Abstract

Amorphous silicon/crystalline silicon (a-Si/c-Si) micromorph tandem cells, with best confirmed efficiency of 12.3%, have yet to fully approach their theoretical performance limits. In this work, we consider a strategy for improving the light trapping and charge collection of a-Si/c-Si micromorph tandem cells using random texturing with adjustable short-range correlations and long-range periodicity. In order to consider the full-spectrum absorption of a-Si and c-Si, a novel dispersion model known as a quadratic complex rational function (QCRF) is applied to photovoltaic materials (e.g., a-Si, c-Si and silver). It has the advantage of accurately modeling experimental semiconductor dielectric values over the entire relevant solar bandwidth from 300—1000 nm in a single simulation. This wide-band dispersion model is then used to model a silicon tandem cell stack (ITO/a-Si:H/c-Si:H/silver), as two parameters are varied: maximum texturing height h and correlation parameter f. Even without any other light trapping methods, our front texturing method demonstrates 12.37% stabilized cell efficiency and 12.79 mA/cm2 in a 2 μm-thick active layer.

© 2014 Optical Society of America

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2014 (1)

Y.-C. Tsao, C. Fisker, and T. Garm Pedersen, “Optical absorption of amorphous silicon on anodized aluminum substrates for solar cell applications,” Optics Communications 315, 17–25 (2014).
[CrossRef]

2013 (7)

V. Jovanov, U. Palanchoke, P. Magnus, H. Stiebig, J. Hüpkes, P. Sichanugrist, M. Konagai, S. Wiesendanger, C. Rockstuhl, and D. Knipp, “Light trapping in periodically textured amorphous silicon thin film solar cells using realistic interface morphologies,” Optics Express 21, A595–A606 (2013).
[CrossRef] [PubMed]

S.-G. Ha, J. Cho, J. Choi, H. Kim, and K.-Y. Jung, “FDTD dispersive modeling of human tissues based on quadratic complex rational function,” IEEE Transactions on Antennas and Propagation 61, 996–999 (2013).
[CrossRef]

H. Chung, J. Cho, S.-G. Ha, S. Ju, and K.-Y. Jung, “Accurate FDTD dispersive modeling for concrete materials.” ETRI Journal 35, 915–918, (2013).
[CrossRef]

L. T. Varghese, Y. Xuan, B. Niu, L. Fan, P. Bermel, and M. Qi, “Enhanced photon management of thin-film silicon solar cells using inverse opal photonic crystals with 3d photonic bandgaps,” Advanced Optical Materials 1, 692–698 (2013).
[CrossRef]

S. Wiesendanger, M. Zilk, T. Pertsch, F. Lederer, and C. Rockstuhl, “A path to implement optimized randomly textured surfaces for solar cells,” Applied Physics Letters 103, 131115 (2013).
[CrossRef]

M.A. Green, K. Emery, Y. Hishikawa, W. Warta, and E.D. Dunlop, “Solar cell efficiency tables (version 43),” Prog. Photovolt.: Res. Appl. 21, 1–9 (2013).
[CrossRef]

C. L. Tan, A. Karar, K. Alameh, and Y. T. Lee, “Optical absorption enhancement of hybrid-plasmonic-based metal-semiconductor-metal photodetector incorporating metal nanogratings and embedded metal nanoparticles,” Optics express 21, 1713–1725 (2013).
[CrossRef] [PubMed]

2012 (2)

O. D. Miller, E. Yablonovitch, and S. R. Kurtz, “Strong internal and external luminescence as solar cells approach the shockley-queisser limit,” IEEE J. Photovolt. 2, 303–311 (2012).
[CrossRef]

Z. Yu, A. Raman, and S. Fan, “Thermodynamic upper bound on broadband light coupling with photonic structures,” Physical review letters 109, 173901 (2012).
[CrossRef] [PubMed]

2011 (5)

R. Dewan, I. Vasilev, V. Jovanov, and D. Knipp, “Optical enhancement and losses of pyramid textured thin-film silicon solar cells,” Journal of Applied Physics 110, 013101 (2011).
[CrossRef]

Z. Yu, A. Raman, and S. Fan, “Nanophotonic light-trapping theory for solar cells,” Applied Physics A 105, 329–339 (2011).
[CrossRef]

J. Lacombe, O. Sergeev, K. Chakanga, K. von Maydell, and C. Agert, “Three dimensional optical modeling of amorphous silicon thin film solar cells using the finite-difference time-domain method including real randomly surface topographies,” Journal of Applied Physics 110, 023102 (2011).
[CrossRef]

J. Üpping, A. Bielawny, R. B. Wehrspohn, T. Beckers, R. Carius, U. Rau, S. Fahr, C. Rockstuhl, F. Lederer, M. Kroll, T. Pertsch, L. Steidl, and R. Zentel, “Three-dimensional photonic crystal intermediate reflectors for enhanced light-trapping in tandem solar cells,” Advanced Materials 23, 3896–3900 (2011).
[CrossRef] [PubMed]

D. Madzharov, R. Dewan, and D. Knipp, “Influence of front and back grating on light trapping in microcrystalline thin-film silicon solar cells,” Optics express 19, A95–A107 (2011).
[CrossRef] [PubMed]

2010 (2)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the fdtd method,” Computer Physics Communications 181, 687–702 (2010).
[CrossRef]

C. Rockstuhl, S. Fahr, K. Bittkau, T. Beckers, R. Carius, F.-J. Haug, T. Söderström, C. Ballif, and F. Lederer, “Comparison and optimization of randomly textured surfaces in thin-film solar cells,” Optics express 18, A335–A341 (2010).
[CrossRef] [PubMed]

2009 (2)

M. Ghebrebrhan, P. Bermel, Y. Avniel, J. D. Joannopoulos, and S. G. Johnson, “Global optimization of silicon photovoltaic cell front coatings,” Optics express 17, 7505–7518 (2009).
[CrossRef] [PubMed]

A. G. Aberle, “Thin-film solar cells,” Thin Solid Films 517, 4706–4710 (2009).
[CrossRef]

2008 (4)

J. G. Mutitu, S. Shi, C. Chen, T. Creazzo, A. Barnett, C. Honsberg, and D. W. Prather, “Thin film solar cell design based on photonic crystal and diffractive grating structures,” Optics Express 16, 15238–15248 (2008).
[CrossRef] [PubMed]

F. L. Teixeira, “Time-domain finite-difference and finite-element methods for maxwell equations in complex media,” IEEE Transactions on Antennas and Propagation 56, 2150–2166 (2008).
[CrossRef]

H. Sai, H. Fujiwara, M. Kondo, and Y. Kanamori, “Enhancement of light trapping in thin-film hydrogenated microcrystalline si solar cells using back reflectors with self-ordered dimple pattern,” Applied Physics Letters 93, 143501 (2008).
[CrossRef]

A. Bielawny, J. Üpping, P. T. Miclea, R. B. Wehrspohn, C. Rockstuhl, F. Lederer, M. Peters, L. Steidl, R. Zentel, S.-M. Lee, M. Knez, A. Lambertz, and R. Carius, “3d photonic crystal intermediate reflector for micromorph thin-film tandem solar cell,” physica status solidi (a) 205, 2796–2810 (2008).
[CrossRef]

2007 (4)

N.S. Lewis, “Toward Cost-Effective Solar Energy Use,” Science 315, 798–801 (2007).
[CrossRef] [PubMed]

P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Optics Express 15, 16986–17000 (2007).
[CrossRef] [PubMed]

M. Berginski, J. Hupkes, M. Schulte, G. Schope, H. Stiebig, B. Rech, and M. Wuttig, “The effect of front zno: Al surface texture and optical transparency on efficient light trapping in silicon thin-film solar cells,” Journal of Applied Physics 101, 074903 (2007).
[CrossRef]

S.-S. Lo, C.-C. Chen, F. Garwe, and T. Pertch, “Broad-band anti-reflection coupler for a: Si thin-film solar cell,” Journal of Physics D: Applied Physics 40, 754 (2007).
[CrossRef]

2004 (1)

K. Yamamoto, A. Nakajima, M. Yoshimi, T. Sawada, S. Fukuda, T. Suezaki, M. Ichikawa, Y. Koi, M. Goto, T. Meguro, T. Matsuda, M. Kondo, T. Sasaki, and Y. Tawada, “A high efficiency thin film silicon solar cell and module,” Solar Energy 77, 939–949 (2004).
[CrossRef]

2003 (1)

R. Collins, A. Ferlauto, G. Ferreira, C. Chen, J. Koh, R. Koval, Y. Lee, J. Pearce, and C. Wronski, “Evolution of microstructure and phase in amorphous, protocrystalline, and microcrystalline silicon studied by real time spectroscopic ellipsometry,” Solar Energy Materials and Solar Cells 78, 143–180 (2003).
[CrossRef]

1998 (2)

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,” Journal of Applied Physics 83, 3323–3336 (1998).
[CrossRef]

J. Zhao, A. Wang, M. A. Green, and F. Ferrazza, “19.8% efficient honeycomb textured multicrystalline and 24.4% monocrystalline silicon solar cells,” Applied Physics Letters 73, 1991 (1998).
[CrossRef]

1996 (2)

R. Brendel, M. Hirsch, R. Plieninger, and J. Werner, “Quantum efficiency analysis of thin-layer silicon solar cells with back surface fields and optical confinement,” IEEE Transactions on Electron Devices 43, 1104–1113 (1996).
[CrossRef]

G. Jellison and F. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Applied Physics Letters 69, 371–373 (1996).
[CrossRef]

1984 (1)

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Transactions on Electron Devices 31, 711–716 (1984).
[CrossRef]

1982 (1)

E. Yablonovitch, “Statistical ray optics,” JOSA 72, 899–907 (1982).
[CrossRef]

1980 (1)

A. De Vos, “Detailed balance limit of the efficiency of tandem solar cells,” J. Phys. D 13, 839–845 (1980).

1966 (1)

E. L. Haines and A. B. Whitehead, “Pulse height defect and energy dispersion in semiconductor detectors,” Review of Scientific Instruments 37, 190–194 (1966).
[CrossRef]

1961 (1)

W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” Journal of applied physics 32, 510–519 (1961).
[CrossRef]

Aberle, A. G.

A. G. Aberle, “Thin-film solar cells,” Thin Solid Films 517, 4706–4710 (2009).
[CrossRef]

Agert, C.

J. Lacombe, O. Sergeev, K. Chakanga, K. von Maydell, and C. Agert, “Three dimensional optical modeling of amorphous silicon thin film solar cells using the finite-difference time-domain method including real randomly surface topographies,” Journal of Applied Physics 110, 023102 (2011).
[CrossRef]

Alameh, K.

C. L. Tan, A. Karar, K. Alameh, and Y. T. Lee, “Optical absorption enhancement of hybrid-plasmonic-based metal-semiconductor-metal photodetector incorporating metal nanogratings and embedded metal nanoparticles,” Optics express 21, 1713–1725 (2013).
[CrossRef] [PubMed]

Avniel, Y.

M. Ghebrebrhan, P. Bermel, Y. Avniel, J. D. Joannopoulos, and S. G. Johnson, “Global optimization of silicon photovoltaic cell front coatings,” Optics express 17, 7505–7518 (2009).
[CrossRef] [PubMed]

Ballif, C.

C. Rockstuhl, S. Fahr, K. Bittkau, T. Beckers, R. Carius, F.-J. Haug, T. Söderström, C. Ballif, and F. Lederer, “Comparison and optimization of randomly textured surfaces in thin-film solar cells,” Optics express 18, A335–A341 (2010).
[CrossRef] [PubMed]

Barnett, A.

J. G. Mutitu, S. Shi, C. Chen, T. Creazzo, A. Barnett, C. Honsberg, and D. W. Prather, “Thin film solar cell design based on photonic crystal and diffractive grating structures,” Optics Express 16, 15238–15248 (2008).
[CrossRef] [PubMed]

Beckers, T.

J. Üpping, A. Bielawny, R. B. Wehrspohn, T. Beckers, R. Carius, U. Rau, S. Fahr, C. Rockstuhl, F. Lederer, M. Kroll, T. Pertsch, L. Steidl, and R. Zentel, “Three-dimensional photonic crystal intermediate reflectors for enhanced light-trapping in tandem solar cells,” Advanced Materials 23, 3896–3900 (2011).
[CrossRef] [PubMed]

C. Rockstuhl, S. Fahr, K. Bittkau, T. Beckers, R. Carius, F.-J. Haug, T. Söderström, C. Ballif, and F. Lederer, “Comparison and optimization of randomly textured surfaces in thin-film solar cells,” Optics express 18, A335–A341 (2010).
[CrossRef] [PubMed]

Berginski, M.

M. Berginski, J. Hupkes, M. Schulte, G. Schope, H. Stiebig, B. Rech, and M. Wuttig, “The effect of front zno: Al surface texture and optical transparency on efficient light trapping in silicon thin-film solar cells,” Journal of Applied Physics 101, 074903 (2007).
[CrossRef]

Bermel, P.

L. T. Varghese, Y. Xuan, B. Niu, L. Fan, P. Bermel, and M. Qi, “Enhanced photon management of thin-film silicon solar cells using inverse opal photonic crystals with 3d photonic bandgaps,” Advanced Optical Materials 1, 692–698 (2013).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the fdtd method,” Computer Physics Communications 181, 687–702 (2010).
[CrossRef]

M. Ghebrebrhan, P. Bermel, Y. Avniel, J. D. Joannopoulos, and S. G. Johnson, “Global optimization of silicon photovoltaic cell front coatings,” Optics express 17, 7505–7518 (2009).
[CrossRef] [PubMed]

P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Optics Express 15, 16986–17000 (2007).
[CrossRef] [PubMed]

Bielawny, A.

J. Üpping, A. Bielawny, R. B. Wehrspohn, T. Beckers, R. Carius, U. Rau, S. Fahr, C. Rockstuhl, F. Lederer, M. Kroll, T. Pertsch, L. Steidl, and R. Zentel, “Three-dimensional photonic crystal intermediate reflectors for enhanced light-trapping in tandem solar cells,” Advanced Materials 23, 3896–3900 (2011).
[CrossRef] [PubMed]

A. Bielawny, J. Üpping, P. T. Miclea, R. B. Wehrspohn, C. Rockstuhl, F. Lederer, M. Peters, L. Steidl, R. Zentel, S.-M. Lee, M. Knez, A. Lambertz, and R. Carius, “3d photonic crystal intermediate reflector for micromorph thin-film tandem solar cell,” physica status solidi (a) 205, 2796–2810 (2008).
[CrossRef]

Bittkau, K.

C. Rockstuhl, S. Fahr, K. Bittkau, T. Beckers, R. Carius, F.-J. Haug, T. Söderström, C. Ballif, and F. Lederer, “Comparison and optimization of randomly textured surfaces in thin-film solar cells,” Optics express 18, A335–A341 (2010).
[CrossRef] [PubMed]

Brendel, R.

R. Brendel, M. Hirsch, R. Plieninger, and J. Werner, “Quantum efficiency analysis of thin-layer silicon solar cells with back surface fields and optical confinement,” IEEE Transactions on Electron Devices 43, 1104–1113 (1996).
[CrossRef]

Brooks, B. G.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Transactions on Electron Devices 31, 711–716 (1984).
[CrossRef]

Carius, R.

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M. Berginski, J. Hupkes, M. Schulte, G. Schope, H. Stiebig, B. Rech, and M. Wuttig, “The effect of front zno: Al surface texture and optical transparency on efficient light trapping in silicon thin-film solar cells,” Journal of Applied Physics 101, 074903 (2007).
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J. G. Mutitu, S. Shi, C. Chen, T. Creazzo, A. Barnett, C. Honsberg, and D. W. Prather, “Thin film solar cell design based on photonic crystal and diffractive grating structures,” Optics Express 16, 15238–15248 (2008).
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Figures (10)

Fig. 1
Fig. 1

Cross section of a-Si/c-Si tandem solar cell. It is contacted with indium tin oxide on the front, and silver in the back, and encapsulated with glass. The randomly textured front surface is shown from two different perspectives. Note that the same textured surface on the ITO and a-Si is also applied to the top of the c-Si layer. The minimum glass thickness of 1500 nm is used only in simulation. Experimental thicknesses are greater, but Fig. 4 shows that this only has a minor effect on the absorption spectrum.

Fig. 2
Fig. 2

Dispersion curve fittings of photovoltaic materials using the QCRF model. The solid lines and symbols indicate the results of the QCRF model and the experimental data of dispersive material, respectively: (a) Real part of relative permittivity of a-Si. (b) Imaginary part of relative permittivity of a-Si. (c) Real part of relative permittivity of c-Si. (d) Imaginary part of relative permittivity of c-Si. (e) Real part of relative permittivity of silver.

Fig. 3
Fig. 3

The theoretical and simulated absorption rates of 300 nm thick a-Si, the former being obtained from Eq. (3) combined with literature data from ref. [36], and the latter being obtained from our QCRF model. The root mean square error from comparing the two data sets is 3.97%.

Fig. 4
Fig. 4

The left figure indicates the experimental absorption rate for a 1500 nm thick c-Si solar cell. It is adapted from recently published research [38]. The right figure indicates the absorption rate obtained by the simulation.

Fig. 5
Fig. 5

(a) Contour plot showing calculated short-circuit current density as a function of maximum texturing height and correlation factor for 2D solar cells, using TM-polarized light incident at normal incidence. Note that the optimal performance is expected to occur at f = 0.975, ln(1 − f) = −3.689 and h = 1000 nm in 2-D structure. (b) The optimized 2D geometry used to generate our contour plot.

Fig. 6
Fig. 6

Random surface texturing algorithm represented in terms of correlation factor (f).

Fig. 7
Fig. 7

Efficiency versus thickness of (left) indium-tin oxide and (right) a-Si. Each red dot corresponds to a single 3-D FDTD simulation and is projected from a higher-dimension manifold of design space onto the axes displayed, in order to identify the optimal values for these individual parameters. Note that each simulation is performed in a flat solar cell structure without texturing.

Fig. 8
Fig. 8

Contour plot showing silicon tandem cell efficiency versus texturing height and the correlation factor. Note that the optimal performance is predicted to occur when f = 0.999 and h = 1158 nm, as explained in the text.

Fig. 9
Fig. 9

Light absorption rate of the optimized tandem silicon solar cell with two reference absorption curves that are obtained from a flat structure and a totally random structure for normal incidence. (a) Light absorption in the a-Si layer. (b) Light absorption in the a-Si layer. (c) Normalized light absorption in the c-Si layer with rest of light filtered by the a-Si layer and by subtraction of the first reflected light at the SiO2 layer. (d) Total light absorption in both layers.

Fig. 10
Fig. 10

Optimal random surface texturing in a tandem cell application shown from two different perspectives.

Equations (9)

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ε r , QCRF ( ω ) = A 0 + A 1 ( j ω ) + A 2 ( j ω ) 2 1 + B 1 ( j ω ) + B 2 ( j ω ) 2 ,
r ( λ ) = ρ 1 + n = 1 τ 1 τ 1 ( ρ 1 ) n 1 ρ 2 n e j ω t = ρ 1 + τ 1 τ 1 ρ 2 1 e j ω t ρ 1
t ( λ ) = τ 1 τ 2 n = 0 ( ρ 2 ρ 1 ) n e j ω t = τ 1 τ 2 1 ρ 2 ρ 1 e j ω t ,
Z n + 1 = f * Z n + 1 f 2 * r n ,
Z n + 1 = w ( n , N ) * Z n + ( f w ( n , N ) ) * Z N n 1 + 1 f 2 * r n ,
w ( n , N ) = f ( f / 2 ) * exp ( ( N 2 * n + 2 ) ) ,
Z i + 1 , j + 1 = w ( i , N i ) * Z i , j + 1 + ( f / 2 w ( i , N i ) ) * Z N + 2 i , j + 1 + w ( j , N j ) * Z i + 1 , j + ( f / 2 w ( j , N j ) ) * Z i + 1 , N + 2 j + 1 f 2 * r n ,
w ( i , N i ) = f / 2 ( f / 4 ) * exp ( ( N i 2 * i + 2 ) ) , w ( j , N j ) = f / 2 ( f / 4 ) * exp ( ( N j 2 * j + 2 ) ) .
f 2 D = f 3 D ( N Δ y 2 D / Δ y 3 D ) ,

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