Artificial inverted compound eye structured polymer films with light-harvesting and self-cleaning functions for encapsulated III–V solar cell applications

We report the artificial inverted compound eye structured (ICESs) polydimethylsiloxane (PDMS) films with lightharvesting and self-cleaning functions for the enhancement of solar power generation in encapsulated III–V gallium arsenide (GaAs) single-junction solar cells. The ICESs PDMS films are fabricated by facile, simple, and cost-effective soft lithography using sapphire master molds with the CESs consisting of hierarchical nanotextures/periodic microgratings prepared by thermally dewetted gold nanopatterning and subsequent dry etching processes. By attaching the ICESs PDMS film with a hydrophobic surface (i.e., water contact angle (qCA) of 121 ) to the coverglass, the total and diffuse transmittances of the coverglass are simultaneously increased over a wide wavelength range of 350–900 nm, exhibiting higher solar weighted transmittance (SWT) of 94.3% and average haze ratio (Havg) of 67.6% than those of the bare coverglass (i.e., qCA z 32 , SWT z 90.2%, and Havg z 4.1%, respectively). The resulting encapsulated III–V GaAs singlejunction solar cells with the ICESs PDMS/coverglass show an enhanced power conversion efficiency (PCE) of 24.3% compared to the encapsulated solar cell with the bare coverglass (i.e., PCE 1⁄4 22.96%) due to the increased short circuit current density from 26 to 27.64 mA cm , indicating the PCE increment percentage of 5.8%. Moreover, it also exhibits superior device performance at varying angles of incident light. For the long-term self-cleaning effect on the device efficiency, there is no significant variation in the PCE after approximately one month, indicating a low PCE drop percentage of 1.4%.


Introduction
Recently, there has been growing interest for the enhancement of solar energy harvesting in solar cells owing to the energy crisis and environmental issues. To effectively harvest sunlight in solar cells, an efficient antireection layer, which can suppress the surface Fresnel reection losses at the interface between the air and top surface of solar cells over a broad solar spectral range, is vital. [1][2][3] Actually, for practical applications of solar cells, the antireection layer should be considered to reduce the reection at the module level including coverglasses and encapsulants. [2][3][4][5][6][7] However, the conventional dielectric material-based thin-lm antireection layers such as magnesium uorides and porous silicon oxides, which have some drawbacks including durability issues, thermal expansion mismatch, poor or reduced adhesion on certain substrates, sensitivity to thickness variations, and material selection as well as narrow low reection band for incident wavelengths and angles, [8][9][10] may not be suitable under real harsh environments. As an alternative of conventional antireection layers, over the past years, there have been many studies on the efficiency enhancement of solar cells with textured surfaces (i.e., biomimetic micro-or nanostructures) for efficient antireection and light scattering. [11][12][13][14][15] Particularly, articial compound eye structures (CESs) inspired from corneas of insects, which are usually composed of thousands of microstructures covered with nanonipple arrays, effectively reduce the surface reection (or enhance the transmission) over wide ranges of incident wavelengths and angles because of the formation of the effective gradient-refractive-index prole between air and the bulk surface. [16][17][18][19][20][21][22] Besides, the CESs with microscale periods can also extend the effective optical paths and promote the transmitted diffuse lights, while keeping high total transmission properties (e.g., high optical haze). [23][24][25][26] In addition, due to this extension of optical paths, the microstructures (e.g., microlenses, microcones) can help to reduce total internal reection losses in optoelectronic devices like light-emitting diodes. 27,28 On the other hand, polydimethylsiloxane (PDMS) is widely used as conformable and elastomeric replica stamps, substrates, or membranes in the so lithography, which is relatively a more simple, large-scalable, and cost-effective micro-and nanopatterning technique with high-throughput production compared to the energy-intensive patterning methods such as electron-beam lithography, nanoimprint lithography, and photolithography, owing to its low free surface energy, exibility, transparency, and hardness. [29][30][31][32][33] Furthermore, the PDMS can be suitable as an antireective protection layer of the coverglass in encapsulated solar cells because of its lower refractive index of $1.4-1.43 (i.e., n z 1.5-1.52 for glass). [32][33][34][35] Also, the cured PDMS lm attached on other at substrates such as wafers and glasses has shown a very good and strong adhesion property due to the mainly van der Waals force (e.g., adhesive strengths of $180 kPa). 36,37 Therefore, the PDMS lm can not only be powerfully well-laminated on the at surface of coverglasses, but also reversibly easily-detached from it. From these reasons, as an antireective protection layer of coverglasses, the compound eye structured PDMS lm with high optical transparency and haze can boost the light harvesting in the underneath encapsulated solar cells, resulting in the efficiency improvement of devices. In addition, for photovoltaic industry applications, mass production would be also possible because the large-scale fabrication techniques of micro-and nanostructured polymer lms have been developed by roll-to-roll or roll-to-plate processes using the so imprint lithography. [38][39][40] Meanwhile, the roughened structures could enhance the surface hydrophobicity of materials, related to the Cassie-Baxter wetting behavior. 41,42 This hydrophobic surface, which can self-clean the dust particles and contaminants on the surface, is exceedingly useful in practical solar cell applications. 35,43,44 Thus, it is very meaningful to analyze the optical properties and water wettability by applying the hierarchical nano/microstructures into the surface of PDMS lms as the antireective protection layer of coverglasses for efficiency improvement of encapsulated solar cells. In this work, we fabricated the articial inverted CESs (ICESs) on the surface of PDMS lms by the so lithography method using sapphire master molds with the CESs prepared by thermally dewetted gold (Au) nanopatterning and dry etching processes. Their water wetting behaviors as well as optical properties were studied. The effect of the ICESs PDMS lm as an antireection layer of coverglasses on the device characteristics of encapsulated gallium arsenide (GaAs) single-junction solar cells was investigated. For a theoretical analysis of optical light scattering properties, the nite-difference time-domain (FDTD) simulation was performed. Besides, the incident light angle-dependent device performance and the long-term device stability for demonstrating the self-cleaning function were also explored.

Experimental and numerical modeling details
Fabrication of ICESs PDMS lms Fig. 1 shows schematic illustrations of (a) fabrication process steps for (i) CESs on the master mold by thermally dewetted Au nanopatterns and dry etching and (ii) ICESs on the PDMS lm using the CESs patterned mold by the so lithography method and (b) encapsulated III-V GaAs single-junction solar cell structure with the ICESs PDMS lm/coverglass. For the master mold with CESs, the patterned sapphire substrates, which were purchased from AND Corporation, consisting of conical periodic microgratings (p-MGs) with two-dimensional hexagonal pattern arrays, having the average height and period of $1.5 AE 0.1 mm and $2.5 AE 0.1 mm, respectively, were used. For the formation of closely-packed nanotextures (NTs) with periods smaller than 200 nm, the Au thin lm with a thickness of 4 nm was deposited on the p-MGs/sapphire substrate by a thermal evaporation system. And then, the samples were heat-treated by using a rapid thermal annealing system at a temperature of 600 C for 2 min in a nitrogen environment. In this case, the Au thin lm was agglomerated into the nanosized particles due to its increased surface energy by the heat (see Fig. S1 in the ESI †). 16,45 Using the Au nanopatterns as an etch mask, the NTs on the surface of p-MGs/sapphire substrates were fabricated, thus creating the compound eye structures (CESs), as shown in Fig. 1(a)(i). The dry etching was performed with 50 W of RF power and 200 W of additional ICP power at 3 mTorr of process pressure for 7 min in Ar/Cl 2 /BCl 3 (2 : 1 : 4) plasma. The remaining Au was removed using the etchant solution based on potassium iodide and iodine (KI/I 2 ). To fabricate the ICESs on the surface of PDMS lms, as shown in Fig. 1(a)(ii), a hard PDMS, which was oen used to prevent the deformation and distortion of replica nanofeatures, 46 was prepared by mixing a 3.4 g of trimethylsiloxyterminated vinylmethylsiloxanedimethylsiloxane (VDT-731; Gelest, Inc.), one drop of a platinum catalyst (platinum divinyltetramethyldisiloxane, SIP6831.2; Gelest, Inc.), and two drops of a modulator (1,3,5,7tetravinyl-1,3,5,7-tetramethylcyclotetrasiloxane, SIT 7900.0; Gelest, Inc.). Aer that, the methylhydrosiloxanedimethylsiloxane (HMS-301; Gelest, Inc.) was added into this mixture with subsequent stirring for 2 min and degassing for 5 min in the vacuum desiccators. Aerwards, the hard PDMS was spin-coated on the fabricated master molds with CESs at 1000 rpm for 40 s and 500 rpm for 5 min, sequentially, followed by curing at a temperature of 75 C for 25 min in an oven. As a nondestructive and reversible manner, to enable manual application and intimate conformable contact on at surfaces, aer degassing the Sylgard 184 (Dow Corning Co.) polymer with a ratio of 10 : 1 (base : agent) for 1 h, which is the so PDMS, it was poured on the hard PDMS/master molds, and then the samples were cured at 75 C for 2 h in an oven. Finally, the PDMS lms (hard/so PDMS) were carefully separated from the master molds, which resulted in the inverted compound eye structured (ICESs) PDMS lms with a size of 2 Â 2 cm 2 and a thickness of $300 mm. For comparison, the inverted NTs (INTs) PDMS lm was also fabricated using the at sapphire substrate with NTs by the same fabrication process. For the epitaxial growth of GaAs single-junction solar cell structure, an AIXTRON multi-wafer metal organic chemical vapor deposition reactor was used on 2 misoriented n-type GaAs substrate from (100) towards (111) direction. The GaAs single-junction solar cells with a chip aperture area of 0.3025 cm 2 including metal contact grids were fabricated by conventional photolithography, metal evaporation, li-off, and etch processes. And then, the cells were integrated on metalcoated alumina-based printed circuit boards by bonding the top Au wires and the rear silver paste. The cells on printed circuit boards were completely encapsulated with an ultraviolet curable adhesive (NOA 89, Norland Products Inc.) and a costeffective soda lime oat coverglasses (Microscope slides, Sail brand, Cat. no. 7101, manufactured by Yancheng Huida medical instruments Co., China) with a size of 1 Â 1 cm 2 . The NOA89 adhesive was poured onto the cells bonded on printed circuit boards and subsequently covered by the coverglass, followed by exposing an ultraviolet source, which is a 40 W-mercury ultraviolet lamp with a light emission wavelength range of 297-435 nm, for 20 min to cure the NOA 89 adhesive. As can be seen in Fig. 1(b), to improve the light harvesting in the underneath cell absorption layer, the fabricated ICESs PDMS lms with a size of 1 Â 1 cm 2 were laminated on the coverglass of encapsulated III-V GaAs singlejunction solar cells as an antireective protective layer.

Characterization instruments
Field-emission scanning electron microscope (FE-SEM; LEO SUPRA 55, Carl Zeiss) and atomic force microscope (AFM; D3100, Veeco) measurements were carried out to investigate surface morphologies and patterned proles of the fabricated samples. The optical transmittance and reectance properties were characterized by using a UV-vis-NIR spectrophotometer (Cary 5000, Varian) with an integrating sphere (see Fig. S2 in the ESI †). The water contact angles were measured and averaged at three different positions on the surface of samples by using a contact angle measurement system (Phoenix-300, SEO Co., Ltd) with $5 mL droplets of de-ionized water at room temperature. A solar simulator (WXS-220S-L2, Wacom) was used for currentvoltage measurements of devices under 1-sun air mass 1.5 global illumination. The external quantum efficiency (EQE) was characterized by using a QEX7 system (PV Measurements, Inc.).

Numerical modelling and simulations
The theoretical calculation on an optical light scattering behavior of the ICES PDMS lm was performed using the FDTD method. For the FDTD optical simulations, a commercial soware (FullWAVE, Rso Design Group) was utilized. 47 To design the theoretical model, in calculations, the hierarchical inverted nanotextures (nanocones)/periodic microgratings on the surface of PDMS lm were represented by a periodic geometry in the Cartesian coordinate system by a scalar-valued function of two variables, f(x, z), for simplicity. It was assumed that the incident light entered from air into the structure at normal incidence. The amplitude of y-polarized electric eld (E y ) was calculated for the incident plane wave with a slab mode beam prole in the continuous-wave mode, which was normalized at a wavelength (l) ¼ 532 nm. Here, perfectly-matched-layer boundary conditions were enforced. The simulation time step and time were set to be 3 nm per c and 300 mm per c, where c is the speed of light in vacuum, respectively, with a grid size of 5 nm. For the PDMS, the refractive index was assumed to be 1.43 while the extinction coefficient was not considered because it can be ignored.

Results and discussion
Surface morphologies and patterned proles  Fig. 2(a), the NTs, p-MGs, and CESs (i.e., hierarchical NTs/p-MGs) were well formed on the surfaces of corresponding master molds, respectively. By using the so lithography, the micrograting arrayed patterns on sapphire master molds were negatively well transferred into the surface of PDMS lms without any deformation and distortion, as shown in Fig. 2(b)(ii) and (iii). However, the nanotextured patterns on the master mold with the average height of $180 AE 20 nm were poorly copied on the surface of PDMS lm in spite of the use of hard PDMS. This may be attributed to the very closely-packed patterns of NTs (i.e., high density of $70%) with the low average period of $100 AE 20 nm, and thus the hard PDMS solution could not wedge into the empty space between the NTs. As a result, the INTs with a low average depth of $90 AE 10 nm were formed on the surfaces of at and periodic inverted microgratings (p-IMGs) PDMS lms, as can be seen in Fig. 2(b)(i) and (iii). Nevertheless, the relatively favorable INTs, p-IMGs, and ICESs patterns were formed on the surface of PDMS lms from the corresponding master molds, respectively, by the so lithography pattern transfer method, which can be also conrmed in the AFM images of Fig. 2(c).

Surface wettability and self-cleaning behaviors
The dust particles on the surface of coverglass can be harmful to the performance of encapsulated solar cells under real outdoor environments. 35,48 Therefore, it is necessary to employ the antireection layer with a self-cleaning function. For the samples with different surface morphologies, the water contact angles were measured to investigate the wetting behavior. Fig. 3 shows the photographs of (a) a water droplet on (i) the bare coverglass and the PDMS lms with (ii) at INTs, (iii) p-IMGs, and (iv) ICESs and (b) water droplet cleaning behaviors of (i) the bare coverglass and (ii) the PDMS lm with the ICESs. As shown in Fig. 3(a), the bare coverglass had a hydrophilic surface with a water contact angle (q CA ) of $32 while the patterned PDMS lms showed the q CA values of >90 (i.e., hydrophobicity). In particular, the surface of the ICESs PDMS lm exhibited the q CA value of $121 which is higher than those of the other PDMS lms (i.e., q CA $ 100 and 115 for the PDMS lms with the at INTs and the p-IMGs, respectively). This is ascribed to the increased roughness on the surface of PDMS lms with the hydrophobicity, i.e., q CA z 95 for the at bare PDMS lm (see Fig. S3 in the ESI †), which can be explained by the Cassie-Baxter theory. 41,42 This q CA value of $121 is relatively lower than those (i.e., q CA > 150 , superhydrophobicity) reported in other previous works. 35,[42][43][44] However, as can be seen in Fig. 3(b), aer dropping the water droplets, the black charcoal particles on the ICESs PDMS lm were clearly removed by the rolling down water droplets (i.e., self-cleaning). On the other hand, the black charcoal (or dust) particles on the bare coverglass were just relocated, thus partially remaining with water droplets at the edge of coverglass (see Fig. S4 and Video in the ESI †). Thus, this ICESs PDMS lm with a hydrophobic surface is very useful because an optical interface with an additional self-cleaning effect would enhance the practical feasibility in outdoor environments.
Optical properties Fig. 4 shows the measured (a) total and (b) diffuse transmittance spectra of the PDMS lms with the at INTs, the p-IMGs, and the ICESs laminated on the coverglasses. For comparison, the total and diffuse transmittance spectra of the bare coverglass are also shown in Fig. 4(a) and (b), respectively. As shown in Fig. 4(a), by attaching the PDMS lm with the at INTs on the coverglass, the total transmittance was increased compared to the coverglass over a wide wavelength range of 350-900 nm due to the formation of a linear gradient-refractiveindex prole between air and the PDMS caused by the INTs as well as the step gradient-refractive-index variation in the constituent materials from air (n ¼ 1) to the coverglass (n z 1.53) via the PDMS (n z 1.4-1.43). 49,50 For the p-IMGs PDMS lm, on the contrary, the total transmittance spectrum was higher than that of the at INTs PDMS lm. This is the reason why the inverted conical microgratings with a grooved geometry feature have a more linear gradient-refractive-index prole from air to the PDMS due to the large depth of $1.5 mm and also lead to the extension of effective optical path lengths caused by the diffracted and rebounded lights between the inverted microgratings, 24,51,52 which can effectively enhance the transmission in transparent materials by suppressing the surface reection. By introducing the nanotextures on the p-IMGs (i.e., ICESs), the total transmittance was further increased, exhibiting the average total transmittance (T avg ) of $94.1% which is a higher value than those of the other samples (i.e., T avg z 90, 90.6, and 93.3% for the bare coverglass, the at INTs PDMS/coverglass, and the p-IMGs PDMS/coverglass, respectively). This can be also explained by the increased trapping of the reected lights from escaping back to air due to the INTs which have the small period of $100 nm and the effective homogeneous medium with a gradient-refractive-index prole. Therefore, the ICESs can further reduce the reection or enhance the transmission. [16][17][18][19][20][21][22][23][24][25][26] The light diffraction behaviors in these samples  will be covered in the paragraph of Fig. 4(b). For solar cell applications, the solar weighted transmittance (SWT) was estimated using a well-known equation (1) where F(l) is a spectral photon irradiance (i.e., air mass 1.5 global) 54 and T(l) is the total transmittance in Fig. 4(a). As expected, the ICESs PDMS/coverglass had the higher SWT value of $94.3% compared to the other samples (i.e., SWT z 90.2, 90.8, and 93.4% for the bare coverglass, the at INTs PDMS/ coverglass, and the p-IMGs PDMS/coverglass, respectively). For all the samples, the total reectance spectra were also investigated, as shown in the inset of Fig. 4(a). The ICESs PDMS lm considerably reduced the reectance of coverglass over a wide wavelength range of 350-900 nm, exhibiting the lower solar weighted reectance (SWR) value of $5.1% than those of the other samples (i.e., SWR z 9.2, 8.3, and 5.7% for the bare coverglass, the at INTs PDMS/coverglass, and the p-IMGs PDMS/ coverglass, respectively). Herein, the SWR can be also evaluated from the SWT formula in eqn (1) by replacing the transmittance (T) with the reectance (R). Many studies on antireective nanostructures with small dimensions (i.e., period, diameters, and heights) of 200-250 nm for glasses or polymers (e.g., PDMS, polyurethane, and polymethylmethacrylate) with a at surface have reported the reduction of $3-4% in the reection. 43,55-61 Whereas, the at INTs PDMS lm in this work showed a relatively poor antireection effect (i.e., reduction of $0.9% in the SWR) due to its low depth of $90 AE 10 nm. If the INTs PDMS lm has the depths larger than 200-250 nm, it would also decrease the reectance of bare coverglass with a reduction of $3-4%. 55,57,61 However, this low depth of INTs is caused by the limitations due to the relatively small size and thin thickness of the thermally dewetted Au nanopatterns as the etch mask of master molds for the Au lm thickness of 4 nm in this experiment to obtain the tapered NTs with periods of <200 nm which could be fabricated using the overall etching until the Au nanoparticles were completely removed. On the contrary, the nanostructures prepared by the thicker metal lms have a poor transmission at short wavelengths because of the diffraction losses though they have heights (or depths) larger than 200-250 nm. 55,57 Therefore, to achieve the desirable nanostructures on the at surface of polymer lms for efficient antireection, it is necessary to further study for the optimization of master molds in fabrication process conditions such as the nanopattering using thermally-dewetted dot-like metal nanoparticles (e.g., metal lm thickness, heating temperature, heat-treatment time, etc.) and dry etching (i.e., RF power, additional ICP power, process pressure, etching time, gas ow rate, etc.). Additionally, for this ICESs PDMS lm, the improvement in transmittance (or antireection) properties can be veried in the photograph of  lm/coverglass (red-dotted line) exhibits a better legibility for the characters below the sample though the characters are hazy. For a periodic grating structure, when a light enters into the grating with a period of L at normal incidence, the angle of the transmitted diffraction waves, q t,m , in the m-th diffraction order is given by the grating equation: 62 where l is the wavelength of incident light and n is the refractive index of the incident medium. As mentioned above, for the nanograting structures (such as NTs) with periods lower than $200 nm on the transparent medium, the high transmittance can be obtained without diffraction losses, which are strongly dependent on the period of structures, at visible and NIR wavelengths due to the only allowed zeroth order diffracted light wave in the transmission. 55,57,63 On the other hand, the grating structures with periods larger than incident wavelengths generate higher order diffraction lights which would decrease the transmission. However, for the transparent materials with low refractive indices including glasses, quartzes, sapphires, polymers, etc., the cone-shaped structures with desirable microscale periods can lead to the high total and diffuse transmittances, simultaneously. [23][24][25] Therefore, the hierarchical structure consisting of NTs and MGs, i.e., CESs, can further increase both the total and diffuse transmittances. As shown in Fig. 4(b), both the p-IMGs and ICESs PDMS lms on coverglasses have much higher diffuse transmittance spectra over a wide wavelength region of 350-900 nm while there are almost no diffracted lights for the bare coverglass and the at INTs PDMS/coverglass. However, the diffuse transmittance of ICESs PDMS/coverglass was slightly reduced compared to the p-IMGs PDMS/coverglass due to the additional nanotextured surface with a low dimension of $100 nm-period on p-IMGs PDMS lm, which suppresses the light scattering and enhances the light traveling straight. 25 The haze ratio (H), which is dened by the ratio of the diffuse (T d ) to the total (T t ) transmission, i.e., H(%) ¼ T d /T t Â 100, is oen used to characterize the light scattering properties of a sample. For both the p-IMGs PDMS/coverglass and ICESs PDMS/coverglass, the average H (H avg ) values were estimated to be $69.1 and 67.6% at wavelengths of 350-900 nm, respectively, (i.e., H avg z 4.1 and 3.3% for the bare coverglass and the at INTs PDMS/coverglass, respectively). In the transmission, these high diffraction behaviors (i.e., light scattering) can be conrmed in the insets in Fig. 4(b). The photographs of (i) PDMS lms with the at INTs, the p-IMGs, and the ICESs (red-dotted lines) laminated on the coverglass (white-dotted line) and (ii) diffraction phenomenon of the ICESs PDMS/coverglass using a diode laser with l ¼ 532 nm are shown in the insets of Fig. 4(b), respectively. In Fig. 4(b)(i), the characters below the bare coverglass and the at INTs PDMS/coverglass are well seen. On the other hand, for the p-IMGs PDMS/coverglass and the ICESs PDMS/coverglass, the characters below both the samples are not relatively distinguished due to the strong light scattering. In addition, for the ICESs PDMS/coverglass of Fig. 4(b)(ii), high order diffraction patterns in transmitted lights for l ¼ 532 nm are shown. The contour plots of calculated electric eld distributions for the incident light propagating from air to the PDMS lms with (i) the at INTs and (ii) the ICESs and the scale-modied corresponding simulation models used in these calculations are shown in Fig. 4(c). The simulation results indicate that micron-based ICESs, i.e., period (L) ¼ 2.5 mm, exhibit strong light interference patterns with a wide angular spread and help the light propagation across the interface between air and the PDMS while there are no signicant scattering lights for the at INTs due to the subwavelength-scale of 100 nm. 24 From these results, it is noted that the ICESs PDMS lm enables to increase the diffuse transmittance of the coverglass, maintaining the high total transmission, and thus it can lead to the PCE improvement of encapsulated solar cells because of the enhanced light harvesting in the absorption layer of devices caused by the light scattering and antireection effects. [20][21][22][23] Device feasibility For practical device applications, all the PDMS lms were employed onto the coverglass of encapsulated GaAs singlejunction solar cells.  Fig. 5(b). As shown in Fig. 5(a), by attaching the PDMS lms to the coverglass of encapsulated solar cell devices, the increased EQE spectra were obtained compared to the device with the bare coverglass. The device with the ICESs PDMS/coverglass exhibited improved EQE values compared to the other devices at wavelengths of 400-870 nm due to the larger photogenerated carriers caused by its higher total transmittance and haze properties. As can be seen in Fig. 5 To demonstrate the efficient light-harvesting function (i.e., antireection and light scattering) of the ICESs PDMS lm on the device performance under obliquely incident sunlight, for the corresponding encapsulated III-V GaAs single-junction solar cells, their J sc values were measured and the increment percentage in J sc relative to the device with the bare coverglass was estimated at incident angles (q In ) of 20-70 , as shown in Fig. 6. For incident light angle-dependent J-V measurements, inclined mounts with tilting angles of 20-70 were used. As the q In was increased from 20 to 70 , the J sc values of all the devices were generally decreased, which shows a similar trend with the other previous reports. 11,13,64,65 This is ascribed to the reduction of the projection area where the incident light enters into the device due to the tilted device from the normally incident light source of the solar simulator as well as the increased surface reection losses. 11,65 However, the device with the ICESs PDMS/ coverglass showed the higher J sc value at each q In , keeping a larger average increment percentage of $9.2% relative to the device with the bare coverglass at q In ¼ 20-70 (i.e., $3.4% and $6.7% for the at INTs PDMS/coverglass and the p-IMGs PDMS/ coverglass, respectively). Thus, the use of the ICESs DPMS lm as an antireective protective layer could improve the solar power generation in encapsulated photovoltaic systems for an entire day and the seasons.

Self-cleaning effect and stability on device performance under external environment
To investigate the self-cleaning function of the ICESs PDMS lm on the device performance, the encapsulated solar cells were exposed in outdoor environment. Fig. 7 shows the (a) SWT values of the bare coverglass and the ICESs PDMS/coverglass and (b) J sc and PCE values of corresponding encapsulated III-V GaAs single-junction solar cells to show the self-cleaning effect. The photographs of the bare coverglass and the ICESs PDMS/coverglass covered by dusts for 7 days under external environment before and aer cleaning by falling raindrops are shown in the inset of Fig. 7(a). The samples were mounted on the holder with about 30 tilting angle at the rooop of a building. For 6 days, there was little rain, and then it rained on the 7th day. As shown in Fig. 7(a), the SWT values of all the samples covered by dusts were reduced from $90.2 and $94.3% to $88.1 and $92.2% for the bare coverglass and the ICESs PDMS/coverglass, respectively, because of the interrupting of incident light by the dusts. However, aer the cleaning by the falling raindrops, the SWT value of the ICESs PDMS/coverglass was increased by $93.6%, exhibiting the larger recovery percentage of approximately 1.6% compared to that (i.e., $1.2%) of the bare coverglass (i.e., SWT z 89.2%) in the transmittance. As veried in the photographs of Fig. 7(a), aer the cleaning, the dust blotches remained over an entire surface of the bare coverglass while the surface of the ICESs PDMS lm was nearly clear due to its self-cleaning effect caused by the hydrophobicity (i.e., q CA z 121 ). In Fig. 7(b), similarly, the dusts blocked the incident light into the devices, and thus J sc values of all the devices were also decreased with a reduction in their PCE values (i.e., from J sc ¼ 26 and 27.64 mA cm À2 and PCE ¼ 22.96 and 24.3% to J sc ¼ 25.4 and 27.03 mA cm À2 and PCE ¼  22.44 and 23.76% for the devices with the bare coverglass and the ICESs PDMS/coverglass, respectively). However, aer the cleaning, the J sc and PCE values of the device with the ICESs PDMS/coverglass were further enhanced to be 27.44 mA cm À2 and 24.13%, respectively, showing a superior PCE recovery percentage of $1.6% compared to the device with the bare coverglass (i.e., $1.2% recovery percentage, J sc ¼ 25.71 mA cm À2 , PCE ¼ 22.7%). Unlike the J sc , on the other hand, the V oc and FF values were less inuenced by the change of the transmittance due to the dusts. 35,48 Additionally, to evaluate the self-cleaning function on the long-term device stability of the encapsulated solar cells under external environment, their device performance was further explored for approximately one month. Fig. 8 shows (a) SWT values of the bare coverglass and the ICESs PDMS/coverglass and (b) J sc values (c) PCE values of the corresponding encapsulated III-V GaAs single-junction solar cells to show the selfcleaning effect for 32 days under external environment. As expected from Fig. 8, the J sc intensively depended on the SWT, and thus the PCE mainly varied as it. For the device with the bare coverglass, its performance was generally degraded aer 32 days with decreasing the SWT, showing the drop percentages of $2.9% and $3% in J sc and PCE, respectively, compared to the initial values. On the contrary, owing to the good self-cleaning function of the ICESs PDMS lm, the ICESs PDMS/coverglass showed an average increment percentage of $5.3% compared to the bare coverglass in the SWT for 32 days. As a result, the device with the ICESs PDMS/coverglass exhibited the superior long-term stability with the lower drop percentages of $1.3% and $1.4% in J sc and PCE, respectively.

Conclusions
We fabricated the highly-transparent and hazy ICESs PDMS lms with antireective and hydrophobic properties for efficient light-harvesting and self-cleaning effects for encapsulated III-V GaAs single-junction solar cell applications. The ICESs PDMS lm was fabricated by a facile, simple, and cost-effective so lithography method using sapphire mater molds with CESs consisting of hierarchical NTs/p-MGs. The ICESs PDMS lm exhibited larger q CA z 121 , SWT z 94.3%, and H avg z 67.6%, respectively, than those (i.e., q CA z 32 , SWT z 90.2%, and H avg z 4.1%, respectively) of the bare coverglass. By laminating the ICESs PDMS lm on the coverglass in the encapsulated III-V GaAs single-junction solar cell, the increased J sc value of 27.64 mA cm À2 was obtained compared to the encapsulated solar cell  with the bare coverglass (i.e., J sc ¼ 26 mA cm À2 ), and this mainly enhanced the PCE by 24.3% (i.e., PCE ¼ 22.96% for the encapsulated cell with the bare coverglass), exhibiting the PCE increment percentage of $5.8%. Furthermore, it also showed not only superior device performance at obliquely incident lights, but also good long-term device stability with the only PCE drop percentage of $1.4% aer 32 days. These results suggest that the articial inverted compound eye structured polymer lms, which can be easily fabricated by the simple and costeffective so lithography technique, with the high optical transparency and haze as well as the hydrophobic surface have considerable potential for high-performance and long-term stability photovoltaic systems using transparent substrates as well as coverglasses in terms of efficient light-harvesting and self-cleaning functions.