Abstract

In this paper, we report the design of a graphene/silicon thin film solar cell with a novel array of textured dielectric-metal rear side reflectors. In order to minimize the surface recombination and parasitic absorption losses and to increase rear reflections, a unique design of rear side of solar cell reflectors is explored. Our proposed structure geometry has achieved extreme light trapping ability, maximum rear reflections, and high inner scattering, resulting in absorption of up to 90% at a 40° angle of incidence when 1nm thick graphene is used on the top and textured SiO2-Ag was used as the dielectric-metal back reflector. Contrasted with the analogous reference cell devices, the light absorption in the proposed textured solar cell with a back dielectric-metal reflector is essentially improved in the visible to infrared region from 600nm to 1200nm with maximum achieved inner rear reflectance >89% and an attained absorption in the absorber layer from 80% to 90%. The electromagnetic field propagation, reflection, and transmission are calculated by using 2D Maxwell’s and Fresnel equations discretised by the finite element method (FEM). Different configurations, with a plane back reflector/textured dielectric-metal reflector, varied dielectric material/back metal reflector material/texture profile are investigated and reported to attain the best structure configuration. Improved light trapping in the absorber layer and an increase in rear reflection angle (rr(θ)) and photon absorption are accomplished under standard solar irradiation spectrum AM1.5 conditions. The proposed design would have significant impact in promoting optimum solar cell layer assembly with a high light trapping response in a wide variety of silicon thin film solar cells.

© 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 (11)

S. Kim, J. Park, P. D. Phong, C. Shin, S. M. Iftiquar, and J. Yi, “Improving the efficiency of rear emitter silicon solar cell using an optimized n-type silicon oxide front surface field layer,” Sci. Rep. 8(1), 10657 (2018).
[Crossref]

A. Suhail, G. Pan, D. Jenkins, and K. Islam, “Improved efficiency of graphene/Si Schottky junction solar cell based on back contact structure and DUV treatment,” Carbon 129, 520–526 (2018).
[Crossref]

Z. Shi and A. H. Jayatissa, “The impact of graphene on the fabrication of thin film solar cells: Current status and future prospects,” Materials 11(1), 36 (2018).
[Crossref]

M. Lozac’h, S. Nunomura, H. Sai, and K. Matsubara, “Passivation property of ultrathin SiOx:H / a-Si:H stack layers for solar cell applications,” Sol. Energy Mater. Sol. Cells 185, 8–15 (2018).
[Crossref]

P. Fallahazad, N. Naderi, M. J. Eshraghi, and A. Massoudi, “Combination of surface texturing and nanostructure coating for reduction of light reflection in ZnO/Si heterojunction thin film solar cell,” J. Mater. Sci.: Mater. Electron. 29(8), 6289–6296 (2018).
[Crossref]

S. Zhang, M. Liu, W. Liu, Y. Liu, Z. Li, and X. Wang, “Absorption enhancement in thin film solar cells with bilayer silver nanoparticle arrays Absorption enhancement in thin film solar cells with bilayer silver nanoparticle arrays,” J. Phys. Commun. 2(5), 055032 (2018).
[Crossref]

I. Mack, J. Stuckelberger, P. Wyss, G. Nogay, Q. Jeangros, J. Horzel, C. Allebé, M. Despeisse, F. J. Haug, A. Ingenito, P. Löper, and C. Ballif, “Properties of mixed phase silicon-oxide-based passivating contacts for silicon solar cells,” Sol. Energy Mater. Sol. Cells 181, 9–14 (2018).
[Crossref]

J. Melskens, B. W. H. Van De Loo, B. Macco, L. E. Black, S. Smit, and W. M. M. Kessels, “Passivating Contacts for Crystalline Silicon Solar Cells: From Concepts and Materials to Prospects,” IEEE J. Photovoltaics 8(2), 373–388 (2018).
[Crossref]

M. Jabeen and S. Haxha, “Increased Optical Absorption and Light–Matter Interaction in Silicon Thin-Film Solar Cell Nanostructure Using Graphene and 2-D Au/Ag Nanograting,” IEEE J. Quantum Electron. 54(6), 1–12 (2018).
[Crossref]

A. Nematpour, M. Nikoufard, and R. Mehragha, “Design and optimization of the plasmonic graphene/InP thin-film solar-cell structure,” Laser Phys. 28(6), 066202 (2018).
[Crossref]

A. Nematpour and M. Nikoufard, “Plasmonic thin film InP/graphene-based Schottky-junction solar cell using nanorods,” J. Adv. Res. 10, 15–20 (2018).
[Crossref]

2017 (7)

M. I. Hossain, W. Qarony, M. K. Hossain, M. K. Debnath, M. J. Uddin, and Y. H. Tsang, “Effect of back reflectors on photon absorption in thin-film amorphous silicon solar cells,” Appl. Nanosci. 7(7), 489–497 (2017).
[Crossref]

C. Barugkin, F. J. Beck, and K. R. Catchpole, “Diffuse reflectors for improving light management in solar cells: a review and outlook,” J. Opt. 19, 014001 (2017).
[Crossref]

P. H. Wang, M. Theuring, M. Vehse, V. Steenhoff, C. Agert, and A. G. Brolo, “Light trapping in a-Si:H thin film solar cells using silver nanostructures,” AIP Adv. 7(1), 015019 (2017).
[Crossref]

M. Jabeen, S. Haxha, and M. D. B. Charlton, “Improved efficiency of microcrystalline silicon thin-film solar cells with wide bandgap CdS buffer layer,” IEEE Photonics J. 9(6), 1–14 (2017).
[Crossref]

M. Boccard, P. Firth, J. Y. Zhengshan, K. C. Fisher, M. Leilaeioun, S. Manzoor, and Z. C. Holman, “Low-refractive-index nanoparticle interlayers to reduce parasitic absorption in metallic rear reflectors of solar cells,” Phys. Status Solidi A 214(10), 1700179 (2017).
[Crossref]

Q. Zhang, C. Liu, G. Gan, and X. Cui, “Visible perfect reflectors realized with all dielectric metasurface,” Opt. Commun. 402, 226–230 (2017).
[Crossref]

S. Cao, T. Wang, Q. Sun, B. Hu, U. Levy, and W. Yu, “Graphene on meta-surface for super-resolution optical imaging with a sub-10 nm resolution,” Opt. Express 25(13), 14494–14503 (2017).
[Crossref]

2016 (7)

L. Zhang, L. Tang, W. Wei, X. Cheng, W. Wang, and H. Zhang, “Enhanced near-infrared absorption in graphene with multilayer metal-dielectric-metal nanostructure,” Opt. Express 24(18), 20002–20009 (2016).
[Crossref]

Y.-B. Wu, W. Yang, T. B. Wang, X. H. Deng, and J. T. Liu, “Broadband perfect light trapping in the thinnest monolayer graphene-MoS2 photovoltaic cell: The new application of spectrum-splitting structure,” Sci. Rep. 6(1), 1–8 (2016).
[Crossref]

X. Yang, P. Zheng, Q. Bi, and K. Weber, “Silicon heterojunction solar cells with electron selective TiOxcontact,” Sol. Energy Mater. Sol. Cells 150, 32–38 (2016).
[Crossref]

A. Tamang, A. Hongsingthong, P. Sichanugrist, V. Jovanov, H. T. Gebrewold, M. Konagai, and D. Knipp, “On the potential of light trapping in multiscale textured thin film solar cells,” Sol. Energy Mater. Sol. Cells 144, 300–308 (2016).
[Crossref]

C. Barugkin, U. W. Paetzold, K. R. Catchpole, A. Basch, and R. Carius, “Highly Reflective Dielectric Back Reflector for Improved Efficiency of Tandem Thin-Film Solar Cells,” Int. J. Photoenergy 2016, 1–7 (2016).
[Crossref]

L. V. Mercaldo, I. Usatii, E. M. Esposito, P. Delli Veneri, J.-W. Schttauf, E. Moulin, F.-J. Haug, C. Zhang, and M. Meier, “Metal versus dielectric back reflector for thin-film Si solar cells with impact of front electrode surface texture,” Prog. Photovoltaics 24(7), 968–977 (2016).
[Crossref]

Y. Wang, X. Zhang, X. Sun, Y. Qi, Z. Wang, and H. Wang, “Enhanced optical properties in inclined GaAs nanowire arrays for high-efficiency solar cells,” Opt. Laser Technol. 85, 85–90 (2016).
[Crossref]

2015 (4)

J.-H. Im, J. Luo, M. Franckevičius, N. Pellet, P. Gao, T. Moehl, S. M. Zakeeruddin, M. K. Nazeeruddin, M. Grätzel, and N.-G. Park, “Nanowire Perovskite Solar Cell,” Nano Lett. 15(3), 2120–2126 (2015).
[Crossref]

M.-D. Ko, T. Rim, K. Kim, M. Meyyappan, and C.-K. Baek, “High efficiency silicon solar cell based on asymmetric nanowire,” Sci. Rep. 5(1), 11646 (2015).
[Crossref]

Y.-K. Zhong, S.-M. Fu, N. P. Ju, A. Lin, and H. Wang, “Toward ultimate nanophotonic light trapping using pattern-designed quasi-guided mode excitations,” J. Opt. Soc. Am. B 32(6), 1252–1258 (2015).
[Crossref]

T. Cai and S. E. Han, “Effect of symmetry in periodic nanostructures on light trapping in thin film solar cells,” J. Opt. Soc. Am. B 32(11), 2264–2270 (2015).
[Crossref]

2014 (2)

H. Sai, T. Matsui, K. Matsubara, M. Kondo, and I. Yoshida, “11.0%-efficient thin-film microcrystalline silicon solar cells with honeycomb textured substrates,” IEEE J. Photovoltaics 4(6), 1349–1353 (2014).
[Crossref]

Z. C. Holman, M. Filipič, B. Lipovšek, S. De Wolf, F. Smole, M. Topič, and C. Ballif, “Parasitic absorption in the rear reflector of a silicon solar cell: Simulation and measurement of the sub-bandgap reflectance for common dielectric/metal reflectors,” Sol. Energy Mater. Sol. Cells 120, 426–430 (2014).
[Crossref]

2013 (2)

G. W. Hanson, “Erratum:‘Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 113(2), 029902 (2013).
[Crossref]

E. Moulin, U. W. Paetzold, K. Bittkau, J. Owen, J. Kirchhoff, A. Bauer, and R. Carius, “Investigation of the impact of the rear-dielectric/silver back reflector design on the optical performance of thin-film silicon solar cells by means of detached reflectors,” Prog. Photovoltaics 21(5), 1236–1247 (2013).
[Crossref]

2012 (3)

E. Moulin, U. W. Paetzold, J. Kirchhoff, A. Bauer, and R. Carius, “Study of detached back reflector designs for thin-film silicon solar cells,” Phys. Status Solidi RRL 6(2), 65–67 (2012).
[Crossref]

T. K. Chong, J. Wilson, S. Mokkapati, and K. R. Catchpole, “Optimal wavelength scale diffraction gratings for light trapping in solar cells,” J. Opt. 14(2), 024012 (2012).
[Crossref]

H. Sai, K. Saito, and M. Kondo, “Enhanced photocurrent and conversion efficiency in thin-film microcrystalline silicon solar cells using periodically textured back reflectors with hexagonal dimple arrays,” Appl. Phys. Lett. 101(17), 173901 (2012).
[Crossref]

2011 (2)

R. Dewan, I. Vasilev, V. Jovanov, and D. Knipp, “Optical enhancement and losses of pyramid textured thin-film silicon solar cells,” J. Appl. Phys. 110(1), 013101 (2011).
[Crossref]

E. Moulin, U. W. Paetzold, H. Siekmann, J. Worbs, A. Bauer, and R. Carius, “Study of thin-film silicon solar cell back reflectors and potential of detached reflectors,” Energy Procedia 10, 106–110 (2011).
[Crossref]

1990 (1)

1966 (1)

Agert, C.

P. H. Wang, M. Theuring, M. Vehse, V. Steenhoff, C. Agert, and A. G. Brolo, “Light trapping in a-Si:H thin film solar cells using silver nanostructures,” AIP Adv. 7(1), 015019 (2017).
[Crossref]

Allebé, C.

I. Mack, J. Stuckelberger, P. Wyss, G. Nogay, Q. Jeangros, J. Horzel, C. Allebé, M. Despeisse, F. J. Haug, A. Ingenito, P. Löper, and C. Ballif, “Properties of mixed phase silicon-oxide-based passivating contacts for silicon solar cells,” Sol. Energy Mater. Sol. Cells 181, 9–14 (2018).
[Crossref]

Baek, C.-K.

M.-D. Ko, T. Rim, K. Kim, M. Meyyappan, and C.-K. Baek, “High efficiency silicon solar cell based on asymmetric nanowire,” Sci. Rep. 5(1), 11646 (2015).
[Crossref]

Ballif, C.

I. Mack, J. Stuckelberger, P. Wyss, G. Nogay, Q. Jeangros, J. Horzel, C. Allebé, M. Despeisse, F. J. Haug, A. Ingenito, P. Löper, and C. Ballif, “Properties of mixed phase silicon-oxide-based passivating contacts for silicon solar cells,” Sol. Energy Mater. Sol. Cells 181, 9–14 (2018).
[Crossref]

Z. C. Holman, M. Filipič, B. Lipovšek, S. De Wolf, F. Smole, M. Topič, and C. Ballif, “Parasitic absorption in the rear reflector of a silicon solar cell: Simulation and measurement of the sub-bandgap reflectance for common dielectric/metal reflectors,” Sol. Energy Mater. Sol. Cells 120, 426–430 (2014).
[Crossref]

Barugkin, C.

C. Barugkin, F. J. Beck, and K. R. Catchpole, “Diffuse reflectors for improving light management in solar cells: a review and outlook,” J. Opt. 19, 014001 (2017).
[Crossref]

C. Barugkin, U. W. Paetzold, K. R. Catchpole, A. Basch, and R. Carius, “Highly Reflective Dielectric Back Reflector for Improved Efficiency of Tandem Thin-Film Solar Cells,” Int. J. Photoenergy 2016, 1–7 (2016).
[Crossref]

Basch, A.

C. Barugkin, U. W. Paetzold, K. R. Catchpole, A. Basch, and R. Carius, “Highly Reflective Dielectric Back Reflector for Improved Efficiency of Tandem Thin-Film Solar Cells,” Int. J. Photoenergy 2016, 1–7 (2016).
[Crossref]

Bauer, A.

E. Moulin, U. W. Paetzold, K. Bittkau, J. Owen, J. Kirchhoff, A. Bauer, and R. Carius, “Investigation of the impact of the rear-dielectric/silver back reflector design on the optical performance of thin-film silicon solar cells by means of detached reflectors,” Prog. Photovoltaics 21(5), 1236–1247 (2013).
[Crossref]

E. Moulin, U. W. Paetzold, J. Kirchhoff, A. Bauer, and R. Carius, “Study of detached back reflector designs for thin-film silicon solar cells,” Phys. Status Solidi RRL 6(2), 65–67 (2012).
[Crossref]

E. Moulin, U. W. Paetzold, H. Siekmann, J. Worbs, A. Bauer, and R. Carius, “Study of thin-film silicon solar cell back reflectors and potential of detached reflectors,” Energy Procedia 10, 106–110 (2011).
[Crossref]

Beck, F. J.

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A. Tamang, A. Hongsingthong, P. Sichanugrist, V. Jovanov, H. T. Gebrewold, M. Konagai, and D. Knipp, “On the potential of light trapping in multiscale textured thin film solar cells,” Sol. Energy Mater. Sol. Cells 144, 300–308 (2016).
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R. Dewan, I. Vasilev, V. Jovanov, and D. Knipp, “Optical enhancement and losses of pyramid textured thin-film silicon solar cells,” J. Appl. Phys. 110(1), 013101 (2011).
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Li, Z.

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Lipovšek, B.

Z. C. Holman, M. Filipič, B. Lipovšek, S. De Wolf, F. Smole, M. Topič, and C. Ballif, “Parasitic absorption in the rear reflector of a silicon solar cell: Simulation and measurement of the sub-bandgap reflectance for common dielectric/metal reflectors,” Sol. Energy Mater. Sol. Cells 120, 426–430 (2014).
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Q. Zhang, C. Liu, G. Gan, and X. Cui, “Visible perfect reflectors realized with all dielectric metasurface,” Opt. Commun. 402, 226–230 (2017).
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Y.-B. Wu, W. Yang, T. B. Wang, X. H. Deng, and J. T. Liu, “Broadband perfect light trapping in the thinnest monolayer graphene-MoS2 photovoltaic cell: The new application of spectrum-splitting structure,” Sci. Rep. 6(1), 1–8 (2016).
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S. Zhang, M. Liu, W. Liu, Y. Liu, Z. Li, and X. Wang, “Absorption enhancement in thin film solar cells with bilayer silver nanoparticle arrays Absorption enhancement in thin film solar cells with bilayer silver nanoparticle arrays,” J. Phys. Commun. 2(5), 055032 (2018).
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S. Zhang, M. Liu, W. Liu, Y. Liu, Z. Li, and X. Wang, “Absorption enhancement in thin film solar cells with bilayer silver nanoparticle arrays Absorption enhancement in thin film solar cells with bilayer silver nanoparticle arrays,” J. Phys. Commun. 2(5), 055032 (2018).
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I. Mack, J. Stuckelberger, P. Wyss, G. Nogay, Q. Jeangros, J. Horzel, C. Allebé, M. Despeisse, F. J. Haug, A. Ingenito, P. Löper, and C. Ballif, “Properties of mixed phase silicon-oxide-based passivating contacts for silicon solar cells,” Sol. Energy Mater. Sol. Cells 181, 9–14 (2018).
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J. Melskens, B. W. H. Van De Loo, B. Macco, L. E. Black, S. Smit, and W. M. M. Kessels, “Passivating Contacts for Crystalline Silicon Solar Cells: From Concepts and Materials to Prospects,” IEEE J. Photovoltaics 8(2), 373–388 (2018).
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M. Boccard, P. Firth, J. Y. Zhengshan, K. C. Fisher, M. Leilaeioun, S. Manzoor, and Z. C. Holman, “Low-refractive-index nanoparticle interlayers to reduce parasitic absorption in metallic rear reflectors of solar cells,” Phys. Status Solidi A 214(10), 1700179 (2017).
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P. Fallahazad, N. Naderi, M. J. Eshraghi, and A. Massoudi, “Combination of surface texturing and nanostructure coating for reduction of light reflection in ZnO/Si heterojunction thin film solar cell,” J. Mater. Sci.: Mater. Electron. 29(8), 6289–6296 (2018).
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M. Lozac’h, S. Nunomura, H. Sai, and K. Matsubara, “Passivation property of ultrathin SiOx:H / a-Si:H stack layers for solar cell applications,” Sol. Energy Mater. Sol. Cells 185, 8–15 (2018).
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H. Sai, T. Matsui, K. Matsubara, M. Kondo, and I. Yoshida, “11.0%-efficient thin-film microcrystalline silicon solar cells with honeycomb textured substrates,” IEEE J. Photovoltaics 4(6), 1349–1353 (2014).
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H. Sai, T. Matsui, K. Matsubara, M. Kondo, and I. Yoshida, “11.0%-efficient thin-film microcrystalline silicon solar cells with honeycomb textured substrates,” IEEE J. Photovoltaics 4(6), 1349–1353 (2014).
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Y. Wang, X. Zhang, X. Sun, Y. Qi, Z. Wang, and H. Wang, “Enhanced optical properties in inclined GaAs nanowire arrays for high-efficiency solar cells,” Opt. Laser Technol. 85, 85–90 (2016).
[Crossref]

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X. Yang, P. Zheng, Q. Bi, and K. Weber, “Silicon heterojunction solar cells with electron selective TiOxcontact,” Sol. Energy Mater. Sol. Cells 150, 32–38 (2016).
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AIP Adv. (1)

P. H. Wang, M. Theuring, M. Vehse, V. Steenhoff, C. Agert, and A. G. Brolo, “Light trapping in a-Si:H thin film solar cells using silver nanostructures,” AIP Adv. 7(1), 015019 (2017).
[Crossref]

Appl. Nanosci. (1)

M. I. Hossain, W. Qarony, M. K. Hossain, M. K. Debnath, M. J. Uddin, and Y. H. Tsang, “Effect of back reflectors on photon absorption in thin-film amorphous silicon solar cells,” Appl. Nanosci. 7(7), 489–497 (2017).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

H. Sai, K. Saito, and M. Kondo, “Enhanced photocurrent and conversion efficiency in thin-film microcrystalline silicon solar cells using periodically textured back reflectors with hexagonal dimple arrays,” Appl. Phys. Lett. 101(17), 173901 (2012).
[Crossref]

Carbon (1)

A. Suhail, G. Pan, D. Jenkins, and K. Islam, “Improved efficiency of graphene/Si Schottky junction solar cell based on back contact structure and DUV treatment,” Carbon 129, 520–526 (2018).
[Crossref]

Energy Procedia (1)

E. Moulin, U. W. Paetzold, H. Siekmann, J. Worbs, A. Bauer, and R. Carius, “Study of thin-film silicon solar cell back reflectors and potential of detached reflectors,” Energy Procedia 10, 106–110 (2011).
[Crossref]

IEEE J. Photovoltaics (2)

H. Sai, T. Matsui, K. Matsubara, M. Kondo, and I. Yoshida, “11.0%-efficient thin-film microcrystalline silicon solar cells with honeycomb textured substrates,” IEEE J. Photovoltaics 4(6), 1349–1353 (2014).
[Crossref]

J. Melskens, B. W. H. Van De Loo, B. Macco, L. E. Black, S. Smit, and W. M. M. Kessels, “Passivating Contacts for Crystalline Silicon Solar Cells: From Concepts and Materials to Prospects,” IEEE J. Photovoltaics 8(2), 373–388 (2018).
[Crossref]

IEEE J. Quantum Electron. (1)

M. Jabeen and S. Haxha, “Increased Optical Absorption and Light–Matter Interaction in Silicon Thin-Film Solar Cell Nanostructure Using Graphene and 2-D Au/Ag Nanograting,” IEEE J. Quantum Electron. 54(6), 1–12 (2018).
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IEEE Photonics J. (1)

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic view of dielectric-metal reflector-based graphene/Silicon thin film solar cell. Here red ray denotes optical wave scattering and trapping through different angles at front reflectance angle (rr(θ)), and the rear reflectance angle (rf(θ)) denotes wavelength ranges λ=400nm-1200 nm. (b) Electrical schematically cross section view of proposed silicon thin film solar cell device structure with possible integration of Nickle (Ni) contacts inserted in top and bottom dielectric layers attached with semiconductor active layer.
Fig. 2.
Fig. 2. Schematic of a thin film Graphene/Silicon solar cell with dielectric-metal back reflector a) plane Ag back reflector without front/back dielectric layer and textures b) plane dielectric-Ag metal back reflector without textures c) textured front and bottom dielectric-Ag metal back reflector. Graphene layer is 1 nm thick deposited on 20 nm thick SiO2 dielectric spacer. Ag rear reflector is detached from n-layer of silicon by 20 nm thick SiO2 dielectric layer (b) and finally 40 nm thick SiO2 layer is made textured by pyramid and semi-hexagonal shape textures.
Fig. 3.
Fig. 3. Simulated reflectance of graphene/Silicon thin film solar cell with varying dielectric SiO2 reflector configurations for wavelength spectra.
Fig. 4.
Fig. 4. Reflectance of thin film graphene-based silicon solar cell with a) three different kinds of back metal reflector materials Ag, Au and Cu and b) three different rear dielectric materials ZnO/Ag, SiN/Ag, and SiO2/Ag.
Fig. 5.
Fig. 5. Absorption as a function of incident angle (θ) for different texture shape, period ‘p’ and depth ‘d’. Light trapping visualization in active region of graphene/silicon solar cell for a) pyramid shape textures b) semi-hexagon shape textures c) pyramid and semi hexagon shape textures. The red legend represents the maximum magnetic field distribution (visualization of the magnetic field |H|), and total magnitude of current density (A/m).

Equations (8)

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

rs=n1cosθ1n2cosθ2n1cosθ1+n2cosθ2, rp=n2cosθ1n1cosθ2n2cosθ1+n1cosθ2
ts=2n1cosθ1n1cosθ1+n2cosθ2, tp=2n1cosθ1n2cosθ1+n1cosθ2
θB=atan(n2)(n1)
θr=asin(n1sin(θi))(n2)
R=[n2λ1][n2λ+1]22
A(λ,θ)=PinPoutPin
A(λ)=12v1ωε0ε(λ)|E(r)|2dv12s1Re{E(r)×H(r)}.ds
Q(x,y,z)=12cε0ηα|E(x,y,z)|2