Arrays of metal nanoparticles are considered candidates for improved light-coupling into silicon. In periodic arrays the coherent diffractive coupling of particles can have a large impact on the resonant properties of the particles. We have investigated the photocurrent enhancement properties of Al nanoparticles placed on top of a silicon diode in periodic as well as in random arrays. The photocurrent of the periodic array sample is enhanced relative to that of the random array due to the presence of a Fano-like resonance not observed for the random array. Measurements of the photocurrent as a function of angle, reveal that the Fano-like enhancement is caused by diffractive coupling in the periodic array, which is accordingly identified as an important design parameter for plasmon-enhanced light-coupling into silicon.
© 2013 OSA
The use of plasmon resonances in metal nanoparticles has been suggested as a way to increase light collection in silicon for photovoltaic applications . For particles on the front side of a silicon diode a photocurrent enhancement is generally observed at wavelengths larger than the plasmon resonance, whereas a reduction is observed at wavelengths below [2–5]. Periodic arrays of particles are often considered due to the ease of numerical calculations which follows from symmetry considerations. It has been shown that Ag nanoparticles with dimensions of ∼ 150–200 nm in periodic arrays with a pitch close the wavelengths of visible light can efficiently couple light into silicon solar cells , and a number of important design parameters such as the nanoparticle material and geometry have been discussed in the literature [7, 8]. Concerning the optimization of the plasmonic properties of metal nanoparticles for improved photovoltaics, many numerical investigations have focused on single particle properties [2, 7, 9, 10]. In some cases near-field coupling between particles were considered as a cause of a redshift of the plasmon resonance . However, the effects of a long-range diffractive coupling between the particles on the resonant properties have not received much attention. In the present investigation, as a case study, we focus on how coupling in periodic arrays of aluminum nanoparticles affects the photocurrent enhancement in thin film Si solar cells. Aluminum nanoparticles have been considered for photovoltaic applications [5, 11] since they can support tunable localized surface plasmon resonances , and the abundance and low cost of aluminum is desirable for large scale implementation.
We demonstrate that the long range effects of coherent coupling in periodic arrays can lead to a pronounced modulation of the photocurrent enhancement as compared to that of randomly distributed particles, and that this effect might increase the photocurrent enhancement caused by metal nanoparticles on solar cells. Thus, diffractive coupling in periodic arrays constitutes an additional design parameter for metal nanoparticles on thin film solar cells to optimize the plasmonic enhancement of the photocurrent.
2. Collective modes from diffractive coupling of localized surface plasmon resonances (LSPR) of individual particles
It has been established that placing metal nanoparticles in a periodic array can have a profound influence on their resonant properties, when diffractive long range coupling dominates the resonant properties of the particles [13–20].
In periodic arrays, collective modes, sometimes referred to as surface lattice resonances , might appear due to diffractive coupling of localized surface plasmon resonances on the individual particles; the diffractive coupling is mediated by Rayleigh-Wood anomalies, which is an optical phenomenon related to light propagating parallel to the array plane . This diffracted light leads to a strong coupling of the particles in the arrays [14, 15, 20]. The spectral position of Rayleigh-Wood anomalies can be found from the following equation :
When a periodic metal nanoparticle array is placed in a homogenous dielectric environment, numerous studies have shown that the diffractive coupling in the array leads to a profound modification of the particle polarizability as compared to the single particle resonance, and that distinct features in the extinction spectra are observed at the Rayleigh-Wood anomalies [18,20]. In the case of a non-symmetric dielectric environment (substrate different from superstrate) the presence of a high-index substrate, such as silicon in the case of particle arrays placed on solar cells, can substantially alter the coupling, as reflection from the nearby dielectric interface adds contributions to the coupling mechanism [17, 21].
Auguié et al. showed that the presence of a high index substrate near the particle array may in some configurations eliminate the diffractive coupling, but if the particles are sufficiently large, strong diffractive coupling can occur even in asymmetric dielectric environments. Nanoparticle arrays used for photovoltaics are by design almost always placed near the high-index solar cell materials, however, the particle size is often large to ensure sufficient radiative efficiency , so it may not be trivial as to whether strong diffractive coupling occurs. As may be appreciated by the discussion above the complexity of the optical interactions in periodic nanoparticle arrays on solar cells makes the identification of the key mechanisms a challenge. This motivates the need to elucidate the role of diffractive coupling in arrays of metal nanoparticles for plasmon-enhanced photocurrent generation.
3. Experimental methods
The samples consist of Al nanoparticles placed on top of a ∼40 nm SiO2 spacer layer on a Si thin-film test solar cell. The thin film Si test solar cells were synthesized by epitaxial growth of a 700 nm boron doped p-type Si layer (1 × 1017 B/cm3) on top of a highly Sb doped n-type Si subtrate (2 × 1018 Sb/cm3) by use of molecular beam epitaxy (MBE). A 200 nm intrinsic Si layer was grown between the p-type layer and the substrate in order to extend the pn-junction electric field. In order to ensure a good conductivity in the top layer to the electrodes, a 100 nm thick boron doped p+ type (1 × 1019 B/cm3) layer was grown on top of the p-type layer. The details of the growth parameters have been described elsewhere . Aluminum electrodes were formed on the front- and backsides of the cells by subsequent metal evaporation through an electrode pattern mask. The thin film nature of the cell arise from the fact that electron-hole pairs are only effectively collected from the p-type layer, the intrinsic layer, and from within one diffusion length (∼ 10 μm) from the interface into the substrate. From an optical viewpoint, however, the use of the Si substrate means that significant back-reflections only occur from the back-side of the thick substrate and hence no guided modes will be involved in the interactions, which simplifies the analysis. The SiO2 spacer layer was deposited on the test-solar cells by rf-magnetron sputtering using a commercial sputtering system , and the thickness of the layer was determined from reflectance measurements. The investigated Al structures do not represent an optimized configuration with respect to photovoltaics, since the scope of this work is to demonstrate the effect of diffractive coupling on the photocurrent collection properties.
The aluminum nanoparticle shape was defined using electron beam lithography (EBL) in a PMMA resist which was spin-on deposited on the surface of the cells. The aluminum nanoparticles were then formed by thermal evaporation of aluminum and subsequent lift-off in acetone. Two samples were made with aluminum particles in two different configurations, respectively. In one configuration the particles were placed in a periodic 2D square array with a pitch of 400 nm, and in the other sample the particles were placed in a quasi-random array with the same areal density of particles as in the periodic array. The random pattern was made by generation of a random set of coordinates followed by a selection routine that ensured a minimum center to center distance of 280 nm between particles in order to prevent strong proximity effects during EBL exposure. Although this distribution may not be random in the strict mathematical meaning of the word, any long-range order is eliminated; thus, with respect to the optical coupling studied here the distribution can be considered random. The nanoparticle patterns were in areas of 2×2 mm2 consisting of multiple write-fields with dimensions of 100 × 100 μm2, which each contained 250 × 250 nanoparticles placed either in the periodic or random pattern. The shapes and particle profiles were investigated using scanning electron microscopy (SEM). Characteristic SEM images of the structures are shown in Fig. 1. As can be seen from the tilted SEM images shown in the insets the particles are disk shaped, with a slight narrowing of the particle diameter towards the particle top, which is ascribed to a slight narrowing of the EBL defined holes in the resist during Al deposition. The diameters of the particles were determined from analysis of the SEM images to be ∼ 155 nm, and the height determined from AFM measurements were ∼ 115 nm in both the periodic and the random array.
Polarization resolved photocurrent measurements were made at normal incidence as well as for variable angles of incidence using a set-up equipped with a Keithley 6517B electrometer, an Oriel MS257 monochromator and a wire grid polarizer. The external quantum efficiencies (EQE) of the test-solar cells were obtained from the photon flux which was measured with a Newport 818-UV photodiode with calibrated quantum efficiency in the 300–1100 nm spectral range. Measurements of the angular dependence of the photocurrent were made by rotating the sample stage with respect to the incident beam around the y-axis (see Fig. 1 for the orientation). The polarization dependent total reflectance (specular and diffuse) was measured using a Perkin Elmer Lambda 1050 double beam spectrophotometer fitted with an 150 mm integrating sphere and a wire grid polarizer. The polarization dependent total reflectance was measured at an 8° angle of incidence in the spectral range of 300–1200 nm relative to a Spectralon SRS-99 reflectance standard . The 8° angle of incidence, which is used in most integrating sphere reflectance accessories, ensures that the specularly reflected beam is captured within the integrating sphere.
4. Results and discussions
Figure 2 shows the measured external quantum efficiencies (EQE) for normal incidence illumination for the periodic nanoparticle array (blue solid lines) and for the random array (red dashed lines), as well as for a reference sample with the same SiO2 layer but without nanoparticles. In the figure data for both s-polarization (top) and p-polarization (bottom) are shown and as can be seen, the normal incidence measurements for a given sample are similar for the two polarizations as expected.
A distinct increase in the EQEs for the periodic array relative to the random one for both polarizations can be concluded in the wavelength range from 400 to 800 nm. More insight into this increase can be obtained from the relative photocurrent or gain, derived by normalizing the measured photocurrent for the nanoparticle samples to the photocurrent measured for the reference sample. The result is shown in Fig. 3 for s-polarization (top) and for p-polarization (bottom) for the periodic array (blue solid lines) and the random array (red dashed lines) for normal incidence light. In the case of random particles a region of photocurrent enhancement is observed at wavelengths larger than ∼ 550 nm, whereas a slight reduction is observed at shorter wavelengths. In Fig. 3 two arrows are inserted in each subplot to indicate the calculated spectral positions of a dipole like resonance near λ ≈ 600 nm and an additional resonance near λ ≈ 370 nm in a single Al nanodisk. The shown spectral positions are derived from finite difference time domain (FDTD) calculations of the scattering cross section of a single Al nanodisk to be discussed later in the paper. The position of the dipole-like resonance can be seen to coincide with the Fano-like profile near λ ≈ 600 nm in the gain curve for the random array. These observations are consistent with previous observations of Fano-like photocurrent enhancement profiles with metal nanoparticles on the front side of solar cells [4, 6, 9].
The Fano-like shape has been ascribed to destructive interference between the incident light and the light scattered from the particles  at wavelengths below the plasmon resonance wavelength, and constructive interference at larger wavelengths. In the case of the periodic array the gain profile resembles that of the random array at wavelengths above ∼800 nm, whereas an additional Fano-like shape is observed at shorter wavelengths near 400 nm; this could indicate that an additional resonance is active in the spectrum of the periodic array.
For both samples the photocurrent enhancement decreases between ∼750–900 nm, which is likely to be due to ohmic damping in the Al nanoparticles related to the inter-band transitions of Al at ∼ 1.5 eV .
In order to mimic the condition of the reflectance measurements to be described in the following, the gain of the periodic array measured at an angle of incidence of 8° is also shown in Fig. 3 (dash-dotted magenta lines). While the gain profiles for the periodic array at normal incidence are similar for both polarizations as expected, at an angle of 8° the additional Fano-like shape near 400 nm has shifted and changed to two fainter bumps near ∼460 nm and ∼530 nm for p-polarization but not for s-polarization. The measured reflectance from the two nanoparticle arrays and from the reference is shown in Fig. 4 for both polarizations. Substantial reductions of the reflectance from the structures with nanoparticles relative to the references are obvious for both arrays and polarizations. However, it is apparent that the reduction in reflectance in the visible spectral range is not as strong for the random array as for the periodic, which is consistent with the observations of the photocurrent enhancement. The periodic array reflectance differs in the visible spectral range for s- and p-polarization: For s-polarization a single sharp dip is observed at 400 nm, while for the p-polarization this dip is replaced by fainter bumps at ∼460 nm and ∼530 nm. This is consistent with the polarization dependence of the gain measured at the angle of 8°. The change in the optical measurements between the 0° and 8° angle of incidence resembles the strong angular dependence of Rayleigh-Wood anomalies , and the similarity of the spectral position of the dip in the p-polarized reflectance at 400 nm with the lattice pitch of 400 nm in the periodic array indicates that the structural properties of the periodic lattice is linked to the strong additional Fano-like shape observed in the photocurrent enhancement. To further investigate the influence of the periodic array on the photocurrent enhancement, we measured the photocurrent for both s- and p-polarization at six different angles of incidence for the periodic and random arrays. In order to emphasize the role which the particle distribution plays in the photocurrent, the measured photocurrent for the periodic array is plotted relative to the photocurrent measured for the random array in Fig. 5 for both p-polarization (blue solid lines) and s-polarization (red-dashed lines). The wavelength positions of the Rayleigh-Wood anomalies calculated from Eq. (1) for a periodic array with pitch 400 nm in air are included in each of the subplots as vertical lines: They correspond to the (±1,0) and (0,±1) (black), the (−1,±1) (blue) and (−2,0) (red) Rayleigh-Wood anomalies. Calculations from Eq. (1) using SiO2 values for the refractive index of the substrate n2 did not show correlation with the measurements and are not shown.
At normal incidence (the top subplot) the enhancement for the periodic array relative to the random array is found to be almost identical for the two polarizations as expected. Moreover, the main enhancement is at wavelengths just above the (±1,0) and (0,±1) Rayleigh-Wood anomalies, while a clear reduction is observed at wavelengths below. At an angle of 20°, an additional clear Fano-like shape has appeared near 530 nm in p-polarization and it is seen to clearly correlate with the calculated position of the (−1, 0) Rayleigh-Wood anomaly. A similar but faint Fano-like shape is hinted at the same spectral position in the s-polarization measurements. At larger angles of incidence this high-wavelength Fano-shape becomes more pronounced for s-polarization, while at the same time contributions from the (−1,±1) and (−2,0) diffraction orders also appear at smaller wavelengths, which also correlate with Fano-shapes in the relative photocurrent. The correlation of the measurements with the calculated Rayleigh-Wood anomalies for a lattice in air indicates that the diffractive coupling is mediated via the air superstrate.
We note that the measurements for p-polarization shown in Fig. 5 at an angle of 8° display a somewhat more complicated spectral shape in which the Rayleigh-Wood anomaly at 456 nm coincides with a shoulder-like feature in the relative photocurrent instead of a Fano-resonance as observed at larger angles of incidence. Moreover, the s-polarized measurements do not seem affected by the (−1,0) Rayleigh-Wood anomaly .
The connection of the optical properties with the Rayleigh-Wood anomalies was further corroborated by finite difference time-domain (FDTD) calculations shown in Fig. 6. The calculations are performed using the commercial three dimensional FDTD solver provided by Lumerical . In all the calculations a normal plane wave is incident from the top onto a periodic array of Al nanodisks placed on a 40 nm thick SiO2 film on top of a Si substrate. The optical constants for Al, Si, and SiO2 are all taken from Ref.  (the handbook of Palik) and fitted using the routines provided by Lumerical. As in the experiments we choose the height and diameter of the nanodisks to be 115 nm and 155 nm, respectively. In order to perform the calculations a unit cell with periodic boundary conditions on the sides, and perfectly matched layer boundary conditions on the top and bottom is chosen. The top panel of Fig. 6 shows the calculated reflectance for five different array pitches (400 nm to 700 nm in steps of 100 nm) and for a reference without the nanoparticles. The bottom panel of Fig. 6 shows the total power that is coupled into the Si substrate, which can be considered an ideal external quantum efficiency (EQE), again for five different array pitches and a reference without the nanoparticles.
The calculated reflectance from a periodic array of 400 nm pitch is in good agreement with the measured reflectance for the s-polarization shown in Fig. 4 (top). Moreover, the strong dip in the calculated reflectance can be seen to follow the position of the normal incidence (±1,0) and (0,±1) Rayleigh-Wood anomalies which occur at the array pitch value. The lattice pitch also has a profound influence on the calculated idealized EQE shown in the bottom part of Fig. 6, where a distinct increase in the power coupled into the silicon substrate is observed near the pitch values for the different arrays.
It can be seen from Fig. 5 that the photocurrent in the periodic array relative to that of the random array is lifted at the high wavelength side of the (−1,0) Rayleigh-Wood anomaly, but is reduced at wavelengths below the anomaly. However, it is interesting to note that part of the reduction region extending at the low-wavelength side of the (−1,0) anomaly seems to be compensated by the enhancement associated with the (−1,±1) Rayleigh-Wood anomaly which shifts towards larger wavelengths and increases in strength for larger angles of incidence as can be seen in Fig. 5.
As noted previously, it may not be trivial as to whether the strong diffractive coupling will play a dominant role in the presence of a high index substrate as in the case of plasmonic arrays placed near solar cells . However, the experimental observations of Fig. 5 clearly show that the photocurrent enhancement observed in the periodic Al nanoparticle array relative to the random array is governed by diffractively coupled collective modes related to the Rayleigh-Wood anomalies, and that this enhancement is strongly dependent on the angle of incidence.
The fact that for normal incidence light the coupling via the (±1,0) and (0,±1) anomalies in the periodic array extends the photocurrent enhancement region down to wavelengths of 400 nm shows that the diffractive coupling can be a useful, additional design principle. Thus, apart from the particle shape, material and dielectric surroundings [7, 8], the effect of lattice pitch on the optical response of the particles can be used to tailor the scattering properties of metallic nanoparticle arrays for improved photovoltaics. The role of the interface on the strong lattice coupling also introduces an additional consideration regarding the thickness of the dielectric spacer layer [7, 29, 30]. As suggested by Spinelli et al. a reduced thickness leads to a redshift and a less favorable gain profile. However given that the spacer layer also may affect the diffractive coupling , the role of the dielectric spacer layer thickness can be manyfold.
The observations that the periodic array is superior to the random array, may be specific to the structure investigated here, since the strength of the lattice resonances, apart from the nanocrystal size and the detailed layer structure , depend on the spectral overlap of the single particle plasmon resonance with the lattice resonances [15, 18]. In order to show the extent of the spectral overlap between the Rayleigh-Wood anomalies and the single particle resonances we calculated the scattering cross section for a single Al nanodisk using FDTD and the result can be seen in Fig. 7 where the scattering cross section normalized to the cross-sectional area of the nanodisk is shown. The calculation is performed using the ”Total-Field Scattered-Field” source provided by Lumerical , where we calculate the scattering cross section by placing frequency domain power monitors in the scattered-field region of the source. All parameters are the same as in Fig. 6, except that we now use perfectly matched layers on all boundaries of the simulation volume which is increased to 1 μm × 1 μm × 1.35 μm. The Al nanodisk can be seen to scatter strongly almost throughout the investigated spectral range. The distinct peak near λ ≈600 nm is likely due to a dipole-like resonance in the particle whereas the peak-structure near λ ≈370 nm may be a quadrupole-like resonance in line with the assignments of resonances in similar sized Ag nanoparticles in Ref. . By comparison with Fig. 5 it can be seen that the calculated spectral positions of the Rayleigh-Wood anomalies coincide with the broad scattering spectral range of the single nanodisk, showing that in this case the spectral overlap of the single particle resonance and the Rayleigh-Woods anomaly is maintained almost in the entire spectral range investigated. Thus, with lattice pitches in the range of visible wavelengths and broad plasmon resonances aimed for photocurrent enhancement in the solar spectrum, such overlap might occur, if not at normal incidence then at higher angles, where Rayleigh-Wood anomalies can be shifted towards the plasmon resonance.
Photocurrent enhancement properties of Al nanoparticles placed on top of a silicon diode in periodic and random arrays have been compared. It is found that the photocurrent enhancement is larger in the periodic array relative to the random array in a large part of the solar spectrum, due to an additional Fano-like resonance, which lifts the photocurrent enhancement of the periodic array relative to the random. From the analysis of the angular dependence of the photocurrent in the periodic array relative to the random array combined with FDTD calculations it is demonstrated that this additional Fano-like resonance is caused by diffractive coupling in the periodic array of Al-nanoparticles, and that the observed enhancement is very sensitive to the angle of the incident illumination. This shows that diffractive coupling can be an important design parameter in periodic arrays of large metal nanoparticles to be used for improved light coupling into silicon.
The authors greatly acknowledge the financial support from the project Localized surface plasmons and silicon thin-film solar cells-PLATOS financed by the Villum Foundation.
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