Detailed Balance Approach Research Articles

Impact of medium anisotropy on quarkonium dissociation and regeneration

Quarkonium production in ultra-relativistic collisions plays a crucial role in probing the existence of hot QCD matter. This study explores quarkonia states dissociation and regeneration in the hot QCD medium while considering momentum anisotropy. The net quarkonia decay width (ΓD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma _{D}$$\\end{document}) arises from two essential processes: collisional damping and gluonic dissociation. The quarkonia regeneration includes the transition from octet to singlet states within the anisotropic medium. Our study utilizes a medium-modified potential that incorporates anisotropy via particle distribution functions. This modified potential gives rise to collisional damping for quarkonia due to the surrounding medium, as well as the transition of quarkonia from singlet to octet states due to interactions with gluons. Furthermore, we employ the detailed balance approach to investigate the regeneration of quarkonia within this medium. Our comprehensive analysis spans various temperature settings, transverse momentum values, and anisotropic strengths. Notably, we find that, in addition to medium temperatures and heavy quark transverse momentum, anisotropy significantly influences the dissociation and regeneration of various quarkonia states.

Simple Physical Model for the Estimation of Irreversible Dissociation Rates for Bimolecular Complexes.

In this article, we propose a simple method of estimating dissociation rates of bimolecular van der Waals complexes ("wells"), rooted in rigid body dynamics, requiring as input parameters only the bimolecular binding energy, together with the intermolecular equilibrium distance and moments of inertia of the complex. The classical equations of motion are solved for the intermolecular and rotational degrees of freedom in a coordinate system considering only the relative motion of the two molecules, thus bypassing the question of whether the energy of the complex is statistically distributed. Well-escaping trajectories are modeled from these equations, and the escape rate as a function of relative velocity and angular momentum is fitted to an empirical function, which is then integrated over a probability distribution of said quantities. By necessity, this approach makes crude assumptions on the shape of the potential well and neglects the impact of energy quantization, and, more crucially, the coupling between the degrees of freedom included in the equations of motion with those that are not. We quantify the error caused by the first assumption by comparing our model potential with a quantum chemical potential energy surface (PES) and show that while the model does make several compromises and may not be accurate for all classes of bimolecular complexes, it is able to produce physically consistent dissociation rate coefficients within typical atmospheric chemistry confidence intervals for triplet state alkoxyl radical complexes, for which the detailed balance approach has been shown to fail.

Revealing fundamentals of charge extraction in photovoltaic devices through potentiostatic photoluminescence imaging

Revealing fundamentals of charge extraction in photovoltaic devices through potentiostatic photoluminescence imaging

Role of Exciton Diffusion and Lifetime in Organic Solar Cells with a Low Energy Offset.

Despite general agreement that the generation of free charges in organic solar cells is driven by an energetic offset, power conversion efficiencies have been improved using low-offset blends. In this work, we explore the interconnected roles that exciton diffusion and lifetime play in the charge generation process under various energetic offsets. A detailed balance approach is used to develop an analytic framework for exciton dissociation and free-charge generation accounting for exciton diffusion to and dissociation at the donor–acceptor interface. For low-offset systems, we find the exciton lifetime to be a pivotal component in the charge generation process, as it influences both the exciton and CT state dissociation. These findings suggest that any novel low-offset material combination must have long diffusion lengths with long exciton lifetimes to achieve optimum charge generation yields.

Charge transfer state characterization and voltage losses of organic solar cells

A correct determination of voltage losses is crucial for the development of organic solar cells (OSCs) with improved performance. This requires an in-depth understanding of the properties of interfacial charge transfer (CT) states, which not only set the upper limit for the open-circuit voltage of a system, but also govern radiative and non-radiative recombination processes. Over the last decade, different approaches have emerged to classify voltage losses in OSCs that rely on a generic detailed balance approach or additionally include CT state parameters that are specific to OSCs. In the latter case, a correct determination of CT state properties is paramount. In this work, we summarize the different frameworks used today to calculate voltage losses and provide an in-depth discussion of the currently most important models used to characterize CT state properties from absorption and emission data of organic thin films and solar cells. We also address practical concerns during the data recording, analysis, and fitting process. Departing from the classical two-state Marcus theory approach, we discuss the importance of quantized molecular vibrations and energetic hybridization effects in organic donor-acceptor systems with the goal to providing the reader with a detailed understanding of when each model is most appropriate.

A self-consistent interactive model for the study of luminescence coupling in multijunction solar cells

In this work, we propose a self-consistent interactive model based on the detailed balance approach to investigate the impact of luminescence coupling (LC) in multijunction solar cells (MJSCs). The proposed model is innovative in not using any empiric parameter input in considering the interactive nature of LC within the detailed balance framework to correlate the emissive and electrical properties of the junctions under interaction. We apply the model to radiative-limited series-connected MJSCs under different illumination conditions to demonstrate the influence of LC on the current matching condition and the impact on the power conversion efficiency (PCE) limits of such devices. As a result, we show that LC does not change the optimum bandgap energy combination leading to the highest PCE for a given operation condition but widens the span of configurations reaching high PCE, information that aids in the design of high PCE MJSC. Additionally, we analyzed some selected MJSC configurations with two to six junctions, well known from the literature to reach high PCE under different illumination conditions showing that even better performance can be achieved without either the need for changing the existent active materials or using optical thinning but using more efficient photon management concepts. Finally, we indicate MJSC configurations that can achieve high PCE for terrestrial applications under high coupling conditions, including some promises for low-cost high-efficiency photovoltaics, especially the ones involving stacks with silicon, perovskites, chalcogenides, and/or III–V materials.

Spatial profiles of photon chemical potential in near-field thermophotovoltaic cells

Emitted photons stemming from the radiative recombination of electron–hole pairs carry chemical potential in radiative energy converters. This luminescent effect can substantially alter the local net photogeneration in near-field thermophotovoltaic cells. Several assumptions involving the luminescent effect are commonly made in modeling photovoltaic devices; in particular, the photon chemical potential is assumed to be zero or a constant prescribed by the bias voltage. The significance of photon chemical potential depends upon the emitter temperature, the semiconductor properties, and the injection level. Hence, these assumptions are questionable in near-field thermophotovoltaic devices with nanoscale separation distances between the emitter and the cell. In the present work, an iterative solver that combines fluctuational electrodynamics with the drift-diffusion model is developed to tackle the coupled photon and charge transport problem, enabling the determination of the spatial profile of photon chemical potential beyond the detailed balance approach. The difference between the results obtained by allowing the photon chemical potential to vary spatially and by assuming a constant value demonstrates the limitations of the conventional approaches. This study is critically important for performance evaluation of near-field thermophotovoltaic systems with nanoscale vacuum gaps.

Modelling of Intrinsic Loss Processes in the Intermediate Band Solar Cells

Abstract For the first time, the formalism of intrinsic loss processes such as below-band gap, thermalisation, angle mismatch, Carnot and emission loss in the intermediate band solar cells (SCs) is obtained by a theoretical framework based on the principle of detailed balance approach, and with the physical origins of losses discussed in terms of photon absorption and emission in the presence of intermediate energy band (IB). Then, the effect of IB position on each intrinsic loss in the intermediate band SCs is investigated. The results show that the introduction of IB reduces the below-band gap loss due to absorption of low energy photons by narrower sub-band gap and reduces the thermalisation loss due to absorption of high energy photons by the band gap of host semiconductor. Furthermore, the thermalisation and angle mismatch losses are dominant fractions of intrinsic loss, while the emission loss presents less than 2.2 % of intrinsic loss.

Formation and stabilization of C6− by radiative electron attachment

Radiative electron attachment (REA) plays an important role in forming molecular anions in various astrophysical environments. In this work, we determined the rate coefficient for the formation of C6− by REA based on a detailed balance approach. C6− ions are stored in an electrostatic ion beam trap and are photoexcited above their adiabatic detachment energy (4.18 eV). Due to fast internal conversion and intramolecular vibrational redistribution, photoexcitation leads to the formation of temporary negative ions (TNIs), the same as those one formed by the electron attachment. Absolute vibrational autodetachment and recurrent (or Poincaré) fluorescence (RF) rate coefficients have already been reported [V. Chandrasekaran et al., J. Phys. Chem. Lett. 5, 4078 (2014)]. Knowing the branching ratios of the various competing rate coefficients is decisive to the understanding of the formation probability of anions via REA. The radiative stabilization rate of C6−, shown to be dominated by RF, was determined to be 5 × 104 s−1 at the electron detachment energy, i.e., at least a factor of 100 faster than the stabilization by infrared transitions. The RF is found to very effectively stabilize the TNI formed by electron attachment. Using detailed balance to link the measured delayed detachment rate to the rate of electron attachment, we estimate the REA rate leading to the formation of C6− to be 3 × 10−7 cm3 s−1 at 300 K in agreement with theory (1.7 × 10−7 cm3 s−1 [R. Terzieva and E. Herbst, Int. J. Mass Spectrom. 201, 135 (2000)]). Such a high rate for REA to C6 indicates that REA may play a prominent role in the formation of anions in the interstellar medium.

Advanced Device Design for Photoelectrochemical Water Splitting Derived By a Detailed Balance Approach

Solar fuel generation by direct photoelectrolysis of water is a pathway towards energy storage and transportation fuel demands in a sustainable energy economy. High band gap semiconductor materials may drive the water splitting reaction, but cannot use substantial parts of the solar spectrum, while common photovoltaic (PV) absorbers fail to provide sufficient threshold voltage for photoelectrochemical (PEC) conversion. Tandem absorber structures overcome this trade-off featuring promising efficiencies [1]. Tandem cell implementation by epitaxial III-V growth has enabled landmark solar-to-hydrogen (STH) conversion efficiencies [2]. In contrast to the maximum power metric in PV, efficient STH conversion requires maximizing the photocurrent versus a load voltage consisting of the thermodynamic potential of water splitting (1.23V) and various voltage loss mechanisms accumulating throughout the photoelectrochemical cell, often summarized in a generalized overvoltage term for modelling approaches. We discovered that sunlight absorption during illumination through the aqueous PEC electrolyte flawed both efficiency and band gap predictions in earlier theoretical studies and derived PEC tandem device guidelines defining an interdependence between allowable overvoltage loss and electrolyte transmission length [1]. Even though optimum band gap combinations for STH conversion have been discussed for decades, state-of-the-art inverted metamorphic multijunction (IMM) III-V growth and processing strategies developed in the context of high-efficiency PV [3] finally enabled us to tailor water splitting device structures according to maximum performance limits [Fig. 1] and validate our prediction. A first step was to relax the harsh current limitation imposed by the bottom absorber of the classical GaInP/GaAs PEC tandem [2] by replacing it with a metamorphic GaInAs with a band gap of approximately 1.2 eV [Fig. 1(a)]. Further reductions in overvoltage loss and electrolyte layer thickness enable further reductions of top and bottom junctions to unlock higher STH limit efficiency [Fig. 1(b)] that could be implemented by the integration of a 1.7 eV absorber on Si. Advanced PEC measurement protocols [4] drastically reduce performance estimation errors induced by the spectral mismatch of laboratory light sources and light transmission through epoxy used for device area confinement. Valid PEC results of our tailored devices as well as of analogue PV device characterization provide us with important feedback for our detailed balance model, where we start to unravel overvoltage loss into its fundamental components to obtain advanced guidance for future technical development.

Optimum band gap combinations to make best use of new photovoltaic materials

The detailed balance approach has been used to analyze the optimum use of band gaps in a multi-junction device of up to 6 sub-cells. Results for the AM1.5G spectrum suggest that as the number of sub-cells increases the importance of the bottom sub-cell band gap becomes less critical, assuming the optimum band gap combination for that value can be obtained. Given this greater freedom in choice, the potential for the use of silicon as an active substrate is investigated along with a cell thinning ‘current sharing’ approach to improve current mismatch in the device. Results show a more robust design space of multi-junctions with active silicon substrates when the current sharing approach is used, with performances close to the optimum for a completely free choice of band gaps. The use of the AM1.5D spectrum for a concentration ratio of 100, shows similar results for the substrate and a slight increase in band gap sensitivity for the upper band gaps in the stack. Inclusion of optical coupling between the sub-cells lowers limiting efficiency, with luminescent coupling mitigating the band gap sensitivity. The results and approach outlined are useful for determining how best to deploy new photovoltaic materials in multi-junction solar cells.

Network Analysis of Photovoltaic Energy Conversion

Photovoltaic energy conversion in photovoltaic cells has been analyzed by the detailed balance approach or by thermodynamic arguments. Here we introduce a network representation to analyze the performance of such systems once a suitable kinetic model (represented by a master equation in the space of the different system states) has been constructed. Such network representation allows one to decompose the steady state dynamics into cycles, characterized by their cycle affinities. The maximum achievable efficiency of the device is obtained in the zero affinity limit. This method is applied to analyze a microscopic model for a bulk heterojunction organic solar cell that includes the essential optical and interfacial electronic processes that characterize this system, leading to an explicit expression for the theoretical efficiency limit in such system. In particular, the deviation from Carnot's efficiency associated with the exciton binding energy is quantified.

Estimating net N mineralization under unfertilized winter wheat using simulations with NET N and a balance approach

Eliminating uncertainty in soil N supply could reduce fertilizer input, but the amount of N mineralized during plant growth is usually still unknown. We aimed to test the relatively simple two-pool net N mineralization model NET N that uses site-specific temperature and soil water functions as well as pedotransfer functions for deriving the pool sizes and was developed for NW Germany. The objectives were to (1) evaluate, if field net N mineralization under unfertilized winter wheat could be satisfactorily simulated, and to (2) examine the variation in time patterns of net N mineralization within years and sites and from two functional N pools: a rather small, fast mineralizable N pool (Nfast) and a much greater, slowly mineralizable N pool (Nslow). NET N simulations for 36 site-year-combinations and up to five dates within the growing season were evaluated with detailed N balance approaches (calculated from: soil mineral N contents, plant N uptake using estimates of green area index, simulated N leaching). Simulated net N mineralization was highly significantly correlated (r2 = 0.58; root mean square error = 24.2 kg N ha−1) to estimations from the most detailed balance approach, with total simulated net N mineralization until mid August ranging from 62.1 to 196.5 kg N ha−1. It also became evident that N mineralization from pool Nslow—in contrast to pool Nfast—was considerably higher for loess soils than for sandy or loamy soils. The results suggest that NET N was adequate for simulations in unfertilized winter wheat. However, further field studies are necessary for proving its applicability under fertilized conditions.

Design considerations for enhancing absorption in semiconductors on metals through surface plasmon polaritons

Surface plasmon polaritons have attracted attention for energy applications such as photovoltaic and photoelectrochemical cells because of their ability to improve optical absorption in thin films. We show that surface plasmon polaritons enhance absorption most significantly in materials with small positive real permittivity and large positive imaginary permittivity, e.g. organics or CdTe. Additional losses, accounting for dissipation in the metal and the existence of a cutoff frequency above which polaritons are no longer bound, are incorporated into efficiency calculations. Owing to these losses, devices with optical absorption based solely on SPPs will necessarily always have a lower efficiency than that predicted by the Shockley-Queisser limit. Calculations are presented for specific materials, including crystalline and amorphous Si, GaAs, CdTe, a P3HT:PCBM blend, α-Fe2O3 and rutile TiO2, as well as for general materials of arbitrary permittivity. Guidelines for selecting absorber materials and determining whether specific materials are good candidates for improving optical absorption with SPPs are presented.

Auger generation effect on the thermodynamic efficiency of Cu(In,Ga)Se2 thin film solar cells

The effect of Auger generation on the thermodynamic efficiency of a reverse graded band gap Cu(In,Ga)Se2 thin film solar cell is studied using a detailed balance approach. For the graded profile (1.5–1eV), a wider range of photons can be considered as high energy photons to produce hot electrons which can pump an additional electron from the valence band to the conduction band. The effects of the carrier multiplication probability, P, and grading strength of the front band gap on the variation of efficiency are studied. Auger mechanism is more effective at lower band gaps due to higher multiplication probability. A thermodynamic efficiency of about 41% is obtained, which is higher than the maximum efficiency of 31% for a graded band gap cell without Auger generation. Moreover, we study the effect of Auger generation on the current–voltage characteristics of the cell. The carrier multiplication increases the short-circuit current due to the increased photogenerated electrons and almost does not change the open-circuit voltage. However, the band gap grading enhances the open-circuit voltage by reducing the recombination rate. Also, a known result is the red shift in the optimum band gap towards a lower band gap (1.15eV) with respect to the Shockley–Queisser limit.

A semiconductor/mixed ion and electron conductor heterojunction for elevated-temperature water splitting

Photoelectrochemical cells (PECs) have been studied extensively for dissociating water into hydrogen and oxygen. Key bottlenecks for achieving high solar-to-hydrogen efficiency in PECs include increasing solar spectrum utilization, surmounting overpotential losses, and aligning the absorber/electrochemical redox levels. We propose a new class of solid-state PECs based on mixed ionic and electronic conducting (MIEC) oxides that operates at temperatures significantly above ambient and utilizes both the light and thermal energy available from concentrated sunlight to dissociate water vapor. Unlike thermochemical and hybrid photo-thermochemical water-splitting routes, the elevated-temperature PEC is a single-step approach operating isothermally. At the heart of the solid-state PEC is a semiconductor light absorber coated with a thin MIEC layer for improved catalytic activity, electrochemical stability, and ionic conduction. The MIEC, placed between the gas phase and the semiconductor light absorber, provides a facile path for minority carriers to reach the water vapor as well as a path for the ionic carriers to reach the solid electrolyte. Elevated temperature operation allows reasonable band misalignments at the interfaces to be overcome, reduces the required overpotential, and facilitates rapid product diffusion away from the surface. In this work, we simulate the behavior of an oxygen-ion-conducting photocathode in 1-D. Using the detailed-balance approach, in conjunction with recombination and electrochemical reaction rates, the practical efficiency is calculated as a function of temperature, solar flux, and select material properties. For a non-degenerate light absorber with a 2.0 eV band-gap and an uphill band offset of 0.3 eV, an efficiency of 17% and 11% is predicted at 723 and 873 K, respectively.

Time-Asymmetric Photovoltaics

Limits upon photovoltaic energy conversion efficiency generally are formulated using the detailed balance approach of Shockley and Queisser. One key underlying assumption is invariance upon time reversal, underpinning detailed balance itself. Recent proposals for compact, layered, time-asymmetrical, magneto-optical devices make their routine implementation likely. It is shown that such time-asymmetry can alter the relationship between solar cell emission and absorption assumed in the Shockley-Queisser approach, allowing generally accepted photovoltaic performance limits to be exceeded.

Efficiency limit and example of a photonic solar cell

Restricting the angular emission characteristics of a solar cell results in a reduction of entropy generation and allows for higher solar cell efficiencies. In this paper, we present the concept of a photonic solar cell which exhibits the combination of a solar cell and a photonic crystal. The basic idea is to structure a solar cell in such a way that the applied structure is a photonic crystal consisting of the solar cell material. The aim of having a solar cell in the form of a photonic crystal is to restrict the emission of the solar cell into certain angles This reduction reduces the radiative losses and results in a higher VOC and, consequently, a higher efficiency of the cell. To calculate the efficiency of a photonic solar cell we introduce an adaptation of the detailed balance approach. This adaptation takes into account the reduced radiative losses due to the presence of a photonic band structure. In the second part of the paper we use this approach to calculate the efficiency for an exemplary system. The exemplary system is an idealized edge filter, similar to a Bragg stack. The idealization concerns the reflection characteristic of this filter and its dependence on the polarization. For this idealized system we calculate an efficiency that exceeds that of a conventional solar cell by up to 2.5% absolute.

Realistic upconverter-enhanced solar cells with non-ideal absorption and recombination efficiencies

Upconverting materials can be used to increase the energy conversion efficiency of a solar cell. Such materials convert low-energy transmitted photons to higher-energy photons that can be absorbed by the cell, substantially reducing the spectral mismatch between the cell and the solar spectrum. Previously, the performance enhancements achievable with an ideal upconverter-solar cell system were theoretically investigated. Here, we perform a comprehensive analysis to determine the effects of non-ideal cell and upconverter systems, accounting for non-ideal absorption and radiative recombination. We also allow for realistic nonradiative relaxation within the upconverter. The system is modeled using a detailed balance approach, with the upconverter treated as a series connection of two small-bandgap solar cells and a large-bandgap light emitting diode. We demonstrate that significant improvements in efficiency are possible even for nonconcentrated light, as long as the upconverter includes a small nonradiative relaxation pathway. Furthermore, we show that the existence of a nonradiative relaxation event in the upconverter is necessary for improved power conversion when cell absorption efficiency is low. Our results indicate that the efficiencies of both conventional-Si and thin film photovoltaic cells can be substantially improved with upconverting materials, even including non-idealities.

Effect of open-path gas analyzer wetness on eddy covariance flux measurements: A proposed solution

Open-path gas analyzers are popular in eddy covariance flux measurements of trace gasses (i.e. CO 2). The quality of the data, however, may be influenced by several factors. Exposure in an outdoor environment invariably causes the instrument to become colder or warmer than the air temperature. Instruments with internal temperature regulation and/or from heat generated by active electrical components can also influence the sensor temperature. In addition, sensors can have condensation problems on their optical windows thus affecting the quality of the measurement. Unreasonable measurements have been widely discussed, especially in moist, high-latitude regions. As this is a very important research problem facing flux studies, we examined how wetness (dew and raindrops) on the surface of the focus lens of the popular LI-COR LI-7500 infrared gas analyzer may affect flux measurements from the open-path eddy-covariance system. Field experiments showed that additional sensor heating may inhibit dew formation yet greatly improve the quality of flux measurements. A detailed energy balance approach was used to model the gas analyzer window temperature under environmental conditions and dew effect through a pair of LI-COR LI-7500, with and without heat treatment, in a grassland ecosystem in the Netherlands. With the proposed model, existing datasets can be filtered for dew events. Data from three different flux measurement sites were then used to assess the magnitude of dew effects on longer time-scales; 2 years from the Netherlands and 3 weeks of data from an arid coastal desert. About 30% of the measurements were affected by dew in the grassland area versus 4% in the arid region during the dry season. Sensor heating suppresses dew formation but might lead to errors in trace gas fluxes evaluated over long periods, thus we analyzed how sensor heating or cooling affects trace gas flux measurements. Additions to a recent (2006) correction and application to a horizontally and vertically oriented LI-COR LI-7500 are presented as they deal with sensor heating problems in eddy-covariance systems. The sensor energy balance model, together with the proposed modified sensor heating corrections, were used to estimate sensor temperature effects on long-term scale CO 2 flux measurements and showed that additional heating does affect the turbulent trace gas CO 2 fluxes but is very minor, especially for a horizontally mounted LI-COR LI-7500 gas analyzer. Further efforts are urgently needed to improve the data quality and quality of flux measurements.