shockley queisser limit bandgap

From a practical point of view, however, the PP interconnection is too complex to process due to the necessity of introducing two transparent intermediate electrodes. Devos, A. A wide variety of optical systems can be used to concentrate sunlight, including ordinary lenses and curved mirrors, fresnel lenses, arrays of small flat mirrors, and luminescent solar concentrators. In the ShockleyQueisser model, the recombination rate depends on the voltage across the cell but is the same whether or not there is light falling on the cell. Shockley-Queisser solar efficiency Limits - University Wafer A cross-sectional transmission electron microscopy (TEM) image of a SP triple-junction solar cell is shown in Fig. Shockley, W. & Queisser, H. J. (b) A cross-sectional TEM image of the as-prepared triple-junction solar cell. [14][15] Another proposal suggests spreading out an array of microscopic solar cells on a surface, and focusing light onto them via microlens arrays,[16] while yet another proposal suggests designing a semiconductor nanowire array in such a way that light is concentrated in the nanowires.[17]. All the authors commented on the manuscript. Adv. By integrating series- and parallel-interconnections into a triple-junction configuration, we find significantly relaxed material selection and current-matching constraints. Mater. Electrons can be excited by light as well as by heat. In the case of DPPDPP/PCDTBT triple-junction devices, for the purpose of simplicity we fixed the thickness of the top PCDTBT:PC70BM to be 80nm corresponding to the thickness of optimized single-junction reference cells. These photons will pass through the solar cell without being absorbed by the device. A generic concept to overcome bandgap limitations for designing highly efficient multi-junction photovoltaic cells. 3.1 Introduction 28. There has been some work on producing mid-energy states within single crystal structures. [10] This places an immediate limit on the amount of energy that can be extracted from the sun. The light intensity at each wavelength was calibrated with a standard single-crystal Si solar cell. In physics, the radiative efficiency limit (also known as the detailed balance limit, ShockleyQueisser limit, Shockley Queisser Efficiency Limit or SQ Limit) is the maximum theoretical efficiency of a solar cell using a single p-n junction to collect power from the cell where the only loss mechanism is radiative recombination in the solar cell. (a) Schematic architecture of the semitransparent series-tandem solar cells (DPPDPP) with AgNWs top electrode. & Snaith, H. J. V.V.R., V.R.R. and E.S. Lett. 0 1 Energy Environ. 1.5-1.6 eV bandgap Pb-based perovskite solar cells (PSCs) with 30-31% theoretical efficiency limit by the Shockley-Queisser model achieve 21-24% power conversion efficiencies (PCEs). The device structure of the single and tandem reference cells are: Glass/ITO/PEDOT:PSS/DPP:PC60BM/Ca/Ag and Glass/ITO/PEDOT:PSS/DPP:PC60BM/ZnO/N-PEDOT/DPP:PC60BM/Ca/Ag. A major loss factor is related to the energy mismatch between the broad wavelength distribution of sunlight and the mono-band gap of . Energy Mater. Li, N. et al. Article Yao Yao is an academic researcher from University of New South Wales. Photonics 8, 506514 (2014) . . First, there can be absorbance below the band gap of the material at finite temperatures. The EQE spectra were recorded with an EQE measurement system (QE-R) from Enli Technology (Taiwan). Here to demonstrate the general application of our SP triple-junction architecture, we studied two wide bandgap polymers, poly[N-9-hepta-decanyl-2,7-carbazole-alt-5,5-(4,7-di-2-thienyl-2,1,3-benzothiadiazole)] (PCDTBT, Eg, 1.87eV) and OPV12 (Eg, 1.73eV)33, as the top subcells, which give VOC values of 0.9V and 0.8V when mixed with phenyl-C71-butyric acid methyl ester (PC70BM) and PC60BM, respectively. For very low illumination, the curve is more or less a diagonal line, and m will be 1/4. In actual devices the efficiencies are lower due to other recombination mechanisms and losses in parasitic resistances. Shockley and Queisser calculate Qc to be 1700 photons per second per square centimetre for silicon at 300K. Slider with three articles shown per slide. To verify the compatibility of the two wide bandgap donors with the AgNW electrode, single-junction reference cells of PCDTBT:PC70BM and OPV12:PC60BM were first processed on both indium tin oxide (ITO) and AgNWs-coated glass substrates for comparison (Fig. The liftout sample was prepared using a focused ion beam (FIB, FEI Helios NanoLab 660) and imaged subsequently with the TITAN3 aberration-corrected TEM. Transmittance spectra of the intermediate layers and semitransparent devices were measured using a UVvis-NIR spectrometer (Lambda 950, from Perkin Elmer). CAS (c) Typical JV curves of the single-junction DPP reference cell, tandem DPPDPP reference cell and the semitransparent tandem DPPDPP cell with AgNW top electrode. Under normal conditions, the atom will pull off an electron from a surrounding atom in order to neutralize itself. When this occurs, the electron recombines at that atom, and the energy is lost (normally through the emission of a photon of that energy, but there are a variety of possible processes). would like to acknowledge the funding from the China Scholarship Council and the Joint Project Helmholtz-Institute Erlangen Nrnberg (HI-ERN) under project number DBF01253, respectively. In the following, we start with the demonstration of the integrated SP triple-junction cells for solution-processed organic solar cells. J. Phys. c Taking Kirchhoffs law into consideration, these circumstances lead to the VOC values of our triple-junction cells close to the top subcells which exhibited lower VOC. The EQE measurement of a prepared semitransparent perovskite cell (Supplementary Fig. The band gap determines what portion of the solar spectrum a photovoltaic cell absorbs. PDF Eciency above the Shockley Queisser Limit by Using Nanophotonic Eects Towards 15% energy conversion efficiency: a systematic study of the solution-processed organic tandem solar cells based on commercially available materials. It is important to note that the analysis of Shockley and Queisser was based on the following assumptions: None of these assumptions is necessarily true, and a number of different approaches have been used to significantly surpass the basic limit. M. ( EmE g ) . The Shockley-Queisser limit (also known as the detailed balance limit, Shockley Queisser Efficiency Limit or SQ Limit, or in physical terms the radiative efficiency limit) refers to the maximum theoretical efficiency of a solar cell using a single p-n junction to collect power from the cell where the only loss mechanism is radiative recombination Mater. If a very efficient system were found, such a material could be painted on the front surface of an otherwise standard cell, boosting its efficiency for little cost. Prog. Shockley-Queisser limit: loss processes and potential efficiency However, one distinct drawback of the series-connected configuration is the stringent current-matching criterion, which requires careful bandgap engineering in combination with an excellent control of the thicknesses of the respective subcells. Beiley, Z. M. & McGehee, M. D. Modeling low cost hybrid tandem photovoltaics with the potential for efficiencies exceeding 20%. ADS Silvestre, S. & Chouder, A. Sub-1.4eV bandgap inorganic perovskite solar cells with long-term s of states. In our SP triple-junction devices, the top cell is connected in parallel with the bottom series-tandem cell which gives a VOC of 1.1V. To match the voltage between the parallel-connected components and thereby maximize the overall efficiency, a top cell with a VOC value identical or close to the VOC of the bottom series-tandem cell is desired. f & Yang, Y. High-efficiency polymer tandem solar cells with three-terminal structure. Prior to device fabrication, the laser-patterned ITO substrates were cleaned by ultra-sonication in acetone and isopropanol for 10min each. A current density of up to 3mAcm2 is calculated for the series-connected DPPDPP tandem cell, as a benefit of the average 53.4% transmittance (650 and 850nm) of the semitransparent perovksite cell (Supplementary Fig. In the most common design, a high-bandgap solar cell sits on top, absorbing high-energy, shorter-wavelength light, and transmitting the rest. contributed to project planning and manuscript preparation. Hirst, L. C. & Ekins-Daukes, N. J. 16, 141149 (2008) . As the name implies, electrons in the conduction band are free to move about the semiconductor. Fully solution-processing route toward highly transparent polymer solar cells. 5) and the values calculated by integrating the EQE curve with standard AM1.5 G spectrum show a good agreement with the measured JSC values. The most widely explored path to higher efficiency solar cells has been multijunction photovoltaic cells, also known as "tandem cells". Based on the convenient solution-processing along with the impressive high FFs, we expect that significant enhancement in efficiency can be achieved by exploiting high-performance wide bandgap materials with matched VOC in the back subcell. Science 334, 15301533 (2011) . Simultaneously, optical simulations based on the transfer matrix formalism were carried out to calculate the current generation in the individual subcells34,35, which can provide valuable guidance for optimization of our SP triple-junction devices. The thickness of the front perovskite layer is fixed to 200nm which corresponds to the thickness of the optimized reference cells. In particular, to exceed the ShockleyQueisser limit, it is necessary for the fluorescent material to convert a single high-energy photon into several lower-energy ones (quantum efficiency > 1). {\displaystyle I_{0}[\exp(V/V_{c})-1]. Module datasheets normally list this temperature dependency as TNOCT (NOCT - Nominal Operating Cell Temperature). 6, 34073413 (2013) . [24][25], Another, more straightforward way to utilise multiple exciton generation is a process called singlet fission (or singlet exciton fission) by which a singlet exciton is converted into two triplet excitons of lower energy. 2, the absorption profiles of the two active layers are complementary with that of DPP:PC60BM, suggesting they are appropriate material combinations for manufacturing multi-junction devices. Efficient tandem and triple-junction polymer solar cells. The maximum efficiency of a single-junction solar cell as calculated by the Shockley- Queisser model as a function of bandgap energy. In brighter light, when it is concentrated by mirrors or lenses for example, this effect is magnified. Nanoscale 7, 16421649 (2015) . Hendriks, K. H., Li, W. W., Wienk, M. M. & Janssen, R. A. J. Small-bandgap semiconducting polymers with high near-infrared photoresponse. Microcavity-enhanced light-trapping for highly efficient organic parallel tandem solar cells. Optimal Location of the Intermediate Band Gap Energy in the Effects of shadowing on to photovoltaic module performance. Using methods similar to the original ShockleyQueisser analysis with these considerations in mind produces similar results; a two-layer cell can reach 42% efficiency, three-layer cells 49%, and a theoretical infinity-layer cell 68% in non-concentrated sunlight.[5]. Note that in these two simulations the top PCDTBT:PC70BM layer thickness is fixed to 80nm, corresponding to the optimized thickness in their single-junction state. Our recent work demonstrated that a thin layer of ZnO nanoparticles can effectively conduct electrons to the AgNW electrode and, more importantly, enable the deposition of the AgNW electrode by doctor blading from water-based solution.16,17 However, both ZnO and AgNW layers are obviously not compact enough to protect the underlying subcells from solvent infiltration during the top subcell deposition. Another possibility is to use two-photon absorption, but this can only work at extremely high light concentration.[19]. [10] This accounts for about 33% of the incident sunlight, meaning that, for silicon, from spectrum losses alone there is a theoretical conversion efficiency limit of about 48%, ignoring all other factors. As the ratio Vc/Vs goes to zero, the open-circuit voltage goes to the band-gap voltage, and as it goes to one, the open-circuit voltage goes to zero. Triple-junction hybrid tandem solar cells with amorphous silicon and polymer-fullerene blends. That atom will then attempt to remove an electron from another atom, and so forth, producing an ionization chain reaction that moves through the cell. Trupke, T. & Wurfel, P. Improved spectral robustness of triple tandem solar cells by combined series/parallel interconnection. gratefully acknowledge the financial support through the Aufbruch Bayern initiative of the state of Bavaria. Due to the lack of the back reflective electrode, the semitransparent tandem device shows a relatively low short circuit current (JSC) of 5.16mAcm2. Other recombination processes may also exist (see "Other considerations" below), but this one is absolutely required. [31], Thermophotovoltaic cells are similar to phosphorescent systems, but use a plate to act as the downconvertor. 10.5% efficient polymer and amorphous silicon hybrid tandem photovoltaic cell. Adv. Including the effects of recombination and the I versus V curve, the efficiency is described by the following equation: where u, v, and m are respectively the ultimate efficiency factor, the ratio of open-circuit voltage Vop to band-gap voltage Vg, and the impedance matching factor (all discussed above), and Vc is the thermal voltage, and Vs is the voltage equivalent of the temperature of the Sun. 20, 579583 (2008) . Zuo, L. J. et al. Optimal Location of the Intermediate Band Gap Energy in the [24], A related concept is to use semiconductors that generate more than one excited electron per absorbed photon, instead of a single electron at the band edge. Kim, T. et al. Herein, we chose ZnO and neutral PEDOT:PSS (N-PEDOT) as the N- and P-type charge extraction materials, respectively, because the work functions of the two materials match well with the energy levels of the donor DPP and acceptor PC60BM20,23. To push the performances of these solar technologies beyond the ShockleyQueisser limit, several approaches have been proposed, for instance, up-conversion3, multi-junction configuration4,5,6, multiple exciton generation7,8 and concentrator cells, and so on. t Similar simulation results for the triple-junction DPPDPP/OPV12 devices are presented in Supplementary Fig. F.W.F. Chem. CAS PEDOT:PSS (Clevios, P VP AI 4083) and N-PEDOT (NT5-3417286/2) were obtained from Heraeus and Agfa, respectively. Detailed assumptions and calculation procedure are presented in the Supplementary Note 1. Peak external photocurrent quantum efficiency exceeding 100% via MEG in a quantum dot solar cell. Chem. If, however, the intense light heats up the cell, which often occurs in practice, the theoretical efficiency limit may go down all things considered. Chem. Photovoltaics Res. In March 1961, an article entitled Detailed Balance Limit of Efficiency of p-n Junction Solar Cells by William Shockley and Hans Joachim Queisser appeared in the Journal of Applied Physics (Shockley & Queisser, 1961).Following an earlier rejection by the journal (Marx, 2014; Queisser, 2007) and barely noticed for several years after publication, this article has now become an . and JavaScript. . Exceeding the Shockley-Queisser Limit Within the Detailed Balance A blackbody at 6000K puts out 7348W per square centimetre, so a value for u of 44% and a value of 5.731018 photons per joule (corresponding to a band gap of 1.09V, the value used by Shockley and Queisser) gives Qs equal to 1.851022 photons per second per square centimetre. Adv. Green, M. A., Ho-Baillie, A. [4] Adv. Design rules for donors in bulk-heterojunction tandem solar cells-towards 15% energy-conversion efficiency. Am. Quantum dots have been extensively investigated for this effect, and they have been shown to work for solar-relevant wavelengths in prototype solar cells. F.G. and N.L. Electron. The work was supported by the Cluster of Excellence Engineering of Advanced Materials (EAM) and the SFB 953 at the University of Erlangen-Nuremberg. 25, 70207026 (2013) . The scale bar, 400nm. We have, therefore, additionally introduced a thin N-PEDOT layer between the ZnO and AgNWs to realize the second intermediate layer consisting of ZnO/N-PEDOT/AgNWs (second intermediate layer). A generic concept to overcome bandgap limitations for designing highly efficient multi-junction photovoltaic cells. Secondly, reflectance of the material is non-zero, therefore absorbance cannot be 100% above the band gap. Second, the VOC of the back cell, which is consisting of a series-connection of deep NIR absorbers, can be custom fabricated by stacking an arbitrary sequence of semiconductors with different bandgaps in series. 9, 617624 (2008) . Commun. The semitransparent perovskite (mixed halide CH3NH3PbI3xClx) solar cells with a device structure of ITO/PEDOT:PSS/Perovskite/PC60BM/ZnO/AgNWs (Supplementary Fig. By changing the location of the intermediate band, output current and therefore performance can be changed. The ratio of the open-circuit voltage to the band-gap voltage Shockley and Queisser call V. Under open-circuit conditions, we have. Optical simulations are performed to predict the efficiency potential of different types of triple-junction configurations. It was first calculated by William Shockley and Hans-Joachim Queisser at Shockley Semiconductor in 1961, giving a maximum efficiency of 30% at 1.1 eV. Nature Communications (Nat Commun) = III45019, respectively.) ITO-free and fully solution-processed semitransparent organic solar cells with high fill factors. where 6, 6391 (2015) . The hybrid triple-junction solar cell was assembled by stacking a series-connected opaque DPPDPP as back subcell with a semitransparent perovskite device as front subcell. [29] In contrast, considerable progress has been made in the exploration of fluorescent downshifting, which converts high-energy light (e. g., UV light) to low-energy light (e. g., red light) with a quantum efficiency smaller than 1. Sun, S. Y. et al. Guo, F. et al. The curve is wiggly because of IR absorption bands in the atmosphere. As shown in Fig. In addition, 23.14%-efficient all-perovskite tandem solar cells are further obtained by pairing this PSC with a wide-bandgap (1.74 eV) top cell. When the amount of sunlight is increased using reflectors or lenses, the factor f (and therefore f) will be higher. and from the DFG research training group GRK 1896 at the Erlangen University. }, (Shockley and Queisser take fc to be a constant, although they admit that it may itself depend on voltage. We propose to deposit a transparent counter electrode and parallel-connect these semitransparent high-efficiency cells with one or more deep NIR sensitizers as back subcells. A., Roman, L. S. & Inganas, O. The calculated bandgap required for the semiconductor to achieve the Shockley-Queisser limit is 1.34 eV , which is higher than the average band gap of perovskite materials. The Shockley-Queisser-Limit is a limit of light-based devices. Accordingly, the SP interconnection provides a more feasible approach to reach its theoretical efficiency limit. Green, M. A., Emery, K., Hishikawa, Y., Warta, W. & Dunlop, E. D. Solar cell efficiency tables (Version 45). Pettersson, L. A. While blue light has roughly twice the energy of red light, that energy is not captured by devices with a single p-n junction. (At that value, 22% of the blackbody radiation energy would be below the band gap.) A lamella containing a cross-section of the solar cell was then attached to a TEM half grid for final thinning. "Detailed Balance Limit of Efficiency of p-n Junction Solar Cells", "Photovoltaic Cells (Solar Cells), How They Work", "Photon Collection Efficiency of Fluorescent Solar Collectors", "Microsystems Enabled Photovoltaics, Sandia National Laboratories", "Hot Carrier Solar Cell: Implementation of the Ultimate Photovoltaic Converter", "Peak External Photocurrent Quantum Efficiency Exceeding 100% via MEG in a Quantum Dot Solar Cell", "External Quantum Efficiency Above 100% in a Singlet-Exciton-FissionBased Organic Photovoltaic Cell", "Sunovia, EPIR Demonstrate Optical Down-Conversion For Solar Cells", "Theoretical limits of thermophotovoltaic solar energy conversion", Reproduction of the ShockleyQueisser calculation (PDF), https://en.wikipedia.org/w/index.php?title=ShockleyQueisser_limit&oldid=1137475907, Articles with dead external links from January 2018, Articles with permanently dead external links, Creative Commons Attribution-ShareAlike License 3.0, One electronhole pair excited per incoming photon, Thermal relaxation of the electronhole pair energy in excess of the band gap, Illumination with non-concentrated sunlight. Sci. 4, 1400084 (2014) . Given that the perovskite single cell (mixed halide CH3NH3PbI3xClx) provides a high VOC of 1V, which is comparable to our series-connected DPPDPP cells, it is straightforward to fabricate a PS connected triple-junction device by placing a DPPDPP cell behind a semitransparent perovskite cell, and thereby adding up the total current density for the hybrid triple-junction device. overcome the ShockleyQueisser limit. One can see that maximum photocurrents of 10mAcm2 are achievable for our DPPDPP/PCDTBT triple-junction devices when the thicknesses of the bottom and top DPP:PC60BM subcells are in the range of 3060nm and 3580nm, respectively. Detailed Balance | PVEducation 22, E77E80 (2010) . Photovoltaics 23, 19 (2015) . 6) gives a current density of 15.98mAcm2 which is in good agreement with the simulation values (Supplementary Methods for fabrication details). Absorption of a photon creates an electron-hole pair, which could potentially contribute to the current. In fact this expression represents the thermodynamic upper limit of the amount of work that can be obtained from a heat source at the temperature of the sun and a heat sink at the temperature of the cell. It should be no surprise that there has been a considerable amount of research into ways to capture the energy of the carriers before they can lose it in the crystal structure. However, the parallel-connection is more difficult to adapt and optimize for the high-performance semiconductors with non-tunable bandgaps, such as single-crystal silicon or CdTe. Am. F.G. and C.J.B. 32, 236241 (2007) . 32, 510519 (1961) . Triple-junction solar cells DPPDPP/OPV12 were prepared with the same processing procedure as device DPPDPP/PCDTBT. Correspondence to Figure 5c,d show the typical JV curves of the constructed triple-junction solar cells, DPPDPP/PCDTBT and DPPDPP/OPV12, along with the constituent subcells, respectively. In a traditional solid-state semiconductor such as silicon, a solar cell is made from two doped crystals, one an n-type semiconductor, which has extra free electrons, and the other a p-type semiconductor, which is lacking free electrons, referred to as "holes." This means that during the finite time while the electron is moving forward towards the p-n junction, it may meet a slowly moving hole left behind by a previous photoexcitation. Nat. BPVE device under 1 sun illumination exceeds the Shockley-Queisser limit for a material of this bandgap. Li, W. W., Furlan, A., Hendriks, K. H., Wienk, M. M. & Janssen, R. A. J. The JSC values of the top subcells were verified with EQE measurement (Supplementary Fig. Mater. Based on rational interface engineering, two fully solution-processed intermediate layers are successively developed, allowing effectively coupling the three cells into a SP interconnected triple-junction configuration. Colloidal PbS quantum dot solar cells with high fill factor. The key photovoltaic parameters are listed in Table 2. 3 Optical Modeling of Photovoltaic Modules with Ray Tracing Simulations 27 Carsten Schinke, Malte R.Vogt and Karsten Bothe. Using the above-mentioned values of Qs and Qc, this gives a ratio of open-circuit voltage to thermal voltage of 32.4 (Voc equal to 77% of the band gap). J. Appl. 4b. N.p. Adv. Phys. It can be seen that the two triple-junction cells achieved JSC of 9.67mAcm2 (DPPDPP/PCDTBT) and 9.55mAcm2 (DPPDPP/OPV12) which is in good agreement with the optical simulations. Soc. Light absorbers DPP, OPV12 and PCDTBT were purchased from BASF, Polyera and 1-Materials, respectively. Thus the rate of recombination, in this model, is proportional to exp(V/Vc) times the blackbody radiation above the band-gap energy: (This is actually an approximation, correct so long as the cell is thick enough to act as a black body, to the more accurate expression[7][8], The difference in maximum theoretical efficiency however is negligibly small, except for tiny bandgaps below 200meV. C.J.B., F.G. and N.L. Compared with the reference DPPDPP tandem cell, the slightly reduced VOC of 0.020.03V can be attributed to shadow effect36, because a mask with an aperture smaller than either electrode was adopted to define the active area during the JV measurement. We used an internal quantum efficiency of 100% for our simulation41. This process is known as photoexcitation. For both triple-junction solar cells, the bottom series-connected DPPDPP subcells showed VOC values of 1.071.08V, indicating that the solution-processing of the upper layers imposes no negative effect on the established bottom subcells. This is a very small effect, but Shockley and Queisser assume that the total rate of recombination (see below) when the voltage across the cell is zero (short circuit or no light) is proportional to the blackbody radiation Qc. Beiley, Z. M. et al. In our parallel-connected constituent subcells, the two top subcells showed series resistance of 1cm2 which is almost eight times lower than those of bottom DPPDPP subcells (Table 2). 2 2b. ISSN 2041-1723 (online). : . K.F. Modern commercial mono-crystalline solar cells produce about 24% conversion efficiency, the losses due largely to practical concerns like reflection off the front of the cell and light blockage from the thin wires on the cell surface. If the resistance of the load is too high, the current will be very low, while if the load resistance is too low, the voltage drop across it will be very low. F.G., N.L. Energy Mater. MRS Bull. [12] According to Shockley-Quiesser limit, solar cell efficiency of semiconductors depend on the band gap of the material. Mater. A generic concept to overcome bandgap limitations for - Nature and V.V.R. This process reduces the efficiency of the cell. A solar cell's energy conversion efficiency is the percentage of power converted from sunlight to electrical energy under "standard test conditions" (STC). Q Tandem cells are not restricted to high-performance applications; they are also used to make moderate-efficiency photovoltaics out of cheap but low-efficiency materials. Shockley: Queisser detailed balance limit after 60 years One example is amorphous silicon solar cells, where triple-junction tandem cells are commercially available from Uni-Solar and other companies. Junke Wang, Valerio Zardetto, Ren A. J. Janssen, Nicola Gasparini, Alberto Salleo, Derya Baran, Daniel N. Micha & Ricardo T. Silvares Junior, Xiaozhou Che, Yongxi Li, Stephen R. Forrest, Tomas Leijtens, Kevin A. Bush, Michael D. McGehee, Sebastian Z. Oener, Alessandro Cavalli, Erik C. Garnett, Abdulaziz S. R. Bati, Yu Lin Zhong, Munkhbayar Batmunkh, Nature Communications 0 Limiting solar cell efficiency as a function of the material bandgap for one-sun illumination.