# Super-Multi-Junction Solar Cells—Device Configuration with the Potential for More Than 50% Annual Energy Conversion Efficiency (Non-Concentration)

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## Abstract

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## Featured Application

**This technology is expected to be applied to vehicle-integrated photovoltaic and therefore the installation area is limited, but high performance is demanded.**

## Abstract

## 1. Introduction

^{2}GaInP/GaAs multi-junction cell [23]. Recently, 37.9% efficiency and 38.8% efficiencies have been achieved with InGaP/GaAs/InGaAs 3-junction cell by Sharp [24] and with a 5-junction cell by Spectrolab [25].

^{2}concentrated irradiance was obtained [66]. The measurement and identification of radiative coupling and photon recycling was done in several types of solar cells, including GaAs cells [67], strain-balanced quantum well cells [68], and even emerging solar cells such as Perovskite solar cells [69]. Radiative coupling also affects the measurement of multi-junction solar cells, and it is often called luminescence coupling [70,71,72].

## 2. Model

#### 2.1. What Is the Super-Multi-Junction Solar Cell

#### 2.2. Monte Carlo Simulation for Analyzing the Annual Performance of Multi-Junction Cells

#### 2.3. Modeling Multi-Junction Solar Cells Affected by a Variety of Spectra

^{2}, and the fill factor FF was calculated by the ratio of the spectrum mismatching—specifically, generating a correlation chart between calculated FF and the ratio of mismatching at first; then, general trend of these two parameters was fitted to the parabolic curve so that the FF is represented as the function of the spectrum-mismatching index. This step significantly accelerated the computation time. Otherwise, it would have been necessary to calculate every dataset of the output current and voltage (typically 100 points of the voltage and current of the I-V curve); then, the maximum power point would have been calculated by optimization problem. For the calculation of the performance ratio, this routine needed to be repeated for 12 representative days every month or 365 days (depending on the available solar irradiance data and computing time) multiplied by the number of division of the time in the daytime, or every 1 h, depending on the available solar irradiance database, for every attempt to seek the combination of the bandgaps of each junction in the optimization step. The external quantum efficiency was assumed to be unity by the wavelength corresponding to the bandgap of the junction. The angular characteristics in the photon absorption were assumed to be Lambertian. The open-circuit voltage at 1 kW/m

^{2}irradiance of each junction was assumed to the bandgap voltage minus 0.3 V, namely the best crystal quality in the current epitaxial growth conditions [97]. Figure 3 and Figure 4 summarize the assumptions in the calculation of the efficiency potential of the solar cell.

## 3. Results

#### 3.1. Validation of the Outdoor Operating Model for Non-Concentrating Multi-Junction Solar Cells

^{2}) was about 15% [103].

#### 3.2. Normal Multi-Junction vs. Super-Multi-Junction; Practical Conditions

#### 3.2.1. Modeling the Practical Spectrum Variation

#### 3.2.2. Computation Results of the Monte Carlo Simulation in the Practical Conditions

## 4. Discussion

^{3}cm

^{−2}, but should be as small as possible [110].

## 5. Conclusions

- Multi-junction cells: highest efficiency but lower energy yield.
- Super-multi-junction cell: compensation of spectrum-mismatching loss by sharing photons generated by radiation recombination due to surplus current of spectrum mismatching.
- Annual performance: the model considering spectrum mismatching was validated and applied to super-multi-junction design.
- Super-multi-junction solar cell performance: robust to spectrum change. Its annual average efficiency levels off at 50% with realistic spectrum fluctuation.
- Future multi-junction solar cells: may not be needed to tune the bandgap for matching the standard solar spectrum, or for relying upon artificial technologies such as ELO, wafer-bonding, mechanical-stacking, and reverse-growth, but merely to be used for upright and lattice-matching growth technologies.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Araki, K.; Ji, L.; Kelly, G.; Yamaguchi, M. To Do List for Research and Development and International Standardization to Achieve the Goal of Running a Majority of Electric Vehicles on Solar Energy. Coatings
**2018**, 8, 251. [Google Scholar] [CrossRef] - Yamaguchi, M. Super-High-Efficiency III-V Multi-Junction and Multi-Junction Cells, 2nd ed.; Archer, M.D., Green, M.A., Eds.; Clean Electricity from Photovoltaics; Imperial Collage Press: London, UK, 2015; pp. 307–338. [Google Scholar]
- Bett, A.W. Multi-Junction Cells for Very High Concentration; Marti, A., Luque, A., Eds.; Next Generation Photovoltaics; IOP: London, UK, 2004; pp. 64–90. [Google Scholar]
- Bett, A.W.; Dimroth, F.; Siefer, G. Multijunction Concentrator Solar Cells; Luue, A., Andreev, V., Eds.; Concentrator Photovoltaics; Springer: Berlin, Gemany, 2007; pp. 67–87. [Google Scholar]
- Green, M.A.; Dunlop, E.D.; Levi, D.H.; Hohl-Ebinger, J.; Yoshita, M.; Ho-Baillie, A.W. Solar cell efficiency tables (version 54). Prog. Photovolt. Res. Appl.
**2019**, 27, 565–575. [Google Scholar] [CrossRef] - Green, M.A.; Emery, K.; Hishikawa, Y.; Warta, W.; Dunlop, E.D.; Levi, D.H.; Ho-Baillie, A.W.Y. Solar cell efficiency tables (version 51). Prog. Photovolt.
**2017**, 25, 668–676. [Google Scholar] [CrossRef] - Yamaguchi, M.; Lee, K.H.; Araki, K.; Kojima, N.; Ohshita, Y. Analysis for efficiency potential of crystalline Si solar cells. J. Mater. Res.
**2018**, 33, 2621–2626. [Google Scholar] [CrossRef] - Yamaguchi, M.; Yamada, H.; Katsumata, Y.; Lee, K.H.; Araki, K.; Kojima, N. Efficiency potential and recent activities of high-efficiency solar cells. J. Mater. Res.
**2017**, 32, 3445–3457. [Google Scholar] [CrossRef] - Yamaguchi, M.; Lee, K.H.; Araki, K.; Kojima, N.; Yamada, H.; Katsumata, Y. Analysis for efficiency potential of high-efficiency and next-generation solar cells. Prog. Photovolt. Res. Appl.
**2018**, 26, 543–552. [Google Scholar] [CrossRef] - Yamaguchi, M.; Zhu, L.; Akiyama, H.; Kanemitsu, Y.; Tampo, H.; Shibata, H.; Lee, K.H.; Araki, K.; Kojima, N. Analysis of future generation solar cells and materials. Jpn. J. Appl. Phys.
**2018**, 54, 04FS03. [Google Scholar] [CrossRef] - Yamaguchi, M.; Lee, K.H.; Araki, K.; Kojima, N. A review of recent progress in heterogeneous silicon multi-junction solar cells. J. Phys. D Appl. Phys.
**2018**, 51, 133002. [Google Scholar] [CrossRef] - Jackson, E.D. Areas for Improving of the Semiconductor Solar Energy Converter. In Proceedings of the Transzation Conference on the Use of Solar Energy, Tucson, AZ, USA, 31 October–1 November 1955; University of Arizona Press: Tucson, AZ, USA, 1958; Volume 5, pp. 122–126. [Google Scholar]
- Wolf, M. Limitations and possibilities for improvement of photovoltaic solar energy converters. Proc. Inst. Radio Eng.
**1960**, 48, 1246–1263. [Google Scholar] - Hutchby, J.A.; Markunas, R.J.; Timmons, M.L.; Chiang, P.K.; Bedair, S.M. A Review of Multijunction Concentrator Solar Cells. In Proceedings of the 18th IEEE Photovoltaic Specialists Conference, Las Vegas, NV, USA, 21–25 October 1985; IEEE: New York, NY, USA, 1985; pp. 20–27. [Google Scholar]
- Ludowise, M.J.; LaRue, R.A.; Borden, P.G.; Gregory, P.E.; Dietz, W.T. High-efficiency organometallic vapor phase epitaxy AlGaAs/GaAs monolithic cascade solar cell using metal interconnects. Appl. Phys. Lett.
**1982**, 41, 550–552. [Google Scholar] [CrossRef] - Flores, C. A three-terminal double junction GaAs/GaAlAs cascade solar cells. IEEE Electron. Device Lett.
**1983**, EDL–4, 96–99. [Google Scholar] [CrossRef] - Chung, B.C.; Virshup, G.F.; Hikido, S.; Kaminar, N.R. 27.6% efficiency (1 Sun, air mass 1.5) monolithic Al0.37 Ga0.63 As/GaAs two-junction cascade solar cell with prismatic cover glass. Appl. Phys. Lett.
**1989**, 55, 1741–1743. [Google Scholar] [CrossRef] - Fan, J.C.C.; Tsaur, B.Y.; Palm, B.J. Optical Design of High-Efficiency Multi-Junction Cells. In Proceedings of the 16th IEEE Photovoltaic Specialists Conference, San Diego, CA, USA, 27–30 September 1982; IEEE: New York, NY, USA, 1982; pp. 692–701. [Google Scholar]
- Yamaguchi, M.; Amano, C.; Sugiura, H.; Yamamoto, A. High efficiency AlGaAs/GaAs multi-junction solar cells. In Proceedings of the 19th IEEE Photovoltaic Specialists Conference, New Orleans, LA, USA, 4–8 May 1987; IEEE: New York, NY, USA, 1987; pp. 1484–1485. [Google Scholar]
- Ando, K.; Amano, C.; Sugiura, H.; Yamaguchi, M.; Saletesm, A. Non-radiative e-h recombination characteristics of mid-gap electron trap in AlxGa1–x As (x = 0.4) grown by molecular beam epitaxy. Jpn. J. Appl. Phys.
**1987**, 26, L266–L269. [Google Scholar] [CrossRef] - Sugiura, H.; Amano, C.; Yamamoto, A.; Yamaguchi, M. Double hetero¬structure GaAs tunnel junction for AlGaAs/GaAs multi-junction solar cells. Jpn. J. Appl. Phys.
**1988**, 27, 269–272. [Google Scholar] [CrossRef] - Olson, J.M.; Kurtz, S.R.; Kibbler, A.E. A 27.3% efficient Ga0.5In0.5P/ GaAs multi-junction solar cell. Appl. Phys. Lett.
**1990**, 56, 623–625. [Google Scholar] [CrossRef] - Bertness, K.A.; Kurtz, S.R.; Friedman, D.J.; Kibbler, A.E.; Kramer, C.; Olson, J.M. 29.5%-efficiency GaInP/GaAs multi-junction solar cells. Appl. Phys. Lett.
**1994**, 65, 989–991. [Google Scholar] [CrossRef] - Sasaki, K.; Agui, T.; Nakaido, K.; Takahashi, N.; Onitsuka, R.; Takamoto, T. Development of InGaP/GaAs/InGaAs inverted triple junction concentrator solar cells. Aip Conf. Proc.
**2013**, 1556, 22–25. [Google Scholar] - Chiu, P.T.; Law, D.L.; Woo, R.L.; Singer, S.; Bhusari, D.; Hong, W.D.; Zakaria, A.; Boisvert, J.C.; Mesropian, S.; King, R.R.; et al. 35.8% space and 38.8% terrestrial 5J direct bonded cells. In Proceedings of the 40th IEEE Photovoltaic Specialist Conference, Denver, CO, USA, 8–13 June 2014; pp. 11–13. [Google Scholar]
- Yamaguchi, M.; Luque, L. High efficiency and high concentration in photovoltaics. IEEE Trans. Electron Devices
**1999**, 46, 2139–2144. [Google Scholar] [CrossRef] - Swanson, R.M. Photovoltaic Concentrators. In Handbook of Photovoltaic Science and Engineering; Luque, A., Hegedus, S., Eds.; Wiley: Hoboken, NJ, USA, 2003; pp. 449–503. [Google Scholar]
- Philipps, S.P.; Bett, A.W.; Horowitz, K.; Kurtz, S. Current Status of Concentrator Photovoltaic (CPV) Technology; Version 1.3; National Renewable Energy Lab NREL: Lakewood, CO, USA, 2017; pp. 10–11. [Google Scholar]
- Araki, K.; Yamaguchi, M. Influences of spectrum change to 3-junction concentrator cells. Sol. Energy Mater. Sol. Cells
**2003**, 75, 707–714. [Google Scholar] [CrossRef] - Faine, P.; Kurtz, S.R.; Riordan, C.; Olson, J.M. The influence of spectral solar irradiance variations on the performance of selected single-junction and multijunction solar cells. Sol. Cells
**1991**, 31, 259–278. [Google Scholar] [CrossRef] - Kurtz, S.R.; Olson, J.M.; Faine, P. The difference between standard and average efficiencies of multijunction compared with single-junction concentrator cells. Solar Cells
**1991**, 30, 501–513. [Google Scholar] [CrossRef] - Philipps, S.P.; Peharz, G.; Hoheisel, R.; Hornung, T.; Al-Abbadi, N.M.; Dimroth, F.; Bett, A.W. Energy harvesting efficiency of III–V triple-junction concentrator solar cells under realistic spectral conditions. Sol. Energy Mater. Sol. Cells
**2010**, 94, 869–877. [Google Scholar] [CrossRef] - Kinsey, G.S.; Edmondson, K.M. Spectral response and energy output of concentrator multijunction solar cells. Prog. Photovolt. Res. Appl.
**2009**, 17, 279–288. [Google Scholar] [CrossRef] - Araki, K.; Emery, K.; Siefer, G.; Bett, A.W.; Sakakibara, T.; Kemmoku, Y.; Ekins-Daukes, N.J.; Lee, H.S.; Yamaguchi, M. Comparison of efficiency measurements for a HCPV module with 3J cells in 3 sites. In Proceedings of the Conference Record of the Thirty-First IEEE Photovoltaic Specialists Conference, Lake Buena Vista, FL, USA, 3–7 January 2005; pp. 846–849. [Google Scholar]
- Lee, H.S.; Ekins-Daukes, N.J.; Araki, K.; Kemmoku, Y.; Yamaguchi, M. Field test and analysis: The behavior of 3-J concentrator cells under the control of cell temperature. In Proceedings of the Conference Record of the Thirty-First IEEE Photovoltaic Specialists Conference, Lake Buena Vista, FL, USA, 3–7 January 2005; pp. 754–757. [Google Scholar]
- Al Husna, H.; Ota, Y.; Minemoto, T.; Nishioka, K. Field test analysis of concentrator photovoltaic system focusing on average photon energy and temperature. Jpn. J. Appl. Phys.
**2015**, 54, 08KE05. [Google Scholar] [CrossRef] - Verlinden, P.J.; Lasich, J.B. Energy rating of concentrator PV systems using multi-junction III–V solar cells. In Proceedings of the 33rd IEEE Photovoltaic Specialists Conference, San Diego, CA, USA, 11–16 May 2008; pp. 1–6. [Google Scholar]
- Victoria, M.; Askins, S.; Nuñez, R.; Domínguez, C.; Herrero, R.; Antón, I.; Sala, G.; Ruíz, J.M. Tuning the current ratio of a CPV system to maximize the energy harvesting in a particular location. Aip Conf. Proc.
**2013**, 1556, 156–161. [Google Scholar] - Muller, M.; Marion, B.; Kurtz, S.; Rodriguez, J. An investigation into spectral parameters as they impact CPV module performance. Aip Conf. Proc.
**2010**, 1277, 307–311. [Google Scholar] - Domínguez, C.; Antón, I.; Sala, G.; Askins, S. Current-matching estimation for multijunction cells within a CPV module by means of component cells. Prog. Photovolt. Res. Appl.
**2013**, 21, 1478–1488. [Google Scholar] [CrossRef] - Núñez, R.; Jin, C.; Antón, I.; Sala, G. Spectral classification of worldwide locations using SMR indexes. Aip Conf. Proc.
**2016**, 1766, 090007. [Google Scholar] [Green Version] - Araki, K.; Yamaguchi, M.; Kondo, M.; Uozumi, H. Which is the best number of junctions for solar cells under ever-changing terrestrial spectrum? In Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion, Osaka, Japan, 11–18 May 2003; pp. 307–310. [Google Scholar]
- Letay, G.; Baur, C.; Bett, A. Theoretical investigations of III-V multi-junction concentrator cells under realistic spectral conditions. In Proceedings of the 19th European Photovoltaic Solar Energy Conference, Paris, France, 7–11 June 2004; p. 11. [Google Scholar]
- Ekins-Daukes, N.J.; Betts, T.R.; Kemmoku, Y.; Araki, K.; Lee, H.S.; Gottschalg, R.; Boreland, M.B.; Infield, D.G.; Yamaguchi, M. Syracuse-a multi-junction concentrator system computer model. In Proceedings of the Conference Record of the Thirty-First IEEE Photovoltaic Specialists Conference, Lake Buena Vista, FL, USA, 3–7 January 2005; pp. 651–654. [Google Scholar]
- Ekins-Daukes, N.J.; Kemmoku, Y.; Araki, K.; Betts, T.R.; Gottschalg, R.; Infield, D.G.; Yamaguchi, M. The design specification for syracuse; a multi-junction concentrator system computer model. In Proceedings of the 19th European Photovoltaic Solar Energy Conference, Paris, France, 7–11 June 2004. [Google Scholar]
- Cameron, C.; Crawford, C.; Foresi, J.; King, D.; McConnell, R.; Riley, D.; Sahm, A.; Stein, J. Performance Model Assessment for Multi-Junction Concentrating Photovoltaic Systems. Aip Conf. Proc.
**2010**, 1277, 290–293. [Google Scholar] - Araki, K.; Uozumi, H.; Kondo, M.; Takamoto, T.; Agui, T.; Kaneiwa, M.; Egami, T.; Hiramatsu, M.; Miyazaki, Y.; Kemmoku, Y.; et al. Development of a new 550/spl times/concentrator module with 3J cells-performance and reliability. In Proceedings of the Conference Record of the Thirty-First IEEE Photovoltaic Specialists Conference, Lake Buena Vista, FL, USA, 3–7 January 2005; pp. 631–634. [Google Scholar]
- Araki, K.; Yamaguchi, M. Extended distributed model for analysis of non-ideal concentration operation. Sol. Energy Mater. Sol. Cells
**2003**, 75, 467–473. [Google Scholar] [CrossRef] - Herrero, R.; Victoria, M.; Domínguez, C.; Askins, S.; Antón, I.; Sala, G. Concentration photovoltaic optical system irradiance distribution measurements and its effect on multi-junction solar cells. Prog. Photovolt. Res. Appl.
**2012**, 20, 423–430. [Google Scholar] [CrossRef] - Garcia, I.; Algora, C.; Rey-Stolle, I.; Galiana, B. Study of non-uniform light profiles on high concentration III–V solar cells using quasi-3D distributed models. In Proceedings of the 33rd IEEE Photovoltaic Specialists Conference, San Diego, CA, USA, 11–16 May 2008; pp. 1–6. [Google Scholar]
- Kurtz, S.R.; O’Neill, M.J. Estimating and controlling chromatic aberration losses for two-junction, two-terminal devices in refractive concentrator systems. In Proceedings of the Conference Record of the Twenty Fifth IEEE Photovoltaic Specialists Conference, Washington, DC, USA, 13–17 May 1996; pp. 361–364. [Google Scholar]
- James, L.W. Effects of concentrator chromatic aberration on multi-junction cells. In Proceedings of the 1994 IEEE 1st World Conference on Photovoltaic Energy Conversion-WCPEC (A Joint Conference of PVSC, PVSEC and PSEC), Waikoloa, HI, USA, 5–9 December 1994; pp. 1799–1802. [Google Scholar]
- Rey-Stolle, I.; Algora, C.; García, I.; Baudrit, M.; Espinet, P.; Galiana, B.; Barrigón, E. Simulating III–V concentrator solar cells: A comparison of advantages and limitations of lumped analytical models; distributed analytical models and numerical simulation. In Proceedings of the 34th IEEE Photovoltaic Specialists Conference (PVSC), Philadelphia, PA, USA, 7–12 June 2009; pp. 001622–001627. [Google Scholar]
- Araki, K.; Kondo, M.; Uozumi, H.; Yamaguchi, M. Experimental proof and theoretical analysis on effectiveness of passive homogenizers to 3J concentrator solar cells. In Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion, Osaka, Japan, 11–18 May 2003; pp. 853–856. [Google Scholar]
- Araki, K.; Leutz, R.; Kondo, M.; Akisawa, A.; Kashiwagi, T.; Yamaguchi, M. Development of a metal homogenizer for concentrator monolithic multi-junction-cells. In Proceedings of the Conference Record of the Twenty-Ninth IEEE Photovoltaic Specialists Conference, New Orleans, LA, USA, 19–24 May 2002; pp. 1572–1575. [Google Scholar]
- Brown, A.S.; Green, M.A. Radiative coupling as a means to reduce spectral mismatch in monolithic multi-junction solar cell stacks theoretical considerations. In Proceedings of the Conference Record of the Twenty-Ninth IEEE Photovoltaic Specialists Conference, New Orleans, LA, USA, 19–24 May 2002; pp. 868–871. [Google Scholar]
- Chan, N.L.; Young, T.B.; Brindley, H.E.; Ekins-Daukes, N.J.; Araki, K.; Kemmoku, Y.; Yamaguchi, M. Validation of energy prediction method for a concentrator photovoltaic module in Toyohashi Japan. Prog. Photovolt. Res. Appl.
**2013**, 21, 1598–1610. [Google Scholar] [CrossRef] - Chan, N.L.; Thomas, T.; Führer, M.; Ekins-Daukes, N.J. Practical limits of multijunction solar cell performance enhancement from radiative coupling considering realistic spectral conditions. IEEE J. Photovolt.
**2014**, 4, 1306–1313. [Google Scholar] [CrossRef] - Chan, N.L.; Brindley, H.E.; Ekins-Daukes, N.J. Impact of individual atmospheric parameters on CPV system power, energy yield and cost of energy. Prog. Photovolt. Res. Appl.
**2014**, 22, 1080–1095. [Google Scholar] [CrossRef] - Chan, N.L.; Young, T.; Brindley, H.; Chaudhuri, B.; Ekins-Daukes, N.J. Variation in spectral irradiance and the consequences for multi-junction concentrator photovoltaic systems. In Proceedings of the 35th IEEE Photovoltaic Specialists Conference, Honolulu, HI, USA, 20–25 June 2010; pp. 003008–003012. [Google Scholar]
- Araki, K.; Ota, Y.; Lee, K.H.; Nishioka, K.; Yamaguchi, M. Optimization of the Partially Radiative-coupling Multi-junction Solar Cells Considering Fluctuation of Atmospheric Conditions. In Proceedings of the IEEE 7th World Conference on Photovoltaic Energy Conversion (WCPEC) (A Joint Conference of 45th IEEE PVSC, 28th PVSEC & 34th EU PVSEC), Waikoloa Village, HI, USA, 10–15 June 2018; pp. 1661–1666. [Google Scholar]
- Araki, K.; Lee, K.H.; Kojima, N.; Yamaguchi, M. Super-Multijunction Cell, A new Solar Cell Overcoming the Spectrum Loss of Multijunction Cells. Grand Renew. Energy Proc. Jpn. Counc. Renew. Energy
**2018**, 2018, 45. [Google Scholar] - Araki, K.; Lee, K.H.; Yamaguchi, M. Opportunities for breaking an energy generation limit of photovoltaic using multijunction and super-multijunction cells. In Proceedings of the 18th International Workshop on Junction Technology (IWJT), Shanghai, China, 8–9 March 2018; pp. 1–4. [Google Scholar]
- Araki, K.; Lee, K.H.; Yamaguchi, M. Risks and Opportunities in Challenging New Bandgap Materials for Increasing Number of Junctions—Probability Study. In Proceedings of the PVSEC-27, Otsu, Japan, 12–17 November 2017. [Google Scholar]
- Kayes, B.M.; Nie, H.; Twist, R.; Spruytte, S.G.; Reinhardt, F.; Kizilyalli, I.C.; Higashi, G.S. 27.6% conversion efficiency, a new record for single-junction solar cells under 1 sun illumination. In Proceedings of the 37th IEEE Photovoltaic Specialists Conference, Seattle, WA, USA, 19–24 June 2011; pp. 000004–000008. [Google Scholar]
- Schilling, C.L.; Hoehn, O.; Micha, D.N.; Heckelmann, S.; Klinger, V.; Oliva, E.; Glunz, S.W.; Dimroth, F. Combining photon recycling and concentrated illumination in a GaAs heterojunction solar cell. IEEE J. Photovolt.
**2017**, 8, 348–354. [Google Scholar] [CrossRef] - Kosten, E.D.; Kayes, B.M.; Atwater, H.A. Experimental demonstration of enhanced photon recycling in angle-restricted GaAs solar cells. Energy Environ. Sci.
**2014**, 7, 1907–1912. [Google Scholar] [CrossRef] [Green Version] - Johnson, D.C.; Ballard, I.M.; Barnham, K.W.J.; Connolly, J.P. Mazzer. Observation of photon recycling in strain-balanced quantum well solar cells. Appl. Phys. Lett.
**2007**, 90, 213505. [Google Scholar] [CrossRef] - Pazos-Outón, L.M.; Szumilo, M.; Lamboll, R.; Richter, J.M.; Crespo-Quesada, M.; Abdi-Jalebi, M.; Beeson, H.J.; Vrućinić, M.; Alsari, M.; Snaith, H.J.; et al. Photon recycling in lead iodide perovskite solar cells. Science
**2016**, 351, 1430–1433. [Google Scholar] [CrossRef] - Sogabe, T.; Ogura, A.; Hung, C.Y.; Evstropov, V.; Mintairov, M.; Shvarts, M.; Okada, Y. Experimental characterization and self-consistent modeling of luminescence coupling effect in III-V multijunction solar cells. Appl. Phys. Lett.
**2013**, 103, 263907. [Google Scholar] [CrossRef] - Steiner, M.A.; Geisz, J.F. Non-linear luminescent coupling in series-connected multijunction solar cells. Appl. Phys. Lett.
**2012**, 100, 251106. [Google Scholar] [CrossRef] - Allen, C.R.; Lim, S.H.; Li, J.J.; Zhang, Y.H. Simple method for determining luminescence coupling in multi-junction solar cells. In Proceedings of the 37th IEEE Photovoltaic Specialists Conference, Seattle, WA, USA, 19–24 June 2011; pp. 000452–000453. [Google Scholar]
- Ota, Y.; Masuda, T.; Araki, K.; Yamaguchi, M. A mobile multipyranometer array for the assessment of solar irradiance incident on a photovoltaic-powered vehicle. Sol. Energy
**2019**, 184, 84–90. [Google Scholar] [CrossRef] - Ota, Y.; Nishioka, K.; Araki, K.; Ikeda, K.; Lee, K.H.; Yamaguchi, M. Optimization of static concentrator photovoltaics with aspherical lens for automobile. In Proceedings of the IEEE 43rd Photovoltaic Specialists Conference (PVSC), Portland, OR, USA, 5–10 June 2016; pp. 0570–0573. [Google Scholar]
- Araki, K.; Ota, Y.; Ikeda, K.; Lee, K.H.; Nishioka, K.; Yamaguchi, M. Possibility of static low concentrator PV optimized for vehicle installation. Aip Conf. Proc.
**2016**, 1766, 020001. [Google Scholar] - Araki, K.; Nagai, H.; Yamaguchi, M. Possibility of solar station to EV. Aip Conf. Proc.
**2016**, 1766, 080001. [Google Scholar] - Schuss, C.; Gall, H.; Eberhart, K.; Illko, H.; Eichberger, B. Alignment and interconnection of photovoltaics on electric and hybrid electric vehicles. In Proceedings of the 2014 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings, Montevideo, Uruguay, 12–15 May 2014; pp. 153–158. [Google Scholar]
- Schuss, C.; Eichberger, B.; Rahkonen, T. Impact of sampling interval on the accuracy of estimating the amount of solar energy. In Proceedings of the IEEE International Instrumentation and Measurement Technology Conference Proceedings, Taipei, Taiwan, 23–26 May 2016; pp. 1–6. [Google Scholar]
- Sato, D.; Lee, K.H.; Araki, K.; Masuda, T.; Yamaguchi, M.; Yamada, N. Design of low-concentration static III-V/Si partial CPV module with 27.3% annual efficiency for car-roof application. Prog. Photovolt. Res. Appl.
**2019**, 27, 501–510. [Google Scholar] [CrossRef] - Sato, D.; Lee, K.H.; Araki, K.; Masuda, T.; Yamaguchi, M.; Yamada, N. Design and Evaluation of Low-concentration Static III-V/Si Partial CPV Module for Car-rooftop Application. In Proceedings of the IEEE 7th World Conference on Photovoltaic Energy Conversion (WCPEC) (A Joint Conference of 45th IEEE PVSC, 28th PVSEC & 34th EU PVSEC), Waikoloa Village, HI, USA, 10–15 June 2018; pp. 0954–0957. [Google Scholar]
- Masuda, T.; Araki, K.; Okumura, K.; Urabe, S.; Kudo, Y.; Kimura, K.; Nakado, T.; Sato, A.; Yamaguchi, M. Next environment-friendly cars: Application of solar power as automobile energy source. In Proceedings of the 2016 IEEE 43rd Photovoltaic Specialists Conference (PVSC), Portland, OR, USA, 5–10 June 2016; pp. 0580–0584. [Google Scholar]
- Araki, K.; Algora, C.; Siefer, G.; Nishioka, K.; Leutz, R.; Carter, S.; Wang, S.; Askins, S.; Ji, L.; Kelly, G. Standardization of the CPV and car-roof PV technology in 2018–Where are we going to go? Aip Conf. Proc.
**2018**, 2012, 070001. [Google Scholar] - Araki, K.; Algora, C.; Siefer, G.; NIshioka, K.; Muller, M.; Leutz, R.; Carter, S.; Wang, S.; Askins, S.; Ji, L.; et al. Toward Standardization of Solar trackers, concentrator PV, and car-ROOF pv. Grand Renew. Energy Proc. Jpn. Counc. Renew. Energy
**2018**, 2018, 37. [Google Scholar] - Araki, K.; Lee, K.H.; Yamaguchi, M. The possibility of the static LCPV to mechanical-stack III-V//Si module. Aip Conf. Proc.
**2018**, 2012, 090002. [Google Scholar] - Ota, Y.; Masuda, T.; Araki, K.; Yamaguchi, M. Curve-correction factor for characterization of the output of a three-dimensional curved photovoltaic module on a car roof. Coatings
**2018**, 8, 432. [Google Scholar] [CrossRef] - Peharz, G.; Siefer, G.; Bett, A.W. A simple method for quantifying spectral impacts on multi-junction solar cells. Sol. Energy
**2009**, 83, 1588–1598. [Google Scholar] [CrossRef] - Peharz, G.; Siefer, G.; Araki, K.; Bett, A.W. Spectrometric outdoor characterization of CPV modules using isotype monitor cells. In Proceedings of the 33rd IEEE Photovoltaic Specialists Conference, San Diego, CA, USA, 11–16 May 2008; pp. 1–5. [Google Scholar]
- Dobbin, A.L.; Lumb, M.P.; Tibbits, T.N. How Important Is The Resolution Of Atmospheric Data In Calculations Of Spectral Irradiance And Energy Yield For (III–V) Triple-Junction Cells? Aip Conf. Proc.
**2010**, 1277, 303–306. [Google Scholar] - Gueymard, C.A. Daily spectral effects on concentrating PV solar cells as affected by realistic aerosol optical depth and other atmospheric conditions. In Optical Modeling and Measurements for Solar Energy Systems III 2009; SPIE: Bellingham WA, USA, 2009; p. 741007. [Google Scholar]
- Muller, M.; Marion, B.; Rodriguez, J.; Kurtz, S. Minimizing variation in outdoor CPV power ratings. Aip Conf. Proc.
**2011**, 1407, 336–340. [Google Scholar] - Araki, K.; Kemmoku, Y.; Yamaguchi, M. A simple rating method for CPV modules and systems. In Proceedings of the 33rd IEEE Photovoltaic Specialists Conference, San Diego, CA, USA, 11–16 May 2008; pp. 1–6. [Google Scholar]
- Saiki, H.; Sakai, T.; Araki, K.; Ota, Y.; Lee, K.H.; Yamaguchi, M.; Nishioka, K. Verification of uncertainty in CPV’s outdoor performance. In Proceedings of the IEEE 7th World Conference on Photovoltaic Energy Conversion (WCPEC)(A Joint Conference of 45th IEEE PVSC, 28th PVSEC & 34th EU PVSEC), Waikoloa Village, HI, USA, 10–15 June 2018; pp. 0949–0953. [Google Scholar]
- Araki, K.; Ota, Y.; Lee, K.H.; Sakai, T.; Nishioka, K.; Yamaguchi, M. Analysis of fluctuation of atmospheric parameters and its impact on performance of CPV. Aip Conf. Proc.
**2018**, 2012, 080002. [Google Scholar] - Araki, K.; Lee, K.H.; Yamaguchi, M. Impact of the atmospheric conditions to the bandgap engineering of multi-junction cells for optimization of the annual energy yield of CPV. Aip Conf. Proc.
**2017**, 1881, 070002. [Google Scholar] - Araki, K.; Ota, Y.; Lee, K.H.; Nishioka, K.; Yamaguchi, M. Improvement of the Spectral Sensitivity of CPV by Enhancing Luminescence Coupling and Fine-tuning to the Bottom-bandgap Matched to Local Atmospheric Conditions. Aip Conf. Proc.
**2019**, 2149, 060001. [Google Scholar] - Araki, K.; Lee, K.H.; Yamaguchi, M. Bandgaps of multi-junction solar cells potentially determined at the sun height of the culmination on the winter solstice. Sol. Energy
**2017**, 153, 445–453. [Google Scholar] [CrossRef] - King, R.R.; Bhusari, D.; Boca, A.; Larrabee, D.; Liu, X.Q.; Hong, W.; Fetzer, C.M.; Law, D.C.; Karam, N.H. Band gap-voltage offset and energy production in next-generation multijunction solar cells. Prog. Photovolt. Res. Appl.
**2011**, 19, 797–812. [Google Scholar] [CrossRef] - Bird, R.E.; Riordan, C. Simple Solar Spectrum Model for Direct and Diffused Irradiation on Horizontal and Tilted at the Earth’s surface for Cloudless Atmospheres. Sol. Energy
**1984**, 32, 461–471. [Google Scholar] [CrossRef] - Araki, K.; Ota, Y.; Sakai, T.; Lee, K.H.; Nishioka, K.; Yamaguchi, M. Energy yield prediction of multi-junction cells considering atmospheric parameters fluctuation using Monte Carlo methods. In Proceedings of the PVSEC-27, Otsu, Japan, 12–17 November 2017. [Google Scholar]
- Araki, K.; Ota, Y.; Sakai, T.; Lee, K.H.; Yamaguchi, M. Inherent uncertainty of energy ratings of multi-junction cells by the fluctuation of atmospheric parameters. In Proceedings of the PVSEC-27, Otsu, Japan, 12–17 November 2017. [Google Scholar]
- Ota, Y.; Ueda, K.; Takamoto, T.; Nishioka, K. Output evaluation of a world’s highest efficiency flat sub module with InGaP/GaAs/InGaAs inverted triple-junction solar cell under outdoor operation. Jpn. J. Appl. Phys.
**2018**, 57, 08RD08. [Google Scholar] [CrossRef] - Takamoto, T.; Washio, H.; Juso, H. Application of InGaP/GaAs/InGaAs triple junction solar cells to space use and concentrator photovoltaic. In Proceedings of the 2014 IEEE 40th Photovoltaic Specialist Conference (PVSC), Denver, CO, USA, 8–13 June 2014; pp. 0001–0005. [Google Scholar]
- Derkacs, D.; Bilir, T.; Sabnis, V.A. Luminescent coupling in GaAs/GaInNAsSb multijunction solar cells. IEEE J. Photovolt.
**2012**, 3, 520–527. [Google Scholar] - Kamath, H.G.; Ekins-Daukes, N.J.; Araki, K.; Ramasesha, S.K. The potential for concentrator photovoltaics: A feasibility study in India. Prog. Photovolt. Res. Appl.
**2019**, 27, 316–327. [Google Scholar] [CrossRef] - Kamath, H.G.; Ekins-Daukes, N.J.; Araki, K.; Ramasesha, S.K. Performance analysis and fault diagnosis method for concentrator photovoltaic modules. IEEE J. Photovolt.
**2018**, 9, 424–430. [Google Scholar] [CrossRef] - Massey, F.J., Jr. The Kolmogorov-Smirnov test for goodness of fit. J. Am. Stat. Assoc.
**1951**, 46, 68–78. [Google Scholar] [CrossRef] - Lee, K.H.; Araki, K.; Wang, L.; Kojima, N.; Ohshita, Y.; Yamaguchi, M. Assessing material qualities and efficiency limits of III–V on silicon solar cells using external radiative efficiency. Prog. Photovolt. Res. Appl.
**2016**, 24, 1310–1318. [Google Scholar] [CrossRef] - Green, M.A. Radiative efficiency of state-of-the-art photovoltaic cells. Prog. Photovolt. Res. Appl.
**2012**, 20, 472–476. [Google Scholar] [CrossRef] - Chan, N.L.; Ekins-Daukes, N.J.; Adams, J.G.J.; Lumb, M.P.; Gonzalez, M.; Jenkins, P.P.; Vurgaftman, I.; Meyer, J.R.; Walters, R.J. Optimal bandgap combinations—Does material quality matter? IEEE J. Photovolt.
**2012**, 2, 202–208. [Google Scholar] [CrossRef] - Yamaguchi, M.; Amano, C.; Itoh, Y. Numerical analysis for high-efficiency GaAs solar cells fabricated on Si substrates. J. Appl. Phys.
**1989**, 66, 915–919. [Google Scholar] [CrossRef] - Vogel, E.M. Glasses as nonlinear photonic materials. J. Am. Ceram. Soc.
**1989**, 72, 719–724. [Google Scholar] [CrossRef] - Lea, C.T. Crossover minimization in directional-coupler-based photonic switching systems. IEEE Trans. Commun.
**1988**, 36, 355–363. [Google Scholar] [CrossRef] - Park, I.; Lee, H.S.; Kim, H.J.; Moon, K.M.; Lee, S.G.; Beom-Hoan, O.; Park, S.G.; Lee, E.H. Photonic crystal power-splitter based on directional coupling. Opt. Express
**2004**, 12, 3599–3604. [Google Scholar] [CrossRef] - Martinez, A.; Cuesta, F.; Marti, J. Ultrashort 2-D photonic crystal directional couplers. IEEE Photonics Technol. Lett.
**2003**, 15, 694–696. [Google Scholar] [CrossRef]

**Figure 1.**The energy flow of multi-junction cells. Left: Normal multi-junction cell; Right: Super-multi-junction cell. ERE—external radiative efficiency [61].

**Figure 4.**Assumptions in the calculation of the efficiency potential of the solar cell using three factors.

**Figure 5.**Modeling performance of the non-concentrating multi-junction solar cells considering the complicated spectrum and angle interaction described in Table 1. In this study, we only considered the flat plate, so that correction to the curved surface in the integrated tool was not applied.

**Figure 6.**Comparison between the measured and modeled seasonal trends of the performance of the PV module using multi-junction solar cells [96]. Performance ratio can be calculated by the formula defined as PR = Yf/Yr, where PR is performance ratio, and Yf is the integrated energy yield of one day, and Yr is the nominal energy yield of one day calculated by the standard testing condition (STC) module efficiency and total insolation.

**Figure 7.**Recovery of the spectrum-mismatching loss due to water absorption in summer by enhancing the ratio of luminescence coupling between the middle junction and the bottom junction, added and modified from the original chart in [97]. The multiple colored lines correspond to the level of the luminescence coupling between the middle junction and the bottom junction, from the bottom to the top, 0%, 10%, 20%, …, 90%. Please note that the variation of the performance ratio impacted by the spectrum change was reduced by the increase of the level of luminescence coupling, but the right depth in summer corresponds to the ones of 10% and 20% of the luminescence coupling. Performance ratio can be calculated by the formula defined as PR = Yf/Yr, where PR is performance ratio, and Yf is the integrated energy yield of one day, and Yr is the nominal energy yield of one day calculated by the STC module efficiency and total insolation.

**Figure 8.**Seasonal fluctuation of the atmospheric parameters around the University of Miyazaki, taken by the curve-fitting method to the spectral profile modeled by Spectrl2 [95]. The trend line was defined by the local least-square-error method.

**Figure 9.**Histogram of the residual errors of the measured atmospheric parameters from the trend line (relative to the values in the trend line): (

**a**) Aerosol density; (

**b**) Water precipitation.

**Figure 10.**Quantile–quantile plot that examines the values of two distributions: (

**a**) Aerosol density; (

**b**) Water precipitation.

**Figure 11.**Optimization design result of the normal multi-junction solar cells (distribution of the annual average efficiency) under the worst-case combination of climate, atmospheric conditions, latitude, and orientation angle. The y-axis is normalized so that the integration of the distribution becomes unity: (

**a**) Normal multi-junction solar cell; (

**b**) Super-multi-junction solar cell.

**Figure 12.**Optimization design result of the normal multi-junction solar cells (trend of an average of the annual average efficiency by variation of the spectrum) under worst-case combination of climate, atmospheric conditions, latitude, and orientation angle. m indicates average of the annual average efficiency, and σ indicates its standard deviation: (

**a**) Normal multi-junction solar cell; (

**b**) Super-multi-junction solar cell.

**Figure 13.**Distribution of the bandgap energy of the optimized (to the spectrum and other climate conditions given by random numbers according to Figure 2) multi-junction solar cells under the modeled fluctuation in the climate in Miyazaki, Japan (N 31.83°, E 131.42°). This is an example of 10 junctions. Please note that the histogram of the calculated optimized bandgap energy in each junction is normalized so that the integral of the range becomes unity. Also, note that the overlap of each peak does not mean that the higher bandgap junction has lower bandgap energy than that of the lower peak. It is constrained that the bandgap structure was equivalently modeled by allowing the bandgap energy of the (i + 1)th junction to be equal or greater than that of the (i)th junction, but not allowing the bandgap energy of the (i + 1)th junction to be less than that of the (i)th junction. The y-axis is normalized so that the integration of the distribution becomes unity: (

**a**) Normal multi-junction solar cell; (

**b**) Super-multi-junction solar cell.

**Figure 14.**Possibility of the future high-efficiency solar cell technology based on the implication from the super-multi-junction solar cell.

CPV ^{1} | Normal Installation | |
---|---|---|

Solar spectrum | Only direct | A mixture of direct, diffused from the sky, and reflection |

Angle | Always normal | Varies by time and seasons |

Spectrum by angle | Constant (only normal) | Needs consider coupling to angle |

^{1}It only generates power only by direct solar irradiance using a 2-axis solar tracker.

**Table 2.**List of the probability parameters for modeling variation of annual performance (independent parent parameters).

Range and Type | Description | |
---|---|---|

Variation factor in aerosol density | Normal distribution centered on 0 | Calculated by the residual errors in the measured point form the smooth trend line. |

Variation factor in water precipitation | Normal distribution centered on 0 | Calculated by the residual errors in the measured point form the smooth trend line. |

Variation factor in solar irradiance ^{1} | Ranged uniform distribution in [–1,1] | −1: Lowest irradiance year, 0: Normal year, 1: Highest irradiance year. The irradiance data is calculated by the linear coupling of three parameters depends on the value of the probability factor. The base irradiance data was given in 24 h × 365 days by METPV-11 and METPV-Asia database. |

^{1}The same factor is applied both to direct and diffused sunlight.

**Table 3.**List of the probability parameters for modeling variation of annual performance (dependent parameters).

Parent Parameters | Description | |
---|---|---|

Aerosol density | Variation factor in aerosol density | The variation factor gives a relative displacement from the trend line of the aerosol density. |

Water precipitation | Variation factor in water precipitation | The variation factor gives a relative displacement from the trend line of water precipitation. |

Direct irradiance | Variation factor in solar irradiance | Calculated by linear coupling of the data of the highest year, normal year, and the lowest year depends on the value of the probability factor. |

Diffused irradiance from the sky | Variation factor in solar irradiance | Calculated by linear coupling of the data of the highest year, normal year, and the lowest year depends on the value of the probability factor. |

The slope angle of the installation ^{1} | Both direct and diffused solar irradiance | Calculated by the optimization calculation given by the datasets of the solar irradiance affected by the variation factor in solar irradiance (parent parameter). |

^{1}Meaning that the slope angle is determined simultaneously by the combination of the optimized bandgaps in the junctions by the measured one year irradiance (affected in the measurement in the first step in Figure 2).

Bandgap Energy (eV) from Top to Bottom Junction | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

2J | 1.72 ± 0.03 | 1.12 ± 0.02 | ||||||||

3J | 1.89 ± 0.05 | 1.33 ± 0.07 | 0.89 ± 0.08 | |||||||

4J | 1.99 ± 0.07 | 1.47 ± 0.07 | 1.07 ± 0.09 | 0.73 ± 0.11 | ||||||

5J | 2.11 ± 0.09 | 1.63 ± 0.07 | 1.27 ± 0.09 | 0.97 ± 0.08 | 0.72 ± 0.10 | |||||

6J | 2.08 ± 0.15 | 1.68 ± 0.11 | 1.34 ± 0.11 | 1.07 ± 0.11 | 0.84 ± 0.11 | 0.66 ± 0.11 | ||||

7J | 2.17 ± 0.16 | 1.80 ± 0.11 | 1.48 ± 0.10 | 1.21 ± 0.12 | 0.99 ± 0.11 | 0.77 ± 0.12 | 0.62 ± 0.12 | |||

8J | 2.19 ± 0.16 | 1.84 ± 0.09 | 1.53 ± 0.11 | 1.28 ± 0.10 | 1.05 ± 0.10 | 0.86 ± 0.09 | 0.67 ± 0.09 | 0.55 ± 0.09 | ||

9J | 2.25 ± 0.19 | 1.88 ± 0.13 | 1.61 ± 0.12 | 1.37 ± 0.11 | 1.13 ± 0.10 | 0.95 ± 0.10 | 0.70 ± 0.10 | 0.62 ± 0.08 | 0.52 ± 0.08 | |

10J | 2.21 ± 0.21 | 1.89 ± 0.14 | 1.63 ± 0.14 | 1.40 ± 0.12 | 1.19 ± 0.14 | 1.00 ± 0.11 | 0.82 ± 0.12 | 0.66 ± 0.10 | 0.55 ± 0.09 | 0.46 ± 0.09 |

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## Share and Cite

**MDPI and ACS Style**

Araki, K.; Ota, Y.; Saiki, H.; Tawa, H.; Nishioka, K.; Yamaguchi, M.
Super-Multi-Junction Solar Cells—Device Configuration with the Potential for More Than 50% Annual Energy Conversion Efficiency (Non-Concentration). *Appl. Sci.* **2019**, *9*, 4598.
https://doi.org/10.3390/app9214598

**AMA Style**

Araki K, Ota Y, Saiki H, Tawa H, Nishioka K, Yamaguchi M.
Super-Multi-Junction Solar Cells—Device Configuration with the Potential for More Than 50% Annual Energy Conversion Efficiency (Non-Concentration). *Applied Sciences*. 2019; 9(21):4598.
https://doi.org/10.3390/app9214598

**Chicago/Turabian Style**

Araki, Kenji, Yasuyuki Ota, Hiromu Saiki, Hiroki Tawa, Kensuke Nishioka, and Masafumi Yamaguchi.
2019. "Super-Multi-Junction Solar Cells—Device Configuration with the Potential for More Than 50% Annual Energy Conversion Efficiency (Non-Concentration)" *Applied Sciences* 9, no. 21: 4598.
https://doi.org/10.3390/app9214598