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Simulation of Boosting Efficiency of GaAs Absorption Layers with KNbO_{3} Scatterers for Solar Cells

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## Abstract

**:**

_{3}, having good dielectric, photoelectric, and piezoelectric properties, served as a scattering element for the improvement in absorption efficiency of solar cells. Benefited by the high absorption efficiency of KNbO

_{3}, the utilization of the ultraviolet and infrared bands for solar cells can be strengthened. In addition, the ferroelectric and photovoltaic characteristics of KNbO

_{3}enable the realization of decreased thickness of solar cells. Based on the simulation of the shape, width, and period of the scattering element, the effect of the thickness of the scattering element on the absorption efficiency, quantum efficiency, and total efficiency of absorption efficiency was comprehensively simulated. The results show that the absorption layer delivers the optimal performance when using a hexagonal KNbO

_{3}scattering element. The absorption efficiency of the GaAs absorption layer with KNbO

_{3}as the scattering element is increased by 28.42% compared with that of a GaAs absorption layer with empty holes. In addition, the quantum efficiency is maintained above 98% and the total efficiency is 91.59%. At the same time, the efficiency of such an absorption layer is still above 90% when the angle ranges from 0 to 70°. This work provides theoretical guidance for the rational design of solar cells based on photonic crystal structures.

## 1. Introduction

_{3}NH

_{3}PbI

_{3}perovskite photonic crystal as the absorption layer of solar cells with the scattering elements of an InAs cylinder, enabling a high absorption efficiency of 82.45%. Since the photonic crystals play a very important role in solar cells, it is meaningful to improve the absorption efficiency and photoelectric conversion efficiency of solar cells by utilizing the slow light characteristics of photonic crystals [17]. Our group has designed photonic crystal of a GaAs absorption layer with a thickness of only 0.20 μm [18]. Such a structure is ideal for the filling of quantum dots, which can greatly improve the photoelectric conversion efficiency of the corresponding solar cell.

## 2. Material Selection and Absorption Layer Design

#### 2.1. Material Selection

_{3}Nh

_{3}PbI

_{3}perovskite cells [27,28,29,30], in particular, increasing. However, since Ch

_{3}Nh

_{3}PbI

_{3}contains toxic elements and poses serious stability issues, it has not been used in practice. KNbO

_{3}, as a typical perovskite oxide, has an optical band gap of 1.10–3.80 eV [31,32,33], and possesses good physical and chemical stability. The light absorption of KNbO

_{3}is 3–6 times higher than that of other classical ferroelectric materials, while the optical current density is 50 times that of other classical ferroelectric materials [34]. In addition, the additional electric field in bulk KNbO

_{3}can induce the ferroelectric photovoltaic effect and improve the photoelectric conversion efficiency. The recombination of photogenerated carriers of ferroelectric materials is not affected by the thickness. Conversely, in the traditional P-N junction solar cells, the increasing thickness of the absorption layer is accompanied by the increasing possibility of photogenerated carrier recombination, leading to a low photoelectric conversion efficiency. KNbO

_{3}exhibits fast recombination of photogenerated electrons and holes, high Curie temperature, and good dielectric properties, as well as good photoelectric, piezoelectric, and nonlinear optical properties. KNbO

_{3}is a kind of ferroelectric material with an extra fixed electric field in the matrix and variable polarity, which can produce a ferroelectric photovoltaic effect that exceeds the Shockley–Quesel limit of photoelectric conversion efficiency for current solar cell materials. In addition, KNbO

_{3}can solve the issue of electron–hole pair recombination during the photocatalytic process [35] and improve the photocatalytic activity. From the perspective of environmental protection, KNbO

_{3}is stable against air, thereby improving the stability of the corresponding solar cells and extend the working life of the cells. Scientists from University of Pennsylvania and Drexel University [34] have combined KNbO

_{3}and barium nickel niobate into perovskite crystals, whose absorption efficiency was six times that of the current thin-film solar cell compounds. By adjusting the stoichiometric ratios of perovskite crystal, the band gap can be regulated to realize the application in the field of absorption layers for solar cells. Herein, the two-dimensional GaAs photonic crystal structure is used as a solar absorption layer, and the KNbO

_{3}scatterers are introduced into the above absorption layer in the form of a tetragonal lattice arrangement, which greatly improves the efficiency of the absorption layer. Figure 1 shows the light absorption curves of various semiconductor materials. According to Figure 1, the absorption efficiency of GaAs and KNbO

_{3}is much greater than that of Si material.

#### 2.2. Simulation Methods

_{3}on the absorption efficiency of the absorption layer, the KNbO

_{3}column-type scattering element and the air pore-type scattering element were respectively introduced into perfect GaAs photonic crystal absorption layers for comparison.

_{3}cylindrical and air-hole scattering elements were 0.5 and 0.1 μm. The lattice constants (A) were 1.2 and 0.6 μm. In addition, the values of parameter W for tetragonal KNbO

_{3}cylindrical and air-hole scattering elements were 0.4 and 0.5 μm. The lattice constants (A) were 1.0 and 0.9 μm. The thickness H of scattering element was set as 0.1–1.0 μm in the “Solar-Cell” module. Regarding the “DiffractMOD” module, the type of incident wave was a plane wave, the boundary condition was periodic, the step size was 0.1 μm, and the grid size was 0.005 μm. The simulation range of the wavelength was set as 0.3~1.2 μm with an interval of 0.1 μm. The open circuit voltage was set as 0.7 V. Finally, the quantum efficiency could be obtained by optical and electrical simulation, as calculated by the following equations.

^{−15}eV s) is the Planck constant, c (3 × 10

^{8}m/s) is the speed of light, and λ is the wavelength. Given a specific incident spectrum S(λ), the total number of photons incident at a wavelength of λ is presented as follows:

_{i}(λ):

_{i}) are defined for each absorptive layer. Moreover, it can be useful to consider the shadowing effect of electrodes via another efficiency η

_{s}. The combined number of electron–hole pairs generated at a wavelength of λ and collected by the electrodes is therefore:

## 3. Simulation of Absorption Efficiency for Absorption Layer

#### 3.1. Absorption Layer Design

#### 3.2. Hexagonal Scatterers

_{3}column and air-hole hexagon scatterers on side length W. The lattice constants A and the thickness H are 1 and 0.5 µm, respectively.

_{3}column hexagon scatterers decreases when the wavelength is greater than 0.80 µm, but the whole distribution of absorption efficiency lies in the yellow-green region. However, regarding the absorption layer with air-hole hexagon scatterers, the absorption efficiency sharply drops when the wavelength is greater than 0.80 µm, accompanied with the main range in the purple color. The specific results presented in Figure 3a,b are plotted in Table 2.

_{3}generally presents an upward trend until it reaches the maximum value of 86.03% when W = 0.50 µm. However, the absorption layer comprising an air-hole structure shows a continuously decreasing trend, and the absorption efficiency is about 21.07% lower than that of the former counterpart.

_{3}cylindrical hexagon scatterers was simulated using the lattice constant A = 0.50 µm. Considering the decreasing tendency of absorption efficiency with the increasing side length for absorption layer with air-hole hexagon scatterers, the simulation started from A = 0.10 µm in this case. The simulation results are shown in Figure 4a,b. Figure 4a,b shows the dependance of the absorption efficiency of the absorption layer with KNbO

_{3}column and air-hole hexagon scatterers on lattice constant A.

_{3}column hexagonal scatterers delivers a high absorptivity at the wavelength of 0.30–0.80 µm. When the wavelength is higher than 0.80 µm, the absorptivity begins to decay. In addition, the absorptivity increases with the increasing lattice constant. Regarding the absorption layer with air-hole hexagon scatterers, the absorptivity begins to decay at the wavelength of 0.70 µm. When the wavelength is greater than 0.90 µm, the absorption range is dominated by the purple color, and the absorption efficiency is close to 0. To further study the relationship between absorption efficiency and lattice constants, the specific data in Figure 4a,b are presented in Table 3.

_{3}columnar hexagon scatterers slowly increases until the lattice constant A reaches 1.20 µm, while the value of absorption layer with air-hole hexagon scatterers slowly increases until the lattice constant A reaches 0.60 µm. Therefore, the optimal lattice constants for the two cases are determined to be A = 1.20 µm and A = 0.60 µm, respectively.

_{3}column and air-hole hexagon scatterers on the thickness H.

_{3}column hexagonal scatterers mostly lies in the red, yellow, and green regions, that is, the absorption efficiency is higher than 50%. In addition, the overlapping of three colors occurs at wavelengths larger than 0.80 µm. When the wavelength is greater than 0.90 µm, the absorption efficiency for the absorption layer with air-hole hexagonal scatterers mainly lies in the purple region, indicating the greatly decreased absorption efficiency. To further study the relationship between absorption efficiency and scatterer thickness H, the results of Figure 5a,b are plotted in Table 4.

_{3}hexagonal scatterers is ~33.66% higher than that for the air-hole structure. Regarding the absorption layer with air-hole hexagonal scatterers, the absorption efficiency increases with thickness. However, the large thickness introduces the increased possibility of photo-generated carrier recombination, leading to the low photoelectric conversion efficiency. It can be concluded from Table 4 that the thickness H has negligible influence on the absorption efficiency for the absorbing layer with KNbO

_{3}cylindrical scatterers. Thus, considering the cost issue, H = 0.20 μm was selected as the optimal value, corresponding to the absorption efficiency of 92.33%.

_{3}column and air-hole scatterers in terms of the incident light of 0.3–0.9 μm. In the wavelength of 0.9–1.2 μm, the absorption efficiency of absorption layer with KNbO

_{3}column scatterers is much higher than that of the air-hole structure. This indicates that the absorption layer with KNbO

_{3}scatterers exhibits higher light absorption efficiency for long-wavelength incident light, which can be attributed to the spin-induced transitions presented in the metal compounds [34]. The faster the electron transition, the more efficient the light absorption. Compared with air, KNbO

_{3}has no molecules that hinder the flow of electrons, so the electron transition of KNbO

_{3}is faster than that of air, and the absorption efficiency is higher. In addition, KNbO

_{3}has greater absorption bandwidth and higher absorbance compared with air. Specifically, it has six absorption peaks, while air has only one absorption peak; as a result, the absorption efficiency of the KNbO

_{3}absorption layer is significantly higher in the infrared wavelength (0.9~1.2 μm) than that of air.

#### 3.3. Square Scatterers

_{3}cylindrical square scatterers or air-hole square scatterers was simulated with adjustments to the side length W, lattice constant A, and thickness H. The simulation results of the effect of side length W on absorption efficiency are shown in Figure 6. The lattice constants A and the thickness H were set as 1 and 0.5 µm.

## 4. Simulation of Quantum Efficiency for Absorption Layer

_{3}are very high and are not affected by the thickness. Overall, the total cost of GaAs and KNbO

_{3}based solar cells is less than that of Si based solar cells, while obtaining nearly the same photoelectric conversion efficiency.

_{3}, hexagonal), 2D PC (KNbO

_{3}, square), 2D PC (Air, hexagonal), and 2D PC (Air, square) are the optimal values as previously determined (i.e., W = 0.5, 0.4, 0.1 and 0.1 µm, A = 1.2, 1.3, 0.6 and 0.7 µm).

_{3}cylindrical scatterers, which is always above 98%, exceeds that of the other three absorption layers, and it has little change with the increase in height. This indicates that the introduction of KNbO

_{3}photonic crystal can improve the quantum efficiency, and causing the quantum efficiency to be independent of the thickness of the absorption layer. The quantum efficiency of the absorption layer with an air-hole structure greatly varies with the increase in height, but it still exceeds that of the absorption layer without a photonic crystal structure.

_{sc}) is a very important physical quantity in solar cells, and it is an important indicator to measure the photoelectric conversion efficiency of solar cells. This value represents the current density value of a solar cell under the standard light source. The short circuit corresponds to an open-circuit voltage of 0. It can usually be expressed as in Equation (9):

_{s}is the incident light intensity, and Q(E) refers to the quantum efficiency. Therefore, J

_{sc}is closely related to the light absorption capacity of the absorption layer. The strength of the light absorption capacity directly affects J

_{sc}, thus affecting the photoelectric performance of solar cells. The relationship of J

_{sc}on two different hexagonal scatterers and H is plotted in Table 5. During the simulation, W and A of two structures of 2D PC (KNbO

_{3}, hexagonal) and 2D PC (Air, hexagonal) were the optimal values simulated above (i.e., W = 0.5 and 0.1 µm, A = 1.2 and 0.6 µm), and the open circuit voltage was 0.7 V.

_{3}is much larger than the absorption layer containing air holes. In addition, in the absorption layer containing air holes, the short-circuit current density generally decreases with the increase in thickness. However, the short circuit density of the absorption layer containing a KNbO

_{3}scattering element is not affected by the thickness. The changing trend and quantum efficiency of the short-circuit current density in the two absorption layers are similar. This can be explained by the introduction of photonic crystals into the solar cell absorption layer. The inherent photon confinement feature reflects the specific light back to the active layer, leading to the reduced light loss. The more light energy absorbed by the active layer, the more electron–hole pairs generated by illumination in the active layer, and the greater the current formed in the solar cell. The increase in light absorption capacity of the active layer significantly improves the short-circuit current density, and then improves the photoelectric conversion efficiency.

## 5. Results and Discussion

_{3}and GaAs contributes to the best absorption efficiency of above 90%. Meanwhile, considering the photoelectric conversion efficiency and cost issues caused by the cell thickness, the optimal parameters of absorption layer were selected as the side length W of 0.5 μm, period A of 1.2 μm, and height H of 0.2 μm, achieving an absorption efficiency of 92.33%. By comparison, the optimal absorption efficiency of photonic crystal composed of GaAs and air holes was 64.07%, which is ~30% lower than that of the proposed structure. In order to further study the influence of KNbO

_{3}on the efficiency of solar cells, the simulation results of total efficiency (the product of absorption efficiency and quantum efficiency) for solar cells are displayed in Figure 11. During the simulation, W and A of the four structures of 2D PC (KNbO

_{3}, hexagonal), 2D PC (KNbO

_{3}, square), 2D PC (Air, hexagonal), and 2D PC (Air, square) were the optimal values as previously determined (i.e., W = 0.5, 0.4, 0.1, and 0.1 µm, A = 1.2, 1.3, 0.6, and 0.7 µm).

_{3}improves the total efficiency of solar cells to a great extent. The total efficiency of the absorption layer with KNbO

_{3}is far higher than that of the absorption layer with air holes and the absorption layer without a photonic crystal structure. This can be attributed to the superior band gap adjustability and extremely high photocurrent density of KNbO

_{3}.

_{3}improves the quantum efficiency of the absorption layer. Unlike traditional solar cells, the quantum efficiency is not affected by the thickness of the absorption layer. This is due to the ferroelectric properties of KNbO

_{3}. The absorption layer with KNbO

_{3}photonic crystal is different from the traditional solar cells based on the P-N junction. Regarding the traditional P-N junction solar cells, the built-in electric field is formed based on the depletion layer that separates the photogenerated electrons and hole pairs. However, with the increased thickness of the absorption layer, the recombination possibility of photogenerated carriers increases during the transport process, resulting in the decrease in photoelectric conversion efficiency. In contrast, KNbO

_{3}is a kind of ferroelectric perovskite-type material with variable polarity, which can realize the separation of photogenerated electrons and hole pairs by generating a potential gradient through internal spontaneous polarization [35]. This process does not rely on the P-N junction, so the photoelectric conversion efficiency is no longer limited by the thickness of the absorption layer. On the other hand, most ferroelectric oxides have large photonic band gaps; as a result, ferroelectric oxide based solar cells only utilize a very small part of solar spectrum, thereby limiting the improvement in photoelectric conversion efficiency. However, the direct band gap of KNbO

_{3}can be adjusted within the range of 1.1–3.8 eV, endowing KNbO

_{3}with compatibility with lights in different frequency ranges, thereby improving the photoelectric conversion efficiency. The light absorption properties of KNbO

_{3}can also be regulated by doping transition metal ions. This can make full use of the wide band gap characteristics of KNbO

_{3}photonic crystal, and the band gap can be reduced to a band gap similar to that of visible light, increasing the absorption capability of light and simultaneously increasing the absorption of ultraviolet light.

_{3}photonic crystal structure and without a photonic crystal structure was simulated, as shown in Figure 12. During the simulation, W and A of the 2D PC (KNbO

_{3}, hexagonal) were the optimal values as previously determined (i.e., W = 0.5 µm, A = 1.2 µm, H = 0.2 µm).

_{3}photonic crystal is much higher than that without photonic crystal. Although the absorption efficiency of both absorption layers decreases with the increase in the deflection angle of incident light, the absorption layer with KNbO

_{3}photonic crystal maintains absorption efficiency of ~90% even when the deflection angle is 70°. When the deflection angle is in the range of 70 to 80°, the effective area of light decreases with the increase in incidence angle, leading to the obviously reduced absorption efficiency. Therefore, the absorption layer with KNbO

_{3}photonic crystal can adapt to different dip angles, obtaining greater absorption efficiency. At present, the electron beam etching techniques can be used to fabricate micro-nano structures with an accuracy of less than 5 nm. Hence, the photonic crystal structures can be prepared by electron beam etching techniques and vapor deposition technology. In the actual fabrication process, the negative photoresist is needed for the dielectric column photonic crystal structure, while the positive photoresist is needed for the air-hole photonic crystal structure. The different masks should be made according to the specific structures, and the corresponding KNbO

_{3}mask is introduced into the GaAs absorption layer using the processes of gumming, exposure, post-drying, developing, vertical mold, graphic transfer, degumming, etching, etc.

## 6. Conclusions

_{3}hexagonal scatterers are arranged in a tetragonal lattice form in the GaAs absorption layer with a side length W of 0.5 μm, lattice constant A of 1.2 μm, and height H of 0.2 μm, the maximum absorption efficiency can reach 92.33%. Regarding the practical applications, KNbO

_{3}can be further doped with transition metal ions to enhance its performance. Moreover, the doping cannot change the crystal structure of KNbO

_{3}, but it preserves the ferroelectric properties of KNbO

_{3}. The transition metal ion doping combines the optimized optical band gap with ferroelectric properties, thereby obtaining high absorption efficiency and photoelectric conversion efficiency.

_{3}into the absorption layer of solar cells, reducing the influence of thickness on absorption efficiency and photoelectric efficiency. In this way, the quantum efficiency and the adaptation to different angles can be improved. This offers important guidance for the optimization of the absorption layer structure for novel thin-film solar cells.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**(

**a**) Schematic structure of the solar cell. (

**b**) Schematic structure of the photonic crystal absorption layer. (

**c**) Schematic structure of the hexagonal scattering element. (

**d**) Schematic structure of the square scattering element.

**Figure 3.**(

**a**) The dependance of the absorption efficiency of the absorption layer with KNbO

_{3}column hexagon scatterers on side length W. (

**b**) The dependance of the absorption efficiency of the absorption layer with the air-hole hexagon scatterers on side length W.

**Figure 4.**(

**a**) The dependance of the absorption efficiency of the absorption layer with KNbO

_{3}column hexagon scatterers on lattice constant A. (

**b**) The dependance of the absorption efficiency of the absorption layer with the air-hole hexagon scatterers on lattice constant A.

**Figure 5.**(

**a**) The dependance of the absorption efficiency of the absorption layer with KNbO

_{3}column hexagon scatterers on thickness H. (

**b**) The dependance of the absorption efficiency of the absorption layer with the air-hole hexagon scatterers on thickness H.

**Figure 6.**The effect of side length W for two different types of scatterers on the absorption efficiency of the absorption layer.

**Figure 7.**The effect of lattice constant A for two different types of scatterers on the absorption efficiency of the absorption layer.

**Figure 8.**The effect of thickness H for two different types of scatterers on the absorption efficiency of the absorption layer.

**Figure 10.**(

**a**) The current–voltage curves of the optimal structure. (

**b**) The dependance of total absorption spectrum and quantum efficiency of the absorption layer on the wavelength.

**Figure 12.**The dependance of the absorption efficiency for the two absorption layers on incidence angle.

Layer | Materials | Refractive Index | Extinction Coefficient |
---|---|---|---|

Transparent conductive layer/electrode | ITO | 1.635–2.064 | 0.002–0.012 |

Absorption layer | GaAs | 3.485–5.052 | 0.080–2.288 |

KNbO_{3} | 2.113–2.317 | 0.041–0.220 | |

Auxiliary absorption layer | ZnO | 1.935–2.105 | 0.060–0.430 |

Reflective layer, electrode | Ag | 0.040–1.340 | 0.392–8.699 |

**Table 2.**The relationship between absorption efficiency of absorption layers with two different hexagonal scatterers and W.

Parameter W (µm) | Absorption of KNbO_{3} Column (%) | Absorption of Air Hole (%) |
---|---|---|

0.10 | 71.25 | 64.96 |

0.20 | 82.33 | 64.60 |

0.30 | 85.34 | 63.30 |

0.40 | 85.92 | 63.06 |

0.50 | 86.03 | 62.43 |

0.60 | 85.27 | 62.18 |

0.70 | 85.18 | 62.04 |

0.80 | 84.85 | 61.99 |

0.90 | 84.65 | 61.95 |

1.00 | 84.32 | 61.92 |

**Table 3.**The relationship between absorption efficiency of absorption layers with two different hexagonal scatterers and A.

Parameter A (µm) | Absorption of KNbO_{3} Column (%) | Parameter A (µm) | Absorption of Air Hole (%) |
---|---|---|---|

0.50 | 82.25 | 0.10 | 56.07 |

0.60 | 83.04 | 0.20 | 60.52 |

0.70 | 83.83 | 0.30 | 62.36 |

0.80 | 84.43 | 0.40 | 63.22 |

0.90 | 85.01 | 0.50 | 63.81 |

1.00 | 86.06 | 0.60 | 64.07 |

1.10 | 86.97 | 0.70 | 64.28 |

1.20 | 87.91 | 0.80 | 64.42 |

1.30 | 87.96 | 0.90 | 64.51 |

1.40 | 88.20 | 1.00 | 64.57 |

**Table 4.**The relationship between the absorption efficiency of absorption layers with two different hexagonal scatterers and H.

Parameter H (µm) | Absorption of KNbO_{3} Column (%) | Absorption of Air Hole (%) |
---|---|---|

0.10 | 91.51 | 57.28 |

0.20 | 92.33 | 58.67 |

0.30 | 90.58 | 58.32 |

0.40 | 92.07 | 59.60 |

0.50 | 90.21 | 60.53 |

0.60 | 93.10 | 60.64 |

0.70 | 91.46 | 61.36 |

0.80 | 93.47 | 62.06 |

0.90 | 91.89 | 64.07 |

1.00 | 93.74 | 64.68 |

Parameter H (µm) | The J_{sc} of 2D PC KNbO_{3} Hexagonal (A/m ^{2}) | The J_{sc} of 2D PC Air Hexagonal (A/m ^{2}) |
---|---|---|

0.1 | 349.503 | 266.437 |

0.2 | 337.541 | 258.303 |

0.3 | 331.968 | 254.246 |

0.4 | 349.024 | 253.724 |

0.5 | 348.038 | 253.956 |

0.6 | 346.149 | 250.122 |

0.7 | 346.526 | 250.195 |

0.8 | 349.181 | 245.524 |

0.9 | 346.382 | 246.432 |

1.0 | 346.698 | 241.451 |

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## Share and Cite

**MDPI and ACS Style**

Zhou, L.; Wu, Y.; Liu, X.; Quan, J.; Bi, Z.; Yuan, F.; Wan, Y. Simulation of Boosting Efficiency of GaAs Absorption Layers with KNbO_{3} Scatterers for Solar Cells. *Energies* **2023**, *16*, 3067.
https://doi.org/10.3390/en16073067

**AMA Style**

Zhou L, Wu Y, Liu X, Quan J, Bi Z, Yuan F, Wan Y. Simulation of Boosting Efficiency of GaAs Absorption Layers with KNbO_{3} Scatterers for Solar Cells. *Energies*. 2023; 16(7):3067.
https://doi.org/10.3390/en16073067

**Chicago/Turabian Style**

Zhou, Lin, Yihua Wu, Xiaoning Liu, Jiajia Quan, Zhijie Bi, Feng Yuan, and Yong Wan. 2023. "Simulation of Boosting Efficiency of GaAs Absorption Layers with KNbO_{3} Scatterers for Solar Cells" *Energies* 16, no. 7: 3067.
https://doi.org/10.3390/en16073067