Abstract

A theoretical study of randomly rough interfaces to obtain light trapping in thin-film silicon solar cells is presented. Roughness is modeled as a surface with Gaussian disorder, described using the root mean square of height and the lateral correlation length as statistical parameters. The model is shown to describe commonly used rough substrates. Rigorous calculations, with short-circuit current density as a figure of merit, lead to an optimization of disorder parameters and to a significant absorption enhancement. The understanding and optimization of disorder is believed to be of general interest for various realizations of thin-film solar cells.

© 2012 Optical Society of America

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References

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2012

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, ACS Nano 6, 2790 (2012).
[CrossRef]

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, Appl. Phys. Lett. 100, 181110 (2012).
[CrossRef]

A. Bozzola, M. Liscidini, and L. C. Andreani, Opt. Express 20, A224 (2012).
[CrossRef]

2011

2010

2008

H. Sai, H. Fujiwara, M. Kondo, and Y. Kanamori, Appl. Phys. Lett. 93, 143501 (2008).
[CrossRef]

M. Liscidini, D. Gerace, L. C. Andreani, and J. E. Sipe, Phys. Rev. B 77, 035324 (2008).
[CrossRef]

A. Chutinan and S. John, Phys. Rev. A 78, 023825 (2008).
[CrossRef]

S. Fahr, C. Rockstuhl, and F. Lederer, Appl. Phys. Lett. 92, 171114 (2008).
[CrossRef]

2007

M. Berginski, J. Hüpkes, M. Schulte, G. Schöpe, H. Stiebig, B. Rech, and M. Wuttig, J. Appl. Phys. 101, 074903 (2007).
[CrossRef]

2005

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef]

2004

1999

D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999).
[CrossRef]

1997

V. Freilikher, E. Kanzieper, and A. Maradudin, Phys. Rep. 288, 127 (1997).
[CrossRef]

1990

A. A. Maradudin and T. Michel, J. Stat. Phys. 58, 485(1990).
[CrossRef]

1982

Alexander, D. T. L.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, ACS Nano 6, 2790 (2012).
[CrossRef]

Andreani, L. C.

Ballif, C.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, ACS Nano 6, 2790 (2012).
[CrossRef]

C. Rockstuhl, S. Fahr, K. Bittkau, T. Beckers, R. Carius, F.-J. Haug, T. Söderström, C. Ballif, and F. Lederer, Opt. Express 18, A335 (2010).
[CrossRef]

D. Dominé, F.-J. Haug, C. Battaglia, and C. Ballif, J. Appl. Phys. 107, 044504 (2010).
[CrossRef]

Battaglia, C.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, ACS Nano 6, 2790 (2012).
[CrossRef]

D. Dominé, F.-J. Haug, C. Battaglia, and C. Ballif, J. Appl. Phys. 107, 044504 (2010).
[CrossRef]

Beckers, T.

Berginski, M.

M. Berginski, J. Hüpkes, M. Schulte, G. Schöpe, H. Stiebig, B. Rech, and M. Wuttig, J. Appl. Phys. 101, 074903 (2007).
[CrossRef]

Bittkau, K.

Boccard, M.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, ACS Nano 6, 2790 (2012).
[CrossRef]

Bozzola, A.

Brendel, R.

R. Brendel, Thin-Film Crystalline Silicon Solar Cells(Wiley-VCH, 2003).

Cantoni, M.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, ACS Nano 6, 2790 (2012).
[CrossRef]

Carius, R.

Charrière, M.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, ACS Nano 6, 2790 (2012).
[CrossRef]

Chutinan, A.

A. Chutinan and S. John, Phys. Rev. A 78, 023825 (2008).
[CrossRef]

Cui, Y.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, ACS Nano 6, 2790 (2012).
[CrossRef]

Culshaw, I. S.

D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999).
[CrossRef]

Depauw, V.

V. Depauw, Y. Qiu, K. Van Nieuwenhuysen, I. Gordon, and J. Poortmans, Prog. Photovoltaics 19, 844 (2011).
[CrossRef]

Despeisse, M.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, ACS Nano 6, 2790 (2012).
[CrossRef]

Dominé, D.

D. Dominé, F.-J. Haug, C. Battaglia, and C. Ballif, J. Appl. Phys. 107, 044504 (2010).
[CrossRef]

Escarré, J.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, ACS Nano 6, 2790 (2012).
[CrossRef]

Fahr, S.

Fan, S.

Favuzzi, P. A.

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, Appl. Phys. Lett. 100, 181110 (2012).
[CrossRef]

Freilikher, V.

V. Freilikher, E. Kanzieper, and A. Maradudin, Phys. Rep. 288, 127 (1997).
[CrossRef]

Fujiwara, H.

H. Sai, H. Fujiwara, M. Kondo, and Y. Kanamori, Appl. Phys. Lett. 93, 143501 (2008).
[CrossRef]

Gerace, D.

M. Liscidini, D. Gerace, L. C. Andreani, and J. E. Sipe, Phys. Rev. B 77, 035324 (2008).
[CrossRef]

D. Gerace and L. C. Andreani, Opt. Lett. 29, 1897 (2004).
[CrossRef]

Gordon, I.

V. Depauw, Y. Qiu, K. Van Nieuwenhuysen, I. Gordon, and J. Poortmans, Prog. Photovoltaics 19, 844 (2011).
[CrossRef]

Haug, F.-J.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, ACS Nano 6, 2790 (2012).
[CrossRef]

C. Rockstuhl, S. Fahr, K. Bittkau, T. Beckers, R. Carius, F.-J. Haug, T. Söderström, C. Ballif, and F. Lederer, Opt. Express 18, A335 (2010).
[CrossRef]

D. Dominé, F.-J. Haug, C. Battaglia, and C. Ballif, J. Appl. Phys. 107, 044504 (2010).
[CrossRef]

Hsu, C.-M.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, ACS Nano 6, 2790 (2012).
[CrossRef]

Hughes, S.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef]

Hüpkes, J.

M. Berginski, J. Hüpkes, M. Schulte, G. Schöpe, H. Stiebig, B. Rech, and M. Wuttig, J. Appl. Phys. 101, 074903 (2007).
[CrossRef]

John, S.

A. Chutinan and S. John, Phys. Rev. A 78, 023825 (2008).
[CrossRef]

Johnson, S. G.

Kanamori, Y.

H. Sai, H. Fujiwara, M. Kondo, and Y. Kanamori, Appl. Phys. Lett. 93, 143501 (2008).
[CrossRef]

Kanzieper, E.

V. Freilikher, E. Kanzieper, and A. Maradudin, Phys. Rep. 288, 127 (1997).
[CrossRef]

Kawakami, Y.

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, Appl. Phys. Lett. 100, 181110 (2012).
[CrossRef]

Kimerling, L. C.

Kirchartz, T.

S. Fahr, T. Kirchartz, C. Rockstuhl, and F. Lederer, Opt. Express 19, A865 (2011).
[CrossRef]

F. Lederer, S. Fahr, C. Rockstuhl, and T. Kirchartz, in MRS Proceedings (2012), Vol. 1391.

Kondo, M.

H. Sai, H. Fujiwara, M. Kondo, and Y. Kanamori, Appl. Phys. Lett. 93, 143501 (2008).
[CrossRef]

Lederer, F.

Liscidini, M.

A. Bozzola, M. Liscidini, and L. C. Andreani, Opt. Express 20, A224 (2012).
[CrossRef]

M. Liscidini, D. Gerace, L. C. Andreani, and J. E. Sipe, Phys. Rev. B 77, 035324 (2008).
[CrossRef]

Maradudin, A.

V. Freilikher, E. Kanzieper, and A. Maradudin, Phys. Rep. 288, 127 (1997).
[CrossRef]

Maradudin, A. A.

A. A. Maradudin and T. Michel, J. Stat. Phys. 58, 485(1990).
[CrossRef]

Michel, J.

Michel, T.

A. A. Maradudin and T. Michel, J. Stat. Phys. 58, 485(1990).
[CrossRef]

Nelson, J.

J. Nelson, The Physics of Solar Cells (Imperial College, 2003).

Noda, S.

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, Appl. Phys. Lett. 100, 181110 (2012).
[CrossRef]

Oskooi, A.

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, Appl. Phys. Lett. 100, 181110 (2012).
[CrossRef]

Palik, E. D.

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

Poortmans, J.

V. Depauw, Y. Qiu, K. Van Nieuwenhuysen, I. Gordon, and J. Poortmans, Prog. Photovoltaics 19, 844 (2011).
[CrossRef]

Qiu, Y.

V. Depauw, Y. Qiu, K. Van Nieuwenhuysen, I. Gordon, and J. Poortmans, Prog. Photovoltaics 19, 844 (2011).
[CrossRef]

Raman, A.

Ramunno, L.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef]

Rech, B.

M. Berginski, J. Hüpkes, M. Schulte, G. Schöpe, H. Stiebig, B. Rech, and M. Wuttig, J. Appl. Phys. 101, 074903 (2007).
[CrossRef]

Rockstuhl, C.

Sai, H.

H. Sai, H. Fujiwara, M. Kondo, and Y. Kanamori, Appl. Phys. Lett. 93, 143501 (2008).
[CrossRef]

Schöpe, G.

M. Berginski, J. Hüpkes, M. Schulte, G. Schöpe, H. Stiebig, B. Rech, and M. Wuttig, J. Appl. Phys. 101, 074903 (2007).
[CrossRef]

Schulte, M.

M. Berginski, J. Hüpkes, M. Schulte, G. Schöpe, H. Stiebig, B. Rech, and M. Wuttig, J. Appl. Phys. 101, 074903 (2007).
[CrossRef]

Sheng, X.

Shigeta, H.

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, Appl. Phys. Lett. 100, 181110 (2012).
[CrossRef]

Simonsen, I.

I. Simonsen, Eur. Phys. J. Special Topics 181, 1 (2010).
[CrossRef]

Sipe, J. E.

M. Liscidini, D. Gerace, L. C. Andreani, and J. E. Sipe, Phys. Rev. B 77, 035324 (2008).
[CrossRef]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef]

Söderström, K.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, ACS Nano 6, 2790 (2012).
[CrossRef]

Söderström, T.

Stiebig, H.

M. Berginski, J. Hüpkes, M. Schulte, G. Schöpe, H. Stiebig, B. Rech, and M. Wuttig, J. Appl. Phys. 101, 074903 (2007).
[CrossRef]

Tanaka, Y.

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, Appl. Phys. Lett. 100, 181110 (2012).
[CrossRef]

Van Nieuwenhuysen, K.

V. Depauw, Y. Qiu, K. Van Nieuwenhuysen, I. Gordon, and J. Poortmans, Prog. Photovoltaics 19, 844 (2011).
[CrossRef]

Whittaker, D. M.

D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999).
[CrossRef]

Wuttig, M.

M. Berginski, J. Hüpkes, M. Schulte, G. Schöpe, H. Stiebig, B. Rech, and M. Wuttig, J. Appl. Phys. 101, 074903 (2007).
[CrossRef]

Yablonovitch, E.

Young, J. F.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef]

Yu, Z.

ACS Nano

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, ACS Nano 6, 2790 (2012).
[CrossRef]

Appl. Phys. Lett.

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, Appl. Phys. Lett. 100, 181110 (2012).
[CrossRef]

H. Sai, H. Fujiwara, M. Kondo, and Y. Kanamori, Appl. Phys. Lett. 93, 143501 (2008).
[CrossRef]

S. Fahr, C. Rockstuhl, and F. Lederer, Appl. Phys. Lett. 92, 171114 (2008).
[CrossRef]

Eur. Phys. J. Special Topics

I. Simonsen, Eur. Phys. J. Special Topics 181, 1 (2010).
[CrossRef]

J. Appl. Phys.

D. Dominé, F.-J. Haug, C. Battaglia, and C. Ballif, J. Appl. Phys. 107, 044504 (2010).
[CrossRef]

M. Berginski, J. Hüpkes, M. Schulte, G. Schöpe, H. Stiebig, B. Rech, and M. Wuttig, J. Appl. Phys. 101, 074903 (2007).
[CrossRef]

J. Opt. Soc. Am.

J. Stat. Phys.

A. A. Maradudin and T. Michel, J. Stat. Phys. 58, 485(1990).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rep.

V. Freilikher, E. Kanzieper, and A. Maradudin, Phys. Rep. 288, 127 (1997).
[CrossRef]

Phys. Rev. A

A. Chutinan and S. John, Phys. Rev. A 78, 023825 (2008).
[CrossRef]

Phys. Rev. B

D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999).
[CrossRef]

M. Liscidini, D. Gerace, L. C. Andreani, and J. E. Sipe, Phys. Rev. B 77, 035324 (2008).
[CrossRef]

Phys. Rev. Lett.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef]

Prog. Photovoltaics

V. Depauw, Y. Qiu, K. Van Nieuwenhuysen, I. Gordon, and J. Poortmans, Prog. Photovoltaics 19, 844 (2011).
[CrossRef]

Other

F. Lederer, S. Fahr, C. Rockstuhl, and T. Kirchartz, in MRS Proceedings (2012), Vol. 1391.

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

J. Nelson, The Physics of Solar Cells (Imperial College, 2003).

R. Brendel, Thin-Film Crystalline Silicon Solar Cells(Wiley-VCH, 2003).

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Figures (5)

Fig. 1.
Fig. 1.

Sketch of (a) rough interface and (b) solar-cell structure under investigation.

Fig. 2.
Fig. 2.

(a) Haze for the interface between two rough TCO substrates (nTCO=1.915) and a medium with varying refractive index n. Curves are guides to the eye. (b) ARS function for the two interfaces. Substrate parameters: see [5] and text. The wavelength is λ=633nm.

Fig. 3.
Fig. 3.

Absorption spectra for structures with lc=100nm and different values of RMS height. The black curve for σ=0 corresponds to the flat structure.

Fig. 4.
Fig. 4.

Short-circuit current density as a function of RMS height for lc=100nm and dTCO=70nm. Inset: blow-up of small-σ region for 70 nm and 1 μm TCO thickness.

Fig. 5.
Fig. 5.

Short-circuit current density as a function of RMS height and correlation length. The two points denote the parameters of two common rough substrates.

Equations (1)

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ξ(x)=σ2Λm=1g(2πmΛ)×[α2m1sin(2πmxΛ)+α2mcos(2πmxΛ)],

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