1. Introduction

Disordered diffraction gratings constitute a class of optical elements that are relevant for a wealth of applications. [1, 2] Indeed, as quasi-periodic structures, they display controllable optical properties. Simultaneously, they are perturbed by structural irregularities, which make them effective over a broader spectral and angular range with respect to periodic diffraction gratings. [3–5] These irregularities, impacting the grating height and/or period distribution, have been tailored and introduced deterministically [6, 7] or stochastically [8] depending on the application targeted.

Thus, disorder implemented according to a pre-determined pattern has been employed to design transparent transmission gratings which improve indoor lighting [4], and to reduce the angular color shift of organic light-emitting diodes (OLEDs) integrating a light out-coupling grating. [3,9] It was also demonstrated that more perturbed configurations, such as quasi-periodic surface wrinkles, can serve as broadband light extractors in monochromatic and white OLEDs [10–13]. Similar wrinkled structures were introduced in solar cells and exploited as light-trapping elements for enhancing light absorption. [14–16] Aside these optical properties, disordered diffractive structures can prevent strong specular reflection as well as intense diffraction orders [17]. As such, they can be engineered to create photovoltaic (PV) light harvesting coatings that limit disability glare, defined as a reduced visibility due to light scattering in the eye media [18]. This attribute ultimately promotes the societal acceptance of PV panels [19] and improves the safety for urban and air traffic. [20, 21]

However, up to now, many of the disordered diffraction gratings proposed were fabricated using serial lithography techniques such as e-beam lithography, which necessitates a long exposure time to pattern such structures over few cm². [6, 22] Herein, we now present a rapid, highly scalable and cost-effective method to produce disordered transmission gratings using an all-polymer wrinkling process. With mechanically directed self-assembly of a polymer film supported by a shape-memory polymer (SMP) substrate, we generate one-dimensional (1D) quasi-periodic surface wrinkles exhibiting disorder in both, height and period size distributions.

In the following sections, we first introduce our fabrication method and demonstrate its versatility by fabricating disordered transmission gratings with various, tailorable mean periodicities. Their transmissive and reflective properties are then analyzed angle-dependently and with respect to the direction of the incident light. To investigate the influence of structural disorder, we compare the diffractive properties of gratings possessing the same (1D) symmetry but either based on a perfectly periodic array or on the quasi-periodic wrinkled structures. We show that our surface wrinkles can be employed as a light harvesting coating, and are therefore relevant for PV applications. As a proof-of-concept, we replicate them into a transparent resist layer deposited on the planar front side of crystalline silicon (c-Si) solar cells, and evaluate their optoelectrical properties.

2. Experimental

2.1. Surface wrinkle fabrication

Tecoflex EG 72D granulate was purchased from Lubrizol and used as received. The granulate was melted into rectangular substrates with a dimension of 2.5 cm × 6 cm × 1 mm (width × length × thickness) and with a surface roughness of R_rms ≈ 14 nm using a partly self-made hot embossing machine based on a Zwick 1488 tensile testing machine at 155 °C and 3000 kPa as the permanent shape. For the temporary shapes the samples were stretched in an Instron 4505 tensile testing machine at room temperature with 2 mm/min to ≈130%. Tecoflex EG 72D switching temperature is in the range of 40–80 °C and its melting temperature around 155 °C. [23] Subsequently, the surface of the substrates were covered with PMMA (PLEXIGLAS 8NL22, Evonik Degussa GmbH) by spin coating PMMA/xylene solutions of 0.75, 1, 2, 3, and 5 wt.% at 3000 rpm for 1 min with an acceleration rate of 150 rpm/s in nitrogen atmosphere (Laurell WS 650MZ 23NPPB spin coater) to achieve different wrinkle sizes. After drying the samples for 2 h on a 30 °C hot plate (Harry Gestigkeit GmbH Präzitherm), they were submerged in 80 °C de-ionized (DI) water for ≈ 5 sec to conduct the recovery of the permanent shape and to generate the wrinkles.

2.2. Periodic grating fabrication

A grating with a period of Λ = 1.30 µm was fabricated by two-beam interference lithography. Therefore, a glass substrate was treated with the adhesion promoter bis(trimethylsilyl)amine inside an evacuated desiccator for 20 min. Afterwards, a 800 nm thick layer of the photoresist ARP-3120 from Allresist was deposited by spin coating, followed by a soft-bake step for 2 min at 80 °C on a hot plate. For exposure, a CW 266 nm laser was used. The laser beam was split into two equipollent beams, which were directed onto the sample surface under an incident angle of around 5.9° to the normal. The exposure was terminated reaching a dose of 25 mJ cm⁻² on the sample surface. Afterwards, the sample was bath-developed for one minute in a mixture of developer AR-300-35 from Allresist and DI-water (volume ratio 5:1), then rinsed in DI-water.

2.3. Replication process

To replicate the wrinkles and periodic grating into a transparent resist layer, the original samples were first fixed with a double-sided adhesive tape on a microscope slide and then placed inside an aluminum container. A mixture of 10:1 (weight ratio) Sylgard Silicone Elastomer 184 and Sylgard Curing Agent 184 was prepared, air bubbles within the mixture were removed by placing it in an evacuated desiccator for 20 min. Subsequently, the mixture was soused over the samples. No pressure was applied during the curing step. After two days at room temperature, the hardened PDMS mold was separated from the samples. In order to reproduce positives of the surface structures on various substrates (glass slides, c-Si solar cell), the PDMS mold with the negatives of the original samples’ surfaces were used for an UV-imprint process under ambient atmosphere. The following steps were thus carried out: a drop (around 50 µL) of UV-curing adhesive Norland Optical Adhesive 68 (NOA68) was placed on the substrate and the PDMS mold was carefully pressed into the drop, ensuring that any air bubbles were directed to the sample edges. After 20 min of UV exposure at 1.5 mW cm⁻² radiation power, the PDMS stamp was separated from the cured NOA68 to be reused for further replicas.

2.4. Characterization methods

J-V measurements

The current density-voltage characteristics of the planar heterojunction crystalline silicon solar cells were measured on a class AAA (WAVOM WXS-90S-L2, Japan) solar simulator. The silicon solar cell equipped with the planar reference encapsulation, the grating or the SW structure was covered with a shadow mask with an area of 32 mm².

EQE measurements

All details on the planar heterojunction crystalline silicon solar cell architecture and fabrication process can be found in Ref. [24]. The EQE spectra were measured with a modulated monochromatic light between 300 nm and 1100 nm using an in-house setup. A slit aperture in the beam path restricted the spot size to a well-defined area of five grid lines.

Reflection measurements

For the reflection measurements, the respective structures were replicated on 25×25 mm² glass slides (SLG, Carl-Roth-Objektträger). To collect surface reflection, the back of the glass substrates was covered by a black adhesive foil with high broadband absorption. The samples were placed in the center of a 150 mm integrating sphere using a vise-type center-mount in a Perkin Elmer Lambda 1050 spectrometer equipped with a depolarizer. For angle-resolved measurements, the sample holder was rotated around the vertical axis, as depicted in Figure 6. The probe beam spot size of 2 × 10 mm² for close-to-normal incidence widened to 10 × 10 mm² for an AOI=80°. To gather reflection at near normal incidence (at 8°) for front and backside illumination, the samples were placed behind the integrating sphere at the back port. The reflection measurements, including both the specular and diffuse components, were finally integrated between 400 nm and 1100 nm. The measurements performed with the coated c-Si solar cells to obtain their absorptance were carried out the same way.

Measurement of the spectrally-resolved angular distribution of the transmitted light intensity

These measurements were carried out on the replicated structures applied on top of glass substrates. For proper light extraction, we attached a glass hemisphere with a refractive index matching oil (Immersol F518) at the sample backside ensuring that all transmitted light hits the rear glass/air interface perpendicularly. Thus, the real angular profile in the far-field could be measured with minimal back reflection. A white LED source with a beam collimator was used for the normal incidence illumination of the samples. Sample, light source and glass hemisphere were mounted on a bi-axial rotation stage. The transmitted light was collected by an optical fiber attached to a monochromator (Acton Research Corporation Spectra Pro-300i, 0.3 m triple gate; slit width 12 µm). A schematic of the setup is shown in Figure 6. The data reported in this study correspond to a relative intensity, which has been integrated over the azimuth angle ϕ in order to reduce the two-dimensional data array of the scanned half space to one dimension with altitude angle θ being the only variable.

Measurement of the spectrally-resolved angular distribution of the reflected light intensity

To acquire the θ- and λ-resolved intensity distribution of the light which is reflected on the sample surface, the samples were mounted onto a WOOLLAM variable angle spectroscopic ellipsometer using the scatterometry option. The light was kept constant at AOI=20°, while the detector moved within the plane of incidence to collect the angle resolved, specular and non-specular part of the reflected light. The scatter angle is here the angle relative to the angle of specular reflection.

Characterization of the wrinkles and grating morphology

All AFM images and the R_rms measurement were obtained in tapping mode using a Dimension Icon from Veeco with a NanoScope V controller. The SEM pictures of the surface wrinkles were obtained with a Supra 55P, Zeiss, Germany at 3 kV, whereas the electron micrographs of the reference grating were recorded with an JEOL CarryScope JCM5700.

2.5. Optical simulations

The finite-difference time-domain method available in Lumerical [25] was used to perform all optical simulations. The curved surface of a single wrinkle was defined by the function $w(x)=h\cdot \cos {\left(\pi \cdot \frac{x}{\mathrm{\Lambda }}\right)}^2$. The period Λ = 1.30 µm and the height h = 0.65 µm were either set to fixed values along the simulated wrinkles, or an additional variance ΔΛ and Δh was introduced to investigate the influence of structural disorder on their optical properties (where ΔΛ and Δh are normally distributed numbers). The statistical nature of disorder was ensured by introducing these size variations within a set of 100 wrinkles constituting the unit cell. A plane wave launched under normal incidence at three wavelengths (470 nm, 570 nm and 670 nm) was used to simulate the angular distribution of the transmitted light. Monitors for reflection and transmission were placed at the edges of the simulation area. The electromagnetic field obtained at the monitors below and above the wrinkles were used for a far-field projection. The angular resolved far-fields led to the diffraction patterns shown in Figure 7. To analyze and compare the reflected light angular pattern with experimental data, an angle of incidence of 20° was used.

3. Results and discussions

3.1. Fabrication of tailorable surface wrinkle structures

SMPs are a special class of smart materials, which are able to morph from one to a second distinct shape on demand. [26–31] When exposed to a proper trigger such as heat, light or magnetic field, they transform from a programmable, temporary shape back to their memorized original, permanent shape.

For the fabrication of our disordered transmission gratings, we use a cycloaliphatic polyether urethane (Tecoflex EG 72D from Lubrizol) with a thermally activated one-way shape-memory effect (SME). Due to its amorphousness, it is transparent over the visible spectrum and its thermoplastic nature enables easy structuring with common polymer processing techniques such as injection molding or hot embossing. [23,32] In the present study we utilize the SME of our polymer to temporarily change the surface area of SMP samples through controlled stretching in a tensile testing machine. As shown in Fig. 1(a), these stretched samples serve as substrates and are subsequently covered with a thin film of a second polymer, namely polymethylmethacrylate (PMMA), by spin-coating from solution. When the SME is triggered by rising the sample’s temperature above the SMP’s switching temperature, the substrates contract to their original size. This causes the PMMA coating to wrinkle in order to compensate the compressive stresses and surface area changes, resulting in 1D disordered gratings. For a detailed description of the fabrication of PMMA surface wrinkles on SMPs, we refer to the method presented in Ref. [33]. In order to replicate the surface wrinkles produced with this method, they are covered by a thick polydimethylsiloxane (PDMS) layer as shown in Fig. 1(b). After curing and demolding, the inverse texture is transferred into the PDMS layer which is then used as a mold to imprint the disordered gratings into a transparent resist layer (with a refractive index n =1.5 at 560 nm) that is directly applied onto the desired substrates or devices. More details are provided in the Experimental section. We note that the curing time of the mold can be dramatically reduced without sacrificing the quality of the replicated structures if a UV-curing PDMS is used.

 

Fig. 1 Overview of the fabrication and replication routes of disordered diffraction gratings. (a) A shape-memory polymer substrate is stretched uniaxially and subsequently coated with a thin film of a second polymer. Subsequently, the sample shrinks back to its original size upon triggering the recovery process and 1D wrinkles form on the surface. (b) The transfer of the wrinkles onto various substrates, such as the planar front side layer of c-Si solar cells, is achieved by replicating the inverse texture into a PDMS layer, which is then used as a mold to imprint the disordered diffraction grating into a transparent resist layer.

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In contrast to wrinkling based on metal films or hard silica shells supported by soft substrates such as PDMS, polymer-SMP wrinkle systems are mostly crack free on arbitrarily up-scalable areas. This benefit is a consequence of the soft polymer coating being able to counterbalance the reversion of the lateral contraction with its intrinsic elasticity in opposition to stiff coatings. [34–36] Furthermore, the wrinkle dimensions, in terms of the averaged period $\overline{\mathrm{\Lambda }}$ and height $\overline{h}$, are widely adjustable through multiple fabrication parameters. [33] To illustrate the versatility of our approach, we show in Fig. 2(a) 1D wrinkles with varying mean periods of $\overline{\mathrm{\Lambda }}=0.40,0.60,1.30,1.87$ and 3.52 µm and with corresponding mean heights of $\overline{h}=0.11,0.17,0.65,0.91$ and 1.73 µm, respectively. All samples displayed are homogeneously structured over an area of 2 × 2.5 cm². The analysis of their topography reveals an average standard deviation of period and height in the order of ΔΛ = 30% and Δh = 20%.

 

Fig. 2 Versatility of the shape-memory polymer wrinkling approach for the fabrication of disordered diffraction gratings. (a) The range of periods over which the wrinkled structures can be tailored is exemplified by the AFM pictures of SMP-PMMA samples with mean periods ranging from 0.40 µm (top) to 3.52 µm (bottom). (b) Structural disorder, visible in both the period (SEM images) and height (AFM cross-section) variation, is revealed for the selected Λ = 1.30 µm wrinkled structure. (c) The topography of the periodic grating fabricated with laser interference lithography and used as a reference is also shown. The AFM profiles reported here are representative of their corresponding samples.

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For the following evaluation of the wrinkles’ optical properties and potential for PV applications, we choose to focus on the structure with the period of $\overline{\mathrm{\Lambda }}=1.30\mathrm{\mu }\mathrm{m}$ and height of $\overline{h}=0.65\mathrm{\mu }\mathrm{m}$, and refer to this configuration as “SW”. However, we note that our conclusions are not restricted to this particular structure. The corresponding period distribution and height variation of Λ = 1.30 ± 0.39 µm and h = 0.65 ± 0.13 µm, respectively, are evidenced in the scanning electron microscope (SEM) images and in the cross-sections derived from atomic force microscope (AFM) measurements shown in Fig. 2(b). For the experimental comparison of diffractive structures with and without structural disorder, we use a perfectly periodic 1D grating (“grating”) as a reference. This grating is fabricated by laser interference lithography, as described in the Experimental section. Fig. 2(c) highlights the regularity of this structure. For best possible comparison to the selected wrinkle sample, the period of the grating is set to Λ = 1.30 µm and the height to 0.50 µm, which is the highest height achievable of our laser interference lithography setup for the period considered.

3.2. Optical properties of surface wrinkles

The influence of structural disorder on the angular distribution of the diffracted light is investigated by comparing the diffraction patterns generated by the grating (Fig. 3(a)) and by the SW structure (Fig. 3(b)). To exclude effects arising from the different materials, both structures are transferred into the same transparent resist on a glass substrate (according to the sequence schematized in Fig. 1(b)).

 

Fig. 3 Influence of surface wrinkles’ structural disorder on the diffracted light angular distribution. (a) The measured and normalized diffracted light angular distribution is displayed for reflection (left column) and for transmission (right column) of the periodic grating. Photographs obtained under white light illumination also illustrate the color dissociation and distinct diffraction orders caused by the diffraction grating. (b) As shown in the photographs, a faint background between attenuated diffraction orders is generated by the structural disorder of surface wrinkle structures. The angular broadening of the diffraction peaks is also verified quantitatively.

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The photographs in Figure 3 give a qualitative impression of the diffraction patterns obtained for reflected (R_VIS) and transmitted (T_VIS) light by illuminating these samples with a collimated white LED source. As expected, vivid and clearly dissociated colors are observed for the first order diffracted light in the case of the periodic grating. While this dissociation can still be distinguished in the SW case, the presence of structural irregularities randomly distributed within the wrinkle pattern leads to the so-called “grass”, namely to a diffuse background between the diffraction orders. [37] These observations are corroborated by quantitative measurements performed at three wavelengths (blue: λ = 470 nm, green: λ = 570 nm and red: λ = 670 nm) and obtained for scattering angles ranging from 0° to 60° relative to the angle of the incident specular light path. The grating generates discrete diffraction peaks in the zeroth and first diffraction orders with a full width at half maximum below 2°, as shown in Fig. 3(a). For the surface wrinkles, the angular spread of the diffracted light is substantially larger and results in a strong overlap of the peaks (Fig. 3(b)). The diffraction orders and a certain dispersion can still be observed. This proves that the wrinkles do not scatter light in random directions as with a sandblasted surface [38] for example, but have to be considered as disordered diffraction gratings.

To further analyze the optical influence of height and period variations over the SW surface, we conducted wave-optics simulations based on the finite-difference time-domain method. We find that disorder in the wrinkle’s period strongly affects the relative intensity and angular spread of the diffraction peaks (see Figure 7 for details). Thus, our combined experimental and numerical analysis proves that the period variations observed in the fabricated surface wrinkles allow preserving deterministic diffraction orders, and are mostly responsible for the peak broadening effect.

Another salient feature of these disordered diffraction gratings is their ability to efficiently collect and transmit the incoming photons as forward propagating light. To achieve this, good in-coupling properties are firstly required. This aspect is assessed for the SW sample by measuring the overall surface reflectance from a close-to-the-normal incidence of 10° to a glancing angle of incidence (AOI) of 80°. For comparison, the front side reflectivity is also collected for two reference cases, including the previously introduced periodic grating, and a flat layer made of the same transparent resist. Those values are integrated between λ = 400 nm and 1100 nm for each AOI, and displayed in Fig. 4(a). At an AOI of 10°, the integrated surface reflectance of the wrinkled surface is close to 3%, that is lower than the value of 5% measured for the periodic grating and the planar surface. Importantly, the reduction of surface reflectance is not only observed for all AOIs, but is also more prominent as the incidence angle increases. Thus, the two references surpass a surface reflectance of 40% for an AOI of 80°, whereas the surface wrinkles do not exceed 23%. Irrespective of the AOI, our surface wrinkles reduce surface reflection by almost 50% compared to a planar surface or to the periodic grating. These measurements examine only the in-coupling properties of the light impinging on the gratings from the free space. However, the collected light propagating below the (disordered) grating surface will partly experience reflection at the first interface between the light harvesting coating and the underlying substrate, and is thus likely to escape the coating from its front side. In turn, this deleterious effect limits the overall amount of harvested light. For this reason, it is also essential to limit the out-coupling of the backward-propagating light into the free space or equivalently, to increase the fraction of reflected light redirected towards the substrate.

 

Fig. 4 Light harvesting properties of the surface wrinkles. (a) The overall front side reflectance of a flat surface, the periodic grating, and of the SW sample, averaged between λ = 400 nm and 1100 nm, is plotted as a function of the AOI. The dashed lines are a guide for the eye only. Relative to the two references, the surface wrinkles improve light in-coupling by roughly 50% for all AOIs. All the samples include a black absorber on their rear side to prevent reflection from the back surface. (b) The graph shows the overall reflectance measured by illuminating the grating and the SW samples under near normal incidence, either from their front or back side. The shaded region represents the reflectance difference between backward and forward propagating light in the surface wrinkles case, and emphasizes the retro-reflection potential of the SW sample.

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We illustrate this retro-reflection effect by measuring the overall reflectance (accounting for front and back side reflections) of the periodic grating and of the SW coatings on planar glass substrates. These two samples were illuminated either on their front side (“front”) or on their back side (“back”). Fig. 4(b) shows that an almost similar reflectance of more than 7% is obtained for the two illumination conditions using the grating sample. Conversely, a significantly higher reflectance is measured for the back side illumination at a near normal AOI in the SW configuration. Its value is more than doubled below 700 nm compared to that obtained with a front side illumination. This reflectance increase can be explained by considering the angular distribution reported in Fig. 3(b) (in transmission). The latter exhibits a strongly reduced intensity of the zeroth diffraction order with respect to the grating case, and compared to its first diffraction order. Consequently, a higher fraction of the light propagating in the backward direction and under normal incidence will be reflected back towards the substrate, leading to the higher reflectance measured in that configuration. More generally, the broadening of all diffraction peaks experienced in the SW sample distributes the peaks’ intensities in transmission more evenly over the angular range. Regardless of the propagation angle of the backward-propagating light, this signifies that the probability to out-couple the light into the free space decreases compared to the grating sample, which possesses narrow and high intensity diffraction peaks. This retro-reflection mechanism therefore gives a second chance for recapturing the light following its reflection at the coating/substrate interface. We note that in the present case, the gradual decrease of the measured reflectance with increasing wavelengths (for SW with back side illumination) is attributed to an increasing amount of light guided inside the substrate resulting from higher scattering angles, and which is not directly accessible with the used setup.

3.3. Surface wrinkles as light harvesting coatings for photovoltaics

As shown in the previous section, gratings perturbed by randomly distributed irregularities broaden the diffraction peaks significantly with respect to periodic gratings, enabling both a reduction of disability glare and a more efficient retro-reflection mechanism. Altogether, these optical properties can be exploited to improve light management in solar cells. To illustrate this point, we substitute the glass substrate used in the previous section by a c-Si solar cell, and make use of the optical effects discussed above to interpret its enhanced absorption properties. To test the potential of surface wrinkles for PV applications, we apply our exemplary SW coatings ($\overline{\mathrm{\Lambda }}=1.30\mathrm{\mu }\mathrm{m}$, $\overline{h}=0.65\mathrm{\mu }\mathrm{m}$) onto planar heterojunction c-Si solar cells. [24] A schematic of the corresponding PV devices is shown in Fig. 5(a), where the p-type absorber has a thickness of 250 µm and the planar indium tin oxide (ITO) layer serves as a transparent and conductive front side electrode. For comparison, we characterize equivalent devices that integrate the periodic grating (Λ = 1.30 µm and h = 0.50 µm, see Fig. 2(c)) into the same coating material (UV-curing optical adhesive, see Section 2.3 for details). The photograph in Fig. 5(b), captured under a viewing angle of approximately 50°, shows the solar cell covered by the wrinkles and illuminated by a white light source. Unlike the periodic grating case, which exhibits a strong specular reflection (white spot) together with an intense first diffraction order (blue background), the wrinkles-coated solar cell displays less and only diffused reflected light. Consequently it circumvents the disability glare issue stressed out previously. The dull blue coloration nevertheless indicates the presence of a first diffraction order, in agreement with the measurements and simulations shown in Figure 3 and Figure 7, respectively.

 

Fig. 5 Anti-glaring effect and enhanced light harvesting properties in c-Si solar cells covered with wrinkled coatings. (a) The schematic illustrates the planar heterojunction c-Si solar cell stack incorporating the replicated wrinkles on its front side. (b) The photographs highlight the low disability glare potential of the cells covered by wrinkles $(\overline{\mathrm{\Lambda }}=1.30\mathrm{\mu }\mathrm{m})$ compared to periodic diffraction gratings (also with Λ = 1.30 µm) observed in the same conditions (viewing angle around 50°). These two light harvesting structures were imprinted in the same transparent coating material. (c) An absorption increase in the c-Si solar cell with the wrinkled light harvesting coating is observed compared to a flat resist coating. (d) The corresponding external quantum efficiency is shown. All measurements were carried out at near normal incidence.

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The overall impact of the wrinkled light harvesting coating on the c-Si solar cell absorption properties is evaluated in Fig. 5(c) in comparison to a cell covered by a flat resist layer used as a reference. We note that the optical properties of the latter case correspond to those of a solar module commonly encapsulated by a flat glass panel. A substantial increase of absorption is measured for the SW configuration over the whole spectral range of interest. Quantitatively, this translates into a ≈ 4.7% integrated absorptance increase under near normal incidence. This enhancement overcomes the gain that would be obtained by only suppressing the front side reflection (absorption increase higher than 4%, see for example at λ = 400 nm in Fig. 5(c)), and partly arises from the previously described retro-reflection effect. We additionally display in Fig. 5(d) the external quantum efficiency (EQE) spectra of the two solar cells (active area of 1 × 0.5 cm² each). With the wrinkled front side coating we observe a significant increase of the EQE, except at short wavelengths (λ < 400 nm) due to stronger parasitic absorption effects in the resist and solar cell front side layers. Despite this, we demonstrate that the application of our wrinkled coatings enhances the resulting short-circuit current density of the solar cell from 31.4 mA cm⁻² to 32.9 mA cm⁻² with respect to the reference device and under normal incidence. As the integration of the light harvesting coating leaves the collection of the charge carriers unaffected, a relative increase reaching 4.8% is achieved.

We additionally compare the performances of the SW and of the periodic grating coatings, which are processed onto separated and similar solar cells together with their respective flat reference. The current density-voltage characteristics of the corresponding devices can be found in Figure 8. With a relative increase of the short-circuit current density of only 1.2% with respect to its flat reference, the grating only slightly improves current generation. Its light harvesting properties, analyzed in Figure 9, are substantially surpassed by those of the SW (compare with Figs. 5(c) and 5(d)), which stresses once more the benefits of structural disorder for such PV coatings.

4. Conclusion

We have introduced a highly up-scalable method for generating surface wrinkles within a thin polymer layer upon the shrinkage of a shape-memory polymer substrate. This route enabled us to fabricate crack-free, 1D wrinkles with adjustable size that feature a limited amount of disorder in their period (ΔΛ = 30%) and height (Δh = 20%) distribution. The light harvesting properties of the wrinkles outperform those of periodic gratings obtained by laser interference lithography in two ways: by improving light in-coupling into the coating by around 50%, irrespective of the angle of incidence; and by introducing an efficient retro-reflection mechanism, promoting the reflection of the backward propagating light that would be otherwise out-coupled. These properties stemmed from the peculiar profile involved that is based on raised and irregularly arranged wrinkles. In particular, we have demonstrated that the broad angular spread of the diffracted light mostly originates from variations in period, and could be judiciously exploited to avoid disability glare. For these reasons, we have tested our wrinkle-based transmission gratings on planar heterojunction c-Si solar cells. We measured a short-circuit current density increase reaching 4.8% under normal incidence due to the combined light in-coupling and retro-reflection effects. Considering the superior light in-coupling capability of the wrinkles over planar coatings or periodic gratings at high angles of incidence, greater photocurrent enhancements are anticipated using oblique illumination. Lastly, we suggest that our surface wrinkles can be directly used to provide flexible OLEDs with broadband light out-coupling properties.

5. Appendix

 

Fig. 6 Schematic of the setups used for the optical characterization. (a) The samples are placed inside an integrating sphere on a rotation sample holder. As the investigated surface structures are 1D, they are measured in two orientations with respect to the incidence plane (here shown in ⊥-orientation). The measured intensity of the reflected, monochromatic light includes both its specular and diffuse components. (b) Mounted on a bi-axial rotation stage, the white, LED-based light source together with the glass hemisphere and the sample can be moved around both azimuth φ and polar angle θ. By collecting the light at a fixed position and guiding it via an optical fiber to a monochromator with CCD-camera, one obtains the spectral intensity distribution of every (φ, θ) position of the half-space.

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Fig. 7 Impact of the grating height and period variations on its simulated diffracted light angular distribution. (a) In the absence of structural disorder (ΔΛ = 0 µm and Δh = 0 µm), discrete and narrow diffraction peaks are simulated and match those measured with the grating (compare with Fig. 3(a)). (b) A deviation in the height (Δh = 0.13 µm) of surface wrinkles, which are otherwise periodically arranged, mostly affects the relative peaks intensities in reflection. (c) A pronounced modification of the angular distribution occurs upon the introduction of disorder in the wrinkles period (ΔΛ = 0.39 µm), leading to both a redistribution of the peaks intensities and to strong peak broadening effects. (d) When disorder in both height and period is considered, using perturbation magnitudes that correspond to actual values extracted from AFM scans of the SW sample (ΔΛ = 0.39 µm and Δh = 0.13 µm), a diffused background is obtained in reflection, and a large angular spread is observed in transmission. In reflection, different peak intensities appear for positive and negative scattering angles. This effect is attributed to the simulated oblique angle of incidence of 20° used to reproduce the experimental measurement conditions, where the scattering angles of the reflected light are relative values with respect to the zeroth order set to 0°.

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Fig. 8 Current density-voltage characteristics of the solar cells integrating the SW and the grating coatings (a) Current density-voltage (J-V) curves of the planar heterojunction c-Si solar cells coated by a flat and by a SW patterned transparent resist layer. The short-circuit current density difference corresponds to a relative enhancement of 4.8% upon integration of the SW. (b) (J-V) characteristics of the grating coated solar cell reveal a relative increase of only 1.2% with respect to its flat reference. The two configurations (SW or grating) and their corresponding flat reference were implemented in separated but equivalent devices.

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Fig. 9 Light harvesting properties of the grating coated solar cells (a) The external quantum efficiency (EQE) spectrum of the c-Si solar cell coated with the grating is compared to the one measured with devices integrating a flat coating. (b) Corresponding absorptance spectra. All measurements were carried out at near normal incidence.

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Funding

Karlsruhe School of Optics and Photonics; Helmholtz Postdoctoral Program; Initiating and Networking Funding of the Helmholtz Association; KIT Young Investigator Network.

Acknowledgments

S.S. and R.S. contributed equally to this work. It is our pleasure to thank Johanna Wolf and Richard Thelen for their kind help in the lab. Furthermore, we are grateful to Jan G. Korvink for his continuous support. This work was partly carried out with the support of the Karlsruhe Nano Micro Facility (KNMF, www.kit.edu/knmf), a Helmholtz research infrastructure at Karlsruhe Institute of Technology (KIT, www.kit.edu).

References and links

1. S. M. Mahpeykar, Q. Xiong, J. Wei, L. Meng, B. K. Russell, P. Hermansen, A. V. Singhal, and X. Wang, “Stretchable hexagonal diffraction gratings as optical diffusers for in situ tunable broadband photon management,” Adv. Opt. Mater. 4, 1106–1114 (2016). [CrossRef]  

2. P. Kim, Y. Hu, J. Alvarenga, M. Kolle, Z. Suo, and J. Aizenberg, “Rational design of mechano-responsive optical materials by fine tuning the evolution of strain-dependent wrinkling patterns,” Adv. Opt. Mater. 1, 381–388 (2013). [CrossRef]  

3. C. Kluge, M. Rädler, A. Pradana, M. Bremer, P.-J. Jakobs, N. Barié, M. Guttmann, and M. Gerken, “Extraction of guided modes from organic emission layers by compound binary gratings,” Opt. Lett. 37, 2646–2648 (2012). [CrossRef]   [PubMed]  

4. T. Buß, J. Teisseire, S. Mazoyer, C. L. Smith, M. B. Mikkelsen, A. Kristensen, and E. Søndergård, “Controlled angular redirection of light via nanoimprinted disordered gratings,” Appl. Opt. 52, 709–716 (2013). [CrossRef]  

5. A. Bozzola, M. Liscidini, and L. C. Andreani, “Broadband light trapping with disordered photonic structures in thin-film silicon solar cells,” Prog. Photovoltaics 22, 1237–1245 (2014).

6. R. A. Pala, J. S. Liu, E. S. Barnard, D. Askarov, E. C. Garnett, S. Fan, and M. L. Brongersma, “Optimization of non-periodic plasmonic light-trapping layers for thin-film solar cells,” Nat. Commun. 4, 2095 (2013). [CrossRef]   [PubMed]  

7. J. Liu, L. Lalouat, E. Drouard, and R. Orobtchouk, “Binary coded patterns for photon control using necklace problem concept,” Opt. Express 24, 1133–1142 (2016). [CrossRef]   [PubMed]  

8. J. Bingi and V. M. Murukeshan, “Individual speckle diffraction based 1d and 2d random grating fabrication for detector and solar energy harvesting applications,” Sci. Rep. 6, 20501 (2016). [CrossRef]   [PubMed]  

9. T.-B. Lim, K. H. Cho, Y.-H. Kim, and Y.-C. Jeong, “Enhanced light extraction efficiency of oleds with quasiperiodic diffraction grating layer,” Opt. Express 24, 17950–17959 (2016). [CrossRef]   [PubMed]  

10. W. H. Koo, Y. Zhe, and F. So, “Direct fabrication of organic light-emitting diodes on buckled substrates for light extraction,” Adv. Opt. Mater. 1, 404–408 (2013). [CrossRef]  

11. J.-H. Park, W.-S. Chu, M.-C. Oh, K. Lee, J. Moon, S. K. Park, H. Cho, and D.-H. Cho, “Outcoupling efficiency analysis of oleds fabricated on a wrinkled substrate,” J. Display Technol. 12, 801–807 (2016). [CrossRef]  

12. H. Cho, E. Kim, J. Moon, C. W. Joo, E. Kim, S. K. Park, J. Lee, B.-G. Yu, J.-I. Lee, S. Yoo, et al., “Organic wrinkles embedded in high-index medium as planar internal scattering structures for organic light-emitting diodes,” Org. Electron. 46, 139–144 (2017). [CrossRef]  

13. W. H. Koo, S. M. Jeong, F. Araoka, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, “Light extraction from organic light-emitting diodes enhanced by spontaneously formed buckles,” Nat. Photon. 4, 222–226 (2010).

14. J. B. Kim, P. Kim, N. C. Pégard, S. J. Oh, C. R. Kagan, J. W. Fleischer, H. A. Stone, and Y.-L. Loo, “Wrinkles and deep folds as photonic structures in photovoltaics,” Nat. Photon. 6, 327–332 (2012). [CrossRef]  

15. S. K. Ram, D. Desta, R. Rizzoli, B. P. Falcão, E. H. Eriksen, M. Bellettato, B. R. Jeppesen, P. B. Jensen, C. Summonte, R. N. Pereira, et al., “Efficient light-trapping with quasi-periodic uniaxial nanowrinkles for thin-film silicon solar cells,” Nano Energy 35, 341–349 (2017). [CrossRef]  

16. S. Y. Ryu, J. H. Seo, H. Hafeez, M. Song, J. Y. Shin, D. H. Kim, Y. C. Jung, and C. S. Kim, “Effects of the wrinkle structure and flat structure formed during static low-temperature annealing of zno on the performance of inverted polymer solar cells,” J. Phys. Chem. C 121, 9191–9201 (2017). [CrossRef]  

17. Y.-C. Tsao, T. Søndergaard, E. Skovsen, L. Gurevich, K. Pedersen, and T. G. Pedersen, “Pore size dependence of diffuse light scattering from anodized aluminum solar cell backside reflectors,” Opt. Express 21, A84–A95 (2013). [CrossRef]   [PubMed]  

18. J. J. Vos, “On the cause of disability glare and its dependence on glare angle, age and ocular pigmentation,” Clinical and experimental optometry 86, 363–370 (2003). [CrossRef]   [PubMed]  

19. F. Ruesch, A. Bohren, M. Battaglia, and S. Brunold, “Quantification of glare from reflected sunlight of solar installations,” Energy Procedia 91, 997–1004 (2016). [CrossRef]  

20. J. Jakubiec and C. Reinhart, “Assessing disability glare potential of reflections from new construction: Case study analysis and recommendations for the future,” Transport. Res. Rec. 2449, 114–122 (2014). [CrossRef]  

21. T. Rose and A. Wollert, “The dark side of photovoltaic-3D simulation of glare assessing risk and discomfort,” Environ. Impact Assess. Rev. 52, 24–30 (2015). [CrossRef]  

22. E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665 (2013). [CrossRef]   [PubMed]  

23. S. Schauer, T. Meier, M. Reinhard, M. Röehrig, M. Schneider, M. Heilig, A. Kolew, M. Worgull, and H. Hölscher, “Tunable diffractive optical elements based on shape-memory polymers fabricated via hot embossing,” ACS Appl. Mater. Interfaces 8, 9423–9430 (2016). [CrossRef]   [PubMed]  

24. K. Ding, U. Aeberhard, F. Finger, and U. Rau, “Silicon heterojunction solar cell with amorphous silicon oxide buffer and microcrystalline silicon oxide contact layers,” Phys. Status Solidi 6, 193–195 (2012).

25. Lumerical Inc., http://www.lumerical.com/tcad-products/fdtd/.

26. A. Lendlein and S. Kelch, “Shape memory polymers,” Angew. Chem. 41, 2034–2057 (2002). [CrossRef]  

27. C. Liu, H. Qin, and P. T. Mather, “Review of Progress in Shape-Memory Polymers,” J. Mater. Chem. 17, 1543–1558 (2007). [CrossRef]  

28. P. T. Mather, X. Luo, and I. A. Rousseau, “Shape Memory Polymer Research,” Annu. Rev. Mater. Res. 39, 445–471 (2009). [CrossRef]  

29. A. Lendlein, Shape-Memory Polymers (Springer, Berlin, 2010). [CrossRef]  

30. Q. Zhao, H. J. Qi, and T. Xie, “Recent progress in shape memory polymer: New behavior, enabling materials, and mechanistic understanding,” Prog. Polym. Sci. 49–50, 1–42 (2015).

31. M. D. Hager, S. Bode, C. Weber, and U. S. Schubert, “Shape Memory Polymers: Past, Present and Future Developments,” Prog. Polym. Sci. 49–50, 1–31 (2015).

32. M. Worgull, Hot Embossing - Theory and Technology of Microreplication (Elsevier Science,).

33. S. Schauer, M. Worgull, and H. Hölscher, “Bio-inspired hierarchical micro- and nano-wrinkles obtained via mechanically directed self-assembly on shape-memory polymers,” Soft Matter 13, 4328–4334 (2017). [CrossRef]   [PubMed]  

34. T. Xie, X. Xioa, J. Li, and R. Wang, “Encoding localized strain history through wrinkle based structural colors,” Adv. Mater. 22, 4390–4394 (2010). [CrossRef]   [PubMed]  

35. Z. Chen, Y. Y. Kim, and S. Krishnaswamy, “Anisotropic wrinkle formation on shape-memory polymer substrates,” J. Appl. Phys. 112, 124319 (2012). [CrossRef]  

36. A. Schweikart and A. Fery, “Controlled wrinkling as a novel method for the fabrication of patterned surfaces,” Microchim Acta 165, 249–263 (2009). [CrossRef]  

37. C. A. Palmer and E. G. Loewen, Diffraction Grating Handbook (Newport CorporationNew York, 2005).

38. N. Adjouadi, N. Laouar, C. Bousbaa, N. Bouaouadja, and G. Fantozzi, “Study of light scattering on a soda lime glass eroded by sandblasting,” J. Eur. Ceram. Soc. 27, 3221–3229 (2007). [CrossRef]