Symmetry considerations in the empirical k.p Hamiltonian for the study of intermediate band solar cells

With the purpose of assessing the absorption coefficients of quantum dot solar cells, symmetry considerations are introduced into a Hamiltonian whose eigenvalues are empirical. In this way, the proper transformation from the Hamiltonian's diagonalized form to the form that relates it with Γ-point exact solutions through k.p envelope functions is built accounting for symmetry. Forbidden transitions are thus determined reducing the calculation burden and permitting a thoughtful discussion of the possible options for this transformation. The agreement of this model with the measured external quantum efficiency of a prototype solar cell is found to be excellent.

The influence of quantum dot size on the sub-bandgap intraband photocurrent in intermediate band solar cells

The effect of quantum dot (QD) size on the performance of quantum dot intermediate band solar cells is investigated. A numerical model is used to calculate the bound state energy levels and the absorption coefficient of transitions from the ground state to all other states in the conduction band. Comparing with the current state of the art, strong absorption enhancements are found for smaller quantum dots, as well as a better positioning of the energy levels, which is expected to reduce thermal carrier escape. It is concluded that reducing the quantum dot size can increase sub-bandgap photocurrent and improve voltage preservation.

Guide to intermediate band solar cell research

The intermediate band solar cell (IBSC) is a solar cell that, in order to increase its efficiency over that of single gap solar cells, takes advantage of the absorption of below-bandgap energy photons by means of an intermediate band (IB) located in the semiconductor bandgap. For this process to improve the solar cell performance, the belowbandgap photon absorption has to be effective and the IB cannot limit the open-circuit voltage of the cell. In this paper we provide a guide to the new researcher interested in the idea in order he can quickly become familiar with the concept and updated with the most relevant experimental results.

Nano-imprinted rear-side diffraction gratings for absorption enhancement in solar cells

As wafer-based solar cells become thinner, light-trapping textures for absorption enhancement will gain in importance. In this work, crystalline silicon wafers were textured with wavelength-scale diffraction grating surface textures by nanoimprint lithography using interference lithography as a mastering technology. This technique allows fine-tailored nanostructures to be realized on large areas with high throughput. Solar cell precursors were fabricated, with the surface textures on the rear side, for optical absorption measurements. Large absorption enhancements are observed in the wavelength range in which the silicon wafer absorbs weakly. It is shown experimentally that bi-periodic crossed gratings perform better than uni-periodic linear gratings. Optical simulations have been made of the fabricated structures, allowing the total absorption to be decomposed into useful absorption in the silicon and parasitic absorption in the rear reflector. Using the calculated silicon absorption, promising absorbed photocurrent density enhancements have been calculated for solar cells employing the nano-textures. Finally, first results are presented of a passivation layer deposition technique that planarizes the rear reflector for the purpose of reducing the parasitic absorption.

IBPOWER Project, Intermediate band materials and solar cells for photovoltaics with high efficiency and reduced cost

IBPOWER is a Project awarded under the 7th European Framework Programme that aims to advance research on intermediate band solar cells (IBSCs). These are solar cells conceived to absorb below bandgap energy photons by means of an electronic energy band that is located within the semiconductor bandgap, whilst producing photocurrent with output voltage still limited by the total semiconductor bandgap. IBPOWER employs two basic strategies for implementing the IBSC concept. The first is based on the use of quantum dots, the IB arising from the confined energy levels of the electrons in the dots. Quantum dots have led to devices that demonstrate the physical operation principles of the IB concept and have allowed identification of the problems to be solved to achieve actual high efficiencies. The second approach is based on the creation of bulk intermediate band materials by the insertion of an appropriate impurity into a bulk semiconductor. Under this approach it is expected that, when inserted at high densities, these impurities will find it difficult to capture electrons by producing a breathing mode and will cease behaving as non-radiative recombination centres. Towards this end the following systems are being investigated: a) Mn: In1-xGax N; b) transition metals in GaAs and c) thin films.

Full-Wafer Roller-NIL Processes for Silicon Solar Cell Texturisation

The highest solar cell efficiencies both for c-Si and mc-Si were reached using template based texturing processes. Especially for mc-Si the benefit of a defined texture, the so called honeycomb texture, was demonstrated impressively. However, up until now, no industrially feasible process has been available to pattern the necessary etching masks with the sufficient resolution. Roller-Nanoimprint Lithography (Roller-NIL) has the potential to overcome these limitations and to allow high quality pattern transfers, even in the sub-micron regime, in continuous in-line processes. Therefore, this etch-mask patterning technique is a suitable solution to bring such elaborate features like the honeycomb texture to an industrial realization. Beyond that, this fast printing-like technology opens up new possibilities to introduce promising concepts like photonic structures into solar cells.

Nanoimprinted diffraction gratings for crystalline silicon solar cells: implementation, characterization and simulation

Light trapping is becoming of increasing importance in crystalline silicon solar cells as thinner wafers are used to reduce costs. In this work, we report on light trapping by rear-side diffraction gratings produced by nano-imprint lithography using interference lithography as the mastering technology. Gratings fabricated on crystalline silicon wafers are shown to provide significant absorption enhancements. Through a combination of optical measurement and simulation, it is shown that the crossed grating provides better absorption enhancement than the linear grating, and that the parasitic reflector absorption is reduced by planarizing the rear reflector, leading to an increase in the useful absorption in the silicon. Finally, electro-optical simulations are performed of solar cells employing the fabricated grating structures to estimate efficiency enhancement potential.

A numerical study into the influence of quantum dot size on the sub-bandgap interband photocurrent in intermediate band solar cells

A numerical study is presented of the sub-bandgap interband photon absorption in quantum dot intermediate band solar cells. Absorption coefficients and photocurrent densities are calculated for the valence band to intermediate band transitions using a four-band k · p method. It is found that reducing the quantum dot width in the plane perpendicular to the growth direction increases the photocurrent from the valence band to the intermediate-band ground state if the fractional surface coverage of quantum dots is conserved. This provides a path to increase the sub-bandgap photocurrent in intermediate band solar cells.

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.

Interband absorption of photons by extended states in intermediate band solar cells

This paper considers sub-bandgap photon absorption in an InAs/GaAs quantum dot matrix. Absorption coefficients are calculated for transitions from the extended states in the valence band to confined states in the conduction band. This completes a previous body of work in which transitions between bound states were calculated. The calculations are based on the empirical k·p Hamiltonian considering the quantum dots as parallelepipeds. The extended states may be only partially extended?in one or two dimensions?or extended in all three dimensions. It is found that extended-to-bound transitions are, in general, weaker than bound-to-bound transitions, and that the former are weaker when the initial state is extended in more coordinates. This study is of direct application to the research of intermediate band solar cells and other semiconductor devices based on light absorption in semiconductors nanostructured with quantum dots.

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.

Six not so easy pieces in intermediate band solar cell research

The concept of "intermediate band solar cell" (IBSC) is, apparently, simple to grasp. However, since the idea was proposed, our understanding has improved and we feel now that we can explain better some concepts than we initially introduced. Clarifying these concepts is important, even if they are well-known for the advanced researcher, so that efforts can be driven in the right direction from start. The six pieces of this work are: Does a miniband need to be formed when the IBSC is implemented with quantum dots?; What are the problems of each of the main practical approaches that exist today? What are the simplest experimental techniques to demonstrate whether an IBSC is working as such or not? What is the issue with the absorption coefficient overlap? and Mott's transition? What the best system would be, if any?

Virtual-bound, filamentary and layered states in a box-shaped quantum dot of square potential form the exact numerical solution of the effective mass Schrodinger equation

The effective mass Schrodinger equation of a QD of parallelepipedic shape with a square potential well is solved by diagonalizing the exact Hamiltonian matrix developed in a basis of separation-of-variables wavefunctions. The expected below bandgap bound states are found not to differ very much from the former approximate calculations. In addition, the presence of bound states within the conduction band is confirmed. Furthermore, filamentary states bounded in two dimensions and extended in one dimension and layered states with only one dimension bounded, all within the conduction band which are similar to those originated in quantum wires and quantum wells coexist with the ordinary continuum spectrum of plane waves. All these subtleties are absent in spherically shaped quantum dots, often used for modeling.

Células solares de banda intermedia

Las células solares de banda intermedia se inventaron en España. Constituyen una propuesta para aumentar la eficiencia de las células solares por encima del límite de Shockley y Queisser para células de un solo gap. El número de ideas para llevarlas a la práctica (desde la utilización de puntos cuánticos a la implantación selectiva de impurezas) se ha ido expandiendo a medida que nuestra comprensión ha ido aumentando. En este artículo repasamos el concepto de célula solar de banda intermedia y algunas de estas ideas para llevarla a la práctica.

Empiric k·p Hamiltonian calculation of the band-to-band photon absorption in semiconductors

The Empiric k·p Hamiltonian method is usually applied to nanostructured semiconductors. In this paper, it is applied to a homogeneous semiconductor in order to check the adequacy of the method. In this case, the solutions of the diagonalized Hamiltonian, as well as the envelope functions, are plane waves. The procedure is applied to the GaAs and the interband absorption coefficients are calculated. They result in reasonable agreement with the measured values, further supporting the adequacy of the Empiric k·p Hamiltonian method.