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.

Wide-bandgap InAs/InGaP quantum-dot intermediate band solar cells

Current prototypes of quantum-dot intermediate band solar cells suffer from voltage reduction due to the existence of carrier thermal escape. An enlarged sub-bandgap EL would not only minimize this problem, but would also lead to a bandgap distribution that exploits more efficiently the solar spectrum. In this work we demonstrate InAs/InGaP QD-IBSC prototypes with the following bandgap distribution: EG = 1.88 eV, EH = 1.26 eV and EL > 0.4 eV. We have measured, for the first time in this material, both the interband and intraband transitions by means of photocurrent experiments. The activation energy of the carrier thermal escape in our devices has also been measured. It is found that its value, compared to InAs/GaAs-based prototypes, does not follow the increase in EL. The benefits of using thin AlGaAs barriers before and after the quantum-dot layers are analyzed.

Quantum dot parameters determination from quantum-efficiency measurements

The energy spectrum of the confined states of a quantum dot intermediate band (IB) solar cell is calculated with a simplified model. Two peaks are usually visible at the lowest energy side of the subbandgap quantum-efficiency spectrum in these solar cells. They can be attributed to photon absorption between well-defined states. As a consequence, the horizontal size of the quantum dots can be determined, and the conduction (valence) band offset is also determined if the valence (conduction) offset is known.

Role of the wetting layer in the enhanced responsivity of InAs/GaAsSb quantum dot infrared photodetectors

InAs/GaAs1−xSbx Quantum Dot (QD) infrared photodetectors are analyzed by photocurrent spectroscopy. We observe that the integrated responsivity of the devices is improved with the increasing Sb mole fraction in the capping layer, up to 4.2 times for x = 17%. Since the QD layers are not vertically aligned, the vertical transport of the carriers photogenerated within the QDs takes place mainly through the bulk material and the wetting layer of the additional QD regions. The lower thickness of the wetting layer for high Sb contents results in a reduced capture probability of the photocarriers, thus increasing the photoconductive gain and hence, the responsivity of the device. The growth of not vertically aligned consecutive QD layers with a thinner wetting layer opens a possibility to improve the performance of quantum dot infrared photodetectors.

Bending reinforcement of timber beams with composite carbon fiber and basalt fiber materials

En el presente trabajo se lleva a cabo un estudio basado en datos obtenidos experimentalmente mediante el ensayo a flexión de vigas de madera de pino silvestre reforzadas con materiales compuestos. Las fibras que componen los tejidos utilizados para la ejecución de los refuerzos son de basalto y de carbono. En el caso de los compuestos de fibra de basalto se aplican en distintos gramajes, y los de carbono en tejido unidireccional y bidireccional. El material compuesto se realizó in situ, simultáneamente a la ejecución del refuerzo. Se aplicaron en una y en dos capas, según el caso, y la forma de colocación fue en ?U?, adhiriéndose al canto inferior y a las caras laterales de la viga mediante resina o mortero epoxi. Se analiza el comportamiento de las vigas según las variables de refuerzo aplicadas y se comparan con los resultados de vigas ensayadas sin reforzar. Con este trabajo queda demostrado el buen funcionamiento del FRP de fibra de basalto aplicado en el refuerzo de vigas de madera y de los tejidos de carbono bidireccionales con respecto a los unidireccionales.

Self-organized colloidal quantum dots and metal nanoparticles for plasmon-enhanced intermediate-band solar cells

A colloidal deposition technique is presented to construct long-range ordered hybrid arrays of self-assembled quantum dots and metal nanoparticles. Quantum dots are promising for novel opto-electronic devices but, in most cases, their optical transitions of interest lack sufficient light absorption to provide a significant impact in their implementation. A potential solution is to couple the dots with localized plasmons in metal nanoparticles. The extreme confinement of light in the near-field produced by the nanoparticles can potentially boost the absorption in the quantum dots by up to two orders of magnitude. In this work, light extinction measurements are employed to probe the plasmon resonance of spherical gold nanoparticles in lead sulfide colloidal quantum dots and amorphous silicon thin-films. Mie theory computations are used to analyze the experimental results and determine the absorption enhancement that can be generated by the highly intense near-field produced in the vicinity of the gold nanoparticles at their surface plasmon resonance. The results presented here are of interest for the development of plasmon-enhanced colloidal nanostructured photovoltaic materials, such as colloidal quantum dot intermediate-band solar cells.

Room temperature photoluminescence of InGaAs Surface Quantum Dots

Self-assembled InGaAs quantum dots show unique physical properties such as three dimensional confinement, high size homogeneity, high density and low number of dislocations. They have been extensively used in the active regions of laser devices for optical communications applications [1]. Therefore, buried quantum dots (BQDs) embedded in wider band gap materials have been normally studied. The wave confinement in all directions and the stress field around the dot affect both optical and electrical properties [2, 3]. However, surface quantum dots (SQDs) are less affected by stress, although their optical and electrical characteristics have a strong dependence on surface fluctuation. Thus, they can play an important role in sensor applications

Mid-infrared photodetectors based on GaAsSb-capped InAs quantum dots

Quantum dot infrared photodetectors (QDIPs) are very attractive for many applications such as infrared imaging, remote sensing and gas sensing, thanks to its promising features such as high temperature operation, normal incidence response and low dark current [1]. However, the key issue is to obtain a high-quality active region which requires an optimization of the nanostructure. By using GaAsSb capping layer, InAs QDs have improved their optical emission in the range between 1.15 and 1.3 m (at Sb composition of 14 %), due to a reduction of a compressive strain in QD and an increment of a QD height [2]. In this work, we have demonstrated strong and narrow intraband photoresponses at ~ 5 m from GaAsSb-capped InAs/GaAs QDIPs under normal light-incidence.

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.

Realistic performance prediction in nanostructured solar cells as a function of nanostructure dimensionality and density

The behavior of quantum dot, quantum wire, and quantum well InAs/GaAs solar cells is studied with a very simplified model based on experimental results in order to assess their performance as a function of the low bandgap material volume fraction fLOW. The efficiency of structured devices is found to exceed the efficiency of a non-structured GaAs cell, in particular under concentration, when fLOW is high; this condition is easier to achieve with quantum wells. If three different quasi Fermi levels appear with quantum dots the efficiency can be much higher.

Research on wide-bandgap intermediate band solar cells and development of experimental techniques for their characterization

El trabajo que ha dado lugar a esta Tesis Doctoral se enmarca en la invesitagación en células solares de banda intermedia (IBSCs, por sus siglas en inglés). Se trata de un nuevo concepto de célula solar que ofrece la posibilidad de alcanzar altas eficiencias de conversión fotovoltaica. Hasta ahora, se han demostrado de manera experimental los fundamentos de operación de las IBSCs; sin embargo, esto tan sólo has sido posible en condicines de baja temperatura. El concepto de banda intermedia (IB, por sus siglas en inglés) exige que haya desacoplamiento térmico entre la IB y las bandas de valencia y conducción (VB and CB, respectivamente, por sus siglas en inglés). Los materiales de IB actuales presentan un acoplamiento térmico demasiado fuerte entre la IB y una de las otras dos bandas, lo cual impide el correcto funcionamiento de las IBSCs a temperatura ambiente. En el caso particular de las IBSCs fabricadas con puntos cuánticos (QDs, por sus siglas en inglés) de InAs/GaAs - a día de hoy, la tecnología de IBSC más estudiada - , se produce un rápido intercambio de portadores entre la IB y la CB, por dos motivos: (1) una banda prohibida estrecha (< 0.2 eV) entre la IB y la CB, E^, y (2) la existencia de niveles electrónicos entre ellas. El motivo (1) implica, a su vez, que la máxima eficiencia alcanzable en estos dispositivos es inferior al límite teórico de la IBSC ideal, en la cual E^ = 0.71 eV. En este contexto, nuestro trabajo se centra en el estudio de IBSCs de alto gap (o banda prohibida) fabricadsas con QDs, o lo que es lo mismo, QD-IBSCs de alto gap. Hemos fabricado e investigado experimentalmente los primeros prototipos de QD-IBSC en los que se utiliza AlGaAs o InGaP para albergar QDs de InAs. En ellos demostramos une distribución de gaps mejorada con respecto al caso de InAs/GaAs. En concreto, hemos medido valores de E^ mayores que 0.4 eV. En los prototipos de InAs/AlGaAs, este incremento de E^ viene acompaado de un incremento, en más de 100 meV, de la energía de activación del escape térmico. Además, nuestros dispositivos de InAs/AlGaAs demuestran conversión a la alza de tensión; es decir, la producción de una tensión de circuito abierto mayor que la energía de los fotones (dividida por la carga del electrón) de un haz monocromático incidente, así como la preservación del voltaje a temperaura ambiente bajo iluminación de luz blanca concentrada. Asimismo, analizamos el potencial para detección infrarroja de los materiales de IB. Presentamos un nuevo concepto de fotodetector de infrarrojos, basado en la IB, que hemos llamado: fotodetector de infrarrojos activado ópticamente (OTIP, por sus siglas en inglés). Nuestro novedoso dispositivo se basa en un nuevo pricipio físico que permite que la detección de luz infrarroja sea conmutable (ON y OFF) mediante iluminación externa. Hemos fabricado un OTIP basado en QDs de InAs/AlGaAs con el que demostramos fotodetección, bajo incidencia normal, en el rango 2-6/xm, activada ópticamente por un diodoe emisor de luz de 590 nm. El estudio teórico del mecanismo de detección asistido por la IB en el OTIP nos lleva a poner en cuestión la asunción de quasi-niveles de Fermi planos en la zona de carga del espacio de una célula solar. Apoyados por simuaciones a nivel de dispositivo, demostramos y explicamos por qué esta asunción no es válida en condiciones de corto-circuito e iluminación. También llevamos a cabo estudios experimentales en QD-IBSCs de InAs/AlGaAs con la finalidad de ampliar el conocimiento sobre algunos aspectos de estos dispositivos que no han sido tratados aun. En particular, analizamos el impacto que tiene el uso de capas de disminución de campo (FDLs, por sus siglas en inglés), demostrando su eficiencia para evitar el escape por túnel de portadores desde el QD al material anfitrión. Analizamos la relación existente entre el escape por túnel y la preservación del voltaje, y proponemos las medidas de eficiencia cuántica en función de la tensión como una herramienta útil para evaluar la limitación del voltaje relacionada con el túnel en QD-IBSCs. Además, realizamos medidas de luminiscencia en función de la temperatura en muestras de InAs/GaAs y verificamos que los resltados obtenidos están en coherencia con la separación de los quasi-niveles de Fermi de la IB y la CB a baja temperatura. Con objeto de contribuir a la capacidad de fabricación y caracterización del Instituto de Energía Solar de la Universidad Politécnica de Madrid (IES-UPM), hemos participado en la instalación y puesta en marcha de un reactor de epitaxia de haz molecular (MBE, por sus siglas en inglés) y el desarrollo de un equipo de caracterización de foto y electroluminiscencia. Utilizando dicho reactor MBE, hemos crecido, y posteriormente caracterizado, la primera QD-IBSC enteramente fabricada en el IES-UPM. ABSTRACT The constituent work of this Thesis is framed in the research on intermediate band solar cells (IBSCs). This concept offers the possibility of achieving devices with high photovoltaic-conversion efficiency. Up to now, the fundamentals of operation of IBSCs have been demonstrated experimentally; however, this has only been possible at low temperatures. The intermediate band (IB) concept demands thermal decoupling between the IB and the valence and conduction bands. Stateof- the-art IB materials exhibit a too strong thermal coupling between the IB and one of the other two bands, which prevents the proper operation of IBSCs at room temperature. In the particular case of InAs/GaAs quantum-dot (QD) IBSCs - as of today, the most widely studied IBSC technology - , there exist fast thermal carrier exchange between the IB and the conduction band (CB), for two reasons: (1) a narrow (< 0.2 eV) energy gap between the IB and the CB, EL, and (2) the existence of multiple electronic levels between them. Reason (1) also implies that maximum achievable efficiency is below the theoretical limit for the ideal IBSC, in which EL = 0.71 eV. In this context, our work focuses on the study of wide-bandgap QD-IBSCs. We have fabricated and experimentally investigated the first QD-IBSC prototypes in which AlGaAs or InGaP is the host material for the InAs QDs. We demonstrate an improved bandgap distribution, compared to the InAs/GaAs case, in our wide-bandgap devices. In particular, we have measured values of EL higher than 0.4 eV. In the case of the AlGaAs prototypes, the increase in EL comes with an increase of more than 100 meV of the activation energy of the thermal carrier escape. In addition, in our InAs/AlGaAs devices, we demonstrate voltage up-conversion; i. e., the production of an open-circuit voltage larger than the photon energy (divided by the electron charge) of the incident monochromatic beam, and the achievement of voltage preservation at room temperature under concentrated white-light illumination. We also analyze the potential of an IB material for infrared detection. We present a IB-based new concept of infrared photodetector that we have called the optically triggered infrared photodetector (OTIP). Our novel device is based on a new physical principle that allows the detection of infrared light to be switched ON and OFF by means of an external light. We have fabricated an OTIP based on InAs/AlGaAs QDs with which we demonstrate normal incidence photodetection in the 2-6 /xm range optically triggered by a 590 nm light-emitting diode. The theoretical study of the IB-assisted detection mechanism in the OTIP leads us to questioning the assumption of flat quasi-Fermi levels in the space-charge region of a solar cell. Based on device simulations, we prove and explain why this assumption is not valid under short-circuit and illumination conditions. We perform new experimental studies on InAs/GaAs QD-IBSC prototypes in order to gain knowledge on yet unexplored aspects of the performance of these devices. Specifically, we analyze the impact of the use of field-damping layers, and demonstrate this technique to be efficient for avoiding tunnel carrier escape from the QDs to the host material. We analyze the relationship between tunnel escape and voltage preservation, and propose voltage-dependent quantum efficiency measurements as an useful technique for assessing the tunneling-related limitation to the voltage preservation of QD-IBSC prototypes. Moreover, we perform temperature-dependent luminescence studies on InAs/GaAs samples and verify that the results are consistent with a split of the quasi-Fermi levels for the CB and the IB at low temperature. In order to contribute to the fabrication and characterization capabilities of the Solar Energy Institute of the Universidad Polite´cnica de Madrid (IES-UPM), we have participated in the installation and start-up of an molecular beam epitaxy (MBE) reactor and the development of a photo and electroluminescence characterization set-up. Using the MBE reactor, we have manufactured and characterized the first QD-IBSC fully fabricated at the IES-UPM.

A numerical study of Bi-periodic binary diffraction gratings for solar cell applications

In this paper, a numerical study is made of simple bi-periodic binary diffraction gratings for solar cell applications. The gratings consist of hexagonal arrays of elliptical towers and wells etched directly into the solar cell substrate. The gratings are applied to two distinct solar cell technologies: a quantum dot intermediate band solar cell (QD-IBSC) and a crystalline silicon solar cell (SSC). In each case, the expected photocurrent increase due to the presence of the grating is calculated assuming AM1.5D illumination. For each technology, the grating period, well/tower depth and well/tower radii are optimised to maximise the photocurrent. The optimum parameters are presented. Results are presented for QD-IBSCs with a range of quantum dot layers and for SSCs with a range of thicknesses. For the QD-IBSC, it is found that the optimised grating leads to an absorption enhancement above that calculated for an ideally Lambertian scatterer for cells with less than 70 quantum dot layers. In a QD-IBSC with 50 quantum dot layers equipped with the optimum grating, the weak intermediate band to conduction band transition absorbs roughly half the photons in the corresponding sub-range of the AM1.5D spectrum. For the SSC, it is found that the optimised grating leads to an absorption enhancement above that calculated for an ideally Lambertian scatterer for cells with thicknesses of 10 ?m or greater. A 20um thick SSC equipped with the optimised grating leads to an absorption enhancement above that of a 200um thick SSC equipped with a planar back reflector.

Desarrollo de estructuras nanofotonicas de campo cercano para intensificacion localizada de luz en celulas solares de banda intermedia - Near-field nanophotonic structures for localized light enhancement in intermediate band solar cells

This doctoral thesis explores some of the possibilities that near-field optics can bring to photovoltaics, and in particular to quantum-dot intermediate band solar cells (QD-IBSCs). Our main focus is the analytical optimization of the electric field distribution produced in the vicinity of single scattering particles, in order to produce the highest possible absorption enhancement in the photovoltaic medium in their surroundings. Near-field scattering structures have also been fabricated in laboratory, allowing the application of the previously studied theoretical concepts to real devices. We start by looking into the electrostatic scattering regime, which is only applicable to sub-wavelength sized particles. In this regime it was found that metallic nano-spheroids can produce absorption enhancements of about two orders of magnitude on the material in their vicinity, due to their strong plasmonic resonance. The frequency of such resonance can be tuned with the shape of the particles, allowing us to match it with the optimal transition energies of the intermediate band material. Since these metallic nanoparticles (MNPs) are to be inserted inside the cell photovoltaic medium, they should be coated by a thin insulating layer to prevent electron-hole recombination at their surface. This analysis is then generalized, using an analytical separation-of-variables method implemented in Mathematica7.0, to compute scattering by spheroids of any size and material. This code allowed the study of the scattering properties of wavelengthsized particles (mesoscopic regime), and it was verified that in this regime dielectric spheroids perform better than metallic. The light intensity scattered from such dielectric spheroids can have more than two orders of magnitude than the incident intensity, and the focal region in front of the particle can be shaped in several ways by changing the particle geometry and/or material. Experimental work was also performed in this PhD to implement in practice the concepts studied in the analysis of sub-wavelength MNPs. A wet-coating method was developed to self-assemble regular arrays of colloidal MNPs on the surface of several materials, such as silicon wafers, amorphous silicon films, gallium arsenide and glass. A series of thermal and chemical tests have been performed showing what treatments the nanoparticles can withstand for their embedment in a photovoltaic medium. MNPs arrays are then inserted in an amorphous silicon medium to study the effect of their plasmonic near-field enhancement on the absorption spectrum of the material. The self-assembled arrays of MNPs constructed in these experiments inspired a new strategy for fabricating IBSCs using colloidal quantum dots (CQDs). Such CQDs can be deposited in self-assembled monolayers, using procedures similar to those developed for the patterning of colloidal MNPs. The use of CQDs to form the intermediate band presents several important practical and physical advantages relative to the conventional dots epitaxially grown by the Stranski-Krastanov method. Besides, this provides a fast and inexpensive method for patterning binary arrays of QDs and MNPs, envisioned in the theoretical part of this thesis, in which the MNPs act as antennas focusing the light in the QDs and therefore boosting their absorption

Synthesis and characterization of GaAsSb-capped InAs-based QDIPs

Quantum dot infrared photodetectors (QDIPs) are very attractive for infrared imaging applications due to its promising features such as high temperature operation, normal incidence response and low dark current [1]. However, the key issue is to obtain a high quality active region which requires a structural optimization of the nanostructures. With using GaAsSb capping layer, the optical properties, such as the PL intensity and its full width at half maximum (FWHM), of InAs QDs have been improved in the range between 1.15 and 1.5 m, because of the reduction of the compressive strain in QDs and the increment of QD height [2]. In this work, we have demonstrated strong and narrow intraband photoresponse spectra from GaAsSb-capped InAs-based QDIPs

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.