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Abstract
Novel diffractive surface structures are designed, evaluated, and optimized to achieve a significant increase in current density in organic solar cells. The surface relief phase gratings are patterned based on concentric rings, a Fermat’s spiral, and an Archimedean spiral, respectively, and thus diffract incident light independent of its azimuthal angle, as they all exhibit circularly symmetric diffraction patterns. The grating pillars are arranged on the rings or spirals according to periodic or deterministic aperiodic Thue-Morse and Rudin-Shapiro sequences, tailoring the desired diffraction patterns. After evaluating the surface patterns against each other and further parameter optimization, a final current density enhancement of 5 % is achieved for one of the most promising patterns, the Thue-Morse sequence on an Archimedean spiral.
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1. Introduction
Organic solar cells exhibit several beneficial properties, such as their mechanical flexibility, light weight and tunable absorption [1–3]. However, the greatest advantage over their inorganic counterparts is probably their energy- and cost-effective production using low temperature manufacturing processes like roll-to-roll printing, which also boast low material consumption [4–6]. Nevertheless, despite all these advantages, organic solar cells remain a niche product. While increasing strongly in the past years, their power conversion efficiency still lags behind the one of other solar cell types, such as silicon or emerging lead halide perovskite solar cells [7–9]. This is partly due to the low charge carrier mobility in organic active materials, which requires a thin active layer for sufficient charge carrier extraction, but in turn leads to low optical absorption [10,11]. The usually chosen active layer thickness of ${100}\;\textrm {nm}\;\textrm {to}\;{200}\;\textrm {nm}$ thus always represents a compromise between the two antagonistic processes of optical absorption and charge carrier extraction [12–14].
For this reason, various techniques for increasing the absorption without increasing the active layer thickness have been investigated in recent years. These include the incorporation of nanoparticles for plasmonic field enhancement or frequency conversion, the realization of novel cell geometries and the application of anti-reflection coatings [15–21]. The latter, for example, vary largely in efficiency, durability and cost, reducing reflection by 1 % up to over 60 %, depending on the exact method and the solar cell type [19,22,23].
Another strategy is to apply a structured surface layer to the cell. It diffracts the incident light, thereby increasing its path length through the active layer and thus enhancing its absorption probability [24–28]. Usually fully periodic or completely random structures are implemented due to their ease of fabrication [29–32]. However, due to their ordered, discrete diffraction patterns, diffraction by standard periodic structures is strongly dependent on the azimuthal angle of the incident light [33]. Furthermore, periodic structures are ideally suited to provide strong absorption enhancement at specific wavelengths, rather than in a broadband range [34]. Random structures, on the other hand, exhibit a broadband and disordered diffraction spectrum, and are thus more suitable for broadband absorption enhancement but inherently cannot be optimized [35–37]. Therefore, recent research has focused on using aperiodic surface structures instead, which can be tailored to specific solar cell materials and layouts based on their Fourier transform to optimize absorption. [38–43].
In this contribution, we design several novel aperiodic phase structures with circular symmetric diffraction patterns to diffract light independently of its azimuthal angle, more precisely structures based on concentric rings, a Fermat’s and an Archimedean spiral. We fine-tune the diffraction spectra of these fundamental patterns by arranging pillars according to different sequences with widely varying diffractive properties: a periodic sequence and the two famous aperiodic deterministic Thue-Morse and Rudin-Shapiro sequences [44–47]. We use calculations based on Fourier optics to investigate the diffraction characteristics of corresponding phase gratings made of the transparent polymer Polydimethylsiloxane (PDMS), a functional material used to create surface structures for various types of solar cells [48–50]. We further adapt our calculations to determine the current density increase in a realistic, state-of-the-art organic solar cell due to the surface structure, taking into account specific material properties of the cell, e.g., refractive indices and absorption spectrum. For the structure that causes the strongest current density increase, we further optimize structure size and depth to determine an optimal surface structure.
2. Surface structure design
Surface phase gratings are used on solar cells to diffract the incident light, thus elongating the path length through the active layer and consequently increasing the absorption probability. The phase grating consists of the transparent polymer polydimethylsiloxane (PDMS) and is attached on the solar cell surface. Figure 1 depicts the diffraction of a plane wave with wavelength $\lambda$ that is incident on such a phase grating with relief height ${\Delta } h$, pillar diameter $d$, grating vectors $|G|$ and refractive index $n_{\textrm {PDMS}}={1.4}$ on top of the organic solar cell (OSC) [51]. The light is diffracted with the angle $\delta$, that changes while passing through the different solar cell layers with different refractive indices, leading to a path length elongation $P$ in the active layer compared to the straight light path (dashed line). The individual layers are described in section 3.
Fig. 1. Simplified representation of light diffraction from PDMS phase grating with relief height ${\Delta } h$, pillar diameter $d$ and grating vectors $|G|$ on an organic solar cell with reflecting back electrode. $\lambda$ is the wavelength of the incident light. The light is diffracted in the PDMS layer at angle $\delta$, which changes as it passes through the different solar cell layers with their different refractive indices according to Snell’s law. The layers are a glass substrate, an indium tin oxide (ITO) cathode, a zinc oxide (ZnO) electron transport layer (ETL), a PBDB-T:ITIC bulk heterojunction (BHJ) active layer, a molybdenum oxide (MoO$_3$) hole transport layer (HTL), and a silver (Ag) anode. For more details, see section 3. Here, the light’s path is shown exemplary for $\delta = {30}^{\circ }$ and $\lambda = {400}\;\textrm {nm}$. In the active layer the oblique incidence of the light leads to a path length elongation $P$ compared to straight incidence (dashed line). For the exact calculation of the absorption increase, we take into account multiple reflection and refraction at layers adjacent to the active layer, indicated by the thinner arrows.
Here, various structures are investigated for their suitability as surface phase gratings, see Fig. 2. They were all chosen for their nearly circular symmetric diffraction properties, which allow diffraction independent of the azimuthal angle of the incident light. The structures consist of pillars arranged either periodically or deterministic aperiodically on concentric rings, a Fermat’s and an Archimedean spiral. The two deterministic aperiodic sequences used for this purpose are the Rudin-Shapiro and the Thue-Morse sequences. They exhibit strongly contrasting diffraction spectra, both in relation to each other and in comparison to a periodic sequence. While the Rudin-Shapiro sequence has an absolutely continuous diffraction spectrum and thus resembles a random sequence, the Thue-Morse sequence exhibits a singular continuous diffraction spectrum [52]. These different spectra indicate different optical effects of the sequences when used as diffractive surface structures. Thus, this choice of structures makes it possible to compare sequences with widely different diffractive properties in terms of their utility for implementation in solar cell surface structures, while maintaining the independence of diffraction from the azimuthal angle of the incident light.
Fig. 2. Structures used as surface phase gratings: Periodic, Rudin-Shapiro, and Thue-Morse sequences arranged on concentric rings (a1, b1, and c1), on a Fermat’s spiral (d1, e1, and f1) and on an Archimedean spiral (g1, h1, and i1). The corresponding Fourier transform for a relief height ${\Delta } h$ of ${500}\;\textrm {nm}$, a diameter $d$ of ${500}\;\textrm {nm}$ and an incident wavelength $\lambda$ of ${400}\;\textrm {nm}$ is shown next to each of the patterns, always having the same axis scales.
The Rudin-Shapiro sequence $RS_{n}$ is given by
where $e_{2;11}(n)$ is the number of occurrences of the block 11 in the binary expansion of $n$. Thus, each element of the sequence is either 1 or −1.The Thue-Morse sequence $TM_{n}$ is defined by
with $s_{2}(n)$ being the sum of the entries of the binary representation of $n$. If this sum is odd, then $TM_{n}$ equals 1, otherwise 0.The first three structures are generated by arranging a periodic sequence of alternating ones and zeros as well as these two deterministic aperiodic on concentric rings. For this purpose, black and white rings are arranged according to the sequences. In order to obtain finer features not only in radial but also azimuthal direction, the sequences are also arranged along these rings. Depending on the circumference of the rings, more or less elements of the sequences are used. Pillars are placed for every 1 in case of the black rings, the inverse is done for the white rings, see Figs. 2(a1, b1, and c1). Finally, the angle from which the arrangement starts is rotated by one position for each of the rings to prevent a straight line from appearing in any of the structures.
According to the Fraunhofer equation, the field strength in the far field, $U(x,y)$, is given by the Fourier transform of the field $U(\epsilon,\eta )$ directly behind the phase grating,
The FT can be used to determine how much light is diffracted at each angle, because the diffracted intensity is $I=|U(x,y)|^{2}$, see Eq. (7). The radial distance from the center of the FT image is a measure for the diffraction angle, while the local intensity at a certain radial distance indicates how much light is diffracted into this angle. Thus, the center of the FT image always corresponds to light that is not diffracted, while an increasing radial distance indicates diffraction to higher angles. To improve comparability, all structures are constructed from pillars of equal diameter and depth. In addition, the ratio of pillar to groove area is always 50 %, because a duty cycle of 50 % is known to yield the highest diffraction efficiency in the first order for periodic diffraction gratings [24]. The Fourier spectra in Fig. 2 are all plotted logarithmically and have the same axis scales.
In the concentric ring structures, all FTs exhibit a circular symmetric spectrum with a wider inner circle and a second ring around it. However, there are some important differences between the three cases as shown in their respective FTs: For the periodic ring structure (a2), the intensity in the center is very low, but much brighter in a ring around it. Therefore, little light is diffracted into small angles, the most is diffracted into angles corresponding to the bright ring. The FT of the Rudin-Shapiro ring structure (b2), on the other hand, shows a wide bright area in the center, so the light is diffracted with a wide angular distribution. The Thue-Morse ring structure again exhibits a darker area in the center, but smaller than for the periodic structure, and a wider bright distribution around this dark area (c2).
A second type of structure is constructed by placing pillars on a Fermat’s spiral only at positions corresponding to a 1 in the respective sequence. The Fermat’s spiral is given by the equation
where $r$ is the radius or distance from the center, $\phi$ is the angle, and $n$ is the index number of the pillar and $a$ is a constant scaling factor. The three resulting structures (d1, e1 and f1) all have a very low density of pillars in the center, making them quite inhomogeneous overall. Their FTs (d2, e2 and f2) are circular symmetric and exhibit a broad circle in the center with another broad ring around it. Thus, these structures lead to diffraction with a broad angular distribution. However, for the periodic Fermat’s spiral and the TM Fermat’s spiral, the intensity in the very centre is again very low, meaning that for these two structures only little light is diffracted into small angles.Finally, to construct a more homogeneous spiral structure, the sequences are arranged on an Archimedean spiral (g1, h1 and i1), which has the following polar coordinate representation:
As with Fermat’s spiral structures, $a$ is chosen for each structures so that the duty cycle is 50 %. The corresponding FTs (g2, h2 and i2) are again circular symmetric, but unlike the other structures, they exhibit defined thin rings. Thus, the light is diffracted into narrow angular regions. Also, as with the Fermat’s spiral and the rings, the FT of the periodic and TM structures is darker in the centre, preventing diffraction of light into small angles.
3. Path length elongation
To evaluate the effectiveness of the different patterns as surface phase gratings, the path length elongation of light in the active layer is calculated. All calculations are based on the solar cell layout shown in Fig. 1, but can easily be adapted to other layouts as well. Here, the cell is composed of a silver (Ag) anode, a molybdenum oxide (MoO$_3$) hole transport layer (HTL), a bulk-heterojunction (BHJ) active layer, a zinc oxide (ZnO) electron transport layer (ETL), an indium tin oxide (ITO) cathode and a glass substrate.
The active layer materials are exemplarily chosen to be the high-performance donor polymer Poly[(2,6-(4,8-bis(5-(2-ethylhexyl)thiophen-2-yl)-benzo[1,2-b:4,5-b′]dithiophene))-alt-(5,5-(1′,3′-di-2-thienyl-5′,7′-bis(2-ethylhexyl)benzo[1′,2′-c:4′,5′-c′]dithiophene-4,8-dione)] (PBDB-T) and the small molecule acceptor 3,9-bis(2-methylene-(3-(1,1-dicyanomethylene)-indanone))-5,5,11,11-tetrakis(4-hexylphenyl)-dithieno[2,3-d:2′,3′-d′]-s-indaceno[1,2-b:5,6-b′]dithiophene (ITIC). Solar cells based on these materials have recently reached an efficiency of over 12 %, providing a good basis for further optimization through surface structures [54]. The phase grating itself is attached on the solar cell surface on top of the glass substrate. Both the surface layer and the solar cell have an approximate thickness of ${1}\;\textrm {mm}$.
Figure 3 illustrates the corresponding analytical steps to quantify the path length elongation in the active layer of the OSC using the TM sequence on an Archimedean spiral as an example. The same calculations are done for the other structures as well (see Figs. S1-S8, Supplement 1).
Fig. 3. Visualization of steps for calculating the path length elongation using the example of the Thue-Morse sequence on an Archimedean spiral. (a) Surface relief for a relief height ${\Delta } h$ of ${500}\;\textrm {nm}$ and a diameter $d$ of ${500}\;\textrm {nm}$, as well as phase difference between light incident on the pillars and on the grooves for $\lambda ={400}\;\textrm {nm}$. (b) Intensity distribution of grating vectors $G_x$ and $G_y$ of the phase grating in $x$- and $y$-direction. (c) Intensity distribution of absolute value of grating vector, $|G|$, for wavelengths between ${370}\;\textrm {nm}$ and ${750}\;\textrm {nm}$. (d) Wave vector of incident light in PDMS. (e) Diffraction angle in active layer in dependence of wavelength and grating vector $|G|$ of the surface grating. (f) Active path elongation.
In Fig. 3(a) the surface relief of the phase grating for ${\Delta } h={500}\;\textrm {nm}$ and $d={500}\;\textrm {nm}$ is presented. These size parameters can be varied as well in a later optimization step.
For a plane wave, the phase difference ${\Delta }\phi (x,y,\lambda )$ between the light incident on the phase grating at position (x,y) and the light incident on the grooves is given by [24]
The second scale in Fig. 3(a) shows this phase difference exemplarily for an incident wavelength of ${400}\;\textrm {nm}$.
Next, the intensity distribution $I$ of the grating vectors $G_x$ and $G_y$ of the phase grating in $x$- and $y$-direction is calculated via its Fourier transform (FT):
It corresponds to the diffraction efficiency of the different grating vectors. As the phase difference ${\Delta }\phi$ is wavelength-dependent, so is the respective diffraction efficiency. In Fig. 3(b) the intensity distribution $I$ is plotted for $\lambda ={400}\;\textrm {nm}$.
Since this distribution has a strong radial symmetry, as already shown for all structures in Fig. 2, it can be summed over elements with the same absolute value of grating vector, $|G|$, to determine $I(|G|,\lambda )$ independent of direction:
It is depicted in Fig. 3(c) for different wavelengths between ${370}\;\textrm {nm}$ and ${750}\;\textrm {nm}$. Underneath, in Fig. 3(d), the wave vector of the incident light in PDMS is plotted.
This incident light is diffracted by the surface phase grating. Its diffraction angle $\delta (|G|,\lambda )$ in dependence of the grating vector $|G|$ of the surface grating is given by
However, the different $|G|$ values occur with different intensity $I(|G|,\lambda )$. Therefore, the diffraction angles are weighted in a later step with the occurrence of the respective $|G|$ values.
To determine the diffraction angle in the active layer, its variation from the phase grating through the different layers of the solar cell is calculated using Snell’s law, taking into account the different refractive indices of the materials [55–58]. For example, for the transition from glass with a refractive index of 1.52 to ITO with a refractive index of 1.95, the diffraction angle decreases. In the case of ZnO and the active material, the refractive index is strongly wavelength-dependent, varying between 1.61 and 1.74 for ZnO and between 1.32 and 2.76 for the active material in the investigated wavelength range from ${370}\;\textrm {nm}$ to ${750}\;\textrm {nm}$.
Figure 3(e) shows the final diffraction angle in the active layer of the solar cell as a function of $|G|$ and $\lambda$. For grating vectors larger than the wave vector of the incident light, the light is not diffracted and the diffraction angle thus zero. Between ${480}\;\textrm {nm}$ and ${580}\;\textrm {nm}$, there is a strong transition between diffraction angles greater than ${80}^{\circ }$ and ${0}^{\circ }$. In this wavelength range, the refractive index of the active material is lower than the one of the layer above, ZnO. At certain angles of incidence on this boundary there is thus strong diffraction into steep angles, however, for others, total reflection occurs and no light can enter the active layer.
Finally, the path length elongation $P(|G|,\lambda )$ in an active layer with a thickness $t$ is calculated via
For better visualization, $P(|G|,\lambda )$ can be weighted by how often the respective grating vector $|G|$ actually occurs, i.e., by Fig. 3(c):
This weighted path length elongation is plotted in Fig. 3(f) for a standard active layer thickness of $t={100}\;\textrm {nm}$ as a function of wavelength and exhibits a broad peak in the wavelength range with the diffraction in steep angles. A second narrow peak on this broader peak corresponds to the wavelengths with an overlap of the second line of higher intensity in Fig. 3(c) and the steep diffraction angles in Fig. 3(e). The other structures cause a path length elongation with a similar broader peak but different additional narrow peaks and different amplitude (see Figs. S1-S8, Supplement 1).
Overall, looking again at the Fourier transforms in Fig. 2, high radial distances from the center of the FT and thus high diffraction angles behind the grating often result in a strong path length elongation in the active layer. However, they can also lead to total internal reflections or prevent diffraction of longer wavelengths. Thus, an adequate surface structure would have a FT with high intensities in the regions that, after passing the overlying cell layers, lead to diffraction at high angles in the active layer (see Fig. 3(e)). However, a final evaluation of the effects of the different surface patterns on the solar cell performance is only possible if the wavelength dependence of the absorption and the solar spectrum is also taken into account, which will be explained in the next section.
4. Current density increase
While the path length elongation required to absorb close to all incident photons depends on the absorption spectrum of the active material, the number of incident photons varies with the solar spectrum. The current density increase takes both these spectra into account. Since the solar cell layout itself is not changed, except for adding an additional phase structure on top, the electrical properties of the cell are not impaired. Therefore, only minor changes in open-circuit voltage and fill factor should occur due to a slightly higher effective intensity caused by the elongated active path length [59]. The final power conversion efficiency enhancement is thus dominated by the increase in current density, which is therefore used to evaluate the different surface structures.
For this purpose, the total absorption $A_{\textrm {tot}}$ in the active layer with and without the surface layer is calculated first. The absorption after a single path is given by
The results are shown in Fig. 4(a) using the TM Archimedean spiral structure as an example and exhibit an increase in absorption when using the surface layer, especially for wavelengths below ${550}\;\textrm {nm}$.
Fig. 4. Thue-Morse Archimedean spiral structure. (a) Total absorption in the active layer with and without surface layer. (b) Spectral current density with and without surface layer and the difference between the two.
The current density $J$ is described by
where $I_{\textrm {sol}}(\lambda )$ is the solar irradiance spectrum and $e$ the elementary charge [60]. The solar irradiance spectrum is used in terms of number of photons per area, time and wavelength, since each photon can only generate up to one exciton, even if its energy is higher. In addition to the optical factors, the absorption spectrum and the irradiance spectrum, the electrical factors exciton dissociation, charge carrier transport and collection also have an influence on the current density [61]. However, these electrical properties are not affected by the surface structure. Thus, the relative change in current density is determined only by the change in absorption due to the surface structure.Figure 4(b) therefore shows the current density with and without surface structure as well as the difference between the two assuming an optimal quantum efficiency. The total change in current density is then calculated via integration over the entire wavelength range and is listed in Table 1 for the different surface structures. The corresponding plots are shown in Figs. S9-S16 (Supplement 1).
Table 1. Increase in current density using the different surface structures for a relief height and pillar diameter of ${500}\;\textrm {nm}$.
For the selected relief height and pillar diameter, the structures show current density increases between 4.2 % and 4.7 %. The variation is mainly due to the fact that the final current density increase strongly depends on the strength of the overlap of the respective maxima of the intensity distribution of the grating vectors with the areas of diffraction at steep angles. Accordingly, the structures based on the Fermat’s spiral show the lowest increases, while the ones based on the Archimedean spiral show the highest. Furthermore, the patterns fine structured according to the Rudin-Shapiro sequence induce lower current density increases than the ones arranged according to the periodic or Thue-Morse sequence. The latter two perform similarly, with only a slight difference in case of the ring structures. Thus, the next optimization steps on pillar diameter and relief depth will be performed for one of the two most promising structure, the TM Archimedean spiral.
5. Parameter optimization
In a first step, the current density (J) increase is calculated for pillar diameters $d$ between ${300}\;\textrm {nm}$ and ${1100}\;\textrm {nm}$. The results shown in Fig. 5(a) indicate a broad maximum around ${460}\;\textrm {nm}$ with decreasing values at smaller and bigger diameters. This is because the grating vectors (see Fig. 3(c)) become shorter (longer) as the diameter of the pillars increases (decreases). When they overlap with the grating vectors causing steep diffraction angles (see Fig. 3(e)), a strong path length elongation and thus strong current density increase occurs. The severe decrease for diameters below ${400}\;\textrm {nm}$ is due to a cut-off behaviour of diffraction for grating vectors larger than the wavevector of the incident light, see Fig. 3(e).
Fig. 5. Parameter optimization for TM Archimedean spiral. (a) Pillar diameter $d$. (b) Relief height $h$. (c) Active layer thickness t.
Next, using the optimized pillar diameter of ${460}\;\textrm {nm}$, the current density increase is calculated for relief heights ${\Delta } h$ between ${300}\;\textrm {nm}$ and ${1100}\;\textrm {nm}$. The plot in Fig. 5(b) shows that the highest J increase of 5.0 % is achieved for ${\Delta } h={610}\;\textrm {nm}$, while the value drops for lower and higher depths. This is due to the fact that, depending on the relief height, the phase difference between the light incident on the pillars and that incident on the grooves can be $2\pi$ for certain wavelengths, see Eq. (6). In this case, there is no path length increase for these wavelengths, resulting in an overall smaller J increase.
In a final optimization step, the influence of the active layer thickness on the exciton generation $G$ is investigated. The calculations are performed using the previously calculated optimal pillar diameter and relief depth. In general, as the thickness of the active layer increases, the absorption in the active layer increases as well, and so does the exciton generation. However, the current density is not only dependent on exciton generation, but also on exciton dissociation, charge carrier transport, and collection [61]. As the charge carrier transport decreases with increasing active layer thickness, a material-dependent ideal thickness exists, which constitutes a compromise between optimized exciton generation and charge carrier transport. Using surface structures to increase the absorption, this ideal thickness can become smaller, while maintaining a high current density. Fig. 5(c) shows the exciton generation $G(t)$ for an active layer thickness between ${40}\;\textrm {nm}$ and ${200}\;\textrm {nm}$ with and without a surface layer in relation to the exciton generation $G(100\;\textrm {nm},\textrm {w/o}))$ for the ${100}\;\textrm {nm}$ thick layer without surface layer. While the exciton generation without the surface layer decreases rapidly for thicknesses below ${100}\;\textrm {nm}$, it is still higher for a ${80}\;\textrm {nm}$ thick active layer with a surface layer than for a ${100}\;\textrm {nm}$ thick layer without a surface layer. At the same time, the charge carrier transport is also better with such a thinner active layer. However, in order to find the overall optimal active layer thickness, calculations on the exact dependence of charge carrier transport on the active layer thickness would have to be performed, which is beyond the scope of this work.
6. Conclusion
In summary, we investigated the impact of several novel aperiodic surface structures on the current density of organic solar cells. In order to achieve a strong enhancement independent of the azimuthal angle of the incident light, structures with circular symmetric diffraction spectra are developed, more specifically structures based on concentric rings, Fermat’s and Archimedean spirals. On these fundamental structures a periodic as well as the deterministic aperiodic Thue-Morse and Rudin-Shapiro sequences are arranged and their diffraction properties are evaluated.
To determine the optimal diffractive surface structure, the respective current density increase is quantified by calculating the wavelength-dependent path elongation in the active layer and considering the absorption and solar spectra. The path length elongation depends strongly on the interaction of the grating vectors of the surface structure and the material properties of the solar cell. The surface structures that cause the strongest current density increase are those based on the Archimedean spiral. Among them, the two patterns fine structured according to the Thue-Morse and the periodic sequence perform best. Accordingly, for the Thue-Morse Archimedean spiral, the pillar diameter and relief depth are further optimized. The highest current density increase of 5.0 % is achieved for a diameter of ${460}\;\textrm {nm}$ and a depth of ${610}\;\textrm {nm}$.
Also, we found that with the optimized surface layer, even for much thinner active layers down to below ${80}\;\textrm {nm}$, higher exciton generation rates can be achieved than in the original cell without a surface layer. Since thinner layers also enable better charge carrier transport, a new, thinner optimal active layer thickness results from the surface layer.
The calculations presented here can also be transferred to other thin-film solar cells. While the absorption is already high from the beginning for high performance active materials as in this case, the increase in current density can be even stronger for active materials with a lower absorption coefficient. In addition, these calculations can also be adapted to determine the current density increase caused by other types of surface structures. Ultimately, the optimized surface layers are to be manufactured. Due to the small optimal structure sizes, a high-resolution fabrication method is required, e.g., electron beam lithography. It can be used to fabricate a silicon master for subsequent replica molding in PDMS [62]. Potentially, the surface structures can also be combined with other optimization techniques, such as nanoparticle incorporation or layer thickness optimization.
Funding
Deutsche Forschungsgemeinschaft (PAK 943 DE 486/22-1).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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