Detailed Balance Theory Research Articles

Global optimization of solar thermophotovoltaic systems

ABSTRACTIn 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. Copyright © 2012 John Wiley & Sons, Ltd.

Microstructured silicon with two impurity bands for solar cells

A low-cost, large area, random, maskless texturing scheme independent of crystal orientation is expected to have an impact on terrestrial photovoltaic technology significantly. We investigated microstructured silicon formed by irradiating the surface of a Si wafer with femtosecond laser pulses in the presence of a sulfur-bearing gas. It is widely believed that microstructured silicon is a potential material for efficient multi intermediate bands silicon solar cell. Using a four-band model, the loss of sunlight for silicon with two different chalcogenide impurity bands was analyzed, and the levels of the minimum loss of sunlight can be found. Then the effect of the position at which the intermediate bands that have minimum sunlight loss rate on the theoretical conversion efficiency of the corresponding solar cell was discussed with the Detailed Balance Theory. After that, the influence of impact ionization on the efficiency of four-band Solar Cells was analyzed in detail. Finally, problems that need to be resolved in making intermediate band solar cell based on femtosecond laser microstructured silicon are pointed out with great emphasis.

ZnO/ZnSe Type II Core-Shell Nanowire Array Solar Cell

ABSTRACTShockley-Queisser detailed balance theory predicts that under one sun a semiconductor with its bandgap in the range of 1.0 – 1.6 eV can potentially achieve an energy conversion efficiency > 30%. Therefore, the conversional wisdom would suggest looking for a semiconductor with a bandgap in this range for a single junction solar cell. Here we explore an alternative way of selecting the absorber material for PV, which allows using semiconductors with much larger bandgaps, in conjunction with new device architecture. Specifically, our device is based on an array of core-shell semiconductor nanowires, such as ZnO-ZnSe, where the two components exhibit type II band alignment. Our approach relies on the most basic property of a type II heterojunction, i.e., the staggered band alignment, that provides the function of charge separation, as in the case of dye-sensitized solar cell or (organic) bulk heterojunction solar cell. However, they differ in two important aspects: (1) the current structure is all inorganic, thus, expected to offer better chemical and photo- stability; and (2) In this approach, the interfacial transition provides an effective absorption or photo-response threshold that can be much lower than that of either component. In this work, using a ZnO-ZnSe core-shell nanowire array, we report the observation of the key signatures associated with the type II optical transition, and the demonstration of a solar cell based on the core-shell nanowire array.

Probing the Radiative Limits of III-V Quantum Wells

High-voltage InGaAs quantum well devices are shown to operate in a regime of suppressed radiative recombination. A novel extended heterojunction structure is employed to reduce non-radiative recombination and expose the limiting n=1 component of the diode current. Short circuit current versus open circuit voltage curves derived from illuminated current-voltage measurements on several sets of InGaAs quantum well solar cells are analyzed, and the underlying saturation current densities extracted. Diode currents lower than those expected from detailed balance theory are observed, and possible mechanisms for the apparent suppression in radiative recombination are discussed.

Sunlight loss for femtosecond microstructured silicon with two impurity bands

Black silicon, produced by irradiating the surface of a silicon wafer with femtosecond laser pulses in the presence of a sulfur-bearing gas, is widely believed to be a potential material for efficient multi-intermediate-band silicon solar cells. Taking chalcogen as an example, we analyse the loss of sunlight for silicon with two impurity bands and we find that loss of the sunlight can be minimized to 0.332 when Te0(0.307 eV) and Te+(0.411 eV) are doped into microstructured silicon. Finally, problems needed to be resolved in analysing the relationship between conversion efficiency of the ideal four-band silicon solar cell and the position of the introduced two intermediated bands in silicon according to detailed balance theory are pointed out with great emphasis.

Carrier density and compensation in semiconductors with multiple dopants and multiple transition energy levels: Case of Cu impurities in CdTe

Doping is one of the most important issues in semiconductor physics. In many cases, when people describe carrier concentration as a function of dopant density and Fermi energy, they usually assume only one type of dopant with single transition energy level in the system. However, in reality, the situation is often more complicated, that is, in a semiconductor device, it usually contains multidopants and each can have multitransition energy levels. In this paper, using detailed balance theory and first-principles calculated defect formation energies and transition energy levels, we derive formulas to calculate carrier density for semiconductor with multidopants and multitransition energy levels. As an example, we studied CdTe doped with Cu, in which ${\mathrm{V}}_{\mathrm{Cd}}$, ${\mathrm{Cu}}_{\mathrm{Cd}}$, and ${\mathrm{Cu}}_{\mathrm{i}}$ are the dominant defects/impurities. We show that in this system, when Cu concentration increases, the doping properties of the system can change from a poor p-type, to a poorer p-type, to a better p-type, and then to poor p-type again, in good agreement with experimental observations.

Analysis of sunlight loss for femtosecond laser microstructed silicon and its solar cell efficiency

Black silicon, which is obtained by irradiating the surface of a Si wafer with femtosecond laser pulses in the presence of a sulfur-bearing gas, holds great promise in the preparation of high-performance intermediate band silicon solar cells. Using a three-level model, the enhanced usefulness of sunlight of the microstructured silicon was firstly analyzed. A detailed study on the relationship between the light loss, the ionization energy of doped impurities in silicon and the impurity band width were given. Then the effect of the position of intermediate band within the forbidden gap of silicon on the theoretical conversion efficiency for the corresponding solar cell is discussed using the Detailed Balance Theory. Finally problems need to be resolved in making intermediate band solar cells based on femtosecond laser microstructured silicon are pointed out with great emphasis.

Requisites to realize high conversion efficiency of solar cells utilizing carrier multiplication

We have calculated the limiting conversion efficiency of solar cells utilizing carrier multiplication (CM), using the detailed balance theory. The solar cells were assumed to comprise quantum dots (QDs) embedded in another material. It has been elucidated that three requisites must be fulfilled, so that a sufficient number of photons in the solar spectrum contribute to CM, resulting in significantly higher conversion efficiency than the values of conventional cells. These requisites are as follows: (1) the effective mass of electrons in the QDs should be much lighter than that of holes, so that the threshold photon energy above which CM can occur is close to the energy gap of the QDs. In this respect, InAs is a promising candidate for the QD material, but PbSe and Si are not. (2) The potential barrier height for electrons in the QDs, which determines the upper limit of the quantum yield of photon-to-carrier conversion ( γ limit), should be slightly larger than the energy gap of the QDs to achieve a γ limit value of 2, when the solar cells are used under the non-concentrated insolation. InAs QDs embedded in Al x Ga 1− x As y Sb 1− y is a possible candidate to fulfill these two criteria. A higher barrier does not contribute to generation of more carriers, but likely disturbs electron transport. In contrast, under the concentrated insolation, a potential barrier slightly higher than twice the energy gap to achieve a γ limit value of 3 leads to higher conversion efficiency. (3) The quantum yield of photon-to-carrier conversion as a function of photon energy should rise as steeply as possible at the threshold photon energy. The experimentally observed quantum yield with a sloping rise leads to little improvement in conversion efficiency due to CM, under the non-concentrated insolation. Although it could be improved under the concentrated insolation, the conversion efficiency cannot reach the limiting value for triple-junction solar cells.

On the origin of the open-circuit voltage of polymer–fullerene solar cells

The increasing amount of research on solution-processable, organic donor-acceptor bulk heterojunction photovoltaic systems, based on blends of conjugated polymers and fullerenes has resulted in devices with an overall power-conversion efficiency of 6%. For the best devices, absorbed photon-to-electron quantum efficiencies approaching 100% have been shown. Besides the produced current, the overall efficiency depends critically on the generated photovoltage. Therefore, understanding and optimization of the open-circuit voltage (Voc) of organic solar cells is of high importance. Here, we demonstrate that charge-transfer absorption and emission are shown to be related to each other and Voc in accordance with the assumptions of the detailed balance and quasi-equilibrium theory. We underline the importance of the weak ground-state interaction between the polymer and the fullerene and we confirm that Voc is determined by the formation of these states. Our work further suggests alternative pathways to improve Voc of donor-acceptor devices.

Detailed balance theory of excitonic and bulk heterojunction solar cells

A generalized solar cell model for excitonic and classical bipolar solar cells describes the combined transport and interaction of electrons, holes, and excitons in accordance with the principle of detailed balance. Conventional inorganic solar cells, single-phase organic solar cells and bulk heterojunction solar cells, i.e., nanoscale mixtures of two organic materials, are special cases of this model. For high mobilities, the compatibility with the principle of detailed balance ensures that our model reproduces the Shockley-Queisser limit irrespective of how the energy transport is achieved. For less ideal devices distinct differences become visible between devices that are described by linear differential equations and those with nonlinear effects, such as a voltage-dependent collection in bipolar $p\text{\ensuremath{-}}i\text{\ensuremath{-}}n$-type devices. These differences in current-voltage characteristics are also decisive for the validity of the reciprocity theorem between photovoltaic quantum efficiency and electroluminescent emission. Finally, we discuss the effect of band offset at the heterointerface in a bulk heterojunction cell and the effect of the average distances between these heterointerfaces on the performance of a solar cell in order to show how our detailed balance model includes also these empirically important quantities.

Self-consistent modeling of escape and capture of carriers in quantum wells

A self-consistent model for escape and capture of carriers in quantum wells is described. The model accounts for carrier dynamics in the quantum wells by calculating the rates of escape and capture of photo-excited carriers in the wells, and including these rates in a self-consistent solution of the Poisson, Schrödinger, and drift–diffusion equations. The results obtained are in good agreement with those experimentally measured or theoretically calculated by others. Furthermore, the escape and capture rates calculated are in compliance with the requirements of detailed balance theory.

TIME AND ENERGY-RESOLVED THERMIONIC EMISSION IN CARBON CLUSTERS

We present experimental measurements of time-dependent photoelectron spectra observed in thermionic emission of small carbon cluster anions and C 60 fullerenes. The combination of photoelectron velocity-map imaging with time-gated detection allowed to resolve delayed electron emission at different stages of the emission process. This unique capability allows us to analyze pure thermionic energy spectra under well-defined conditions. Experimental spectra are analyzed within the framework of the detailed balance theory.

Time-dependent spectrum of thermionic emission from hot C60

Experimental measurements of time-dependent photoelectron spectra observed in thermionic emission of hot C60 excited by multiphoton absorption are presented. Time resolved velocity-map imaging is used to record photoelectron spectra and to disentangle direct and delayed processes. The evolution of the kinetic energy distribution of thermal electrons as a function of the delay after multiphoton excitation is described within the general formalism of the detailed balance theory. Experimental spectra obtained in the near-UV are in excellent agreement with the assumption of thermal equilibrium.

Time-dependent spectrum of thermionic emission from hot clusters: Model and example ofC60

We have studied the evolution of the kinetic energy distribution of thermal electrons emitted from energy-rich clusters as a function of the delay after multiphoton excitation. In this paper we emphasize the description of thermionic emission based on the general formalism of the detailed balance theory. Our description accounts for competing decay channels and underlines the fundamental role of the observation time window. Simulations including two decay channels (namely, delayed electron emission and loss of ${\mathrm{C}}_{2}$ fragments) are compared with experimental results in the case of hot fullerenes ${\mathrm{C}}_{60}$. The most striking result of the model is the close connection between the effective temperature of the electron distribution and the time delay of observation. Our model is in very good agreement with our experimental measurements of time-dependent photoelectron spectra.

Do we know the value of the Gspann parameter?

We reanalyze some of the data used by Klots to establish an experimental basis for the claim by Gspann that clusters have a highest temperature in molecular beams. The value of this temperature is given by the evaporative activation energy and a dimensionless parameter called the Gspann parameter. The value of the Gspann parameter we derive from the data is higher than the value found by Klots, and is consistent with the predictions from detailed balance theory, although a number of uncertainties persist. More recent data on oxygen clusters are analyzed with the same methods and the model dependent uncertainties are shown to be fairly large.

Dissociation energies of silver clusters Ag n+, n=14, 15, 16, 18

A recently developed method to determine dissociation energies has been applied to positively charged silver clusters of size n=14, 15, 16 and 18. The method uses a combination of sequential and single step decays. It requires an uncalibrated thermometer which here is provided by the evaporation rate constants of the product clusters. For this purpose, earlier measurements [J. Chem. Phys. 57 (1998) 2786] are reanalyzed with the new method. The resulting dissociation energies are compared with the liquid drop values and the measured decay rate constants with expected rate constants from detailed balance theory.

Temperature-dependent study of the quasi-Fermi level separation in double quantum well P-I-N structures

We have developed a method which allows us to measure calibrated electroluminescence (EL) spectra from quantum well (QW) structures at moderate forward biases. This method has been successfully applied for the first time to asymmetric double QW (DQW) p-i-n diodes in the AlGaAs/GaAs system at temperatures between 200 and 295 K. We have measured the EL signal from both QW and a theoretical model has been used to extract the quasi-Fermi level separation (Δ φ F) in the QWs and thus the n·p product of the excess electron and hole pairs. We have made several significant observations: (1) both Δ φ F decrease relative to the applied bias ( V app) with increasing temperature. (2) Δ φ F is not the same in both wells in contradiction with the assumption of the detailed balance theory. (3) At lower temperatures the quantum well Δ φ F show a dependence on the separation between the two QWs.

Photon recycling and Shockley’s diode equation

The Shockley’s diode equation predicts a current-voltage characteristic different from that used by Shockley and Queisser to compute the limiting efficiency of photovoltaic energy conversion under the assumptions of the detailed balance theory. The reasons for such discrepancy are discussed being the neglect of photon recycling effects in Shockley’s diode equation the main cause. This interpretation is crucial to understand the fundamentals on which the computation of the limiting efficiency of solar cells is based. Without photon recycling effects, it can be concluded that the limiting efficiency (one sun) of a gallium arsenide solar cell is 26.8% (with the sun assumed as blackbody at 6000 K) while the true figure is 30.7%, 38.7% as long as the angle of emission of photons from the cell is fully restricted.

Limiting efficiencies for photovoltaic energy conversion in multigap systems

Multigap systems are better matched to the sun's spectrum than single gap systems and are, therefore, more efficient as photovoltaic converters. This paper reviews the different thermodynamic approaches used in the past for computing the limiting efficiency for the conversion of solar energy into work. Within this thermodynamic context, the limit ranges from 85.4% to 95.0% depending on the assumptions made. Detailed balance theory provides a more accurate model of the photovoltaic converter. It leads to a limit of 86.8% for a system with an infinite number of cells, as already pointed out by other authors. In this work, however, we use the concepts of angle and energy restriction to emphasize that this limit is independent of the light concentration. Systems with a finite number of cells are also studied and their limiting efficiency is found to be higher than previously reported. Data for AM1.5 Direct spectrum, never computed before, are included.

Experimental analysis of the efficiency of heterostructure GaAsAlGaAs solar cells

Some years ago Multiple Quantum Wells (MQW) solar cells were introduced as an alternative to obtain high efficiencies. Based on the simple Shockley diode model, the short-circuit current could be increased without loss in the open-circuit voltage. Applying the Detailed Balance Theory, including radiative recombination in the i-region, leads to less optimistic predictions of the limiting efficiency of MQW cells. We present an experimental study in order to compare the efficiency of MQW solar cells with heterostructure cells with graded Al compositions and single bandgap solar cells. Compared to the homojunction AlGaAs cell, an increase of the short-circuit current is observed by the incorporation of GaAs in the i-region. However, the open-circuit voltage is reduced by the implementation of GaAs, due to an increase of the non-radiative recombination current. To estimate the maximum possible open-circuit voltage, the radiative recombination current is determined by measuring the light emission as a function of the applied voltage. From this experiment we conclude that the maximum possible open-circuit voltage of all the heterostructure cells is considerably lower than the homogeneous AlGaAs cell and close to the value of the GaAs cell, showing the relation between the open-circuit voltage and the smallest bandgap in the cell. The measured curves can be well predicted by calculations based on the Detailed Balance Theory. We find no principal advantage of MQW cells over cells with graded composition or single bandgap cells.