and the results are verified to be accurate. Experimental results also indicate that the proposed method is efficient in pre-simulation strategy and 3D ray searching scheme and is suitable for different indoor environments.

Adaptive scheme for Accurate orbit propagation

Two extensions of the fast and accurate special perturbation method recently developed by Peláez et al. are presented for respectively elliptic and hyperbolic motion. A comparison with Peláez?s method and with the very efficient Stiefel- Scheifele?s method, for the problems of oblate Earth plus Moon and continuous radial thrust, shows that the new formulations can appreciably improve the accuracy of Peláez?s method and have a better performance of Stiefel-Scheifele?s method. Future work will be to include the two new formulations and the original one due to Peláez into an adaptive scheme for highly accurate orbit propagation

Applied continuous modelling in the study of pyrotechnic shock propagation on Ariane 5

This paper deals with the theoretical method and the modelling problems on the analysis of the Pyrotechnic Shock Propagation in the Vehicle Equipment Bay Structure of the ARIANE 5 during the separation of the upper stage. This work has been developed under a contract with the Spanish Firm Construcciones Aeronáuticas S.A. From all the analysis and the studies it can be concluded that: 1.- The mathematical method used for the study of the pyrotechnic shock phenomena is very well suited for conducting parametric studies. 2.- A careful model of the structure should be developed taking into account the realistic stiffness and dissipation properties at the junctions. 3.- The load produced by the pyrotechnic device should be carefully calibrated to reach a good agreement between theoretical and test results. 4.- In any case with the adquired experience it can be said that with the modelling of continuous elements the order of magnitude of the accelerations can be predicted with the accuracy needed in practical applications.

Comparison of multi-year Ka-band propagation characteristics at four sites in North America and Europe

Tropospheric phenomena such as clouds and mainly rain cause higher attenuation at Ka-band than at lower frequencies. In this collaborative paper, the main results of four long-term Ka-band propagation campaigns are presented. The experiments are carried out in Ottawa, Canada (satellite Anik F2); Aveiro, Portugal; Madrid, Spain; and Toulouse, France (satellite HotBird 6 in the last three cases) and have been running since 2004 in Aveiro, 2006 in Ottawa and Madrid, and 2008 in Toulouse. After a brief introduction of the experiments, rain rate and excess attenuation results are discussed, first for a common two-year measurement period and later for the whole database available. Seasonal attenuation statistics for Madrid, Ottawa and Aveiro are compared. Finally, fade duration and fade slope statistics derived at three locations are presented and discussed.

Five-year results of a slant-path propagation experiment at 20 GHz in Madrid

Satellite operators are starting to use the Ka-band (30/20 GHz) for communications systems requiring higher traffic capacity. The use of this band is expected to experience a significant growth in the next few years, as several operators have reported plans to launch new satellites with Ka-band capacity. It is worth mentioning the Ka-Sat satellite in Europe, launched in 2010, and ViaSat-1, of 2011, with coverage of USA1. Some other examples can be found in other parts of the World. Recent satellite communications standards, such as DVB-S22 or DVB-RCS3, which provide means to mitigate propagation impairments, have been developed with the objective of improving the use of the Ka-band, in comparison with previous technical standards. In the next years, the ALPHASAT satellite will bring about new opportunities4 for carrying out propagation and telecommunication experiments in the Ka- and Q/V-bands. Commercial uses are focused on the provision of high speed data communications, for Internet access and other applications. In the near future, it is expected that higher and higher data rates will also be needed to broadcast richer multimedia contents, including HD-TV, interactive content or 3D-TV. All of these services may be provided in the future by satellites of the current generation, whose life span can extend up to 2025 in some cases. Depending on local regulations, the available bandwidth for the satellite fixed and broadcasting services in the Ka-band is in excess of several hundred MHz, bidirectional, comprising more than 1 GHz for each sub-band in some cases. In this paper, the results of a propagation experiment that is being carried out at Universidad Politécnica de Madrid (UPM), Spain, are presented5. The objective of the experiment is twofold: gathering experimental time series of attenuation and analyzing them in order to characterize the propagation channel at these frequencies6. The experiment and statistical results correspond to five complete years of measurements. The experiment is described in more detail in Section II. Yearly characteristics of rain attenuation are presented in Section III, whereas Section IV is dedicated to the monthly, seasonal, and hourly characteristics. Section V covers the dynamic characteristics of this propagation effect, just before the conclusions are described in Section VI.

Monte Carlo uncertainty propagation approaches in ADS burn-up calculations

In activation calculations, there are several approaches to quantify uncertainties: deterministic by means of sensitivity analysis, and stochastic by means of Monte Carlo. Here, two different Monte Carlo approaches for nuclear data uncertainty are presented: the first one is the Total Monte Carlo (TMC). The second one is by means of a Monte Carlo sampling of the covariance information included in the nuclear data libraries to propagate these uncertainties throughout the activation calculations. This last approach is what we named Covariance Uncertainty Propagation, CUP. This work presents both approaches and their differences. Also, they are compared by means of an activation calculation, where the cross-section uncertainties of 239Pu and 241Pu are propagated in an ADS activation calculation.

Propagation of Cross-Section Uncertainties in Criticality Calculations in the Framework of UAM-Phase I Using MCNPX-2.7e and SCALE-6.1

In the framework of the OECD/NEA project on Benchmark for Uncertainty Analysis in Modeling (UAM) for Design, Operation, and Safety Analysis of LWRs, several approaches and codes are being used to deal with the exercises proposed in Phase I, “Specifications and Support Data for Neutronics Cases.” At UPM, our research group treats these exercises with sensitivity calculations and the “sandwich formula” to propagate cross-section uncertainties. Two different codes are employed to calculate the sensitivity coefficients of to cross sections in criticality calculations: MCNPX-2.7e and SCALE-6.1. The former uses the Differential Operator Technique and the latter uses the Adjoint-Weighted Technique. In this paper, the main results for exercise I-2 “Lattice Physics” are presented for the criticality calculations of PWR. These criticality calculations are done for a TMI fuel assembly at four different states: HZP-Unrodded, HZP-Rodded, HFP-Unrodded, and HFP-Rodded. The results of the two different codes above are presented and compared. The comparison proves a good agreement between SCALE-6.1 and MCNPX-2.7e in uncertainty that comes from the sensitivity coefficients calculated by both codes. Differences are found when the sensitivity profiles are analysed, but they do not lead to differences in the uncertainty.

GRS Results for the Burnup Pin-cell Benchmark Propagation of Cross-Section, Fission Yields and Decay Data Uncertainties

GRS Results for the Burnup Pin-cell Benchmark Propagation of Cross-Section, Fission Yields and Decay Data Uncertainties

Propagation of U235-238, Pu239 and STL Nuclear Data Uncertainties for PWR core analysis

An uncertainty propagation methodology based on Monte Carlo method is applied to PWR nuclear design analysis to assess the impact of nuclear data uncertainties in 235,238 U, 239 Pu and Scattering Thermal Library for Hydrogen in water. This uncertainty analysis is compared with the design and acceptance criteria to assure the adequacy of bounding estimates in safety margins.

Nuclear Data Uncertainty Propagation to Reactivity Coefficients of a Sodium Fast Reactor

The assessment of the uncertainty levels on the design and safety parameters for the innovative European Sodium Fast Reactor (ESFR) is mandatory. Some of these relevant safety quantities are the Doppler and void reactivity coefficients, whose uncertainties are quantified. Besides, the nuclear reaction data where an improvement will certainly benefit the design accuracy are identified. This work has been performed with the SCALE 6.1 codes suite and its multigroups cross sections library based on ENDF/B-VII.0 evaluation.

Propagation of Neutron Cross Section, Fission Yield, and Decay Data Uncertainties in Depletion Calculations

Propagation of nuclear data uncertainties in reactor calculations is interesting for design purposes and libraries evaluation. Previous versions of the GRS XSUSA library propagated only neutron cross section uncertainties. We have extended XSUSA uncertainty assessment capabilities by including propagation of fission yields and decay data uncertainties due to the their relevance in depletion simulations. We apply this extended methodology to the UAM6 PWR Pin-Cell Burnup Benchmark, which involves uncertainty propagation through burnup.

Towards a complete propagation of nuclear data uncertainties Fission yields and decay data

Propagation of nuclear data uncertainties to calculated values is interesting for design purposes and libraries evaluation. XSUSA, developed at GRS, propagates cross section uncertainties to nuclear calculations. In depletion simulations, fission yields and decay data are also involved and suppose a possible source of uncertainty that must be taken into account. We have developed tools to generate varied fission yields and decay libraries and to propagate uncertainties trough depletion in order to complete the XSUSA uncertainty assessment capabilities. A simple test to probe the methodology is defined and discussed.

Cooperative localization in mobile networks using nonparametric variants of belief propagation

Of the many state-of-the-art methods for cooperative localization in wireless sensor networks (WSN), only very few adapt well to mobile networks. The main problems of the well-known algorithms, based on nonparametric belief propagation (NBP), are the high communication cost and inefficient sampling techniques. Moreover, they either do not use smoothing or just apply it o ine. Therefore, in this article, we propose more flexible and effcient variants of NBP for cooperative localization in mobile networks. In particular, we provide: i) an optional 1-lag smoothing done almost in real-time, ii) a novel low-cost communication protocol based on package approximation and censoring, iii) higher robustness of the standard mixture importance sampling (MIS) technique, and iv) a higher amount of information in the importance densities by using the population Monte Carlo (PMC) approach, or an auxiliary variable. Through extensive simulations, we confirmed that all the proposed techniques outperform the standard NBP method.

Nonparametric generalized belief propagation based on pseudo-junction tree for cooperative localization in wireless networks

Non-parametric belief propagation (NBP) is a well-known message passing method for cooperative localization in wireless networks. However, due to the over-counting problem in the networks with loops, NBP’s convergence is not guaranteed, and its estimates are typically less accurate. One solution for this problem is non-parametric generalized belief propagation based on junction tree. However, this method is intractable in large-scale networks due to the high-complexity of the junction tree formation, and the high-dimensionality of the particles. Therefore, in this article, we propose the non-parametric generalized belief propagation based on pseudo-junction tree (NGBP-PJT). The main difference comparing with the standard method is the formation of pseudo-junction tree, which represents the approximated junction tree based on thin graph. In addition, in order to decrease the number of high-dimensional particles, we use more informative importance density function, and reduce the dimensionality of the messages. As by-product, we also propose NBP based on thin graph (NBP-TG), a cheaper variant of NBP, which runs on the same graph as NGBP-PJT. According to our simulation and experimental results, NGBP-PJT method outperforms NBP and NBP-TG in terms of accuracy, computational, and communication cost in reasonably sized networks.