Nanopyramids and rear-located Ag nanoparticles for broad spectrum absorption enhancement in thin-film solar cells Yanpeng Shi,1 Xiaodong Wang,1,* Wen Liu,1 Tianshu Yang,1 Jing Ma,1 and Fuhua Yang2 1
Engineering Research Center for Semiconductor Integrated Technology, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China 2 [email protected] * [email protected]
Abstract: Light trapping is essential to improve the performance of thinfilm solar cells. In this paper, we performed a parametric optimization of nanopyramids and rear-located Ag nanoparticles that act as light trapping scheme to increase light absorption in thin-film c-Si solar cells. Our optimization reveals that the short-circuit current density in a solar cell employing only 5 μm silicon could exceed that of a standard 300 μm csilicon wafer-based cell. Furthermore, we analyzed the underlying physics of the light absorption enhancement through the electric field intensity profiles. ©2014 Optical Society of America OCIS codes: (040.5350) Photovoltaic; (050.1950) Diffraction gratings; (310.6628) Subwavelength structures, nanostructures; (350.4990) Particles; (350.6050) Solar energy.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). Y. Shi, X. Wang, W. Liu, T. Yang, R. Xu, and F. Yang, “Multilayer silver nanoparticles for light trapping in thin film solar cells,” J. Appl. Phys. 113(17), 176101 (2013). V. E. Ferry, M. A. Verschuuren, M. C. Lare, R. E. Schropp, H. A. Atwater, and A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett. 11(10), 4239–4245 (2011). K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008). E. Garnett and P. Yang, “Light trapping in silicon nanowire solar cells,” Nano Lett. 10(3), 1082–1087 (2010). Y. Chen, W. Han, and F. Yang, “Enhanced optical absorption in nanohole-textured silicon thin-film solar cells with rear-located metal particles,” Opt. Lett. 38(19), 3973–3975 (2013). J. Buencuerpo, L. E. Munioz-Camuniez, M. L. Dotor, and P. A. Postigo, “Optical absorption enhancement in a hybrid system photonic crystal - thin substrate for photovoltaic applications,” Opt. Express 20(S4 Suppl 4), A452–A464 (2012). S. B. Mallick, M. Agrawal, and P. Peumans, “Optimal light trapping in ultra-thin photonic crystal crystalline silicon solar cells,” Opt. Express 18(6), 5691–5706 (2010). M. D. Kelzenberg, D. B. Turner-Evans, M. C. Putnam, S. W. Boettcher, R. M. Briggs, J. Y. Baek, N. S. Lewis, and H. A. Atwater, “High-performance Si microwire photovoltaics,” Energy Environ. Sci. 4(3), 866 (2011). M. A. Green, “The path to 25% silicon solar cell efficiency: History of silicon cell evolution,” Prog. Photovolt. Res. Appl. 17(3), 183–189 (2009). J. L. Cruz-Campa, M. Okandan, P. J. Resnick, P. Clews, T. Pluym, R. K. Grubbs, V. P. Gupta, D. Zubia, and G. N. Nielson, “Microsystems enabled photovoltaics: 14.9% efficient 14 μm thick crystalline silicon solar cell,” Sol. Energy Mater. Sol. Cells 95(2), 551–558 (2011). J. Yoon, L. Li, A. V. Semichaevsky, J. H. Ryu, H. T. Johnson, R. G. Nuzzo, and J. A. Rogers, “Flexible concentrator photovoltaics based on microscale silicon solar cells embedded in luminescent waveguides,” Nat. Commun. 2, 343 (2011). G. Li, H. Li, J. Y. L. Ho, M. Wong, and H. S. Kwok, “Nanopyramid Structure for Ultrathin c-Si Tandem Solar Cells,” Nano Lett. 14(5), 2563–2568 (2014). A. Mavrokefalos, S. E. Han, S. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett. 12(6), 2792–2796 (2012).
#215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20473
15. S. E. Han and G. Chen, “Toward the Lambertian limit of light trapping in thin nanostructured silicon solar cells,” Nano Lett. 10(11), 4692–4696 (2010). 16. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72(7), 899–907 (1982). 17. M. A. Green, “Lambertian light trapping in textured solar cells and light-emitting diodes: analytical solutions,” Prog. Photovolt. Res. Appl. 10(4), 235–241 (2002). 18. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. 107(41), 17491–17496 (2010). 19. S. Eyderman, S. John, and A. Deinega, “Solar light trapping in slanted conical-pore photonic crystals: Beyond statistical ray trapping,” J. Appl. Phys. 113(15), 154315 (2013). 20. Y. Shi, X. Wang, W. Liu, T. Yang, J. Ma, and F. Yang, “Extraordinary optical absorption based on diffraction grating and rear-located bilayer silver nanoparticles,” Appl. Phys. Express 7(6), 062301 (2014). 21. D. M. Callahan, J. N. Munday, and H. A. Atwater, “Solar Cell light trapping beyond the ray optic limit,” Nano Lett. 12(1), 214–218 (2012). 22. N. A. Yahaya, N. Yamada, Y. Kotaki, and T. Nakayama, “Characterization of light absorption in thin-film silicon with periodic nanohole arrays,” Opt. Express 21(5), 5924–5930 (2013).
1. Introduction Bulk crystalline silicon (c-Si) solar cells dominate the photovoltaic (PV) market. Typically, 180−300 μm thick c-Si wafers are used to ensure adequate absorption of sunlight. In c-Si solar cells, the material accounts for more than 40% of the total module cost. To reduce the cost, thin-film solar cells with a thickness of a few micrometers have stimulated enormous research interest as a cheap alternative. But light transmission losses increase due to the thinner absorber layers. Therefore, light trapping technologies such as metal nanoparticles (NPs) [1–4], nanowires [5] and nanoholes [6–8], have been developed to achieve high absorption. However, one major reason for the low efficiency in solar cells with nanowires and nanoholes is the high surface recombination rates due to the large surface area, which is usually more than an order of magnitude larger than flat cells [9]. Their efficiencies are limited to around 10%, far smaller than 25% efficiency for state-of-the-art solar cells [10]. If thin-film solar cell with a thickness of a few micrometers can be made to absorb as efficiently as thick Si wafers, a significant cost reduction is expected. Recently, Cruz-Campa et al. [11] obtained an impressive 14.9% efficiency within 14 μm thick crystalline silicon solar cells. Yoon et al. [12] reported ~17.5% within 15 μm thick c-Si solar cells embedded in luminescent waveguides, utilizing luminescent solar concentrators. Li et al. [13] introduced a nanopyramid structure in ultrathin a-Si/c-Si tandem solar cells and they obtained conversion efficiencies of up to 13.3% for cells employed only 8 μm of silicon. Subsequently, Mavrokefalos et al. [14] attempted to demonstrate that thin-film silicon with nanopyramids could absorb equal light with bulk silicon. And they got the short-circuit current density (Jsc) of 37.5 mA/cm2 in 10 μm, which is comparable to 37.2 mA/cm2 of bulk silicon solar cell. The nanopyramid structure [14, 15] is promising in thin-film solar cell applications. In general, nanopyramid suffers relatively smaller surface area than other nanostructures such as nanowire, nanocylinder. Then, gratings couple well to incident light when they are tapered because the optical density varies gradually. When used on the front surfaces, they can largely decrease reflection. Ag is usually the preferred metal for plasmonic applications, as it offers lower absorption losses and generally higher optical cross-section than other metals. Especially, when placed on the bottom, it could scatter the transmitted light more efficiently. In this letter, we intend to improve the nanopyramids with rear-located Ag NPs to further enhance optical absorption. The expected role of the nanopyramids is to suppress surface reflection, and that of the rear Ag NPs is to supply light trapping. This proposed thin-film solar cell aims to generate Jsc higher than 300 μm wafer-based solar cell. We infer in this combined structure, the nanopyramids play the dominated role, and the Ag NPs supply assistance to make the performance progress further. The optical properties can be optimized by adjusting the parameters of nanopyramids and Ag NPs independently.
#215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20474
2. Numerical method A numerical analysis of the electromagnetic field features is performed utilizing finitedifference time-domain (FDTD) method (https://www.lumerical.com/). The dielectric functions are modeled using a Drude model for Ag and a Drude–Lorentz model for Si. Periodic boundary conditions are applied in the x- and y-directions while perfect matched layer boundary conditions are used for the z-direction. The calculated absorption is obtained through the difference of power flux through the monitors located on the front and the back surfaces of silicon. Figure 1 shows the schematic diagram of the nanopyramid thin-film silicon with rearlocated Ag NPs. The front surface of thin-film silicon is patterned as nanopyramids. Semispherical Ag NPs are located on the bottom. The Ag reflector is followed on the bottom of the whole structure. The main parameters of the device are displayed in the figure, the period P, the lattice constant of the nanopyramid A, the height of the nanopyramid H and the diameter D of Ag NPs. The solar cell is illuminated from the top by a plane wave with a wavelength range from 300 to 1100 nm.
Fig. 1. The sketch diagram of the solar cell used in the simulations.
A quantitative measure is needed for comparison of the different parameters. In addition to the above mentioned parameters, the parameters also include the filling factor FF, defined as the base area of the nanopyramids divided by the total area. A suitable measure of the performance of the structure is Jsc excited by the AM1.5 solar spectrum, which is calculated according to the following equation assuming unit internal quantum efficiency: J sc = e
λ Pabs (λ ) I AM 1.5 (λ ) d λ hc Pin (λ )
(1)
where IAM1.5 is reference solar spectral irradiance, Pabs is the power absorbed by silicon, Pin is the incident power, h is Planck’s constant, and c is the speed of light. 3.Simulation results 3.1 Optimizations of the nanopyramids We optimized the dimension of the nanopyramids, including the period, the height, and the lattice constant. As the antireflection effect of the nanopyramids is closely related with the #215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20475
period, we firstly optimized the period. In this optimization of P, we set the lattice constant A equaling to P, and the height H is 900 nm. The lattice constant and height will be further optimized in the following section. The short-circuit current density of the solar cells as a function of the period P and the height H is illustrated in Figs. 2(a) and 2(b). It could be clearly seen that these two curves have similar trends. At first, the Jsc increases with the period (or the height), and decreases after the period (or the height) reaches a certain value. It is known that gratings couple well to incident light when the period is slightly smaller than the typical wavelength [15]. If the period is too small, light does not sense the structural details and optical diffraction is weak. The Jsc gets the maximum value 40.58 mA/cm2 when P is 700 nm. The height H varies from 300 to 2100 nm with a step of 300 nm. The Jsc of the solar cell with H equaling to 300 nm is much smaller than the rest and there is little difference among other Jsc of the solar cells with H bigger than 300 nm. The Jsc gets its maximum value when H is 1200 nm. However, the surface area increases with the height, in other words, the electrical performance gets worse with the increasing height. Hence, we choose the height as 900 nm to make a trade-off between 600 nm and 1200 nm. When the height is 900 nm, the surface area increases by a factor of only 2.8, which limits surface recombination losses in comparison with other nanostructured light trapping schemes.
Fig. 2. The short-circuit current density of the solar cells as a function of the period (a) and the height (b) of the nanopyramids
Figure 3 shows the Jsc of the solar cells as a function of the filling factor FF, which is defined as the lattice constant A divided by the period P. The Jsc gets its maximum value when the lattice constant A is equal to the period P. Actually, this could be easy to understand. Firstly, if the filling factor is not 1, there must be some flat surface at the bottom of the nanopyramids. These flat surfaces would increase the surface reflection. Secondly, compared to other nanostructures such as nanowire, the nanopyramids could couple well to incident light because the optical density varies gradually. If the filling factor is not 1, there would be a sharp change of the optical density at the bottom of the nanopyramids, which may decrease the absorption.
#215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20476
Fig. 3. The short-circuit current density of the solar cells as a function of the filling factor of the nanopyramids
3.2 Optimizations of Ag NPs Figure 4 displays the Jsc of the solar cells as a function of the diameter of Ag NPs. Generally, Ag NPs cannot only scatter the transmitted light but also absorb part of them. With the diameter of the Ag NPs increasing, the proportion of light scattered or absorbed by Ag NPs is different. The Jsc without Ag NPs is 40.58 mA/cm2 as shown in Fig. 4. It could be seen that the Jsc is further increased when the diameter is small, meanwhile the Jsc is even decreased when the diameter is large as there is too much parasitic absorption in Ag NPs. The highest Jsc of 40.67 mA/cm2 is obtained when the diameter of Ag NPs is 150 nm.
Fig. 4. The short-circuit current density of the solar cells as a function of the diameter of Ag NPs
3.3 The optimal structure With these above calculations we have obtained the optimal parameters. For the top nanopyramids, the period is 700 nm, the base lattice is 700 nm, and the height is 900 nm, and for the bottom Ag NPs, the diameter is 150 nm. In Fig. 5, we compare the performance of our structure to both the single-pass ansorption and the Yablonovitch limit of 5 μm thick silicon film as well as three other structures as references. These references include a unpatterned thin-film solar cell and two solar cells with only nanopyramids, with only Ag NPs on the rear, labeled as “Unpatterned”, “Only nanopyramids”, and “Only Ag NPs”. Assuming perfect #215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20477
antireflection but no light trapping, that is, light passing through the material only once, the single-pass absorption spectrum (the black curves in Fig. 5) in a thin-film with thickness d is given by Asin glepass = 1 − e −α d
(2)
where α is the absorption coefficient. Assuming perfect antireflection and perfect light trapping, the absorption spectrum (the red curves in Fig. 5) in a thin-film with thickness d is given by the Yablonovitch limit [16, 17] AYablonovitch = 1 −
1 1 + 4n 2α d
(3)
where n is the real part of the refractive index. The absorption spectrum of our optimized structure is much higher than the single-pass absorption spectrum given by Eq. (2). The Jsc for the single-pass absorption spectrum is 23.55 mA/cm2 and that of the theoretical limit is 37.4 mA/cm2. With the same amount of silicon, the Jsc of our proposed solar cell could reach up to 40.67 mA/cm2, much higher than 23.55 mA/cm2 and even higher than the theoretical limit of 37.4 mA/cm2.
Fig. 5. Absorption spectra under normal incidence from AM1.5 solar irradiance.The red curves represent the Yablonovitch limit, the black curves represent the single-pass absorption spectra, and the blue curves are the absorption spectra for the corresponding structures. The absorption spectra of the hybrid structure (a), the “Only nanopyramid” structure (b), the “Only Ag NPs” (c) and the “Unpatterned” (d). (e) Comparison of the short-circuit currents generated by the four structures (gray bars), the Yablonovitch limit (red line), the single-pass absorption (black line), and the full absorption (green line)
#215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20478
4. Discussion To describe the underlying device physics in detail, the electric filed intensity profiles in unit cell for two representative wavelength 400 nm and 970 nm are displayed in Fig. 6. For the short wavelength such as 400 nm, light absorption enhancement originates mainly from antireflection. The nanopyramids suppress reflection because the nanostructures provide a graded index from air to silicon as the radius of its cross section increases from the top to the bottom. The reflection suppression is broadband since the index-matching is largely independent of wavelength. The short wavelength light is mainly absorbed by the nanopyramids as it couldn’t transmit too long in the silicon. Hence, the rear-located Ag NPs play no significant role in the short wavelengths. Similar results can also be seen in Figs. 5(c) and 5(d). The light absorption spectra of the short wavelengths are nearly the same in the “Unpatterned” and “Only Ag NPs” cells. For the long wavelengths, besides the antireflection effect of the nanopyramids, the incident light angular redistribution effect of the nanopyramids largely increases the optical path length in the silicon. Moreover, the light trapping of Ag NPs also contribute a lot to light absorption enhancement. This impact could be clearly seen from Figs. 5(c) and 5(d). For wavelengths from 750 to 1050 nm, light absorption in the “Only Ag NPs” cell is largely enhanced compared to the “Unpatterned” cell. The enhancement details could be clearly seen from the electric field for 970 nm shown in Figs. 6(e)-6(h). Compared to Fig. 6(h), the electric field in Fig. 6(g) is much stronger owing to the scattering of Ag NPs. As for the electric field in Figs. 6(e) and 6(f), with the antireflection effect and light angular redistribution effect, there is much less transmitted light in the “Only nanopyramids” cell than the “Unpatterned” cell. Hence the electric field enhancement in Fig. 6(e) is not so obvious compared to Fig. 6(h). But it still could be seen that there is a strong absorption area array vertically above Ag NPs. With the assistance of Ag NPs, the Jsc is increased from 40.58 mA/cm2 to 40.67 mA/cm2.
Fig. 6. Electric field intensity profiles at (a)–(d) 400 nm and (e)–(h) 970 nm for (a, e) “Hybrid” solar cell, (b, f) “Only nanopyramid” solar cell, (c, g) “Only Ag NPs” solar cell, (d, h) “Unpatterned” solar cell.
Lambertian light trapping sets the thermodynamic limit of maximum absorption in a slab of thickness in the geometric optics regime [16]. According to this principle, optical length #215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20479
can be increased by a factor of 4n2, where n is the refractive index of the film. The 4n2 enhancement is also known as the Yablonovitch limit. It may seem unreasonable that the Jsc of our proposed cell exceeds the theoretical limit, however many groups have found similar results exceeding the Yablonovitch limit theoretically [8,15, 18–21] or experimentally [22]. Yu et al. have demonstrated that when the period of the light trapping structure is comparable to the incident light wavelength, the enhancement can be as high as 12n2 [18]. Eyderman et al. obtained a Jsc as high as 35.5 mA/cm2 with 1 μm thick c-Si solar cell, exceeding 32.6 mA/cm2 for the Yablonovitch limit of 1 μm, utilizing slanted conical-pore photonic crystals [19]. In our case, the period of nanostructures is 700 nm, which is comparable to the incident light wavelength. Hence, the Jsc of 40.67 mA/cm2 is reasonable, exceeding the 4n2 theoretical limit. 5. Conclusion To summarize, we have presented the results of our investigation of the optical properties of light trapping structures for photovoltaic applications and found that their absorption performance is significantly improved. Our calculations indicate that with our proposed light trapping structure, thin-film silicon solar cell with the thickness of 5 μm could generate a Jsc higher than a standard 300 μm wafer-based silicon solar cell, which is also the highest photocurrent within 5 μm silicon to our knowledge. The strong absorption enhancement is attributed to the antireflection, light angular redistribution effects of the nanopyramids and the light trapping effect of the Ag NPs. Since the nanopyramids and Ag NPs can be fabricated with well-established techniques, experimental studies can follow directly. Further experimental investigations of both optical and electrical performances may prove that thinfilm silicon solar cells can replace wafer-based solar cells completely. Acknowledgments The authors greatly acknowledge the support from the National Basic Research Program of China (973 Program) under grant number 2012CB934204 and the National Natural Science Foundation of China under grant numbers 61076077, 61274066.
#215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20480
Engineering Research Center for Semiconductor Integrated Technology, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China 2 [email protected] * [email protected]
Abstract: Light trapping is essential to improve the performance of thinfilm solar cells. In this paper, we performed a parametric optimization of nanopyramids and rear-located Ag nanoparticles that act as light trapping scheme to increase light absorption in thin-film c-Si solar cells. Our optimization reveals that the short-circuit current density in a solar cell employing only 5 μm silicon could exceed that of a standard 300 μm csilicon wafer-based cell. Furthermore, we analyzed the underlying physics of the light absorption enhancement through the electric field intensity profiles. ©2014 Optical Society of America OCIS codes: (040.5350) Photovoltaic; (050.1950) Diffraction gratings; (310.6628) Subwavelength structures, nanostructures; (350.4990) Particles; (350.6050) Solar energy.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). Y. Shi, X. Wang, W. Liu, T. Yang, R. Xu, and F. Yang, “Multilayer silver nanoparticles for light trapping in thin film solar cells,” J. Appl. Phys. 113(17), 176101 (2013). V. E. Ferry, M. A. Verschuuren, M. C. Lare, R. E. Schropp, H. A. Atwater, and A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett. 11(10), 4239–4245 (2011). K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008). E. Garnett and P. Yang, “Light trapping in silicon nanowire solar cells,” Nano Lett. 10(3), 1082–1087 (2010). Y. Chen, W. Han, and F. Yang, “Enhanced optical absorption in nanohole-textured silicon thin-film solar cells with rear-located metal particles,” Opt. Lett. 38(19), 3973–3975 (2013). J. Buencuerpo, L. E. Munioz-Camuniez, M. L. Dotor, and P. A. Postigo, “Optical absorption enhancement in a hybrid system photonic crystal - thin substrate for photovoltaic applications,” Opt. Express 20(S4 Suppl 4), A452–A464 (2012). S. B. Mallick, M. Agrawal, and P. Peumans, “Optimal light trapping in ultra-thin photonic crystal crystalline silicon solar cells,” Opt. Express 18(6), 5691–5706 (2010). M. D. Kelzenberg, D. B. Turner-Evans, M. C. Putnam, S. W. Boettcher, R. M. Briggs, J. Y. Baek, N. S. Lewis, and H. A. Atwater, “High-performance Si microwire photovoltaics,” Energy Environ. Sci. 4(3), 866 (2011). M. A. Green, “The path to 25% silicon solar cell efficiency: History of silicon cell evolution,” Prog. Photovolt. Res. Appl. 17(3), 183–189 (2009). J. L. Cruz-Campa, M. Okandan, P. J. Resnick, P. Clews, T. Pluym, R. K. Grubbs, V. P. Gupta, D. Zubia, and G. N. Nielson, “Microsystems enabled photovoltaics: 14.9% efficient 14 μm thick crystalline silicon solar cell,” Sol. Energy Mater. Sol. Cells 95(2), 551–558 (2011). J. Yoon, L. Li, A. V. Semichaevsky, J. H. Ryu, H. T. Johnson, R. G. Nuzzo, and J. A. Rogers, “Flexible concentrator photovoltaics based on microscale silicon solar cells embedded in luminescent waveguides,” Nat. Commun. 2, 343 (2011). G. Li, H. Li, J. Y. L. Ho, M. Wong, and H. S. Kwok, “Nanopyramid Structure for Ultrathin c-Si Tandem Solar Cells,” Nano Lett. 14(5), 2563–2568 (2014). A. Mavrokefalos, S. E. Han, S. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett. 12(6), 2792–2796 (2012).
#215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20473
15. S. E. Han and G. Chen, “Toward the Lambertian limit of light trapping in thin nanostructured silicon solar cells,” Nano Lett. 10(11), 4692–4696 (2010). 16. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72(7), 899–907 (1982). 17. M. A. Green, “Lambertian light trapping in textured solar cells and light-emitting diodes: analytical solutions,” Prog. Photovolt. Res. Appl. 10(4), 235–241 (2002). 18. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. 107(41), 17491–17496 (2010). 19. S. Eyderman, S. John, and A. Deinega, “Solar light trapping in slanted conical-pore photonic crystals: Beyond statistical ray trapping,” J. Appl. Phys. 113(15), 154315 (2013). 20. Y. Shi, X. Wang, W. Liu, T. Yang, J. Ma, and F. Yang, “Extraordinary optical absorption based on diffraction grating and rear-located bilayer silver nanoparticles,” Appl. Phys. Express 7(6), 062301 (2014). 21. D. M. Callahan, J. N. Munday, and H. A. Atwater, “Solar Cell light trapping beyond the ray optic limit,” Nano Lett. 12(1), 214–218 (2012). 22. N. A. Yahaya, N. Yamada, Y. Kotaki, and T. Nakayama, “Characterization of light absorption in thin-film silicon with periodic nanohole arrays,” Opt. Express 21(5), 5924–5930 (2013).
1. Introduction Bulk crystalline silicon (c-Si) solar cells dominate the photovoltaic (PV) market. Typically, 180−300 μm thick c-Si wafers are used to ensure adequate absorption of sunlight. In c-Si solar cells, the material accounts for more than 40% of the total module cost. To reduce the cost, thin-film solar cells with a thickness of a few micrometers have stimulated enormous research interest as a cheap alternative. But light transmission losses increase due to the thinner absorber layers. Therefore, light trapping technologies such as metal nanoparticles (NPs) [1–4], nanowires [5] and nanoholes [6–8], have been developed to achieve high absorption. However, one major reason for the low efficiency in solar cells with nanowires and nanoholes is the high surface recombination rates due to the large surface area, which is usually more than an order of magnitude larger than flat cells [9]. Their efficiencies are limited to around 10%, far smaller than 25% efficiency for state-of-the-art solar cells [10]. If thin-film solar cell with a thickness of a few micrometers can be made to absorb as efficiently as thick Si wafers, a significant cost reduction is expected. Recently, Cruz-Campa et al. [11] obtained an impressive 14.9% efficiency within 14 μm thick crystalline silicon solar cells. Yoon et al. [12] reported ~17.5% within 15 μm thick c-Si solar cells embedded in luminescent waveguides, utilizing luminescent solar concentrators. Li et al. [13] introduced a nanopyramid structure in ultrathin a-Si/c-Si tandem solar cells and they obtained conversion efficiencies of up to 13.3% for cells employed only 8 μm of silicon. Subsequently, Mavrokefalos et al. [14] attempted to demonstrate that thin-film silicon with nanopyramids could absorb equal light with bulk silicon. And they got the short-circuit current density (Jsc) of 37.5 mA/cm2 in 10 μm, which is comparable to 37.2 mA/cm2 of bulk silicon solar cell. The nanopyramid structure [14, 15] is promising in thin-film solar cell applications. In general, nanopyramid suffers relatively smaller surface area than other nanostructures such as nanowire, nanocylinder. Then, gratings couple well to incident light when they are tapered because the optical density varies gradually. When used on the front surfaces, they can largely decrease reflection. Ag is usually the preferred metal for plasmonic applications, as it offers lower absorption losses and generally higher optical cross-section than other metals. Especially, when placed on the bottom, it could scatter the transmitted light more efficiently. In this letter, we intend to improve the nanopyramids with rear-located Ag NPs to further enhance optical absorption. The expected role of the nanopyramids is to suppress surface reflection, and that of the rear Ag NPs is to supply light trapping. This proposed thin-film solar cell aims to generate Jsc higher than 300 μm wafer-based solar cell. We infer in this combined structure, the nanopyramids play the dominated role, and the Ag NPs supply assistance to make the performance progress further. The optical properties can be optimized by adjusting the parameters of nanopyramids and Ag NPs independently.
#215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20474
2. Numerical method A numerical analysis of the electromagnetic field features is performed utilizing finitedifference time-domain (FDTD) method (https://www.lumerical.com/). The dielectric functions are modeled using a Drude model for Ag and a Drude–Lorentz model for Si. Periodic boundary conditions are applied in the x- and y-directions while perfect matched layer boundary conditions are used for the z-direction. The calculated absorption is obtained through the difference of power flux through the monitors located on the front and the back surfaces of silicon. Figure 1 shows the schematic diagram of the nanopyramid thin-film silicon with rearlocated Ag NPs. The front surface of thin-film silicon is patterned as nanopyramids. Semispherical Ag NPs are located on the bottom. The Ag reflector is followed on the bottom of the whole structure. The main parameters of the device are displayed in the figure, the period P, the lattice constant of the nanopyramid A, the height of the nanopyramid H and the diameter D of Ag NPs. The solar cell is illuminated from the top by a plane wave with a wavelength range from 300 to 1100 nm.
Fig. 1. The sketch diagram of the solar cell used in the simulations.
A quantitative measure is needed for comparison of the different parameters. In addition to the above mentioned parameters, the parameters also include the filling factor FF, defined as the base area of the nanopyramids divided by the total area. A suitable measure of the performance of the structure is Jsc excited by the AM1.5 solar spectrum, which is calculated according to the following equation assuming unit internal quantum efficiency: J sc = e
λ Pabs (λ ) I AM 1.5 (λ ) d λ hc Pin (λ )
(1)
where IAM1.5 is reference solar spectral irradiance, Pabs is the power absorbed by silicon, Pin is the incident power, h is Planck’s constant, and c is the speed of light. 3.Simulation results 3.1 Optimizations of the nanopyramids We optimized the dimension of the nanopyramids, including the period, the height, and the lattice constant. As the antireflection effect of the nanopyramids is closely related with the #215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20475
period, we firstly optimized the period. In this optimization of P, we set the lattice constant A equaling to P, and the height H is 900 nm. The lattice constant and height will be further optimized in the following section. The short-circuit current density of the solar cells as a function of the period P and the height H is illustrated in Figs. 2(a) and 2(b). It could be clearly seen that these two curves have similar trends. At first, the Jsc increases with the period (or the height), and decreases after the period (or the height) reaches a certain value. It is known that gratings couple well to incident light when the period is slightly smaller than the typical wavelength [15]. If the period is too small, light does not sense the structural details and optical diffraction is weak. The Jsc gets the maximum value 40.58 mA/cm2 when P is 700 nm. The height H varies from 300 to 2100 nm with a step of 300 nm. The Jsc of the solar cell with H equaling to 300 nm is much smaller than the rest and there is little difference among other Jsc of the solar cells with H bigger than 300 nm. The Jsc gets its maximum value when H is 1200 nm. However, the surface area increases with the height, in other words, the electrical performance gets worse with the increasing height. Hence, we choose the height as 900 nm to make a trade-off between 600 nm and 1200 nm. When the height is 900 nm, the surface area increases by a factor of only 2.8, which limits surface recombination losses in comparison with other nanostructured light trapping schemes.
Fig. 2. The short-circuit current density of the solar cells as a function of the period (a) and the height (b) of the nanopyramids
Figure 3 shows the Jsc of the solar cells as a function of the filling factor FF, which is defined as the lattice constant A divided by the period P. The Jsc gets its maximum value when the lattice constant A is equal to the period P. Actually, this could be easy to understand. Firstly, if the filling factor is not 1, there must be some flat surface at the bottom of the nanopyramids. These flat surfaces would increase the surface reflection. Secondly, compared to other nanostructures such as nanowire, the nanopyramids could couple well to incident light because the optical density varies gradually. If the filling factor is not 1, there would be a sharp change of the optical density at the bottom of the nanopyramids, which may decrease the absorption.
#215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20476
Fig. 3. The short-circuit current density of the solar cells as a function of the filling factor of the nanopyramids
3.2 Optimizations of Ag NPs Figure 4 displays the Jsc of the solar cells as a function of the diameter of Ag NPs. Generally, Ag NPs cannot only scatter the transmitted light but also absorb part of them. With the diameter of the Ag NPs increasing, the proportion of light scattered or absorbed by Ag NPs is different. The Jsc without Ag NPs is 40.58 mA/cm2 as shown in Fig. 4. It could be seen that the Jsc is further increased when the diameter is small, meanwhile the Jsc is even decreased when the diameter is large as there is too much parasitic absorption in Ag NPs. The highest Jsc of 40.67 mA/cm2 is obtained when the diameter of Ag NPs is 150 nm.
Fig. 4. The short-circuit current density of the solar cells as a function of the diameter of Ag NPs
3.3 The optimal structure With these above calculations we have obtained the optimal parameters. For the top nanopyramids, the period is 700 nm, the base lattice is 700 nm, and the height is 900 nm, and for the bottom Ag NPs, the diameter is 150 nm. In Fig. 5, we compare the performance of our structure to both the single-pass ansorption and the Yablonovitch limit of 5 μm thick silicon film as well as three other structures as references. These references include a unpatterned thin-film solar cell and two solar cells with only nanopyramids, with only Ag NPs on the rear, labeled as “Unpatterned”, “Only nanopyramids”, and “Only Ag NPs”. Assuming perfect #215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20477
antireflection but no light trapping, that is, light passing through the material only once, the single-pass absorption spectrum (the black curves in Fig. 5) in a thin-film with thickness d is given by Asin glepass = 1 − e −α d
(2)
where α is the absorption coefficient. Assuming perfect antireflection and perfect light trapping, the absorption spectrum (the red curves in Fig. 5) in a thin-film with thickness d is given by the Yablonovitch limit [16, 17] AYablonovitch = 1 −
1 1 + 4n 2α d
(3)
where n is the real part of the refractive index. The absorption spectrum of our optimized structure is much higher than the single-pass absorption spectrum given by Eq. (2). The Jsc for the single-pass absorption spectrum is 23.55 mA/cm2 and that of the theoretical limit is 37.4 mA/cm2. With the same amount of silicon, the Jsc of our proposed solar cell could reach up to 40.67 mA/cm2, much higher than 23.55 mA/cm2 and even higher than the theoretical limit of 37.4 mA/cm2.
Fig. 5. Absorption spectra under normal incidence from AM1.5 solar irradiance.The red curves represent the Yablonovitch limit, the black curves represent the single-pass absorption spectra, and the blue curves are the absorption spectra for the corresponding structures. The absorption spectra of the hybrid structure (a), the “Only nanopyramid” structure (b), the “Only Ag NPs” (c) and the “Unpatterned” (d). (e) Comparison of the short-circuit currents generated by the four structures (gray bars), the Yablonovitch limit (red line), the single-pass absorption (black line), and the full absorption (green line)
#215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20478
4. Discussion To describe the underlying device physics in detail, the electric filed intensity profiles in unit cell for two representative wavelength 400 nm and 970 nm are displayed in Fig. 6. For the short wavelength such as 400 nm, light absorption enhancement originates mainly from antireflection. The nanopyramids suppress reflection because the nanostructures provide a graded index from air to silicon as the radius of its cross section increases from the top to the bottom. The reflection suppression is broadband since the index-matching is largely independent of wavelength. The short wavelength light is mainly absorbed by the nanopyramids as it couldn’t transmit too long in the silicon. Hence, the rear-located Ag NPs play no significant role in the short wavelengths. Similar results can also be seen in Figs. 5(c) and 5(d). The light absorption spectra of the short wavelengths are nearly the same in the “Unpatterned” and “Only Ag NPs” cells. For the long wavelengths, besides the antireflection effect of the nanopyramids, the incident light angular redistribution effect of the nanopyramids largely increases the optical path length in the silicon. Moreover, the light trapping of Ag NPs also contribute a lot to light absorption enhancement. This impact could be clearly seen from Figs. 5(c) and 5(d). For wavelengths from 750 to 1050 nm, light absorption in the “Only Ag NPs” cell is largely enhanced compared to the “Unpatterned” cell. The enhancement details could be clearly seen from the electric field for 970 nm shown in Figs. 6(e)-6(h). Compared to Fig. 6(h), the electric field in Fig. 6(g) is much stronger owing to the scattering of Ag NPs. As for the electric field in Figs. 6(e) and 6(f), with the antireflection effect and light angular redistribution effect, there is much less transmitted light in the “Only nanopyramids” cell than the “Unpatterned” cell. Hence the electric field enhancement in Fig. 6(e) is not so obvious compared to Fig. 6(h). But it still could be seen that there is a strong absorption area array vertically above Ag NPs. With the assistance of Ag NPs, the Jsc is increased from 40.58 mA/cm2 to 40.67 mA/cm2.
Fig. 6. Electric field intensity profiles at (a)–(d) 400 nm and (e)–(h) 970 nm for (a, e) “Hybrid” solar cell, (b, f) “Only nanopyramid” solar cell, (c, g) “Only Ag NPs” solar cell, (d, h) “Unpatterned” solar cell.
Lambertian light trapping sets the thermodynamic limit of maximum absorption in a slab of thickness in the geometric optics regime [16]. According to this principle, optical length #215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20479
can be increased by a factor of 4n2, where n is the refractive index of the film. The 4n2 enhancement is also known as the Yablonovitch limit. It may seem unreasonable that the Jsc of our proposed cell exceeds the theoretical limit, however many groups have found similar results exceeding the Yablonovitch limit theoretically [8,15, 18–21] or experimentally [22]. Yu et al. have demonstrated that when the period of the light trapping structure is comparable to the incident light wavelength, the enhancement can be as high as 12n2 [18]. Eyderman et al. obtained a Jsc as high as 35.5 mA/cm2 with 1 μm thick c-Si solar cell, exceeding 32.6 mA/cm2 for the Yablonovitch limit of 1 μm, utilizing slanted conical-pore photonic crystals [19]. In our case, the period of nanostructures is 700 nm, which is comparable to the incident light wavelength. Hence, the Jsc of 40.67 mA/cm2 is reasonable, exceeding the 4n2 theoretical limit. 5. Conclusion To summarize, we have presented the results of our investigation of the optical properties of light trapping structures for photovoltaic applications and found that their absorption performance is significantly improved. Our calculations indicate that with our proposed light trapping structure, thin-film silicon solar cell with the thickness of 5 μm could generate a Jsc higher than a standard 300 μm wafer-based silicon solar cell, which is also the highest photocurrent within 5 μm silicon to our knowledge. The strong absorption enhancement is attributed to the antireflection, light angular redistribution effects of the nanopyramids and the light trapping effect of the Ag NPs. Since the nanopyramids and Ag NPs can be fabricated with well-established techniques, experimental studies can follow directly. Further experimental investigations of both optical and electrical performances may prove that thinfilm silicon solar cells can replace wafer-based solar cells completely. Acknowledgments The authors greatly acknowledge the support from the National Basic Research Program of China (973 Program) under grant number 2012CB934204 and the National Natural Science Foundation of China under grant numbers 61076077, 61274066.
#215160 - $15.00 USD Received 2 Jul 2014; accepted 4 Aug 2014; published 15 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020473 | OPTICS EXPRESS 20480
