Abstract

Light scattering at randomly textured interfaces is essential to improve the absorption of thin-film silicon solar cells. Aluminium-induced texture (AIT) glass provides suitable scattering for amorphous silicon (a-Si:H) solar cells. The scattering properties of textured surfaces are usually characterised by two properties: the angularly resolved intensity distribution and the haze. However, we find that the commonly used haze equations cannot accurately describe the experimentally observed spectral dependence of the haze of AIT glass. This is particularly the case for surface morphologies with a large rms roughness and small lateral feature sizes. In this paper we present an improved method for haze calculation, based on the power spectral density (PSD) function of the randomly textured surface. To better reproduce the measured haze characteristics, we suggest two improvements: i) inclusion of the average lateral feature size of the textured surface into the haze calculation, and ii) considering the opening angle of the haze measurement. We show that with these two improvements an accurate prediction of the haze of AIT glass is possible. Furthermore, we use the new equation to define optimum morphology parameters for AIT glass to be used for a-Si:H solar cell applications. The autocorrelation length is identified as the critical parameter. For the investigated a-Si:H solar cells, the optimum autocorrelation length is shown to be 320 nm.

© 2013 Optical Society of America

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2013 (1)

N. Sahraei, S. Venkataraj, A. G. Aberle, and I. M. Peters, “Investigation of the optical absorption of a-Si:H solar cells on micro- and nano-textured surfaces,” Energy Procedia 33, 166–172 (2013).
[CrossRef]

2012 (5)

K. Jäger, M. Fischer, R. A. C. M. M. van Swaaij, and M. Zeman, “A scattering model for nano-textured interfaces and its application in opto-electrical simulations of thin-film silicon solar cells,” J. Appl. Phys. 111(8), 083108 (2012).
[CrossRef]

J. Wang, S. Venkataraj, C. Battaglia, P. Vayalakkara, and A. G. Aberle, “Analysis of optical and morphological properties of aluminium induced texture glass superstrates,” Jpn. J. Appl. Phys. 51, 10NB08 (2012).
[CrossRef]

M. Zeman, O. Isabella, K. Jager, R. Santbergen, S. Solntsev, M. Topic, and J. Krc, “Advanced light management approaches for thin-film silicon solar cells,” Energy Procedia 15, 189–199 (2012).
[CrossRef]

A. Hongsingthong, A. Aino, P. Sichanugrist, M. Konagai, H. Kuramochi, R. Akiike, H. Iigusa, K. Utsumi, and T. Shibutami, “Development of novel Al-doped zinc oxide films fabricated on etched glass and their application to solar cells,” Jpn. J. Appl. Phys. 51, 10NB09 (2012).
[CrossRef]

J. E. Harvey, S. Schröder, N. Choi, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[CrossRef]

2011 (1)

2010 (4)

C. Battaglia, K. Söderström, J. Escarré, F.-J. Haug, D. Dominé, P. Cuony, M. Boccard, G. Bugnon, C. Denizot, M. Despeisse, A. Feltrin, and C. Ballif, “Efficient light management scheme for thin film silicon solar cells via transparent random nanostructures fabricated by nanoimprinting,” Appl. Phys. Lett. 96(21), 213504 (2010).
[CrossRef]

O. Isabella, J. Krc, and M. Zeman, “Modulated surface textures for enhanced light trapping in thin-film silicon solar cells,” Appl. Phys. Lett. 97(10), 101106 (2010).
[CrossRef]

D. Dominé, F. J. Haug, C. Battaglia, and C. Ballif, “Modeling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107(4), 044504 (2010).
[CrossRef]

M. Boccard, P. Cuony, C. Battaglia, M. Despeisse, and C. Ballif, “Unlinking absorption and haze in thin film silicon solar cells front electrodes,” Phys. Status Solidi 4, 326–328 (2010).

2009 (2)

I. Simonsen, A. Larsen, E. Andreassen, E. Ommundsen, and K. Nord-Varhaug, “Haze of surface random systems: An approximate analytic approach,” Phys. Rev. A 79(6), 063813 (2009).
[CrossRef]

H. L. Yu and C. C. Hsaio, “Comparison of different measurement methods for transmittance haze,” Metrologia 46(4), S233–S237 (2009).
[CrossRef]

2007 (1)

P. I. Widenborg and A. G. Aberle, “Polycrystalline silicon thin-film solar cells on AIT-textured glass superstrates,” Adv. OptoElectronics. 2007, 1–7 (2007).

2004 (1)

J. Springer, A. Poruba, and M. Vanecek, “Improved three-dimensional optical model for thin-film silicon solar cells,” J. Appl. Phys. 96(9), 5329–5337 (2004).
[CrossRef]

2003 (1)

J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topic, “Effect of surface roughness of ZnO:Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426(1–2), 296–304 (2003).
[CrossRef]

2002 (1)

J. Krč, M. Zeman, F. Smole, and M. Topič, “Optical modeling of a-Si:H solar cells deposited on textured glass/SnO2 substrates,” J. Appl. Phys. 92(2), 749–755 (2002).
[CrossRef]

2000 (2)

A. Poruba, A. Fejfar, Z. Remeš, J. Špringer, M. Vaněček, J. Kočka, J. Meier, P. Torres, and A. Shah, “Optical absorption and light scattering in microcrystalline silicon thin films and solar cells,” J. Appl. Phys. 88(1), 148–160 (2000).
[CrossRef]

M. Zeman, R. van Swaaij, J. W. Metselaar, and R. E. I. Schropp, “Optical modeling of a-Si: H solar cells with rough interfaces: Effect of back contact and interface roughness,” J. Appl. Phys. 88(11), 6436–6443 (2000).
[CrossRef]

1989 (1)

H. Sakai, T. Yoshida, S. Fujikake, Y. Ichikawa, A. Ueda, O. Ishiwata, and M. Nagano, “Effects of the surface morphology of transparent electrode on film deposition and photovoltaic performance of a-Si:H solar cells,” J. Non-Cryst. Solids 115(1–3), 198–200 (1989).
[CrossRef]

1983 (2)

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]

H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous-silicon solar-cells,” Appl. Phys. Lett. 42(11), 968–970 (1983).
[CrossRef]

1979 (1)

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18(2), 104–115 (1979).
[CrossRef]

1963 (1)

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]

Aberle, A. G.

N. Sahraei, S. Venkataraj, A. G. Aberle, and I. M. Peters, “Investigation of the optical absorption of a-Si:H solar cells on micro- and nano-textured surfaces,” Energy Procedia 33, 166–172 (2013).
[CrossRef]

J. Wang, S. Venkataraj, C. Battaglia, P. Vayalakkara, and A. G. Aberle, “Analysis of optical and morphological properties of aluminium induced texture glass superstrates,” Jpn. J. Appl. Phys. 51, 10NB08 (2012).
[CrossRef]

P. I. Widenborg and A. G. Aberle, “Polycrystalline silicon thin-film solar cells on AIT-textured glass superstrates,” Adv. OptoElectronics. 2007, 1–7 (2007).

Aino, A.

A. Hongsingthong, A. Aino, P. Sichanugrist, M. Konagai, H. Kuramochi, R. Akiike, H. Iigusa, K. Utsumi, and T. Shibutami, “Development of novel Al-doped zinc oxide films fabricated on etched glass and their application to solar cells,” Jpn. J. Appl. Phys. 51, 10NB09 (2012).
[CrossRef]

Akiike, R.

A. Hongsingthong, A. Aino, P. Sichanugrist, M. Konagai, H. Kuramochi, R. Akiike, H. Iigusa, K. Utsumi, and T. Shibutami, “Development of novel Al-doped zinc oxide films fabricated on etched glass and their application to solar cells,” Jpn. J. Appl. Phys. 51, 10NB09 (2012).
[CrossRef]

Andreassen, E.

I. Simonsen, A. Larsen, E. Andreassen, E. Ommundsen, and K. Nord-Varhaug, “Haze of surface random systems: An approximate analytic approach,” Phys. Rev. A 79(6), 063813 (2009).
[CrossRef]

Ballif, C.

D. Dominé, F. J. Haug, C. Battaglia, and C. Ballif, “Modeling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107(4), 044504 (2010).
[CrossRef]

M. Boccard, P. Cuony, C. Battaglia, M. Despeisse, and C. Ballif, “Unlinking absorption and haze in thin film silicon solar cells front electrodes,” Phys. Status Solidi 4, 326–328 (2010).

C. Battaglia, K. Söderström, J. Escarré, F.-J. Haug, D. Dominé, P. Cuony, M. Boccard, G. Bugnon, C. Denizot, M. Despeisse, A. Feltrin, and C. Ballif, “Efficient light management scheme for thin film silicon solar cells via transparent random nanostructures fabricated by nanoimprinting,” Appl. Phys. Lett. 96(21), 213504 (2010).
[CrossRef]

Battaglia, C.

J. Wang, S. Venkataraj, C. Battaglia, P. Vayalakkara, and A. G. Aberle, “Analysis of optical and morphological properties of aluminium induced texture glass superstrates,” Jpn. J. Appl. Phys. 51, 10NB08 (2012).
[CrossRef]

C. Battaglia, K. Söderström, J. Escarré, F.-J. Haug, D. Dominé, P. Cuony, M. Boccard, G. Bugnon, C. Denizot, M. Despeisse, A. Feltrin, and C. Ballif, “Efficient light management scheme for thin film silicon solar cells via transparent random nanostructures fabricated by nanoimprinting,” Appl. Phys. Lett. 96(21), 213504 (2010).
[CrossRef]

D. Dominé, F. J. Haug, C. Battaglia, and C. Ballif, “Modeling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107(4), 044504 (2010).
[CrossRef]

M. Boccard, P. Cuony, C. Battaglia, M. Despeisse, and C. Ballif, “Unlinking absorption and haze in thin film silicon solar cells front electrodes,” Phys. Status Solidi 4, 326–328 (2010).

Boccard, M.

M. Boccard, P. Cuony, C. Battaglia, M. Despeisse, and C. Ballif, “Unlinking absorption and haze in thin film silicon solar cells front electrodes,” Phys. Status Solidi 4, 326–328 (2010).

C. Battaglia, K. Söderström, J. Escarré, F.-J. Haug, D. Dominé, P. Cuony, M. Boccard, G. Bugnon, C. Denizot, M. Despeisse, A. Feltrin, and C. Ballif, “Efficient light management scheme for thin film silicon solar cells via transparent random nanostructures fabricated by nanoimprinting,” Appl. Phys. Lett. 96(21), 213504 (2010).
[CrossRef]

Brammer, T.

H. Stiebig, T. Brammer, T. Repmann, O. Kluth, N. Senoussaoui, A. Lambertz, and H. Wagner, “Light scattering in microcrystalline silicon thin-film solar cells,” in Proc. of the 16th EU-PVSEC (Glasgow, 2000), pp. 549–552.

Bugnon, G.

C. Battaglia, K. Söderström, J. Escarré, F.-J. Haug, D. Dominé, P. Cuony, M. Boccard, G. Bugnon, C. Denizot, M. Despeisse, A. Feltrin, and C. Ballif, “Efficient light management scheme for thin film silicon solar cells via transparent random nanostructures fabricated by nanoimprinting,” Appl. Phys. Lett. 96(21), 213504 (2010).
[CrossRef]

Carniglia, C. K.

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18(2), 104–115 (1979).
[CrossRef]

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]

Choi, N.

J. E. Harvey, S. Schröder, N. Choi, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[CrossRef]

Coriand, L.

Cuony, P.

M. Boccard, P. Cuony, C. Battaglia, M. Despeisse, and C. Ballif, “Unlinking absorption and haze in thin film silicon solar cells front electrodes,” Phys. Status Solidi 4, 326–328 (2010).

C. Battaglia, K. Söderström, J. Escarré, F.-J. Haug, D. Dominé, P. Cuony, M. Boccard, G. Bugnon, C. Denizot, M. Despeisse, A. Feltrin, and C. Ballif, “Efficient light management scheme for thin film silicon solar cells via transparent random nanostructures fabricated by nanoimprinting,” Appl. Phys. Lett. 96(21), 213504 (2010).
[CrossRef]

Deckman, H. W.

H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous-silicon solar-cells,” Appl. Phys. Lett. 42(11), 968–970 (1983).
[CrossRef]

Denizot, C.

C. Battaglia, K. Söderström, J. Escarré, F.-J. Haug, D. Dominé, P. Cuony, M. Boccard, G. Bugnon, C. Denizot, M. Despeisse, A. Feltrin, and C. Ballif, “Efficient light management scheme for thin film silicon solar cells via transparent random nanostructures fabricated by nanoimprinting,” Appl. Phys. Lett. 96(21), 213504 (2010).
[CrossRef]

Despeisse, M.

C. Battaglia, K. Söderström, J. Escarré, F.-J. Haug, D. Dominé, P. Cuony, M. Boccard, G. Bugnon, C. Denizot, M. Despeisse, A. Feltrin, and C. Ballif, “Efficient light management scheme for thin film silicon solar cells via transparent random nanostructures fabricated by nanoimprinting,” Appl. Phys. Lett. 96(21), 213504 (2010).
[CrossRef]

M. Boccard, P. Cuony, C. Battaglia, M. Despeisse, and C. Ballif, “Unlinking absorption and haze in thin film silicon solar cells front electrodes,” Phys. Status Solidi 4, 326–328 (2010).

Dominé, D.

C. Battaglia, K. Söderström, J. Escarré, F.-J. Haug, D. Dominé, P. Cuony, M. Boccard, G. Bugnon, C. Denizot, M. Despeisse, A. Feltrin, and C. Ballif, “Efficient light management scheme for thin film silicon solar cells via transparent random nanostructures fabricated by nanoimprinting,” Appl. Phys. Lett. 96(21), 213504 (2010).
[CrossRef]

D. Dominé, F. J. Haug, C. Battaglia, and C. Ballif, “Modeling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107(4), 044504 (2010).
[CrossRef]

Duparré, A.

J. E. Harvey, S. Schröder, N. Choi, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[CrossRef]

S. Schröder, A. Duparré, L. Coriand, A. Tünnermann, D. H. Penalver, and J. E. Harvey, “Modeling of light scattering in different regimes of surface roughness,” Opt. Express 19(10), 9820–9835 (2011).
[CrossRef] [PubMed]

Escarré, J.

C. Battaglia, K. Söderström, J. Escarré, F.-J. Haug, D. Dominé, P. Cuony, M. Boccard, G. Bugnon, C. Denizot, M. Despeisse, A. Feltrin, and C. Ballif, “Efficient light management scheme for thin film silicon solar cells via transparent random nanostructures fabricated by nanoimprinting,” Appl. Phys. Lett. 96(21), 213504 (2010).
[CrossRef]

Fejfar, A.

A. Poruba, A. Fejfar, Z. Remeš, J. Špringer, M. Vaněček, J. Kočka, J. Meier, P. Torres, and A. Shah, “Optical absorption and light scattering in microcrystalline silicon thin films and solar cells,” J. Appl. Phys. 88(1), 148–160 (2000).
[CrossRef]

Feltrin, A.

C. Battaglia, K. Söderström, J. Escarré, F.-J. Haug, D. Dominé, P. Cuony, M. Boccard, G. Bugnon, C. Denizot, M. Despeisse, A. Feltrin, and C. Ballif, “Efficient light management scheme for thin film silicon solar cells via transparent random nanostructures fabricated by nanoimprinting,” Appl. Phys. Lett. 96(21), 213504 (2010).
[CrossRef]

Fischer, M.

K. Jäger, M. Fischer, R. A. C. M. M. van Swaaij, and M. Zeman, “A scattering model for nano-textured interfaces and its application in opto-electrical simulations of thin-film silicon solar cells,” J. Appl. Phys. 111(8), 083108 (2012).
[CrossRef]

Fujikake, S.

H. Sakai, T. Yoshida, S. Fujikake, Y. Ichikawa, A. Ueda, O. Ishiwata, and M. Nagano, “Effects of the surface morphology of transparent electrode on film deposition and photovoltaic performance of a-Si:H solar cells,” J. Non-Cryst. Solids 115(1–3), 198–200 (1989).
[CrossRef]

Harvey, J. E.

J. E. Harvey, S. Schröder, N. Choi, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[CrossRef]

S. Schröder, A. Duparré, L. Coriand, A. Tünnermann, D. H. Penalver, and J. E. Harvey, “Modeling of light scattering in different regimes of surface roughness,” Opt. Express 19(10), 9820–9835 (2011).
[CrossRef] [PubMed]

Haug, F. J.

D. Dominé, F. J. Haug, C. Battaglia, and C. Ballif, “Modeling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107(4), 044504 (2010).
[CrossRef]

Haug, F.-J.

C. Battaglia, K. Söderström, J. Escarré, F.-J. Haug, D. Dominé, P. Cuony, M. Boccard, G. Bugnon, C. Denizot, M. Despeisse, A. Feltrin, and C. Ballif, “Efficient light management scheme for thin film silicon solar cells via transparent random nanostructures fabricated by nanoimprinting,” Appl. Phys. Lett. 96(21), 213504 (2010).
[CrossRef]

Hongsingthong, A.

A. Hongsingthong, A. Aino, P. Sichanugrist, M. Konagai, H. Kuramochi, R. Akiike, H. Iigusa, K. Utsumi, and T. Shibutami, “Development of novel Al-doped zinc oxide films fabricated on etched glass and their application to solar cells,” Jpn. J. Appl. Phys. 51, 10NB09 (2012).
[CrossRef]

Hsaio, C. C.

H. L. Yu and C. C. Hsaio, “Comparison of different measurement methods for transmittance haze,” Metrologia 46(4), S233–S237 (2009).
[CrossRef]

Ichikawa, Y.

H. Sakai, T. Yoshida, S. Fujikake, Y. Ichikawa, A. Ueda, O. Ishiwata, and M. Nagano, “Effects of the surface morphology of transparent electrode on film deposition and photovoltaic performance of a-Si:H solar cells,” J. Non-Cryst. Solids 115(1–3), 198–200 (1989).
[CrossRef]

Iigusa, H.

A. Hongsingthong, A. Aino, P. Sichanugrist, M. Konagai, H. Kuramochi, R. Akiike, H. Iigusa, K. Utsumi, and T. Shibutami, “Development of novel Al-doped zinc oxide films fabricated on etched glass and their application to solar cells,” Jpn. J. Appl. Phys. 51, 10NB09 (2012).
[CrossRef]

Isabella, O.

M. Zeman, O. Isabella, K. Jager, R. Santbergen, S. Solntsev, M. Topic, and J. Krc, “Advanced light management approaches for thin-film silicon solar cells,” Energy Procedia 15, 189–199 (2012).
[CrossRef]

O. Isabella, J. Krc, and M. Zeman, “Modulated surface textures for enhanced light trapping in thin-film silicon solar cells,” Appl. Phys. Lett. 97(10), 101106 (2010).
[CrossRef]

Ishiwata, O.

H. Sakai, T. Yoshida, S. Fujikake, Y. Ichikawa, A. Ueda, O. Ishiwata, and M. Nagano, “Effects of the surface morphology of transparent electrode on film deposition and photovoltaic performance of a-Si:H solar cells,” J. Non-Cryst. Solids 115(1–3), 198–200 (1989).
[CrossRef]

Jager, K.

M. Zeman, O. Isabella, K. Jager, R. Santbergen, S. Solntsev, M. Topic, and J. Krc, “Advanced light management approaches for thin-film silicon solar cells,” Energy Procedia 15, 189–199 (2012).
[CrossRef]

Jäger, K.

K. Jäger, M. Fischer, R. A. C. M. M. van Swaaij, and M. Zeman, “A scattering model for nano-textured interfaces and its application in opto-electrical simulations of thin-film silicon solar cells,” J. Appl. Phys. 111(8), 083108 (2012).
[CrossRef]

Kluth, O.

J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topic, “Effect of surface roughness of ZnO:Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426(1–2), 296–304 (2003).
[CrossRef]

H. Stiebig, T. Brammer, T. Repmann, O. Kluth, N. Senoussaoui, A. Lambertz, and H. Wagner, “Light scattering in microcrystalline silicon thin-film solar cells,” in Proc. of the 16th EU-PVSEC (Glasgow, 2000), pp. 549–552.

Kocka, J.

A. Poruba, A. Fejfar, Z. Remeš, J. Špringer, M. Vaněček, J. Kočka, J. Meier, P. Torres, and A. Shah, “Optical absorption and light scattering in microcrystalline silicon thin films and solar cells,” J. Appl. Phys. 88(1), 148–160 (2000).
[CrossRef]

Konagai, M.

A. Hongsingthong, A. Aino, P. Sichanugrist, M. Konagai, H. Kuramochi, R. Akiike, H. Iigusa, K. Utsumi, and T. Shibutami, “Development of novel Al-doped zinc oxide films fabricated on etched glass and their application to solar cells,” Jpn. J. Appl. Phys. 51, 10NB09 (2012).
[CrossRef]

Krc, J.

M. Zeman, O. Isabella, K. Jager, R. Santbergen, S. Solntsev, M. Topic, and J. Krc, “Advanced light management approaches for thin-film silicon solar cells,” Energy Procedia 15, 189–199 (2012).
[CrossRef]

O. Isabella, J. Krc, and M. Zeman, “Modulated surface textures for enhanced light trapping in thin-film silicon solar cells,” Appl. Phys. Lett. 97(10), 101106 (2010).
[CrossRef]

J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topic, “Effect of surface roughness of ZnO:Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426(1–2), 296–304 (2003).
[CrossRef]

J. Krč, M. Zeman, F. Smole, and M. Topič, “Optical modeling of a-Si:H solar cells deposited on textured glass/SnO2 substrates,” J. Appl. Phys. 92(2), 749–755 (2002).
[CrossRef]

Kuramochi, H.

A. Hongsingthong, A. Aino, P. Sichanugrist, M. Konagai, H. Kuramochi, R. Akiike, H. Iigusa, K. Utsumi, and T. Shibutami, “Development of novel Al-doped zinc oxide films fabricated on etched glass and their application to solar cells,” Jpn. J. Appl. Phys. 51, 10NB09 (2012).
[CrossRef]

Lambertz, A.

H. Stiebig, T. Brammer, T. Repmann, O. Kluth, N. Senoussaoui, A. Lambertz, and H. Wagner, “Light scattering in microcrystalline silicon thin-film solar cells,” in Proc. of the 16th EU-PVSEC (Glasgow, 2000), pp. 549–552.

Larsen, A.

I. Simonsen, A. Larsen, E. Andreassen, E. Ommundsen, and K. Nord-Varhaug, “Haze of surface random systems: An approximate analytic approach,” Phys. Rev. A 79(6), 063813 (2009).
[CrossRef]

Meier, J.

A. Poruba, A. Fejfar, Z. Remeš, J. Špringer, M. Vaněček, J. Kočka, J. Meier, P. Torres, and A. Shah, “Optical absorption and light scattering in microcrystalline silicon thin films and solar cells,” J. Appl. Phys. 88(1), 148–160 (2000).
[CrossRef]

Metselaar, J. W.

M. Zeman, R. van Swaaij, J. W. Metselaar, and R. E. I. Schropp, “Optical modeling of a-Si: H solar cells with rough interfaces: Effect of back contact and interface roughness,” J. Appl. Phys. 88(11), 6436–6443 (2000).
[CrossRef]

Nagano, M.

H. Sakai, T. Yoshida, S. Fujikake, Y. Ichikawa, A. Ueda, O. Ishiwata, and M. Nagano, “Effects of the surface morphology of transparent electrode on film deposition and photovoltaic performance of a-Si:H solar cells,” J. Non-Cryst. Solids 115(1–3), 198–200 (1989).
[CrossRef]

Nord-Varhaug, K.

I. Simonsen, A. Larsen, E. Andreassen, E. Ommundsen, and K. Nord-Varhaug, “Haze of surface random systems: An approximate analytic approach,” Phys. Rev. A 79(6), 063813 (2009).
[CrossRef]

Ommundsen, E.

I. Simonsen, A. Larsen, E. Andreassen, E. Ommundsen, and K. Nord-Varhaug, “Haze of surface random systems: An approximate analytic approach,” Phys. Rev. A 79(6), 063813 (2009).
[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]

Penalver, D. H.

Peters, I. M.

N. Sahraei, S. Venkataraj, A. G. Aberle, and I. M. Peters, “Investigation of the optical absorption of a-Si:H solar cells on micro- and nano-textured surfaces,” Energy Procedia 33, 166–172 (2013).
[CrossRef]

Porteus, J. O.

Poruba, A.

J. Springer, A. Poruba, and M. Vanecek, “Improved three-dimensional optical model for thin-film silicon solar cells,” J. Appl. Phys. 96(9), 5329–5337 (2004).
[CrossRef]

A. Poruba, A. Fejfar, Z. Remeš, J. Špringer, M. Vaněček, J. Kočka, J. Meier, P. Torres, and A. Shah, “Optical absorption and light scattering in microcrystalline silicon thin films and solar cells,” J. Appl. Phys. 88(1), 148–160 (2000).
[CrossRef]

Remeš, Z.

A. Poruba, A. Fejfar, Z. Remeš, J. Špringer, M. Vaněček, J. Kočka, J. Meier, P. Torres, and A. Shah, “Optical absorption and light scattering in microcrystalline silicon thin films and solar cells,” J. Appl. Phys. 88(1), 148–160 (2000).
[CrossRef]

Repmann, T.

H. Stiebig, T. Brammer, T. Repmann, O. Kluth, N. Senoussaoui, A. Lambertz, and H. Wagner, “Light scattering in microcrystalline silicon thin-film solar cells,” in Proc. of the 16th EU-PVSEC (Glasgow, 2000), pp. 549–552.

Sahraei, N.

N. Sahraei, S. Venkataraj, A. G. Aberle, and I. M. Peters, “Investigation of the optical absorption of a-Si:H solar cells on micro- and nano-textured surfaces,” Energy Procedia 33, 166–172 (2013).
[CrossRef]

Sakai, H.

H. Sakai, T. Yoshida, S. Fujikake, Y. Ichikawa, A. Ueda, O. Ishiwata, and M. Nagano, “Effects of the surface morphology of transparent electrode on film deposition and photovoltaic performance of a-Si:H solar cells,” J. Non-Cryst. Solids 115(1–3), 198–200 (1989).
[CrossRef]

Santbergen, R.

M. Zeman, O. Isabella, K. Jager, R. Santbergen, S. Solntsev, M. Topic, and J. Krc, “Advanced light management approaches for thin-film silicon solar cells,” Energy Procedia 15, 189–199 (2012).
[CrossRef]

Schröder, S.

J. E. Harvey, S. Schröder, N. Choi, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[CrossRef]

S. Schröder, A. Duparré, L. Coriand, A. Tünnermann, D. H. Penalver, and J. E. Harvey, “Modeling of light scattering in different regimes of surface roughness,” Opt. Express 19(10), 9820–9835 (2011).
[CrossRef] [PubMed]

Schropp, R. E. I.

M. Zeman, R. van Swaaij, J. W. Metselaar, and R. E. I. Schropp, “Optical modeling of a-Si: H solar cells with rough interfaces: Effect of back contact and interface roughness,” J. Appl. Phys. 88(11), 6436–6443 (2000).
[CrossRef]

Senoussaoui, N.

H. Stiebig, T. Brammer, T. Repmann, O. Kluth, N. Senoussaoui, A. Lambertz, and H. Wagner, “Light scattering in microcrystalline silicon thin-film solar cells,” in Proc. of the 16th EU-PVSEC (Glasgow, 2000), pp. 549–552.

Shah, A.

A. Poruba, A. Fejfar, Z. Remeš, J. Špringer, M. Vaněček, J. Kočka, J. Meier, P. Torres, and A. Shah, “Optical absorption and light scattering in microcrystalline silicon thin films and solar cells,” J. Appl. Phys. 88(1), 148–160 (2000).
[CrossRef]

Shibutami, T.

A. Hongsingthong, A. Aino, P. Sichanugrist, M. Konagai, H. Kuramochi, R. Akiike, H. Iigusa, K. Utsumi, and T. Shibutami, “Development of novel Al-doped zinc oxide films fabricated on etched glass and their application to solar cells,” Jpn. J. Appl. Phys. 51, 10NB09 (2012).
[CrossRef]

Sichanugrist, P.

A. Hongsingthong, A. Aino, P. Sichanugrist, M. Konagai, H. Kuramochi, R. Akiike, H. Iigusa, K. Utsumi, and T. Shibutami, “Development of novel Al-doped zinc oxide films fabricated on etched glass and their application to solar cells,” Jpn. J. Appl. Phys. 51, 10NB09 (2012).
[CrossRef]

Simonsen, I.

I. Simonsen, A. Larsen, E. Andreassen, E. Ommundsen, and K. Nord-Varhaug, “Haze of surface random systems: An approximate analytic approach,” Phys. Rev. A 79(6), 063813 (2009).
[CrossRef]

Smole, F.

J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topic, “Effect of surface roughness of ZnO:Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426(1–2), 296–304 (2003).
[CrossRef]

J. Krč, M. Zeman, F. Smole, and M. Topič, “Optical modeling of a-Si:H solar cells deposited on textured glass/SnO2 substrates,” J. Appl. Phys. 92(2), 749–755 (2002).
[CrossRef]

Söderström, K.

C. Battaglia, K. Söderström, J. Escarré, F.-J. Haug, D. Dominé, P. Cuony, M. Boccard, G. Bugnon, C. Denizot, M. Despeisse, A. Feltrin, and C. Ballif, “Efficient light management scheme for thin film silicon solar cells via transparent random nanostructures fabricated by nanoimprinting,” Appl. Phys. Lett. 96(21), 213504 (2010).
[CrossRef]

Solntsev, S.

M. Zeman, O. Isabella, K. Jager, R. Santbergen, S. Solntsev, M. Topic, and J. Krc, “Advanced light management approaches for thin-film silicon solar cells,” Energy Procedia 15, 189–199 (2012).
[CrossRef]

Springer, J.

J. Springer, A. Poruba, and M. Vanecek, “Improved three-dimensional optical model for thin-film silicon solar cells,” J. Appl. Phys. 96(9), 5329–5337 (2004).
[CrossRef]

Špringer, J.

A. Poruba, A. Fejfar, Z. Remeš, J. Špringer, M. Vaněček, J. Kočka, J. Meier, P. Torres, and A. Shah, “Optical absorption and light scattering in microcrystalline silicon thin films and solar cells,” J. Appl. Phys. 88(1), 148–160 (2000).
[CrossRef]

Stiebig, H.

H. Stiebig, T. Brammer, T. Repmann, O. Kluth, N. Senoussaoui, A. Lambertz, and H. Wagner, “Light scattering in microcrystalline silicon thin-film solar cells,” in Proc. of the 16th EU-PVSEC (Glasgow, 2000), pp. 549–552.

Tiedje, T.

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]

Topic, M.

M. Zeman, O. Isabella, K. Jager, R. Santbergen, S. Solntsev, M. Topic, and J. Krc, “Advanced light management approaches for thin-film silicon solar cells,” Energy Procedia 15, 189–199 (2012).
[CrossRef]

J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topic, “Effect of surface roughness of ZnO:Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426(1–2), 296–304 (2003).
[CrossRef]

J. Krč, M. Zeman, F. Smole, and M. Topič, “Optical modeling of a-Si:H solar cells deposited on textured glass/SnO2 substrates,” J. Appl. Phys. 92(2), 749–755 (2002).
[CrossRef]

Torres, P.

A. Poruba, A. Fejfar, Z. Remeš, J. Špringer, M. Vaněček, J. Kočka, J. Meier, P. Torres, and A. Shah, “Optical absorption and light scattering in microcrystalline silicon thin films and solar cells,” J. Appl. Phys. 88(1), 148–160 (2000).
[CrossRef]

Tünnermann, A.

Ueda, A.

H. Sakai, T. Yoshida, S. Fujikake, Y. Ichikawa, A. Ueda, O. Ishiwata, and M. Nagano, “Effects of the surface morphology of transparent electrode on film deposition and photovoltaic performance of a-Si:H solar cells,” J. Non-Cryst. Solids 115(1–3), 198–200 (1989).
[CrossRef]

Utsumi, K.

A. Hongsingthong, A. Aino, P. Sichanugrist, M. Konagai, H. Kuramochi, R. Akiike, H. Iigusa, K. Utsumi, and T. Shibutami, “Development of novel Al-doped zinc oxide films fabricated on etched glass and their application to solar cells,” Jpn. J. Appl. Phys. 51, 10NB09 (2012).
[CrossRef]

van Swaaij, R.

M. Zeman, R. van Swaaij, J. W. Metselaar, and R. E. I. Schropp, “Optical modeling of a-Si: H solar cells with rough interfaces: Effect of back contact and interface roughness,” J. Appl. Phys. 88(11), 6436–6443 (2000).
[CrossRef]

van Swaaij, R. A. C. M. M.

K. Jäger, M. Fischer, R. A. C. M. M. van Swaaij, and M. Zeman, “A scattering model for nano-textured interfaces and its application in opto-electrical simulations of thin-film silicon solar cells,” J. Appl. Phys. 111(8), 083108 (2012).
[CrossRef]

Vanecek, M.

J. Springer, A. Poruba, and M. Vanecek, “Improved three-dimensional optical model for thin-film silicon solar cells,” J. Appl. Phys. 96(9), 5329–5337 (2004).
[CrossRef]

A. Poruba, A. Fejfar, Z. Remeš, J. Špringer, M. Vaněček, J. Kočka, J. Meier, P. Torres, and A. Shah, “Optical absorption and light scattering in microcrystalline silicon thin films and solar cells,” J. Appl. Phys. 88(1), 148–160 (2000).
[CrossRef]

Vayalakkara, P.

J. Wang, S. Venkataraj, C. Battaglia, P. Vayalakkara, and A. G. Aberle, “Analysis of optical and morphological properties of aluminium induced texture glass superstrates,” Jpn. J. Appl. Phys. 51, 10NB08 (2012).
[CrossRef]

Venkataraj, S.

N. Sahraei, S. Venkataraj, A. G. Aberle, and I. M. Peters, “Investigation of the optical absorption of a-Si:H solar cells on micro- and nano-textured surfaces,” Energy Procedia 33, 166–172 (2013).
[CrossRef]

J. Wang, S. Venkataraj, C. Battaglia, P. Vayalakkara, and A. G. Aberle, “Analysis of optical and morphological properties of aluminium induced texture glass superstrates,” Jpn. J. Appl. Phys. 51, 10NB08 (2012).
[CrossRef]

Wagner, H.

H. Stiebig, T. Brammer, T. Repmann, O. Kluth, N. Senoussaoui, A. Lambertz, and H. Wagner, “Light scattering in microcrystalline silicon thin-film solar cells,” in Proc. of the 16th EU-PVSEC (Glasgow, 2000), pp. 549–552.

Wang, J.

J. Wang, S. Venkataraj, C. Battaglia, P. Vayalakkara, and A. G. Aberle, “Analysis of optical and morphological properties of aluminium induced texture glass superstrates,” Jpn. J. Appl. Phys. 51, 10NB08 (2012).
[CrossRef]

Widenborg, P. I.

P. I. Widenborg and A. G. Aberle, “Polycrystalline silicon thin-film solar cells on AIT-textured glass superstrates,” Adv. OptoElectronics. 2007, 1–7 (2007).

Witzke, H.

H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous-silicon solar-cells,” Appl. Phys. Lett. 42(11), 968–970 (1983).
[CrossRef]

Wronski, C. R.

H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous-silicon solar-cells,” Appl. Phys. Lett. 42(11), 968–970 (1983).
[CrossRef]

Yablonovitch, E.

H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous-silicon solar-cells,” Appl. Phys. Lett. 42(11), 968–970 (1983).
[CrossRef]

Yoshida, T.

H. Sakai, T. Yoshida, S. Fujikake, Y. Ichikawa, A. Ueda, O. Ishiwata, and M. Nagano, “Effects of the surface morphology of transparent electrode on film deposition and photovoltaic performance of a-Si:H solar cells,” J. Non-Cryst. Solids 115(1–3), 198–200 (1989).
[CrossRef]

Yu, H. L.

H. L. Yu and C. C. Hsaio, “Comparison of different measurement methods for transmittance haze,” Metrologia 46(4), S233–S237 (2009).
[CrossRef]

Zeman, M.

M. Zeman, O. Isabella, K. Jager, R. Santbergen, S. Solntsev, M. Topic, and J. Krc, “Advanced light management approaches for thin-film silicon solar cells,” Energy Procedia 15, 189–199 (2012).
[CrossRef]

K. Jäger, M. Fischer, R. A. C. M. M. van Swaaij, and M. Zeman, “A scattering model for nano-textured interfaces and its application in opto-electrical simulations of thin-film silicon solar cells,” J. Appl. Phys. 111(8), 083108 (2012).
[CrossRef]

O. Isabella, J. Krc, and M. Zeman, “Modulated surface textures for enhanced light trapping in thin-film silicon solar cells,” Appl. Phys. Lett. 97(10), 101106 (2010).
[CrossRef]

J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topic, “Effect of surface roughness of ZnO:Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426(1–2), 296–304 (2003).
[CrossRef]

J. Krč, M. Zeman, F. Smole, and M. Topič, “Optical modeling of a-Si:H solar cells deposited on textured glass/SnO2 substrates,” J. Appl. Phys. 92(2), 749–755 (2002).
[CrossRef]

M. Zeman, R. van Swaaij, J. W. Metselaar, and R. E. I. Schropp, “Optical modeling of a-Si: H solar cells with rough interfaces: Effect of back contact and interface roughness,” J. Appl. Phys. 88(11), 6436–6443 (2000).
[CrossRef]

Adv. OptoElectronics. (1)

P. I. Widenborg and A. G. Aberle, “Polycrystalline silicon thin-film solar cells on AIT-textured glass superstrates,” Adv. OptoElectronics. 2007, 1–7 (2007).

Appl. Phys. Lett. (4)

C. Battaglia, K. Söderström, J. Escarré, F.-J. Haug, D. Dominé, P. Cuony, M. Boccard, G. Bugnon, C. Denizot, M. Despeisse, A. Feltrin, and C. Ballif, “Efficient light management scheme for thin film silicon solar cells via transparent random nanostructures fabricated by nanoimprinting,” Appl. Phys. Lett. 96(21), 213504 (2010).
[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]

H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous-silicon solar-cells,” Appl. Phys. Lett. 42(11), 968–970 (1983).
[CrossRef]

O. Isabella, J. Krc, and M. Zeman, “Modulated surface textures for enhanced light trapping in thin-film silicon solar cells,” Appl. Phys. Lett. 97(10), 101106 (2010).
[CrossRef]

Energy Procedia (2)

M. Zeman, O. Isabella, K. Jager, R. Santbergen, S. Solntsev, M. Topic, and J. Krc, “Advanced light management approaches for thin-film silicon solar cells,” Energy Procedia 15, 189–199 (2012).
[CrossRef]

N. Sahraei, S. Venkataraj, A. G. Aberle, and I. M. Peters, “Investigation of the optical absorption of a-Si:H solar cells on micro- and nano-textured surfaces,” Energy Procedia 33, 166–172 (2013).
[CrossRef]

J. Appl. Phys. (6)

K. Jäger, M. Fischer, R. A. C. M. M. van Swaaij, and M. Zeman, “A scattering model for nano-textured interfaces and its application in opto-electrical simulations of thin-film silicon solar cells,” J. Appl. Phys. 111(8), 083108 (2012).
[CrossRef]

D. Dominé, F. J. Haug, C. Battaglia, and C. Ballif, “Modeling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107(4), 044504 (2010).
[CrossRef]

M. Zeman, R. van Swaaij, J. W. Metselaar, and R. E. I. Schropp, “Optical modeling of a-Si: H solar cells with rough interfaces: Effect of back contact and interface roughness,” J. Appl. Phys. 88(11), 6436–6443 (2000).
[CrossRef]

A. Poruba, A. Fejfar, Z. Remeš, J. Špringer, M. Vaněček, J. Kočka, J. Meier, P. Torres, and A. Shah, “Optical absorption and light scattering in microcrystalline silicon thin films and solar cells,” J. Appl. Phys. 88(1), 148–160 (2000).
[CrossRef]

J. Springer, A. Poruba, and M. Vanecek, “Improved three-dimensional optical model for thin-film silicon solar cells,” J. Appl. Phys. 96(9), 5329–5337 (2004).
[CrossRef]

J. Krč, M. Zeman, F. Smole, and M. Topič, “Optical modeling of a-Si:H solar cells deposited on textured glass/SnO2 substrates,” J. Appl. Phys. 92(2), 749–755 (2002).
[CrossRef]

J. Non-Cryst. Solids (1)

H. Sakai, T. Yoshida, S. Fujikake, Y. Ichikawa, A. Ueda, O. Ishiwata, and M. Nagano, “Effects of the surface morphology of transparent electrode on film deposition and photovoltaic performance of a-Si:H solar cells,” J. Non-Cryst. Solids 115(1–3), 198–200 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (2)

J. Wang, S. Venkataraj, C. Battaglia, P. Vayalakkara, and A. G. Aberle, “Analysis of optical and morphological properties of aluminium induced texture glass superstrates,” Jpn. J. Appl. Phys. 51, 10NB08 (2012).
[CrossRef]

A. Hongsingthong, A. Aino, P. Sichanugrist, M. Konagai, H. Kuramochi, R. Akiike, H. Iigusa, K. Utsumi, and T. Shibutami, “Development of novel Al-doped zinc oxide films fabricated on etched glass and their application to solar cells,” Jpn. J. Appl. Phys. 51, 10NB09 (2012).
[CrossRef]

Metrologia (1)

H. L. Yu and C. C. Hsaio, “Comparison of different measurement methods for transmittance haze,” Metrologia 46(4), S233–S237 (2009).
[CrossRef]

Opt. Eng. (2)

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18(2), 104–115 (1979).
[CrossRef]

J. E. Harvey, S. Schröder, N. Choi, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[CrossRef]

Opt. Express (1)

Phys. Rev. A (1)

I. Simonsen, A. Larsen, E. Andreassen, E. Ommundsen, and K. Nord-Varhaug, “Haze of surface random systems: An approximate analytic approach,” Phys. Rev. A 79(6), 063813 (2009).
[CrossRef]

Phys. Status Solidi (1)

M. Boccard, P. Cuony, C. Battaglia, M. Despeisse, and C. Ballif, “Unlinking absorption and haze in thin film silicon solar cells front electrodes,” Phys. Status Solidi 4, 326–328 (2010).

Thin Solid Films (1)

J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topic, “Effect of surface roughness of ZnO:Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426(1–2), 296–304 (2003).
[CrossRef]

Other (7)

A. G. Aberle, P. I. Widenborg, and N. Chuangsuwanich, “Glass texturing,” European patent, EP1613562 B1, 2011.

E. Sidick, H. Bosse, B. Bodermann, and R. M. Silver, eds., “Power spectral density specification and analysis of large optical surfaces,” in Modeling Aspects in Optical Metrology II, H. Bosse, B. Bodermann, and R. M. Silver, eds. (Proceedings of SPIE, Munich, Germany, 2009), pp. 73009L.
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E. L. Church and P. Z. Takacs, “Light scattering from non-Gaussian surfaces,” in Optical Scattering in the Optics, Semiconductor, and Computer Disk Industries, J. C. Stover, ed. (SPIE, 1995), pp. 91–107.

J. M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, 1989).

V. Premachandran, S. Venkataraj, J. Wang, J. Long, Z. Ren, Y. Yin, P. I. Widenborg, and A. G. Aberle, “Aluminium induced glass texturing process on borosilicate and soda- lime glass superstrate for thin-film solar cells,” in Proc. 37th IEEE Photovoltaic Specialist Conference (Seattle, 2011), pp. L28–871.

D. Domine, “The role of front electrodes and intermediate reflectors in the optoelectronic properties of high-efficiency micromorph solar cells,” PhD thesis (Faculté des Sciences, Institut de Microtechnique, Université de Neuchâtel, 2009), p. 179.

H. Stiebig, T. Brammer, T. Repmann, O. Kluth, N. Senoussaoui, A. Lambertz, and H. Wagner, “Light scattering in microcrystalline silicon thin-film solar cells,” in Proc. of the 16th EU-PVSEC (Glasgow, 2000), pp. 549–552.

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Figures (9)

Fig. 1
Fig. 1

Schematic drawing illustrating a haze measurement setup with an integrating sphere. The opening angle of the haze measurement is 2Δθ. The coherently transmitted light and parts of the incoherently transmitted light fall within the cone of the opening angle and thus escape from the integrating sphere.

Fig. 2
Fig. 2

AFM images of the four investigated AIT samples. The rms roughness ( σ r m s ) of each sample was calculated based on the height distribution and is shown in the image. Note that samples AIT-3 and AIT-4 have the same σ r m s but different morphology.

Fig. 3
Fig. 3

ARS of the transmitted light for the samples shown in Fig. 1, at λ = 620 nm.

Fig. 4
Fig. 4

Simulated haze in transmission for four AIT samples. The symbols show the measured haze, while the lines show the simulated haze using the calculated ARS of the samples. a) Samples AIT-1 and AIT2 with different σrms ; b) Samples AIT-3 and AIT-4 with the same σrms.

Fig. 5
Fig. 5

Haze in transmission for the four AIT samples of Fig. 2. The symbols show the measured data, while the lines show the haze calculated from Eq. (3).

Fig. 6
Fig. 6

Measured power spectral density (symbols) of the four investigated AIT samples and, as a reference, of a textured AZO sample. The lines are fitted PSD functions using Eq. 10(a).

Fig. 7
Fig. 7

a) Calculated fit factor C(λ) using Eqs. (7) and (12) b) Relevant roughness values σ r e l ( λ ) , using Eq. (13).

Fig. 8
Fig. 8

Haze calculated using Eq. (14). Here, both the incoherent light scattered inside the opening angle of the haze measurement as well as the relevant roughness for the scattered wavelength are considered.

Fig. 9
Fig. 9

Calculated haze values at λ = 650 nm as a function of intrinsic roughness σint and autocorrelation length. Graphs show the transmission haze value of a) glass (n1 = 1.5) into air (n2 = 1), and b) AZO (n1 = 2) into a-Si:H (n2 = 4).

Tables (2)

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Table 1 Sample preparation conditions

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Table 2 Surface characteristics of the samples shown in Fig. 2

Equations (16)

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H T = 1 T c o h e r e m t T t o t a l
H T1 = 1 T total 2π Δθ π 2 ARS( θ )Sinθdθ
H T2 =1exp[ ( 2π σ rms ( n 1 n 2 ) λ ) 2 ]
H T3 =1exp[ ( 2π σ rms C( λ )( n 1 n 2 ) λ ) m ]
H T4 =1exp[ 4 π 2 ε 1 ( σ rms λ ) 2 × { ε 2 ε 1 1 } 2 ×{ 12 ε 2 G( l ) λ SinΔθ } ]
G( l )= 1 2Δq Δq Δq PS D 1D ( q )dq
C( λ )= 12 n 2 G( l ) λ SinΔθ
σ rel 2 ( λ )=2π f=0 1 λ PSD( f )fdf
PSD( f )= A [ 1+ ( Bf ) 2 ] ( C+1 ) 2
PS D 2D ( f )= 2π σ int 2 l 2 [ 1+ ( 2πlf ) 2 ] 3 2
PS D 1D ( f x )= 4 σ int 2 l 1+ ( 2πl f x ) 2
ACV( τ )= σ int 2 exp( τ /l )
σ int 2 =2π f=0 PS D 2D ( f )fdf
G( l )= 2 Δq tan 1 ( lΔq )
σ rel = σ int 1 1 1+ 4 π 2 l 2 λ 2
H T4 =1exp[ 4 π 2 ε 1 ( σ int λ ) 2 ×{ 11/ 1+ 4 π 2 l 2 λ 2 }× { ε 2 ε 1 1 } 2 ×{ 12 ε 2 G( l ) λ SinΔθ } ]

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