Abstract

Light absorption by thin-film amorphous Si solar cells patterned with metallic nanogratings is investigated theoretically. Propagative bounded modes that include the surface plasmon polariton (SPP) and the photonic mode (PM) are extracted from the total field to quantitatively evaluate their contribution to the light absorption. Our results show that after removing the propagative bounded modes from the total field, the residual field still contributes to a major part of the total light absorption. This proves, at a quantitative level, that the light absorption of the structure is largely attributed to the residual field that is composed of unbounded or evanescent modes arising from the grating scattering, and the SPP and the PM do not play a dominant role, which is out of the previous intuitive expectations.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]

2011

E. C. Garnett, M. L. Brongersma, Y. Cui, and M. D. McGehee, Annu. Rev. Mater. Res. 41, 269 (2011).
[CrossRef]

J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, Adv. Mater. 23, 1272 (2011).
[CrossRef]

A. Williamson, É. McClean, D. Leipold, D. Zerulla, and E. Runge, Appl. Phys. Lett. 99, 093307 (2011).
[CrossRef]

Y. Liu and J. Kim, J. Opt. Soc. Am. B 28, 1934 (2011).
[CrossRef]

V. E. Ferry, A. Polman, and H. A. Atwater, ACS Nano 5, 10055 (2011).
[CrossRef]

2010

V. E. Ferry, J. N. Munday, and H. A. Atwater, Adv. Mater. 22, 4794 (2010).
[CrossRef]

J. Zhu, C. Hsu, Z. Yu, S. Fan, and Y. Cui, Nano Lett. 10, 1979 (2010).
[CrossRef]

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef]

W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, Nano Lett. 10, 2012 (2010).
[CrossRef]

H. T. Liu and P. Lalanne, Phys. Rev. B 82, 115418(2010).
[CrossRef]

2009

2008

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, Nano Lett. 8, 4391 (2008).
[CrossRef]

K. Nakayama, K. Tanabe, and H. A. Atwater, Appl. Phys. Lett. 93, 121904 (2008).
[CrossRef]

H. T. Liu and P. Lalanne, Nature 452, 728 (2008).
[CrossRef]

2005

J. P. Hugonin and P. Lalanne, J. Opt. Soc. Am. A 22, 1844 (2005).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

2002

H. Hoppe, N. S. Sariciftci, and D. Meissner, Mol. Cryst. Liq. Cryst. 385, 113 (2002).
[CrossRef]

1995

1991

B. O’Regan and M. Gräzel, Nature 353, 737 (1991).
[CrossRef]

Atwater, H. A.

J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, Adv. Mater. 23, 1272 (2011).
[CrossRef]

V. E. Ferry, A. Polman, and H. A. Atwater, ACS Nano 5, 10055 (2011).
[CrossRef]

V. E. Ferry, J. N. Munday, and H. A. Atwater, Adv. Mater. 22, 4794 (2010).
[CrossRef]

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef]

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, Opt. Express 17, 20975 (2009).
[CrossRef]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, Nano Lett. 8, 4391 (2008).
[CrossRef]

K. Nakayama, K. Tanabe, and H. A. Atwater, Appl. Phys. Lett. 93, 121904 (2008).
[CrossRef]

Bai, W.

Barnard, E.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, Adv. Mater. 21, 3504 (2009).
[CrossRef]

Bartoli, F.

Brongersma, M. L.

E. C. Garnett, M. L. Brongersma, Y. Cui, and M. D. McGehee, Annu. Rev. Mater. Res. 41, 269 (2011).
[CrossRef]

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, Adv. Mater. 21, 3504 (2009).
[CrossRef]

Cai, L.

Callahan, D. M.

J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, Adv. Mater. 23, 1272 (2011).
[CrossRef]

Chen, S.

W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, Nano Lett. 10, 2012 (2010).
[CrossRef]

Cui, Y.

E. C. Garnett, M. L. Brongersma, Y. Cui, and M. D. McGehee, Annu. Rev. Mater. Res. 41, 269 (2011).
[CrossRef]

J. Zhu, C. Hsu, Z. Yu, S. Fan, and Y. Cui, Nano Lett. 10, 1979 (2010).
[CrossRef]

Fan, S.

J. Zhu, C. Hsu, Z. Yu, S. Fan, and Y. Cui, Nano Lett. 10, 1979 (2010).
[CrossRef]

Ferry, V. E.

V. E. Ferry, A. Polman, and H. A. Atwater, ACS Nano 5, 10055 (2011).
[CrossRef]

V. E. Ferry, J. N. Munday, and H. A. Atwater, Adv. Mater. 22, 4794 (2010).
[CrossRef]

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, Opt. Express 17, 20975 (2009).
[CrossRef]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, Nano Lett. 8, 4391 (2008).
[CrossRef]

Gan, Q.

Garnett, E. C.

E. C. Garnett, M. L. Brongersma, Y. Cui, and M. D. McGehee, Annu. Rev. Mater. Res. 41, 269 (2011).
[CrossRef]

Gaylord, T. K.

Grandidier, J.

J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, Adv. Mater. 23, 1272 (2011).
[CrossRef]

Grann, E. B.

Gräzel, M.

B. O’Regan and M. Gräzel, Nature 353, 737 (1991).
[CrossRef]

Hoppe, H.

H. Hoppe, N. S. Sariciftci, and D. Meissner, Mol. Cryst. Liq. Cryst. 385, 113 (2002).
[CrossRef]

Hsu, C.

J. Zhu, C. Hsu, Z. Yu, S. Fan, and Y. Cui, Nano Lett. 10, 1979 (2010).
[CrossRef]

Huang, Y.

Hugonin, J. P.

J. P. Hugonin and P. Lalanne, J. Opt. Soc. Am. A 22, 1844 (2005).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Kim, J.

Lalanne, P.

H. T. Liu and P. Lalanne, Phys. Rev. B 82, 115418(2010).
[CrossRef]

H. T. Liu and P. Lalanne, Nature 452, 728 (2008).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

J. P. Hugonin and P. Lalanne, J. Opt. Soc. Am. A 22, 1844 (2005).
[CrossRef]

Leipold, D.

A. Williamson, É. McClean, D. Leipold, D. Zerulla, and E. Runge, Appl. Phys. Lett. 99, 093307 (2011).
[CrossRef]

Liu, H. T.

H. T. Liu and P. Lalanne, Phys. Rev. B 82, 115418(2010).
[CrossRef]

H. T. Liu and P. Lalanne, Nature 452, 728 (2008).
[CrossRef]

Liu, J.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, Adv. Mater. 21, 3504 (2009).
[CrossRef]

Liu, Y.

Lu, Y.

W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, Nano Lett. 10, 2012 (2010).
[CrossRef]

McClean, É.

A. Williamson, É. McClean, D. Leipold, D. Zerulla, and E. Runge, Appl. Phys. Lett. 99, 093307 (2011).
[CrossRef]

McGehee, M. D.

E. C. Garnett, M. L. Brongersma, Y. Cui, and M. D. McGehee, Annu. Rev. Mater. Res. 41, 269 (2011).
[CrossRef]

Meissner, D.

H. Hoppe, N. S. Sariciftci, and D. Meissner, Mol. Cryst. Liq. Cryst. 385, 113 (2002).
[CrossRef]

Moharam, M. G.

Munday, J. N.

J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, Adv. Mater. 23, 1272 (2011).
[CrossRef]

V. E. Ferry, J. N. Munday, and H. A. Atwater, Adv. Mater. 22, 4794 (2010).
[CrossRef]

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, Opt. Express 17, 20975 (2009).
[CrossRef]

Nakayama, K.

K. Nakayama, K. Tanabe, and H. A. Atwater, Appl. Phys. Lett. 93, 121904 (2008).
[CrossRef]

O’Regan, B.

B. O’Regan and M. Gräzel, Nature 353, 737 (1991).
[CrossRef]

Pacifici, D.

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, Opt. Express 17, 20975 (2009).
[CrossRef]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, Nano Lett. 8, 4391 (2008).
[CrossRef]

Pala, R. A.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, Adv. Mater. 21, 3504 (2009).
[CrossRef]

Palik, E.

E. Palik, Handbook of Optical Constants of Solids(Academic, 1985).

Polman, A.

V. E. Ferry, A. Polman, and H. A. Atwater, ACS Nano 5, 10055 (2011).
[CrossRef]

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef]

Pommet, D. A.

Reinhardt, K.

W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, Nano Lett. 10, 2012 (2010).
[CrossRef]

Rodier, J. C.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Runge, E.

A. Williamson, É. McClean, D. Leipold, D. Zerulla, and E. Runge, Appl. Phys. Lett. 99, 093307 (2011).
[CrossRef]

Saeta, P. N.

Sariciftci, N. S.

H. Hoppe, N. S. Sariciftci, and D. Meissner, Mol. Cryst. Liq. Cryst. 385, 113 (2002).
[CrossRef]

Song, G.

Sweatlock, L. A.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, Nano Lett. 8, 4391 (2008).
[CrossRef]

Tanabe, K.

K. Nakayama, K. Tanabe, and H. A. Atwater, Appl. Phys. Lett. 93, 121904 (2008).
[CrossRef]

Vassallo, C.

C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).

Wang, W.

W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, Nano Lett. 10, 2012 (2010).
[CrossRef]

White, J.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, Adv. Mater. 21, 3504 (2009).
[CrossRef]

Williamson, A.

A. Williamson, É. McClean, D. Leipold, D. Zerulla, and E. Runge, Appl. Phys. Lett. 99, 093307 (2011).
[CrossRef]

Wu, S.

W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, Nano Lett. 10, 2012 (2010).
[CrossRef]

Yu, Z.

J. Zhu, C. Hsu, Z. Yu, S. Fan, and Y. Cui, Nano Lett. 10, 1979 (2010).
[CrossRef]

Zerulla, D.

A. Williamson, É. McClean, D. Leipold, D. Zerulla, and E. Runge, Appl. Phys. Lett. 99, 093307 (2011).
[CrossRef]

Zhang, J.

Zhu, J.

J. Zhu, C. Hsu, Z. Yu, S. Fan, and Y. Cui, Nano Lett. 10, 1979 (2010).
[CrossRef]

ACS Nano

V. E. Ferry, A. Polman, and H. A. Atwater, ACS Nano 5, 10055 (2011).
[CrossRef]

Adv. Mater.

V. E. Ferry, J. N. Munday, and H. A. Atwater, Adv. Mater. 22, 4794 (2010).
[CrossRef]

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, Adv. Mater. 21, 3504 (2009).
[CrossRef]

J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, Adv. Mater. 23, 1272 (2011).
[CrossRef]

Annu. Rev. Mater. Res.

E. C. Garnett, M. L. Brongersma, Y. Cui, and M. D. McGehee, Annu. Rev. Mater. Res. 41, 269 (2011).
[CrossRef]

Appl. Phys. Lett.

K. Nakayama, K. Tanabe, and H. A. Atwater, Appl. Phys. Lett. 93, 121904 (2008).
[CrossRef]

A. Williamson, É. McClean, D. Leipold, D. Zerulla, and E. Runge, Appl. Phys. Lett. 99, 093307 (2011).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Mol. Cryst. Liq. Cryst.

H. Hoppe, N. S. Sariciftci, and D. Meissner, Mol. Cryst. Liq. Cryst. 385, 113 (2002).
[CrossRef]

Nano Lett.

W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, Nano Lett. 10, 2012 (2010).
[CrossRef]

J. Zhu, C. Hsu, Z. Yu, S. Fan, and Y. Cui, Nano Lett. 10, 1979 (2010).
[CrossRef]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, Nano Lett. 8, 4391 (2008).
[CrossRef]

Nat. Mater.

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef]

Nature

B. O’Regan and M. Gräzel, Nature 353, 737 (1991).
[CrossRef]

H. T. Liu and P. Lalanne, Nature 452, 728 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

H. T. Liu and P. Lalanne, Phys. Rev. B 82, 115418(2010).
[CrossRef]

Phys. Rev. Lett.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Other

E. Palik, Handbook of Optical Constants of Solids(Academic, 1985).

C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).

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Figures (3)

Fig. 1.
Fig. 1.

Illustration of the SPP and the PM with yellow and red horizontal arrows that propagate horizontally on the ridge or in the groove. For the notations the ψ denotes the mode field, the subscripts “SP” and “PM” refer to the SPP and the PM, the subscripts “r” and “g” correspond to the ridge and the groove of the grating, and the superscripts “+” and “” mean right-going and left-going modes [see Eq. (1)].

Fig. 2.
Fig. 2.

Amplitude |Ex| (top row) and |Ez| (bottom row) of electric field under TM illumination at the wavelength of 750 nm. The incident plane wave is normalized to have unitary electric-field amplitude. (a) Total field. (b) Summation of the field of the right-going and left-going SPP modes. (c) Summation of the field of the right-going and left-going PMs. (d) Residual field. (e) Field of the reference case. The refractive indices of ITO, a-Si, and Ag at λ=750nm are 1.61+0.015i, 4.07+0.23i and 0.15+4.90i, respectively.

Fig. 3.
Fig. 3.

(a) and (b) Absorption rates for the illumination of TE and TM polarizations. Aflat, Atotal, Atotal-SPP and Ares are shown with blue-solid, green-solid, cyan-dashed, and pink-dotted curves. (c) Absorption enhancement factor for the illumination of TE (pink curves) and TM (blue curves) polarizations. Atotal/Aflat and Ares/Aflat are shown with the solid and dotted curves, respectively.

Equations (3)

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

ψSP,r(x,z)=CSP,r+ψSP,r+(z)exp(ikSPx)+CSP,rψSP,r(z)exp(ikSPx),
CSP,r+=[Ez,SP,r(x0,z)Hy(x0,z)Ez(x0,z)Hy,SP,r(x0,z)]dz[Ez,SP,r(x0,z)Hy,SP,r+(x0,z)Ez,SP,r+(x0,z)Hy,SP,r(x0,z)]dz,
A=ωIm(ε)V|E|2dvΦinc,

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