Limiting efficiency of indoor silicon photovoltaic devices

Vahid Bahrami-Yekta; Thomas Tiedje

doi:10.1364/OE.26.028238

Optics Express
Vol. 26,
Issue 22,
pp. 28238-28248
(2018)
•https://doi.org/10.1364/OE.26.028238

Limiting efficiency of indoor silicon photovoltaic devices

Vahid Bahrami-Yekta and Thomas Tiedje

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Vahid Bahrami-Yekta and Thomas Tiedje, "Limiting efficiency of indoor silicon photovoltaic devices," Opt. Express 26, 28238-28248 (2018)

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Abstract

Energy harvesting from ambient light can be used to power wireless sensors and other standalone electronic devices. The intensity of light used for illumination is 300-3000x lower than sunlight and the spectrum of artificial light is normally narrowly concentrated in the visible range. As a result, the optimal design of photovoltaic devices for energy harvesting from ambient light differs from conventional solar cells. We calculate the maximum efficiency for Si photovoltaic devices operating under conditions expected indoors as a function of the cell thickness, taking into account the relevant properties of Si. The optimum thickness for devices operating under 250 lux illumination produced by white LED’s is 1.8 µm and the efficiency is 29.0%, whereas for direct sunlight, the optimum thickness is much larger at 109 µm, while the maximum efficiency is almost the same (29.7%). The relative efficiency increases logarithmically with light intensity at 8.5% per decade.

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References

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Year
Author
Publication

V. Bhatnagar and P. Owende, “Energy Harvesting for Assistive and Mobile Applications,” Energy Sci. Eng. 3(3), 153–173 (2015).
[Crossref]
M. Gorlatova, A. Wallwater, and G. Zussman, “Networking Low Power Energy Harvesting Devices: Measurements and Algorithms,” IEEE Trans. Mobile Comput. 12(9), 1853–1865 (2013).
[Crossref]
A. Roy, A. Klinefelter, F. B. Yahya, X. Chen, L. P. Gonzalez-Guerrero, C. J. Lukas, D. A. Kamakshi, J. Boley, K. Craig, M. Faisal, S. Oh, N. E. Roberts, Y. Shakhsheer, A. Shrivastava, D. P. Vasudevan, D. D. Wentzloff, and B. H. Calhoun, “A 6.45 μW Self-Powered SoC With Integrated Energy-Harvesting Power Management and ULP Asymmetric Radios for Portable Biomedical Systems,” IEEE Trans. Biomed. Circuits Syst. 9(6), 862–874 (2015).
[Crossref] [PubMed]
Z. L. Wang and W. Wu, “Nanotechnology-enabled energy harvesting for self-powered micro-/nanosystems,” Angew. Chem. Int. Ed. Engl. 51(47), 11700–11721 (2012).
[Crossref] [PubMed]
B. Minnaert and P. Veelaert, “A Proposal for Typical Artificial Light Sources for the Characterization of Indoor Photovoltaic Applications,” Energies 7(3), 1500–1516 (2014).
[Crossref]
M. A. Green, K. Emery, Y. Hishikawa, W. Warta, E. D. Dunlop, D. H. Levi, and A. W. Y. Ho-Baillie, “Solar cell efficiency tables (version 49),” Prog. Photovolt. Res. Appl. 25(1), 3–13 (2017).
[Crossref]
M. Freunek, M. Freunek, and L. M. Reindl, “Maximum Efficiencies of Indoor Photovoltaic Devices,” IEEE J. Photovoltaics 3(1), 59–64 (2013).
[Crossref]
Design Standards and Guidelines, City of Los Angeles, Department of Public Works, Bureau of Street Lighting, Los Angeles, CA, USA ( http://bsl.lacity.org/downloads/business/bsldesignstandardsandguidelines0507web.pdf )
T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting Efficiency of Silicon Solar Cells,” IEEE Trans. Electron Dev. 31(5), 711–716 (1984).
[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. Photovoltaics 2(3), 303–311 (2012).
[Crossref]
T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983).
[Crossref]
A. Richter, S. W. Glunz, F. Werner, J. Schmidt, and A. Cuevas, “Improved quantitative description of Auger recombination in crystalline silicon,” Phys. Rev. B Condens. Matter Mater. Phys. 86(16), 165202 (2012).
[Crossref]
A. Schenk, “Finite-temperature full random-phase approximation model of band gap narrowing for silicon device simulation,” J. Appl. Phys. 84(7), 3684–3695 (1998).
[Crossref]
M. Rüdiger, J. Greulich, A. Richter, and M. Hermle, “Parameterization of Free Carrier Absorption in Highly Doped Silicon for Solar Cells,” IEEE Trans. Electron Dev. 60(7), 2156–2163 (2013).
[Crossref]
C. H. Su, “Energy band gap, intrinsic carrier concentration, and Fermi level of CdTe bulk crystal between 304 and 1067K,” J. Appl. Phys. 103(8), 084903 (2008).
[Crossref]
E. D. Palik, Handbook of Optical Constants of Solids (Elsevier, 1998).
https://www.nrel.gov
https://www.osram-americas.com
https://www.noao.edu
M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
[Crossref]
A. Richter, M. Hermle, S. W. Glunz, “Reassessment of the Limiting Efficiency for Crystalline Silicon Solar Cells”, IEEE J. Photovoltaics, 3, 4 1184-1191 (2013).
J. F. Randall and J. Jacot, “The performance and modelling of 8 photovoltaic materials under variable light intensity and spectra,” World Renewable Energy Congress VII & Expo (2002).
I. Mathews, P. J. King, F. Stafford, and R. Frizzell, “Performance of III–V Solar Cells as Indoor Light Energy Harvesters,” IEEE J. Photovoltaics 6(1), 2030–2035 (2015).

2017 (1)

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, E. D. Dunlop, D. H. Levi, and A. W. Y. Ho-Baillie, “Solar cell efficiency tables (version 49),” Prog. Photovolt. Res. Appl. 25(1), 3–13 (2017).
[Crossref]

2015 (3)

V. Bhatnagar and P. Owende, “Energy Harvesting for Assistive and Mobile Applications,” Energy Sci. Eng. 3(3), 153–173 (2015).
[Crossref]

A. Roy, A. Klinefelter, F. B. Yahya, X. Chen, L. P. Gonzalez-Guerrero, C. J. Lukas, D. A. Kamakshi, J. Boley, K. Craig, M. Faisal, S. Oh, N. E. Roberts, Y. Shakhsheer, A. Shrivastava, D. P. Vasudevan, D. D. Wentzloff, and B. H. Calhoun, “A 6.45 μW Self-Powered SoC With Integrated Energy-Harvesting Power Management and ULP Asymmetric Radios for Portable Biomedical Systems,” IEEE Trans. Biomed. Circuits Syst. 9(6), 862–874 (2015).
[Crossref] [PubMed]

I. Mathews, P. J. King, F. Stafford, and R. Frizzell, “Performance of III–V Solar Cells as Indoor Light Energy Harvesters,” IEEE J. Photovoltaics 6(1), 2030–2035 (2015).

2014 (1)

B. Minnaert and P. Veelaert, “A Proposal for Typical Artificial Light Sources for the Characterization of Indoor Photovoltaic Applications,” Energies 7(3), 1500–1516 (2014).
[Crossref]

2013 (3)

M. Rüdiger, J. Greulich, A. Richter, and M. Hermle, “Parameterization of Free Carrier Absorption in Highly Doped Silicon for Solar Cells,” IEEE Trans. Electron Dev. 60(7), 2156–2163 (2013).
[Crossref]

M. Gorlatova, A. Wallwater, and G. Zussman, “Networking Low Power Energy Harvesting Devices: Measurements and Algorithms,” IEEE Trans. Mobile Comput. 12(9), 1853–1865 (2013).
[Crossref]

M. Freunek, M. Freunek, and L. M. Reindl, “Maximum Efficiencies of Indoor Photovoltaic Devices,” IEEE J. Photovoltaics 3(1), 59–64 (2013).
[Crossref]

2012 (3)

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

Z. L. Wang and W. Wu, “Nanotechnology-enabled energy harvesting for self-powered micro-/nanosystems,” Angew. Chem. Int. Ed. Engl. 51(47), 11700–11721 (2012).
[Crossref] [PubMed]

A. Richter, S. W. Glunz, F. Werner, J. Schmidt, and A. Cuevas, “Improved quantitative description of Auger recombination in crystalline silicon,” Phys. Rev. B Condens. Matter Mater. Phys. 86(16), 165202 (2012).
[Crossref]

2008 (2)

C. H. Su, “Energy band gap, intrinsic carrier concentration, and Fermi level of CdTe bulk crystal between 304 and 1067K,” J. Appl. Phys. 103(8), 084903 (2008).
[Crossref]

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
[Crossref]

1998 (1)

A. Schenk, “Finite-temperature full random-phase approximation model of band gap narrowing for silicon device simulation,” J. Appl. Phys. 84(7), 3684–3695 (1998).
[Crossref]

1984 (1)

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting Efficiency of Silicon Solar Cells,” IEEE Trans. Electron Dev. 31(5), 711–716 (1984).
[Crossref]

1983 (1)

T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983).
[Crossref]

Abeles, B.

T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983).
[Crossref]

Bhatnagar, V.

V. Bhatnagar and P. Owende, “Energy Harvesting for Assistive and Mobile Applications,” Energy Sci. Eng. 3(3), 153–173 (2015).
[Crossref]

Boley, J.

Brooks, B. G.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting Efficiency of Silicon Solar Cells,” IEEE Trans. Electron Dev. 31(5), 711–716 (1984).
[Crossref]

Calhoun, B. H.

Cebulka, J. M.

T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983).
[Crossref]

Chen, X.

Cody, G. D.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting Efficiency of Silicon Solar Cells,” IEEE Trans. Electron Dev. 31(5), 711–716 (1984).
[Crossref]

Craig, K.

Cuevas, A.

Dunlop, E. D.

Emery, K.

Faisal, M.

Freunek, M.

M. Freunek, M. Freunek, and L. M. Reindl, “Maximum Efficiencies of Indoor Photovoltaic Devices,” IEEE J. Photovoltaics 3(1), 59–64 (2013).
[Crossref]

Frizzell, R.

I. Mathews, P. J. King, F. Stafford, and R. Frizzell, “Performance of III–V Solar Cells as Indoor Light Energy Harvesters,” IEEE J. Photovoltaics 6(1), 2030–2035 (2015).

Glunz, S. W.

Gonzalez-Guerrero, L. P.

Gorlatova, M.

M. Gorlatova, A. Wallwater, and G. Zussman, “Networking Low Power Energy Harvesting Devices: Measurements and Algorithms,” IEEE Trans. Mobile Comput. 12(9), 1853–1865 (2013).
[Crossref]

Green, M. A.

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
[Crossref]

Greulich, J.

Hermle, M.

Hishikawa, Y.

Ho-Baillie, A. W. Y.

Kamakshi, D. A.

King, P. J.

I. Mathews, P. J. King, F. Stafford, and R. Frizzell, “Performance of III–V Solar Cells as Indoor Light Energy Harvesters,” IEEE J. Photovoltaics 6(1), 2030–2035 (2015).

Klinefelter, A.

Kurtz, S. R.

Levi, D. H.

Lukas, C. J.

Mathews, I.

I. Mathews, P. J. King, F. Stafford, and R. Frizzell, “Performance of III–V Solar Cells as Indoor Light Energy Harvesters,” IEEE J. Photovoltaics 6(1), 2030–2035 (2015).

Miller, O. D.

Minnaert, B.

B. Minnaert and P. Veelaert, “A Proposal for Typical Artificial Light Sources for the Characterization of Indoor Photovoltaic Applications,” Energies 7(3), 1500–1516 (2014).
[Crossref]

Oh, S.

Owende, P.

V. Bhatnagar and P. Owende, “Energy Harvesting for Assistive and Mobile Applications,” Energy Sci. Eng. 3(3), 153–173 (2015).
[Crossref]

Pelz, J.

T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983).
[Crossref]

Reindl, L. M.

M. Freunek, M. Freunek, and L. M. Reindl, “Maximum Efficiencies of Indoor Photovoltaic Devices,” IEEE J. Photovoltaics 3(1), 59–64 (2013).
[Crossref]

Richter, A.

Roberts, N. E.

Roy, A.

Rüdiger, M.

Schenk, A.

A. Schenk, “Finite-temperature full random-phase approximation model of band gap narrowing for silicon device simulation,” J. Appl. Phys. 84(7), 3684–3695 (1998).
[Crossref]

Schmidt, J.

Shakhsheer, Y.

Shrivastava, A.

Stafford, F.

I. Mathews, P. J. King, F. Stafford, and R. Frizzell, “Performance of III–V Solar Cells as Indoor Light Energy Harvesters,” IEEE J. Photovoltaics 6(1), 2030–2035 (2015).

Su, C. H.

C. H. Su, “Energy band gap, intrinsic carrier concentration, and Fermi level of CdTe bulk crystal between 304 and 1067K,” J. Appl. Phys. 103(8), 084903 (2008).
[Crossref]

Tiedje, T.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting Efficiency of Silicon Solar Cells,” IEEE Trans. Electron Dev. 31(5), 711–716 (1984).
[Crossref]

T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983).
[Crossref]

Vasudevan, D. P.

Veelaert, P.

B. Minnaert and P. Veelaert, “A Proposal for Typical Artificial Light Sources for the Characterization of Indoor Photovoltaic Applications,” Energies 7(3), 1500–1516 (2014).
[Crossref]

Wallwater, A.

M. Gorlatova, A. Wallwater, and G. Zussman, “Networking Low Power Energy Harvesting Devices: Measurements and Algorithms,” IEEE Trans. Mobile Comput. 12(9), 1853–1865 (2013).
[Crossref]

Wang, Z. L.

Z. L. Wang and W. Wu, “Nanotechnology-enabled energy harvesting for self-powered micro-/nanosystems,” Angew. Chem. Int. Ed. Engl. 51(47), 11700–11721 (2012).
[Crossref] [PubMed]

Warta, W.

Wentzloff, D. D.

Werner, F.

Wu, W.

Z. L. Wang and W. Wu, “Nanotechnology-enabled energy harvesting for self-powered micro-/nanosystems,” Angew. Chem. Int. Ed. Engl. 51(47), 11700–11721 (2012).
[Crossref] [PubMed]

Yablonovitch, E.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting Efficiency of Silicon Solar Cells,” IEEE Trans. Electron Dev. 31(5), 711–716 (1984).
[Crossref]

Yahya, F. B.

Zussman, G.

M. Gorlatova, A. Wallwater, and G. Zussman, “Networking Low Power Energy Harvesting Devices: Measurements and Algorithms,” IEEE Trans. Mobile Comput. 12(9), 1853–1865 (2013).
[Crossref]

Angew. Chem. Int. Ed. Engl. (1)

Z. L. Wang and W. Wu, “Nanotechnology-enabled energy harvesting for self-powered micro-/nanosystems,” Angew. Chem. Int. Ed. Engl. 51(47), 11700–11721 (2012).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983).
[Crossref]

Energies (1)

B. Minnaert and P. Veelaert, “A Proposal for Typical Artificial Light Sources for the Characterization of Indoor Photovoltaic Applications,” Energies 7(3), 1500–1516 (2014).
[Crossref]

Energy Sci. Eng. (1)

V. Bhatnagar and P. Owende, “Energy Harvesting for Assistive and Mobile Applications,” Energy Sci. Eng. 3(3), 153–173 (2015).
[Crossref]

IEEE J. Photovoltaics (3)

M. Freunek, M. Freunek, and L. M. Reindl, “Maximum Efficiencies of Indoor Photovoltaic Devices,” IEEE J. Photovoltaics 3(1), 59–64 (2013).
[Crossref]

I. Mathews, P. J. King, F. Stafford, and R. Frizzell, “Performance of III–V Solar Cells as Indoor Light Energy Harvesters,” IEEE J. Photovoltaics 6(1), 2030–2035 (2015).

IEEE Trans. Biomed. Circuits Syst. (1)

IEEE Trans. Electron Dev. (2)

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting Efficiency of Silicon Solar Cells,” IEEE Trans. Electron Dev. 31(5), 711–716 (1984).
[Crossref]

IEEE Trans. Mobile Comput. (1)

M. Gorlatova, A. Wallwater, and G. Zussman, “Networking Low Power Energy Harvesting Devices: Measurements and Algorithms,” IEEE Trans. Mobile Comput. 12(9), 1853–1865 (2013).
[Crossref]

J. Appl. Phys. (2)

C. H. Su, “Energy band gap, intrinsic carrier concentration, and Fermi level of CdTe bulk crystal between 304 and 1067K,” J. Appl. Phys. 103(8), 084903 (2008).
[Crossref]

A. Schenk, “Finite-temperature full random-phase approximation model of band gap narrowing for silicon device simulation,” J. Appl. Phys. 84(7), 3684–3695 (1998).
[Crossref]

Phys. Rev. B Condens. Matter Mater. Phys. (1)

Prog. Photovolt. Res. Appl. (1)

Sol. Energy Mater. Sol. Cells (1)

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
[Crossref]

Other (7)

A. Richter, M. Hermle, S. W. Glunz, “Reassessment of the Limiting Efficiency for Crystalline Silicon Solar Cells”, IEEE J. Photovoltaics, 3, 4 1184-1191 (2013).

J. F. Randall and J. Jacot, “The performance and modelling of 8 photovoltaic materials under variable light intensity and spectra,” World Renewable Energy Congress VII & Expo (2002).

Design Standards and Guidelines, City of Los Angeles, Department of Public Works, Bureau of Street Lighting, Los Angeles, CA, USA ( http://bsl.lacity.org/downloads/business/bsldesignstandardsandguidelines0507web.pdf )

E. D. Palik, Handbook of Optical Constants of Solids (Elsevier, 1998).

https://www.nrel.gov

https://www.osram-americas.com

https://www.noao.edu

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Fig. 1 The spectra of three different light sources: sunlight (AM1.5G), white LED (2700 K) and F3, white fluorescent lamp, standard illumination equivalent to 3450 K. The spectra are normalized to their peak values. The solar spectrum is from the National Renewable Energy Lab website [17]. The white LED and F3 spectra are taken from the Osram ColorCalculator software [18].

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Fig. 2 The efficiency of Si solar cells as a function of thickness with randomly textured antireflection coated front surface and perfectly reflecting back surface with three different light sources: sunlight (AM1.5G), white LED (2700 K), and F3 white fluorescent lamp. The light source intensities were all normalized to 250 lux, an appropriate illumination level for an easy office environment.

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Fig. 3 Summary of the relative magnitudes of the various loss processes in Si solar cells under (a) AM 1.5 global solar illumination and b) white LED at an illumination of 250 lux at the maximum power point. The losses are represented as currents.

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Fig. 4 The calculated efficiency of silicon solar cells illuminated by the AM1.5G solar spectrum at three different intensities, as indicated. The maximum efficiency and optimum solar cell thickness increase with light intensity. The low intensity curve (10⁻⁶x one sun) is approximately the intensity of moonlight.

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Fig. 5 Calculated power output as a function of illumination intensity for Si photovoltaic cells illuminated by a light spectrum matching AM1.5G, triangles, and by a white LED (2700K), circles. The electrical output is a power law function of the light intensity with exponent 1.037.

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Fig. 6 Optimum thickness as a function of illumination intensity for photovoltaic cells illuminated by a light spectrum matching AM1.5G and by a white LED (2700K).

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Fig. 7 Calculated output voltage at maximum power as a function of illumination intensity for silicon photovoltaic cells illuminated by a light spectrum matching AM1.5G (triangles) and by a white LED (2700K) (circles).

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Tables (2)

Table 1 Material parameters for crystalline silicon, GaAs and CdTe used in this paper

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Table 2 Calculated maximum solar cell efficiencies for sunlight (AM1.5G) and white LED (2700 K) illumination. The Si solar cell thicknesses are optimized for the light source and illumination level while the GaAs and CdTe solar cells have a fixed thickness of 0.5 µm. Because of strong absorption at the bandgap and abrupt absorption edges the GaAs and CdTe efficiencies have a weak thickness dependence above a threshold thickness. Sun is the AM1.5G spectrum, F3 is a white fluorescent lamp, and LED is a white LED with a colour temperature of 2700K.

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Equations (4)

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

A = \frac{α}{α + 1 / 4 n^{2} L}

(α_{1} + \frac{1}{4 n^{2} L}) e^{μ / k T} \iint A (E) b_{n} (E, T) d E d Ω + C (n) = \frac{I_{S C}}{e L} (1 - f)

n^{2} = n_{i}^{2} e^{μ / k T}

C (n) = 3.0 \times 10^{- 29} n^{2.92}

	Auger recombination (cm⁻³s⁻¹)	Intrinsic carrier conc. (cm⁻³)	Free carrier absorption (cm⁻¹)	IR refractive index	Bandgap (eV)
c-Si	$3.0 \times 10^{- 29} n^{2.92}$ [12]	8.28 × 10⁹ [13]	5.8 × 10⁻¹⁸ × n [14]	3.5355 [9]	1.12 [9]
GaAs	$7 \times 10^{- 30} n^{3}$ [10]	2.1 × 10⁶ [10]	0 [10]	3.66 [10]	1.42
CdTe	0	2 × 10⁶ [15]	0	2.86 [16]	1.5

Spectrum	Sun	Sun	F3	LED
Illumination (lux)	121472	250	250	250
Total incident power (mW/cm²)	100.04	0.20	0.07	0.08
Si efficiency (%)	29.7	24.5	27.0	29.0
Si optimum thickness (µm)	109	69	1.2	1.8
GaAs efficiency (%)	32.8	27.7	37.1	40.3
CdTe efficiency (%)	31.9	27.3	40.3	43.7

	Auger recombination (cm⁻³s⁻¹)	Intrinsic carrier conc. (cm⁻³)	Free carrier absorption (cm⁻¹)	IR refractive index	Bandgap (eV)
c-Si	$3.0 \times 10^{- 29} n^{2.92}$ [12]	8.28 × 10⁹ [13]	5.8 × 10⁻¹⁸ × n [14]	3.5355 [9]	1.12 [9]
GaAs	$7 \times 10^{- 30} n^{3}$ [10]	2.1 × 10⁶ [10]	0 [10]	3.66 [10]	1.42
CdTe	0	2 × 10⁶ [15]	0	2.86 [16]	1.5

Spectrum	Sun	Sun	F3	LED
Illumination (lux)	121472	250	250	250
Total incident power (mW/cm²)	100.04	0.20	0.07	0.08
Si efficiency (%)	29.7	24.5	27.0	29.0
Si optimum thickness (µm)	109	69	1.2	1.8
GaAs efficiency (%)	32.8	27.7	37.1	40.3
CdTe efficiency (%)	31.9	27.3	40.3	43.7