Improving dielectric nanoresonator array coatings for solar cells

Abstract

Antireflection coatings based on dielectric nanosphere arrays are discussed in application to photovoltaic materials including silicon and gallium arsenide. We perform macro- and nanoscale characterization and finite-difference time-domain calculations demonstrating the enhanced optoelectronic properties. A significant absorptivity enhancement is achieved due to the collective resonant coupling of excited whispering gallery-like modes and thin-film interference effects. The resonant coupling is masked in macroscale measurements by the size variation of nanospheres, but it is clearly seen through imaging photocurrent at the nanoscale with near-field scanning photocurrent microscopy. The resonant coupling can be effectively tuned by the material, configuration, or size of nanospheres. Hybrid coatings combining nanospheres of different materials yield the highest efficiency gain, more than 30 %. We also evaluate an impact of manufacturing defects such as double layer formation. While the performance degrades, the antireflection coating still offers marked improvement in comparison with bare cells.

TOC image

We present an advanced light management and an efficiency enhancement of solar cells using a variety of dielectric nanospheres-based antireflection coatings. By optimally selecting size, materials, and/or combinations of nanospheres, optoelectronic properties can be improved by as much as 30 %. The physical origin of the enhancement is clearly established using macro- and nanoscale measurements and calculations.

1. Introduction

Increasing light absorption within solar cells has been one of the most significant pathways to achieve high efficiency. Antireflection coatings (ARCs) based on dielectric thin-films atop active materials of solar cells with controlled refractive index, thickness, or multilayer structures can suppress light reflection over visible wavelengths.^[1–3] However, such ARCs often require high temperature vacuum processes adding significant manufacturing and deployment costs. Various nanoscale surface patterning techniques have been suggested as lower costs methods to improve light absorption within active material of solar cells due to light trapping schemes.^[4–11] However, such approaches may lead to a negative impact on solar cells’ performance as they can increase surface recombination and decrease the open circuit voltage. To address this issue, light management techniques using metal nanostructures,^[12–19] dielectric resonators,^[20–30] or dielectric nanomaterials^[31–38] that do not require a surface processing have been introduced. A recent example of inexpensive ARC uses cellulose fibers that are earth abundant and environmentally friendly materials.^[34–37] Specially treated transparent cellulose paper applied atop solar cells results in more than 20 % enhanced power conversion efficiency due to the combined effect of gradual index change and path length enhancement.^[35] Furthermore, the surface texturing of the transparent paper leads to angle-insensitive optical behaviors, which eliminates the need for costly mechanical solar trackers.^[35–37] However, further durability study is needed for commercial applications.

Another promising example of a new class of ARC is based on nanosphere arrays made of earth abundant, environmentally friendly, and robust dielectric resonating nanospheres. Light absorption and photocurrent are increased due to collective optical couplings of excited resonances within nanosphere arrays.^{[26–30, 39, 40]} The recent progress of the manufacturing of dielectric nanospheres increases their potential for future applications on photovoltaics (PVs). However, there are some factors hinder the practical applications of such ARCs on commercial PVs. First, despite its some attractive characteristics, the performance enhancements with the dielectric nanosphere-based ARC are still lacking compared to the conventional thin-film-based ARC technologies. Second, most of studies made so far are lack of nanoscale experimental demonstration of resonant couplings as they have been made at macro-/microscale. Therefore, we do not have sufficient understanding of physical origins of enhancements. Third, to further improve the optoelectronic properties with such ARCs, more studies on the effect of size, material, or configuration of dielectric nanosphere arrays should be made. Next, to fully test its versatility and usefulness, studies on various PV materials should be made.

In this paper, to address these issues, we demonstrate optical resonant couplings of nanosphere arrays and the resulting photocurrent enhancements of various solar cell materials including silicon (Si) and gallium arsenide (GaAs) at different length scales from macroscale to nanoscale. We also show that the wavelengths of resonance excitation can be tuned by selecting different size, material, and/or configuration of dielectric resonator arrays. We then suggest novel hybrid configurations of dielectric nanosphere arrays that can offer potentially higher optoelectronic properties than those from thin-film-based ARCs. While close-packed monolayer arrays provide marked enhancements, assembly defects such as voids and multilayer patches can be present in practical ARC applications. Therefore, the double layer arrays are also investigated by macro- and nanoscale experiments.

2. Results and Discussion

We first deposit close-packed 700 nm silicon dioxide (SiO₂) nanosphere arrays as antireflection coatings on a GaAs solar cell to improve optoelectronic properties. We employ the Meyer rod rolling technique to deposit nanospheres, which is illustrated in Fig. 1a. With a proper concentration of water-based SiO₂ suspension and a Meyer rod size, we can deposit either a single layer or multiple layers of nanosphere arrays by pulling the Meyer rod across the GaAs substrate. An inset scanning electron microscope (SEM) image in Fig. 1a shows a part of the deposited monolayer SiO₂ nanosphere arrays atop a GaAs solar cell. The size distribution of the deposited SiO₂ nanospheres determined by image analysis is shown in the inset histogram (mean diameter: 697 nm, standard deviation: 80 nm). Calculations are made based on the finite-difference time-domain (FDTD) method. Figure 1b shows the simulation structures on each plane in a Cartesian coordinate system. The white box represents a unit cell repeated in the model. Blue lines and red lines at the boundaries of the unit cell represent periodic boundary conditions and perfectly matched layer boundary conditions, respectively. Bloch boundary conditions instead of periodic boundary conditions are used if the light is propagating at non-normal incidence (see Experimental Section for more details). Information of refractive index for each material for calculations is adopted from Ref. [41]. Transverse electric (TE) and transverse magnetic (TM) incident polarizations at normal incidence in our simulation structures are defined in Fig. 1b.

Figure 1.

(a) Deposition of ARC using the Meyer rod rolling technique. A droplet of water-based SiO₂ nanosphere suspension is spread onto a solar cell, and a Meyer rod is pulled across the surface to form close-packed nanosphere arrays. Inset: right - SEM image of deposited monolayer 700 nm SiO₂ nanosphere arrays. Scale bar is 2 μm; left - size distribution of the deposited nanospheres. (b) Simulation structures used for FDTD calculations in projections to orthogonal planes. Gray circles indicate SiO₂ nanospheres, green box represents a solar cell active material, and the white box indicates the unit cell. Blue lines and red lines respectively represent periodic and perfectly matched layer boundary conditions used in the simulations. Two incident polarizations at normal incidence and the direction of non-normal incidence in calculations are also defined in the schematic. Schematic is not to scale.

To test the usefulness of the monolayer nanosphere arrays as ARCs on photovoltaics (PVs), we calculate light absorptivity of a bare GaAs solar cell (see Fig. 2a) and the cell with monolayer 700 nm SiO₂ nanosphere arrays on top (see Fig. 2b and c). FDTD calculations are made over the operational wavelengths of a GaAs solar cell (λ = 400 nm to 860 nm) and a wide range of angles of incidence (θ = 0° to 55°). With the addition of monolayer close-packed 700 nm SiO₂ nanosphere arrays atop the GaAs substrate, absorptivity is significantly increased both for TE and TM incident polarizations (see Fig. 2b and c). For both polarizations, broadband and narrowband spectral features are observed. Broadband features are centered at wavelengths of ≈ 480 nm and ≈ 685 nm at normal incidence for both polarizations evolving into neighboring wavelengths as incident angle increases. Narrowband features correspond to the excitation of well-defined optical modes at specific wavelengths within the close-packed nanosphere arrays dispersing as a function of incident angle.

Figure 2.

(a–c) Calculated absorptivity of (a) a bare GaAs substrate and that of a GaAs substrate with close-packed monolayer 700 nm SiO₂ nanosphere arrays for (b) TE and (c) TM incident polarization. Calculations are based on FDTD methods and made as a function of both incident angles (θ = 0° to 55°) and wavelengths (λ = 400 nm to 860 nm). (d–e) Measured absorptivity of (d) a bare GaAs solar cell and (e) that of a GaAs solar cell with SiO₂ nanospheres atop. Measured absorptivity is determined as a function of both incident angles (θ = 10° to 55°) and wavelengths (λ = 400 nm to 860 nm), and measurements are made using an integrating sphere with monochromatic light from a xenon arc lamp. (f) Normalized electric field intensity profiles (|E|²) within nanospheres at selected wavelengths for both incident polarizations at normal incidence. Scale bars are 250 nm.

To investigate the physical origins of the absorptivity enhancements with this ARC, we examine the normalized electric field intensity profiles within nanospheres at the wavelengths corresponding to the broadband and narrowband features at normal incidence shown in Fig. 2b and c (see Fig. 2f). At wavelengths of 480 nm and 685 nm (broadband features in Fig. 2b and c), interference patterns are observed for both incident polarizations. The deposited nanosphere layer effectively acts as a thin-film ARC enhancing absorptivity within the GaAs substrate due to the thin-film interference effect. Meanwhile, at wavelengths of 635 nm and 798 nm (narrowband features in Fig. 2b and c), we observe strong excited modes around the shell of the nanosphere resembling whispering gallery modes.^[27] However, at a wavelength of 850 nm, no enhanced fields are observed within nanospheres in agreement with data in Fig. 2b and c. We refer to the excited resonance modes within nanospheres as whispering gallery-like modes to differentiate from the pure whispering gallery modes that exist only if the surrounding media is sufficiently homogeneous.^[42–47] Here, nanospheres are in contact with a high index substrate (e.g., GaAs), with their neighbors, and with air yielding a very asymmetric surrounding medium. Thin-film interference patterns and excited whispering gallery-like modes within nanospheres explain broadband and narrowband absorptivity enhancements observed in Fig. 2b and c, respectively.

We then experimentally determine light absorptivity of a GaAs solar cell with and without nanosphere ARCs (see Fig. 2d and e). Macroscale measurements are conducted using an integrating sphere coupled with a monochromatic light. The light spot size on samples during measurements is ≈ 0.5 cm². Due to the geometrical constraint of the integrating sphere, we determine the light absorptivity from an incident angle of 10° (see Experimental Section for more details). Compared to a bare GaAs solar cell (see Fig. 2d), significant absorptivity enhancements are observed with the ARC (see Fig. 2e). The broadband features predicted by FDTD calculations are prominent in Fig. 2e. However, the narrowband features due to the excited whispering gallery-like modes are not clearly visible in the macroscale measurements. We attribute the lack of the narrowband enhancements to the non-uniform size of nanospheres used in the real sample as shown in the inset to Fig. 1a. The size distribution of nanospheres is rather broad resulting in a spectral spreading and smearing of the narrowband resonance modes. To evaluate the effect of the inhomogeneity, we calculate absorptivity of cells with nanosphere diameters from 630 nm to 770 nm as a function of wavelength and average these with the weights in accordance with the size distribution in Fig. 1a (see Fig. S1 of the Supporting Information for more details). The final result, the absorptivity averaged over the entire operational spectrum of a GaAs solar cell, is ≈ 70.87 % for the non-uniform nanosphere arrays that is comparable to the one of a close-packed equal-size 700 nm nanosphere arrays (≈ 70.82 %). While the narrowband features become smaller and broader merging with broadband features in the non-uniform case, the total absorptivity enhancement is conserved showing the usefulness of this ARC.

Up to now, only close-packed nanosphere arrays with high surface coverage have been studied.^{[26–30, 39, 40]} In practice, however, an ARC can contain defects such as voids and multilayer patches that might decrease its usability. While the losses from voids can be accounted for in a straightforward manner, the effects of multilayers cannot be unambiguously modeled and should be addressed experimentally. Controlling the concentration of SiO₂ suspension and the Meyer rod size, we have made coatings with large single and double layer patches. As seen in the inset SEM images of Fig. 3, the second layer is not as densely and regularly packed as the lower layer complicating its modeling. Thus, we experimentally determine optoelectronic properties of a GaAs solar cell with and without these double-layer nanosphere arrays. First, we measure macroscale light reflection from the sample using an integrating sphere as described above (see Fig. 3). The determined external quantum efficiency (EQE), the ratio of the collected electron-hole pairs to the number of incident photons, is also shown in Fig. 3. EQE is improved by more than 20 % for the operational wavelengths range in the case of a single layer. For the double layer, the EQE is also noticeably better than that of the bare sample. However, in comparison with the single layer ARC, the EQE is reduced over the entire spectrum and the broadband features are shifted and flattened. The red-shift of broadband features is caused by the increased effective thickness of the double layer ARC. Additionally, the air gap between the two layers leads to an index mismatch, which results in increased light scattering and reduced EQEs.

Figure 3.

Experimentally determined light reflectivity and EQE for a bare GaAs solar cell (blue and red dotted lines, respectively), a cell with monolayer SiO₂ nanosphere arrays (blue and red lines with closed circles, respectively), and a cell with double layer SiO₂ nanosphere arrays (blue and red lined with open squares, respectively). Inset: SEM images of monolayer and double layer nanosphere arrays. Scale bars are 1 μm.

To experimentally detect the existence of the resonance couplings due to the excitation of whispering gallery-like modes not seen at macroscale, we measure photocurrent locally using near-field scanning optical microscopy (NSOM) setup. An NSOM probe is a sharpened metal-coated optical fiber with a small output hole (≈ 200 nm) attached to a tuning fork. NSOM probe is scanned in a non-contact atomic force microscopy (AFM) mode injecting light in the near-field, and photo-generated current is measured from the sample (see Fig. S2 of the Supporting Information for more details). The black solid box of the SEM image in Fig. 4a shows the scanned area, and the topography of the scanned area is shown in Fig. 4b. With the monolayer ARC, we observe a substantial photocurrent enhancement at the wavelength of 635 nm corresponding to the excitation of the whispering gallery-like modes (see Fig. 4d). The photocurrent enhancement is the strongest near the center of nanospheres, and it has the highest value for nanospheres with a diameter close to 700 nm. At the wavelength of 850 nm, however, no photocurrent enhancement is observed in agreement with the FDTD calculations in Fig. 2b and c (see Fig. 4e). We note that the illumination conditions here are different from those of the macroscale measurements. To properly model the unpolarized near-field light injection in NSOM experiments, we use three orthogonal point dipole sources in three-dimensional system, and the FDTD simulation results are averaged over the three different dipole orientations. FDTD calculations of normalized electric field intensity profiles at the interface between the nanosphere and the GaAs substrate shown in the insets to Fig. 4d and e qualitatively describe the experimentally demonstrated photocurrent enhancement or its absence at the corresponding wavelengths in the NSOM photocurrent measurements. Examining a double layer patch, we also observe a photocurrent enhancement, in agreement with the macroscale measurements. AFM topography of the double layer patch and the resultant photocurrent imaging are shown in Fig. 4c and 4f, respectively. At the wavelength of 635 nm, the photocurrent is enhanced compared to the bare GaAs but the enhancement is smaller than that obtained with the monolayer arrays (see the upper region in Fig. 4c and f), both due to the nanosphere size variation and due to a sub-optimal coupling between the layers.

Figure 4.

Nanoscale NSOM photocurrent measurements of a GaAs solar cell with SiO₂ nanosphere arrays. (a) An SEM image showing the area with and without monolayer SiO₂ nanosphere arrays. A black solid box shows the scanned area. (b) AFM topography of the area in the black solid box in (a). (c) AFM topography of another area with double layer SiO₂ nanosphere arrays. (d-e) Photocurrent enhancement (I_E) mappings over the monolayer arrays in (b) at wavelengths of (d) 635 nm and (e) 850 nm. (f) Photocurrent enhancement (I_E) mapping over the double layer nanosphere arrays shown in (c). Scale bars are 1 μm. Insets: normalized electric field intensity profiles (|E|²) at the interface between the nanosphere and the GaAs substrate obtained from FDTD calculations using point dipole sources. White dotted lines represent the circumference of the nanosphere. Scale bars in insets are 500 nm.

Having demonstrated the usefulness of the SiO₂ nanosphere arrays-based ARC and established the validity and the predictive capability of the model, we apply the same approach to different photovoltaic material to test the versatility of the ARC. We select Si solar cells as Si is the most popular and dominant material in the photovoltaic market, and therefore broader practical potential of this ARC can be analyzed. Also, we can test enhancement through the resonant coupling in broader wavelength range as Si has longer operational spectrum than GaAs. From macroscale experiments and calculations, we determine the enhancement of the optical absorption within a Si substrate. The effect of different sizes of SiO₂ nanospheres on optical resonances is also investigated to find the optimal configuration of this ARC for a Si solar cell. The same deposition method, the Meyer rod rolling technique, is employed for nanosphere deposition. Measurements and calculations are performed for both a bare Si substrate and a cell with SiO₂ nanosphere arrays having three different diameters (500nm, 700nm, and 1000 nm) atop a Si substrate. Measurements are made as a function of wavelength (λ = 400 nm to 1000 nm) and incident angle (θ = 10° to 65°) using the same measurement technique used for the GaAs sample. Calculations (λ = 400 nm to 1000 nm, θ = 0° to 65°) are again based on the FDTD method. Figure 5a, d, and g show experimentally determined absorptivity enhancement with SiO₂ nanosphere arrays of three different diameters (500nm, 700nm, and 1000 nm, SEM images in the inset to corresponding figures). As already shown with 700 nm SiO₂ nanospheres in Fig. 1, both 500 nm and 1000 nm nanospheres have a finite size distribution: 502 nm ± 75 nm and 994 nm ± 87 nm, respectively (see Fig. S3 of the Supporting Information for more details). Absorptivity enhancement is determined by normalizing light absorption of Si substrate with nanosphere arrays on top to that obtained from a bare Si substrate. Similar to the GaAs case, the measured absorptivity enhancements in Fig. 5a, d, and g are mainly broadband dispersing with incident angle (starting from λ ≈ 480 nm and ≈ 800 nm for the structure with 500 nm SiO₂ nanospheres, λ ≈ 500 nm and ≈ 700 nm for the structure with 700 nm SiO₂ nanospheres, and λ ≈ 500 nm, ≈ 550 nm, ≈ 700 nm, and ≈ 900 nm for the structure with 1000 nm SiO₂ nanospheres at normal incidence), and the narrowband features are smeared due to the distribution of size (see Fig. S1 of the Supporting Information for more detail). Meanwhile, calculated absorptivity in Fig. 5b, e, and h demonstrates both broadband and narrowband enhancements. A simplified thin-film model in Fig. 5c, f, and i can explain broadband enhancements observed in experiments and calculations. The effective refractive index is calculated by averaging refractive indices of air and SiO₂ in accordance with the geometric fraction of two materials (see the inset schematic in Fig. 5): the effective refractive index near the top and the bottom is close to that of air (n = 1) and has the highest value, equal to that of SiO₂, at the center (n = 1.5). The calculated normalized electric field intensity profiles under TM incident polarization of light at the wavelengths corresponding to the sharp absorptivity peaks with SiO₂ nanospheres in Fig. 5b, e, and h (λ = 455 nm and 573 nm for 500 nm SiO₂ nanosphere arrays, λ = 635 nm and 798 nm for 700 nm nanosphere arrays, and λ = 906 nm for 1000 nm nanosphere arrays; each resonant peak is marked with numbers from 1 to 5, respectively) are shown in Fig. 5j. The strong lobes around nanosphere walls (marked with white dotted lines) are indicative of the excited resonances originated from the whispering gallery modes.^[27] Whispering gallery-like modes under TM incident polarization observed in 500 nm nanospheres (number 1 and 2 in Fig. 5b) shift to longer wavelengths as the diameter of SiO₂ nanosphere increases (number 3, 4 in Fig. 5e, and number 5 in Fig. 5h). Thus, the nanosphere size can be used to tune the optical responses at specific wavelength ranges in optical sensor applications.

Figure 5.

Measured absorptivity enhancement as a function of both incident angles (θ = 10° to 65°) and wavelengths (λ = 400 nm to 1000 nm) with (a) 500 nm, (d) 700 nm, and (g) 1000 nm SiO₂ nanosphere arrays atop a Si substrate. Absorptivity enhancement is determined by normalizing the absorptivity determined from the structure with SiO₂ nanosphere arrays with that obtained from a bare Si substrate. Inset SEM images show depostied (a) 500 nm, (d) 700 nm, and (g) 1000 nm SiO₂ nanospheres on a Si substrate, respectively. Scale bars in inset SEM images are 2 μm. Calculated absorptivity enhancement as a function of both incident angles (θ = 0° to 65°) and wavelengths (λ = 400 nm to 1000 nm) with close-packed (b) 500 nm, (e) 700 nm, and (h) 1000 nm SiO₂ nanosphere arrays atop a Si substrate. Absorptivity enhancement as a function of both incident angles (θ = 0° to 65°) and wavelengths (λ = 400 nm to 1000 nm) with an effective thin-film having a thickness of (c) 500 nm, (f) 700 nm, and (i) 1000 nm. In this thin-film model, the refractive index of the thin-film varies depending on the distance above the Si substrate (n = 1 to 1.5) to mimic the geometry of nanosphere arrays. Inset schematics (not to scale) above (a), (b), and (c) describe the cell structure. (j) Normalized electric field intensity profiles within SiO₂ nanospheres under transverse magnetic incident polarization when whispering gallery-like modes are excited. Each profile corresponds to numbered data point (from 1 to 5) in (b), (e), and (h). A white dotted line in (j) indicates SiO₂ nanospheres and a white solid line indicates an interface between SiO₂ nanospheres and a Si substrate. Scale bars in (j) are 250 nm.

As the absorption spectrum depends on the size of nanospheres, one has to find an optimal size maximizing the efficiency gain from this ARC. For this, we calculate the expected current densities of a Si solar cell under air mass 1.5 global (AM1.5G) illumination conditions varying the diameter of close-packed SiO₂ nanospheres. In this calculation, the spectrally dependent absorption is weighted by the solar irradiance based on the following equation:

$$J={\displaystyle {\int }_{{\lambda }_{\mathit{shortest}}}^{{\lambda }_{E_g}}q\cdot A\left(\lambda \right)\cdot S_{AM1.5G}\left(\lambda \right)d\lambda }$$

where J is the expected AM1.5G solar spectrum-weighted photocurrent density, λ_shortest is the shortest wavelength of the calculation (400 nm), ${\lambda }_{E_g}$ is the wavelength corresponding to the bandgap of Si (1100 nm), q is the charge of an electron, A(λ) is the absorptivity within a Si solar cell, and S_AM1.5G(λ) is the AM1.5G solar irradiance spectrum. Here, we assume a 100 % internal quantum efficiency for the solar cell. Figure 6a shows absorptivity of a Si solar cell as a function of the diameter of close-packed SiO₂ nanospheres atop the Si substrate, and Figure 6b shows its corresponding AM1.5G solar spectrum-weighted photocurrent density. As seen in Fig. 6a, larger diameters of nanospheres lead to red-shifts of the resonance peaks to the longer wavelengths. As the diameter increases, second order resonance peaks are observed at shorter wavelengths within the AM1.5G solar spectrum range that ultimately result in higher photocurrent. Numbered resonance peaks in Fig. 5 are also marked in Fig. 6a. Based on Fig. 6b, we conclude that the optimal diameter of SiO₂ nanosphere arrays for a Si solar cell is ≈ 940 nm with the highest AM1.5G solar spectrum-weighted photocurrent density of ≈ 31 mA/cm².

Figure 6.

(a) Spectrally resolved absorptivity as a function of SiO₂ nanosphere diameter in ARC arrays. (b) Overall short-circuit current density (J_SC) calculated using absorptivity under AM1.5G illumination. The maximum current density is achieved when the diameter is ≈ 940 nm.

The spectral properties of the ARC can be controlled not only by the size but, alternatively, by the refractive index of nanospheres. We compare the absorptivity enhancement of a Si solar cell with three different materials including close-packed 500 nm SiO₂, 500 nm silicon nitride (Si₃N₄), and 500 nm titanium dioxide (TiO₂) nanosphere arrays as shown in Fig. 7a. Among these, the structure with 500 nm Si₃N₄ nanosphere arrays demonstrates the highest absorptivity enhancement over the entire spectrum. The optimum refractive index of a single layer of antireflection coating placed between air and a solar cell is determined by the following expression:

$$n_{\mathit{\text{optimum\_ARC}}}=\sqrt{n_{\mathit{air}}\cdot n_{\mathit{sub}}}$$

where n_air is the refractive index of air, and n_sub is the refractive index of a substrate of a solar cell, yielding the value closest to that of Si₃N₄ when the substrate material is Si. As shown in Fig. 7a, both broadband and narrowband spectral features are affected and can be selectively controlled through the material choice. Further improvement can be achieved through a proper balance between the weak broadband and the strong narrowband enhancements. In this regard, we explore the use of nanospheres made of materials with different refractive indices to increase the number of resonances. We combine 500 nm SiO₂, Si₃N₄, and TiO₂ nanospheres in hybrid arrays and calculate the absorptivity enhancement on a Si solar cell. Three hybrid arrays and their corresponding absorptivity profiles are shown in Fig. 7b. The presence of different materials within the arrays does yield additional resonances and enhances absorptivity beyond that of single material-based arrays, by as much as ≈ 30%, and well beyond a bare Si solar cell (Fig. 7b). The enhancement is much higher as these hybrid combinations support more photonic modes with increased numbers of resonances. The recent progress in making high quality dielectric nanospheres (i.e., SiO₂,^[48] Si₃N₄,^[49] and TiO₂^{[50, 51]}) with nearly equal size and quality will enable such novel coatings in the near future.

Figure 7.

(a) Spectrally resolved absorptivity showing the effect of materials of nanosphere arrays on the solar cell’s performance. Absorptivity determined from a bare Si (black dotted line), a Si cell with 500 nm SiO₂ nanosphere arrays (gray solid line), 500 nm Si₃N₄ nanosphere arrays (blue solid line), and 500 nm TiO₂ nanosphere arrays (orange solid line). Insets (not to scale) show how each combination is constructed. The transparent gray box in the inset indicates a unit boundary for repetition. (b) Spectrally resolved absorptivity for three different combinations of nanospheres. Combinations consist of 500 nm SiO₂, Si₃N₄, and TiO₂ nanospheres. The first combination (combination 1, red solid line) has an equally distributed number of each type of nanosphere, the second combination (combination 2, purple solid line) has more Si₃N₄ nanospheres, and the third combination (combination 3, green solid line) has more TiO₂ nanospheres within a unit boundary. Absorptivity determined from a bare Si (black dotted line), a Si cell with the first combination (red solid line), the second combination (purple solid line), and the third combination (green solid line) of nanosphere arrays on a Si substrate is shown, respectively. AM1.5G solar spectrum-weighted current densities and enhancement from a bare Si cell are determined for all structures. Insets (not to scale) show how each combination is constructed. The gray box in the inset indicates a unit boundary for repetition.

3. Conclusions

Antireflection coatings based on dielectric nanosphere arrays have been modeled, fabricated, and characterized on multiple length scales. Significant absorptivity enhancement is observed with close-packed SiO₂ nanosphere arrays due to the combined effects of excited whispering gallery-like modes and thin-film interference. The light coupling is increased even at steep incident angles demonstrating a wide-angle acceptability of this ARC with a potential of eliminating costly mechanical solar trackers. While the enhancement from excited whispering gallery-like modes is spread out over some spectral range in macroscale measurements due to nanosphere size inhomogeneity, nanoscale photocurrent measurement confirms the existence and the strong photocurrent enhancement through the resonant coupling. While decreased, the overall enhancement remains significant for double layers, demonstrating the robustness the ARC under non-perfect manufacturing conditions. We also show that the spectral properties of the ARC can be controlled by either size or materials of nanospheres for better spectral match with solar spectrum or for tuning of the resonant absorption. By constructing diverse material-combined hybrid nanosphere coatings, more photonic modes are obtained, which can further improve the performance of solar cells. The proposed nanosphere arrays-based antireflection coating, based on a simple, inexpensive, and room temperature process, suggests a route to significantly improve solar cells. Also, this method does not cause the loss of the open circuit voltage, as no direct surface patterning on active materials is required. Therefore, it is an excellent candidate to replace conventional thin-film-based antireflection coatings that require complicated, costly, and high temperature vacuum processes.

4. Experimental Section

Deposition of close-packed nanosphere arrays

The Meyer rod deposition technique is applied to coat nanosphere arrays atop Si and GaAs substrate. Water-based SiO₂ suspension is dropped by a pipette onto the substrate, and a metal wire-wound Meyer rod is pulled across the substrate to deposit close-packed nanosphere arrays. Either by selecting different wire sizes (0.3 mm to 0.61 mm) or by adjusting concentration of SiO₂ suspension, the coverage and the number of total deposited layers can be accurately controlled. A surfactant is used to prevent agglomeration of nanospheres. After the coating process, a mild annealing treatment at 50 °C for 1 min is performed to evaporate the water.

FDTD calculations

Three-dimensional finite-difference time-domain (FDTD) method is applied to calculate optical responses. In our simulation structures, close-packed single material-based nanospheres (i.e., one of among SiO₂, Si₃N₄, and TiO₂) and close-packed multiple materials-combined nanosphere arrays (i.e., combination of SiO₂, Si₃N₄, and TiO₂ nanospheres) are placed atop a Si substrate, and close-packed SiO₂ nanospheres are placed atop a GaAs substrate. The absorptivity within the substrate is calculated by subtracting light reflection of the structure from unity. Plane wave sources at two different incident polarizations are used. At normal incidence, periodic boundary conditions are applied in the horizontal direction of the simulation volume while Bloch boundary conditions are applied at non-normal incidence. We assume that each active material (i.e., Si, GaAs) of solar cells is sufficiently thick and all electron-hole pair generations take place within this layer. For this, we applied a perfectly matched layer boundary condition at the bottom of each active material. Perfectly matched layer boundary condition is also applied to the top of the simulation structure. All calculations were performed to calculate optical properties, and no factors (e.g., doping concentrations, layer thicknesses, carrier mobilities, surface recombination velocities, etc.) to calculate electronic properties were considered. For the calculation mimicking the nanoscale NSOM measurements, dipole sources instead of plane wave sources are used. Three calculations under three dipole sources with orthogonal orientations are performed, and the normalized electric field intensities are then incoherently added. Refractive indices of materials for all calculations are adopted from Ref. [41].

Macroscale optical measurements

Macroscale absorptivity of samples is determined using an integrating sphere, monochromatic light, and relevant optics. A monochromator is connected to a 150 W xenon arc lamp, and the light from the monochromator is passing through relevant optical lenses to form a collimated beam. Samples are positioned in the center of the integrating sphere with a diameter of 15.24 cm and can be rotated for angle dependent measurements. The collimated light enters through an input port of the integrating sphere, and reflected light from samples is collected by a Si photodetector placed at the bottom of the integrating sphere. The measurement geometry limits the range of incident angles to 10° or larger: for angles smaller than 8°, the reflected light will escape directly through the input port of the integrating sphere causing measurement artifacts. The signal from the Si photodetector is measured by a lock-in amplifier. For all measurements, light spot size on samples is ≈ 0.5 cm². For macroscale absorptivity measurements, repeated readings under identical conditions yields maximum measurement variation less than 1%.^[52]

Macroscale electrical measurements

Macroscale external quantum efficiency (EQE) of samples is determined using a monochromator coupled with a 150 W xenon arc lamp, an iris, and relevant optical lenses at normal incidence. Light is landing on samples forming a spot size of ≈ 0.2 cm². Two measurements at each wavelength are performed to determine EQE. First, we measure the incident power on the measurement stage at each wavelength using a Si photodetector with known responsivity to determine the total number of incident photons. Next, we measure the photo-generated current of samples at each wavelength under the same illumination condition. EQEs at each wavelength are obtained by determining the ratio between the number of photo-generated electrons in samples and the number of incident photons obtained from two different measurements. For macroscale EQE measurements, repeated readings under identical conditions yields maximum measurement variation less than 1%.^[52]

Nanoscale photocurrent measurements

A near-field scanning optical microscopy (NSOM) is used to locally probe photocurrent enhancements originating from the excitation of whispering gallery-like modes within nanospheres. A multimode optical fiber (3m in length) is attached to an NSOM probe. The end of the tapered optical fiber coated with metal (20 nm Cr and 200 nm Au) is bent down for local light injection on samples. During a scan, topography and photocurrent are simultaneously obtained. The distance between the end of the NSOM probe and the top of the sample is kept ≈ 10 nm. The NSOM probe has a spring constant of ≈ 15 N/m at a resonant frequency of ≈ 35 kHz. The measured photocurrent is amplified with a low-noise amplifier (a gain of 10⁹ V/A), and is detected with a lock-in amplifier.