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Energy Express

  • Editor: Christian Seassal
  • Vol. 22, Iss. S1 — Jan. 13, 2014
  • pp: A111–A119
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Hexagonal sphere gratings for enhanced light trapping in crystalline silicon solar cells

Johannes Eisenlohr, Jan Benick, Marius Peters, Benedikt Bläsi, Jan Christoph Goldschmidt, and Martin Hermle  »View Author Affiliations


Optics Express, Vol. 22, Issue S1, pp. A111-A119 (2014)
http://dx.doi.org/10.1364/OE.22.00A111


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Abstract

Enhanced absorption of near infrared light in silicon solar cells is important for achieving high conversion efficiencies while reducing the solar cell’s thickness. Hexagonal gratings on the rear side of solar cells can achieve such absorption enhancement. Our wave optical simulations show photocurrent density gains of up to 3 mA/cm2 for solar cells with a thickness of 40 µm and a planar front side. Hexagonal sphere gratings have been fabricated and optical measurements confirm the predicted absorption enhancement. The measured absorption enhancement corresponds to a photocurrent density gain of 1.04 mA/cm2 for planar wafers with a thickness of 250 µm and 1.49 mA/cm2 for 100 µm.

© 2013 Optical Society of America

1. Introduction

Silicon solar cells do not utilize a considerable fraction of light in the near infrared, close to the band gap of silicon, due to weak absorption. The penetration depth of photons in the wavelength range between 900 and 1100 nm is up to 3 mm and therefore exceeds typical crystalline silicon solar cell thicknesses of about 180 µm. To increase absorption, the effective path length within the solar cell has to be increased for the photons in this wavelength range. This becomes even more important as the photovoltaic industry aims for thinner solar cells. The effective path length is enhanced when the photons are directed into shallow angles within the solar cell and are subsequently totally internally reflected. In present commercial crystalline silicon solar cells a chemically etched pyramidal front side texture causes light paths deviating from the direction perpendicular to the solar cell’s surface. The size of the pyramids is typically in the range of several µm and hence the processing gets more and more difficult for very thin solar cells. Also a planar front surface might be beneficial concerning the electrical properties. The light trapping can also be achieved with randomizing structures on the rear side of the cell. With such structures a maximum enhancement factor of 4n2, with n being the refractive index of the solar cell material, can be achieved in the limit of vanishing absorption [1

1. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72(7), 899–907 (1982). [CrossRef]

, 2

2. E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982). [CrossRef]

]. With periodic rear side structures also significant path length enhancements can be reached, as they can diffract light into certain directions that are very effectively trapped within the solar cell [3

3. I. M. Peters, “Photonic Concepts for Solar Cells”, PhD thesis (Universität Freiburg, Freiburg, Germany, 2009).

, 4

4. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18(S3Suppl 3), A366–A380 (2010). [CrossRef] [PubMed]

]. Several analytical and numerical investigations indicated that diffractive structures can achieve efficient light trapping [3

3. I. M. Peters, “Photonic Concepts for Solar Cells”, PhD thesis (Universität Freiburg, Freiburg, Germany, 2009).

, 5

5. P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43(6), 579–581 (1983). [CrossRef]

7

7. P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15(25), 16986–17000 (2007). [CrossRef] [PubMed]

]. The approach presented in this paper are hexagonal gratings made of monodisperse, hexagonally ordered silica spheres embedded in a high refractive index matrix followed by a reflecting metal layer. The sphere grating is separated from the silicon bulk by a very thin passivation layer (for example 10 nm Al2O3) [8

8. J. Schmidt, A. Merkle, R. Brendel, B. Hoex, M. C. M. van de Sanden, and W. M. M. Kessels, “Surface passivation of high-efficiency silicon solar cells by atomic-layer-deposited Al2O3,” Prog. Photovolt. Res. Appl. 16(6), 461–466 (2008). [CrossRef]

], which has a negligible influence on the optical properties of the rear side and maintains a high-quality surface passivation reducing surface recombination at the silicon surface. A schematic sketch of the concept is shown in Fig. 1.
Fig. 1 Schematic sketch of the investigated structure. A hexagonally ordered sphere layer at the rear side of a silicon wafer causes diffraction and hence a light path length enhancement.

The grating structures can be realized via spin coating processes, and should be compatible with solar cell processing. Important questions of interest that we intend to answer in this work are the extent of the potential absorption enhancement achievable with such structures, the effects leading to such an enhancement and the necessary design parameters to exploit the full potential.

2. Simulations using rigorous coupled wave analysis

Furthermore we investigated the absorption enhancement considering the near field data to understand where the absorption enhancement occurs. To calculate the local absorption at a point r from the local values of the electric field E(r,ω) which are the result of the RCWA-calculations, we used the theorem of Poynting [18

18. J. H. Poynting, “On the Transfer of Energy in the Electromagnetic Field,” Philos. Trans. R. Soc. Lond. 175(0), 343–361 (1884). [CrossRef]

] and followed the method of [19

19. K.-H. Brenner, “Aspects for calculating local absorption with the rigorous coupled-wave method,” Opt. Express 18(10), 10369–10376 (2010). [CrossRef] [PubMed]

]:
A(r,ω)=12ωε0Im(ε(r,ω))|E(r,ω)|2,
(2)
where ε0 is the vacuum permittivity, Im(ε) the imaginary part of the spectrally and spatially dependent dielectric function and ω the frequency of the light. The local absorption depends on the frequency and hence on the wavelength of the light. Important in terms of light trapping for silicon solar cells is a spectral range between 950 and 1200 nm. We calculated the local absorption in this range in steps of 10 nm and subsequently averaged the values to generate an absorption distribution for this wavelength range, displayed in Fig. 3 for a 40 µm thick solar cell with a sphere grating at the rear side. It can be seen that the absorption enhancement occurs for all depth values (z dimension). There are some lateral modulations that follow the periodicity of the sphere grating and some vertical modulations due to interference effects that are not relevant under illumination with sunlight. The important result is that there is no overall trend of absorption enhancement in a certain area of the solar cell, especially not near the grating. The reason is the large penetration depth of the photons in this wavelength range and the occurrence of several diffraction orders for the presented size of spheres. Furthermore, this finding legitimates the simplification that we treat each absorbed photon equally in its contribution to the maximum possible photo current density as defined in Eq. (1).
Fig. 3 Left: Average absorption distribution of light in the spectral region from 950 to 1200 nm in a 40 µm thick silicon wafer with a hexagonal sphere grating (sphere diameter 1100 nm, matrix material amorphous silicon) at the rear side calculated from RCWA near field data according to Eq. (2). Displayed is a cross section in the x-z-plane (with different scaling in x- and z-direction) and two periods in x-direction. Blue color indicates no absorption, red color strong absorption (in arbitrary units). The position of the spheres in the simulated volume has been indicated in black. No absorption within the spheres occurs in the simulation. The inserted sketch shows the simulated structure. The black rectangle indicates the area displayed in the absorption graph. Right: Absorption integrated over x-direction. The equally distributed absorption values for all depth values can be seen.

3. Fabrication and experimental verification

For experimental verification of the simulated absorption enhancement, we fabricated hexagonal sphere gratings. The fabrication was realized in two steps. In the first step, the monodisperse silica spheres (diameter 922 nm), which were suspended in a solution consisting of 2-propanol and water, were spin coated on the rear side of a silicon wafer. Due to self-organized growth, a dense, hexagonally ordered layer can be generated. A sphere concentration of 210 mg/ml and spin speed of 4000 rpm was used. For each 4 inch wafer 0.5 ml of the sphere suspension were dropped onto the wafer surface and the rotation was started immediately.
Fig. 4 (a) A monolayer of silica spheres (diameter 922 nm) after the spin coating process. A characteristic part of a 4 inch wafer is shown. Hexagonal order is achieved over a range of a few µm. (b) A monolayer after the inversion process. Amorphous titaniumoxide has been successfully infiltrated into the voids between the spheres by atomic layer deposition. Very small voids remain due to the conformal deposition.
Figure 4(a) shows a representative part of a 4 inch wafer after the spin coating process. A homogenous monolayer of spheres can be seen. There are still some line defects and discontinuities, but in the range of a few µm a hexagonal order exists. Any kind of defect represents a deviation from the ideal lattice structure assumed in the simulations and will result into scattering, which also leads to a light path length enhancement. Therefore the visible defects in Fig. 4 are not considered to be a significant change for the worse. In the second step, the voids between the spheres were infiltrated with amorphous titaniumoxide using atomic layer deposition as shown in Fig. 4(b). The deposition took place at 130° C and was done in a batch reactor from Beneq. The refractive index of the titaniumoxide is 2.38 for a wavelength of 1000 nm, compared to the refractive index of the spheres of 1.5, as determined by spectral ellipsometry.

By spectrophotometric measurements the potential absorption enhancement in solar cells was estimated. We therefore used a Cary 5000i from Varian and mounted the samples inside an integrating sphere. By such a “center mount” measurement setup all light that is not absorbed inside the sample is detected. To determine just the absorption enhancement in the silicon bulk, a metal rear reflector, which would be necessary in complete solar cells, has not been deposited. We verified in several simulations that for systems without a mirror a very similar absorption enhancement can be expected as for systems with a mirror. Only small quantitative changes or small spectral shiftings of the absorption enhancement have been observed in the outcome of the simulation. Thus the measurements can be seen as a strong evidence for the light trapping properties of fully processed solar cells. The measurements show a significant absorption enhancement in the near infrared due to the inverted monolayer of spheres (Fig. 5).
Fig. 5 The left graph shows the absorption measurements of wafers with hexagonal rear side grating in comparison to flat reference wafers. The absorption enhancement (difference between samples with grating and planar reference) is shown on the right side. For thinner wafers, the maximum absorption enhancement occurs for shorter wavelengths, as expected from theory.
Under illumination with the AM 1.5 spectrum this absorption enhancement corresponds to a photocurrent density gain of 1.04 mA/cm2 for a wafer thickness of 250 µm. Given the overall total photocurrent density without sphere grating (and without antireflection coating) of 26.8 mA/cm2 (with a single layer antireflection coating 37.4 mA/cm2) this constitutes a relative increase of 3.9%. A photocurrent density gain of 1.49 mA/cm2 was achieved for a 100 µm thick wafer, which is equivalent to an increase of 5.8% based on the 25.7 mA/cm2 photocurrent density without the structure. Due to the absorption enhancement the photocurrent density in a wafer with a thickness of 100 µm with the sphere grating exceeds the photocurrent density in a planar wafer with a thickness of 250 µm. This highlights the potential of the proposed light trapping concept with regard to thinner solar cells. These values are comparable to results achieved with nano-imprinted gratings where an increase of 1.6 mA/cm2 and 1.7 mA/cm2 was determined for a wafer thickness of 200 µm for crossed gratings and planarized line gratings, respectively [20

20. A. Mellor, H. Hauser, C. Wellens, J. Benick, J. Eisenlohr, M. Peters, A. Guttowski, I. Tobías, A. Martí, A. Luque, and B. Bläsi, “Nanoimprinted diffraction gratings for crystalline silicon solar cells: implementation, characterization and simulation,” Opt. Express 21(S2Suppl 2), A295–A304 (2013). [CrossRef] [PubMed]

]. In the case of crossed gratings additional parasitic absorption in a metallic rear side reflector was considered. With an optimum Lambertian scatterer an overall enhancement of about 3 mA/cm2 could be achieved for a wafer thickness of 250 µm.

For direct comparison of the simulation and measurement, simulations of the produced structures were conducted. In contrast to the optimization calculations presented above, where an amorphous silicon matrix was assumed, for the matrix material the measured n-values (2.38 at 1000 nm) of the deposited TiO2 were used here. The wave optical simulations using RCWA show a smaller absorption enhancement than the measurements (see Fig. 6).
Fig. 6 Measured absorption enhancement due to the hexagonal grating for a wafer thickness of 250 µm (left side) and 100 µm (right side) and comparison to simulation results. The observed absorption enhancement can be described by the combination of diffractive effects and scattering. Scattering was assumed to be wavelength-independent and to be leading to an effective solar cell thickness enhancement by a factor of 4. Scattering and diffraction were weighted equally. This approach leads to good accordance between the simulation and the measurement for both wafer thicknesses.
One possible explanation for this deviation is scattering. The produced rear side structure is not perfectly regular but has some dislocations and irregularities. These lead to scattering. Scattering also causes a light path length enhancement [21

21. A. Goetzberger, “Optical confinement in thin Si-solar cells by diffuse back reflectors,” in Proceedings of the 15th IEEE Photovoltaic Specialists Conference, 1981, 867–870.

]. A wavelength-independent light path length enhancement can be simulated by an increased wafer thickness. The relative weight of scattering and diffraction depends on the regularity of the sphere layer and is difficult to deduce analytically from a given structure. The factor by which the wafer thickness is enhanced due to scattering and the relative weight was determined by comparison to the measurement. For our structure, a cell thickness enhancement by a factor of four was found for both sample thicknesses, when it is assumed that half the number of photons at each wavelength is subjected to diffraction and the other half is subjected to scattering. The light path length enhancement due to diffraction has its maximum at higher wavelengths than the enhancement corresponding to scattering. The absorption enhancement observed in our measurement covers the complete spectral range that is affected by both the enhancements due to diffraction and scattering.

Our simulation results presented in Fig. 6 (left side) show that for the 250 µm thick wafer, the measured absorption enhancement can be modeled by a combination of scattering and diffraction. This result could be reproduced with the same approach and the same parameters for the samples with a thickness of 100 µm as can be seen in Fig. 6 (right side). This demonstrates that the used model that includes both, scattering and diffraction, is a good description for the real structure.

4. Summary

In summary, a hexagonal sphere grating for the rear side of crystalline silicon solar cells has been optimized by wave optical simulations and realized by spin coating and atomic layer deposition. Simulation and experiment show that such structures enhance the absorption in the near infrared within the silicon, and that the observed effect is very likely caused by a combination of diffraction and scattering. Simulations showed possible photocurrent density gains of up to 3 mA/cm2 for planar wafers with a thickness of 40 µm corresponding to a 9% increase. Measured absorption enhancements can be converted to a possible photocurrent density gain of 1.49 mA/cm2 and 1.04 mA/cm2 for thicknesses of 100 µm and 250 µm, respectively, corresponding to 5.8% and 3.9% increase.

Acknowledgment

The research leading to these results has received funding from the German Federal Ministry of Education and Research in the project “InfraVolt” (project number 03SF0401B) and from the German Federal Ministry for the Environment, Nature Conservation and Nuclear Safety under contract number 0325292 “ForTeS”. The authors also thank Beneq for atomic layer depositions. Jan Christoph Goldschmidt gratefully acknowledges the scholarship support from the German Academic Exchange Service (DAAD). Johannes Eisenlohr gratefully acknowledges the scholarship support from the Deutsche Bundesstiftung Umwelt DBU.

References and links

1.

E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72(7), 899–907 (1982). [CrossRef]

2.

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982). [CrossRef]

3.

I. M. Peters, “Photonic Concepts for Solar Cells”, PhD thesis (Universität Freiburg, Freiburg, Germany, 2009).

4.

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18(S3Suppl 3), A366–A380 (2010). [CrossRef] [PubMed]

5.

P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43(6), 579–581 (1983). [CrossRef]

6.

C. Heine and R. H. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt. 34(14), 2476–2482 (1995). [CrossRef] [PubMed]

7.

P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15(25), 16986–17000 (2007). [CrossRef] [PubMed]

8.

J. Schmidt, A. Merkle, R. Brendel, B. Hoex, M. C. M. van de Sanden, and W. M. M. Kessels, “Surface passivation of high-efficiency silicon solar cells by atomic-layer-deposited Al2O3,” Prog. Photovolt. Res. Appl. 16(6), 461–466 (2008). [CrossRef]

9.

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995). [CrossRef]

10.

IEC, Photovoltaic Devices - Part 3: Measurement Principles for Terrestrial Photovoltaic (PV) Solar Devices with Reference Spectral Irradiance Data., 2nd ed., International Standard, IEC 60904–3 (International Electrotechnical Commission, 2008).

11.

D. Kray, “Hocheffiziente Solarzellenstrukturen für Kristallines Silicium-Material Industrieller Qualität,” PhD thesis (Universität Konstanz, Konstanz, 2004).

12.

M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Progr. Photovolt.: Res. Appl. 20, 862–873 (2011).

13.

A. Mellor, I. Tobias, A. Marti, and A. Luque, “A numerical study of Bi-periodic binary diffraction gratings for solar cell applications,” Sol. Energy Mater. Sol. Cells 95(12), 3527–3535 (2011). [CrossRef]

14.

J. Gjessing, A. S. Sudbø, and E. S. Marstein, “Comparison of periodic light-trapping structures in thin crystalline silicon solar cells,” J. Appl. Phys. 110(3), 033104 (2011). [CrossRef]

15.

S. Janz, P. Voisin, D. Suwito, M. Peters, M. Hermle, and S. W. Glunz, “Photonic crystals as rear-side diffusers and reflectors for high efficiency silicon solar cells,” in Proceedings of the 24th European Solar Energy Conference, 2009, 1529–1533.

16.

P. Voisin, M. Peters, H. Hauser, C. Helgert, E.-B. Kley, T. Pertsch, B. Bläsi, M. Hermle, and S. W. Glunz, “Nanostructured back side silicon solar cells,” in Proceedings of the 24th European Solar Energy Conference,2009, 1997–2000.

17.

P. Berger, H. Hauser, D. Suwito, S. Janz, M. Peters, B. Bläsi, and M. Hermle,R. B. Wehrspohn and A. Gombert, eds., “Realization and Evaluation of Diffractive Systems on the Back Side of Silicon Solar Cells,” in Proceedings of SPIE, R. B. Wehrspohn and A. Gombert, eds. (2010), p. 772504. [CrossRef]

18.

J. H. Poynting, “On the Transfer of Energy in the Electromagnetic Field,” Philos. Trans. R. Soc. Lond. 175(0), 343–361 (1884). [CrossRef]

19.

K.-H. Brenner, “Aspects for calculating local absorption with the rigorous coupled-wave method,” Opt. Express 18(10), 10369–10376 (2010). [CrossRef] [PubMed]

20.

A. Mellor, H. Hauser, C. Wellens, J. Benick, J. Eisenlohr, M. Peters, A. Guttowski, I. Tobías, A. Martí, A. Luque, and B. Bläsi, “Nanoimprinted diffraction gratings for crystalline silicon solar cells: implementation, characterization and simulation,” Opt. Express 21(S2Suppl 2), A295–A304 (2013). [CrossRef] [PubMed]

21.

A. Goetzberger, “Optical confinement in thin Si-solar cells by diffuse back reflectors,” in Proceedings of the 15th IEEE Photovoltaic Specialists Conference, 1981, 867–870.

OCIS Codes
(040.5350) Detectors : Photovoltaic
(050.1950) Diffraction and gratings : Diffraction gratings

ToC Category:
Light Trapping for Photovoltaics

History
Original Manuscript: September 30, 2013
Revised Manuscript: November 13, 2013
Manuscript Accepted: November 13, 2013
Published: December 16, 2013

Citation
Johannes Eisenlohr, Jan Benick, Marius Peters, Benedikt Bläsi, Jan Christoph Goldschmidt, and Martin Hermle, "Hexagonal sphere gratings for enhanced light trapping in crystalline silicon solar cells," Opt. Express 22, A111-A119 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-S1-A111


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References

  1. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am.72(7), 899–907 (1982). [CrossRef]
  2. E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev.29(2), 300–305 (1982). [CrossRef]
  3. I. M. Peters, “Photonic Concepts for Solar Cells”, PhD thesis (Universität Freiburg, Freiburg, Germany, 2009).
  4. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express18(S3Suppl 3), A366–A380 (2010). [CrossRef] [PubMed]
  5. P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett.43(6), 579–581 (1983). [CrossRef]
  6. C. Heine and R. H. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt.34(14), 2476–2482 (1995). [CrossRef] [PubMed]
  7. P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express15(25), 16986–17000 (2007). [CrossRef] [PubMed]
  8. J. Schmidt, A. Merkle, R. Brendel, B. Hoex, M. C. M. van de Sanden, and W. M. M. Kessels, “Surface passivation of high-efficiency silicon solar cells by atomic-layer-deposited Al2O3,” Prog. Photovolt. Res. Appl.16(6), 461–466 (2008). [CrossRef]
  9. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A12(5), 1068–1076 (1995). [CrossRef]
  10. IEC, Photovoltaic Devices - Part 3: Measurement Principles for Terrestrial Photovoltaic (PV) Solar Devices with Reference Spectral Irradiance Data., 2nd ed., International Standard, IEC 60904–3 (International Electrotechnical Commission, 2008).
  11. D. Kray, “Hocheffiziente Solarzellenstrukturen für Kristallines Silicium-Material Industrieller Qualität,” PhD thesis (Universität Konstanz, Konstanz, 2004).
  12. M. Peters, M. Rüdiger, H. Hauser, M. Hermle, and B. Bläsi, “Diffractive gratings for crystalline silicon solar cells—optimum parameters and loss mechanisms,” Progr. Photovolt.: Res. Appl.20, 862–873 (2011).
  13. A. Mellor, I. Tobias, A. Marti, and A. Luque, “A numerical study of Bi-periodic binary diffraction gratings for solar cell applications,” Sol. Energy Mater. Sol. Cells95(12), 3527–3535 (2011). [CrossRef]
  14. J. Gjessing, A. S. Sudbø, and E. S. Marstein, “Comparison of periodic light-trapping structures in thin crystalline silicon solar cells,” J. Appl. Phys.110(3), 033104 (2011). [CrossRef]
  15. S. Janz, P. Voisin, D. Suwito, M. Peters, M. Hermle, and S. W. Glunz, “Photonic crystals as rear-side diffusers and reflectors for high efficiency silicon solar cells,” in Proceedings of the 24th European Solar Energy Conference, 2009, 1529–1533.
  16. P. Voisin, M. Peters, H. Hauser, C. Helgert, E.-B. Kley, T. Pertsch, B. Bläsi, M. Hermle, and S. W. Glunz, “Nanostructured back side silicon solar cells,” in Proceedings of the 24th European Solar Energy Conference,2009, 1997–2000.
  17. P. Berger, H. Hauser, D. Suwito, S. Janz, M. Peters, B. Bläsi, and M. Hermle,R. B. Wehrspohn and A. Gombert, eds., “Realization and Evaluation of Diffractive Systems on the Back Side of Silicon Solar Cells,” in Proceedings of SPIE, R. B. Wehrspohn and A. Gombert, eds. (2010), p. 772504. [CrossRef]
  18. J. H. Poynting, “On the Transfer of Energy in the Electromagnetic Field,” Philos. Trans. R. Soc. Lond.175(0), 343–361 (1884). [CrossRef]
  19. K.-H. Brenner, “Aspects for calculating local absorption with the rigorous coupled-wave method,” Opt. Express18(10), 10369–10376 (2010). [CrossRef] [PubMed]
  20. A. Mellor, H. Hauser, C. Wellens, J. Benick, J. Eisenlohr, M. Peters, A. Guttowski, I. Tobías, A. Martí, A. Luque, and B. Bläsi, “Nanoimprinted diffraction gratings for crystalline silicon solar cells: implementation, characterization and simulation,” Opt. Express21(S2Suppl 2), A295–A304 (2013). [CrossRef] [PubMed]
  21. A. Goetzberger, “Optical confinement in thin Si-solar cells by diffuse back reflectors,” in Proceedings of the 15th IEEE Photovoltaic Specialists Conference, 1981, 867–870.

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