Abstract

The front-coating (FC) of a solar cell controls its efficiency, determining admission of light into the absorbing material and potentially trapping light to enhance thin absorbers. Single-layer FC designs are well known, especially for thick absorbers where their only purpose is to reduce reflections. Multilayer FCs could improve performance, but require global optimization to design. For narrow bandwidths, one can always achieve nearly 100% absorption. For the entire solar bandwidth, however, a second FC layer improves performance by 6.1% for 256 μm wafer-based cells, or by 3.6% for 2 μm thin-film cells, while additional layers yield rapidly diminishing returns.

© 2009 Optical Society of America

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2008 (2)

2007 (1)

P. Bermel, C. Luo, L. Zeng, L. Kimerling, and J. D. Joannopoulos, "Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals," Opt. Express 15, 16,986-17,000 (2007).
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2005 (2)

S. Kucherenko and Y. Sytsko, "Application of deterministic low-discrepancy sequences in global optimization," Computational Optimization and Applications 30, 297-318 (2005).
[CrossRef]

A. Mahdjoub and L. Zighed, "New designs for graded refractive index antireflection coatings," Thin Solid Films 478, 299-304 (2005).
[CrossRef]

2004 (1)

M. Lipinski, P. Zieba, S. Kluska, M. Sokolowski, and H. Czternastek, "Optimization of SiNx:H layer for multicrystalline silicon solar cells," Opto-Electron.Rev. 12, 41-44 (2004).

2003 (2)

B. Richards, "Single-material TiO2 double-layer antireflection coatings," Sol. Energy Mat. Sol. Cells 79, 369-390 (2003).
[CrossRef]

S. Joe and F. Y. Kuo, "Remark on algorithm 659: Implementing Sobol’s quasirandom sequence generator," ACM Trans. Math. Soft. 29, 49-57 (2003).
[CrossRef]

2002 (1)

M. Farooq and M. Hutchins, "A novel design in composites of various materials for solar selective coatings," Sol. Energ. Mater. Sol. Cells 71, 523-535 (2002).
[CrossRef]

2001 (1)

J. M. Gablonsky and C. T. Kelley, "A locally-biased form of the DIRECT algorithm," J. Global Optim. 21(1), 27-37 (2001).
[CrossRef]

2000 (1)

J. Sukmanowski, C. Paulick, O. Sohr, K. Andert, and F. Royer, "Light absorption enhancement in thin silicon layers," J. Appl. Phys. 88, 2484-2489 (2000).
[CrossRef]

1999 (5)

P. Nubile, "Analytical design of antireflection coatings for silicon photovoltaic devices," Thin Solid Films 342, 257-261 (1999).
[CrossRef]

H. Nagel, A. G. Aberle, and R. Hezel, "Optimised Antireflection Coatings for Planar Silicon Solar Cells using Remote PECVD Silicon Nitride and Porous Silicon Dioxide," Prog. Photovoltaics: Res. Appl. 7, 245-260 (1999).
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M. A. Contreras, B. Egaas, K. Ramanathan, J. Hiltner, A. Swartzlander, F. Hasoon, and R. Noufi, "Progress Toward 20% Efficiency in Cu(In,Ga)Se2 Polycrystalline Thin-film Solar Cells," Prog. Photovolt: Res. Appl. 7, 311-316 (1999).
[CrossRef]

J. Zhao, A. Wang, P. Campbell, and M. A. Green, "A 19.8% Efficient Honeycomb Multicrystalline Silicon Solar Cell with Improved Light Trapping," IEEE Trans. Electron Dev. 46, 1978-1983 (1999).
[CrossRef]

D. Whittaker and I. Culshaw, "Scattering-matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999).
[CrossRef]

1998 (3)

M. Cid, N. Stem, C. Brunetti, A. Beloto, and C. Ramos, "Improvements in anti-reflection coatings for highefficiency silicon solar cells," Surf. Coat Technol. 106, 117-120 (1998).
[CrossRef]

J. Zhao, A. Wang, M. Green, and F. Ferrazza, "Novel 19.8% efficient ’honeycomb’ textured multicrystalline and 24.4% monocrystalline silicon solar cells," Appl. Phys. Lett. 73, 1991-1993 (1998).
[CrossRef]

C. Herzinger, B. Johs, W. McGahan, J. Woollam, and W. Paulson, "Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation," J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

1997 (3)

S. Chaudhuri, D. Bhattacharyya, A. Maity, and A. Pal, "Surface coatings for solar application," Mater. Sci. Forum 246, 181-206 (1997).
[CrossRef]

C. Lampert, "International development and advances in solar selective absorbers," Proc. SPIE 3138, 134-145 (1997).
[CrossRef]

F. Zhu, P. Jennings, J. Cornish, G. Hefter, and K. Luczak, "Optimal optical design of thin-film photovoltaic devices," Sol. Energ. Mat. Sol. Cells 49, 163-169 (1997).
[CrossRef]

1996 (2)

J. Schoen and E. Bucher, "Computer modeling of the performance of some metal/dielectric multilayers for hightemperature solar selective absorbers," Sol. Energy Mater. Sol. Cells 43, 59-65 (1996).
[CrossRef]

L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. A 13, 1024-1035 (1996).
[CrossRef]

1995 (1)

G. Was, V. Rotberg, D. Platts, and J. Bomback, "Optical properties of Ti and N implanted soda lime glass," Appl. Phys. Lett. 66, 142-144 (1995).
[CrossRef]

1994 (1)

J. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comp. Phys. 114, 185-200 (1994).
[CrossRef]

1991 (1)

J. Zhao and M. Green, "Optimized Antireflection Coatings for High-Efficiency Silicon Solar Cells," IEEE Trans. Electron Dev. 38, 1925 (1991).
[CrossRef]

1988 (1)

P. Bratley and B. L. Fox, "Algorithm 659: Implementing Sobol’s quasirandom sequence generator," ACM Trans. Math. Soft. 14, 88-100 (1988).
[CrossRef]

1987 (1)

A. H. G. R. Kan and G. T. Timmer, "Stochastic global optimization methods," Math. Program. 39, 27-78 (1987).
[CrossRef]

1985 (2)

L. DeSandre, D. Song, H. MacLeod, M. Jacobson, and D. Osborn, "Thin-film multilayer filter designs for hybrid solar energy conversion systems," Proc. SPIE 562, 155-159 (1985).

A. Chandra and M. Mishra, "Solar absorption behavior of multilayer stacks," Energ. Convers. Manage. 25, 387-390 (1985).
[CrossRef]

1980 (4)

O. Abreu and G. Best, "Transmission, reflexion and absorption of visible radiation by the multiple covers of flat plate solar collectors," Sol. Energy Mater. 3, 371-380 (1980).
[CrossRef]

J. Nocedal, "Updating quasi-Newton matrices with limited storage," Math. Comput. 35, 773-782 (1980).
[CrossRef]

C. Carniglia and J. Apfel, "Maximum reflectance of multilayer dielectric mirrors in the presence of slight absorption," J. Opt. Soc. Am. 70, 523-534 (1980).
[CrossRef]

D. Gibson and P. Lissberger, "Use of the concept of equivalent layers in the design of multilayer dielectric reflectors with minimum absorption," Optica Acta 27, 1295-1299 (1980).
[CrossRef]

1978 (2)

B. Thornton and Q. Tran, "Optimum design of wideband selective absorbers with provision for specified included layers," Sol. Energy 20, 371-377 (1978).
[CrossRef]

Y. Pirogov and A. Tikhonravov, "Resonance absorption of wave energy in asymmetrical multilayer structures," Radioelektronika 21, 15-20 (1978).

1966 (1)

K. S. Yee, "Numerical solution of inital boundary value problems involving maxwell’s equations in isotropic media," IEEE Trans. Attennas Propag. AP-14, 302-307 (1966).

1961 (1)

W. Shockley and H. Queisser, "Detailed balance limit of efficiency of p-n junction solar cells," J. Appl. Phys. 32, 510 (1961).
[CrossRef]

Aberle, A. G.

H. Nagel, A. G. Aberle, and R. Hezel, "Optimised Antireflection Coatings for Planar Silicon Solar Cells using Remote PECVD Silicon Nitride and Porous Silicon Dioxide," Prog. Photovoltaics: Res. Appl. 7, 245-260 (1999).
[CrossRef]

Abreu, O.

O. Abreu and G. Best, "Transmission, reflexion and absorption of visible radiation by the multiple covers of flat plate solar collectors," Sol. Energy Mater. 3, 371-380 (1980).
[CrossRef]

Agrawal, M.

Andert, K.

J. Sukmanowski, C. Paulick, O. Sohr, K. Andert, and F. Royer, "Light absorption enhancement in thin silicon layers," J. Appl. Phys. 88, 2484-2489 (2000).
[CrossRef]

Apfel, J.

Beloto, A.

M. Cid, N. Stem, C. Brunetti, A. Beloto, and C. Ramos, "Improvements in anti-reflection coatings for highefficiency silicon solar cells," Surf. Coat Technol. 106, 117-120 (1998).
[CrossRef]

Berenger, J.

J. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comp. Phys. 114, 185-200 (1994).
[CrossRef]

Bermel, P.

P. Bermel, C. Luo, L. Zeng, L. Kimerling, and J. D. Joannopoulos, "Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals," Opt. Express 15, 16,986-17,000 (2007).
[CrossRef]

Best, G.

O. Abreu and G. Best, "Transmission, reflexion and absorption of visible radiation by the multiple covers of flat plate solar collectors," Sol. Energy Mater. 3, 371-380 (1980).
[CrossRef]

Bhattacharyya, D.

S. Chaudhuri, D. Bhattacharyya, A. Maity, and A. Pal, "Surface coatings for solar application," Mater. Sci. Forum 246, 181-206 (1997).
[CrossRef]

Bomback, J.

G. Was, V. Rotberg, D. Platts, and J. Bomback, "Optical properties of Ti and N implanted soda lime glass," Appl. Phys. Lett. 66, 142-144 (1995).
[CrossRef]

Bratley, P.

P. Bratley and B. L. Fox, "Algorithm 659: Implementing Sobol’s quasirandom sequence generator," ACM Trans. Math. Soft. 14, 88-100 (1988).
[CrossRef]

Brunetti, C.

M. Cid, N. Stem, C. Brunetti, A. Beloto, and C. Ramos, "Improvements in anti-reflection coatings for highefficiency silicon solar cells," Surf. Coat Technol. 106, 117-120 (1998).
[CrossRef]

Bucher, E.

J. Schoen and E. Bucher, "Computer modeling of the performance of some metal/dielectric multilayers for hightemperature solar selective absorbers," Sol. Energy Mater. Sol. Cells 43, 59-65 (1996).
[CrossRef]

Campbell, P.

J. Zhao, A. Wang, P. Campbell, and M. A. Green, "A 19.8% Efficient Honeycomb Multicrystalline Silicon Solar Cell with Improved Light Trapping," IEEE Trans. Electron Dev. 46, 1978-1983 (1999).
[CrossRef]

Carniglia, C.

Chandra, A.

A. Chandra and M. Mishra, "Solar absorption behavior of multilayer stacks," Energ. Convers. Manage. 25, 387-390 (1985).
[CrossRef]

Chaudhuri, S.

S. Chaudhuri, D. Bhattacharyya, A. Maity, and A. Pal, "Surface coatings for solar application," Mater. Sci. Forum 246, 181-206 (1997).
[CrossRef]

Cid, M.

M. Cid, N. Stem, C. Brunetti, A. Beloto, and C. Ramos, "Improvements in anti-reflection coatings for highefficiency silicon solar cells," Surf. Coat Technol. 106, 117-120 (1998).
[CrossRef]

Contreras, M. A.

M. A. Contreras, B. Egaas, K. Ramanathan, J. Hiltner, A. Swartzlander, F. Hasoon, and R. Noufi, "Progress Toward 20% Efficiency in Cu(In,Ga)Se2 Polycrystalline Thin-film Solar Cells," Prog. Photovolt: Res. Appl. 7, 311-316 (1999).
[CrossRef]

Cornish, J.

F. Zhu, P. Jennings, J. Cornish, G. Hefter, and K. Luczak, "Optimal optical design of thin-film photovoltaic devices," Sol. Energ. Mat. Sol. Cells 49, 163-169 (1997).
[CrossRef]

Culshaw, I.

D. Whittaker and I. Culshaw, "Scattering-matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999).
[CrossRef]

Czternastek, H.

M. Lipinski, P. Zieba, S. Kluska, M. Sokolowski, and H. Czternastek, "Optimization of SiNx:H layer for multicrystalline silicon solar cells," Opto-Electron.Rev. 12, 41-44 (2004).

DeSandre, L.

L. DeSandre, D. Song, H. MacLeod, M. Jacobson, and D. Osborn, "Thin-film multilayer filter designs for hybrid solar energy conversion systems," Proc. SPIE 562, 155-159 (1985).

Egaas, B.

M. A. Contreras, B. Egaas, K. Ramanathan, J. Hiltner, A. Swartzlander, F. Hasoon, and R. Noufi, "Progress Toward 20% Efficiency in Cu(In,Ga)Se2 Polycrystalline Thin-film Solar Cells," Prog. Photovolt: Res. Appl. 7, 311-316 (1999).
[CrossRef]

Farooq, M.

M. Farooq and M. Hutchins, "A novel design in composites of various materials for solar selective coatings," Sol. Energ. Mater. Sol. Cells 71, 523-535 (2002).
[CrossRef]

Ferrazza, F.

J. Zhao, A. Wang, M. Green, and F. Ferrazza, "Novel 19.8% efficient ’honeycomb’ textured multicrystalline and 24.4% monocrystalline silicon solar cells," Appl. Phys. Lett. 73, 1991-1993 (1998).
[CrossRef]

Fox, B. L.

P. Bratley and B. L. Fox, "Algorithm 659: Implementing Sobol’s quasirandom sequence generator," ACM Trans. Math. Soft. 14, 88-100 (1988).
[CrossRef]

Gablonsky, J. M.

J. M. Gablonsky and C. T. Kelley, "A locally-biased form of the DIRECT algorithm," J. Global Optim. 21(1), 27-37 (2001).
[CrossRef]

Gibson, D.

D. Gibson and P. Lissberger, "Use of the concept of equivalent layers in the design of multilayer dielectric reflectors with minimum absorption," Optica Acta 27, 1295-1299 (1980).
[CrossRef]

Green, M.

J. Zhao, A. Wang, M. Green, and F. Ferrazza, "Novel 19.8% efficient ’honeycomb’ textured multicrystalline and 24.4% monocrystalline silicon solar cells," Appl. Phys. Lett. 73, 1991-1993 (1998).
[CrossRef]

J. Zhao and M. Green, "Optimized Antireflection Coatings for High-Efficiency Silicon Solar Cells," IEEE Trans. Electron Dev. 38, 1925 (1991).
[CrossRef]

Green, M. A.

J. Zhao, A. Wang, P. Campbell, and M. A. Green, "A 19.8% Efficient Honeycomb Multicrystalline Silicon Solar Cell with Improved Light Trapping," IEEE Trans. Electron Dev. 46, 1978-1983 (1999).
[CrossRef]

Hasoon, F.

M. A. Contreras, B. Egaas, K. Ramanathan, J. Hiltner, A. Swartzlander, F. Hasoon, and R. Noufi, "Progress Toward 20% Efficiency in Cu(In,Ga)Se2 Polycrystalline Thin-film Solar Cells," Prog. Photovolt: Res. Appl. 7, 311-316 (1999).
[CrossRef]

Hefter, G.

F. Zhu, P. Jennings, J. Cornish, G. Hefter, and K. Luczak, "Optimal optical design of thin-film photovoltaic devices," Sol. Energ. Mat. Sol. Cells 49, 163-169 (1997).
[CrossRef]

Herzinger, C.

C. Herzinger, B. Johs, W. McGahan, J. Woollam, and W. Paulson, "Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation," J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

Hezel, R.

H. Nagel, A. G. Aberle, and R. Hezel, "Optimised Antireflection Coatings for Planar Silicon Solar Cells using Remote PECVD Silicon Nitride and Porous Silicon Dioxide," Prog. Photovoltaics: Res. Appl. 7, 245-260 (1999).
[CrossRef]

Hiltner, J.

M. A. Contreras, B. Egaas, K. Ramanathan, J. Hiltner, A. Swartzlander, F. Hasoon, and R. Noufi, "Progress Toward 20% Efficiency in Cu(In,Ga)Se2 Polycrystalline Thin-film Solar Cells," Prog. Photovolt: Res. Appl. 7, 311-316 (1999).
[CrossRef]

Hutchins, M.

M. Farooq and M. Hutchins, "A novel design in composites of various materials for solar selective coatings," Sol. Energ. Mater. Sol. Cells 71, 523-535 (2002).
[CrossRef]

Jacobson, M.

L. DeSandre, D. Song, H. MacLeod, M. Jacobson, and D. Osborn, "Thin-film multilayer filter designs for hybrid solar energy conversion systems," Proc. SPIE 562, 155-159 (1985).

Jennings, P.

F. Zhu, P. Jennings, J. Cornish, G. Hefter, and K. Luczak, "Optimal optical design of thin-film photovoltaic devices," Sol. Energ. Mat. Sol. Cells 49, 163-169 (1997).
[CrossRef]

Joannopoulos, J. D.

P. Bermel, C. Luo, L. Zeng, L. Kimerling, and J. D. Joannopoulos, "Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals," Opt. Express 15, 16,986-17,000 (2007).
[CrossRef]

Joe, S.

S. Joe and F. Y. Kuo, "Remark on algorithm 659: Implementing Sobol’s quasirandom sequence generator," ACM Trans. Math. Soft. 29, 49-57 (2003).
[CrossRef]

Johs, B.

C. Herzinger, B. Johs, W. McGahan, J. Woollam, and W. Paulson, "Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation," J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

Kan, A. H. G. R.

A. H. G. R. Kan and G. T. Timmer, "Stochastic global optimization methods," Math. Program. 39, 27-78 (1987).
[CrossRef]

Kelley, C. T.

J. M. Gablonsky and C. T. Kelley, "A locally-biased form of the DIRECT algorithm," J. Global Optim. 21(1), 27-37 (2001).
[CrossRef]

Kim, J. K.

Kim, Y. S.

Kimerling, L.

P. Bermel, C. Luo, L. Zeng, L. Kimerling, and J. D. Joannopoulos, "Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals," Opt. Express 15, 16,986-17,000 (2007).
[CrossRef]

Kluska, S.

M. Lipinski, P. Zieba, S. Kluska, M. Sokolowski, and H. Czternastek, "Optimization of SiNx:H layer for multicrystalline silicon solar cells," Opto-Electron.Rev. 12, 41-44 (2004).

Kucherenko, S.

S. Kucherenko and Y. Sytsko, "Application of deterministic low-discrepancy sequences in global optimization," Computational Optimization and Applications 30, 297-318 (2005).
[CrossRef]

Kuo, F. Y.

S. Joe and F. Y. Kuo, "Remark on algorithm 659: Implementing Sobol’s quasirandom sequence generator," ACM Trans. Math. Soft. 29, 49-57 (2003).
[CrossRef]

Kuo, M.

Lampert, C.

C. Lampert, "International development and advances in solar selective absorbers," Proc. SPIE 3138, 134-145 (1997).
[CrossRef]

Li, L.

Lin, S.

Lipinski, M.

M. Lipinski, P. Zieba, S. Kluska, M. Sokolowski, and H. Czternastek, "Optimization of SiNx:H layer for multicrystalline silicon solar cells," Opto-Electron.Rev. 12, 41-44 (2004).

Lissberger, P.

D. Gibson and P. Lissberger, "Use of the concept of equivalent layers in the design of multilayer dielectric reflectors with minimum absorption," Optica Acta 27, 1295-1299 (1980).
[CrossRef]

Luczak, K.

F. Zhu, P. Jennings, J. Cornish, G. Hefter, and K. Luczak, "Optimal optical design of thin-film photovoltaic devices," Sol. Energ. Mat. Sol. Cells 49, 163-169 (1997).
[CrossRef]

Luo, C.

P. Bermel, C. Luo, L. Zeng, L. Kimerling, and J. D. Joannopoulos, "Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals," Opt. Express 15, 16,986-17,000 (2007).
[CrossRef]

MacLeod, H.

L. DeSandre, D. Song, H. MacLeod, M. Jacobson, and D. Osborn, "Thin-film multilayer filter designs for hybrid solar energy conversion systems," Proc. SPIE 562, 155-159 (1985).

Mahdjoub, A.

A. Mahdjoub and L. Zighed, "New designs for graded refractive index antireflection coatings," Thin Solid Films 478, 299-304 (2005).
[CrossRef]

Maity, A.

S. Chaudhuri, D. Bhattacharyya, A. Maity, and A. Pal, "Surface coatings for solar application," Mater. Sci. Forum 246, 181-206 (1997).
[CrossRef]

McGahan, W.

C. Herzinger, B. Johs, W. McGahan, J. Woollam, and W. Paulson, "Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation," J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

Mishra, M.

A. Chandra and M. Mishra, "Solar absorption behavior of multilayer stacks," Energ. Convers. Manage. 25, 387-390 (1985).
[CrossRef]

Mont, F.W.

Nagel, H.

H. Nagel, A. G. Aberle, and R. Hezel, "Optimised Antireflection Coatings for Planar Silicon Solar Cells using Remote PECVD Silicon Nitride and Porous Silicon Dioxide," Prog. Photovoltaics: Res. Appl. 7, 245-260 (1999).
[CrossRef]

Nocedal, J.

J. Nocedal, "Updating quasi-Newton matrices with limited storage," Math. Comput. 35, 773-782 (1980).
[CrossRef]

Noufi, R.

M. A. Contreras, B. Egaas, K. Ramanathan, J. Hiltner, A. Swartzlander, F. Hasoon, and R. Noufi, "Progress Toward 20% Efficiency in Cu(In,Ga)Se2 Polycrystalline Thin-film Solar Cells," Prog. Photovolt: Res. Appl. 7, 311-316 (1999).
[CrossRef]

Nubile, P.

P. Nubile, "Analytical design of antireflection coatings for silicon photovoltaic devices," Thin Solid Films 342, 257-261 (1999).
[CrossRef]

Osborn, D.

L. DeSandre, D. Song, H. MacLeod, M. Jacobson, and D. Osborn, "Thin-film multilayer filter designs for hybrid solar energy conversion systems," Proc. SPIE 562, 155-159 (1985).

Pal, A.

S. Chaudhuri, D. Bhattacharyya, A. Maity, and A. Pal, "Surface coatings for solar application," Mater. Sci. Forum 246, 181-206 (1997).
[CrossRef]

Paulick, C.

J. Sukmanowski, C. Paulick, O. Sohr, K. Andert, and F. Royer, "Light absorption enhancement in thin silicon layers," J. Appl. Phys. 88, 2484-2489 (2000).
[CrossRef]

Paulson, W.

C. Herzinger, B. Johs, W. McGahan, J. Woollam, and W. Paulson, "Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation," J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

Peumans, P.

Pirogov, Y.

Y. Pirogov and A. Tikhonravov, "Resonance absorption of wave energy in asymmetrical multilayer structures," Radioelektronika 21, 15-20 (1978).

Platts, D.

G. Was, V. Rotberg, D. Platts, and J. Bomback, "Optical properties of Ti and N implanted soda lime glass," Appl. Phys. Lett. 66, 142-144 (1995).
[CrossRef]

Poxson, D. J.

Queisser, H.

W. Shockley and H. Queisser, "Detailed balance limit of efficiency of p-n junction solar cells," J. Appl. Phys. 32, 510 (1961).
[CrossRef]

Ramanathan, K.

M. A. Contreras, B. Egaas, K. Ramanathan, J. Hiltner, A. Swartzlander, F. Hasoon, and R. Noufi, "Progress Toward 20% Efficiency in Cu(In,Ga)Se2 Polycrystalline Thin-film Solar Cells," Prog. Photovolt: Res. Appl. 7, 311-316 (1999).
[CrossRef]

Ramos, C.

M. Cid, N. Stem, C. Brunetti, A. Beloto, and C. Ramos, "Improvements in anti-reflection coatings for highefficiency silicon solar cells," Surf. Coat Technol. 106, 117-120 (1998).
[CrossRef]

Richards, B.

B. Richards, "Single-material TiO2 double-layer antireflection coatings," Sol. Energy Mat. Sol. Cells 79, 369-390 (2003).
[CrossRef]

Rotberg, V.

G. Was, V. Rotberg, D. Platts, and J. Bomback, "Optical properties of Ti and N implanted soda lime glass," Appl. Phys. Lett. 66, 142-144 (1995).
[CrossRef]

Royer, F.

J. Sukmanowski, C. Paulick, O. Sohr, K. Andert, and F. Royer, "Light absorption enhancement in thin silicon layers," J. Appl. Phys. 88, 2484-2489 (2000).
[CrossRef]

Schoen, J.

J. Schoen and E. Bucher, "Computer modeling of the performance of some metal/dielectric multilayers for hightemperature solar selective absorbers," Sol. Energy Mater. Sol. Cells 43, 59-65 (1996).
[CrossRef]

Schubert, E. F.

Shockley, W.

W. Shockley and H. Queisser, "Detailed balance limit of efficiency of p-n junction solar cells," J. Appl. Phys. 32, 510 (1961).
[CrossRef]

Sohr, O.

J. Sukmanowski, C. Paulick, O. Sohr, K. Andert, and F. Royer, "Light absorption enhancement in thin silicon layers," J. Appl. Phys. 88, 2484-2489 (2000).
[CrossRef]

Sokolowski, M.

M. Lipinski, P. Zieba, S. Kluska, M. Sokolowski, and H. Czternastek, "Optimization of SiNx:H layer for multicrystalline silicon solar cells," Opto-Electron.Rev. 12, 41-44 (2004).

Song, D.

L. DeSandre, D. Song, H. MacLeod, M. Jacobson, and D. Osborn, "Thin-film multilayer filter designs for hybrid solar energy conversion systems," Proc. SPIE 562, 155-159 (1985).

Stem, N.

M. Cid, N. Stem, C. Brunetti, A. Beloto, and C. Ramos, "Improvements in anti-reflection coatings for highefficiency silicon solar cells," Surf. Coat Technol. 106, 117-120 (1998).
[CrossRef]

Sukmanowski, J.

J. Sukmanowski, C. Paulick, O. Sohr, K. Andert, and F. Royer, "Light absorption enhancement in thin silicon layers," J. Appl. Phys. 88, 2484-2489 (2000).
[CrossRef]

Swartzlander, A.

M. A. Contreras, B. Egaas, K. Ramanathan, J. Hiltner, A. Swartzlander, F. Hasoon, and R. Noufi, "Progress Toward 20% Efficiency in Cu(In,Ga)Se2 Polycrystalline Thin-film Solar Cells," Prog. Photovolt: Res. Appl. 7, 311-316 (1999).
[CrossRef]

Sytsko, Y.

S. Kucherenko and Y. Sytsko, "Application of deterministic low-discrepancy sequences in global optimization," Computational Optimization and Applications 30, 297-318 (2005).
[CrossRef]

Thornton, B.

B. Thornton and Q. Tran, "Optimum design of wideband selective absorbers with provision for specified included layers," Sol. Energy 20, 371-377 (1978).
[CrossRef]

Tikhonravov, A.

Y. Pirogov and A. Tikhonravov, "Resonance absorption of wave energy in asymmetrical multilayer structures," Radioelektronika 21, 15-20 (1978).

Timmer, G. T.

A. H. G. R. Kan and G. T. Timmer, "Stochastic global optimization methods," Math. Program. 39, 27-78 (1987).
[CrossRef]

Tran, Q.

B. Thornton and Q. Tran, "Optimum design of wideband selective absorbers with provision for specified included layers," Sol. Energy 20, 371-377 (1978).
[CrossRef]

Wang, A.

J. Zhao, A. Wang, P. Campbell, and M. A. Green, "A 19.8% Efficient Honeycomb Multicrystalline Silicon Solar Cell with Improved Light Trapping," IEEE Trans. Electron Dev. 46, 1978-1983 (1999).
[CrossRef]

J. Zhao, A. Wang, M. Green, and F. Ferrazza, "Novel 19.8% efficient ’honeycomb’ textured multicrystalline and 24.4% monocrystalline silicon solar cells," Appl. Phys. Lett. 73, 1991-1993 (1998).
[CrossRef]

Was, G.

G. Was, V. Rotberg, D. Platts, and J. Bomback, "Optical properties of Ti and N implanted soda lime glass," Appl. Phys. Lett. 66, 142-144 (1995).
[CrossRef]

Whittaker, D.

D. Whittaker and I. Culshaw, "Scattering-matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999).
[CrossRef]

Woollam, J.

C. Herzinger, B. Johs, W. McGahan, J. Woollam, and W. Paulson, "Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation," J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

Yee, K. S.

K. S. Yee, "Numerical solution of inital boundary value problems involving maxwell’s equations in isotropic media," IEEE Trans. Attennas Propag. AP-14, 302-307 (1966).

Zeng, L.

P. Bermel, C. Luo, L. Zeng, L. Kimerling, and J. D. Joannopoulos, "Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals," Opt. Express 15, 16,986-17,000 (2007).
[CrossRef]

Zhao, J.

J. Zhao, A. Wang, P. Campbell, and M. A. Green, "A 19.8% Efficient Honeycomb Multicrystalline Silicon Solar Cell with Improved Light Trapping," IEEE Trans. Electron Dev. 46, 1978-1983 (1999).
[CrossRef]

J. Zhao, A. Wang, M. Green, and F. Ferrazza, "Novel 19.8% efficient ’honeycomb’ textured multicrystalline and 24.4% monocrystalline silicon solar cells," Appl. Phys. Lett. 73, 1991-1993 (1998).
[CrossRef]

J. Zhao and M. Green, "Optimized Antireflection Coatings for High-Efficiency Silicon Solar Cells," IEEE Trans. Electron Dev. 38, 1925 (1991).
[CrossRef]

Zhu, F.

F. Zhu, P. Jennings, J. Cornish, G. Hefter, and K. Luczak, "Optimal optical design of thin-film photovoltaic devices," Sol. Energ. Mat. Sol. Cells 49, 163-169 (1997).
[CrossRef]

Zieba, P.

M. Lipinski, P. Zieba, S. Kluska, M. Sokolowski, and H. Czternastek, "Optimization of SiNx:H layer for multicrystalline silicon solar cells," Opto-Electron.Rev. 12, 41-44 (2004).

Zighed, L.

A. Mahdjoub and L. Zighed, "New designs for graded refractive index antireflection coatings," Thin Solid Films 478, 299-304 (2005).
[CrossRef]

ACM Trans. Math. Soft. (2)

P. Bratley and B. L. Fox, "Algorithm 659: Implementing Sobol’s quasirandom sequence generator," ACM Trans. Math. Soft. 14, 88-100 (1988).
[CrossRef]

S. Joe and F. Y. Kuo, "Remark on algorithm 659: Implementing Sobol’s quasirandom sequence generator," ACM Trans. Math. Soft. 29, 49-57 (2003).
[CrossRef]

Appl. Phys. Lett. (2)

G. Was, V. Rotberg, D. Platts, and J. Bomback, "Optical properties of Ti and N implanted soda lime glass," Appl. Phys. Lett. 66, 142-144 (1995).
[CrossRef]

J. Zhao, A. Wang, M. Green, and F. Ferrazza, "Novel 19.8% efficient ’honeycomb’ textured multicrystalline and 24.4% monocrystalline silicon solar cells," Appl. Phys. Lett. 73, 1991-1993 (1998).
[CrossRef]

Computational Optimization and Applications (1)

S. Kucherenko and Y. Sytsko, "Application of deterministic low-discrepancy sequences in global optimization," Computational Optimization and Applications 30, 297-318 (2005).
[CrossRef]

Energ. Convers. Manage. (1)

A. Chandra and M. Mishra, "Solar absorption behavior of multilayer stacks," Energ. Convers. Manage. 25, 387-390 (1985).
[CrossRef]

IEEE Trans. Attennas Propag. (1)

K. S. Yee, "Numerical solution of inital boundary value problems involving maxwell’s equations in isotropic media," IEEE Trans. Attennas Propag. AP-14, 302-307 (1966).

IEEE Trans. Electron Dev. (2)

J. Zhao, A. Wang, P. Campbell, and M. A. Green, "A 19.8% Efficient Honeycomb Multicrystalline Silicon Solar Cell with Improved Light Trapping," IEEE Trans. Electron Dev. 46, 1978-1983 (1999).
[CrossRef]

J. Zhao and M. Green, "Optimized Antireflection Coatings for High-Efficiency Silicon Solar Cells," IEEE Trans. Electron Dev. 38, 1925 (1991).
[CrossRef]

J. Appl. Phys. (3)

C. Herzinger, B. Johs, W. McGahan, J. Woollam, and W. Paulson, "Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation," J. Appl. Phys. 83, 3323-3336 (1998).
[CrossRef]

J. Sukmanowski, C. Paulick, O. Sohr, K. Andert, and F. Royer, "Light absorption enhancement in thin silicon layers," J. Appl. Phys. 88, 2484-2489 (2000).
[CrossRef]

W. Shockley and H. Queisser, "Detailed balance limit of efficiency of p-n junction solar cells," J. Appl. Phys. 32, 510 (1961).
[CrossRef]

J. Comp. Phys. (1)

J. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comp. Phys. 114, 185-200 (1994).
[CrossRef]

J. Global Optim. (1)

J. M. Gablonsky and C. T. Kelley, "A locally-biased form of the DIRECT algorithm," J. Global Optim. 21(1), 27-37 (2001).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Mater. Sci. Forum (1)

S. Chaudhuri, D. Bhattacharyya, A. Maity, and A. Pal, "Surface coatings for solar application," Mater. Sci. Forum 246, 181-206 (1997).
[CrossRef]

Math. Comput. (1)

J. Nocedal, "Updating quasi-Newton matrices with limited storage," Math. Comput. 35, 773-782 (1980).
[CrossRef]

Math. Program. (1)

A. H. G. R. Kan and G. T. Timmer, "Stochastic global optimization methods," Math. Program. 39, 27-78 (1987).
[CrossRef]

Opt. Express (2)

M. Agrawal and P. Peumans, "Broadband optical absorption enhancement through coherent light trapping in thin-film photovoltaic cells," Opt. Express 16, 5385-5396 (2008).
[CrossRef] [PubMed]

P. Bermel, C. Luo, L. Zeng, L. Kimerling, and J. D. Joannopoulos, "Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals," Opt. Express 15, 16,986-17,000 (2007).
[CrossRef]

Opt. Lett. (1)

Optica Acta (1)

D. Gibson and P. Lissberger, "Use of the concept of equivalent layers in the design of multilayer dielectric reflectors with minimum absorption," Optica Acta 27, 1295-1299 (1980).
[CrossRef]

Opto-Electron. (1)

M. Lipinski, P. Zieba, S. Kluska, M. Sokolowski, and H. Czternastek, "Optimization of SiNx:H layer for multicrystalline silicon solar cells," Opto-Electron.Rev. 12, 41-44 (2004).

Phys. Rev. B (1)

D. Whittaker and I. Culshaw, "Scattering-matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999).
[CrossRef]

Proc. SPIE (2)

L. DeSandre, D. Song, H. MacLeod, M. Jacobson, and D. Osborn, "Thin-film multilayer filter designs for hybrid solar energy conversion systems," Proc. SPIE 562, 155-159 (1985).

C. Lampert, "International development and advances in solar selective absorbers," Proc. SPIE 3138, 134-145 (1997).
[CrossRef]

Prog. Photovolt: Res. Appl. (1)

M. A. Contreras, B. Egaas, K. Ramanathan, J. Hiltner, A. Swartzlander, F. Hasoon, and R. Noufi, "Progress Toward 20% Efficiency in Cu(In,Ga)Se2 Polycrystalline Thin-film Solar Cells," Prog. Photovolt: Res. Appl. 7, 311-316 (1999).
[CrossRef]

Prog. Photovoltaics: Res. Appl. (1)

H. Nagel, A. G. Aberle, and R. Hezel, "Optimised Antireflection Coatings for Planar Silicon Solar Cells using Remote PECVD Silicon Nitride and Porous Silicon Dioxide," Prog. Photovoltaics: Res. Appl. 7, 245-260 (1999).
[CrossRef]

Radioelektronika (1)

Y. Pirogov and A. Tikhonravov, "Resonance absorption of wave energy in asymmetrical multilayer structures," Radioelektronika 21, 15-20 (1978).

Sol. Energ. Mat. Sol. Cells (1)

F. Zhu, P. Jennings, J. Cornish, G. Hefter, and K. Luczak, "Optimal optical design of thin-film photovoltaic devices," Sol. Energ. Mat. Sol. Cells 49, 163-169 (1997).
[CrossRef]

Sol. Energ. Mater. Sol. Cells (1)

M. Farooq and M. Hutchins, "A novel design in composites of various materials for solar selective coatings," Sol. Energ. Mater. Sol. Cells 71, 523-535 (2002).
[CrossRef]

Sol. Energy (1)

B. Thornton and Q. Tran, "Optimum design of wideband selective absorbers with provision for specified included layers," Sol. Energy 20, 371-377 (1978).
[CrossRef]

Sol. Energy Mat. Sol. Cells (1)

B. Richards, "Single-material TiO2 double-layer antireflection coatings," Sol. Energy Mat. Sol. Cells 79, 369-390 (2003).
[CrossRef]

Sol. Energy Mater. (1)

O. Abreu and G. Best, "Transmission, reflexion and absorption of visible radiation by the multiple covers of flat plate solar collectors," Sol. Energy Mater. 3, 371-380 (1980).
[CrossRef]

Sol. Energy Mater. Sol. Cells (1)

J. Schoen and E. Bucher, "Computer modeling of the performance of some metal/dielectric multilayers for hightemperature solar selective absorbers," Sol. Energy Mater. Sol. Cells 43, 59-65 (1996).
[CrossRef]

Surf. Coat Technol. (1)

M. Cid, N. Stem, C. Brunetti, A. Beloto, and C. Ramos, "Improvements in anti-reflection coatings for highefficiency silicon solar cells," Surf. Coat Technol. 106, 117-120 (1998).
[CrossRef]

Thin Solid Films (2)

A. Mahdjoub and L. Zighed, "New designs for graded refractive index antireflection coatings," Thin Solid Films 478, 299-304 (2005).
[CrossRef]

P. Nubile, "Analytical design of antireflection coatings for silicon photovoltaic devices," Thin Solid Films 342, 257-261 (1999).
[CrossRef]

Other (10)

ASTMG173-03, Standard Tables for Reference Solar Spectral Irradiances: Direct Normal and Hemispherical on 37 degree Tilted Surface (ASTM International, West Conshohocken, Pennsylvania, 2005).
[PubMed]

J. Hanak, V. Korsun, and J. Pellicane, "Optimization studies of materials in hydrogenated amorphous silicon solar cells," No. 2nd in E.C. Photovoltaic Sol. Energ. Conf., pp. 270-277 (1979).

R. Brendel, Thin-Film Crystalline Silicon Solar Cells (Wiley-VCH, Weinheim, Germany, 2003).
[CrossRef]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, The Art of Scientific Computing (Cambridge University Press, New York, 2007).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton, Princeton, NJ, 2008).

J. Jackson, Classical Electrodynamics (Wiley, New York, 1999).

S. A. Campbell, Fabrication Engineering at the Micro- and Nanoscale (Oxford University Press, USA, 2008).

L. Luksan, "PLIS.FOR," Limited-memory BFGS method based on vector recurrences for large-scale unconstrained and box constrained minimization, URL http://www.uivt.cas.cz/ luksan/subroutines.html.

S. G. Johnson. URL http://ab-initio.mit.edu/nlopt.

G. Strang, Computational Science and Engineering (Wellesley-Cambridge Press, Wellesley, MA, 2007).

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Figures (9)

Fig. 1.
Fig. 1.

(Color online) Schematic illustration of solar cell designs studied in this paper: (a) a photovoltaically active silicon region (green), backed by a perfectly reflecting metal (gray), (b) diagram (a) with one or more front coating depicted in shades of blue, and (c) diagram (b) with one back dielectric coating layer.

Fig. 2.
Fig. 2.

(Color online) Fits of calculation parameters (red curves) to actual data derived from references (blue curves): (a) real index of crystalline silicon [4] (b) absorption length of crystalline silicon [4] (c) current weights w(λ) in Eq. (1), fit with a degree-100 Chebyshev approximation [35].

Fig. 3.
Fig. 3.

(Color online) A contour plot of the FOM of a cell with two front-coating layers versus the layer thickness (the indices of each layer are fixed at 1.27 and 4.35). The FOM ranges from 0.30 (black) to 0.38 (white). Clearly there are many local optima, necessitating a global optimization approach.

Fig. 4.
Fig. 4.

(Color online) The generated current efficiency as a function of wavelength; the parameters for each structure class (e.g., two front layers) are optimized separately at each wavelength i.e., this is the reflection spectrum for many different structures. Note that structures with one or more front layers display full absorption up to a particular wavelength λt that increases with the number of front layers.

Fig. 5.
Fig. 5.

(Color online) The generated current efficiency versus the bandwidth of incoming radiation; for bandwidths up to 265 nm the central wavelength is 902.8 nm, for band-widths above 265 nm, the maximum wavelength is fixed, while the minimum wavelength is decreased (which corresponds to a blue shift of the central wavelength).

Fig. 6.
Fig. 6.

(Color online) Absorption spectrum over the full absorbing bandwidth for a thin-film crystalline silicon solar cell (t = 2μm). (a) Optimized over the full bandwidth and (b) optimized only at λ = 902.8 nm.

Fig. 7.
Fig. 7.

(Color online) Figure of merit versus silicon slab thickness, both for a structure with no front layer (based on Fig. 1(a)) and optimized structures with 1-3 front layers (based on Fig. 1(b)).

Fig. 8.
Fig. 8.

(Color online) Relative difference in figure of merit, calculated as the relative difference of the FOM for the optimized structure with the given reflection phase and the FOM of a structure with the given phase and with the optimized front coating of the reference phase (θ= 0), versus the Fresnel reflection amplitude phase of the silicon-metal boundary.

Fig. 9.
Fig. 9.

(Color online) Absorption spectrum of the optimized single front coating reference structure for two different back-reflector phases (π/4 blue, and π red). The back-reflector simply shifts the peaks, but has a only negligible effect on the integrated absorption or the FOM.

Tables (1)

Tables Icon

Table 1. Table of optimized front-coating designs for one, two, and three front-coating layers, as in Fig. 1(b). Layers are ordered from closest to air. Coating thickness d in units of nm.

Equations (5)

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J sc = ∫dλ [ hc dI A ( λ ) ] w ( λ ) A ( λ )
FOM = w ( λ ) A ( λ ) w ( λ )
Q = 4 πtn ( λ ) λ R 1 R
R = 1 n ( λ ) ( n 2 / n 1 ) 3 1 + n ( λ ) ( n 2 / n 1 ) 3 2
r = e i ϕ 1 ( e i ϕ 0 + r 0 r 1 ) + r 1 e i ϕ 0 + r 0 e i ϕ 1 ( r 0 e i ϕ 0 + r 1 ) + r 0 r 1 e i ϕ 0 + 1

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