Abstract

We expand in detail on a new approach to current matching in double junction solar cells that increases the theoretical maximum efficiencies attainable for many bandgap pairs. In this approach, either or both cell types are repeated one or more times, which provides for improved current matching and 2-terminal operation for a wide variety of bandgap pairs, opening up the opportunity to utilize materials not previously considered. While a multijunction design in which the bandgap of every cell is fully optimized will have higher efficiency, this approach achieves simplicity and potential cost savings by using only two cell types. Of particular interest are tandem cells with silicon as the base cell, where significant improvements in efficiency can be achieved with composite-cell current matching. This is illustrated for a 2.19 eV/Si(3) device with a theoretical maximum efficiency of 42.9%, well in excess of the 27.7% achievable for a 2.19 eV/Si device. The benefits of utilizing composite-cell stacks in Si-based triple-junction devices are also discussed.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (6)

M. A. Green, Y. Hishikawa, E. D. Dunlop, D. H. Levi, J. Hohl-Ebinger, and A. W. Y. Ho-Baillie, “Solar cell efficiency tables (version 52),” Prog. Photovolt. Res. Appl. 26(7), 427–436 (2018).
[Crossref]

R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 3(4), 326–333 (2018).
[Crossref]

M. C. A. York, A. Mailhot, A. Boucherif, R. Arès, V. Aimez, and S. Fafard, “Challenges and strategies for implementing the vertical epitaxial heterostructure architecture (VEHSA) design for concentrated photovoltaic applications,” Sol. Energy Mater. Sol. Cells 181, 46–52 (2018).
[Crossref]

N. Jain, K. L. Schulte, J. F. Geisz, D. J. Friedman, R. M. France, E. E. Perl, A. G. Norman, H. L. Guthrey, and M. A. Steiner, “High-efficiency inverted metamorphic 1.7/1.1 eV GaInAsP/GaInAs dual-junction solar cells,” Appl. Phys. Lett. 112(5), 053905 (2018).
[Crossref]

F. Sahli, J. Werner, B. A. Kamino, M. Bräuninger, R. Monnard, B. Paviet-Salomon, L. Barraud, L. Ding, J. J. Diaz Leon, D. Sacchetto, G. Cattaneo, M. Despeisse, M. Boccard, S. Nicolay, Q. Jeangros, B. Niesen, and C. Ballif, “Fully textured monolithic perovskite/silicon tandem solar cells with 25.2% power conversion efficiency,” Nat. Mater. 17(9), 820–826 (2018).
[Crossref] [PubMed]

Z. Xiao, Y. Zhou, H. Hosono, T. Kamiya, and N. P. Padture, “Bandgap optimization of perovskite semiconductors for photovoltaic applications,” Chemistry 24(10), 2305–2316 (2018).
[Crossref] [PubMed]

2017 (6)

Z. Ren, H. Liu, Z. Liu, C. S. Tan, A. G. Aberle, T. Buonassisi, and I. M. Peters, “The GaAs/GaAs/Si solar cell – towards current matching in an integrated two terminal tandem,” Sol. Energy Mater. Sol. Cells 160, 94–100 (2017).
[Crossref]

F. Proulx, M. C. A. York, P. O. Provost, R. Arès, V. Aimez, D. P. Masson, and S. Fafard, “Measurement of strong photon recycling in ultra-thin GaAs n/p junctions monolithically integrated in high-photovoltage vertical epitaxial heterostructure architectures with conversion efficiencies exceeding 60%,” Phys. Status Solidi Rapid Res. Lett. 11(2), 1600385 (2017).
[Crossref]

J. F. Geisz, M. A. Steiner, N. Jain, K. L. Schulte, R. M. France, W. E. McMahon, E. E. Perl, K. A. W. Horowitz, and D. J. Friedman, “Pathway to 50% efficient inverted metamorphic concentrator solar cells,” AIP Conf. Proc. 1881, 040003 (2017).
[Crossref]

K. Yoshikawa, H. Kawasaki, W. Yoshida, T. Irie, K. Konishi, K. Nakano, T. Uto, D. Adachi, M. Kanematsu, H. Uzu, and K. Yamamoto, “Silicon heterojunction solar cell with interdigitated back contacts for a photoconversion efficiency over 26%,” Nat. Energy 2(5), 17032 (2017).
[Crossref]

S. Essig, C. Allebé, T. Remo, J. F. Geisz, M. A. Steiner, K. Horowitz, L. Barraud, J. S. Ward, M. Schnabel, A. Descoeudres, D. L. Young, M. Woodhouse, M. Despeisse, C. Ballif, and A. Tamboli, “Raising the one-sun conversion efficiency of III–V-Si solar cells to 32.8% for two junctions and 35.9% for three junctions,” Nat. Energy 2(9), 17144 (2017).
[Crossref]

F. T. Si, O. Isabella, and M. Zeman, “Too many junctions? A case study of multijunction thin-film silicon solar cells,” Adv. Sustainable Syst. 1(10), 1700077 (2017).
[Crossref]

2016 (3)

H. Sai, T. Matsui, and K. Matsubara, “Stabilized 14.0%-efficient triple-junction thin-film silicon solar cell,” Appl. Phys. Lett. 109(18), 183506 (2016).
[Crossref]

S. Fafard, F. Proulx, M. C. A. York, L. S. Richard, P. O. Provost, R. Arès, V. Aimez, and D. P. Masson, “High-photovoltage GaAs vertical epitaxial monolithic heterostructures with 20 thin p/n junctions and a conversion efficiency of 60%,” Appl. Phys. Lett. 109(13), 131107 (2016).
[Crossref]

A. Polman, M. Knight, E. C. Garnett, B. Ehrler, and W. C. Sinke, “Photovoltaic materials: Present efficiencies and future challenges,” Science 352(6283), aad4424 (2016).
[Crossref] [PubMed]

2015 (2)

H. Sai, T. Matsui, T. Koida, K. Matsubara, M. Kondo, S. Sugiyama, H. Katayama, Y. Takeuchi, and I. Yoshida, “Triple-junction thin-film silicon solar cell fabricated on periodically textured substrate with a stabilized efficiency of 13.6%,” Appl. Phys. Lett. 106(21), 213902 (2015).
[Crossref]

M. Yao, S. Cong, S. Arab, N. Huang, M. L. Povinelli, S. B. Cronin, P. D. Dapkus, and C. Zhou, “Tandem solar cells using GaAs nanowires on Si: design, fabrication, and observation of voltage addition,” Nano Lett. 15(11), 7217–7224 (2015).
[Crossref] [PubMed]

2014 (1)

J. Yang, Z. Peng, D. Cheong, and R. Kleiman, “Fabrication of high-efficiency III–V on silicon multijunction solar cells by direct metal interconnect,” IEEE J. Photovolt. 4(4), 1149–1155 (2014).
[Crossref]

2013 (3)

S. Kim, J.-W. Chung, H. Lee, J. Park, Y. Heo, and H.-M. Lee, “Remarkable progress in thin-film silicon solar cells using high-efficiency triple-junction technology,” Sol. Energy Mater. Sol. Cells 119, 26–35 (2013).
[Crossref]

A. Richter, M. Hermle, and S. W. Glunz, “Reassessment of the limiting efficiency for crystalline silicon solar cells,” IEEE J. Photovoltaics 3(4), 1184–1191 (2013).
[Crossref]

M. A. Steiner, J. F. Geisz, I. García, D. J. Friedman, A. Duda, W. J. Olavarria, M. Young, D. Kuciauskas, and S. R. Kurtz, “Effects of internal luminescence and internal optics on Voc and Jsc of III-V solar cells,” IEEE J. Photovolt. 3(4), 1437–1442 (2013).
[Crossref]

2012 (4)

J. Yang, J. Goguen, and R. Kleiman, “Silicon solar cell with integrated tunnel junction for multi-junction photovoltaic applications,” IEEE Electron Device Lett. 33(12), 1732–1734 (2012).
[Crossref]

O. D. Miller, E. Yablonovitch, and S. R. Kurtz, “Strong internal and external luminescence as solar cells approach the Shockley–Queisser limit,” IEEE J. Photovolt. 2(3), 303–311 (2012).
[Crossref]

R. Peña and C. Algora, “One-watt fiber-based power-by-light system for satellite applications,” Prog. Photovolt. Res. Appl. 20(1), 117–123 (2012).
[Crossref]

H. Mizuno, K. Makita, and K. Matsubara, “Electrical and optical interconnection for mechanically stacked multi-junction solar cells mediated by metal nanoparticle arrays,” Appl. Phys. Lett. 101(19), 191111 (2012).
[Crossref]

2009 (1)

J. Schubert, E. Oliva, F. Dimroth, W. Guter, R. Loeckenhoff, and A. W. Bett, “High-voltage GaAs photovoltaic laser power converters,” IEEE Trans. Electron Dev. 56(2), 170–175 (2009).
[Crossref]

2008 (1)

S. P. Bremner, M. Y. Levy, and C. B. Honsberg, “Analysis of tandem solar cell efficiencies under AM1.5G spectrum using a rapid flux calculation method,” Prog. Photovolt. Res. Appl. 16(3), 225–233 (2008).
[Crossref]

2003 (1)

K. Feldrapp, R. Horbelt, R. Auer, and R. Brendel, “Thin-film (25.5 μm) solar cells from layer transfer using porous silicon with 32.7 mA/cm2 short-circuit current density,” Prog. Photovolt. Res. Appl. 11(2), 105–112 (2003).
[Crossref]

2000 (1)

M. W. Dashiell, R. T. Troeger, S. L. Rommel, T. N. Adam, P. R. Berger, C. Guedj, J. Kolodzey, A. C. Seabaugh, and R. Lake, “Current-voltage characteristics of high current density silicon Esaki diodes grown by molecular beam epitaxy and the influence of thermal annealing,” IEEE Trans. Electron Dev. 47(9), 1707–1714 (2000).
[Crossref]

1997 (1)

T. Soga, K. Baskar, T. Kato, T. Jimbo, and M. Umeno, “MOCVD growth of high efficiency current-matched AlGaAs/Si tandem solar cell,” J. Cryst. Growth 174(1-4), 579–584 (1997).
[Crossref]

1995 (2)

C. A. Zorman, A. J. Fleischman, A. S. Dewa, M. Mehregany, C. Jacob, S. Nishino, and P. Pirouz, “Epitaxial growth of 3C–SiC films on 4 in. diam (100) silicon wafers by atmospheric pressure chemical vapor deposition,” J. Appl. Phys. 78(8), 5136–5138 (1995).
[Crossref]

M. A. Green and M. Keevers, “Optical properties of intrinsic silicon at 300 K,” Prog. Photovolt. Res. Appl. 3(3), 189–192 (1995).
[Crossref]

1990 (1)

S. R. Kurtz, P. Faine, and J. M. Olson, “Modeling of two-junction, series-connected tandem solar cells using top-cell thickness as an adjustable parameter,” J. Appl. Phys. 68(4), 1890–1895 (1990).
[Crossref]

1987 (1)

M. E. Nell and A. M. Barnett, “The spectral p-n junction model for tandem solar-cell design,” IEEE Trans. Electron Dev. 34(2), 257–266 (1987).
[Crossref]

1986 (1)

M. A. Green, “Crystalline and polycrystalline silicon tandem junction solar cells: theoretical advantages,” Sol. Cells 18(1), 31–40 (1986).
[Crossref]

1980 (2)

C. H. Henry, “Limiting efficiencies of ideal single and multiple energy gap terrestrial solar cells,” J. Appl. Phys. 51(8), 4494–4500 (1980).
[Crossref]

A. De Vos, “Detailed balance limit of the efficiency of tandem solar cells,” J. Phys. D Appl. Phys. 13(5), 839–846 (1980).
[Crossref]

1961 (1)

W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
[Crossref]

Aberle, A. G.

Z. Ren, H. Liu, Z. Liu, C. S. Tan, A. G. Aberle, T. Buonassisi, and I. M. Peters, “The GaAs/GaAs/Si solar cell – towards current matching in an integrated two terminal tandem,” Sol. Energy Mater. Sol. Cells 160, 94–100 (2017).
[Crossref]

Adachi, D.

K. Yoshikawa, H. Kawasaki, W. Yoshida, T. Irie, K. Konishi, K. Nakano, T. Uto, D. Adachi, M. Kanematsu, H. Uzu, and K. Yamamoto, “Silicon heterojunction solar cell with interdigitated back contacts for a photoconversion efficiency over 26%,” Nat. Energy 2(5), 17032 (2017).
[Crossref]

Adam, T. N.

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S. Fafard, F. Proulx, M. C. A. York, L. S. Richard, P. O. Provost, R. Arès, V. Aimez, and D. P. Masson, “High-photovoltage GaAs vertical epitaxial monolithic heterostructures with 20 thin p/n junctions and a conversion efficiency of 60%,” Appl. Phys. Lett. 109(13), 131107 (2016).
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N. Jain, K. L. Schulte, J. F. Geisz, D. J. Friedman, R. M. France, E. E. Perl, A. G. Norman, H. L. Guthrey, and M. A. Steiner, “High-efficiency inverted metamorphic 1.7/1.1 eV GaInAsP/GaInAs dual-junction solar cells,” Appl. Phys. Lett. 112(5), 053905 (2018).
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J. F. Geisz, M. A. Steiner, N. Jain, K. L. Schulte, R. M. France, W. E. McMahon, E. E. Perl, K. A. W. Horowitz, and D. J. Friedman, “Pathway to 50% efficient inverted metamorphic concentrator solar cells,” AIP Conf. Proc. 1881, 040003 (2017).
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M. W. Dashiell, R. T. Troeger, S. L. Rommel, T. N. Adam, P. R. Berger, C. Guedj, J. Kolodzey, A. C. Seabaugh, and R. Lake, “Current-voltage characteristics of high current density silicon Esaki diodes grown by molecular beam epitaxy and the influence of thermal annealing,” IEEE Trans. Electron Dev. 47(9), 1707–1714 (2000).
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W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
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A. Polman, M. Knight, E. C. Garnett, B. Ehrler, and W. C. Sinke, “Photovoltaic materials: Present efficiencies and future challenges,” Science 352(6283), aad4424 (2016).
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N. Jain, K. L. Schulte, J. F. Geisz, D. J. Friedman, R. M. France, E. E. Perl, A. G. Norman, H. L. Guthrey, and M. A. Steiner, “High-efficiency inverted metamorphic 1.7/1.1 eV GaInAsP/GaInAs dual-junction solar cells,” Appl. Phys. Lett. 112(5), 053905 (2018).
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H. Sai, T. Matsui, T. Koida, K. Matsubara, M. Kondo, S. Sugiyama, H. Katayama, Y. Takeuchi, and I. Yoshida, “Triple-junction thin-film silicon solar cell fabricated on periodically textured substrate with a stabilized efficiency of 13.6%,” Appl. Phys. Lett. 106(21), 213902 (2015).
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Z. Ren, H. Liu, Z. Liu, C. S. Tan, A. G. Aberle, T. Buonassisi, and I. M. Peters, “The GaAs/GaAs/Si solar cell – towards current matching in an integrated two terminal tandem,” Sol. Energy Mater. Sol. Cells 160, 94–100 (2017).
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M. W. Dashiell, R. T. Troeger, S. L. Rommel, T. N. Adam, P. R. Berger, C. Guedj, J. Kolodzey, A. C. Seabaugh, and R. Lake, “Current-voltage characteristics of high current density silicon Esaki diodes grown by molecular beam epitaxy and the influence of thermal annealing,” IEEE Trans. Electron Dev. 47(9), 1707–1714 (2000).
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B. S. Richards, A. S. Brown, T. Trupke, R. P. Corkish, and M. A. Green, “β-SiC–based photovoltaic and optical devices,” Proceedings of ANZSES Conference (2002).

Umeno, M.

T. Soga, K. Baskar, T. Kato, T. Jimbo, and M. Umeno, “MOCVD growth of high efficiency current-matched AlGaAs/Si tandem solar cell,” J. Cryst. Growth 174(1-4), 579–584 (1997).
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S. Essig, C. Allebé, T. Remo, J. F. Geisz, M. A. Steiner, K. Horowitz, L. Barraud, J. S. Ward, M. Schnabel, A. Descoeudres, D. L. Young, M. Woodhouse, M. Despeisse, C. Ballif, and A. Tamboli, “Raising the one-sun conversion efficiency of III–V-Si solar cells to 32.8% for two junctions and 35.9% for three junctions,” Nat. Energy 2(9), 17144 (2017).
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R. Cariou, J. Benick, F. Feldmann, O. Höhn, H. Hauser, P. Beutel, N. Razek, M. Wimplinger, B. Bläsi, D. Lackner, M. Hermle, G. Siefer, S. W. Glunz, A. W. Bett, and F. Dimroth, “III–V-on-silicon solar cells reaching 33% photoconversion efficiency in two-terminal configuration,” Nat. Energy 3(4), 326–333 (2018).
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S. Essig, C. Allebé, T. Remo, J. F. Geisz, M. A. Steiner, K. Horowitz, L. Barraud, J. S. Ward, M. Schnabel, A. Descoeudres, D. L. Young, M. Woodhouse, M. Despeisse, C. Ballif, and A. Tamboli, “Raising the one-sun conversion efficiency of III–V-Si solar cells to 32.8% for two junctions and 35.9% for three junctions,” Nat. Energy 2(9), 17144 (2017).
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Z. Xiao, Y. Zhou, H. Hosono, T. Kamiya, and N. P. Padture, “Bandgap optimization of perovskite semiconductors for photovoltaic applications,” Chemistry 24(10), 2305–2316 (2018).
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S. Fafard, F. Proulx, M. C. A. York, L. S. Richard, P. O. Provost, R. Arès, V. Aimez, and D. P. Masson, “High-photovoltage GaAs vertical epitaxial monolithic heterostructures with 20 thin p/n junctions and a conversion efficiency of 60%,” Appl. Phys. Lett. 109(13), 131107 (2016).
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H. Sai, T. Matsui, T. Koida, K. Matsubara, M. Kondo, S. Sugiyama, H. Katayama, Y. Takeuchi, and I. Yoshida, “Triple-junction thin-film silicon solar cell fabricated on periodically textured substrate with a stabilized efficiency of 13.6%,” Appl. Phys. Lett. 106(21), 213902 (2015).
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K. Yoshikawa, H. Kawasaki, W. Yoshida, T. Irie, K. Konishi, K. Nakano, T. Uto, D. Adachi, M. Kanematsu, H. Uzu, and K. Yamamoto, “Silicon heterojunction solar cell with interdigitated back contacts for a photoconversion efficiency over 26%,” Nat. Energy 2(5), 17032 (2017).
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K. Yoshikawa, H. Kawasaki, W. Yoshida, T. Irie, K. Konishi, K. Nakano, T. Uto, D. Adachi, M. Kanematsu, H. Uzu, and K. Yamamoto, “Silicon heterojunction solar cell with interdigitated back contacts for a photoconversion efficiency over 26%,” Nat. Energy 2(5), 17032 (2017).
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Young, D. L.

S. Essig, C. Allebé, T. Remo, J. F. Geisz, M. A. Steiner, K. Horowitz, L. Barraud, J. S. Ward, M. Schnabel, A. Descoeudres, D. L. Young, M. Woodhouse, M. Despeisse, C. Ballif, and A. Tamboli, “Raising the one-sun conversion efficiency of III–V-Si solar cells to 32.8% for two junctions and 35.9% for three junctions,” Nat. Energy 2(9), 17144 (2017).
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Young, M.

M. A. Steiner, J. F. Geisz, I. García, D. J. Friedman, A. Duda, W. J. Olavarria, M. Young, D. Kuciauskas, and S. R. Kurtz, “Effects of internal luminescence and internal optics on Voc and Jsc of III-V solar cells,” IEEE J. Photovolt. 3(4), 1437–1442 (2013).
[Crossref]

Zeman, M.

F. T. Si, O. Isabella, and M. Zeman, “Too many junctions? A case study of multijunction thin-film silicon solar cells,” Adv. Sustainable Syst. 1(10), 1700077 (2017).
[Crossref]

Zhou, C.

M. Yao, S. Cong, S. Arab, N. Huang, M. L. Povinelli, S. B. Cronin, P. D. Dapkus, and C. Zhou, “Tandem solar cells using GaAs nanowires on Si: design, fabrication, and observation of voltage addition,” Nano Lett. 15(11), 7217–7224 (2015).
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Figures (14)

Fig. 1
Fig. 1 An M:N tandem cell with a composite cell current matching (CCCM) structure is illustrated schematically, for M = 2 and N = 3. The device is illuminated from the top and a full back contact and partially shadowing front contacts are shown. The M repeated top cells are made from the same material, with the same bandgap and internally current matched by the choice of layer thicknesses. Similarly, the N repeated bottom cells are made from the same material, with the same bandgap and internally current matched by the choice of layer thicknesses. All cells are linked through tunnel junctions (TJ) or equivalent low loss interconnects.
Fig. 2
Fig. 2 A contour plot of the theoretical maximum efficiency (TME) of a 2 junction (2J) tandem cell, where both top (upper) and bottom (lower) cells are fully absorbing. This is referred to as the 2-terminal full absorption (2T-FA) configuration. The current matching line where the photocurrent from the top and bottom cells is equal is shown in white. The TME is nominally maximized along the current matching line and its peak value of 45.8% occurs at (0.94, 1.60). The TME falls to zero when the lower cell bandgap (EL) is equal to the upper cell bandgap (EU) since the top cell absorption precludes any photocurrent in the bottom cell. The contour lines have increments of 1%. The region where EU < EL is not of practical significance and values are omitted in this and subsequent contour plots.
Fig. 3
Fig. 3 A contour plot of the theoretical maximum efficiency (TME) of a 2J tandem cell, where the top cell absorption is optimized to achieve the maximum efficiency. This is referred to as the 2-terminal optimized absorption (2T-OA) configuration. The current matching line where the photocurrent from the top and bottom cells is equal is shown in white. The TME is nominally maximized along the current matching line and its peak value of 45.8% occurs at (0.94, 1.60) eV. Top layer absorption optimization is only beneficial below the current matching line. For EU = EL the single junction (1J) efficiency is nominally recovered, since the top cell absorption is adjusted to allow half the light to transmit to the bottom cell. The contour lines have increments of 1%.
Fig. 4
Fig. 4 A contour plot of the TME of a 2J tandem cell operated in 3-terminal (3T) configuration where power is captured independently from each cell. This yields the highest efficiency for the two cells at the cost of increased system-level complexity. The efficiency is everywhere higher than the 2T-OA efficiency and a much wider range of bandgap pairs yields high efficiency. The peak value of 46.1% occurs at (0.94, 1.73) eV. The contour lines have increments of 1%.
Fig. 5
Fig. 5 A contour plot of the ratio of the TME for the 2T-OA configuration to that of the 3T configuration. Along the current matched line the ratio is unity. Along the line EU = EL the ratio approaches unity, with minor deviations at low bandgap as explained in the text. The 2T-OA most significantly underperforms the 3T configuration for the combination of intermediate lower bandgap and high upper bandgap. The contour lines have increments of 0.02.
Fig. 6
Fig. 6 A cut through the contour plots of Figs. 2-4 for EL = 1.12 eV, the bandgap of silicon. The TME for the 2T-FA configuration is the lowest of the three curves and peaks at the current matching point, EU = 1.73 eV. Above the current matching point, the bottom cell has excess photocurrent, while below the current matching point the top cell has excess photocurrent. As such, below the current matching point, the efficiency is greatly improved by top cell absorption optimization in the 2T-OA configuration. In the 3T configuration, the efficiency is moderately higher for EU < 1.73 eV and substantially higher for EU > 1.73 eV. For EU = EL = 1.12 eV the efficiency for the 2T-OA configuration is reduced due to the 2kTln(2) offset in photovoltage, resulting from the photocurrent being split evenly by the two cells.
Fig. 7
Fig. 7 The current matching lines for different CCCM configurations, labelled M:N where M is the number of cells comprising the top stack and N is the number of cells comprising the bottom stack. The current matching lines are determined by photocurrent matching only, based on Eq. (2). The conventional current matching line for 2J devices is indicated for the 1:1 structure, as shown in Figs. 2 and 3. For M < N the current matched lines become more closely spaced at higher bandgap. For M > N, the current matched lines asymptotically approach the EU = EL line. Only structures for N + M ≤ 6 have been considered.
Fig. 8
Fig. 8 A contour plot summarizing the maximum TME for the eleven CCCM structures considered. For each M:N structure a contour plot similar to Fig. 3 was calculated, maximizing efficiency for each bandgap pair. The maximum efficiency value from each of the eleven structures is shown for each bandgap pair. Also shown in white are the current matching lines from Fig. 7. Straddling the 1:1 current matching line, the values are identical to Fig. 3. For M < N, successive local maxima occur along their respective current matching lines. For M > N, the maximum values from each structure blend into one another and deviate from their respective current matching lines. The overall efficiency of the CCCM structures is greatly enhanced as compared to the 2T-OA structure of Fig. 3 and is more closely comparable to the 3T values shown in Fig. 4. The contour lines have increments of 1%.
Fig. 9
Fig. 9 This plot indicates which CCCM structure maximizes the TME shown in Fig. 8, which the structures indicated in the legend. The green region indicates the 1:1 structure which is equivalent to the 2T-OA structure. For M < N, the regions of maximum efficiency follow the current matching lines shown in Figs. 7 and 8. For M > N, the region of maximum efficiency follows the sequence indicated in the legend and then reverses, ending at the 1:1 structure along the EU = EL line.
Fig. 10
Fig. 10 A contour plot of the relative improvement (%) of the efficiency of the CCCM structures as indicated by Fig. 8 over the efficiency of the conventional 2T-OA structure as indicated by Fig. 3. Along the 1:1 current matched line and along the EU = EL line there is no improvement since the structures are identical. For M < N there is significant improvement whereas for M > N there is modest improvement, in keeping with the opportunities for improvement indicated by Fig. 5. Each contour line represents a change of 12.2% with respect to adjacent regions.
Fig. 11
Fig. 11 A contour plot of the ratio of the TME for the CCCM configurations shown in Fig. 8 to that of the 3T configuration shown in Fig. 4. This plot shows that near 3T performance is achieved in 2T operation with the CCCM structures over a wide range of bandgap pairs. The contour lines have increments of 0.02.
Fig. 12
Fig. 12 The TME for the eleven M:N CCCM structures is shown for EL = 1.12 eV, the bandgap of silicon. For each structure, the efficiency is peaked near its current matching point. For each structure, just as for the 1:1 structure, above the current matching point the bottom stack has excess photocurrent, while below the current matching point the top stack has excess photocurrent, so top stack absorption optimization is beneficial. The maximum of all of these efficiencies for each value of EU is what is plotted in Fig. 8 along the cut EL = 1.12 eV. Also shown is the 3T efficiency for EL = 1.12 eV, which meets the value for the current matching point of the 1:1 structure at EU = 1.73 eV. The maximum values of the CCCM efficiencies fall below the 3T value at higher and lower values of EU due to kTln(N) deviations as described in the text. For EU = EL = 1.12 eV the efficiency for the CCCM configurations is reduced from its 3T value due to the (M + N)kTln(M + N) offset in photovoltage, resulting from the photocurrent being split evenly amongst the M + N cells.
Fig. 13
Fig. 13 The ratio of the efficiencies of the 2T-FA, 2T-OA (1:1) and the CCCM structures relative to that for 3T operation, for EL = 1.12 eV, the bandgap of silicon. The 2T-OA/3T ratio is a cut through Fig. 5 for EL = 1.12 eV. The CCCM/3T ratio is a cut through Fig. 11 for EL = 1.12 eV. All three curves have value unity for the 1:1 current matching point at EU = 1.73 eV. The 2T-FA/3T ratio shows the narrow range of bandgaps that lead to maximum possible efficiency. This range is greatly expanded by top cell absorption optimization, but only for EU < 1.73 eV. With the CCCM structures, the range of bandgaps that lead to maximum possible efficiency is greatly expanded for EU > 1.73 eV and efficiencies are also modestly improved for EU < 1.73 eV. The CCCM/3T ratio is above 94.0% for all EU values up to 2.46 eV, after which it decreases because the 1:6 structure was not included.
Fig. 14
Fig. 14 The allocation of the spectral current density amongst the four cells for a 1:3 CCCM structure, with a top cell having Eg = 2.19 eV and the bottom cells having Eg = 1.12 eV, the bandgap of silicon. Based on the wavelength dependent absorption of silicon, the thickness of the top and middle silicon cells is set to achieve current matching amongst the silicon cells, with the bottom silicon cell assumed to be fully absorbing. The top cell is assumed to be fully absorbing in this wavelength range. The integral under each of the four curves is equal in order to achieve overall current matching.

Tables (3)

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Table 1 Single junction cell parameters for common photovoltaic materials used in subsequent efficiency calculations.

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Table 2 Device parameters for CCCM structures with 2 materials (2M). Several 1:1 structures are included for reference.

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Table 3 Device parameters for CCCM structures with 3 materials (3M). Several conventional structures are included for reference.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

E L E U ϕ( E )dE= E U ϕ( E )dE
1 N E L E U ϕ( E )dE = 1 M E U ϕ( E )dE .
E Si E T ϕ( E ) e α( E ) W T dE = 2 3 E Si E T ϕ( E )dE ,
E Si E T ϕ( E ) e α( E )( W T + W M ) dE = 1 3 E Si E T ϕ( E )dE .

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