We report a study of the optical properties of silicon moth-eye structures using a custom-made fully automated broadband spectroscopic reflectometry system (goniometer). This measurement system is able to measure specular reflectance as a function of wavelength, polar incidence angle and azimuth orientation angle, from normal to near-parallel polar incidence angle. The system uses a linear polarized broadband super-continuum laser light source. It is shown that a moth-eye structure composed of a regular array of protruding silicon rods, with finite sidewall angle reduces reflectance and sensitivity to incident wavelength in comparison to truly cylindrical rods with perpendicular sidewalls. It is also shown that moth-eye structures have omnidirectional reflectance properties in response to azimuth orientation of the sample. The importance of applying the reflectometer setup to study the optical properties of solar cell antireflective structures is highlighted.
© 2014 Optical Society of America
The efficiency of solar cells is far from being close to the maximum theoretical value of 93 – 95%; most commercial single junction solar cells have the efficiency of 5% to 22% . The field of photovoltaics is suffering from the well-known problem of surface reflection as one of the main sources of energy loss in the field of energy harvesting. At normal incidence the loss of the solar irradiation due to surface reflectance at the air-silicon interface of silicon solar cells is between 31% to 61% over the solar spectrum which leads to a reduction of approximately 36% in the short circuit current produced by a silicon solar cell . Thus it is of great importance to develop effective anti-reflective technologies to reduce surface reflection losses and consequently increase solar cell efficiency.
Methods of reducing reflection in the field of photovoltaics are generally based on one of the following mechanisms: destructive interference, multiple reflectance and graded refractive index. Thin film anti-reflection coatings are based on the theory of the destructive interference of electromagnetic waves. Single layer antireflectives (SLARs) reduce the total surface reflectance of silicon to 8% – 15%  and perform optimally only for a specific wavelength and over a limited range of angles of incidence. Employing double layer antireflectives (DLARs) instead of SLARs improves the spectral range of incident angles over which the AR performs optimally. Introducing micron scale texturing at the surface of the air-silicon interface of solar cells is another technique used to reduce the surface reflection. The texturing at the interface causes the incident light to reflect multiple times coupling a larger proportion of the light into the solar cell and consequently reducing the surface reflection. The textures also cause the transmitted light to be refracted, changing the angle of propogation through the cell and so increasing the optical path length. This is known as light trapping as it increases the proportion of light that passes through the cell multiple times, thereby increasing the amount absorbed in the active region. The textures are normally in the form of random arrays of pyramids [4, 5, 6], microgrooves , random textures  and regular inverted pyramids [5, 9]. The reflectance of micron scale textured structures is further reduced by SLAR or DLAR coating on top of the texturing [8, 9, 10, 11, 12]. Thin film coatings and micron-scale texturing are widely used in laboratory and commercial solar cells. A combination of micron scale texturing in the form of a lithographically-defined regular array of inverse pyramids, formed by etching in KOH, and a DLAR coating are employed in the 25% efficient PERL cell that currently holds the record for the highest efficiency of a single junction silicon solar cell [11, 13]. However, the amount of material etched away from the top surface during fabrication is considerable and thus this texturing technique cannot be used for thin silicon solar cells. Also the reflectance of these structures increases with the angle of incidence which is not favourable in solar cells.
Another way to confer antireflective properties to a surface is by introducing graded refractive index by means of texturing on the subwavelength scale. This approach was inspired by the so called “moth-eye” structures in nature that were found to confer an AR effect by decreasing the discontinuity in refractive index experienced by light as it passed from air into the eye. These subwavelength structures, discovered by Bernhard, Miller and Moller in 1962 , are roughly conical in shape, approximately 200nm tall and arranged in a hexagonal array with a centre-to-centre distance of 200nm. Similar structures were later observed on both sides of the wing of a hawk-moth, Cephonodes hylas, making it transparent and so conferring a camouflage effect [15, 16] (Fig. 1).
Since the discovery of moth-eye structures, there have been many studies on applying them to reduce surface reflection [17, 18, 19]. In photovoltaics, moth-eye structures have been investigated as replacements for thin film coatings [20, 21, 22]. Thin film coatings exhibit problems with material selection, adhesion, thermal mismatch or diffusion of one material into another, which are not present in moth-eye structures . Thus silicon-based solar cells can have a silicon moth-eye array as the anti-reflection layer replacing conventional anti-reflection coatings.
Previous studies have shown that the antireflective spectrum of moth-eye structures can be tuned by changing the height and period of the protuberance arrays [23, 24]. Computational studies have been performed to optimize silicon moth-eye structures for solar cell applications. One such optimization resulted in a height of 400nm and period of 280nm . Another important parameter affecting the reflectance properties of moth-eye structures is the pillar shape of the protuberances. According to effective medium theory, since these are sub-wavelength structures with dimensions below Bragg diffraction limit, changes in shape of the pillars causes a gradual variation in effective-refractive index and so pillar shapes can be optimized to minimize reflectance. In the previous work moth-eye structures with various pillar profiles were fabricated and studied at normal incidence . However a full study of their reflectance properties is yet to be done.
Optical characterisation of ARCs is studied using various measurement systems. Normal incidence reflectance is often measured using a reflectance probe technique consisting of a ring of outer optical fibres surrounding a central fibre. White light is delivered to the sample through the outer fibres and reflected light is collected and delivered to a spectrometer by the central fibre. This is a simple setup and an easy measurement to perform, however the numerical aperture of fibres within the probe limits the extent of the scattered light that can be measured using this system, thus it is not adequate for measuring reflection from scattering surfaces. Integrating sphere techniques have been widely used to measure reflectance of surfaces. The sample is mounted at a port on a hollow sphere with a highly reflective and highly scattering inner surface. Light incident at a near-normal angle (usually 8°) reflected from the sample undergoes multiple reflections in the sphere resulting in the inner surface of the sphere being uniformly illuminated by the reflected light. A photodetector or optical fibre linked to a spectrometer is mounted at another port on the sphere to sample this light. By comparing the signal with that measured from a sample of known reflectance, the total hemispherical (specular and diffuse) reflectance of the sample is determined. The specular component can be removed by placing an absorber at the appropriate positioned port on the sphere. To perform angle resolved measurements the angle of incidence (AOI) can be changed by mounting the sample on a mount at the center of the integrating sphere and rotating the sample. The specular reflectance cannot be removed from angle resolved measurements as this would require an absorbing port for every AOI and commercial integrating spheres do not have such a capability. Parretta et al. [5, 26, 27] developed a setup called ROSE to measure reflectance properties of solar cells in which the specular reflectance can be removed with ports placed at every 10°. Using this device, the diffuse reflectance at certain AOIs can be measured. Subtracting the diffuse reflectance from hemispherical reflectance will result in the specular reflectance at those angles. However this measurement setup is still limited to certain AOIs and a measurement of a full spectrum of AOI cannot be performed. Absolute specular reflectance measurement requires a setup in which the specularly reflected light off the sample is collected by a photodetector or fibre placed along the route of the reflected beam. As the angle of incidence changes, the reflected beam will rotate and so the detector should rotate. There are a few commercial devices that perform specular angle resolved measurements. Shimadzu UV3600 and Hitachi U-4100 spectrophotometers both employ separate compartments for this purpose and thus the AOIs are limited to only certain AOIs; 5°, 12°, 35° (30° for Hitachi U-4100) and 45°. In both cases the largest AOI is only at 45°. The Cary spectrophotometer from Agilent Technologies has an accessory called VASRA (variable angle specular reflectance accessory) that is capable of measuring the absolute specular reflectance for a range of AOIs from 20 – 70° at every 1°. Measuring specular reflectance for a wide range of wavelengths and AOIs from normal to parallel incidence is challenging since it requires precise alignment. The alignment is to ensure the illuminated spot on the sample does not move as the sample is rotated to change the AOI and the specularly reflected beam enters the detection fibre.
We have developed a motorized reflectometer system that employs a super-continuum (white light, λ = 350 – 1000nm) laser and is able to probe a full range of AOIs from near-to-normal (2°) to near-to-parallel (83°) with a step size of 0.1° and is able to change the effective azimuth angle by rotating the sample. This setup was previously used to identify localized and plasmon dispersion lines . We have used our reflectometer setup to study the optical properties of a type of subwavelength AR, silicon moth-eye structures.
2. Experimental technique
To fully characterize the absolute specular reflectance of silicon moth-eye structures over a range of incidence angles, wavelengths, polarisations (s and p) and in-plane azimuth orientations, angle-resolved reflection measurements are performed using a custom built motorised goniometer system (Fig. 2). The system can be used for specular reflection measurements, and angular scattering in transmission and reflection. The light source is a white laser beam (Fianium SC450 super continuum fibre laser). The laser beam is passed through two crossed polarisers, which regulates the power, and sets the polarisation of the beam to one of two linear polarisations: “s” where the electric field is perpendicular to the plane of incidence (TE), and “p” where the electric field is parallel to the plane of incidence (TM). The detection fibre rotates around the sample by 2θ as the sample is rotated to alter the angle of incidence (θ). The fibre collects the specular part of the reflected laser beam and couples it into the BTC112E spectrometer.
Measurements are normalised with respect to the incident power according to Eq. (1).
- Rmoth–eye is the measured reflectance of the moth-eye sample,
- Imoth–eye is the signal of the beam reflected from the moth-eye sample,
- Isource is the signal of the light source incident on the sample, and
- Idark is the dark measurement to remove background light.
A mini integrating sphere is used to collect reflected light. This is coupled by a large core (50μm) diameter multimode fibre to a spectrometer. The entrance port of the mini integrating sphere can have size of 1, 2 and 3mm. For these measurements a 2mm aperture is used. The integrating sphere aperture size sets the limit of angular resolution of the measurement system. Use of an integrating sphere eases alignment tolerance, but at the expense of less light reaching the spectrometer and so a lower signal-to-noise ratio.
The laser power and the integration time were varied in order to provide a high enough signal-to-noise ratio (see Table 1).
Measurements with acceptable levels of signal-to-noise could be obtained between angles of incidence of 2° and 83° and over a wavelength range of 450–850nm. The sample was rotated in the azimuth plane in steps of 5° from a reference angle 0° to 75°. The maximum azimuth rotation angle was chosen as 75° so a full symmetry unit of the hexagonal lattice was covered (60°) and the repetition of reflectance spectrum with repeated symmetry was verified (from 60° to 75°).
The reflectance data of samples at near normal incidence were extracted from these measurements at an incidence angle of 2°.
In order to validate the reflectometer and its accuracy in measuring the specular reflectance of arbitrary samples, the specular reflectance of silicon was measured and compared to the theoretical value calculated via Fresnel equations . Figure 3 shows the specular reflectance of silicon at the two orthogonal polarisations for the wavelength range of 450–850nm for the aforementioned AOI range; it compares the theoretical value to measurement results. Figure 4 shows the angular reflectance of silicon measured by the reflectometer versus the theoretical value at three different wavelengths taken from three separate runs to confirm the repeatability of results.
A figure of merit can be extracted from the reflectometer measurements containing the specular reflectance properties of a sample at normal to near to parallel incidence. Firstly the angular reflectance, weighted by the solar spectrum, is calculated using Eq. (2).
In this equation R(λ, θ) is the reflectance of the sample averaged over s and p polarisation, and PFD(λ, θ) is the solar spectrum, expressed as a photon flux density in units of photons/m2/s taken from National Renewable Energy Laboratory (NREL) known as SPCTRL2  and previously used to evaluate the performance of thin film antireflective coatings . The Weighted Specular Reflectance, WSR, is then calculated by taking the average of Rw(θ) over all angles of incidence (θ). The WSR can be used as a figure of merit to evaluate the reflectance properties of surfaces over broad wavelength and angle of incidence ranges. The theoretical value of WSR can be calculated using the theoretical value of reflectance from Eq. (1). A comparison of theoretical WSR and experimental WSR provides a gauge of the accuracy of the reflectometer. As an example, the theoretical WSR value for silicon is 0.3647, while the value determined from reflectometer experiment is 0.3558.
3. Nano-imprinted silicon moth-eye samples
Silicon moth-eye structures were fabricated over areas of 1 cm × 1 cm using nano-imprint lithography. A detailed explanation of the fabrication process is presented in . The process involves an isotropic etch of 90s followed by an oxidation stage to alter the pillar profile. In this paper we are looking at two sets of samples with the different oxidation process. Wafer 1 without any oxidation and wafer 2 with 5 minute oxidation. Figure 5 shows top and side view SEM images of the samples. The periodicity of the two structures is extracted from SEM images and approximated to 270nm. The top view of pillars shows an unexpected square cross section as opposed to a circular cross section. SEM images of the imprinting stage shows that the stamp and Aluminium masks produced circular shape holes and rods respectively. Thus the square shapes are due to the effect of etching stages on the crystalline structure of the silicon, either during the anisotropic etch to produce vertical wall cylinders or during the isotropic etch to produce tapered cylinders. Pillars in wafer 1 are thick and have near vertical walls, so they look closer to cylindrical rods. Pillars in wafer 2 have tapered profile and so are referred as tapered rods in this paper. The width of the pillars at top and bottom of the moth-eye layer are extracted from SEM images and noted in Fig. 5. The height of pillars is 400nm.
4. Experimental results
4.1. Normal incidence measurement
Normal incidence reflectance spectra for silicon moth-eye structures collected using the reflectometer are presented in Fig. 6. Also plotted are results from measurements on the same samples using the well-established reflectance probe system [2, 24]. The spectra from the two different measurement techniques are in good agreement, validating the reflectometer technique for normal incidence reflectance measurement on these samples. Wafer 1, which has protuberances with vertical walls shows higher reflectance values and more fluctuations with wavelength compared to the moth-eye structure with tapered cylinders. Wafer 2 shows lower reflectance values across the whole spectral range and a wider low reflectance region in the spectrum; the near to zero reflectance region is between 550–650nm. In summary the vertical walled, flat-topped pillars appear to act similar to a homogeneous thin film, due to their step profile effective refractive index. In such cases interference occurs between waves reflected at the top and bottom of the pillars, leading to peaks (constructive interference) and troughs (destructive interference) in the spectra. These disappear with tapered walls as the sharp interfaces no longer exist at the top and bottom of the pillars and instead the effective refractive index changes smoothly from the top to the bottom of the moth-eye layer. The comparison of the mean average of the normal incidence reflectance of wafer 1 and 2 confirms that the tapered cylinders reduce the reflectance of moth-eye structure further.
4.2. Angular reflectance measurement
The reflectance data of silicon moth-eyes over a range of angles of incidence (2 – 83°) and wavelengths (450–850nm) for s and p polarisation are presented in Fig. 7. The angular reflectance of wafer 1(cylindrical walls) has weak dispersion features (characterized by narrow bandwidth) with low reflectance (below 10%) for both s and p polarisation at certain wavelengths which either stay at a constant wavelength as AOI increases or shifts to neighbouring wavelengths (shorter or longer). These dispersive features correspond to conditions required for strong coupling to lateral modes of the lattice of rods (photonic crystal Bloch modes). However, wafer 2 (tapered rods) does not show such dispersive features but instead has a broad wavelength range with low overall reflectance. This is characteristic of a reduced average refractive index (this effect is independent of wavelength) rather than the more complex and distinct signature associated with coupling to Bloch modes of the periodic lattice (which is very specific to wavelength). The width of the low reflectance region is wider for p polarisation than s polarisation. Results show that the reflectance of wafer 1 (cylindrical rods) stays under 30% up to the AOI of 50° for s polarisation, but up to an AOI of 75° for p polarisation. Wafer 2 (tapered rods) has a reflectance above 30% for wavelengths of 450 – 700nm only for AOIs larger than 75° for s polarisation and 70° for p polarisation.
The angular reflectance of silicon moth-eyes averaged over all wavelengths is plotted as a function of angle in Fig. 8. The difference between s and p polarisation reflectance is most significant for wafer 1 (cylindrical rods). This wafer shows higher reflectance values at s polarisation compared to wafer 2 (tapered rods), reaching a value of above 60% for AOI of 80° as opposed to 25% for wafer 2 (tapered rods). Wafer 1 (cylindrical rods) shows the biggest range of angular insensitivity when comparing the angular reflectance of unpolarised light, from normal incidence to 40°. The angular reflectance of unpolarised light from wafer 2 is not constant, however for p polarisation the reflectance stays constant up to an AOI of 40°. There is an inverse polarisation behaviour in the reflectance spectra of wafer 2 (tapered rods) at AOI=62°, where the reflectance of s polarisation is lower than reflectance value of p polarisation which is in contrast to flat silicon. This is a new property in the moth-eye structures, also observed by Chuang et al . The inverse polarisation is observed at AOIs around the Brewster angle. The moth-eye layer distorts the incident wave and prevents the zero reflection at the Brewster angle at p polarisation to take place, hence the reflectance at p polarisation of moth-eye silicon surfaces increases in comparison to p polarisation reflection from silicon. However the reflectance at s polarisation is reduced from its corresponding value from silicon and in some cases it reduces to values smaller than the p polarisation reflection, hence leading to the appearance of inverse polarisation.
Comparing the average angular reflectance of silicon moth-eyes with that of flat silicon (also presented in Fig. 8), shows a great reduction of reflectance at normal incidence for both samples (approximately 70%). Between the two samples, wafer 2 (tapered rods) has total reflectance lower than silicon for all angles of incidence while wafer 1 (cylindrical rods) shows reflectance values slightly higher than silicon above AOI = 79.6°. The difference between total reflectance of both samples with silicon reduces as the angle of incidence increases.
The antireflective properties of silicon moth-eye samples are once again compared with silicon in visible light in Fig. 9. It can be observed that moth-eye structures have reduced the reflection properties of a flat silicon. Wafer 2 with tapered walls have reduced the surface reflection of silicon to a greater extent in comparison with wafer 1 with cylindrical rods.
The comparison between the reflectance spectra of the two silicon moth-eye samples shows that the sample with vertical walls and wider pillars exhibits higher reflectance and more sensitivity to wavelength than the sample with tapered protuberances. This is a result of the discontinuity that the shape of pillars produces in the transition of refractive index from the top to the bottom of the moth-eye layer. Protuberances with a flat top produce a larger discontinuity at the interface which causes more reflection. However, thinner protuberances with a tapered profile have a sharper tip and reduce the extent of discontinuity in the refractive index between the two layers and consequently reduce the reflectance.
It was shown in the literature that height and periodicity are the two factors to play the main role in tuning the low reflectance region in moth-eye structures . However we have observed differences in the reflectance spectra between moth-eye structures of different pillar profiles. This proves that when height and periodicity are kept constant the shape of pillars is an important factor in determining the reflectance spectrum of moth-eye structures.
5.1. Weighted specular reflectance
The performance of silicon moth-eyes in response to the solar spectrum can be evaluated using the WSR. WSR values for wafer 1 and 2 are calculated and presented in the bar chart and compared to the experimental value for polished silicon (Fig. 10). The WSR of SLAR (Si3N4) and DLAR (SiO2/TiO2) optimized in  are also presented. The WSR values for these ARs are calculated using their angular reflectance simulation results from Rigorous Coupled Wave Analysis (DiffractMOD, RSoft Design Group) for both s and p polarisation. The bar chart shows that moth-eye structures on wafer 1 and 2 are able to reduce the WSR of silicon by 55% and 72% respectively, having similar values to SLAR and DLAR structures.
A thorough comparison of the WSR value of moth-eye structures with other anti-reflectives from literature is unfortunately not possible because characterisation of angular reflectance is generally limited to single wavelength measurements. In this study, the reflectometer setup has enabled reflectance measurements to be carried out over broad ranges of wavelength and AOI but this information is not generally available for other antireflective structures in literature.
5.2. Azimuth orientation
The effect of azimuth orientation on the reflectance spectrum of AR structures has been scarcely studied in the past. The only data available on this in the literature, to which results from the present study can be compared, is from Parretta et al. who used a custom made variable angle reflectometer, ROSE . Their device is capable of rotating the sample in azimuth plane for both normal and oblique incident angles. They showed that the rotation of a structure in the azimuth plane does not affect the angular reflectance of SLAR and DLAR structures, where the structure is homogeneous in the azimuth plane. However it affects the reflectance of PERL, Honeycomb and micron-scale textured surfaces which consist of angularly inhomogeneous patterns. The angular reflectance data over a range of azimuth angles for a PERL structure at λ =632nm for unpolarized light is taken from  and presented in Fig. 11. The PERL structure consists of arrays of inverse pyramids etched into silicon in a square lattice, therefore the structure has four-fold rotational symmetry in the azimuthal plane. The reflectance at azimuth rotations of 0°, 45° and 90°, taken from , is presented in Fig. 11. Reflectance results were expected to be identical at azimuth rotations of 0° and 90° due to the square array arrangement of the pillars, however small differences are observed due to fabrication inaccuracies. The angular reflectance results of the silicon moth-eye wafer 2 averaged for unpolarised incident ( average of s and p polarisation) are also presented in Fig. 11 providing a comparison at azimuth rotations of 0°, 30° and 60°. It is expected to observe similar behaviour at azimuth rotations of 0° and 60°, and a maximum difference at azimuth rotation of 30° due to the 6-fold symmetry of the hexagonal lattice within moth-eye structures. Unlike the PERL structure the azimuth orientation does not appear to affect the angular reflectance of the moth-eye structure.
It should be noted that results collected from the ROSE measurement system includes specular and diffused reflectance (total reflectance) while reflectometer results only include absolute specular reflectance. However these results show an outstanding feature of moth-eye structures that even though they exhibit rotational symmetry, the sub-micron nature of the features cancels this effect so that no change in reflectance with azimuth orientation is observed.
When considering potential PV applications of these structures, it should be noted that employing moth-eye structures without the adequate passivation might reduce the solar cell efficiency. This is a result of increased surface recombination due to increased surface area and the creation of defects during dry etching. Applying a well optimized passivation layer will therefore be necessary to reduce the effect of the surface recombination and its negative effects on the efficiency of solar cells, whilst maintaining the antireflective properties of the subwavelength structures.
Another important factor to consider for PV applications is the potential scalability of the technique to large areas. Although planar nanoimprinting over 1cm2 areas as described in this paper is cheaper than electron beam lithography, a low-cost and fully scalable commercial implementation would require wafer scale nanoimprinting and possibly roll-to-roll techniques. Advances in these techniques have been made over recent years [33, 34, 35], demonstrating the potential for commercially viable large area patterning.
We have presented analysis of specular reflectance of silicon moth-eye structures using an angular reflectance measurement setup. This reflectometer setup is capable of measuring the absolute specular reflectance at incidence angles of 2 – 83°, over the visible wavelength range, with s and p polarisations and over a range of azimuth orientations. Based on the reflectometer results, a figure of merit, WSR, was introduced to evaluate the weighted specular reflectance properties of the samples. This corresponds to the behaviour of an antireflective structure during half a day illuminated by solar spectrum. Such degree of evaluation is important for a comprehensive comparison of solar cell antireflective structures. Employing the reflectometer in conjunction with conventional integrating sphere and reflectance probe techniques provides a more thorough, in-depth characterisation of antireflective structures.
Measurement results of moth-eye structures with different pillar profiles have shown that pillars with a more tapered profile are less sensitive to the incident wavelength. A comparison of WSR values for silicon moth-eye structures and a flat silicon surface shows that these moth-eye structures have reduced the WSR of silicon to values similar to those which can be achieved by conventional optimized thin film coatings. It is expected that further optimization of the moth-eye pillar profile will result in AR surfaces that exceed the performance of thin film coatings.
While employing moth-eye structures for PV antireflective applications few issues should be considered. The dry etching process causes surface defects, and the moth-eye rods increase the surface area of the Silicon surface. These two increase the surface recombination of the PV cell which is not desired. Applying a well optimized passivation layer is then necessary to reduce the effect of surface recombination.
An additional capability of the reflectometer measurement setup used in this work is to measure the reflectance properties at different azimuth orientation of the sample. It is shown that moth-eye structures exhibit specular reflectance that is insensitive to variations in azimuthal angle, unlike their microstructured counterparts. Such property is useful for solar cells in applications where light is incident from a wide range of angles which changes with time.
Surface passivation techniques will however be required to limit any increase in surface recombination due to the etching processes involved in the fabrication of these structures if they are to be successfully applied in PV applications. Scale up, possibly through the use of roll-to-roll technology will also be necessary for this approach to be economically viable for PV.
References and links
1. D. M. Bagnall and S. A. Boden, Energy Harvesting for Autonomous Systems (Artech House, 2010).
2. S. Boden, “Biomimetic nanostructured surfaces for antireflection in photovoltaics,” Ph.D. thesis, University of Southampton (2009).
3. S. Koynov, M. S. Brandt, and M. Stutzmann, “Black multi-crystalline silicon solar cells,” Phys. Status Solidi Rapid Res. Lett. 1, R53–R55 (2007). [CrossRef]
4. D. King and M. E. Buck, “Experimental optimization of an anisotropic etching process for random texturization of silicon solar cells,” in Proc. 22nd IEEE Photovolt. Spec. Conf., Las Vegas, Nevada (1991).
5. A. Parretta, A. Sarno, P. Tortora, H. Yakubu, P. Maddalena, J. Zhao, and A. Wang, “Angle-dependent reflectance measurements on photovoltaic materials and solar cells,” Opt. Commun. 172, 139–151 (1999). [CrossRef]
6. M. Abbott and J. Cotter, “Optical and electrical properties of laser texturing for high-efficiency solar cells,” Prog. Photovoltaics Res. Appl. 14(3), 225–235 (2006). [CrossRef]
7. J. Zhao and M. A. Green, “Optimized antireflection coatings for high-efficiency silicon solar cells,” IEEE Trans. Electron Dev. 38, 1925–1934 (1991). [CrossRef]
8. U. Gangopadhyay, K. Kim, D. Mangalaraj, and J. Yi, “Low cost CBD ZnS antireflection coating on large area commercial mono-crystalline silicon solar cells,” Appl. Surf. Sci. 230, 364–370 (2004). [CrossRef]
9. J. Zhao, A. Wang, P. Altermatt, and M. A. Green, “Twenty-four percent efficient silicon solar cells with double layer antireflection coatings and reduced resistance loss,” Appl. Phys. Lett. 66, 3636–3638 (1995). [CrossRef]
10. R. Kishore, S. Singh, and B. Das, “PECVD grown silicon nitride AR coatings on polycrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 26, 27–35 (1992). [CrossRef]
11. J. Zhao, A. Wang, M. A. Green, and F. Ferrazza, “19.8% efficient honeycomb textured multicrystalline and 24.4% monocrystalline silicon solar cells,” Appl. Phys. Lett. 73, 1991–1993 (1998). [CrossRef]
12. I. Parm, K. Kim, D. Lim, J. Lee, J. Heo, J. Kim, D. Kim, S. Lee, and J. Yi, “High-density inductively coupled plasma chemical vapor deposition of silicon nitride for solar cell application,” Sol. Energy Mater. Sol. Cells 74, 97–105 (2002). [CrossRef]
13. M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 42),” Prog. Photovoltaics Res. Appl. 21, 827–837 (2013). [CrossRef]
14. C. G. Bernhard, “Structural and functional adaptation in a visual system,” Endeavour 26, 79–84 (1967).
15. A. Yoshida, M. Motoyama, A. Kosaku, and K. Miyamoto, “Nanoprotuberance array in the transparent wing of a hawkmoth, cephonodes hylas,” Zool. Sci. 13, 525–526 (1996). [CrossRef]
16. A. Yoshida, M. Motoyama, A. Kosaku, and K. Miyamoto, “Antireflective nanoprotuberance array in the transparent wing of a hawkmoth, cephonodes hylas,” Zool. Sci. 14, 737–741 (1997). [CrossRef]
17. W. L. Min, A. P. Betancourt, P. Jiang, and B. Jiang, “Bioinspired broadband antireflection coatings on GaSb,” Appl. Phys. Lett. 92, 141109 (2008). [CrossRef]
18. S. J. Wilson and M. C. Hutley, “The optical properties of moth eye antireflection surfaces,” J. Mod. Opt. 29, 993–1009 (1982).
19. P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8, 53–57 (1997). [CrossRef]
20. K.-S. Han, J.-H. Shin, and H. Lee, “Enhanced transmittance of glass plates for solar cells using nano-imprint lithography,” Sol. Energy Mater. Sol. Cells 94, 583–587 (2010). [CrossRef]
21. K.-S. Han, J.-H. Shin, K.-I. Kim, and H. Lee, “Nanosized structural anti-reflection layer for thin film solar cells,” Jpn. J. Appl. Phys. 50, 020207 (2011).
22. S. Koynov, M. S. Brandt, and M. Stutzmann, “Black nonreflecting silicon surfaces for solar cells,” Appl. Phys. Lett. 88, 203107 (2006). [CrossRef]
23. S. A. Boden and D. M. Bagnall, “Optimization of moth-eye antireflection schemes for silicon solar cells,” Prog. Photovoltaics Res. Appl. 18, 195–203 (2010). [CrossRef]
24. S. A. Boden and D. M. Bagnall, “Tunable reflection minima of nanostructured antireflective surfaces,” Appl. Phys. Lett. 93, 133108 (2008). [CrossRef]
25. S. A. Boden and D. M. Bagnall, “Nanostructured biomimetic moth-eye arrays in silicon by nanoimprint lithography,” Proc. SPIE 7401, 74010J (2009). [CrossRef]
26. A. Parretta, A. Sarno, and H. Yakubu, “Non-destructive optical characterization of photovoltaic modules by integrating sphere, Part I: Mono-Si modules,” Opt. Commun. 161, 297–309 (1999). [CrossRef]
27. P. Maddalena, A. Parretta, A. Sarno, and P. Tortora, “Novel techniques for the optical characterization of photovoltaic materials and devices,” Opt. Lasers Eng. 39, 165–177 (2003). [CrossRef]
28. M. F. A. Muttalib, S. Z. Oo, and M. D. B. Charlton, “Experimental measurement of photonic/plasmonic crystal dispersion, applied to the investigation of surface plasmon dispersion for sers sensing applications,” Proc. SPIE 8264, 82641C (2012). [CrossRef]
29. E. Hecht, Optics (Addison Wesley, 2002).
30. R. E. Bird and C. Riordan, “Simple solar spectral model for direct and diffuse irradiance on horizontal and tilted planes at the earth’s surface for cloudless atmospheres,” J. Clim. Appl. Meteorol. 25, 87–97 (1986). [CrossRef]
31. S. A. Boden and D. M. Bagnall, “Sunrise to sunset optimization of thin film antireflective coatings for encapsulated planar silicon solar cells,” Prog. Photovoltaics Res. Appl. 17, 241–252 (2009). [CrossRef]
32. S.-Y. Chuang, H.-L. Chen, J. Shieh, C.-H. Lin, C.-C. Cheng, H.-W. Liu, and C.-C. Yu, “Nanoscale of biomimetic moth eye structures exhibiting inverse polarization phenomena at the brewster angle,” Nanoscale 2, 799–805 (2010). [CrossRef] [PubMed]
33. C. Gourgon, C. Perret, J. Tallal, F. Lazzarino, S. Landis, O. Joubert, and R. Pelzer, “Uniformity across 200mm silicon wafers printed by nanoimprint lithography,” J. Phys. D Appl. Phys. 38, 70 (2005). [CrossRef]
34. J. Lee, S. Park, K. Choi, and G. Kim, “Nano-scale patterning using the roll typed uv-nanoimprint lithography tool,” Microelectron. Eng. 85, 861–865 (2008). [CrossRef]
35. C.-J. Ting, F.-Y. Chang, C.-F. Chen, and C. P. Chou, “Fabrication of an antireflective polymer optical film with subwavelength structures using a roll-to-roll micro-replication process,” J. Micromech. Microeng. 18, 075001 (2008). [CrossRef]