Realistic detailed balance study of the quantum efficiency of quantum dot solar cells

An attractive but challenging technology for high efficiency solar energy conversion is the intermediate band solar cell (IBSC), whose theoretical efficiency limit is 63%, yet which has so far failed to yield high efficiencies in practice. The most advanced IBSC technology is that based on quantum dots (QDs): the QD-IBSC. In this paper, k·p calculations of photon absorption in the QDs are combined with a multi-level detailed balance model. The model has been used to reproduce the measured quantum efficiency of a real QD-IBSC and its temperature dependence. This allows the analysis of individual sub-bandgap transition currents, which has as yet not been possible experimentally, yielding a deeper understanding of the failure of current QD-IBSCs. Based on the agreement with experimental data, the model is believed to be realistic enough to evaluate future QD-IBSC proposals.

The lead salt quantum dot intermediate band solar cell

We propose a new kind of quantum dot (QD) materials for the implementation of the intermediate band solar cell (IBSC) [1]. The materials are formed by lead salt QDs of the family IV-VI (PbTe, PbSe or PbS) embedded in a semiconductor of the family II-VI (Cd1-xMgxTe, CdxZn1-xTe, and CdS1-xSex or ZnSe1-xTex, respectively). These QDs are not nucleated due to lattice mismatch, as it is the case of the InAs/GaAs QD material system grown by the Stranski-Krastanov (S-K) mode. In these materials, the QDs precipitate due to the difference in lattice type: the QD lead salt material crystallizes in the rocksalt structure, while the II-VI host material has the zincblende structure [2]. Therefore, it is possible to use lattice-matched QD/host combinations, avoiding all the strain-related problems found in previous QD-IBSC developments. In this paper we discuss the properties of the lead salt QD materials and propose that they are appropriate to overcome the fundamental drawbacks of present III-V-based QD-IBSC prototypes. We also calculate the band diagram for some examples of IV-VI/II-VI QD materials. The detailed balance efficiency limit of QD-IBSCs based on the studied materials is found to be over 60% under maximum concentration.

Research on intermediate band solar cells and development of experimental techniques for their characterization under concentrated illumination

Abstract This work is a contribution to the research and development of the intermediate band solar cell (IBSC), a high efficiency photovoltaic concept that features the advantages of both low and high bandgap solar cells. The resemblance with a low bandgap solar cell comes from the fact that the IBSC hosts an electronic energy band -the intermediate band (IB)- within the semiconductor bandgap. This IB allows the collection of sub-bandgap energy photons by means of two-step photon absorption processes, from the valence band (VB) to the IB and from there to the conduction band (CB). The exploitation of these low energy photons implies a more efficient use of the solar spectrum. The resemblance of the IBSC with a high bandgap solar cell is related to the preservation of the voltage: the open-circuit voltage (VOC) of an IBSC is not limited by any of the sub-bandgaps (involving the IB), but only by the fundamental bandgap (defined from the VB to the CB). Nevertheless, the presence of the IB allows new paths for electronic recombination and the performance of the IBSC is degraded at 1 sun operation conditions. A theoretical argument is presented regarding the need for the use of concentrated illumination in order to circumvent the degradation of the voltage derived from the increase in the recombi¬nation. This theory is supported by the experimental verification carried out with our novel characterization technique consisting of the acquisition of photogenerated current (IL)-VOC pairs under low temperature and concentrated light. Besides, at this stage of the IBSC research, several new IB materials are being engineered and our novel character¬ization tool can be very useful to provide feedback on their capability to perform as real IBSCs, verifying or disregarding the fulfillment of the “voltage preservation” principle. An analytical model has also been developed to assess the potential of quantum-dot (QD)-IBSCs. It is based on the calculation of band alignment of III-V alloyed heterojunc-tions, the estimation of the confined energy levels in a QD and the calculation of the de¬tailed balance efficiency. Several potentially useful QD materials have been identified, such as InAs/AlxGa1-xAs, InAs/GaxIn1-xP, InAs1-yNy/AlAsxSb1-x or InAs1-zNz/Alx[GayIn1-y]1-xP. Finally, a model for the analysis of the series resistance of a concentrator solar cell has also been developed to design and fabricate IBSCs adapted to 1,000 suns. Resumen Este trabajo contribuye a la investigación y al desarrollo de la célula solar de banda intermedia (IBSC), un concepto fotovoltaico de alta eficiencia que auna las ventajas de una célula solar de bajo y de alto gap. La IBSC se parece a una célula solar de bajo gap (o banda prohibida) en que la IBSC alberga una banda de energía -la banda intermedia (IB)-en el seno de la banda prohibida. Esta IB permite colectar fotones de energía inferior a la banda prohibida por medio de procesos de absorción de fotones en dos pasos, de la banda de valencia (VB) a la IB y de allí a la banda de conducción (CB). El aprovechamiento de estos fotones de baja energía conlleva un empleo más eficiente del espectro solar. La semejanza antre la IBSC y una célula solar de alto gap está relacionada con la preservación del voltaje: la tensión de circuito abierto (Vbc) de una IBSC no está limitada por ninguna de las fracciones en las que la IB divide a la banda prohibida, sino que está únicamente limitada por el ancho de banda fundamental del semiconductor (definido entre VB y CB). No obstante, la presencia de la IB posibilita nuevos caminos de recombinación electrónica, lo cual degrada el rendimiento de la IBSC a 1 sol. Este trabajo argumenta de forma teórica la necesidad de emplear luz concentrada para evitar compensar el aumento de la recom¬binación de la IBSC y evitar la degradación del voltage. Lo anterior se ha verificado experimentalmente por medio de nuestra novedosa técnica de caracterización consistente en la adquisicin de pares de corriente fotogenerada (IL)-VOG en concentración y a baja temperatura. En esta etapa de la investigación, se están desarrollando nuevos materiales de IB y nuestra herramienta de caracterizacin está siendo empleada para realimentar el proceso de fabricación, comprobando si los materiales tienen capacidad para operar como verdaderas IBSCs por medio de la verificación del principio de preservación del voltaje. También se ha desarrollado un modelo analítico para evaluar el potencial de IBSCs de puntos cuánticos. Dicho modelo está basado en el cálculo del alineamiento de bandas de energía en heterouniones de aleaciones de materiales III-V, en la estimación de la energía de los niveles confinados en un QD y en el cálculo de la eficiencia de balance detallado. Este modelo ha permitido identificar varios materiales de QDs potencialmente útiles como InAs/AlxGai_xAs, InAs/GaxIni_xP, InAsi_yNy/AlAsxSbi_x ó InAsi_zNz/Alx[GayIni_y]i_xP. Finalmente, también se ha desarrollado un modelado teórico para el análisis de la resistencia serie de una célula solar de concentración. Gracias a dicho modelo se han diseñado y fabricado IBSCs adaptadas a 1.000 soles.

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.

Global optimization of solar thermophotovoltaic systems

n this paper, we present a theoretical model based on the detailed balance theory of solar thermophotovoltaic systems comprising multijunction photovoltaic cells, a sunlight concentrator and spectrally selective surfaces. The full system has been defined by means of 2n + 8 variables (being n the number of sub-cells of the multijunction cell). These variables are as follows: the sunlight concentration factor, the absorber cut-off energy, the emitter-to-absorber area ratio, the emitter cut-off energy, the band-gap energy(ies) and voltage(s) of the sub-cells, the reflectivity of the cells' back-side reflector, the emitter-to-cell and cell-to-cell view factors and the emitter-to-cell area ratio. We have used this model for carrying out a multi-variable system optimization by means of a multidimensional direct-search algorithm. This analysis allows to find the set of system variables whose combined effects results in the maximum overall system efficiency. From this analysis, we have seen that multijunction cells are excellent candidates to enhance the system efficiency and the electrical power density. Particularly, multijunction cells report great benefits for systems with a notable presence of optical losses, which are unavoidable in practical systems. Also, we have seen that the use of spectrally selective absorbers, rather than black-body absorbers, allows to achieve higher system efficiencies for both lower concentration and lower emitter-to-absorber area ratio. Finally, we have seen that sun-to-electricity conversion efficiencies above 30% and electrical power densities above 50 W/cm2 are achievable for this kind of systems.

Implications of redesigned, high-radiative-efficiency GaInP junctions on III-V multijunction concentrator solar cells

Nonradiative recombination in inverted GaInP junctions is dramatically reduced using a rear-heterojunction design rather than the more traditional thin-emitter homojunction design. When this GaInP junction design is included in inverted multijunction solar cells, the high radiative efficiency translates into both higher subcell voltage and high luminescence coupling to underlying subcells, both of which contribute to improved performance. Subcell voltages within two and four junction devices are measured by electroluminescence and the internal radiative efficiency is quantified as a function of recombination current using optical modeling. The performance of these concentrator multijunction devices is compared with the Shockley–Queisser detailed-balance radiative limit, as well as an internal radiative limit, which considers the effects of the actual optical environment in which a perfect junction may exist.

Three-terminal heterojunction bipolar transistor solar cell for high-efficiency photovoltaic conversion

Here we propose, for the first time, a solar cell characterized by a semiconductor transistor structure (n/p/n or p/n/p) where the base-emitter junction is made of a high-bandgap semiconductor and the collector is made of a low-bandgap semiconductor. We calculate its detailed-balance efficiency limit and prove that it is the same one than that of a double-junction solar cell. The practical importance of this result relies on the simplicity of the structure that reduces the number of layers that are required to match the limiting efficiency of dual-junction solar cells without using tunnel junctions. The device naturally emerges as a three-terminal solar cell and can also be used as building block of multijunction solar cells with an increased number of junctions.