Two-dimensional (2D) Si-nanorod arrays offer a promising architecture that has been widely recognized as attractive devices for photovoltaic applications. To further reduce the Fresnel reflection that occurs at the interface between the air and the 2D Si-nanorod array because of the large difference in their effective refractive indices, we propose and adopt a slanted ITO film as an intermediate layer by using oblique-angle sputtering deposition. The nearly continuous surface of the slanted ITO film is lossless and has high electrical conductivity; therefore, it could serve as an electrode layer for solar cells. As a result, the combination of the above-mentioned nanostructures exhibits high optical absorption over a broad range of wavelengths and incident angles, along with a calculated short-circuit current density of JSC = 32.81 mA/cm2 and a power generation efficiency of η = 22.70%, which corresponds to an improvement of approximately 42% over that of its bare single-crystalline Si counterpart.
© 2012 OSA
Recently, the elimination of Fresnel reflection from surface interfaces by the application of antireflection coatings (ARC) has become a topic of significant research interest [1–4]. The employment of ARC for reducing Fresnel reflection has mainly been applied to minimize reflections in optical components , to enhance the light extraction of light-emitting diodes [6,7], and to improve the coupling of sunlight into solar cells [8,9]. In particular, the development of novel ARCs that enhance the power generation efficiency of solar cells has attracted much attention because the demand for solar energy has become more intense than ever. For the day-to-day operation of solar cells, the design of ARCs with low reflectivity over the broadband spectrum and omnidirectional incidence is necessary to efficiently harvest energy from sunlight . In accordance with these design principles, several artificial nanostructures with various porous geometries, such as rods [11–13], holes [14,15], cones [16,17], pyramids [18,19], and tips [20–22], have been proposed and fabricated. Among them, most nanostructures are created with top-down or bottom-up processes, and they typically demonstrate excellent ARC functionality, as required for the daily applications of solar cells. Additionally, depending on the continuity of the refractive index of the nanostructures, ARCs are mainly classified into two types, i.e., homogeneous and inhomogeneous layers . Homogeneous ARCs (also known as step-index coatings) can reduce reflection by destructive interference of incident light that is reflected at different interfaces. For these coatings, the choice of coating material and the thickness of the deposited layer must be carefully considered for the incident wavelengths . The other type of ARC is the inhomogeneous coating (also known as the graded-index coating), which is generally advantageous over its homogeneous counterpart because of its superior characteristics with respect to broadband spectra and omnidirectional incidence [8,24]. However, the gradual change of refractive index in inhomogeneous ARCs must be precisely controlled in the nanostructure to achieve the specific required outline during the fabrication process . Therefore, to provide evidence for enhanced absorption in solar cells, the development of novel ARCs must consider the difference in the fundamental properties of various nanostructures and further manipulates them as necessary.
In the current study, a novel ARC that combines a 2-dimensional (2D) Si-nanorod array with a slanted indium-tin-oxide (ITO) film was proposed and demonstrated to enhance the quantum efficiency of solar cells. Here, we recognize the intrinsic antireflection effect of the 2D Si-nanorod array that arises from the sub-wavelength scale of the nanorods, improving optical absorption for photovoltaic applications. Moreover, to further reduce the Fresnel reflection that occurs at the interface between the 2D Si-nanorod array and the air caused by the large difference in their refractive indices, a slanted ITO film was applied to the top of nanorods to serves as an optical transparent layer with an intermediate refractive index (between that of the nanorods and that of the air). The ITO film also provided an important functionality as the electrode layer of the solar cells. Herein, we report the design, implementation and demonstration of 2D Si-nanorod arrays with a slanted ITO film that shows strong absorption over a broadband spectrum (λ = 400−1000nm) and a variety of incidence angles (θ = 0−80°), as well as high short-circuit current density (JSC = 32.81 mA/cm2) and power generation efficiency (η = 22.70%) obtained by the numerical calculation.
Figure 1(a) shows a schematic of the fabrication process for the proposed ARC. First, the 500μm thick single-crystalline bare silicon (Si) was cleaned with acetone in an ultrasonic bath, followed by an isopropyl alcohol and deionized water rinse. The 2D Si-nanorods were then fabricated with self-assembled nickel (Ni) clusters as a hard mask for inductively coupled-plasma (ICP) dry etching. Here, the 10nm Ni film was deposited on the cleaned Si by radio-frequency (RF) magnetron sputtering [step (i)]. The sample was then subjected to rapid thermal annealing (RTA) at 900 °C under a nitrogen atmosphere to produce nano-sized Ni clusters [step (ii)]. An RTA duration of 1 min was used to ensure that all Ni cluster were isolated. Figure 1(b) presents a scanning electron micrograph (SEM) of the nano-sized Ni cluster. Because of the nature of self-assembly under the RTA process, the Ni clusters are randomly arranged. As shown in the insert of Fig. 1(b), the diameter of an individual Ni cluster ranges from 40 to 90 nm, and exhibits a Gaussian-like distribution. On average, the diameter of the Ni clusters is approximately 60 nm, which is primarily determined and well controlled by the deposited thickness of the Ni film and the RTA condition . The sample was then etched down to 350nm by an ICP system, using a mixture reactive gases (Cl2 /Ar = 20/20 sccm) with an ICP power source, a bias power set at 200/100 W, and a chamber pressure of 5 mTorr for 1 min of etching time [step (iii)]. The hard mask of Ni clusters was removed by sulfuric acid solutions (H2SO4: H2O2: H2O = 5:2:1) to expose the 2D Si-nanorod array. Finally, the slanted ITO film was grown by oblique-angle deposition using RF magnetron sputtering [step (iv)]. The apparatus used in the oblique-angle deposition has a sample stage on which the substrate is loaded, with controllable polar-angle rotation. During the deposition, an argon flux of 8 sccm is supplied at a working pressure of 6 mTorr, and there was no movement of the substrate. The sample stage maintains a fixed polar angle so that the substrate has a controlled tilt angle of θ = 60° with respect to the ITO vapor-flow direction. For our oblique-angle deposition system, the tilt angle (β) of deposited ITO is less than the incident angle of vapor-flow (θ), and follows the empirical tangent rule [27,28]. Additionally, because of the shadowing effect produced by the 2D Si-nanorod array, the incident ITO vapor-flow is deposited preferentially on the top of the individual nanorods . As a result, a continuous and porous morphology was observed on the top surface of the slanted ITO layer, as shown in the SEM image in Fig. 1(c). The surface morphology of the sample was also examined by atomic force microscopy [right-hand in Fig. 1(c)]. The measured roughness (root-mean-square, RMS) of the top surface of our ARC is approximately 30.7nm. Compared to that of a planar ITO layer with identical thickness (RMS = 1.4 nm), a much larger RMS value was observed on our ARC, primarily because of the porous morphology of the slanted ITO layer. Additionally, the resistivity of the planar and slanted ITO films are ρ = 4.76 × 10−4 Ω-cm and ρ = 2.33 × 10−3 Ω-cm, respectively. The slightly higher resistivity obtained in the slanted ITO film is mainly due to the intrinsic nano-porosity that would scatter electrons, and thus hinders their transportation inside the material . Nevertheless, for the slanted ITO film, the electrical property is not much degraded as compared to the planar ITO film, reducing the impact on the collection efficiency of photo-generated carriers.
3. Results and discussion
To quantitatively examine the optical characteristics of our ARC, we first measured the refractive index (n) and extinction coefficient () of our samples, as shown in Fig. 2 . The wavelength-dependent complex refractive indices of the samples, , are determined by ellipsometry with a normal-incidence white light source (180W halogen-lamp). In Fig. 2(a), the n value of the bare Si (black solid-line) gradually decreases with increasing wavelength, exhibiting normal dispersion behavior. In contrast, the n value of the 2D Si-nanorod array (blue solid-line) is relatively stable and has a much smaller value of n = 2.18 for most of wavelengths (λ = 400−1000nm). The improved stability and reduction of n are caused by the low filling-fraction (f.f.) of the array. Generally, the effective refractive index of the 2D Si-nanorod array is defined as the average refractive index between the air and the bare Si, weighted by their respective volumes. It can be expressed as follows :Eq. (1) is f.f.~40%, which is consistent with the previous observation from the SEM image of Ni clusters in Fig. 1(b). More importantly, compared to that of the bare Si (black dashed-line), thevalue of the 2D Si-nanorod array (blue dashed-line) is remarkably enhanced, especially for the region of visible light (λ = 400−700nm). It is well known that the absorption coefficient () of a material is defined as , and the larger would be expected to lead to a larger value of . As a result, the enhanced absorption of the 2D Si-nanorod array enables high quantum efficiencies for photovoltaic applications. The randomly distributed and non-planar geometry of the 2D Si-nanorod array is mainly responsible for the enhanced absorption coefficient because of it effectively scatters and traps incident photons . Similarly, the refractive indices of the normal and slanted ITO films as a function of wavelength are shown in Fig. 2(b). Again, the refractive indices of both samples decrease with wavelength and exhibit the normal dispersion profile. The refractive index of the normally deposited ITO is higher than that of the slanted ITO. On average, the n values of the normal and slanted ITO films are 1.98 and 1.63, respectively. For the slanted film, that value corresponds to a porosity of ~34.8%, as evaluated by the Bruggemann effective medium approximation . The extinction coefficients of both samples, however, are nearly identical and approximately zero, which allows most of the incident solar energy to propagate in a near-lossless fashion inside the film.
Figure 3(a) shows the cross-sectional SEM image of the normally deposited (planar-sheet) ITO film. SEM images of 2D Si-nanorod arrays (b) without and (c) with the slanted ITO film deposited on top are shown in Fig. 3(b) and Fig. 3(c), respectively. The variation of the refractive index along the z-direction of all samples is also plotted in the figure. In Fig. 3(a), the normally deposited ITO film was chosen as the quarter-wavelength ARC because its refractive index (n = 1.98) is approximately equal to the geometric mean of those of the air and bare Si [33,34]. Additionally, ITO films are widely used as the electrode layers of solar cells because of their good electrical conductivity. The thickness of the ITO film was controlled to d = 400nm (odd multiples of λ/4n), leading to destructive interference with extremely low reflection at certain incident wavelengths. For other incident wavelengths, the reflectivity of the ITO quarter-wavelength ARC is considerably increased, hindering the absorption of solar energy. In comparison to the ITO quarter-wavelength ARC, 2D Si-nanorod array has been suggested as a promising candidate for solar energy harvesting because of its advantageous optical property . According to Fig. 3(b), each individual nanorod is well defined, with diameters between 40 and 90 nm, and each has a constant thickness of d = 350 nm. It is well known that a nanorod diameter that is comparable to or smaller than the incident wavelengths, produces a strong scattering effect and enhances the absorption of solar energy . However, because of the porous structure (f.f. = 40%) of the 2D Si-nanorod array, its effective refractive index (n = 2.18) is much smaller than that of the bare Si (n = 3.95), which provides a similar functionality to the ITO quarter-wavelength ARC. Therefore, although the nanorod array itself can effectively trap incident photons, a significant amount of solar energy is still reflected and wasted because of the large difference between the refractive index of the air and the 2D Si-nanorod arrays. We recognize the intrinsic antireflection effect of the 2D Si-nanorod array. To further reduce the Fresnel reflection that occurs at its interface with the air, it is necessary to insert an optically transparency (~0) intermediate layer (1<n<2.18). Here, we used the slanted ITO film with controllable porosity as the intermediate layer. As shown in Fig. 3(c), the slanted ITO film (d = 350nm), which consists of nearly continuous nanorods with tilt angle of β = 40° grown by oblique-angle deposition, has a lower refractive index (n = 1.68) than dense ITO (n = 1.98) because of its nano-porous nature. Furthermore, because of the shadowing effect provided by the 2D Si-nanorod arrays, the incident vapor of ITO vapor flow is deposited preferentially on top of the nanorods, and it eventually coalesces altogether. This coalescence forms an optically transparent thin film with a flat surface morphology, as previously discussed with reference to Fig. 1(c). In fact, an optically transparent and electrically conductive slanted ITO film with a nearly continuous surface morphology is extremely important for the subsequent fabrication of the electrode pads of solar cells.
The following discussion concerns the optical characteristics of the samples of interest. Figure 4(a) plots the measured reflectivity versus the incident wavelength. The photographs of all samples (with the identical sizes of 2cm × 2cm) are also shown as inserts in the figure. Accordingly, the color images of all samples are uniform with reasonable fluctuations, suggesting that our fabrication processes for all samples are stable and reliable. The profile of the measured reflectivity of the bare Si (black solid line) decreases monotonically from R = 48.5% to R = 31.8% as the incident wavelength increases from λ = 400 nm to λ = 1000 nm, because of the slight decrease of the refractive index of Si with wavelength. On average, the reflectivity of the bare Si is R = 35.4%. The measured reflectivity is reduced for unmodified Si with the ITO quarter-wavelength ARC. The corresponding profile of the measured reflectivity (red solid line) oscillates decreasingly with respect to that of the bare Si substrate because of the influence of destructive interference of incident light. This film exhibits an average reflectivity of R = 18.7%, with an extremely low reflectivity of R<0.5% at incident wavelengths of λ = 470nm, λ = 640nm, and λ = 990 nm. Furthermore, the average reflectivity of the 2D Si-nanorod array decreases to R = 13.2% with non-significant oscillation fringes (green solid line). This decrease is primarily caused by the randomly distributed Si-nanorods, which effectively scatter and traps incident photons, thus decreasing their reflection and interference in the materials. Most importantly, by inserting the slanted ITO film as an intermediate layer, the Fresnel reflection at the interface between the air and the 2D Si-nanorod array can be further reduced, and the measured reflectivity and corresponding profile (blue solid line) become stable and independent of the incident wavelengths, especially over the visible light region. As a result, a low reflectivity with average value of R = 9.2% is achievable over a broad spectrum. It should be noted that, although the measured reflectivity of the samples is still higher than those ever reported in other studies [4,8], the interaction of the ARC design with the nanostructures accounts for the elimination of the Fresnel reflection, which is of primary concern in the current study.
To study the dependence of the reflectivity of the samples on the incident angle of solar illumination, the measured reflectivity at normal incidence was numerically fitted, and the result is shown in Fig. 4(b). The angular-dependent reflectivity of the incident wave,, in the stack with m layers [inset of Fig. 4(b)] is expressed by the Airy formula as follow :Fig. 4(b) are in agreement with the measured reflectivity in Fig. 4(a), suggesting that the consideration of the 2D Si-nanorod array and the slanted ITO film as homogeneous materials with effective refractive indices is indeed feasible, when the propagation of incident waves between the layers is treated numerically.
To gauge the absorption ability of the samples, the calculated absorption values obtained by were plotted in Fig. 4(c), in which was determined from the Airy formula for the TM polarized light, and the transmission of the samples is negligible because the thickness of the Si substrate is larger than 500 μm. Across the incident wavelengths studied here, the peak absorption of bare Si (upper left) is relatively low at normal incidence and increases at steeper incidence angles, until the Brewster angle (θB = 75.8°) is reached. This absorption profile limits the practical applications for photovoltaics. The average absorption of bare Si (θ = 0−80°; λ = 400−700 nm) is A = 75.85%. With the assistance of the ITO quarter-wavelength ARC (upper right), the normal-incidence absorption is significantly increased at certain wavelengths at which the destructive interference of incident light occurs, which causes to exhibit a band-like profile. However, the enhancement of the overall absorption remains insignificant (A = 85.00%). As expected, the incorporation of 2D Si-nanorod arrays (lower left) can virtually eliminate the angular sensitivity of , and increases the normal-incidence absorption, except for incident light in the visible region. On average, the absorption of the 2D Si-nanorod arrays is A = 88.09%. With the addition of the slanted ITO film (lower right), the average absorption of the 2D Si-nanorod arrays is increased to A = 92.70%, andbecomes nearly angle-independent over the broadband spectrum. Similarly, the absorption values of all samples for the TE polarized light were also calculated (not be shown here). The average absorption values (θ = 0−80°; λ = 400−700 nm) are A = 47.83% and A = 71.48% for the bare Si without and with the ITO quarter-wavelength ARC, respectively. The average absorption values of the 2D Si-nanorod arrays without and with slanted ITO films are A = 77.64% and A = 83.67%, respectively. The average absorption values of all samples obtained by the incidence of TM polarized light are obviously larger than those obtained by the incidence of TE polarized light, entirely due to the existence of the Brewster angle at which TM polarized light is perfectly transmitted through the surface of sample, and then absorbed by the silicon substrate underneath. Most importantly, for the incidence of both TE and TM polarized light, the 2D Si-nanorod arrays with the slanted ITO films exhibit high optical absorption over a broad range of wavelengths and incident angles.
To calculate the power generation efficiency (η) of the samples, we assume that each absorbed photon with energy larger than the band-gap energy of Si generates an electron-hole pair that reaches the electrical contacts. Therefore, the current density J versus the voltage V is expressed by the sum of the photon-generated current minus the intrinsic current generated by radiative recombination as follow :39]), is the absorption calculated by the Airy formula (as mentioned above), Eg is the band-gap energy of Si, is the thermal energy at the operating temperature T in Kelvin unit, and n is average refractive index of Si . The resulting calculated J-V curves of all samples are shown in Fig. 5(a) . As depicted, the calculated short-circuit current densities are JSC = 23.39mA/cm2 and JSC = 29.19 mA/cm2 for the bare Si without and with the ITO quarter-wavelength ARC, respectively. The short- circuit current values of the 2D Si-nanorod arrays without and with slanted ITO films are JSC = 31.20mA/cm2 and JSC = 32.81 mA/cm2, respectively. Theoretically, the open-circuit voltage (VOC) and the fill factor (FF) of all samples are identical and remain approximately VOC = 0.8V and FF = 0.85, respectively. Compared to the bare Si, the enhancement of the power generation efficiency observed for the other samples is attributable to the enhanced short-circuit current density; i.e., it is attributable to the enhanced absorption according to Eq. (8). As a result, a power generation efficiency of η = 22.70% is achievable for the 2D Si-nanorod arrays with the slanted ITO film, corresponding to an improvement of approximately 42% with respect to that of the bare Si sample.
Finally, to distinguish the incident solar light and the spectrally weighted absorption of all samples throughout the operating day of a non-tracking solar cell, the overall fraction of the above band-gap photons that our samples would absorb, Aavg, was calculated based on a time-resolved reference spectrum of direct solar insolation in conjunction with the calculated angle- and wavelength-dependent absorption values, . The fraction of above band-gap incident photons that would be absorbed from the reference spectrum, Aavg, is given by the following expression :41,42]. Figure 5(b) shows the Aavg calculations that correspond to the contour plot of absorption, , shown in Fig. 4(c). Importantly, compared to that of the bare Si sample, the 2D Si-nanorod arrays with the slanted ITO films have Aavg = 86.21%, which corresponds to a remarkable enhancement of ~50% and implies the fundamental optical concentration characteristic of the 2D Si-nanorod arrays.
In conclusion, we have successfully demonstrated that 2D Si-nanorod arrays with slanted ITO films have strong and angle-insensitive optical absorption over a broad range of incident wavelengths and that they are advantageous for photovoltaic applications. With the experimentally measured properties, such as the complex refractive index, optical reflectivity and physical thickness of the 2D Si-nanorod arrays and slanted ITO film, as the fitted parameters for the Airy formula, their combination and effect on the output performances of the silicon solar cells was numerically investigated. Additionally, the results of this study concerning the optical properties of 2D nanorod arrays and slanted ITO films are not limited to Si-based solar cell, and the revealed geometry suggests techniques to produce high efficiencies in other kinds of nanoscale photovoltaic devices.
The authors gratefully acknowledge the financial support from the National Science Council of Republic of China (ROC) in Taiwan under contract Nos. NSC–100–2112–M–003–006–MY3 and NSC–100–2112–M–006–002–MY3, and from the National Taiwan Normal University under award NTNU100-D-01.
References and links
1. J.-Y. Jung, Z. Guo, S.-W. Jee, H.-D. Um, K.-T. Park, and J.-H. Lee, “A strong antireflective solar cell prepared by tapering silicon nanowires,” Opt. Express 18(S3), A286–A292 (2010). [CrossRef] [PubMed]
2. S. L. Diedenhofen, G. Vecchi, R. E. Algra, A. Hartsuiker, O. L. Muskens, G. Immink, E. P. A. M. Bakkers, W. L. Vos, and J. G. Rivas, “Broad-band and omnidirectional antireflection coatings based on semiconductor nanorods,” Adv. Mater. (Deerfield Beach Fla.) 21(9), 973–978 (2009). [CrossRef]
3. K. M. Rosfjord, J. K. W. Yang, E. A. Dauler, A. J. Kerman, V. Anant, B. M. Voronov, G. N. Gol’tsman, and K. K. Berggren, “Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating,” Opt. Express 14(2), 527–534 (2006). [CrossRef] [PubMed]
4. J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).
5. T. Lohmüller, M. Helgert, M. Sundermann, R. Brunner, and J. P. Spatz, “Biomimetic interfaces for high-performance optics in the deep-UV light range,” Nano Lett. 8(5), 1429–1433 (2008). [CrossRef] [PubMed]
6. S. J. An, J. H. Chae, G.-C. Yi, and G. H. Park, “Enhanced light output of GaN-based light-emitting diodes with ZnO nanorod arrays,” Appl. Phys. Lett. 92(12), 121108 (2008). [CrossRef]
7. J. K. Kim, S. Chhajed, M. F. Schubert, E. F. Schubert, A. J. Fischer, M. H. Crawford, J. Cho, H. Kim, and C. Sone, “Light-extraction enhancement of GaInN light-emitting diodes by graded-refractive-index Indium Tin Oxide anti-reflection contact,” Adv. Mater. (Deerfield Beach Fla.) 20(4), 801–804 (2008). [CrossRef]
8. S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, “Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics,” Appl. Phys. Lett. 93(25), 251108 (2008). [CrossRef]
9. P. Yu, C.-H. Chang, C.-H. Chiu, C.-S. Yang, J.-C. Yu, H.-C. Kuo, S.-H. Hsu, and Y.-C. Chang, “Efficiency enhancement of GaAs photovoltaics employing antireflective Indium Tin Oxide nanocolumns,” Adv. Mater. (Deerfield Beach Fla.) 21(16), 1618–1621 (2009). [CrossRef]
10. J. A. Dobrowolski, Handbook of Optics (McGraw-Hill, 1995).
11. C. H. Chiu, P. Yu, H. C. Kuo, C. C. Chen, T. C. Lu, S. C. Wang, S. H. Hsu, Y. J. Cheng, and Y. C. Chang, “Broadband and omnidirectional antireflection employing disordered GaN nanopillars,” Opt. Express 16(12), 8748–8754 (2008). [CrossRef] [PubMed]
12. Y.-J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, and J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008). [CrossRef] [PubMed]
13. J. Li, H. Y. Yu, S. M. Wong, X. Li, G. Zhang, P. G.-Q. Lo, and D.-L. Kwong, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. 95(24), 243113 (2009). [CrossRef]
16. J. Zhu, Z. F. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Q. Xu, Q. Wang, M. McGehee, S. H. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009). [CrossRef] [PubMed]
18. C. T. Wu, F. H. Ko, and C. H. Lin, “Self-organized tantalum oxide nanopyramidal arrays for antireflective structure,” Appl. Phys. Lett. 90(17), 171911 (2007). [CrossRef]
19. C.-H. Sun, W.-L. Min, N. C. Linn, P. Jiang, and B. Jiang, “Templated fabrication of large area subwavelength antireflection gratings on silicon,” Appl. Phys. Lett. 91(23), 231105 (2007). [CrossRef]
20. Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007). [CrossRef] [PubMed]
21. H. Sai, H. Fujii, K. Arafune, Y. Ohshita, M. Yamaguchi, Y. Kanamori, and H. Yugami, “Antireflective subwavelength structures on crystalline Si fabricated using directly formed anodic porous alumina masks,” Appl. Phys. Lett. 88(20), 201116 (2006). [CrossRef]
22. A. P. Li, F. Muller, A. Birner, K. Nielsch, and U. Gosele, “Hexagonal pore arrays with a 50-420 nm interpore distance formed by self-organization in anodic alumina,” J. Appl. Phys. 84(11), 6023–6026 (1998). [CrossRef]
24. S. J. Jang, Y. M. Song, C. I. Yeo, C. Y. Park, J. S. Yu, and Y. T. Lee, “Antireflective property of thin film a-Si solar cell structures with graded refractive index structure,” Opt. Express 19(S2), A108–A117 (2011). [CrossRef] [PubMed]
25. M.-F. Chen, H.-C. Chang, A. S. P. Chang, S.-Y. Lin, J.-Q. Xi, and E. F. Schubert, “Design of optical path for wide-angle gradient-index antireflection coatings,” Appl. Opt. 46(26), 6533–6538 (2007). [CrossRef] [PubMed]
26. G.-R. Lin, H.-C. Kuo, H.-S. Lin, and C.-C. Kao, “Rapid self-assembly of Ni nanodots on Si substrate covered by a less-adhesive and heat-accumulated SiO2 layers,” Appl. Phys. Lett. 89(7), 073108 (2006). [CrossRef]
27. Y.-P. Zhao, D.-X. Ye, G.-C. Wang, and T.-M. Lu, “Designing nanostructures by glancing angle deposition,” Proc. SPIE 5219, 59–73 (2003). [CrossRef]
28. A. Lisfi and J. C. Lodder, “Magnetic domains in Co thin films obliquely sputtered on a polymer substrate,” Phys. Rev. B 63(17), 174441 (2001). [CrossRef]
29. Y.-J. Lee, S.-Y. Lin, C.-H. Chiu, T.-C. Lu, H.-C. Kuo, S.-C. Wang, S. Chhajed, J. K. Kim, and E. F. Schubert, “High output power density from GaN-based two-dimensional nanorod light-emitting diode arrays,” Appl. Phys. Lett. 94(14), 141111 (2009). [CrossRef]
30. F. Wang, H. Y. Yu, J. Li, X. Sun, X. Wang, and H. Zheng, “Optical absorption enhancement in nanopore textured-silicon thin film for photovoltaic application,” Opt. Lett. 35(1), 40–42 (2010). [CrossRef] [PubMed]
31. F. Flory, L. Escoubas, and G. Berginc, “Optical properties of nanostructured materials: a review,” J. Nanophoton. 5(1), 052502 (2011). [CrossRef]
32. D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20(8), 3292–3302 (1979). [CrossRef]
33. J. Jackson, Classical Electrodynamics (Wiley, 1999).
34. B.-S. Chiou and J.-H. Tsai, “Antireflective coating for ITO films deposited on glass substrate,” J. Mater. Sci. Mater. Electron. 10(7), 491–495 (1999). [CrossRef]
35. W. Q. Xie, W. F. Liu, J. I. Oh, and W. Z. Shen, “Optical absorption in c-Si/a-Si:H core/shell nanowire arrays for photovoltaic applications,” Appl. Phys. Lett. 99(3), 033107 (2011). [CrossRef]
36. Y.-J. Lee, C.-J. Lee, and C.-M. Cheng, “Enhancing the conversion efficiency of red emission by spin-coating CdSe quantum dots on the green nanorod light-emitting diode,” Opt. Express 18(S4), A554–A561 (2010). [CrossRef] [PubMed]
37. P. Yeh, Optical Waves in Layered Media (Wiley, 1998).
38. 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]
39. ASTMG173–03, Standard Tables for Reference Solar Spectral Irradiances: Direct Normal and Hemispherical on 37 degree Tilted Surface (ASTM International, 2005).
40. C. Henry, “Limiting efficiencies of ideal single and multiple energy gap terrestrial solar cells,” J. Appl. Phys. 51(8), 4494–4500 (1980). [CrossRef]
41. 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]
42. B. Marion, B. Kroposki, K. Emery, J. del Cueto, D. Myers, and C. Osterwald, Validation of a Photovoltaic Module Energy Ratings Procedure at NREL, Report No. NREL/TP-520-26909 (1999).