Antireflective Si/oxide core-shell nanowire arrays (NWAs) were fabricated by galvanic etching and subsequent annealing process. The excellent light-harvesting characteristics of the core-shell NWAs, such as broadband working ranges, omnidirectionality, and polarization-insensitivity, ascribed to the smooth index transition from air to the substrates, have been demonstrated. By tuning core-shell volume ratios, we obtained enhanced light trapping regions implemented in either the planar Si underneath NWAs or the core regions of NWAs, greatly benefiting the geometry design of planar and radial p-n junction cell structures, respectively. This photon management scheme indicates the potential use in nanostructured photovoltaic applications.
© 2012 OSA
Advances in nanofabrications have drawn intensive interest in enhancing the efficiency of optical devices, such as solar cells and photodetectors via nanostructuring [1–7]. The photon management (PM) strategy employing nanowire arrays (NWAs) has emerged as a powerful mean to boost energy conversion efficiencies and is driven by two pronounced light-trapping effects. First, NWAs can behave like an effective homogeneous medium with continuous gradient of refractive index to reduce the reflectance through the destructive interferences among reflected waves and couple light more efficiently into active regions . The superior antireflection (AR) characteristics of NWAs, such as broadband working ranges , omnidirectionality , and polarization-insensitivity , benefit from the smooth index transition at the air-device interface. Second, NWAs as efficient absorber materials can prolong the optical path length of the incident light in the NWA layers by increasing the frequency of the reflected waves bouncing between nanowires, and therefore reduce the opportunity for the light to escape from the surface . Spectral and angular reflection can be effectively eliminated by controlled geometrical configurations, such as the densities of NWAs, and the interface roughness at the regions of air/NWAs and NWAs/substrates .
To optimize the subwavelength structures for light harvesting, NWAs have been fabricated using either a top-down etching approach or a bottom-up method, and shown to exhibit much high absorption compared to the thin film counterpart [10–22]. Dual-diameter NWAs  using anodic alumina template and vapor-liquid-solid process, and crystalline core/amorphous shell nanoneedle arrays [17,18] using the vapor-solid-solid process have been found to drastically increase absorption in Ge or Si nanostructures. Cao et al. engineered the resonant property inside nanowires by tuning the radius of nanowires so that the light absorption can be enhanced at resonance regions, referred as the leaky-mode resonance enhancement . Syringe-like ZnO nanorods synthesized by the hydrothermal method for eliminating the abrupt optical interface between air and GaAs have been found to improve energy conversion efficiency of GaAs solar cells significantly . The alignment variation of NWAs plays an important role in surface reflection and light scattering [20,21]. Moreover, the NWAs with semiconducting cores encapsulated by dielectric shells are expected to offer a number of advantages over purely semiconducting NWAs. For example, the dielectric shell is capable of simultaneously providing excellent surface passivation for photovoltaic (PV) devices and creating a smooth gradient of refractive index profiles. Passivation of surface defects is necessary to maintain high electronic mobilities in PV devices. Further grading in the index profile by inserting dielectric layers between air and Si is expected to facilitate high absorption for PV devices.
The most used method for the fabrication of Si nanowires is the vapor-liquid-solid growth . However, the severe diffusion of catalyst metal, typically Au, into Si during the nanowire growth is inevitable to form carrier traps and reduce minority carrier lifetimes, which is detrimental to the realization of Si nanowire-based optical devices. Recently, the maskless wet etching, by which the nanowire structure is obtained through a galvanic electrochemistry growth, is considered as one of the most promising methods due to its low cost and the ability to achieve wafer-scale uniformity in geometric profile, doping level, and crystal orientation without metal contamination [24,25].
In this study, we demonstrate a novel PM strategy that capitalizes on strong light-trapping effects at a variety of wavelengths and angles of incidence by employing a heterostructure consisting of a single crystalline Si core and a conformal oxide shell using the lithography-free wet etching and a thermal oxidation process. Compared with the pristine Si NWAs, the core-shell structure not only produces lower surface reflectance, but also shows greater omnidirectionality and polarization-insensitivity. These enhanced light trapping performances are attributed to the smoother transition in refractive index at the air/Si interface. The interaction between the incident light and the core-shell NWAs is realized through the simulation based on rigorous coupled-wave analysis (RCWA) and finite-difference time domains (FDTD) analysis. Surprisingly, we found that through tuning the core-shell thickness ratio the enhanced light trapping can be implemented in either the planar Si underneath NWAs or the core regions of NWAs, greatly benefiting the efficiency boosting of planar and radial p-n junction cell structures, respectively. The PM strategy proposed in this study offers an additional dimension in harnessing the light propagations through NWAs and opens new avenues for third-generation solar cells.
Si NWAs were fabricated by immersing single crystalline p-type Si(001) substrates in an aqueous solution containing AgNO3 and HF, in which the galvanic electrochemistry reaction between Si and Ag+/HF resulted in the NWA structure [24,25]. The concentrations of HF and AgNO3 used here were 4.6 M and 0.02 M, respectively. In order to obtain the Si core/dielectric shell structures, the Si NWAs were annealed in air ambient at 900þC for 1~3 hours. Morphological studies of the annealed NWAs were performed with a JEOL JSM-6500 field emission SEM and a JEOL 2100F TEM operating at 200 kV. The EDS attached to the TEM was utilized to determine the chemical composition. Optical reflectance measurements were carried out by a standard UV-visible spectrometer (JASCO ARN-733) equipped with an integrating sphere.
3. Results and discussion
Figure 1(a) presents the cross-sectional scanning electron microscopy (SEM) image of the annealed NWAs with Si/oxide core-shell structures. The core-shell structure originates from the oxidization of single crystalline Si NWAs during the annealing process. It can be seen that the NWAs are well aligned along the  direction. The formation of Si NWAs is initiated by Ag-induced etching in the AgNO3/HF solution via the electrochemical redox reaction process . The average length of the nanowires is ~1.4 µm. Figure 1(b) presents the cross-sectional transmission electron microscopy (TEM) image of the nanowires annealed for 3 hours at 900 þC in air ambient. In the figure, the contrast difference between the inner and the outer regions suggests that the Si nanowire is surrounded by an oxidized layer. Figure 1(c) shows a high-resolution TEM (HRTEM) image of the interface area, which is corresponding to the rectangle marked in Fig. 1(b), revealing that the core region is single crystalline Si whereas the shell region is an amorphous material presumably formed by the oxidation process. The energy dispersive spectroscopy (EDS) line scan [Fig. 1(d)] performed along the dash line shown in Fig. 1(b) indicates that the EDS intensity difference between Si and O is maximized within the 50-nm core region and decreases in the shell region, confirming the Si/oxide core-shell nanostructure. Similar distributions of Si and O were observed with the nanowires annealed for 1 hour at the same temperature (900 þC).
It is well known that Si surface can be naturally oxidized with very limited oxidation rates depending on oxygen concentration and moisture in the atmosphere. An oxidized layer with proper thickness not only passivates surface recombination centers, but also benefits AR performances, which will be shown later. With planar Si surface, the oxidation process is time-consuming . However, the oxidation of Si NWAs can be significantly expedited due to the large surface area of the convex nanostructures [28,29]. According to the TEM observations, the average shell thicknesses of the nanowires annealed for 1 and 3 hours are 55 and 110 nm, respectively. This implies that the oxidation rate is about 1 nm/min for the first hour and 0.5 nm/min for the last two hours. The slowing of the oxidation process as the time proceeds can be explained by the compressive stress normal to the Si/oxide interface . Since the oxide shell layer is produced by consuming Si in the core region, the expansion of shell volume leads to a stress compressing the inner Si core as the shell grows inward, which would retard the growth of new oxide layers.
The AR performances of the core-shell Si/oxide NWAs were evaluated in the wavelengths ranging from 250 to 850 nm, as shown in Figure 2 . During the measurements, the angle of incidence (AOI) was fixed at 8þ. In order to evaluate the effect of the dielectric shells, the reflectance was measured with the four types of structures: the polished Si substrate, the Si NWAs without annealing process, the NWAs annealed for 1 hour (NWAs with 55-nm oxide), and the NWAs annealed for 3 hours (NWAs with 110-nm oxide). Figures 2(a)-2(b) respectively present the total and the specular reflectance of the four samples. In Fig. 2(a), the total reflectance of the NWAs (even without the oxide layer) is noticeably lower than that of the polished Si substrates. The significant reflectance reduction in NWA layers can be explained by effective medium theory . The subwavelength features and the rough interfaces at the regions of air/NWAs and NWAs/substrates make the NWA layers behave like an effective medium, in which the effective refractive index increases gradually from air to Si substrates . The elimination of the reflection over broadband wavelengths can occur through destructive interferences, in which the waves with different phases partially or wholly cancel one another when the incident light is reflected at different depths in NWA layers .
The superior light trapping performances of the core-shell structure are demonstrated by the lower reflectance of the annealed NWAs, shown in Figs. 2(a)-2(b). The results can be attributed to the additional grading in the effective refractive index contributed by the dielectric oxide layer, which makes the air/Si interfaces less abrupt and therefore facilitates more photons traveling from air to the NWAs. It is also found that the total reflectance can be further suppressed by increasing the annealing time from 1 hour to 3 hours, suggesting that the oxide layer with appropriate thickness is required in order to achieve the lowest reflectance. Figure 2(b) also shows that the NWAs annealed for 1 hour and 3 hours reach the lowest specular reflectance at around 325 nm and 650 nm, respectively. The different wavelengths exhibiting minimum reflectance are caused by the different optical thicknesses of oxide shells. Although the broadband light trapping abilities of these NWAs are mainly explained by the effective medium theory, the nearly normal incidence and the finite oxide layer at the tips of the annealed NWAs also make the incident light experience, to a certain extent, a three-layer structure (i.e., air/oxide/Si). When the thickness of the oxide layer equals a-quarter-wavelength of the incident light, a reflectance minimum could occur . Considering the refractive index of SiO2 (n≈1.47 at 325~650 nm) , it is found that the values of a-quarter-wavelength with λ = 325 nm and 650 nm respectively correspond to 55.3 nm 110.5 nm, which are fairly close to the thicknesses of the oxide layers of the two annealed Si NWAs, indicating that the AR abilities of these oxide layers can be reasonably clarified by thin-film optics. It should be noted that the maxima at ~280 nm and ~370 nm in the reflectance are caused by the interband transitions in Si . This principal spectral feature is observable on both polished and nanostructured surfaces, indicating that the intrinsic material qualities are preserved after the etching and the oxidation processes.
Figure 2(c) shows the diffuse reflectance measured on the four samples. The diffuse reflectance was determined by subtracting the specular reflectance from the total reflectance. For most of the studied wavelengths, the as-synthesized NWAs produce the highest diffuse reflectance, followed by the 1-hour-annealed NWAs. The highest diffuse reflectance reached by the as-synthesized NWAs indicates that light scattering can be magnified on a roughened surface . The 3-hour-annealed NWAs or the polished surface achieve the lowest diffuse reflectance. The decreased diffuse reflectance with increased oxide shell thickness tells that further grading in refractive index profiles by inserting oxide layers between air and Si NWAs not only results in additional destructive interference among the reflected lights, but also reduces the scattering intensities on individual nanowires by improving the impedance match between air and Si.
The different tendencies of specular reflectance and diffuse reflectance of the NWAs can be explained using Fig. 3 , in which the ratios of specular reflectance/total reflectance (Rspec/Rtotal) and diffuse reflectance/total reflectance (Rdiff/Rtotal) for NWAs and the polished Si are plotted as the function of wavelengths. These samples present distinct behaviors. On the polished Si [Fig. 3(a)], the total reflectance is dominated by specular reflectance (average Rspec/Rtotal = 90%), and the ratios remain nearly unchanged at the entire wavelength range. This is because the reflection from a mirror-like Si surface is governed by the ordinary theorem of geometrical optics. In contrast, Rdiff/Rtotal for all kinds of NWAs in the entire wavelength regions maintains high and gradually decreases with wavelengths. This phenomenon manifests the fact that light scattering occurs significantly when the wavelength is comparable to the average distance between NWAs (ca. 180 nm determined by SEM top-view images.) . As the NWAs can be regarded as a diffraction grating, the light impinging the NWAs couples with the grated surface and diffracts to several beams with different diffraction angles [34,35]. That is to say that the grating reduces the zero-order reflectance (i.e., Rspec), but the light beams are redistributed to the diffracted orders, leading to the high ratios of Rdiff/Rtotal in
NWA structures. The high diffracted orders caused by surface grating are expected to increase optical path lengths and light absorption in active regions of optical devices, such as photodetectors and solar cells [21,36].
The lowest reflectance achieved by the 3-hour-annealed NWAs is further confirmed by theoretical calculations. Figure 4 presents the calculated total reflectance based on RCWA in comparison with the measurement results. In the simulation, the size of a unit cell is 2 μm, filled by 11 randomly distributed nanowires with the dimensions determined by the SEM images. It can be seen that the calculated total reflectance generally agrees with the measurement results, supporting the fact that the core-shell structure of NWAs is beneficial to light trapping.
In order to study the influence of the oxide layer on light propagation across the interfaces of NWAs, the steady-state distribution of electromagnetic fields within the nanowire structure was simulated by FDTD analysis by solving Maxwell’s equations. The grid sizes are Δx×Δy×Δz=5×5×5 nm3 in space domain, and the time step (Δt) for every calculation is 0.005 fs. The wavelength for the simulation is 650 nm, and the excitation source is placed at y = 0 μm. Due to the similarity of TM and TE spectra, we show the TE-polarized field distribution only without loss of generality. Figures 5(a) -5(d) present the time-averaged TE-polarized electric field intensity distributions (|Ez|) in polished Si, as-synthesized NWAs, NWAs annealed for 1 hour, and NWAs annealed for 3 hours, respectively. The boundaries of the simulated structures are depicted by the dash lines. The absorption behavior can be described in terms of the field distribution inside NWAs and substrates. Comparing with Figs. 5(a) and 5(b), the increased absorbance of the nanostructured surface is confirmed by its stronger field intensities within the nanowires and the Si substrate. In Fig. 5(b), the high |Ez| confined within the nanowire is caused by the index contrast between air and Si. The effect of the oxide shell on the optical absorption of NWAs is manifested by the two important observations in Figs. 5(c) and 5(d): i) in comparison with the result in Fig. 5(b), the application of oxide shell, with either the thickness of 55 nm or 110 nm, enhances the absorption by the Si substrate, especially in the regions near the nanowires. ii) the 55-nm-thick shells lead to strong light trapping within the nanowires, while the 110-nm-thick ones facilitate enhanced light trapping in the substrate area. The second observation implies that the light-trapping region of the NWAs can be tailored by a proper selection of volume ratio between shells and cores. Thinning the thickness of the shell to 55 nm allows the thick core to accommodate more incident light, which is desirable for the solar cells or photodetectors with coaxial p-n junctions built in the nanowires [37,38]. On the other hand, the structures with 110-nm-thick shells and thin cores enhance the absorption in the underneath substrate. This geometry is beneficial to the planar devices, where the light-absorbing p-n junctions are buried under the substrate surface. It is worthwhile to note that, with our approach, the two distinct absorption regions can be simply controlled by a suitable annealing duration. Another interesting point in Fig. 5 is the field intentiesties seen along the surface of nanowires. The seemingly “leakage” of electric field is the evanescent waves formed when total internal reflection occurs within the core and the shell regions. Since the nanowires are subwavelength objects and the critical angles for total internal reflection at the Si/SiO2 or the SiO2/air interfaces are larger than that at the Si/air interface, the evanescent waves become more significant for the nanowires with core-shell structures.
In addition to the broadband working range, a desired light-harvesting layer for PV applications should be insensitive to AOI since sunlight strikes the Earth surface from different directions during the day. The 1- and 3-hour-annealed NWAs were respectively evaluated with the fixed wavelengths at which these two core-shell NWAs exhibit the lowest specular reflectance, i.e., 325 nm for the 1-hour-annealed NWAs and 650 nm for the other, as shown in Fig. 6 . We evaluate the AOI-dependent reflection with the 1-hour-annealed NWAs at 325 nm first. In this measurement, the angle of detection is always equal to AOI. Figure 6(a) shows the specular reflectance as a function of the AOI measured on the polished Si surface, the NWAs without annealing processes, and the 1-hour-annealed NWAs. TE- and TM-polarized light was used in the measurements. It is found that the reflectance of the 1-hour-annealed NWAs stays below 1% for the AOIs up to 80þ with both TE- and TM-polarized light, revealing the excellent omnidirectionality of core-shell NWAs as compared to the results of the polished surface and the Si NWAs. The polarization-dependent omnidirectionality can be characterized by the ratio of the reflectance of the TE-polarization to that of the TM-polarization (RTE/TM), as presented in Fig. 6(c). Obviously, at 325 nm RTE/TM of the 1-hour-annealed NWAs is lower than those of the other two samples, demonstrating that the light trapping ability of the Si/oxide core-shell structure is polarization-insensitive over a wide range of AOIs. Similar characterizations with the 3-hour-annealed NWAs at 650 nm are shown in Fig. 6(b) and 6(d). Furthermore, in Fig. 6(c) and 6(d), the high maximum of RTE/TM for polished Si and Si NWAs can be attributed to the particular transmission of TM-polarized light at Brewster’s angles (BAs) . The low maximum of RTE/TM (i.e., less pronounced BA) produced by the core-shell Si/oxide NWAs indicates that further grading in refractive index by the oxide layer breaks the distinct interface between air and Si, and thus increases the destructive interferences among the reflected beams, which makes BA less pronounced due to the broadband reflectance suppression of TM-polarized light.
Si-oxide core-shell NWAs fabricated by lithography-free wet etching and subsequent annealing process possess the excellent light-harvesting characteristics, such as broadband working ranges, omnidirectionality, and polarization-insensitivity, ascribed to the smooth index transition from air to the substrates. By tuning core-shell volume ratios, enhanced light trapping regions can be implemented in either planar Si underneath NWAs or core regions of NWAs, greatly benefiting efficiency boosting of planar and radial p-n junction cell structures, respectively. These enhanced light-harvesting properties and structure design considerations are beneficial to the PM of nanostructured optoelectronic devices.
This work was supported by National Science Council of Taiwan (99-2622-E-002-019-CC3, 99-2112-M-002-024-MY3, and 99-2120-M-007-011) and National Taiwan University (10R70823).
References and links
1. H. P. Wang, K. T. Tsai, K. Y. Lai, T. C. Wei, Y. L. Wang, and J. H. He, “Periodic Si nanowire arrays by anodic aluminum oxide template and catalytic etching for broadband omnidirectional light harvesting,” Opt. Express 20(S1), A94 (2012). [CrossRef]
2. C. H. Sun, P. Jiang, and B. Jiang, “Broadband moth-eye antireflection coatings on silicon,” Appl. Phys. Lett. 92(6), 061112 (2008). [CrossRef]
3. C. G. Someda, Electromagnetic Waves (Chapman & Hall, 1998).
4. I. Gur, N. A. Fromer, C. P. Chen, A. G. Kanaras, and A. P. Alivisatos, “Hybrid solar cells with prescribed nanoscale morphologies based on hyperbranched semiconductor nanocrystals,” Nano Lett. 7(2), 409–414 (2007). [CrossRef] [PubMed]
5. D. S. Tsai, C. A. Lin, W. C. Lien, H. C. Chang, Y. L. Wang, and J. H. He, “Ultra-high-responsivity broadband detection of Si metal-semiconductor-metal Schottky photodetectors improved by ZnO nanorod arrays,” ACS Nano 5(10), 7748–7753 (2011). [CrossRef] [PubMed]
6. P. H. Fu, G. J. Lin, C. H. Ho, C. A. Lin, C. F. Kang, Y. L. Lai, K. Y. Lai, and J. H. He, “Efficiency enhancement of InGaN multi-quantum-well solar cells via light-harvesting SiO2 nano-honeycombs,” Appl. Phys. Lett. 100(1), 013105 (2012). [CrossRef]
7. X. Fang, L. Hu, C. Ye, and L. Zhang, “One-dimensional inorganic semiconductor nanostructures: a new carrier for nanosensors,” Pure Appl. Chem. 82(11), 2185–2198 (2010). [CrossRef]
10. H. C. Chang, K. Y. Lai, Y. A. Dai, H. H. Wang, C. A. Lin, and J. H. He, “Nanowire arrays with controlled structure profiles for maximizing optical collection efficiency,” Energy Environ. Sci. 4(8), 2863 (2011). [CrossRef]
14. S. L. Diedenhofen, O. T. Janssen, G. Grzela, E. P. Bakkers, and J. Gómez Rivas, “Strong geometrical dependence of the absorption of light in arrays of semiconductor nanowires,” ACS Nano 5(3), 2316–2323 (2011). [CrossRef] [PubMed]
15. 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] [PubMed]
16. 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] [PubMed]
17. Y. L. Chueh, Z. Fan, K. Takei, H. Ko, R. Kapadia, A. A. Rathore, N. Miller, K. Yu, M. Wu, E. E. Haller, and A. Javey, “Black Ge based on crystalline/amorphous core/shell nanoneedle arrays,” Nano Lett. 10(2), 520–523 (2010). [CrossRef] [PubMed]
19. L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10(2), 439–445 (2010). [CrossRef] [PubMed]
20. Y. C. Chao, C. Y. Chen, C. A. Lin, and J. H. He, “Light scattering by nanostructured anti-reflection coatings,” Energy Environ. Sci. 4(9), 3436 (2011). [CrossRef]
21. O. L. Muskens, J. G. Rivas, R. E. Algra, E. P. Bakkers, and A. Lagendijk, “Design of light scattering in nanowire materials for photovoltaic applications,” Nano Lett. 8(9), 2638–2642 (2008). [CrossRef] [PubMed]
22. L. K. Yeh, K. Y. Lai, G. J. Lin, P. H. Fu, H. C. Chang, C. A. Lin, and J. H. He, “Giant efficiency enhancement of GaAs solar cells with graded antireflection layers based on syringelike ZnO nanorod arrays,” Adv. Energy Mater. 1(4), 506–510 (2011). [CrossRef]
23. 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]
24. K. Peng, Y. Yan, S. Gao, and J. Zhu, “Dendrite-assisted growth of silicon nanowires in electroless metal deposition,” Adv. Funct. Mater. 13(2), 127–132 (2003). [CrossRef]
25. C. Y. Chen, C. S. Wu, C. J. Chou, and T. J. Yen, “Morphological control of single-crystalline silicon nanowire arrays near room temperature,” Adv. Mater. (Deerfield Beach Fla.) 20(20), 3811–3815 (2008). [CrossRef]
26. Y. A. Dai, H. C. Chang, K. Y. Lai, C. A. Lin, R. J. Chung, G. R. Lin, and J. H. He, “Subwavelength Si nanowire arrays for self-cleaning antireﬂection coatings,” J. Mater. Chem. 20(48), 10924 (2010). [CrossRef]
27. B. E. Deal and A. S. Grove, “General relationship for the thermal oxidation of silicon,” J. Appl. Phys. 36(12), 3770 (1965). [CrossRef]
28. S. Krylyuk, A. V. Davydov, I. Levin, A. Motayed, and M. D. Vaudin, “Rapid thermal oxidation of silicon nanowires,” Appl. Phys. Lett. 94(6), 063113 (2009). [CrossRef]
29. D. Shir, B. Z. Liu, A. M. Mohammad, K. K. Lew, and S. E. Mohney, “Oxidation of silicon nanowires,” J. Vac. Sci. Technol. B 24(3), 1333 (2006). [CrossRef]
30. P. Beckman and A. Spizzichno, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).
31. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55(10), 1205 (1965). [CrossRef]
32. S. Adachi, “Optical dispersion relations for Si and Ge,” J. Appl. Phys. 66(7), 3224 (1989). [CrossRef]
33. Y. C. Chao, C. Y. Chen, C. A. Lin, Y. A. Dai, and J. H. He, “Antireflection effect of ZnO nanorod arrays,” J. Mater. Chem. 20(37), 8134 (2010). [CrossRef]
34. Y. C. Lee, C. F. Huang, J. Y. Chang, and M. L. Wu, “Enhanced light trapping based on guided mode resonance effect for thin-film silicon solar cells with two filling-factor gratings,” Opt. Express 16(11), 7969–7975 (2008). [CrossRef] [PubMed]
35. S. J. Wilson and M. C. Hutley, “The optical properties of 'Moth Eye' antireflection surfaces,” Opt. Acta (Lond.) 29(7), 993–1009 (1982). [CrossRef]
36. H. Sai, Y. Kanamori, K. Arafune, Y. Ohshita, and M. Yamaguchi, “Light trapping effect of submicron surface textures in crystalline Si solar cells,” Prog. Photovolt. Res. Appl. 15(5), 415–423 (2007). [CrossRef]
37. B. M. Kayes, H. A. Atwater, and N. S. Lewis, “Comparison of the device physics principles of planar and radial p-n junction nanorod solar cells,” J. Appl. Phys. 97(11), 114302 (2005). [CrossRef]
38. L. Tsakalakos, J. Balch, J. Fronheiser, B. A. Korevaar, O. Sulima, and J. Rand, “Silicon nanowire solar cells,” Appl. Phys. Lett. 91(23), 233117 (2007). [CrossRef]