The development of backside reflectors (BSRs) is crucial for the efficiency of future low cost thin-film silicon solar cells. In this work, the scattering efficiency of bare aluminum BSRs with different pore sizes and ordering of surface microstructures are investigated. The BSRs were fabricated by utilizing the process of self-ordering anodic oxidation on aluminum foils resulting in regions with an approximately hexagonally periodic surface microstructure. It was found that the total and diffuse light scattering reflectance spectra showed opposite tendencies when increasing the pore size of the microstructures. When the pore size was increased to 700 nm, more than 68% of the incident light with wavelengths from 250 nm to 800 nm was reflected by scattering. For a similar geometry, except that it had less ordering, this number was increased to around 80%. This large fraction of reflected light observed in the form of scattering is promising for the use of the considered geometries as BSRs in thin-film silicon solar cells.
© 2012 OSA
To date, various morphologies of surface micro/nano-structures, i.e., nanopyramids , nanowires , nanopillars , nanocones  and spherical nanostructures  with different materials such as Si [2,5,6], ZnO , Ge  and CIGS  have been fabricated and widely investigated in order to enhance photon management efficiently for different optical devices like photo-detectors, light-emitting diodes (LEDs)  and solar cells. In the case of thin-film silicon solar cells, the question of how to enhance the light capturing within absorption layers is crucial for the conversion efficiency because thickness reduction of silicon solar cells without sacrificing too much efficiency is the trend for developing future low-cost solar cells. In this regard, different kinds of substrates with surface textures have been investigated with emphasis on diffracting or scattering light at oblique angles. This includes textured ZnO , textured ZnO with Ag [11,12], a Ag-Al alloy , and a periodically textured flexible substrate .
Then, absorption of incident light can be increased due to light trapping inside the cells by a longer optical path length in the silicon layers and total internal reflection at interfaces . In fact, these surface textures, can be divided into two types: periodic structures and random structures. Some reports pointed out that periodic structures, such as surface gratings  and photonic crystals  show better performance of the light trapping than conventional random structures, but transparent conductive oxide (TCO)  substrates with random textures in large area, such as SnO2:F glasses (Asahi type U), have been also applied as BSRs in thin-film Si solar cell industries for a long time. A recent work showed similar performance of BSRs based on a random pyramidal morphology, and BSRs based on a periodic nanosphere-lithography-based morphology .
Hence, it is still ambiguous to judge, which concept shows the best performance for light trapping in solar cells. Therefore, understanding the effect of surface texture on light trapping is very interesting for both academic research and for industrial mass production of solar cell. The issue of light trapping is especially important for light of long wavelengths approaching the bandgap in thin-film silicon solar cells because of small absorption. The possibility of having better light trapping in a thin-film solar cell is strongly coupled to having light reflected or scattered into directions where light will have to propagate longer distances in the silicon before it has a chance to escape, and possibly part of this light can be incident on interfaces at such angles that it will experience total-internal reflection increasing further the optical path length in the active material. For sun-light at near-normal incidence this means that we require that the BSR should not reflect light directly backwards at near-normal directions but preferably into oblique-angle directions. This can be achieved if a large part of the light is not specularly reflected but is instead in the form of diffraction or scattering. In order to understand the diffractive and scattering properties of BSRs, it is important to characterize the optical properties, e.g. the total and scattering reflectance spectra, of bare BSRs, because once silicon is added, it becomes difficult experimentally to determine if absorption losses occurred in the BSR or in the silicon.
The motivation of this paper is to enhance the scattering efficiency being the fraction of incident light reflected or scattered into oblique angles in the whole ultraviolet–visible (UV-Vis) wavelength ranges, 250 nm ~1100 nm, by tuning surface microstructures on an aluminum (Al) foil, and in this way trap the light efficiently, especially for the longer wavelengths, when the foil is used as the substrate in solar cells. The paper is organized in the following way. In Sec. 2, we present the fabrication of textured surfaces with different pore sizes and ordering of hexagonal microstructures based on the method of anodic aluminum oxidation (AAO). In Sec. 3, the surface microstructures are characterized by scanning electron microscopy (SEM) and atomic force microscopy (AFM), and the optical properties are investigated by UV-Vis spectroscopy. In Sec. 4, the main features of the measured optical properties are explained by diffraction theory and simulations based on a stack matrix method.
The technique of AAO is quite mature, and many applications of the fabricated structures  as templates for fabrication of nanowires , or nanodots , have been demonstrated. Nanoporous films  have also been applied in for example thermoelectric materials , biosensors , ultrahigh density magnetic recording media , photocatalysis , and various microelectronic devices and nanodevices. In this work, four different BSR samples with various pore sizes or periods (Λ) and uniformity were prepared by our home-built anodization and wet-etching system. Before anodization, 99.98% pure Al foils (Advent Research Materials Ltd. AL103310) were adopted as substrates and cleaned in an ultrasonic cleaner with a sequence of acetone, deionized water and methanol solutions for 1 minute, respectively. Organic and inorganic acid solutions like oxalic, citric and phosphoric acids were chosen as electrolytes to fabricate porous alumina thin films. The reason for choosing oxalic and citric acids is that they are both weak acids with a COOH group and low corrosive ability, so they enable the formation of porous alumina thin films and allow anodizion at high electric potentials to increase the pore size .
Anodization was performed in a home-built Teflon container with a powerful cooling system (Neslab Endocal RTE-110) and vigorous stirring. A high-voltage direct current power supply (DELTA ELEKTRONIKA Power Supply SM 3004-D) connected with the Labview software was used to control the variations of applied voltages. All details of operating parameters of anodization are listed in Table 1 . They are not far from the parameters in a published paper from S. Z. Chu . As shown in Table 1, the sample with small pore size, named Oxalic, was anodized in 0.3M H2C2O4 (oxalic acid solution) at 140V and bath temperature at 283 ± 0.5K for 40 minutes. The sample with medium pore size, named Phosphoric, was anodized in 1M-H3PO4 (phosphoric acid solution) at 180V and bath temperature at 273 ± 0.5K for 100 minutes. The sample with large pore size, named Citric, was anodized in 4wt% C6H8O7 (citric acid solution) at 300V and bath temperature at 293 ± 0.5K for 55 minutes firstly. After removing the porous alumina layer the same procedure was repeated. The sample with large pore size, named Citric*, was also anodized in 4wt% C6H8O7 (citric acid solution) at 300V and bath temperature at 293 ± 0.5K for 100 minutes. In this work, Citric is the only sample that was fabricated by the two-step procedure for enhancing the homogeneity of periodic microstructures. Masuda et al. [28,29] have previously shown that the two-step anodization process can be used to obtain higher ordering of nano-pore arrays than the one-step procedure. Alternatively it has also been shown for phosphoric acid that a higher degree of ordering can be obtained with long-time anodization .
The mechanism of texture formation during anodization involves several steps including (i) formation of a surface oxide, (ii) subsequent initial pore formation, and (iii) self-organization of pores into a roughly hexagonal array with nearly hemispherical growth front at the oxide-metal interface. The pores grow continuously until the applied voltage is cut off. However, in order to prevent run-away currents originating from defects, a non-porous oxide is formed initially during a pre-anodization step. The voltage and anodization time of pre-anodization for Oxalic, Phosphoric and Citric* samples are 40V and 20 minutes. For the Citric sample we chose a shorter pre-anodization time (5 minutes) and a larger pre-anodization voltage (120 V). After anodization the porous alumina films were selectively etched away on the four BSR samples in an acid mixture (chromic acid and phosphoric acid) at around 353K with stirring. A photograph of the four fabricated bare Al BSR samples with different dimensions and orderings of surface microstructures is shown in Fig. 1 . The observed colors reflect the pore size and range from bluish (Oxalic) over green (Phosphoric) to white/gray (Citric and Citric*).
These samples have been examined by scanning electron microscopy (SEM) and atomic force microscopy (AFM), and the optical reflectance properties have been characterized by UV-Vis spectroscopy (PerkinElmer Lambda 1050) with an integrating sphere, where the incident angle was set at near normal incidence (θi = 8°), and the diffuse light-scattering part of the reflection was obtained by introducing an opening in the integrating sphere removing the specularly reflected part of the light from the sphere. Since some diffuse light reflected back and forth inside the sphere after some passes could also leave this opening (covering an angular range of 12.4° seen from the sample) the measurement can be considered a lower limit for the true diffuse part of the reflectance.
Figure 2 shows the SEM images of the Oxalic (a), Phosphoric (b), Citric (c) and Citric* (d) samples. The Oxalic sample shows the best hexagonal ordering and clearer domain confinements than other samples. It is because of a limited grain size in the Al foils such that when the pore size (dpore) increases less periods can fit inside one grain resulting in more random distributions. In order to improve the ordering of microstructures in the Citric* sample, which has more plateaus or shallower dimples, the two-step anodized process was introduced to fabricate the Citric sample. The Citric sample [Fig. 2(c)] is clearly more ordered than the Citric* sample [Fig. 2(d)]. They are both, however, still much more disordered than the Oxalic and the Phosphoric samples [Figs. 2(a),2(b)].
In order to calculate dpore accurately, central points of hundreds of pores from SEM images were located by using the image analysis tool ImageJ, and these were then used to calculate the nearest-neighbor-distances, next-nearest-neighbor distances, and so on. Then the results were sorted into small distance intervals resulting in the graphs in Fig. 3 . The results show that the average nearest-neighbor distances of the Oxalic, Phosphoric, and Citric samples are around 320nm, 430nm and 700nm, respectively, from the location of the first peak. For a hexagonal array of pores the next-nearest-neighbor distance is located at a distance being a factor larger (554 nm, 745 nm, and 1212 nm), which is in reasonable agreement with the location of the second peak in Fig. 3. In order to further classify the degree of disorder, this is quantified here as the full width at half maximum divided by the average nearest-neighbor distance, and is shown as an inset for these three samples. As seen in Fig. 3 the disorder increases from 12% to 30% when increasing the average dpore.
For investigating the morphologies and the dimensions of surface microstructures, all samples were examined by AFM. 3D AFM images of the Oxalic and Phosphoric samples in 2μm square are shown in [Fig. 4(a),(b) ], while 5μm square area of [Fig. 4(c),4(d)] were used in order to compare the larger structure in the Citric and Citric* samples. According to the AFM images there are domains that resemble a periodic structure with hexagonal ordering. The hexagon-shaped unit cell of the surface microstructures consists of an approximately circular dimple within the hexagon with six narrow and high peaks with a rounded top at the hexagon corners. In fact, these rounded tops should be very sharp and narrow cones, and the reason that they appear rounded is because of limited resolution related to the sharpness of the measuring tip. The much sharper features of the actual structure were verified via SEM images of focused ion-beam cuts into the surface (not shown). Similar to the SEM images (Fig. 2) the AFM images show that microstructures become less ordered when increasing the average dpore. From Fig. 4(c),4(d), it is also clear to see that the Citric* sample has more plateaus or shallower dimples than the Citric sample. On the whole, the surface morphology of the Citric* sample can be considered to be more flat than the Citric sample. In order to map the surface microstructures for the reflectance simulation in Sec. 4, cross sections of AFM images are shown in Fig. 5 . The center-to-center distance of Oxalic, Phosphoric and Citric samples for the specific pores considered in Fig. 5 are 324 nm, 430 nm and 693 nm, respectively, and the depths of the dimples are 155 nm, 207 nm and 355 nm, respectively. Roughly, the depth of the dimples is close to being the same as the half length of the center-to-center distances. Note that the values measured from these specific AFM cross sections differ slightly from the results in Fig. 3 because the cross sections of AFM images only consider a few specific pores and are not an average over a large number.
Figure 6 shows the measured UV/Vis reflectance spectra of the Oxalic, Phosphoric, Citric and Citric* samples. The incident angle was set at θi = 8°, the range of wavelengths was from 250 nm to 1100 nm, and total and diffuse reflected light (non-specularly reflected light) are presented by solid and dashed lines, respectively. A flat electro-polished Al sample serving as a reference was also considered in Fig. 6. However, it is not completely flat, and due to some roughness on the surface, 5-7% of the incident light is diffusely reflected. According to the report of H. Ehrenreich et al. , aluminum has a significant inter-band transition at around 1.5 eV. Therefore, all curves of total reflectance in Fig. 6 have a local minimum at a wavelength around 825 nm. The total reflectance of the Oxalic, Phosphoric, Citric and Citric* samples at the wavelength of 600 nm are around 83%, 77%, 68% and 80%, respectively. Thus, it is seen that the total reflectance tends to decrease when increasing the pore size, and thereby also the depth of the dimples, but the diffuse reflectance on the other hand increases when increasing dpore. However, when comparing Citric and Citric* samples, both total and diffuse reflectance increase when decreasing the ordering.
For a perfectly periodic geometry with hexagonal symmetry, there should be only specularly reflected light for wavelengths Especially for the samples Citric and Citric*, where this is app. equivalent to λ > 600 nm (assuming dpore = 693 nm), the large amount of diffuse light for those wavelengths compared with the other samples can be explained from the observed varying degree of ordering for the different samples. The higher amount of diffusion for the sample Citric* compared with the sample Citric agrees with the observation that the latter sample is more ordered. Interestingly, when the wavelength is lower than 600 nm or 700 nm, the total reflectance of the samples Citric and Citric* is almost entirely in the form of diffuse-light-scattering, and this type of reflectance behavior is desirable for a BSR in a thin-film silicon solar cell, for which the non-specularly reflected light will propagate in directions where it is possible to increase the optical path length of light and also obtain some degree of light trapping. Note that it can be expected that the required periodicity of the geometry can be reduced by a factor equivalent to the refractive index of microcrystalline silicon (µc-Si) (app. 3.5) after deposition of a thin-film silicon solar cell on top of the BSRs.
In a study by Sai and Kondo  similar anodized Al films were coated with a silver film. In that case higher reflectivities were obtained for NIR wavelengths, and the reflectivity dip observed here in Fig. 6 for wavelengths near 825 nm was absent. On the other hand a very large absorption was observed for wavelengths below 400 nm. These differences are related to the different optical properties of Ag and Al.
In order to further study the angular distribution of the diffusely reflected light of these four samples, the intensity of scattered light was measured and shown in Fig. 7 as a function of scattering angle for P-polarized normally incident light with wavelengths of 405 nm, 633 nm, and 820 nm, respectively. The photo multiplier tube (PMT) used as detector was scanned between 10 and 90 degrees from the surface normal in steps of 0.5 degrees (at angles below 10 degrees the detector blocked the path of the incident beam). An aperture was placed in front of the PMT to match the angular resolution of the detector to the step size of 0.5 degrees. The incident beam was passed through an optical chopper and the signal from the PMT was averaged by a lock-in amplifier. In agreement with the observations from Fig. 6, the intensity of diffuse light at all three wavelengths follows the ordering Citric* > Citric > Phosphoric > Oxalic. It is observed that the amount of diffuse reflection at large angles increases with the size of dpore and with the degree of disorder in the structure.
From the curves in Fig. 7 it is readily observed that the relative intensity of light scattered at large angles decreases with increasing wavelength. This is due to the fact that as the wavelength increases, the relative size of dpore with respect to the wavelength decreases, and eventually the surface will behave as a flat surface that exhibits only specular reflection and no diffuse reflection. Moreover, when adding silicon films on the top of these samples, the reflected light being incident on the silicon-air interface with angles of incidence larger than approximately 16° will be totally internally reflected and forced to propagate longer within the silicon. The angular distribution of reflected light for similar BSRs being coated with a Ag/ZnO stack are available in Ref.  for the wavelength 375 nm.
4 Discussion and theory
According to diffraction theory for light normally incident on a periodic surface microstructure with hexagonal ordering there will be a cut-off for higher reflection diffraction orders at specific wavelengths (λ). For slightly smaller wavelengths than the cut-off wavelengths the diffracted light will be grazing the surface and thus experience a higher absorption loss that can be observed as a minimum in the total reflectance. The two longest cut-off wavelengths are given by
Therefore, it is also pointed out by arrows in Fig. 6 that there are two local minima in the total reflectance at wavelengths around 270 nm and 370 nm for the samples Oxalic and Phosphoric, respectively, and two at around 350 nm and 600 nm for the samples Citric and Citric*. The latter two minima are not so pronounced, however, because of the limited ordering of those microstructures.
The essence of the physics behind the observation that the total reflectance tends to decrease with increasing the average dpore can be captured from a simple theoretical model. From the cross sections of the AFM analysis in Fig. 5 we note that the shapes of dimples are close to half-spheres, so in our theoretical model we describe the structure with a periodic structure where the dimple in each hexagonally-shaped volume cell is a half-sphere [see Fig. 8(a) ].
At each depth z the fraction of aluminum can be described by the fill factor f. If we divide the geometry along the z-axis in a few hundred slabs of identical thickness and then approximate the dielectric constant in each slab according to the fill factor of that slab as a geometric average, i.e.,33]). In order to simplify the model, Fig. 8(a) shows that in the modeling, the parts of the round peak at the corners of the hexagonal periods are treated as infinitely sharp peaks. Cross sections of the geometry at two different vertical distances into the BSR are shown in Fig. 8(b) and illustrating different fill factors f at different depths. The calculation of the fill factor is as follows:Fig. 8(b)]. Otherwise, the angle can be set to zero. The reflectance calculated with the stack matrix method is shown in Fig. 9 considering a range of depths of the dimples. Comparing with the experimental data, this simple and crude model reproduces the local minima at wavelengths around 825 nm and the feature that increasing periods and depths results in smaller total reflectance. Note that this model does not include any diffraction or diffuse reflectance effects. We are also aware that even for the longer wavelengths our choice of effective dielectric constant [Eq. (2)] is a rather crude approximation . However, it is not our aim with this model to reproduce exactly the experimental results. Instead we want to give a simple physical explanation for the decreasing level of reflectivity with increasing dpore. In addition, for solar cell applications we are mostly interested in the longer wavelengths where the model works reasonably.
According to Fig. 9(b), the change of the refractive index from that of air to that of aluminum takes place over a longer vertical distance in the case of a larger dpore, and is thereby accompanied with a higher absorption by the adiabatic effect, which is in good qualitative agreement with Fig. 6. Moreover, the observation that total and diffuse reflectance of the Citric* sample are both higher than in the case of the sample Citric within the whole range of considered wavelengths can also be explained. According to the SEM and AFM images, the Citric* sample is more flat than the Citric sample, so the effect of a gradually changing refractive index in the Citric* sample is not as pronounced as in the Citric sample, and consequently the Citric* sample reflects more light than the Citric sample. The same situation is also observed in the curves of diffuse reflectance. Therefore, in this case, it is interesting to see that when the sizes of dpore are the same, the on-average more flat sample shows better performance in both total and diffuse reflectance. Of course, if the dimples become even shallower the diffraction and diffuse reflectance effects ultimately disappear leaving only specular reflectance.
We may notice from Fig. 6 that most of the reflected light is in the form of diffuse reflection when the wavelength is smaller than dpore while this is not the case for longer wavelengths. As we have already discussed in this section, for a perfectly periodic geometry there will furthermore only be higher reflection diffraction orders available, corresponding to possible non-normal reflection of light, for wavelengths smaller than This suggests that in order to have primarily diffuse reflection the dpore-to-wavelength ratio should be larger than This guideline for the required dpore for a given free-space wavelength can be satisfied for much smaller values of dpore once silicon is added on top of the BSR since the wavelength in the medium then decreases by a factor equal to the refractive index of silicon. In order to go beyond this guideline more detailed studies are required e.g. along the line of Ref. .
In this work, the AAO technique was successfully used to fabricate Al BSRs, and the reflectance properties of Al BSRs with different pore sizes were investigated. The average dpore (and depth) was controlled by using different acid solutions and different process parameters. Reflectance spectra showed that the surface microstructure with a large average dpore of 700 nm can diffusely reflect near-infrared (NIR) light more effectively than the other samples with shorter average dpore of 320 nm and 430 nm. It was found that around 80% of the light for wavelengths between 250 nm and 800 nm was diffusely reflected in a sample with a period of 700 nm. Furthermore, the light was diffusely reflected into a large range of angles away from the surface normal. Therefore, when using such a BSR in a thin-film silicon solar cell, it is expected to be useful for enhancing light trapping.
The authors would like to acknowledge Morten R. Thomsen, Søren J. Brun, Michele Gastaldo, and Patrick R. Whelan for useful discussions and initial experiments. This project is supported by the Danish strategic research council under the project named thin-film solar cell based on nanocrystalline silicon and structured backside reflectors – THINC.
References and links
2. J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009). [CrossRef]
3. Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y.-L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, and A. Javey, “Ordered arrays of dual-diameter nanopillars for maximized optical absorption,” Nano Lett. 10(10), 3823–3827 (2010). [CrossRef]
4. Y. Yao, J. Yao, V. K. Narasimhan, Z. Ruan, C. Xie, S. Fan, and Y. Cui, “Broadband light management using low-Q whispering gallery modes in spherical nanoshells,” Nat Commun 3, 664 (2012). [CrossRef]
6. M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010). [PubMed]
7. B. Weintraub, Y. Wei, and Z. L. Wang, “Optical fiber/nanowire hybrid structures for efficient three-dimensional dye-sensitized solar cells,” Chem., Int. Ed. 48(47), 8981–8985 (2009). [CrossRef]
8. C. H. Liu, C. H. Chen, S. Y. Chen, Y. T. Yen, W. C. Kuo, Y. K. Liao, J. Y. Juang, H. C. Kuo, C. H. Lai, L. J. Chen, and Y. L. Chueh, “Large scale single-crystal Cu(In,Ga)Se2 nanotip arrays for high efficiency solar cell,” Nano Lett. 11(10), 4443–4448 (2011). [CrossRef]
9. A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78(5), 563–565 (2001). [CrossRef]
10. K. Söderström, F.-J. Haug, J. Escarré, C. Pahud, R. Biron, and C. Ballif, “Highly reflective nanotextured sputtered silver back reflector for flexible high-efficiency n-i-p thin-film silicon solar cells,” Sol. Energy Mater. Sol. Cells 95(12), 3585–3591 (2011). [CrossRef]
11. G. Yue, B. Yan, L. Sivec, Y. Zhou, J. Yang, and S. Guha, “Effect of impurities on performance of hydrogenated nanocrystalline solar cells,” Sol. Energy Mater. Sol. Cells 104, 109–112 (2012). [CrossRef]
12. K. Saito, M. Sano, S. Okabe, S. Sugiyama, and K. Ogawa, “Microcrystalline silicon solar cells fabricated by VHF plasma CVD method,” Sol. Energy Mater. Sol. Cells 86(4), 565–575 (2005). [CrossRef]
13. A. Takano, M. Uno, M. Tanda, S. Iwasaki, H. Tanaka, J. Yasuda, and T. Kamoshita, “Highly textured silver electrode deposition using roll-to-roll low-temperature sputtering process,” Jpn. J. Appl. Phys. 43(No. 2B), L277–L279 (2004). [CrossRef]
14. F.-J. Haug, T. Söderström, M. Python, V. Terrazzoni-Daudrix, X. Niquille, and C. Ballif, “Development of micromorph tandem solar cells on flexible low-cost plastic substrates,” Sol. Energy Mater. Sol. Cells 93(6-7), 884–887 (2009). [CrossRef]
15. H. Sai, H. Fujiwara, M. Kondo, and Y. Kanamori, “Enhancement of light trapping in thin-film hydrogenated microcrystalline Si solar cells using back reflectors with self-ordered dimple pattern,” Appl. Phys. Lett. 93(14), 143501 (2008). [CrossRef]
17. L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006). [CrossRef]
18. K. Sato, Y. Gotoh, Y. Wakayama, Y. Hayashi, K. Adachi, and H. Nishimura, “Highly textured SnO2:F TCO films for a-Si solar cells,” Rep. Res. Lab. Asahi Glass Co. Ltd. 42, 129–137 (1992).
19. C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, “Light trapping in solar cells: can periodic beat random?” ACS Nano 6(3), 2790–2797 (2012). [CrossRef]
20. R. C. Furneaux, W. R. Rigby, and A. P. Davidson, “The formation of controlled-porosity membranes from anodically oxidized aluminium,” Nature 337(6203), 147–149 (1989). [CrossRef]
22. F. Matsumoto, K. Nishio, and H. Masuda, “Flow-through-type DNA array based on ideally ordered anodic porous alumina substrate,” Adv. Mater. (Deerfield Beach Fla.) 16(23-24), 2105–2108 (2004). [CrossRef]
23. S. Z. Chu, K. Wada, S. Inoue, S. I. Todoroki, Y. K. Takahashi, and K. Hono, “Fabrication and characteristics of ordered Ni nanostructures on glass by anodization and direct current electrodeposition,” Chem. Mater. 14(11), 4595–4602 (2002). [CrossRef]
24. M. S. Sander, A. L. Prieto, R. Gronsky, T. Sands, and A. M. Stacy, “Fabrication of high-density, high aspect ratio, large-area bismuth telluride nanowire arrays by electrodeposition into porous anodic alumina templates,” Adv. Mater. (Deerfield Beach Fla.) 14(9), 665–667 (2002). [CrossRef]
25. C. R. Martin, G. Che, B. B. Lakshmi, and E. R. Fisher, “Metal-nanocluster-filled carbon nanotubes: catalytic properties and possible applications in electrochemical energy storage and production,” Nature 393(6683), 346–349 (1998). [CrossRef]
26. S. Z. Chu, S. Inoue, K. Wada, S. Hishita, and K. Kurashima, “Self-organized nanoporous anodic titania films and ordered titania nanodots/nanorods on Glass,” Adv. Funct. Mater. 15(8), 1343–1349 (2005). [CrossRef]
27. S. Z. Chu, K. Wada, S. Inoue, M. Isogai, Y. Katsuta, and A. Yasumori, “Large-scale fabrication of ordered nanoporous alumina films with arbitrary pore intervals by critical-potential anodization,” J. Electrochem. Soc. 153(9), B384–B391 (2006). [CrossRef]
29. H. Masuda, F. Hasegwa, and S. Ono, “Self‐ordering of cell arrangement of anodic porous alumina formed in sulfuric-acid-solution,” J. Electrochem. Soc. 144(5), L127–L130 (1997). [CrossRef]
30. H. Masuda, K. Yada, and A. Osaka, “Self-ordering of cell configuration of anodicporous alumina with large-size pores in phosphoric acid solution,” Jpn. J. Physiol. 37(Part 2, No. 11A), L1340–L1342 (1998). [CrossRef]
31. H. Ehrenreich, H. R. Philipp, and B. Segall, “Optical properties of aluminum,” Phys. Rev. 132(5), 1918–1928 (1963). [CrossRef]
32. H. Sai and M. Kondo, “Effect of self-orderly textured back reflectors on light trapping in thin-film microcrystalline silicon solar cells,” J. Appl. Phys. 105(9), 094511 (2009). [CrossRef]
33. M. V. Klein and T. E. Furtak, Optics, 2nd edition (John Wiley & Sons, 1986).
34. H. Kikuta, H. Yoshida, and K. Iwata, “Ability and limitation of effective medium theory for subwavelength gratings,” Opt. Rev. 2(2), 92–99 (1995). [CrossRef]
35. M. Boccard, P. Cuony, C. Battaglia, M. Despeisse, and C. Ballif, “Unlinking absorption and haze in thin film silicon solar cells front electrodes,” Phys. stat. sol. RRL 4, 326–328 (2010).