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Light trapping nano structures with over 30% enhancement in perovskite solar cells
Organic Electronics 75 (2019) 105385
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Organic Electronics journal homepage: www.elsevier.com/locate/orgel
Light trapping nano structures with over 30% enhancement in perovskite solar cells
T
Shuren Sun, Ziang Xie, Guogang Qin, Lixin Xiao* State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking University, Beijing, 100871, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Perovskite Solar cell FDTD Neural network Light trap
Organic–inorganic metal halide perovskites have drawn a great deal of attention due to their supreme optical and electrical properties and their potential in future application in optoelectronic devices. Here, we carry out finite-difference time-domain (FDTD) simulation on different experimentally realistic structures of perovskite solar cells (PSC) and optimize their parameters with assistance of neural network (NN). We find an optimized structure with 30.48% enhancement comparing to planar structure and the fact that with properly design, 300nm-thick nano-textured structure can outperform 900-nm-thick planar structure. We believe that light trapping structure is essential in thin film PSCs and also has a great potential in lead-free PSCs.
1. Introduction Since the first application of metal halide perovskite as absorber material for solar cells in 2009, the efficiency of perovskite solar cell (PSC) has been skyrocketing from 3.81% to 24.2% [1–7], which is higher than that of best polycrystalline silicon device [8]. A lot of research focused on improving the quality of perovskite material [9–17], interface contact between absorber layer and transport layers [18–20], and performance of transport layers [21,22] but relatively few concerned about light management in perovskite solar cell, which is also an important part in the design of photovoltaic devices. In conventional silicon solar cells, whose absorber layer is typically tens of microns, light trapping can be realized by roughening the semiconductor-air interface. Randomized texture results in randomized light propagation directions inside the material and thus a much longer distance [23]. From ray-optics perspective, this kind of texture has an upper limit of 4n2/sin2 θ [24], in which θ is the angle of the emission cone of light and n is the refractive index of absorber material. However, the theory breaks down when the thickness of material and the size of structure feature approach wavelength scale. Yu et al. used a statistical coupled-mode theory to describe this new situation and acquired a deep understanding of the origin of light trapping in thin-film silicon solar cell [25–27]. In the field of perovskite solar cell, the knowledge about light trapping and optical performance is relatively limited [28–33]. Herein, we use finite-difference-time-domain (FDTD) simulation to study two different sets of textures (Fig. 1) for methylammonium lead
*
iodide (MAPbI3), array of cylindrical nanopillars and array of cylindrical nanoholes. For each situation, multiple parameters, including period of texture, thickness of absorber layer, size of nanostructure and type of infill material, are explored to find the optimization condition. We explore two sets of textures and optimize the cell efficiency over five parameters. It is found that with delicate design, 300-nm-thick nano-textured device can have estimated PCE as high as 26.86%, which is even better than a 900-nm-thick planar cell (25.11%). Moreover, we build a deep learning model to predict simulation results at a much finer grid in hyperparameter space, which helps us find an optimized set of parameters with highest efficiency. 2. Method A 3D optical simulation is carried out using Lumerical FDTD Solution software (version 8.6.0). As Fig. 1 shows, we explore two sets of texture, array of cylindrical nanopillars (a) and array of cylindrical nanoholes (b). In both circumstances, normally incident light is generated by a plane wave source with wavelength from 300 nm to 900 nm which is placed right above the studied structure. The range is chosen so that the major range of absorption spectrum of MAPbI3, when illuminated under the sun (AM 1.5), is covered. In order to simulate a periodic pattern efficiently, we use symmetric boundary conditions for x-direction and asymmetric ones for y-direction respectively (Fig. 2). Along z-direction, Perfectly Matched Layer (PML) boundary condition is selected to prevent unexpected reflection from the upper and lower boundaries. In FDTD simulation space, grid mesh size less than 30 nm
Corresponding author. E-mail address: [email protected] (L. Xiao).
https://doi.org/10.1016/j.orgel.2019.105385 Received 22 June 2019; Received in revised form 27 July 2019; Accepted 27 July 2019 Available online 27 July 2019 1566-1199/ © 2019 Elsevier B.V. All rights reserved.
Organic Electronics 75 (2019) 105385
S. Sun, et al.
where I (λ ) stands for the intensity of solar irradiance at specific wavelength, λ , which is given by AM 1.5 Direct + Circumsolar spectrum in this study. a (λ ) is the absorption of structure and λ g is wavelength corresponding to the band gap of absorber material, which is 779 nm for MAPbI3 [36]. h, q, c are Planck constant, electron charge and speed of light respectively. Radiative recombination current density, Jr , is calculated according to, ∞
Jr (V ) = fg q
2
∫ 2hπE 3c 2 Eg
a (E ) E − qV [e KB TC
dE
− 1]
where fg is a geometrical factor and assigned the value of 1 since the solar cell is only emitting radiation from one side [34]. V is the external applied voltage, KB is the Boltzmann constant and TC , the temperature of cell, is assigned the value of 300 K for simplicity. Then the external current density Jext can be written as,
Fig. 1. Two dimensional and three-dimensional schematic of a) cylindrical nanopillar and b) nanohole. Dark brown material is MAPbI3 and blue material represents infill material. Period (P), radius (R) of pillar (and hole), depth (D) of patterned layer and thickness (T) of absorber layer are shown respectively.
Jext (V ) = Jmax − Jr (V ) Finally, the estimated PCE can be calculated as,
ηe =
max(V ⋅Jext (V )) ΦAM1.5
where ΦAM1.5 is the integrated spectral irradiance of AM 1.5 spectrum. To predict results for a much finer grid search in parameter space a neural network (NN) model containing three hidden layers, each containing 128 dense units (Fig. 3), is built and trained with the data generated by FDTD solution. The program is written in python and based on Tensorflow package (1.12.0). Specifically, FDTD solution generates data for all combinations of P = 300, 500, 700, 900 nm; DR = 0.1, 0.3, 0.5, 0.7, 0.9; RR = 1/2, 1/6, 1/8; T = 300, 500, 700, 900 nm for all infill materials. After learning the pattern in these results, NN model can help predict results for finer grid search, such as P = 300–900 nm with 10 nm gap and find an optimized set of parameters, which can be verified by FDTD method in return.
Fig. 2. Schematics of FDTD simulation. In 3D illustration (left), Orange frame indicates the 3D FDTD simulation space while the semi-transparent blocks represent PML layers. The rainbow-colored curve surface represents the wide bandwidth plane wave source. 2D illustration (right).
3. Results and discussion
(one-tenth of the lower boundary of calculated wavelength) is chosen to ensure the accuracy of simulation. Additionally, a much finer mesh with grid less than 3 nm is applied around the cylinder to improve simulation result for curve interfaces. Two power monitors are set to record transmission and reflection of the structure respectively. Specifically, the reflection monitor is placed 50 nm above the light source whereas the transmission monitor is placed 50 nm beneath the lower surface of metal electrode. And the absorption of MAPbI3 can be achieved by
Fig. 4(a) shows estimated efficiencies for all simulation results (360 points in total) at T = 300 nm. Each column represents a specific infill material and type of texture (hole or pillar) and the horizontal axis shows periods of structures. The red dotted line indicates ηe of the structure with 300 nm-thick planar absorber layer. It can be seen that poorly designed nano-structured device cannot even compete with the planar structures. As shown in Fig. 4, structures that have period of 300 nm or 900 nm more likely have low estimated efficiency since their periods make it difficult to couple with light with wavelength between 500–700 nm, which carries majority of solar energy. Another noticeable factor is infill material, TiO2 structures generally fail to outperform the
Absorption = 1 − Reflection − Transmission considering the fact that infill material absorbs negligible amount of solar energy. For both patterns, five different parameters are studied (Fig. 1): Period (P), which is defined as the distance between the centers of two adjacent pillars (or holes); Thickness (T), which is the total thickness of the absorber layer including the patterned part; Radius ratio (RR), which is defined as the ratio of the nanopillars (or nanoholes) radius to period of the structure; Material (M), which is the type of infill material for the structures, including tin dioxide (SnO2), zinc oxide (ZnO), titanium dioxide (TiO2); Depth ratio (DR), which is defined as the ratio of depth of patterned structure to the total thickness of the absorber layer. To evaluate performance of different structures and parameters, an estimated power conversion efficiency (PCE), ηe, is calculated for each simulated absorption spectrum, which is the detailed balance limit for the spectrum [34,35]. Specifically, maximum photocurrent density, Jmax , can be calculated as, λg
Jmax =
a (λ ) I (λ ) dλ ∫ qλ hc
Fig. 3. Schematic of deep learning network. A network consists of an input layer, a normalization layer, multiple dense layers and an output layer.
0
2
Organic Electronics 75 (2019) 105385
S. Sun, et al.
and textures. The last column (Δηe) of the table shows relative enhancement to the planar structure with corresponding thickness. It can be seen that the enhancement is prominent when the thickness is 500 nm while not much at 700 nm and 900 nm, which may be explained by the already significant absorption of the 700-nm-thick and 900-nm-thick MAPbI3. The best result of all simulations is 29.03% enhancement relative to planar structure at T = 500 nm, P = 700 nm, RR = 1/2, DR = 0.5, infill = “ZnO”, texture = “hole”. It is a noticeable increasement considering that this is only an optical effect, which can easily be applied into any existing planar PSCs and boost their efficiencies. The highest efficiencies for different depth ratios, depth ratios, and pattern periods are shown in Fig. 5(a) and (b) and 5(c) respectively. The most noticeable feature is that the best results for different radius ratios mostly happens at 1/2 for “hole” patterns and 1/4 for “pillar” patterns, both are the situations that contain the least volume of absorber material in the patterned layer. This is an evidence for that the patterned layer works more likely as a guided mode resonance structure than an absorbing structure. In the “depth ratio” (6(a)) and “period” (6(c)) situation, different parameter values make a larger difference in ηe when the thickness is thinner, which means optimization is important particularly in the case of thin film under 500 nm. Another interesting phenomenon is that with all of four types of structures (SnO2 hole, SnO2 pillar, ZnO hole, ZnO pillar) the best results of 300-nm-thick patterned structure can always outperform 900-nm-thick planar structure. It is well known that device with a thinner absorber layer means less recombination, less amount of raw material, lower requirement for crystalline quality yet less absorption comparing to one with a thicker absorber layer. With optimized design of textures, the drawback can finally be overcome. In Fig. 5(d), the best result for 300-nm-thick SnO2-filled-absorber are shown. Specifically, the parameters of structure that has maximum absorption (red line) are, P = 500 nm, RR = 1/2, DR = 0.9, and the estimated PCE is 26.86% while the blue line shows the absorption spectrum of the 300-nm-planar structure, estimated PCE is 22.14%. Multiple absorption peaks are shown in the best structure absorption spectrum, which benefits from a large number of guided mode that the structure supported. As a result, this structure gains efficiency as high as 26.86% with relatively small thickness of 300 nm. Fig. 6(a) shows distribution of electric field at 550 nm in a specific structure (T = 300 nm, P = 500 nm, R = 1/3, D = 7/10, Material = SnO2, ηe = 24.63%). The wavelength is chosen because the absorption line reaches its climax there (Fig. 6(b)). In Fig. 6(a), electric field clearly appears as a guided mode, which is stimulated by the upper patterned layer. The periodic structure here acts as a resonance guide to select and couple with certain modes in incident light and help them to enter the absorber layer, as a result reflection of the structure at certain wavelength is significantly reduced. FDTD simulation is a time-consuming job for every point in parameter grid and it is an impossible task to find an optimal point with high precision in a high-dimensional hyperparameter space. To address this problem, we introduce a Neural Network (NN) assisted method which significantly reduces time for searching. Specifically, instead of carrying out FDTD simulation on every point in hyperparameter space, only few carefully chosen points are studied, which in our case is P = 300, 500, 700, 900 nm; T = 300, 500, 700, 900 nm; RR = 1/2, 1/ 3, 1/4; DR = 1/10, 2/10 … 9/10. Then a neural network with three hidden layers, containing 128 neuron each, is build and trained with data generated by FDTD software. We expect the deep learning model can find and mimic the pattern in data and figure out results at other un-simulated points. Fig. 7(a) shows a grid search for P and D (at point: T = 500 nm, R = 1/2, infill = “SnO2”, pattern = “hole”) calculated by a well-trained neural network (Fig. 3). A local maximum at D = 0.7, P = 590 nm is easily identified and then verified by FDTD method. Fig. 7(b) shows the best result found by both methods(NN and FDTD) at T = 500 nm, Infill = “SnO2”, pattern = “hole” in which green line
Fig. 4. a) Estimated efficiency of all simulation results at T = 300 nm arranged according to period, infill material and type of texture. Circles with different colors represent different DRs. The red dotted line indicates estimated efficiency of 300 nm -thick-planar PSC. b) refractive index of different material. Blue line shows index of ZnO, red line shows index of SnO2, yellow line shows index of TiO2 and purple dotted line shows index of MAPbI3.
planar structure. These can be explained by the fact that a structure can hardly work as a photonic crystal when refractive index difference between absorber material and infill material is small, as a result the infill material cannot help guide the light in, yet it occupies space of absorber. As shown in Fig. 4(b) [36–39], TiO2 and MAPbI3's refractive index, especially in the range of 500–700 nm, are very close. In the following of this section, only “SnO2” and “ZnO” results will be discussed for the reason that “TiO2” results have already been proved inferior. Table 1 lists the best results for different thickness, infill materials
Table 1 Summary of best results for SnO2 and ZnO structures with different thickness. T (nm)
Infill/Pattern
RR
DR
P (nm)
ηe (%)
Δηe (%)
300
SnO2/hole SnO2/pillar ZnO/hole ZnO/pillar SnO2/hole SnO2/pillar ZnO/hole ZnO/pillar SnO2/hole SnO2/pillar ZnO/hole ZnO/pillar SnO2/hole SnO2/pillar ZnO/hole ZnO/pillar
1/2 1/3 1/2 1/3 1/2 1/4 1/2 1/4 1/2 1/4 1/2 1/4 1/2 1/4 1/2 1/4
0.9 0.9 0.9 0.9 0.5 0.5 0.5 0.5 0.5 0.1 0.1 0.1 0.5 0.5 0.3 0.5
500 500 500 500 700 700 700 500 700 500 500 500 700 700 500 700
26.86 26.68 26.32 26.53 27.84 28.82 29.16 28.86 29.12 29.17 29.46 29.62 30.15 30.07 30.00 30.07
21.32 20.51 18.88 19.83 23.19 27.52 29.03 27.70 16.20 16.40 17.56 18.20 20.07 19.75 19.47 19.75
500
700
900
3
Organic Electronics 75 (2019) 105385
S. Sun, et al.
Fig. 5. Highest estimated efficiency for different a) depth ratios, b) radius ratios, c) periods. The dots on the y-axis indicate efficiencies of planar structure with corresponding thickness. d) shows comparisons of best and worst results for 300-nm-thick-SnO2-structure. Red line and blue line represent planar structure and best simulation result at 300 nm respectively.
Fig. 7. a) Grid search by neural network for P and D while other parameters remain the same (T = 500 nm, R = 1/2, Material = SnO2). Estimated efficiency is indicated by color. The optimal condition is indicated by the “x” mark. b) Comparison between FDTD simulation result and neural network result. The dotted green line is the best result found by FDTD method, red line is the best result found by neural network, and blue line has the same paramters as the red line but calculated by FDTD method. The grey curve in the background is normalized AM 1.5 solar spectrum.
Fig. 6. a) Electric field distribution at 550 nm. Structure parameter: T = 300 nm, P = 500 nm, R = 1/3, D = 7/10, infill material = SnO2, Eff = 24.63%. The dotted lines indicate the position of SnO2 b) Absorption spectrum of the above structure. Absorption at 550 nm is a local maxima.
shows the best result found by FDTD method (efficiency is 27.84%), orange line shows that found by NN (efficiency is 28.97%) and blue line shows result at the same set of parameters as orange line but calculated by FDTD method (efficiency is 29.49%). Noticeably, this is the highest PCE in the structures of 500-nm-thick absorber and gains an enhancement of 30.48% comparing to the planar structure. Absorption
spectrum generated by NN successfully predicts most of the peaks and the final estimated PCE. More importantly, by using NN, we find a more optimal result near original parameter points with minimal effort.
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Organic Electronics 75 (2019) 105385
S. Sun, et al.
4. Conclusions
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In conclusion, we explore two sets of textures and optimize the cell efficiency over five parameters. It is found that with delicate design, 300-nm-thick textured device can have estimated PCE as high as 26.86%, which is even better than a 900-nm-thick planar cell (25.11%). Using neural network model, we successfully find a more reasonable set of parameters, a 500-nm-thick nano-textured PSC with enhancement of 30.48% comparing to planar PSC, which is verified by FDTD method. Additionally, with the help of nanosphere lithography, a large area of the periodic pattern described above can be realized quiet easily. The periodic cylindrical nanopillars of absorber can be fabricated via growing perovskite material on periodic hole-shaped electron transport layer and vice versa [40-42]. Nowadays high efficiency perovskite solar cells are commonly fabricated with relatively thick absorber, typically around 500 nm, to balance optical absorption and electrical performance. However, growing a thick and high-quality perovskite layer need delicate control of both experimental environment and process, which can hardly be generalized to industry. Making perovskite layer thinner can not only decrease the amount of material but also lower the requirement of crystalline quality. Meanwhile, delicate light trapping design guarantees an affordable optical performance. Moreover, PCE of lead-free PSCs are limited by the imperfect electrical properties and thin thickness of the absorber material. Importing light trapping structure into non-lead PSCs can overcome both drawbacks and bring substantial improvement to their efficiencies. Therefore, we believe that light trapping design is an important part for future development of both lead and lead-free perovskite solar cells. Acknowledgement This work was supported by the National Natural Science Foundation of China (11674004, 61775004, 61575005), the National Key R&D Program of China (2016YFB0401003). References [1] A. Kojima, K. Teshima, Y. Shirai, T. Miyasaka, J. Am. Chem. Soc. 131 (2009) 6050–6051. [2] J. Burschka, N. Pellet, S.J. Moon, R. Humphry-Baker, P. Gao, M.K. Nazeeruddin, M. Gratzel, Nature 499 (2013) 316–319. [3] M. Liu, M.B. Johnston, H.J. Snaith, Nature 501 (2013) 395–398. [4] W.S. Yang, J.H. Noh, N.J. Jeon, Y.C. Kim, S. Ryu, J. Seo, S.I. Seok, Science 348 (2015) 1234–1237. [5] M. Saliba, T. Matsui, J.-Y. Seo, K. Domanski, J.-P. Correa-Baena, N. Mohammad K, S.M. Zakeeruddin, W. Tress, A. Abate, A. Hagfeldt, M. Grätzel, Energy Environ. Sci. 9 (2016) 1989–1997. [6] W.S. Yang, B.W. Park, E.H. Jung, N.J. Jeon, Y.C. Kim, D.U. Lee, S.S. Shin, J. Seo, E.K. Kim, J.H. Noh, S.I. Seok, Science 356 (2017) 1376–1379. [7] C. Zuo, H.J. Bolink, H. Han, J. Huang, D. Cahen, L. Ding, Adv. Sci. 3 (2016)
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Contents lists available at ScienceDirect
Organic Electronics journal homepage: www.elsevier.com/locate/orgel
Light trapping nano structures with over 30% enhancement in perovskite solar cells
T
Shuren Sun, Ziang Xie, Guogang Qin, Lixin Xiao* State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking University, Beijing, 100871, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Perovskite Solar cell FDTD Neural network Light trap
Organic–inorganic metal halide perovskites have drawn a great deal of attention due to their supreme optical and electrical properties and their potential in future application in optoelectronic devices. Here, we carry out finite-difference time-domain (FDTD) simulation on different experimentally realistic structures of perovskite solar cells (PSC) and optimize their parameters with assistance of neural network (NN). We find an optimized structure with 30.48% enhancement comparing to planar structure and the fact that with properly design, 300nm-thick nano-textured structure can outperform 900-nm-thick planar structure. We believe that light trapping structure is essential in thin film PSCs and also has a great potential in lead-free PSCs.
1. Introduction Since the first application of metal halide perovskite as absorber material for solar cells in 2009, the efficiency of perovskite solar cell (PSC) has been skyrocketing from 3.81% to 24.2% [1–7], which is higher than that of best polycrystalline silicon device [8]. A lot of research focused on improving the quality of perovskite material [9–17], interface contact between absorber layer and transport layers [18–20], and performance of transport layers [21,22] but relatively few concerned about light management in perovskite solar cell, which is also an important part in the design of photovoltaic devices. In conventional silicon solar cells, whose absorber layer is typically tens of microns, light trapping can be realized by roughening the semiconductor-air interface. Randomized texture results in randomized light propagation directions inside the material and thus a much longer distance [23]. From ray-optics perspective, this kind of texture has an upper limit of 4n2/sin2 θ [24], in which θ is the angle of the emission cone of light and n is the refractive index of absorber material. However, the theory breaks down when the thickness of material and the size of structure feature approach wavelength scale. Yu et al. used a statistical coupled-mode theory to describe this new situation and acquired a deep understanding of the origin of light trapping in thin-film silicon solar cell [25–27]. In the field of perovskite solar cell, the knowledge about light trapping and optical performance is relatively limited [28–33]. Herein, we use finite-difference-time-domain (FDTD) simulation to study two different sets of textures (Fig. 1) for methylammonium lead
*
iodide (MAPbI3), array of cylindrical nanopillars and array of cylindrical nanoholes. For each situation, multiple parameters, including period of texture, thickness of absorber layer, size of nanostructure and type of infill material, are explored to find the optimization condition. We explore two sets of textures and optimize the cell efficiency over five parameters. It is found that with delicate design, 300-nm-thick nano-textured device can have estimated PCE as high as 26.86%, which is even better than a 900-nm-thick planar cell (25.11%). Moreover, we build a deep learning model to predict simulation results at a much finer grid in hyperparameter space, which helps us find an optimized set of parameters with highest efficiency. 2. Method A 3D optical simulation is carried out using Lumerical FDTD Solution software (version 8.6.0). As Fig. 1 shows, we explore two sets of texture, array of cylindrical nanopillars (a) and array of cylindrical nanoholes (b). In both circumstances, normally incident light is generated by a plane wave source with wavelength from 300 nm to 900 nm which is placed right above the studied structure. The range is chosen so that the major range of absorption spectrum of MAPbI3, when illuminated under the sun (AM 1.5), is covered. In order to simulate a periodic pattern efficiently, we use symmetric boundary conditions for x-direction and asymmetric ones for y-direction respectively (Fig. 2). Along z-direction, Perfectly Matched Layer (PML) boundary condition is selected to prevent unexpected reflection from the upper and lower boundaries. In FDTD simulation space, grid mesh size less than 30 nm
Corresponding author. E-mail address: [email protected] (L. Xiao).
https://doi.org/10.1016/j.orgel.2019.105385 Received 22 June 2019; Received in revised form 27 July 2019; Accepted 27 July 2019 Available online 27 July 2019 1566-1199/ © 2019 Elsevier B.V. All rights reserved.
Organic Electronics 75 (2019) 105385
S. Sun, et al.
where I (λ ) stands for the intensity of solar irradiance at specific wavelength, λ , which is given by AM 1.5 Direct + Circumsolar spectrum in this study. a (λ ) is the absorption of structure and λ g is wavelength corresponding to the band gap of absorber material, which is 779 nm for MAPbI3 [36]. h, q, c are Planck constant, electron charge and speed of light respectively. Radiative recombination current density, Jr , is calculated according to, ∞
Jr (V ) = fg q
2
∫ 2hπE 3c 2 Eg
a (E ) E − qV [e KB TC
dE
− 1]
where fg is a geometrical factor and assigned the value of 1 since the solar cell is only emitting radiation from one side [34]. V is the external applied voltage, KB is the Boltzmann constant and TC , the temperature of cell, is assigned the value of 300 K for simplicity. Then the external current density Jext can be written as,
Fig. 1. Two dimensional and three-dimensional schematic of a) cylindrical nanopillar and b) nanohole. Dark brown material is MAPbI3 and blue material represents infill material. Period (P), radius (R) of pillar (and hole), depth (D) of patterned layer and thickness (T) of absorber layer are shown respectively.
Jext (V ) = Jmax − Jr (V ) Finally, the estimated PCE can be calculated as,
ηe =
max(V ⋅Jext (V )) ΦAM1.5
where ΦAM1.5 is the integrated spectral irradiance of AM 1.5 spectrum. To predict results for a much finer grid search in parameter space a neural network (NN) model containing three hidden layers, each containing 128 dense units (Fig. 3), is built and trained with the data generated by FDTD solution. The program is written in python and based on Tensorflow package (1.12.0). Specifically, FDTD solution generates data for all combinations of P = 300, 500, 700, 900 nm; DR = 0.1, 0.3, 0.5, 0.7, 0.9; RR = 1/2, 1/6, 1/8; T = 300, 500, 700, 900 nm for all infill materials. After learning the pattern in these results, NN model can help predict results for finer grid search, such as P = 300–900 nm with 10 nm gap and find an optimized set of parameters, which can be verified by FDTD method in return.
Fig. 2. Schematics of FDTD simulation. In 3D illustration (left), Orange frame indicates the 3D FDTD simulation space while the semi-transparent blocks represent PML layers. The rainbow-colored curve surface represents the wide bandwidth plane wave source. 2D illustration (right).
3. Results and discussion
(one-tenth of the lower boundary of calculated wavelength) is chosen to ensure the accuracy of simulation. Additionally, a much finer mesh with grid less than 3 nm is applied around the cylinder to improve simulation result for curve interfaces. Two power monitors are set to record transmission and reflection of the structure respectively. Specifically, the reflection monitor is placed 50 nm above the light source whereas the transmission monitor is placed 50 nm beneath the lower surface of metal electrode. And the absorption of MAPbI3 can be achieved by
Fig. 4(a) shows estimated efficiencies for all simulation results (360 points in total) at T = 300 nm. Each column represents a specific infill material and type of texture (hole or pillar) and the horizontal axis shows periods of structures. The red dotted line indicates ηe of the structure with 300 nm-thick planar absorber layer. It can be seen that poorly designed nano-structured device cannot even compete with the planar structures. As shown in Fig. 4, structures that have period of 300 nm or 900 nm more likely have low estimated efficiency since their periods make it difficult to couple with light with wavelength between 500–700 nm, which carries majority of solar energy. Another noticeable factor is infill material, TiO2 structures generally fail to outperform the
Absorption = 1 − Reflection − Transmission considering the fact that infill material absorbs negligible amount of solar energy. For both patterns, five different parameters are studied (Fig. 1): Period (P), which is defined as the distance between the centers of two adjacent pillars (or holes); Thickness (T), which is the total thickness of the absorber layer including the patterned part; Radius ratio (RR), which is defined as the ratio of the nanopillars (or nanoholes) radius to period of the structure; Material (M), which is the type of infill material for the structures, including tin dioxide (SnO2), zinc oxide (ZnO), titanium dioxide (TiO2); Depth ratio (DR), which is defined as the ratio of depth of patterned structure to the total thickness of the absorber layer. To evaluate performance of different structures and parameters, an estimated power conversion efficiency (PCE), ηe, is calculated for each simulated absorption spectrum, which is the detailed balance limit for the spectrum [34,35]. Specifically, maximum photocurrent density, Jmax , can be calculated as, λg
Jmax =
a (λ ) I (λ ) dλ ∫ qλ hc
Fig. 3. Schematic of deep learning network. A network consists of an input layer, a normalization layer, multiple dense layers and an output layer.
0
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and textures. The last column (Δηe) of the table shows relative enhancement to the planar structure with corresponding thickness. It can be seen that the enhancement is prominent when the thickness is 500 nm while not much at 700 nm and 900 nm, which may be explained by the already significant absorption of the 700-nm-thick and 900-nm-thick MAPbI3. The best result of all simulations is 29.03% enhancement relative to planar structure at T = 500 nm, P = 700 nm, RR = 1/2, DR = 0.5, infill = “ZnO”, texture = “hole”. It is a noticeable increasement considering that this is only an optical effect, which can easily be applied into any existing planar PSCs and boost their efficiencies. The highest efficiencies for different depth ratios, depth ratios, and pattern periods are shown in Fig. 5(a) and (b) and 5(c) respectively. The most noticeable feature is that the best results for different radius ratios mostly happens at 1/2 for “hole” patterns and 1/4 for “pillar” patterns, both are the situations that contain the least volume of absorber material in the patterned layer. This is an evidence for that the patterned layer works more likely as a guided mode resonance structure than an absorbing structure. In the “depth ratio” (6(a)) and “period” (6(c)) situation, different parameter values make a larger difference in ηe when the thickness is thinner, which means optimization is important particularly in the case of thin film under 500 nm. Another interesting phenomenon is that with all of four types of structures (SnO2 hole, SnO2 pillar, ZnO hole, ZnO pillar) the best results of 300-nm-thick patterned structure can always outperform 900-nm-thick planar structure. It is well known that device with a thinner absorber layer means less recombination, less amount of raw material, lower requirement for crystalline quality yet less absorption comparing to one with a thicker absorber layer. With optimized design of textures, the drawback can finally be overcome. In Fig. 5(d), the best result for 300-nm-thick SnO2-filled-absorber are shown. Specifically, the parameters of structure that has maximum absorption (red line) are, P = 500 nm, RR = 1/2, DR = 0.9, and the estimated PCE is 26.86% while the blue line shows the absorption spectrum of the 300-nm-planar structure, estimated PCE is 22.14%. Multiple absorption peaks are shown in the best structure absorption spectrum, which benefits from a large number of guided mode that the structure supported. As a result, this structure gains efficiency as high as 26.86% with relatively small thickness of 300 nm. Fig. 6(a) shows distribution of electric field at 550 nm in a specific structure (T = 300 nm, P = 500 nm, R = 1/3, D = 7/10, Material = SnO2, ηe = 24.63%). The wavelength is chosen because the absorption line reaches its climax there (Fig. 6(b)). In Fig. 6(a), electric field clearly appears as a guided mode, which is stimulated by the upper patterned layer. The periodic structure here acts as a resonance guide to select and couple with certain modes in incident light and help them to enter the absorber layer, as a result reflection of the structure at certain wavelength is significantly reduced. FDTD simulation is a time-consuming job for every point in parameter grid and it is an impossible task to find an optimal point with high precision in a high-dimensional hyperparameter space. To address this problem, we introduce a Neural Network (NN) assisted method which significantly reduces time for searching. Specifically, instead of carrying out FDTD simulation on every point in hyperparameter space, only few carefully chosen points are studied, which in our case is P = 300, 500, 700, 900 nm; T = 300, 500, 700, 900 nm; RR = 1/2, 1/ 3, 1/4; DR = 1/10, 2/10 … 9/10. Then a neural network with three hidden layers, containing 128 neuron each, is build and trained with data generated by FDTD software. We expect the deep learning model can find and mimic the pattern in data and figure out results at other un-simulated points. Fig. 7(a) shows a grid search for P and D (at point: T = 500 nm, R = 1/2, infill = “SnO2”, pattern = “hole”) calculated by a well-trained neural network (Fig. 3). A local maximum at D = 0.7, P = 590 nm is easily identified and then verified by FDTD method. Fig. 7(b) shows the best result found by both methods(NN and FDTD) at T = 500 nm, Infill = “SnO2”, pattern = “hole” in which green line
Fig. 4. a) Estimated efficiency of all simulation results at T = 300 nm arranged according to period, infill material and type of texture. Circles with different colors represent different DRs. The red dotted line indicates estimated efficiency of 300 nm -thick-planar PSC. b) refractive index of different material. Blue line shows index of ZnO, red line shows index of SnO2, yellow line shows index of TiO2 and purple dotted line shows index of MAPbI3.
planar structure. These can be explained by the fact that a structure can hardly work as a photonic crystal when refractive index difference between absorber material and infill material is small, as a result the infill material cannot help guide the light in, yet it occupies space of absorber. As shown in Fig. 4(b) [36–39], TiO2 and MAPbI3's refractive index, especially in the range of 500–700 nm, are very close. In the following of this section, only “SnO2” and “ZnO” results will be discussed for the reason that “TiO2” results have already been proved inferior. Table 1 lists the best results for different thickness, infill materials
Table 1 Summary of best results for SnO2 and ZnO structures with different thickness. T (nm)
Infill/Pattern
RR
DR
P (nm)
ηe (%)
Δηe (%)
300
SnO2/hole SnO2/pillar ZnO/hole ZnO/pillar SnO2/hole SnO2/pillar ZnO/hole ZnO/pillar SnO2/hole SnO2/pillar ZnO/hole ZnO/pillar SnO2/hole SnO2/pillar ZnO/hole ZnO/pillar
1/2 1/3 1/2 1/3 1/2 1/4 1/2 1/4 1/2 1/4 1/2 1/4 1/2 1/4 1/2 1/4
0.9 0.9 0.9 0.9 0.5 0.5 0.5 0.5 0.5 0.1 0.1 0.1 0.5 0.5 0.3 0.5
500 500 500 500 700 700 700 500 700 500 500 500 700 700 500 700
26.86 26.68 26.32 26.53 27.84 28.82 29.16 28.86 29.12 29.17 29.46 29.62 30.15 30.07 30.00 30.07
21.32 20.51 18.88 19.83 23.19 27.52 29.03 27.70 16.20 16.40 17.56 18.20 20.07 19.75 19.47 19.75
500
700
900
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Fig. 5. Highest estimated efficiency for different a) depth ratios, b) radius ratios, c) periods. The dots on the y-axis indicate efficiencies of planar structure with corresponding thickness. d) shows comparisons of best and worst results for 300-nm-thick-SnO2-structure. Red line and blue line represent planar structure and best simulation result at 300 nm respectively.
Fig. 7. a) Grid search by neural network for P and D while other parameters remain the same (T = 500 nm, R = 1/2, Material = SnO2). Estimated efficiency is indicated by color. The optimal condition is indicated by the “x” mark. b) Comparison between FDTD simulation result and neural network result. The dotted green line is the best result found by FDTD method, red line is the best result found by neural network, and blue line has the same paramters as the red line but calculated by FDTD method. The grey curve in the background is normalized AM 1.5 solar spectrum.
Fig. 6. a) Electric field distribution at 550 nm. Structure parameter: T = 300 nm, P = 500 nm, R = 1/3, D = 7/10, infill material = SnO2, Eff = 24.63%. The dotted lines indicate the position of SnO2 b) Absorption spectrum of the above structure. Absorption at 550 nm is a local maxima.
shows the best result found by FDTD method (efficiency is 27.84%), orange line shows that found by NN (efficiency is 28.97%) and blue line shows result at the same set of parameters as orange line but calculated by FDTD method (efficiency is 29.49%). Noticeably, this is the highest PCE in the structures of 500-nm-thick absorber and gains an enhancement of 30.48% comparing to the planar structure. Absorption
spectrum generated by NN successfully predicts most of the peaks and the final estimated PCE. More importantly, by using NN, we find a more optimal result near original parameter points with minimal effort.
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4. Conclusions
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In conclusion, we explore two sets of textures and optimize the cell efficiency over five parameters. It is found that with delicate design, 300-nm-thick textured device can have estimated PCE as high as 26.86%, which is even better than a 900-nm-thick planar cell (25.11%). Using neural network model, we successfully find a more reasonable set of parameters, a 500-nm-thick nano-textured PSC with enhancement of 30.48% comparing to planar PSC, which is verified by FDTD method. Additionally, with the help of nanosphere lithography, a large area of the periodic pattern described above can be realized quiet easily. The periodic cylindrical nanopillars of absorber can be fabricated via growing perovskite material on periodic hole-shaped electron transport layer and vice versa [40-42]. Nowadays high efficiency perovskite solar cells are commonly fabricated with relatively thick absorber, typically around 500 nm, to balance optical absorption and electrical performance. However, growing a thick and high-quality perovskite layer need delicate control of both experimental environment and process, which can hardly be generalized to industry. Making perovskite layer thinner can not only decrease the amount of material but also lower the requirement of crystalline quality. Meanwhile, delicate light trapping design guarantees an affordable optical performance. Moreover, PCE of lead-free PSCs are limited by the imperfect electrical properties and thin thickness of the absorber material. Importing light trapping structure into non-lead PSCs can overcome both drawbacks and bring substantial improvement to their efficiencies. Therefore, we believe that light trapping design is an important part for future development of both lead and lead-free perovskite solar cells. Acknowledgement This work was supported by the National Natural Science Foundation of China (11674004, 61775004, 61575005), the National Key R&D Program of China (2016YFB0401003). References [1] A. Kojima, K. Teshima, Y. Shirai, T. Miyasaka, J. Am. Chem. Soc. 131 (2009) 6050–6051. [2] J. Burschka, N. Pellet, S.J. Moon, R. Humphry-Baker, P. Gao, M.K. Nazeeruddin, M. Gratzel, Nature 499 (2013) 316–319. [3] M. Liu, M.B. Johnston, H.J. Snaith, Nature 501 (2013) 395–398. [4] W.S. Yang, J.H. Noh, N.J. Jeon, Y.C. Kim, S. Ryu, J. Seo, S.I. Seok, Science 348 (2015) 1234–1237. [5] M. Saliba, T. Matsui, J.-Y. Seo, K. Domanski, J.-P. Correa-Baena, N. Mohammad K, S.M. Zakeeruddin, W. Tress, A. Abate, A. Hagfeldt, M. Grätzel, Energy Environ. Sci. 9 (2016) 1989–1997. [6] W.S. Yang, B.W. Park, E.H. Jung, N.J. Jeon, Y.C. Kim, D.U. Lee, S.S. Shin, J. Seo, E.K. Kim, J.H. Noh, S.I. Seok, Science 356 (2017) 1376–1379. [7] C. Zuo, H.J. Bolink, H. Han, J. Huang, D. Cahen, L. Ding, Adv. Sci. 3 (2016)
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