Abstract

In this paper, we show how light absorption in a plasmonic grating nanosurface can be calculated by means of a simple, analytical model based on a transmission line equivalent circuit. The nanosurface is a one-dimensional grating etched into a silver metal film covered by a silicon slab. The transmission line model is specified for both transverse electric and transverse magnetic polarizations of the incident light, and it incorporates the effect of the plasmonic modes diffracted by the ridges of the grating. Under the assumption that the adjacent ridges are weakly interacting in terms of diffracted waves, we show that the approximate, closed form expression for the reflection coefficient at the air-silicon interface can be used to evaluate light absorption of the solar cell. The weak-coupling assumption is valid if the grating structure is not closely packed and the excitation direction is close to normal incidence. Also, we show the utility of the circuit theory for understanding how the peaks in the absorption coefficient are related to the resonances of the equivalent transmission model and how this can help in designing more efficient structures.

© 2011 OSA

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  3. A. Romeo, A. Terheggen, D. Abou-Ras, D. L. Bätzner, F.-J. Haug, M. K. D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt: Res. Appl.12, 93–111 (2004).
    [CrossRef]
  4. W. Koch, A. Endrös, D. Franke, C. Häbler, J. P. Kaleis, and H.-J. Möller, “Bulk crystal growth and wavering for PV,” Handbook of Photovoltaic Science and Engineering, pp. 205–255 (John Wiley2003).
  5. V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater.22, 4794–4808 (2010).
    [CrossRef] [PubMed]
  6. P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express17, 975–20, (2009).
    [CrossRef]
  7. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett.8, 4391–4397 (2008).
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    [CrossRef]
  11. A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” Appl. Phys. Lett.98, 104–107 (2011).
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  14. T. Weiland, “A discretization method for the solution of Maxwell’s equations for six-component fields,” Electron. Commun.31, 116–120 (1977).
  15. N.-N. Feng, J. Michel, L. Zeng, J. Liu, C.-Y. Hong, L. C. Kimerling, and X. Duan, “Design of Highly Efficient Light-Trapping Structures for Thin-Film Crystalline Silicon Solar Cells,” IEEE Trans. Electron Devices54, 1926–1933 (2007).
    [CrossRef]
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  20. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express18, 366–380 (2010).
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  21. I. T. A. Luque and A. Marti, “Light intensity enhancement by diffracting structures in solar cells,” J. Appl. Phys.104, 502–034, (2008).
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  25. A. Polemi, A. Toccafondi, and S. Maci, “High-frequency Green’s function for a semi-infinite array of electric dipoles on a grounded slab. Part I: formulation,” IEEE Trans. Antennas Propag.49, 1667–1677 (2001).
    [CrossRef]
  26. B. Davies, “Locating the zeros of an analytic function,” J. Comput. Phys.66, 36–49 (1986).
    [CrossRef]

2011

D. Madzharov, R. Dewan, and D. Knipp, “Influence of front and back grating on light trapping in microcrystalline thin-film silicon solar cells,” Opt. Express19, 95–107 (2011).
[CrossRef]

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” Appl. Phys. Lett.98, 104–107 (2011).
[CrossRef]

2010

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mater.9, 205–213 (2010).
[CrossRef]

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater.22, 4794–4808 (2010).
[CrossRef] [PubMed]

J. Chen, Q. Wang, and H. Li, “Microstructured design of metallic diffraction gratings for light trapping in thin-film silicon solar cells,” Opt. Commun.283, 5236–5244 (2010).
[CrossRef]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express18, 366–380 (2010).
[CrossRef]

2009

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express17, 975–20, (2009).
[CrossRef]

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater.21, 3504–3509 (2009).
[CrossRef]

2008

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett.8, 4391–4397 (2008).
[CrossRef]

I. T. A. Luque and A. Marti, “Light intensity enhancement by diffracting structures in solar cells,” J. Appl. Phys.104, 502–034, (2008).

A. Chutinan and S. John, “Light trapping and absorption optimization in certain thin-film photonic crystal architectures,” Phys. Rev. A78, 023,825 (2008).
[CrossRef]

2007

N.-N. Feng, J. Michel, L. Zeng, J. Liu, C.-Y. Hong, L. C. Kimerling, and X. Duan, “Design of Highly Efficient Light-Trapping Structures for Thin-Film Crystalline Silicon Solar Cells,” IEEE Trans. Electron Devices54, 1926–1933 (2007).
[CrossRef]

2006

C. Haase and H. Stiebig, “Optical properties of thin-film silicon solar cells with grating couplers,” Prog. Photovolt: Res. Appl.14, 629–641 (2006).
[CrossRef]

2004

A. Romeo, A. Terheggen, D. Abou-Ras, D. L. Bätzner, F.-J. Haug, M. K. D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt: Res. Appl.12, 93–111 (2004).
[CrossRef]

2001

A. Polemi, A. Toccafondi, and S. Maci, “High-frequency Green’s function for a semi-infinite array of electric dipoles on a grounded slab. Part I: formulation,” IEEE Trans. Antennas Propag.49, 1667–1677 (2001).
[CrossRef]

A. Tiwari, A. Romeo, D. Bätzner, and H. Zogg, “Flexible CdTe solar cells on polymer films,” Prog. Photovolt: Res. Appl.9, 211–215 (2001).
[CrossRef]

1996

T. Tamir and S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol.14, 914–927 (1996).
[CrossRef]

1986

B. Davies, “Locating the zeros of an analytic function,” J. Comput. Phys.66, 36–49 (1986).
[CrossRef]

1981

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. A71, 811–818 (1981).
[CrossRef]

1977

T. Weiland, “A discretization method for the solution of Maxwell’s equations for six-component fields,” Electron. Commun.31, 116–120 (1977).

1966

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag.14, 302–307 (1966).
[CrossRef]

Abou-Ras, D.

A. Romeo, A. Terheggen, D. Abou-Ras, D. L. Bätzner, F.-J. Haug, M. K. D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt: Res. Appl.12, 93–111 (2004).
[CrossRef]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mater.9, 205–213 (2010).
[CrossRef]

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater.22, 4794–4808 (2010).
[CrossRef] [PubMed]

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express17, 975–20, (2009).
[CrossRef]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett.8, 4391–4397 (2008).
[CrossRef]

Barnard, E.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater.21, 3504–3509 (2009).
[CrossRef]

Bätzner, D.

A. Tiwari, A. Romeo, D. Bätzner, and H. Zogg, “Flexible CdTe solar cells on polymer films,” Prog. Photovolt: Res. Appl.9, 211–215 (2001).
[CrossRef]

Bätzner, D. L.

A. Romeo, A. Terheggen, D. Abou-Ras, D. L. Bätzner, F.-J. Haug, M. K. D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt: Res. Appl.12, 93–111 (2004).
[CrossRef]

Brongersma, M. L.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater.21, 3504–3509 (2009).
[CrossRef]

Cabrini, S.

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” Appl. Phys. Lett.98, 104–107 (2011).
[CrossRef]

Chen, J.

J. Chen, Q. Wang, and H. Li, “Microstructured design of metallic diffraction gratings for light trapping in thin-film silicon solar cells,” Opt. Commun.283, 5236–5244 (2010).
[CrossRef]

Chutinan, A.

A. Chutinan and S. John, “Light trapping and absorption optimization in certain thin-film photonic crystal architectures,” Phys. Rev. A78, 023,825 (2008).
[CrossRef]

Davies, B.

B. Davies, “Locating the zeros of an analytic function,” J. Comput. Phys.66, 36–49 (1986).
[CrossRef]

Dewan, R.

D. Madzharov, R. Dewan, and D. Knipp, “Influence of front and back grating on light trapping in microcrystalline thin-film silicon solar cells,” Opt. Express19, 95–107 (2011).
[CrossRef]

Dhuey, S.

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” Appl. Phys. Lett.98, 104–107 (2011).
[CrossRef]

Duan, X.

N.-N. Feng, J. Michel, L. Zeng, J. Liu, C.-Y. Hong, L. C. Kimerling, and X. Duan, “Design of Highly Efficient Light-Trapping Structures for Thin-Film Crystalline Silicon Solar Cells,” IEEE Trans. Electron Devices54, 1926–1933 (2007).
[CrossRef]

Endrös, A.

W. Koch, A. Endrös, D. Franke, C. Häbler, J. P. Kaleis, and H.-J. Möller, “Bulk crystal growth and wavering for PV,” Handbook of Photovoltaic Science and Engineering, pp. 205–255 (John Wiley2003).

Fan, S.

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express18, 366–380 (2010).
[CrossRef]

Felsen, L.

L. Felsen and N. Markuvitz, Radiation and scattering of waves, 1st ed. (Prentice-Hall, Englewood Cliffs, NJ, 1973).

Feng, N.-N.

N.-N. Feng, J. Michel, L. Zeng, J. Liu, C.-Y. Hong, L. C. Kimerling, and X. Duan, “Design of Highly Efficient Light-Trapping Structures for Thin-Film Crystalline Silicon Solar Cells,” IEEE Trans. Electron Devices54, 1926–1933 (2007).
[CrossRef]

Ferry, V. E.

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater.22, 4794–4808 (2010).
[CrossRef] [PubMed]

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express17, 975–20, (2009).
[CrossRef]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett.8, 4391–4397 (2008).
[CrossRef]

Franke, D.

W. Koch, A. Endrös, D. Franke, C. Häbler, J. P. Kaleis, and H.-J. Möller, “Bulk crystal growth and wavering for PV,” Handbook of Photovoltaic Science and Engineering, pp. 205–255 (John Wiley2003).

Gaylord, T. K.

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. A71, 811–818 (1981).
[CrossRef]

Haase, C.

C. Haase and H. Stiebig, “Optical properties of thin-film silicon solar cells with grating couplers,” Prog. Photovolt: Res. Appl.14, 629–641 (2006).
[CrossRef]

Häbler, C.

W. Koch, A. Endrös, D. Franke, C. Häbler, J. P. Kaleis, and H.-J. Möller, “Bulk crystal growth and wavering for PV,” Handbook of Photovoltaic Science and Engineering, pp. 205–255 (John Wiley2003).

Harteneck, B.

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” Appl. Phys. Lett.98, 104–107 (2011).
[CrossRef]

Haug, F.-J.

A. Romeo, A. Terheggen, D. Abou-Ras, D. L. Bätzner, F.-J. Haug, M. K. D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt: Res. Appl.12, 93–111 (2004).
[CrossRef]

Hong, C.-Y.

N.-N. Feng, J. Michel, L. Zeng, J. Liu, C.-Y. Hong, L. C. Kimerling, and X. Duan, “Design of Highly Efficient Light-Trapping Structures for Thin-Film Crystalline Silicon Solar Cells,” IEEE Trans. Electron Devices54, 1926–1933 (2007).
[CrossRef]

John, S.

A. Chutinan and S. John, “Light trapping and absorption optimization in certain thin-film photonic crystal architectures,” Phys. Rev. A78, 023,825 (2008).
[CrossRef]

Kaleis, J. P.

W. Koch, A. Endrös, D. Franke, C. Häbler, J. P. Kaleis, and H.-J. Möller, “Bulk crystal growth and wavering for PV,” Handbook of Photovoltaic Science and Engineering, pp. 205–255 (John Wiley2003).

Kimerling, L. C.

N.-N. Feng, J. Michel, L. Zeng, J. Liu, C.-Y. Hong, L. C. Kimerling, and X. Duan, “Design of Highly Efficient Light-Trapping Structures for Thin-Film Crystalline Silicon Solar Cells,” IEEE Trans. Electron Devices54, 1926–1933 (2007).
[CrossRef]

Knipp, D.

D. Madzharov, R. Dewan, and D. Knipp, “Influence of front and back grating on light trapping in microcrystalline thin-film silicon solar cells,” Opt. Express19, 95–107 (2011).
[CrossRef]

Koch, W.

W. Koch, A. Endrös, D. Franke, C. Häbler, J. P. Kaleis, and H.-J. Möller, “Bulk crystal growth and wavering for PV,” Handbook of Photovoltaic Science and Engineering, pp. 205–255 (John Wiley2003).

Li, H.

J. Chen, Q. Wang, and H. Li, “Microstructured design of metallic diffraction gratings for light trapping in thin-film silicon solar cells,” Opt. Commun.283, 5236–5244 (2010).
[CrossRef]

Liu, J.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater.21, 3504–3509 (2009).
[CrossRef]

N.-N. Feng, J. Michel, L. Zeng, J. Liu, C.-Y. Hong, L. C. Kimerling, and X. Duan, “Design of Highly Efficient Light-Trapping Structures for Thin-Film Crystalline Silicon Solar Cells,” IEEE Trans. Electron Devices54, 1926–1933 (2007).
[CrossRef]

Luque, I. T. A.

I. T. A. Luque and A. Marti, “Light intensity enhancement by diffracting structures in solar cells,” J. Appl. Phys.104, 502–034, (2008).

Maci, S.

A. Polemi, A. Toccafondi, and S. Maci, “High-frequency Green’s function for a semi-infinite array of electric dipoles on a grounded slab. Part I: formulation,” IEEE Trans. Antennas Propag.49, 1667–1677 (2001).
[CrossRef]

Madzharov, D.

D. Madzharov, R. Dewan, and D. Knipp, “Influence of front and back grating on light trapping in microcrystalline thin-film silicon solar cells,” Opt. Express19, 95–107 (2011).
[CrossRef]

Markuvitz, N.

L. Felsen and N. Markuvitz, Radiation and scattering of waves, 1st ed. (Prentice-Hall, Englewood Cliffs, NJ, 1973).

Marti, A.

I. T. A. Luque and A. Marti, “Light intensity enhancement by diffracting structures in solar cells,” J. Appl. Phys.104, 502–034, (2008).

Michel, J.

N.-N. Feng, J. Michel, L. Zeng, J. Liu, C.-Y. Hong, L. C. Kimerling, and X. Duan, “Design of Highly Efficient Light-Trapping Structures for Thin-Film Crystalline Silicon Solar Cells,” IEEE Trans. Electron Devices54, 1926–1933 (2007).
[CrossRef]

Moharam, M. G.

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. A71, 811–818 (1981).
[CrossRef]

Möller, H.-J.

W. Koch, A. Endrös, D. Franke, C. Häbler, J. P. Kaleis, and H.-J. Möller, “Bulk crystal growth and wavering for PV,” Handbook of Photovoltaic Science and Engineering, pp. 205–255 (John Wiley2003).

Munday, J. N.

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater.22, 4794–4808 (2010).
[CrossRef] [PubMed]

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express17, 975–20, (2009).
[CrossRef]

Pacifici, D.

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express17, 975–20, (2009).
[CrossRef]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett.8, 4391–4397 (2008).
[CrossRef]

Padmore, H. A.

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” Appl. Phys. Lett.98, 104–107 (2011).
[CrossRef]

Pala, R. A.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater.21, 3504–3509 (2009).
[CrossRef]

Palik, E.

E. Palik, Handbook of optical constants of solids, 1st ed. (Academic Press, Orlando, 1985).

Polemi, A.

A. Polemi, A. Toccafondi, and S. Maci, “High-frequency Green’s function for a semi-infinite array of electric dipoles on a grounded slab. Part I: formulation,” IEEE Trans. Antennas Propag.49, 1667–1677 (2001).
[CrossRef]

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mater.9, 205–213 (2010).
[CrossRef]

Polyakov, A.

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” Appl. Phys. Lett.98, 104–107 (2011).
[CrossRef]

Raman, A.

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express18, 366–380 (2010).
[CrossRef]

Romeo, A.

A. Romeo, A. Terheggen, D. Abou-Ras, D. L. Bätzner, F.-J. Haug, M. K. D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt: Res. Appl.12, 93–111 (2004).
[CrossRef]

A. Tiwari, A. Romeo, D. Bätzner, and H. Zogg, “Flexible CdTe solar cells on polymer films,” Prog. Photovolt: Res. Appl.9, 211–215 (2001).
[CrossRef]

Rudmann, M. K. D.

A. Romeo, A. Terheggen, D. Abou-Ras, D. L. Bätzner, F.-J. Haug, M. K. D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt: Res. Appl.12, 93–111 (2004).
[CrossRef]

Saeta, P. N.

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express17, 975–20, (2009).
[CrossRef]

Schuck, P. J.

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” Appl. Phys. Lett.98, 104–107 (2011).
[CrossRef]

Stiebig, H.

C. Haase and H. Stiebig, “Optical properties of thin-film silicon solar cells with grating couplers,” Prog. Photovolt: Res. Appl.14, 629–641 (2006).
[CrossRef]

Sweatlock, L. A.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett.8, 4391–4397 (2008).
[CrossRef]

Tamir, T.

T. Tamir and S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol.14, 914–927 (1996).
[CrossRef]

Terheggen, A.

A. Romeo, A. Terheggen, D. Abou-Ras, D. L. Bätzner, F.-J. Haug, M. K. D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt: Res. Appl.12, 93–111 (2004).
[CrossRef]

Tiwari, A.

A. Tiwari, A. Romeo, D. Bätzner, and H. Zogg, “Flexible CdTe solar cells on polymer films,” Prog. Photovolt: Res. Appl.9, 211–215 (2001).
[CrossRef]

Tiwari, A. N.

A. Romeo, A. Terheggen, D. Abou-Ras, D. L. Bätzner, F.-J. Haug, M. K. D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt: Res. Appl.12, 93–111 (2004).
[CrossRef]

Toccafondi, A.

A. Polemi, A. Toccafondi, and S. Maci, “High-frequency Green’s function for a semi-infinite array of electric dipoles on a grounded slab. Part I: formulation,” IEEE Trans. Antennas Propag.49, 1667–1677 (2001).
[CrossRef]

Wang, Q.

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Figures (11)

Fig. 1
Fig. 1

(a) Reference geometry for a flat metallic film solar cell. (b) Equivalent transmission line (p=TM,TE)

Fig. 2
Fig. 2

Dispersion diagram of the flat Ag-Si solar cell. The Si slab has height h = 200nm.

Fig. 3
Fig. 3

(a) Calculated absorption compared with a full wave CST simulation for a Si substrate of height h = 200nm. The light is impinging normal to the surface, implying that the two polarizations coincide. (b) Equivalent impedance Zint at the air-Si interface calculated through Eq. (2).

Fig. 4
Fig. 4

Reference geometry for the grating nanosurface

Fig. 5
Fig. 5

Qualitative depiction of the scattering process induced by the grating nanosurface (top of the figure). Electric field distribution for normal incidence at λ = 857 nm: (a) TM polarization; (b) TE polarization.

Fig. 6
Fig. 6

(left) The unit cell is divided into two main zones, one relevant to the ridge and one relevant to its complementary region. For the TE polarization, the electric field tangent to the junction between the two regions is continuous. This implies that the electric potential difference across the two equivalent loads retrieved at the interface is constant, and the connection is in parallel. (right) TE circuit. The equivalent impedance Z int TE at the interface can be calculated by means of two equivalent admittances at the air-Si interface in a shunt connection weighted by the unit cell filling factors.

Fig. 8
Fig. 8

(left) The unit cell is divided into two main zones, one relevant to the ridge and one relevant to its complementary region. For TM polarization, the magnetic field tangent to the junction between the two regions is continuous. This implies that the current flowing through the two equivalent loads retrieved at the interface is constant, and the connection is in series. (right) TM circuit. The equivalent impedance Z int TM at the interface can be calculated by means of two equivalent impedances at the air-Si interface in a series connection weighted by the unit cell filling factors.

Fig. 7
Fig. 7

Comparison of the CST full wave result and absorption calculated with the model for (a) TM and (b) TE excitation for a grating nanosurface with h = 200nm, d = 300nm, w = 100nm, r = 50nm.

Fig. 9
Fig. 9

(a) Reference geometry of the grating nanosurface with a top cover of AR coating. (b) Modification of the transmission line equivalent circuit to account for the extra AR coating.

Fig. 10
Fig. 10

Comparison of the CST full wave result and absorption calculated with the model for (a) TM and (b) TE excitation for a grating nanosurface with an AR coating of TiO2. (hAR = 60nm, h = 200nm, d = 300nm, w = 100nm, r = 50nm.

Fig. 11
Fig. 11

(a) Absorption gain of the 1-D grating nanostructure over the flat film solar cell for TM and TE polarizations. (b) Real and (c) imaginary part of the equivalent impedance at the air-Si interface for the grating nanosurface and for the flat case.

Equations (14)

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Z X TM ( k t ) = ξ X k X 2 k t 2 k X
Z X TE ( k t ) = ξ 0 k 0 k X 2 k t 2
Z int p = Z Si p Z Ag p + jZ Si p tan ( h k Si 2 k t 2 ) Z Si p + j Z Ag p tan ( h k Si 2 k t 2 )
GF p = I g p Z 0 p Z int p Z 0 p + Z int p
GF p = Z 0 p Z Si p [ Z Ag p + jZ Si p tan ( h k Si 2 k t 2 ) ] [ Z Si p ( Z 0 p + Z Ag p ) + j ( Z 0 p Z Ag p + Z Si p 2 ) tan ( h k Si 2 k t 2 ) ] p = TM , TE
k t = k 0 ε Si ε Ag ε Si + ε Ag
A p ( λ ) = 1 | Γ p ( λ ) | 2 p = TM , TE
Γ p ( λ ) = Z int p Z 0 p Z int p + Z 0 p p = TM , TE
Z 1 TE = Z Si TE Z Ag TE + j Z Si TE tan ( h k Si 2 k 0 2 sin 2 θ ) Z Si TE + jZ Ag TE tan ( h k Si 2 k 0 2 sin 2 θ ) .
Z int TE = 1 Y 1 TE f 1 + Y 2 TE f 2
Z 1 TM = Z Si TM Z Ag TM + j Z Si TM tan ( h k Si 2 k 0 2 sin 2 θ ) Z Si TM + j Z Ag TM tan ( h k Si 2 k 0 2 sin 2 θ ) .
Z C = 1 j ω C + R C ,
Z int TM = Z 1 TM f 1 + Z 2 TM f 2
G p ( λ ) = A grating p ( λ ) / A flat p ( λ ) p = TM , TE

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