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Energy Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. S6 — Nov. 7, 2011
  • pp: A1219–A1230
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Design of nanostructured plasmonic back contacts for thin-film silicon solar cells

Ulrich W. Paetzold, Etienne Moulin, Bart E. Pieters, Reinhard Carius, and Uwe Rau  »View Author Affiliations


Optics Express, Vol. 19, Issue S6, pp. A1219-A1230 (2011)
http://dx.doi.org/10.1364/OE.19.0A1219


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Abstract

We report on a plasmonic light-trapping concept based on localized surface plasmon polariton induced light scattering at nanostructured Ag back contacts of thin-film silicon solar cells. The electromagnetic interaction between incident light and localized surface plasmon polariton resonances in nanostructured Ag back contacts was simulated with a three-dimensional numerical solver of Maxwell’s equations. Geometrical parameters as well as the embedding material of single and periodic nanostructures on Ag layers were varied. The design of the nanostructures was analyzed regarding their ability to scatter incident light at low optical losses into large angles in the silicon absorber layers of the thin-film silicon solar cells.

© 2011 OSA

1. Introduction

Thin-film silicon solar cells offer the advantages of low material and manufacturing costs while applying readily available and non-toxic materials. For this technology, highest stabilized efficiencies are obtained with multijunction concepts, as e.g. the tandem solar cell design based on an amorphous silicon (a-Si:H) top cell and a microcrystalline silicon (µc-Si:H) bottom cell (Fig. 1
Fig. 1 (a) Schematic cross-section of the tandem thin-film silicon solar cell with plasmonic back contacts consisting of (b) stochastic distributions of Ag nanostructures or (c) periodically arranged Ag nanostructures on the Ag back contact.
) [1

1. M. A. Green, K. Emery, Y. Hishikawa, and W. Warta, “Solar cell efficiency tables (Version 37),” Prog. Photovolt. Res. Appl. 19(1), 84–92 (2011). [CrossRef]

3

3. G. Yue, L. Sivec, J. M. Owens, B. Yan, J. Yang, and S. Guha, “Optimization of back reflector for high efficiency hydrogenated nanocrystalline silicon solar cells,” Appl. Phys. Lett. 95(26), 263501 (2009). [CrossRef]

]. In order to increase the absorption of the incident light in the optically thin silicon absorber layers, light-trapping concepts need to be applied [2

2. B. Rech, T. Repmann, M. N. van den Donker, M. Berginski, T. Kilper, J. Hüpkes, S. Calnan, H. Stiebig, and S. Wieder, “Challenges in microcrystalline silicon based solar cell technology,” Thin Solid Films 511–512, 548–555 (2006). [CrossRef]

6

6. 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). [CrossRef]

]. Conventional thin-film silicon solar cells make use of the light scattering and diffraction at randomly textured interfaces of the transparent front contact (e.g. ZnO:Al) and the reflective back contact (e.g. Ag) [6

6. 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). [CrossRef]

9

9. T. Söderström, D. Dominé, A. Feltrin, M. Despeisse, F. Meillaud, G. Bugnon, M. Boccard, P. Cuony, F. J. Haug, S. Fay, S. Nicolay, and C. Ballif, “ZnO Transparent conductive oxide for thin-film silicon solar cells,” Proc. SPIE 7603, 76030B, 76030B–12 (2010). [CrossRef]

].

In this contribution, LSPP induced scattering at nanostructured Ag back contacts of tandem thin-film silicon solar cells is studied (Fig. 1). This design implies several advantages. First, instead of nanoparticles, which are often researched, we investigate nanostructured Ag back contacts as their preparation and implementation into the rear side of the solar cell is relatively easy. The recent progress in imprint technologies offers exciting perspectives to realize nanostructured substrates [20

20. V. E. Ferry, M. A. Verschuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett. 95(18), 183503 (2009). [CrossRef]

]. Second, in this configuration the Ag nanostructures are not in contact with the absorber layer. Thus, no additional recombination losses are expected in comparison to the random texture light-trapping concept. Finally, by locating the plasmonic nanostructures at the rear side of the solar cells, we limit the operating spectral range of the plasmonic device to 500 nm < λ < 1100 nm. In typical tandem thin-film silicon solar cells only light of wavelength above 500 nm reaches the rear side [6

6. 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). [CrossRef]

]. For wavelengths longer than 1100 nm the absorption of µc-Si:H or a-Si:H and consequently the contribution to the photocurrent of the solar cell vanishes.

First experimental results in the literature on single junction thin-film silicon solar cells which apply periodic and stochastic nanostructured Ag back contacts show that the LSPP based light-trapping concepts lead to an enhancement of the photocurrent in the solar cells [18

18. S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007). [CrossRef]

20

20. V. E. Ferry, M. A. Verschuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett. 95(18), 183503 (2009). [CrossRef]

]. In order to optimized these back contacts, the appearing challenge is to engineer the nanostructures at the Ag back contact such that the absorption in the a-Si:H and µc-Si:H layers of a tandem thin-film solar cell is maximized. Therefore, in this contribution, we apply a three-dimensional numerical solver of Maxwell’s equations to study the electromagnetic interaction between incident light and LSPPs in nanostructured µc-Si:H/ZnO:Al/Ag layer stacks. These stacks represent the rear side of thin-film silicon solar cells (Fig. 1). Both, single and periodic nanostructures on Ag back contacts are simulated. Geometrical parameters of the plasmonic nanostructures, such as the size, shape, periodicity and embedding layer stack were varied. The design of the nanostructures was analyzed regarding their ability to scatter a maximum amount of incident light to large angles in the µc-Si:H layer of the thin-film silicon solar cell at low optical losses. From the results conclusions for stochastic distributions of nanostructures and square lattice reflection gratings of nanostructures at the back contact of a thin-film silicon solar cell are drawn.

2. Method

The interaction of electromagnetic waves with nanostructured Ag back contacts was studied with a three-dimensional numerical solver of Maxwell’s equations. The simulations were carried out with the commercially available program JCMsuite®. The applied software is based on the Finite Element Method (FEM) and discretizes Maxwell’s equations on a three-dimensional tetrahedral grid [23

23. J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Status Solidi, B Basic Res. 244(10), 3419–3434 (2007). [CrossRef]

]. Optical properties of the materials employed in this work are described via the complex refractive index (N = n + ik). The complex refractive index of µc-Si:H and ZnO:Al is taken from a reference set of experimental data [24

24. U. W. Paetzold, IEK5-Photovoltaik, Forschungszentrum Juelich GmbH, D-52425 Juelich, Germany (optical data can be provided upon request, contact u.paetzold@fz-juelich.de).

]. The materials have been optimized in-house for the designed application in the solar cell layer stack. The applied experimental techniques are photothermal deflection spectroscopy, transmission and reflection measurements and ellipsometry. The optical data of Ag are taken from ellipsometry measurements performed at flat and optically thick Ag layers [24

24. U. W. Paetzold, IEK5-Photovoltaik, Forschungszentrum Juelich GmbH, D-52425 Juelich, Germany (optical data can be provided upon request, contact u.paetzold@fz-juelich.de).

]. The data agrees with standard reference data [25

25. P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370––4379 (1972). [CrossRef]

,26

26. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York 1985).

]. However, regarding the imaginary part of the dielectric function, the references in the literature differ considerably. This leads to a difference in the obtained plasmonic losses. To avoid an underestimation of localized plasmon induced absorption, the applied data in this contribution is chosen conservative. The numerical accuracy of the simulations was evaluated with a reference system and convergence studies. In the case of spherical Ag nanoparticles embedded in non-absorbing materials, an analytical reference, the Mie theory, exists. This geometry was applied to identify reliable numerical parameters for the system under study.

The investigated geometries are nanostructured Ag layers embedded in a layer stack made of ZnO:Al and µc-Si:H, representing the back contact of e.g. a tandem thin-film silicon solar cell (Fig. 1, Fig. 2
Fig. 2 Cross section of the simulated geometries: (a) Isolated hemispherical nanostructure on Ag back layer embedded in ZnO:Al. (b) Isolated nanostructure on the Ag back layer embedded conformally in an 180 nm thick ZnO:Al layer and a µc-Si:H half-space. (c) Square lattice Ag reflection grating at the back contact. The absolute electric field distribution is shown, both, in a plane parallel (center) and a plane perpendicular (right side) to the polarization of the incident light (wavelength of 850 nm). The radius of the hemispherical nanostructure is 150 nm.
). We exclude the impact of dielectric layers at the front side of the solar cell in order to separately investigate the LSPP effects at the back contact. This simplification is strictly speaking only valid as long as the µc-Si:H absorber layer(thickness > 1000 nm) is much thicker than the optical wavelength (λ/n) and the phase of incident light at the front side and the back side is not correlated (e.g. for rough textures at the front side). Also, in first approximation the very thin doped µc-Si:H layers (thickness < 25 nm) are neglected. Three geometries of nanostructured Ag back contacts are investigated in this study (left side of Fig. 2). First, results on the optical properties of isolated nanostructures on Ag layers embedded in dielectric half-space are presented. Second, the influence of the dielectric layer stack at rear side of the solar cell on the LSPP resonance is discussed. Finally, square lattice reflection gratings formed by periodic arrangements of Ag nanostructures at the back contact are investigated. In addition to the cross section of the three geometries, Fig. 2 shows the simulated absolute electric field distribution of the geometry for incident light of 850 nm and a radius of the nanostructure of 150 nm (in a plane parallel and a plane perpendicular to the polarization of the incident electromagnetic wave). For the plane parallel to the polarization of the incident light, the enhanced electric-fields in the vicinity of the nanostructure indicate the LSPP resonance of the nanostructure. For the plane perpendicular to the polarization of the incident electromagnetic wave this enhancement of the electric field is not apparent as the plasmonic resonance oscillates in plane with the exciting electric field of the incident electromagnetic wave.

From the 3D electric field distributions the absorption profiles and intensity distribution of scattered light are calculated. Throughout this study, the incident electromagnetic wave penetrates the geometries under study at normal incidence. The scattering angle α in the µc-Si:H layer is shown in Fig. 2 (b) and Fig. 2 (c). The potential of nanostructures to absorb and scatter irradiated light is specified in the quantities absorption efficiency (Q abs) and scattering efficiency (Q sca). These quantities are calculated by normalizing the power absorbed (Pabs) and power scattered (Psca) by the nanostructure with the irradiated intensity (Iincident) and the geometric cross section (Cnanostructure) of the nanostructure:

Qabs=PabsIincidentCnanostructure                and            Qsca=PscaIincidentCnanostructure
(1)

3. Results and Discussion

3.1 Isolated nanostructure on an Ag layer in a dielectric half-space

Figure 3
Fig. 3 Absorption efficiency Q abs (a) and scattering efficiency Q sca (b) of an isolated hemispherical nanostructure on Ag embedded in a ZnO:Al half-space. The grey region indicates the operating spectral range for a plasmonic back contact (500 nm < λ < 1100 nm).
shows the absorption efficiency (Q abs) and scattering efficiency (Q sca) of an isolated hemispherical nanostructure on an Ag layer covered by a ZnO:Al half-space (cf. Figure 2 (a)). The radius of the nanostructure is varied from 25 nm to 200 nm. Values of Q sca or Q abs larger than unity express that the investigated Ag nanostructures can scatter or absorb more light intensity than irradiated on their cross section (Eq. (1)). This is a clear indication for LSPP resonances, where incident electromagnetic energy from the surrounding space couples to the coherent oscillation of the free electron gas in the Ag nanostructure [16

16. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters, Springer Series in Materials Science (Springer-Verlag, Berlin, 1995).

]. With increasing radius of the hemispherical Ag nanostructure the dominant LSPP resonance shifts to longer wavelengths. Two regimes can be identified. For small radii (radius < 50 nm) the LSSP induced optical losses (represented by Q abs) exceed the LSPP induced scattering (represented by Q sca) of the Ag nanostructures. With increasing radius the maximum Q abs values decrease and the LSPP resonances scatter more efficiently incident light. High scattering efficiencies at low absorption efficiencies in the operating spectral range of the back reflector of thin-film silicon solar cells are obtained for radii larger than 100 nm. Also, for these nanostructures more than one LSPP resonance appear at wavelengths longer than 500 nm. Furthermore, for a given LSPP resonance, the resonance wavelength where Q sca reaches its maximum deviates from the wavelength at which Qabs reaches its maximum. This deviation is well known from Mie Theory for LSPP resonances in isolated Ag nanoparticles and is observed in this contribution also for lSPP resonances in isolated Ag hemispheres [16

16. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters, Springer Series in Materials Science (Springer-Verlag, Berlin, 1995).

,17

17. C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (Wiley-Interscience, 1983).

].

In addition to the size of the nanostructure, the shape and the embedding material influence the LSPP resonance wavelengths. In Fig. 4
Fig. 4 Maximum scattering efficiency Qsca of the dominant LSPP resonance plotted against the resonance wavelength. Hemispherical Ag nanostructures of various radii embedded in SiO2, ZnO:Al and µc-Si:H (top) are studied. The grey region indicates the operating spectral range for a plasmonic back contact (500 nm < λ < 1100 nm).
the maximum values of Q sca at the dominant LSPP resonance of hemispherical Ag nanostructures embedded in different materials are plotted against the resonance wavelength. The embedding material and consequently the refractive index of the material adjacent to the hemispherical Ag nanostructure is varied from SiO2 (n ≈1.45) to ZnO:Al (n ≈1.7) and to µc-Si:H (n ≈3.5). A general increase of the dominant LSPP resonance wavelength is observed with increasing refractive index n of the embedding material. In case of µc-Si:H as the embedding material the LSPP resonances of hemispherical nanostructures shift significantly to longer wavelengths in comparison to ZnO:Al and SiO2. Only the LSPP resonances of small nanostructures (radius < 80 nm) embedded in µc-Si:H are located within the operating spectral range of the back reflector (500 nm < λ < 1100 nm). For these sizes, however, the LSPP resonances show strong optical losses (i.e. maximum Q abs values). Thus, regarding the light scattering at the back contact in solar cells, µc-Si:H (n ≈3.5) is not a favorable embedding material. Instead, the nanostructures on the Ag back contact need to be covered with a material of lower refractive n like ZnO:Al (n ≈1.7) or SiO2 (n ≈1.45). This way, the LSPP resonances of large and efficiently scattering nanostructures (radius > 100 nm) are located in the operating spectral range of the back contact.

In addition to the embedding material the shape of the Ag nanostructures is studied. In Fig. 5
Fig. 5 Maximum absorption efficiency Qabs (a) and maximum scattering efficiency Qsca (b) of the dominant LSPP resonance plotted against the corresponding resonance wavelength λres. Conical, hemispherical and cylindrical nanostructures on Ag layers embedded in ZnO:Al (bottom) are studied. For all geometries the radius of the nanostructures is varied. The grey region indicates the operating spectral range of a plasmonic back contact in thin-film silicon solar cells (500 nm < λ < 1100 nm).
the maximum Q sca and Q abs values of the dominant LSPP resonance of isolated conical (triangles), cylindrical (squares) and hemispherical (circles) nanostructures on Ag layers embedded in ZnO:Al are shown. For all geometries, the height of the structure is equal to the radius of the cross section of the nanostructure. The LSPP resonances of conical nanostructures are shifted to shorter wavelengths and the LSPP resonances of cylindrical nanostructures are shifted to longer wavelengths in comparison to hemispherical Ag nanostructures. Regarding solar cell application, high scattering efficiencies at low optical losses are desired in the operating spectral range of the back reflector. For conical nanostructures the Q sca values are lowest. Thus, this shape is not a favorable geometry to scatter efficiently incident light at the rear side of the solar cell. Highest values of Q sca but also of Q abs are found for cylindrical nanostructures. For example, for a radius of 80 nm the investigated cylindrical nanostructures show a maximum Q sca at the corresponding LSSP resonance of 13.8 and a maximum Q abs of 3.1. When neglecting the deviation for a given lSPP resonance between the resonance wavelengths at which Q sca reaches its maximum and Q abs reaches its maximum, the fraction Q abs_max /Q sca_max is a suitable figure of merit to identify nanostructures which scatter incident light at comparably lowest absorption losses. For the cylindrical nanostructure of radius of 80 nm a Q abs_max /Q sca_max ratio of 22.2% is calculated. A quite similar relative Q abs_max /Q sca_max ratio of 22.3% is also observed for the hemispherical nanostructure of the same radius at a relatively large Q sca of 8.1. Thus, hemispherical and cylindrical nanostructures of the same radius scatter incident light at similar radiative efficiencies, i.e. the ratio between Q abs and Q sca is similar. However, for hemispherical nanostructures also LSPP resonances of larger nanostructures (e.g. of radii around 150 nm) are located in the operational wavelength range of the back reflector. For these nanostructures, the Q abs_max /Q sca_max ratio is much smaller (e.g. for radius of 150 nm Q abs_max /Q sca_max = 7.6%) allowing for a more efficient scattering of incident light at comparably lower optical losses at the back contact of the solar cell.

3.2 Isolated hemispherical nanostructures on Ag back contacts

In conventional thin-film silicon solar cell configurations (Fig. 1) the Ag nanostructures at the back contact are covered conformally by a ZnO:Al/µc-Si:H layer stack as shown in Fig. 2 (b). Thus, when evaluating the scattering properties and the scattering angles of nanostructured Ag back contacts the adjacent layer stack needs to be considered. Figure 6
Fig. 6 (a) Scattering efficiency Q sca and absorption efficiency Q abs as well as (b) normalized intensity distribution of scattered light of hemispherical Ag nanostructures (radius = 150 nm) embedded conformally in ZnO:Al and µc-Si:H. The thickness of the ZnO:Al layer is 180 nm.
shows the absorption efficiency Q abs and scattering efficiency Q sca as well as the intensity distribution of the scattered light for an isolated hemispherical Ag nanostructure (radius = 150 nm) in such a configuration [cf. Figure 3 (b)]. As an example, the thickness of the ZnO:Al interlayer is set to 180 nm. By introducing the ZnO:Al/µc-Si:H interface, the system shows interferences, which superpose the LSPP resonance of the isolated hemispherical nanostructure embedded in a ZnO:Al half-space (Fig. 6 (a)). Depending on the spatial position of these interferences, the LSPP resonance is enhanced or attenuated. Thus, the Q abs and Q sca are modified in comparison to the case of an embedding ZnO:Al half-space. In Fig. 6 (b) the intensity distribution of scattered light is shown as a function of the scattering angle in the µc-Si:H layer and the wavelength. In the operating spectral range of the back reflector (500 nm < λ < 1100 nm) two prominent scattering intensity maxima appear. For wavelengths from 550 nm to 900 nm the maximum of scattering intensity is located at around 15°. The observed scattering angles are located below the angle of total reflection (red dashed line) of the flat ZnO:Al/µc-Si:H interface. Such scattering angles of the refracted light in the µc-Si:H layer are obtained by coupling of the LSPP resonance to propagating modes in the ZnO:Al layer. At the ZnO:Al/µc-Si:H interface, these propagating modes are then refracted according to geometrical optics. For wavelengths from 700 nm to 1100 nm, a second maximum in scattering intensity appears at around 37°. These angles overcome the angle of total reflection at the ZnO:Al/µc-Si:H interface, which would be prohibited in geometrical optics. We explain this effect by the near-field coupling of the plasmonic resonance in the Ag nanostructure to propagating modes in the µc-Si:H layer. As the effect is also observed for flat and non-conformal ZnO:Al/µc-Si:H interfaces it is not attributed to the curvature of the ZnO:Al/µc-Si:H interface. Also the effect decreases with increasing ZnO:Al layer thickness. Thus, near-field coupling of LSPP resonances in the Ag nanostructures into the µc-Si:H absorber layer offers the opportunity to scatter efficiently light at the back contact of thin-film silicon solar cells to large angles.

For solar cell applications the scattering of incident light at the back contact into large angles in the silicon absorber layers is very important. First, the light path in the silicon layers is simply enhanced by the scattering angle. Second, assuming flat silicon absorber layers and a flat ZnO:Al front contact, light scattered to angles beyond the angle of total reflection at the µc-Si:H/ZnO:Al and/or µc-Si:H/air interface will be guided in the silicon absorber layers. Although at the front side of a tandem thin-film silicon solar cell no µc-Si:H/air interface nor a µc-Si:H/ZnO:Al interface is apparent the corresponding total internal reflection angles are important for the light scattering at the back contact. Following Snell’s law of diffraction along the assumingly flat interfaces at the front side of the solar cell, we find that light which is scattered at the back contact beyond the total reflection angle of µc-Si:H/air will be totally reflected at latest at the glass/air front interface. I.e. light scattered at the plasmonic back contact beyond the angle of total internal reflection of a flat µc-Si:H/ZnO:Al interface will be trapped in the solar cell. The same argument applies for scattering angles beyond the total internal reflection angle of the µc-Si:H/ZnO:Al interface. However, in the latter case the scattered light does not propagate in the front ZnO:Al layer, avoiding parasitic optical losses due to absorption in the front ZnO:Al layer. Importantly, for textured solar cells, due to the variation of surface angles at the interfaces, the above presented discussion on scattering angles is not exact. Nevertheless, as a figure of merit to evaluate the scattering angles of a plasmonic back contact, the total internal reflection angles of the flat µc-Si:H/air interface and the flat µc-Si:H/ZnO:Al interface are very useful.

In Fig. 7
Fig. 7 Mean scattering and absorption efficiency of single nanostructures (hemispherical, radius = 150 nm) on Ag back contacts. The data is averaged over the relevant wavelength range (500 nm < λ < 1100 nm).
the average values of Q sca and Q abs over the operating spectral range of the back reflector are shown for nanostructures on Ag back contacts (hemispherical shape, radius = 150 nm) as a function of the ZnO:Al layer thickness. In addition, two fractions of Q sca are presented, which quantify the amount of light scattered beyond the total reflection angle of the µc-Si:H/air interface and the total reflection angle at the µc-Si:H/ZnO:Al interface. The thickness of the ZnO:Al layer was varied from 15 nm to 500 nm. While for smaller thicknesses it is difficult to obtain in practice a uniform and high quality ZnO:Al material, devices with ZnO:Al layer thickness larger than 500 nm are known to suffer from either a poor conductivity or large optical losses [28

28. K. Ellmer, A. Klein, and B. Rech, Transparent Conductive Zinc Oxide: Basics and Applications in Thin-film Solar Cells (Springer, Berlin, 2008).

]. For all thicknesses of the ZnO:Al layer investigated, the LSPP induced optical losses of the Ag nanostructure are low. The average Q abs is always smaller than 10% of the Q sca. A significant variation of the Q sca is observed by changing the thickness of the ZnO:Al. Highest total Q sca values above 4 and 2.5 are found for either large thicknesses (> 500 nm) or small thicknesses (< 45 nm), respectively. Smallest values of the total Q sca around 1.85 are found for the conventional thickness of the back ZnO:Al layer of around 80 nm. However, in this configuration the relative amount of light scattered to large angles beyond the angle of total reflection at the µc-Si:H/ZnO:Al interface (50%) as well as the µc-Si:H/air interface (70%) are highest. With increasing thickness the total Q sca increases but the relative amount of light scattered to large angles decreases. For the application of LSPP induced scattering at nanostructured Ag back contacts, both aspects are important: Larger Q sca values allow for a smaller surface coverage of nanostructures and large scattering angles directly improve the light-trapping in the solar cells. A good tradeoff can be found for ZnO thicknesses of around 180 nm, where a Q sca value of 2.7 is found and 43% and 60% of all incident light is scattered to angles larger than the total reflection angle of µc-Si:H/ZnO:Al and µc-Si:H/air, respectively.

In this section it is shown that incident light can couple at high efficiency to LSPP resonances in hemispherical Ag nanostructures at the back contact of thin-film silicon solar cells. The resonances are found to scatter a multiple of the light irradiated on their cross section at low optical losses into the µc-Si:H layer of the solar cell. Even if averaged over the operating spectral range, depending on the ZnO:Al thickness, between 1.8 and 4 times of the light irradiated on the cross section of the nanostructures is scattered. Up to 70% of the light scattered is scattered to angles larger than the total reflection angle of the µc-Si:H/air interface and will therefore be reflected at the front side. Up to 50% of the scattered light is even scattered to angles larger than the total reflection angle of the µc-Si:H/ZnO:Al interface and will therefore be guided inside the silicon absorber layers. Recent studies showed that the maximum scattering intensity induced by the conventional texture at the front contact of the thin-film silicon solar cell is only around 7° [29

29. K. Jäger, M. Schulte, K. Bittkau, A. M. Ermes, M. Zeeman, and B. E. Pieters, “Optical scattering properties of nano-textured ZnO silicon interfaces,” Proc. SPIE 8001, 800113 (2011).

]. Furthermore, for the conventional light-trapping textures only a very small amount of incident light (at the wavelength of 800 nm) was found to be scattered beyond the total reflection angle of the µc-Si:H/air interface. Thus, nanostructured Ag back contacts carrying LSPP resonances offer a great potential as an alternative light-trapping concept in thin-film silicon solar cells. Neglecting the interaction between the nanostructures, the presented findings on isolated nanostructures at the Ag back contact of thin-film silicon solar cells can be transferred in first approximation to calculate, by multiplying with the surface coverage, the optical parameters like haze, absorption and scattering angle distribution of stochastic arrangements of Ag nanostructures. As the LSPP resonances scatter a multiple of the irradiated light on the nanostructures cross section, realistic stochastic surface coverage below 50% are sufficient to scatter the incident light at the rear side of the solar cell.

3.3 Two dimensional reflection gratings of nanostructured Ag back contacts

Periodically ordered nanostructures on Ag back contacts create 2D surface gratings [Fig. 1 (c)]. The scattering angles of gratings are determined by discrete diffraction orders. In case of square lattice reflection gratings created by Ag nanostructures at the back contact of thin-film silicon solar cells and normal incidence, the scattering angles in µc-Si:H are given by
sin(α)  =Nxyλ     LnμcSiwith​  Nxy=mx2+my2   andmx,my=±     0,1,2,3,4,...
(2)
where λ is the wavelength in air, L is the grating period, m x and m y are the diffraction orders, α is the diffraction angle relative to the surface normal direction and n µc-Si:H is the refractive index of µc-Si:H. Equation (2) indicates, that by varying the period L of a grating the scattering angle distribution can be influenced, thus allowing to control the scattering angles at nanostructured Ag back reflectors.

In Fig. 9
Fig. 9 Simulated absorption A, specular reflection R spec and non-specular reflection R non-spec of reflection gratings formed by hemispherical Ag nanostructures at the back contact of a thin-film silicon solar cell [cf. Figure 2 (c)]. The data, which is averaged over the wavelength range from 500 nm to 1100 nm, is given for various periods of the reflection grating. Also the amount of light reflected non-specular to angles larger than the total reflection angle of the µc-Si:H/Air interface and the µc-Si:H/ZnO interface is given in R non-spec’ and R non-spec”, respectively.
the simulated absorption A, specular reflection R spec and non-specular reflection R non-spec of various square lattice reflection gratings of the type described above are shown. The values are averaged over the operating spectral range of the back reflector in a tandem thin-film silicon solar cell. The optimal light-trapping geometry is expected to have lowest losses and specular reflection at highest non-specular reflection to large angles (i.e. above the total reflection angle at the µc-Si:H /ZnO:Al interface). For the studied geometry this is fulfilled for periods around 450 nm. For these periods up to 63% and 50% of the incident light is scattered at the nanostructured Ag back contact to angles larger than the total reflection angle of the µc-Si:H/air and the µc-Si:H/ZnO:Al interface, respectively. Only 20% of the light is reflected specularly. For an isolated Ag nanostructure at the back contact of similar geometry (radius = 150 nm, ZnO thickness = 180 nm) we find that 63% and 42% of the light that interacts with the Ag nanostructure is scattered to angles larger than the total reflection angle of the µc-Si:H/air and the µc-Si:H/ZnO:Al interface, respectively. Thus, comparing the isolated and periodic case it is shown that the grating arrangement of the Ag nanostructures at the back contact increases the relative amount of light scattered to larger angles. This is particularly interesting, as one might expect that the densely arrangement of the nanostructures in the periodic case disturb or attenuates the lSPP resonances.

4. Conclusions

Localized surface plasmon polariton (LSPP) induced light scattering at nanostructured Ag back contacts of thin-film silicon solar cells has been simulated with a three-dimensional numerical solver of Maxwell’s equations. Both, single nanostructures and square lattice reflection gratings of Ag nanostructures at the back contact of a thin-film silicon solar cell are found to carry LSPP resonances which can scatter large fractions of incident light at low optical losses. The calculated angular intensity distributions of the scattered light at nanostructured Ag back contacts show that a significant amount of the incident light can be scattered to very large angles in the µc-Si:H absorber layer of the solar cell. The scattering angles simulated for nanostructured Ag back contacts are much larger than those reported in the literature for conventional light-trapping structures. Thus, nanostructured Ag back contacts carrying LSPP resonances are very promising for improving the light-trapping in thin-film silicon solar cells. Very critical for the LSPP induced scattering, and consequently the light-trapping properties, are the geometrical parameters of the Ag nanostructures and the embedding dielectric materials. Throughout this study, various geometrical parameters of the nanostructures have been varied and optimized regarding the ability of the nanostructures to scatter incident light at low optical losses to large angles in the silicon absorber layers. Implementations of optimized Ag nanostructures are expected to lead to significantly enhanced efficiencies of thin-film silicon solar cell.

Acknowledgments

The authors thank Karsten Bittkau, Urs Aeberhardt, Matthias Meier, Gero von Plessen, Rudi Santbergen, Dirk Michaelis, Christoph Wächter, Volker Hagemann, Sascha Pust and Sven Burger for very helpful discussions. The authors express their gratitude to the partners of the SUNPLAS project for valuable suggestions. We gratefully acknowledge the financial support from the German Federal Ministry of Education and Research under contract 03SF0354D.

References and links

1.

M. A. Green, K. Emery, Y. Hishikawa, and W. Warta, “Solar cell efficiency tables (Version 37),” Prog. Photovolt. Res. Appl. 19(1), 84–92 (2011). [CrossRef]

2.

B. Rech, T. Repmann, M. N. van den Donker, M. Berginski, T. Kilper, J. Hüpkes, S. Calnan, H. Stiebig, and S. Wieder, “Challenges in microcrystalline silicon based solar cell technology,” Thin Solid Films 511–512, 548–555 (2006). [CrossRef]

3.

G. Yue, L. Sivec, J. M. Owens, B. Yan, J. Yang, and S. Guha, “Optimization of back reflector for high efficiency hydrogenated nanocrystalline silicon solar cells,” Appl. Phys. Lett. 95(26), 263501 (2009). [CrossRef]

4.

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]

5.

D. Redfield, “Multiple-pass thin-film silicon solar cell,” Appl. Phys. Lett. 25(11), 647 (1974). [CrossRef]

6.

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). [CrossRef]

7.

J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light-trapping in silicon thin-film solar cells,” Sol. Energy 77(6), 917–930 (2004). [CrossRef]

8.

T. Matsui, M. Tsukiji, H. Saika, T. Toyama, and M. Okamoto, “Influence of substrate texture on microstructure and photovoltaic performances of thin-film polycrystalline silicon solar cells,” J. Non-Cryst. Solids 299–302, 1152–1156 (2002). [CrossRef]

9.

T. Söderström, D. Dominé, A. Feltrin, M. Despeisse, F. Meillaud, G. Bugnon, M. Boccard, P. Cuony, F. J. Haug, S. Fay, S. Nicolay, and C. Ballif, “ZnO Transparent conductive oxide for thin-film silicon solar cells,” Proc. SPIE 7603, 76030B, 76030B–12 (2010). [CrossRef]

10.

J. Springer, B. Rech, W. Reetz, J. Müller, and M. Vanecek, “Light-trapping and optical losses in microcrystalline silicon pin solar cells deposited on surface-textured glass/ZnO substrates,” Sol. Energy Mater. Sol. Cells 85, 1–11 (2005).

11.

S. Fahr, C. Rockstuhl, and F. Lederer, “Engineering the randomness for enhanced absorption in solar cells,” Appl. Phys. Lett. 92(17), 171114 (2008). [CrossRef]

12.

D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89(9), 093103 (2006). [CrossRef]

13.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi 205(12), 2844–2861 (2008). [CrossRef]

14.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]

15.

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008). [CrossRef]

16.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters, Springer Series in Materials Science (Springer-Verlag, Berlin, 1995).

17.

C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (Wiley-Interscience, 1983).

18.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007). [CrossRef]

19.

E. Moulin, J. Sukmanowski, M. Schulte, A. Gordijn, F. Royer, and H. Stiebig, “Thin-film silicon solar cells with integrated silver nanoparticles,” Thin Solid Films 516(20), 6813–6817 (2008). [CrossRef]

20.

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett. 95(18), 183503 (2009). [CrossRef]

21.

U. W. Paetzold, F. Hallermann, B. E. Pieters, U. Rau, R. Carius, and G. von Plessen, “Localized plasmonic losses at metal back contacts of thin-film silicon solar cells,” Proc. SPIE 7725, 772517, 772517–772519 (2010). [CrossRef]

22.

J. Springer, A. Poruba, L. Müllerova, M. Vanecek, O. Kluth, and B. Rech, “Absorption loss at nanorough silver back reflectors of thin-film silicon solar cells,” J. Appl. Phys. 95(3), 1427–1430 (2004). [CrossRef]

23.

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Status Solidi, B Basic Res. 244(10), 3419–3434 (2007). [CrossRef]

24.

U. W. Paetzold, IEK5-Photovoltaik, Forschungszentrum Juelich GmbH, D-52425 Juelich, Germany (optical data can be provided upon request, contact u.paetzold@fz-juelich.de).

25.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370––4379 (1972). [CrossRef]

26.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York 1985).

27.

C. Rockstuhl, S. Fahr, and F. Lederer, “Absorption enhancement in solar cells by localized plasmon polaritons,” J. Appl. Phys. 104(12), 123102 (2008). [CrossRef]

28.

K. Ellmer, A. Klein, and B. Rech, Transparent Conductive Zinc Oxide: Basics and Applications in Thin-film Solar Cells (Springer, Berlin, 2008).

29.

K. Jäger, M. Schulte, K. Bittkau, A. M. Ermes, M. Zeeman, and B. E. Pieters, “Optical scattering properties of nano-textured ZnO silicon interfaces,” Proc. SPIE 8001, 800113 (2011).

OCIS Codes
(350.6050) Other areas of optics : Solar energy
(250.5403) Optoelectronics : Plasmonics
(310.6845) Thin films : Thin film devices and applications

ToC Category:
Solar Energy

History
Original Manuscript: August 10, 2011
Revised Manuscript: September 16, 2011
Manuscript Accepted: September 21, 2011
Published: October 12, 2011

Virtual Issues
October 28, 2011 Spotlight on Optics

Citation
Ulrich W. Paetzold, Etienne Moulin, Bart E. Pieters, Reinhard Carius, and Uwe Rau, "Design of nanostructured plasmonic back contacts for thin-film silicon solar cells," Opt. Express 19, A1219-A1230 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-S6-A1219


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References

  1. M. A. Green, K. Emery, Y. Hishikawa, and W. Warta, “Solar cell efficiency tables (Version 37),” Prog. Photovolt. Res. Appl.19(1), 84–92 (2011). [CrossRef]
  2. B. Rech, T. Repmann, M. N. van den Donker, M. Berginski, T. Kilper, J. Hüpkes, S. Calnan, H. Stiebig, and S. Wieder, “Challenges in microcrystalline silicon based solar cell technology,” Thin Solid Films511–512, 548–555 (2006). [CrossRef]
  3. G. Yue, L. Sivec, J. M. Owens, B. Yan, J. Yang, and S. Guha, “Optimization of back reflector for high efficiency hydrogenated nanocrystalline silicon solar cells,” Appl. Phys. Lett.95(26), 263501 (2009). [CrossRef]
  4. 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]
  5. D. Redfield, “Multiple-pass thin-film silicon solar cell,” Appl. Phys. Lett.25(11), 647 (1974). [CrossRef]
  6. 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). [CrossRef]
  7. J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light-trapping in silicon thin-film solar cells,” Sol. Energy77(6), 917–930 (2004). [CrossRef]
  8. T. Matsui, M. Tsukiji, H. Saika, T. Toyama, and M. Okamoto, “Influence of substrate texture on microstructure and photovoltaic performances of thin-film polycrystalline silicon solar cells,” J. Non-Cryst. Solids299–302, 1152–1156 (2002). [CrossRef]
  9. T. Söderström, D. Dominé, A. Feltrin, M. Despeisse, F. Meillaud, G. Bugnon, M. Boccard, P. Cuony, F. J. Haug, S. Fay, S. Nicolay, and C. Ballif, “ZnO Transparent conductive oxide for thin-film silicon solar cells,” Proc. SPIE7603, 76030B, 76030B–12 (2010). [CrossRef]
  10. J. Springer, B. Rech, W. Reetz, J. Müller, and M. Vanecek, “Light-trapping and optical losses in microcrystalline silicon pin solar cells deposited on surface-textured glass/ZnO substrates,” Sol. Energy Mater. Sol. Cells85, 1–11 (2005).
  11. S. Fahr, C. Rockstuhl, and F. Lederer, “Engineering the randomness for enhanced absorption in solar cells,” Appl. Phys. Lett.92(17), 171114 (2008). [CrossRef]
  12. D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett.89(9), 093103 (2006). [CrossRef]
  13. F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi205(12), 2844–2861 (2008). [CrossRef]
  14. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010). [CrossRef] [PubMed]
  15. K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett.93(19), 191113 (2008). [CrossRef]
  16. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters, Springer Series in Materials Science (Springer-Verlag, Berlin, 1995).
  17. C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (Wiley-Interscience, 1983).
  18. S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys.101(9), 093105 (2007). [CrossRef]
  19. E. Moulin, J. Sukmanowski, M. Schulte, A. Gordijn, F. Royer, and H. Stiebig, “Thin-film silicon solar cells with integrated silver nanoparticles,” Thin Solid Films516(20), 6813–6817 (2008). [CrossRef]
  20. V. E. Ferry, M. A. Verschuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett.95(18), 183503 (2009). [CrossRef]
  21. U. W. Paetzold, F. Hallermann, B. E. Pieters, U. Rau, R. Carius, and G. von Plessen, “Localized plasmonic losses at metal back contacts of thin-film silicon solar cells,” Proc. SPIE7725, 772517, 772517–772519 (2010). [CrossRef]
  22. J. Springer, A. Poruba, L. Müllerova, M. Vanecek, O. Kluth, and B. Rech, “Absorption loss at nanorough silver back reflectors of thin-film silicon solar cells,” J. Appl. Phys.95(3), 1427–1430 (2004). [CrossRef]
  23. J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Status Solidi, B Basic Res.244(10), 3419–3434 (2007). [CrossRef]
  24. U. W. Paetzold, IEK5-Photovoltaik, Forschungszentrum Juelich GmbH, D-52425 Juelich, Germany (optical data can be provided upon request, contact u.paetzold@fz-juelich.de).
  25. P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370––4379 (1972). [CrossRef]
  26. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York 1985).
  27. C. Rockstuhl, S. Fahr, and F. Lederer, “Absorption enhancement in solar cells by localized plasmon polaritons,” J. Appl. Phys.104(12), 123102 (2008). [CrossRef]
  28. K. Ellmer, A. Klein, and B. Rech, Transparent Conductive Zinc Oxide: Basics and Applications in Thin-film Solar Cells (Springer, Berlin, 2008).
  29. K. Jäger, M. Schulte, K. Bittkau, A. M. Ermes, M. Zeeman, and B. E. Pieters, “Optical scattering properties of nano-textured ZnO silicon interfaces,” Proc. SPIE8001, 800113 (2011).

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