Solar Energy 174 (2018) 803–814
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Novel design of plasmonic and dielectric antireflection coatings to enhance the efficiency of perovskite solar cells
T
Omar A.M. Abdelraoufa,b, Ahmed Shakerb, Nageh K. Allama,* a b
Energy Materials Laboratory (EML), Department of Physics, School of Sciences and Engineering, The American University in Cairo, New Cairo 11835, Egypt Department of Engineering Physics and Mathematics, Faculty of Engineering, Ain Shams University, Cairo 11517, Egypt
A R T I C LE I N FO
A B S T R A C T
Keywords: Plasmonics Dielectric Nanostructures Mie theory Antireflective coating Perovskite Solar cells Light coupling
Recently, nanostructured plasmonic antireflection coatings emerge as a solution to minimize reflection in solar cells over a wideband. However, metals have large light absorption coefficient, making this solution non-reliable for efficient large-scale production. On the other hand, all dielectric antireflection coatings are considered as promising alternative due to the lower losses and easier assembly, especially for third generation photovoltaics such as perovskite solar cells. Herein, we report a first principles methodology for selecting and comparing optimally nanostructured antireflective coatings for enhancing the efficiency of perovskite solar cells based on Mie theory. The first part of the method includes studying absorption and scattering cross sections of five nanostructures and identifying the role of magnetic and electric dipoles. Accordingly, dimensions of each nanostructure that maximizes light coupling to the solar cell active layer was identified. The second part comprises the study of the coupling effect between closed nanostructures. Using three-dimensional finite element method optical and electrical model, periodicity and dimensions of the proposed nanostructures with the highest generated photocurrent were identified. The results showed 15% enhancement in short circuit current (Jsc) over the entire wavelength band, and up to 27% in narrow band spectrum compared to planar perovskite solar cells.
1. Introduction Perovskite thin film solar cells (TFSCs) have recently attracted the attention of the scientific community due to their unique optical and electrical properties, low fabrication cost, high carrier collection efficiency, and large-scale assembly (Yang et al., 2015; Fei et al., 2017). There are many limitations in Perovskite TFSCs performance, such as long-term stability and low light absorption percentage in the perovskite thin film layer. Stability issues are more related to the electrical properties of the materials. A recent paper suggests the use of reduced graphene oxide layer between gold back contact and hole transport material to enhance the stability of perovskite solar cells with +1000 h of stable operation time (Arora et al., 2017). However, the other drawback of perovskite TFSCs is their lower light absorption within the active layer due to the small active layer thickness. In this regard, light trapping nanostructures inside active layer (Xiao et al., 2018; Bawendi and Hess, 2018; Abdelraouf and Allam, 2016; Wu, 2018), or metal nanoparticles (Islam et al., 2014; Islam et al., 2015; Abdelraouf et al., 2017) were used to enhance the optical light absorption in many types of solar cells. Recent techniques for enhancing the efficiency of perovskite TFSCs, in particular, are based on the concept of using
*
antireflective coating using silica nanospheres (Luo et al., 2018; Zeng et al., 2017), or nanophotonics to design front nanoarchitectures (Paetzold et al., 2015), or light trapping nanostructures inside the active layer (Abdelraouf and Allam, 2016), or plasmonic nanostructures atop the metal back contact (Adhyaksa et al., 2017). Recently, plasmonic nanostructures have been integrated in many optoelectronic devices due to their various advantages, including the possibility to guide electromagnetic waves at a dielectric/metal interface using surface plasmon guided modes (SPGM) (Schmidt and Russell, 2008), control the direction of light scattering using subwavelength metallic nanostructures, high suppression of reflected light in the wavelength range of the nanostructure resonance, confine light at subwavelength scale due to large localized surface plasmon resonance (LSPR) (Atwater and Polman, 2010), possibility of tuning light reflection from substrate by changing particles dimensions, shape, interparticle distances, or material. Despite all these advantages, plasmonic nanostructures have some serious limitations. For instance, most of the used metals have large imaginary refractive index in the optical wavelength range, leading to large light losses (Johnson and Christy, 1972) or the formation of Schottky barrier at the dielectric/metal interface that may reduce collection efficiency of charge carriers in solar
Corresponding author. E-mail address:
[email protected] (N.K. Allam).
https://doi.org/10.1016/j.solener.2018.09.066 Received 9 June 2018; Received in revised form 10 September 2018; Accepted 24 September 2018 0038-092X/ © 2018 Elsevier Ltd. All rights reserved.
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dimension and periodicity for each studied plasmonic and dielectric antireflection nanostructured coatings, we used the electrical model to calculate the power conversion efficiency of the promising designs. The main advantage of our proposed method is that it can be applied for any solar cell substrate and enables the design of antireflection coatings that are very close to the exact solution.
cells (Zhou et al., 2014). To this end, plasmonic nanostructured materials have been explored as antireflection coatings to improve the efficiency of TFSCs, due to their capability to control the far field light scattering directivity from nanoparticles front active layer, confine near field light in the subwavelength scale for nanoparticles rear active layer, and increase the short circuit current and photoconversion efficiency (Gu et al., 2012). For instance, the use of nanostructured silver front in a-Si:H TFSCs fabricated by nanoimprinting lithography shows enhancement in the power conversion efficiency from 6.32% to 9.6% (Ferry et al., 2011). Also, P3HT:PCBM-based solar cells showed an increase in the short circuit current by 2.7 mA/cm2 upon the use of silver nanoparticles front active layer (Morfa et al., 2008). The same organic material showed an enhancement in the photoconversion efficiency from 3% to 3.65% upon the deposition of gold nanoparticles front active layer (Lee et al., 2009). Currently, dielectric nanostructures emerged as promising alternatives to plasmonic nanostructures (Spinelli et al., 2012; Raman et al., 2011; Ren and Zhong, 2018). Most of the used dielectrics are semi or fully transparent in the optical wavelength range, resulting in negligible light losses inside the dielectric nanostructures. Also, the high refractive index of the used dielectrics enables the control over light directivity at the nanoscale via tuning the magnetic and electric Mie resonance of the nanostructures. Solving Mie theory (Bohren and Huffman, 2008) for small sphere in free space analytically using spherical harmonic enables the calculation of electric and magnetic multi-poles of the sphere versus the wavelength. Note that Mie resonance refers to peaks of these electric or magnetic multi-poles (Zhao et al., 2009). Tuning the absorption Mie resonance could change the light reflection minima wavelength. Also, changing scattering Mie resonance enables the coupling of incident light into the waveguide modes of the substrate. In this regard, titanium dioxide (TiO2) is one of the most widely used materials for different solar cells due to its large refractive index (n ≈ 2.7), low optical losses in the visible and near-infrared wavelength ranges (Yang et al., 2016), and possibility of tuning its Mie resonance via changing the dimensions and the shape of the nanostructures. Moreover, all-dielectric antireflection nanostructured coatings have been emerged as promising alternatives to overcome the disadvantages of plasmonic nanostructures while having the ability to control the incident light at the nanoscale for many nanophotonics applications (Krasnok et al., 2015). Changing the dimensions of silicon nanopillar-based structure enables wideband antireflection for photovoltaic systems (Bezares et al., 2013). Many research works showed promising results of integrating dielectric nanostructures in solar cells, such as depositing silicon dioxide SiO2 nanospheres over a-Si:H TFSCs that enhanced the photocurrent by 15% compared to flat a-Si:H TFSCs (Grandidier et al., 2011). Also, introducing gallium phosphide (GaP) nanoscatterers on top of the active layer of a-Si:H TFSCs improved the photoconversion efficiency from 8.1% to 9.89% (Wang and Su, 2014). Experimental realization of dielectric nanostructures for enhancing generated photocurrent have been already reported in literature using back contact nanostructures (van Lare et al., 2015) and front dielectric nanostructures (Tamang et al., 2016). Herein, we demonstrate a fast estimation method for selection of silver nanostructured coatings to control the direction of the scattered light from perovskite solar cell substrate. The performance is also compared to that of the low optical losses and high index dielectric TiO2 coating. Our method is based on two separate approaches: (1) Mie scattering theory to investigate the role of optical resonance (electric or magnetic) in the proposed subwavelength nanostructures and its role on enabling guided resonance modes in the underlying perovskite active layer (Brongersma et al., 2014) and selection of the dimension of each studied nanostructure that achieve the highest light coupling in the substrate. (2) investigating the role of coupling between closed optimally dimensions of the nanoscatterers on a substrate. Through the optical model, we examined the role of periodicity on the overall guided light resonance modes inside the substrate. After selecting
2. Modeling details Two separate three-dimensional (3D) electromagnetic wave (EMW) models, based on finite elements method (FEM) COMSOL multi-physics software, were used to construct the model. The first part of the model was built based on the concept of Mie scattering theory to calculate the normalized absorption cross-section (NACS) and normalized scattering cross-section (NSCS) of the proposed scatterers. The second part was based on coupled optical-electrical model to simulate perovskite solar cells with suggested optimally top scatter nanostructures to calculate the overall efficiency of the solar cells. For simulating NACS and NSCS for scatterers on a substrate, we used full field EMW to calculate the incident electric field profile on planar substrate only. Then, we couple this electric field profile as a background field in scatter field EMW for a nanostructure on a substrate. These steps were mandatory because the optical properties of a particle on a planar dielectric surface differ dramatically from those of the same particle embedded in homogenous medium (Lermé et al., 2013). Incident plane waves in full field EMW consider both s-polarization and p-polarization with normal incidence in the z-direction, and use the AM1.5G solar spectrum as an input power in the range of 300–800 nm with a step of 10 nm. The simulation was performed on cell volume surrounded with perfect matched layer (PML) in all directions, and periodic boundary conditions (PBCs) in x-y direction were considered. A tetrahedral mesh type was used with a size below one-tenth of the lowest simulated wavelength in the simulated cell size. Furthermore, a mapped mesh was used in the PML layer to reduce the overall mesh number. The NACS of the studied nanostructures was calculated using Eq. (1):
NACS =
Wabs Pinc ∗Surface Area
(1)
where Wabs is the amount of absorbed power in the nanostructure [W], which is calculated by integrating the resistive energy loss over the volume of the nanostructure, Pinc is the energy flux of the incident wave [W/m2]. The NSCS was calculated using Eq. (2):
NSCS =
Wsca Pinc ∗Surface Area
(2)
where Wsca is the scattered energy rate [W]. Scattered energy rate came from integrated scattered energy over the surface surrounding the nanostructure. Pinc is the energy flux of incident wave [W/m2]. For comparison and selection of optimally nanostructures on a substrate, we defined a parameter called active area absorption enhancement (AAAE), which represents the enhancement in the coupled power to the substrate after depositing the nanostructure on top of the surface. AAAE is the ratio between the integrated power absorbed in the substrate in the presence of a scatterer to the integrated power absorbed in case of a planar substrate only, Eq. (3).
AAAE =
∭ |E|2scatter on substrate dVdλ ∭ |E|2planar substrate dVdλ
(3)
Upon the dimensions selection of each nanostructure with the highest AAAE, we simulated the coupled optical-electrical model to calculate the efficiency of the solar cells. The optical model used the same setup of the EMW model in the first part. The active layer absorption was calculated using Eq. (4):
Absorption (λ ) = 804
|Eactive area (λ )|2 |ETotal (λ )|2
(4)
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cube side length starts with 50 nm to 250 nm. For cones, the cone base was assumed to have a radius equals to the cone height. Therefore, the cone angle would always be constant and equals 90°, with the base radius starts with 50 nm to 250 nm. Finally, the cylindrical shell with same radius and height has wall thickness of 20 nm starts with 50 nm to 250 nm.
The optical generation rate (Goptical) of electrons per wavelength at each active layer material was calculated using Eq. (5) (Deceglie et al., 2012):
Goptical (λ ) =
ε '' |E|2 2ℏ
(5)
The optical generation rate depends on the intensity of the electric field inside the active layer and the imaginary part of the permittivity (ε″). Integrating Goptical over the simulated wavelength for all active layers and dividing by the volume gives the total generation per unit volume as indicated by Eq. (6):
Total Geneation Rate (s−1 m−3) Total Generated electrons in device = Volume of device
3. Results and discussion 3.1. Silver antireflection coating For each simulated dimension of the proposed silver nanostructures, NACS was calculated using Eq. (1) and illustrated in Fig. 2. Increasing the radius of the silver sphere slightly changes the electric dipole wavelength from 350 nm to 380 nm, Fig. 2a. However, the absorption coefficient decreases to nearly zero at wavelengths > 500 nm. These results are good to design efficient solar cells as the solar light spectrum has a peak power value at wavelengths longer than 500 nm. Fig. 2b shows silver cylindrical particle on a perovskite layer, where the electric diploe of the cylindrical particle is shifted from 410 nm to 430 nm. The absorption coefficient of the cylindrical particle is smaller than that of the spherical counterpart at wavelengths below 500 nm, while near zero absorption coefficient can be observed at wavelengths above 500 nm for different radii. Silver cube NACS shows many dipoles at different wavelengths as shown in Fig. 2c. Based on the electric field lines in the silver cube with a side length of 200 nm, Electric dipole mode at 340 nm and 400 nm, and magnetic dipole mode at 470 nm and 540 nm can be identified. These multiple dipoles would increase the light absorption in the nanocube, with the absorption coefficient tends to zero at wavelengths above 700 nm. Silver cone shows lowest absorption coefficient values over the entire wavelength range and single electric dipole at 350 nm, Fig. 2d, with the absorption coefficient approaching zero at wavelengths longer than 450 nm. Finally, Fig. 2e shows NACS for silver cylindrical shell, where multiple dipoles were observed along the entire wavelength range, which would reduce the light coupling efficiency to the perovskite substrate. For cylindrical shell with a radius of 250 nm, an electric dipole mode at 330 and 380 nm, and magnetic dipole mode at 450 nm, 530 nm, 590 nm, and 690 nm were observed. Fig. 3 shows NSCS, calculated using Eq. (2), versus simulated wavelength of the proposed nanostructures. For silver sphere, Fig. 3a, the smaller dimension shows low scattering efficiency at longer wavelength and high scattering efficiency at shorter wavelength. Increasing the radius of the sphere results in increasing the scattering efficiency over the entire visible spectrum and increases light control directivity. The maximum scattering efficiency can be observed at 440 nm for the sphere of a radius of 125 nm. Fig. 3b shows NSCS of silver cylindrical, where the scattering efficiency increases upon increasing the radius of cylindrical over the entire spectrum. However, the maximum scattering efficiency, which is found at a wavelength of 470 nm and a radius of 200 nm, is smaller than that of the silver sphere. The scattering efficiency of silver sphere is five times larger than that of the silver cube counterpart, Fig. 3c. The NSCS of cube has a main scattering peak in the middle of the visible spectrum, where the scattering peak is proportional to the side cube length. Silver cone has the lowest light control directivity, as cone has scattering efficiency nearly half the scattering efficiency of cube, Fig. 3d. The scattering peak wavelength is 350 nm and it is size independent. Further, the NSCS of the cone structure increases uniformly with increasing its radius. Cylindrical shell has scattering efficiency values that are close to those of the cube as shown in Fig. 3e. Multiple peaks are observed over the entire wavelength spectrum. These scattering peaks shift to longer wavelengths as the size increases. Also, the maximum scattering efficiency is located at 690 nm. The observed red shift in the scattering peaks for all metal nanostructures is due to the “surface dressing effect” (Xiao and Bozhevolnyi, 1996; Evlyukhin and Bozhevolnyi, 2005) due to the change in the
(6)
The optical refractive indices of silver and the perovskite active layer were taken from previously reported data (Wang et al., 2013; Rakić et al., 1998; Pattanasattayavong et al., 2013; Xing et al., 2014). The constructed electrical model used the optical generation profile as an input. The current-voltage characteristics of the perovskite solar cells were obtained by solving electrons and holes drift-diffusion equations, electrons and holes continuity equations and Poisson’s equation in 3D. The doping profile inside both active layer materials was assumed to have Gaussian distribution. Shockley-Reed-Hall and direct recombination were considered in our model. Also, series and shunt resistances of the solar cells were used as fitting parameters. Since short circuit current (Jsc) is directly proportional to the total generation rate of electrons and the dimensions of the active layer of the solar cell did not change in the proposed structures, we used the following approximation enhancement in Jsc to be equal to the enhancement in the total generation rate as in Eq. (7):
Jsc enhancements =
Total Generation Rate using nanostructures Total Generation Rate of planar cell (7)
There are some limitations in our optical model. First, the smallest simulated mesh size is λ/10 of the smallest simulated wavelength. Reducing the mesh size to λ/12 or λ/20 would give more accurate results but the computational cost is huge. Second, a large mapped mesh size was used in perfect matched layer to allow the use of overall smaller mesh number. Third, the total number of electron-hole pairs generated in three dimensional solar cells are integrated for each simulated wavelength and added the total generation rate per unit volume and used in the electrical model to calculate the photocurrent. In electrical model, we assumed that any enhancements in light absorption would directly enhance the generated photocurrent. Possible recombination effects upon adding metal nanostructures above the perovskite solar cells were not considered in this study. The electrical parameters of CuSCN and CH3NH3PbI3 used in electrical model were extracted from literature (Kumara et al., 2001; Cheng et al., 2015; Lin et al., 2015; Zhao et al., 2014; Brivio et al., 2013; Butler et al., 2015; Brivio et al., 2014). The selection of the nanostructures to act as antireflection coatings depends on three conditions. The first condition was related to the possibility of fabrication at a large scale from uniform nanostructures over top active layer of perovskite solar cells. The second condition was related to the overall cost of materials used in solar cells. In this respect, deposited nanostructures on top of the active layer should have reasonable thickness. The third condition was that the dimensions of the nanostructures should be subwavelength of solar light to control the scattering light directivity based on Mie theory and investigate the effect of optical resonance modes. Fig. 1 shows the proposed nanostructures on the perovskite substrate taken from previously fabricated structures (Qin et al., 2014). For the silver sphere, we changed the radii from 50 nm to 150 nm. For the silver cylindrical shape, we swept the radii and height from 50 nm to 250 nm. The silver 805
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Fig. 1. Scatter on substrate Mie model. from left to right: silver sphere on perovskite (CH3NH3PbI3) layer of thickness 200 nm, with radius as sweep parameter, silver cylindrical with equal radius and height, silver cube with side length L, silver cone with equal radius and height, and silver cylindrical shell with wall thickness 20 nm and same radius and height. 1.5
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Fig. 2. Normalized absorption cross-section (NACS) for (a) silver sphere with radii from 50 nm to 150 nm, (b) silver cylindrical with radii from 50 nm to 250 nm, (c) silver cube with side length from 50 nm to 250 nm, (d) silver cone with radii from 50 nm to 250 nm, and (e) silver cylindrical shell with radii from 50 nm to 250 nm.
larger silver cylindrical showing larger scattering efficiency. This can be related to the smaller NACS of the cylindrical of radius 150 nm than that of the counterpart of radii of 200 nm and 250 nm at wavelengths longer than 550 nm. Therefore, the light coupling efficiency would be larger at this radius than others. Fig. 4c indicates that increasing the length of the cube side would increase light coupling till reaching a maximum light coupling coefficient with a side length of 200 nm. This is confirmed by the NACS of cube, where increasing the cube side length resulted in a reduction in the absorption coefficient. The degradation in the AAAE at cube with side length of 250 nm can be related to the larger NACS of the cube length of 250 nm than that of the cube length of 200 nm at wavelengths longer than 600 nm. Light coupling enhancement in silver cone is lower than that of the planar substrate only for all simulated dimensions as seen in Fig. 4d. This can be understood from the nature of cone that has the lowest scattering efficiency over the entire wavelength range among all studied nanostructures. Although cone has the lowest absorption coefficient, small
electric polarizability of metal nanostructures upon their deposition on a substrate or their existence in a homogenous medium with permittivity different from that of free space. Although NACS and NSCS provided initial idea about absorption and scattering of the nanostructured coatings, selection of the optimum dimensions depends on how much light is coupled inside the perovskite substrate. The amount of light coupled to substrate is calculated using Eq. (3). The variation of the active area absorption enhancement (AAAE) of silver sphere with the sphere’s radius is shown in Fig. 4a. Note that the smaller radius has smaller light coupling to the substrate. However, as the sphere’s radius increases, coupling coefficient increases till it reaches a maximum at a radius of 125 nm and starts decreasing afterwards. This behavior can be related to the scattering slightly higher efficiency peak of the sphere with a radius of 125 nm than that of the sphere with a radius of 150 nm. In case of silver cylindrical (Fig. 4b), smaller radius has smaller NACS and NSCS, resulting in nearly zero AAAE. The largest light coupling occurs at a radius of 150 nm, with 806
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between centers of closed spheres lower than 470 nm makes the coating to act as a reflective surface with the generation rate of electrons inside the perovskite substrate being reduced even below that of the planar structure only. Increasing the pitch higher than 500 nm, would couple more incident sun light to the substrate and Jsc increases from 19.2 mA/ cm2 in case of planar surface to 20.9 mA/cm2. Larger pitch values were found to result in lower Jsc values. To get a closer explanation for the change in the generation rate, the square of electric field profile was plotted at a wavelength of 800 nm of planar substrate and periodic silver sphere at pitch of 550 nm, 650 nm, and 750 nm, Fig. 7a. Note that the silver sphere does not absorb any field with the electric field values increase in the perovskite layer compared with the planar substrate only. The silver spheres with different pitch values manipulate the near field light to couple with the waveguide modes of the perovskite substrate (Pala et al., 2009). Concentrated area of high electric field square is maximum at a pitch of 650, and decreases at higher or lower pitches. In case of silver cylindrical with radius and height of 150 nm (Fig. 6b), pitch below 630 nm would increase reflection and reduce the generation rate inside solar cell substrate, larger pitch would increase the generation rate till the Jsc reaches 21 mA/cm2 at a pitch of 900 nm, then Jsc decreases at larger pitches. Note that at all three pitches (Fig. 7b), neglected absorbed electric field is observed inside the silver cylindrical, the cylindrical redirect the incident light to support the waveguide modes of substrate, and light concentrates at the cylindrical edge with the substrate. The maximum electric field was observed for the pitch of 900 nm and decreases elsewhere. At pitches below 700 nm, the silver cube with a side length of 200 nm reduces the light coupling to the substrate due to the high reflection coefficient (Fig. 7c). Upon increasing the pitch to 900 nm, the Jsc reaches ca. 20 mA/cm2 and then decreases at higher pitch. A similar approach to sphere and cylindrical
NACS could not make good antireflective coating alone. In Fig. 4e, the AAAE of cylindrical shell shows no enhancement at all for the proposed dimensions, although scattering efficiency of cylindrical shell is comparable to silver cube. Multiple electric and magnetic dipoles in the entire visible range makes this structure absorbing more light than coupling it to the substrate. It can be deduced that the AAAE parameter combines both effects of NACS and NSCS for selecting the suitable dimensions for the antireflective coating over the perovskite substrate. The next step is to study the effect of light coupling between the closed nanostructures with optimum dimensions, by studying the effect of periodicity on the silver sphere, cylindrical, and cube with dimensions of 125 nm, 150 nm, and 200 nm, respectively. The optical model enables the calculation of light absorption inside the active layer using Eq. (4), electron-hole pair generation rate using Eqs. (5) and (6), and enhancement in short circuit current using Eq. (7). Fig. 5 shows the optical model of the simulated solar cell with the optimum silver nanostructured coatings. It consists of planar structure with dimensions that are reported experimentally (Qin et al., 2014), periodic silver sphere with a diameter of 250 nm and sweep parameter called pitch, periodic silver cylindrical with radius and height of 150 nm, and periodic silver cube with a side length of 200 nm. The pitch between the simulated nanostructures was kept very small to study the near field coupling between the nanostructures, and then be increased till reaching the maximum generation rate. At the optimum pitch, the coupling between the nanostructures was used to study far field coupling between the proposed nanostructures. Fig. 6 illustrates the effect of changing the periodicity between the selected dimensions of the proposed silver antireflection coating. For silver spheres with radii of 125 nm (Fig. 6a), having the distance 807
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all proposed nanostructures as in the case of silver. Instead, we will limit our study to sphere and cylindrical structures only due to their remarkable performance over other nanostructures. The selected dielectric has specific criteria. First, the fabrication of the selected dielectric should be compatible with perovskite (CH3NH3PbI3) solar cells. Second, the dielectric should be transparent in the visible region to reduce light losses inside the nanostructure. Third, the chosen dielectric should have good ability to redirect the scattered light into the active layer. Therefore, the chosen dielectric is titanium dioxide (TiO2). Using the solar cells shown in Fig. 1, silver sphere and silver cylindrical were replaced by titanium dioxide and the corresponding NACS, NSCS, and AAAE were calculated. Fig. 8 shows the Mie theory results of the
was observed, from guiding incident light to waveguide modes of perovskite slab, and concentrating the incident light at the cube edge, with the maximum electric field square area observed at a pitch of 900 nm. Therefore, based on the Mie theory and the optical model, the proposed dimensions of silver sphere, cylindrical, and cube are found to be 125 nm, 150 nm, 200 nm, respectively. The optimum pitch for silver sphere, cylindrical, and cube are 650 nm, 900 nm, 900 nm, respectively.
3.2. TiO2 antireflection coating In this part of study, the performance of replacing silver with alldielectric antireflection coating is investigated. Here, we will not repeat
Fig. 5. (I) Planar perovskite solar cell simulating cell consists of silver (Ag) as a back contact, HTM (CuSCN) as a p-type layer, perovskite (CH3NH3PbI3) as an n-type layer. (II) Periodic silver sphere over planar perovskite solar cell, using sphere radius 125 nm. (III) Periodic silver cylindrical on perovskite cell, with cylindrical radius of 150 nm. (IV) Periodic silver cube with side length equal 200 nm. 808
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Fig. 6. Variation of the short circuit current (Jsc) with the pitch length for (a) silver sphere of radius 125 nm, (b) silver cylindrical of radius 150 nm, and (c) silver cube of side length 200 nm.
Fig. 7. Electric field square profile comparison for (a) silver sphere of radius 125 nm at pitch 550 nm, 650 nm, and 750 nm, (b) silver cylindrical of radius 150 nm at pitch 800 nm, 900 nm, and 1000 nm, (c) silver cube of length 200 nm at pitch 800 nm, 900 nm, and 1000 nm. 809
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800
Wavelength (nm) 500
(e)
(f)
400
AAAE (%)
AAAE (%)
80
800
100nm 125nm 150nm 175nm 190nm 225nm
Wavelength (nm) 100
700
1.5
0 300
800
600
(d)
0.5 0 300
500
60 40 20
300 200 100
0
20
40
60
80
100
120
140
100
Sphere radius (nm)
120
140
160
180
200
220
Cylindrical radius (nm)
Fig. 8. Normalized absorption cross-section (NACS) of (a) TiO2 sphere with radii of 20–150 nm, (b) TiO2 cylindrical with radii of 100–225 nm. Normalized scattering cross-section (NSCS) of (c) TiO2 sphere and (d) TiO2 cylindrical with the same dimensions. Active area absorption enhancement (AAAE) versus simulated dimensions for (e) TiO2 sphere and (f) TiO2 cylindrical.
scattering control than that of a radius of 190 nm in the wavelength ranges 300–350 nm, 370–420 nm, and 450–650 nm. For the cylindrical with a radius of 175 nm, it has larger absorption coefficient than that of a radius of 190 nm over the entire wavelength band, and its NSCS is smaller in the wavelength range 650–800 nm. Therefore, our suggested dimensions of the TiO2 sphere and TiO2 cylindrical are 125 nm, and 190 nm, respectively. Next, the periodicity between optimally dimensions of the dielectric antireflection coatings was swept to study the effect of pitch on the light coupling to the perovskite substrate. Based on the simulated cell design shown in Fig. 5, TiO2 sphere with a radius of 125 nm replaced the silver sphere on top of the perovskite substrate, the silver cylindrical was also replaced by TiO2 cylindrical of a radius of 190 nm to perform the optical modelling. The variation of the short circuit current with the pitch length for TiO2 sphere and cylindrical is shown in Fig. 9. For TiO2 sphere, smaller pitches < 450 nm resulted in no enhancement in the Jsc compared to the planar perovskite structure, Fig. 9a. Due to difference in refractive index, when the TiO2 layer covered the entire the surface, light reflection becomes very high and the maximum current was achieved at the pitch length of 650 nm only. To get more insights, the electric field square profiles were constructed, Fig. 10. At the pitch length of 550 nm, the TiO2 sphere redirects light to couple into the waveguide modes of the perovskite layer. Increasing the pitch length to 650 nm, resulted in an increase in the amount of light coupling to the substrate. However, upon increasing the pitch to 750 nm, the TiO2 sphere showed very strong near field light concentration in very narrow area, resulted in a reduction of the field inside the entire perovskite substrate (Pala et al., 2009). In case of TiO2
dielectric sphere and cylindrical on perovskite substrate. TiO2 spheres absorb the light wavelengths below 400 nm, Fig. 8a. Note that increasing the radius of TiO2 sphere resulted in an increase in the absorption cross-section, reaching a maximum at a radius of 80 nm, and decline afterwards. In contrast, TiO2 cylindrical has large absorption at smaller radii (Fig. 8b). Also, the NACS decreases as the cylindrical radius increases, with nearly zero absorption observed at wavelengths higher than 400 nm, due to the zero imaginary refractive index of TiO2 above 400 nm (Wang et al., 2013). Smaller TiO2 spheres have very small light scattering coefficient, Fig. 8c. However, increasing the radius of TiO2 spheres increases and shifts the scattering resonance peaks to longer wavelengths of the visible light. On the other hand, at wavelengths below 500 nm, the TiO2 cylindrical has scattering resonance peaks at small radius. Upon increasing the radius of TiO2 cylindrical, the NSCS of increases over the entire band of visible light. To compare the light coupling coefficient, AAAE was calculated for the simulated dimensions of TiO2 sphere and cylindrical. Smaller radius of TiO2 sphere showed low ability to couple light inside the perovskite substrate, Fig. 8e, due to the low scattering coefficient at smaller sphere radius. Increasing the TiO2 sphere radius will increase the AAAE, reaching a maximum at a radius of 125 nm, afterwards it declines. This can be related to the fact that the scattering efficiency of the sphere with a radius of 125 nm is larger than that of the sphere of a radius of 100 nm at wavelengths higher than 550 nm. Note also that the sphere with a radius of 150 nm has smaller AAAE, because it has smaller NSCS in the wavelength range 400–550 nm. The AAAE of TiO2 cylindrical suggests a radius of 190 nm as selected dimension for light coupling, Fig. 8f. For the cylindrical of a radius of 225 nm, it has smaller light 810
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24
(b)
(a) 23.5 23
Planar
Sphere R = 125nm
Cylindrical R = 190nm
Theoretical maximum
Theoretical maximum
22
2
J sc (mA/cm )
22.5
Planar
21.5 21 20.5 20 19.5 19 450
500
550
600
650
700
750 500
Pitch (nm)
600
700
800
900
Pitch (nm)
Fig. 9. Short circuit current (Jsc) versus pitch length for (a) TiO2 sphere of a radius of 125 nm and (b) TiO2 cylindrical of a radius of 190 nm.
(Wang et al., 2013), the efficiency of guiding light to the substrate is maximum. At the pitch length of 600 nm, the same phenomenon of light coupling is observed, however the amount of electric field square is up to 1.4x times that observed in the case of the pitch length of 500 nm. With a pitch length of 800 nm, the TiO2 cylindrical changes its modes, resulting in strong near field light concentration in narrow region that reduces the overall amount of electric field square inside the entire perovskite substrate, and eventually Jsc decreases. Finally, upon applying Mie theory and optical modelling for all-dielectric antireflection coatings, our proposed dielectric nanostructures are TiO2 sphere with a radius of 125 nm and an pitch length of 650 nm, while TiO2 cylindrical has an radius of 190 nm and an pitch of 600 nm, with Jsc
cylindrical, the Jsc versus pitch length shows different behavior than that of the TiO2 sphere. For any pitch length, the TiO2 cylindrical current is higher than that of the planar perovskite. This can be related to the very large AAAE of TiO2 cylindrical, which enables single cylindrical to couple up to four times the electric field inside the perovskite substrate. The maximum obtained Jsc was found to be 22 mA/ cm2 observed at a pitch length of 600 nm, with enhancement of 15% over that of the planar structure. Based on the electric field profile of TiO2 cylindrical (Fig. 10b), at a pitch length of 500 nm, larger portion of the electric field couples inside the cylindrical, then the cylindrical redirects it to couple in lateral waveguide modes of the perovskite layer. As TiO2 has nearly zero imaginary refractive index above 400 nm
Fig. 10. Electric field square profiles for (a) TiO2 sphere of a radius of 125 nm with pitch lengths of 550 nm, 650 nm, and 750 nm, and (b) TiO2 cylindrical of a radius of 190 nm with pitch lengths of 500 nm, 600 nm, and 800 nm. 811
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Table 1 Generation rates (m−3 sec−1) in the simulated solar cells with optimum silver and titanium dioxide antireflection nanostructures. Generation (m−3 sec−1) in perovskite layer
Optimum Structure/Layer
Ag Sphere R = 125 nm Pitch = 650 nm Ag Cylinder R = 150 nm Pitch = 900 nm Ag Cube L = 200 nm Pitch = 900 nm TiO2 Sphere R = 125 nm Pitch = 650 nm TiO2 Cylinder R = 190 nm Pitch = 600 nm Planar
Table 2 The semiconductor parameters of CH3NH3PbI3 and CuSCN used to construct the electrical model.
Generation (m−3 sec−1) in HTM layer
5.94 × 1029
4.91 × 1028
5.98 × 1029
4.92 × 1028
5.65 × 1029
4.76 × 1028
6.14 × 1029
5.12 × 1028
6.50 × 1029
4.48 × 1028
5.39 × 1029
4.84 × 1028
Thickness (nm) Band gap (eV) CB density of state Nc (cm−3) VB density of state Nv (cm−3) Donor density ND (cm−3) Acceptor density NA (cm−3) Diffusion Length Ln (nm) Diffusion Length Lp (nm) Electron life time τn (nsec) Hole life time τp (nsec)
CuSCN
CH3NH3PbI3
200 3.6 5 × 1015 5 × 1015 – 1 × 1017 – 97 5–20 3–20
600 1.55 1 × 1016 1 × 1016 1 × 1017 – 100 – 6–100 6–100
Table 3 The electrical performance parameters of the proposed solar cells.
enhancement of 12.8% and 15%, respectively. The overall generation rates inside the perovskite and HTM layers of the proposed silver and titanium dioxide structures using the proposed dimensions and periodicity are listed in Table 1. To calculate the overall power conversion efficiency, fill factor, and short circuit current, three-dimensional electrical model based on finite element method was used to construct the current-voltage curves shown in Fig. 11. There is a good agreement between the J-V characteristics of the measured solar cell (Qin et al., 2014) and the simulated planar perovskite solar cell, assuming a series resistance of 10 Ω cm2 and a shunt resistance of 400 Ω cm2 for fitting, Fig. 11a. The JV graphs of the solar cells with Ag or TiO2 with the proposed dimensions and periodicities are shown in Fig. 11b. The largest Jsc of 22.06 mA/cm2 was observed for the solar cell with TiO2 cylindrical, which is 15% larger than that obtained for the planar structure alone. However, the lowest Jsc of 19.88 mA/cm2 was observed for the solar cell with silver cube, which is only 3.5% greater than that of the planner solar cell. The use of plasmonic antireflection coating using silver sphere or cylindrical showed 8.9% or 9% current enhancement, however using all-dielectric antireflection coating using TiO2 cylindrical or sphere, shows higher current enhancements up to 15% or 12.8%. This interesting finding, would suggest the use of dielectric materials over metals for light guiding in nanophotonics applications. Finally, a power conversion efficiency up to 14.42%, with about 2% increase, can be realized. The electrical parameters of CuSCN and CH3NH3PbI3 used in 20
Optimum Structures
Jsc (mA/ cm2)
Series Resistant (Ω cm2)
Voc (mV)
Series Resistant (Ω cm2)
FF
Efficiency (%)
Ag Sphere Ag Cylinder Ag Cube TiO2 Sphere TiO2 Cylinder Planar Simulation
20.91 20.92 19.88 21.66 22.06
10 10 10 10 10
1015 1015 1015 1014 1014
400 400 400 400 400
0.645 0.645 0.645 0.645 0.645
13.67 13.68 13.00 14.16 14.42
19.20
10
1015
400
0.645
12.92
the electrical model are listed in Table 2, while the electrical performance parameters of are listed in Table 3.
4. Conclusion In summary, we proposed a fast method for selecting the optimum antireflection nanostructured coatings over wideband spectrum based on Mie theory and coupled optical-electrical model. This method was applied to enhance the efficiency of perovskite solar cells through the comparison of the performance of nanostructured silver and titanium dioxide in the form of sphere, cylindrical, cone, cube, and cylindrical shell. The cone and cylindrical shell are not recommended to be used due to the various electric and magnetic dipoles over the solar light spectrum, which increase losses in the nanostructures. Silver sphere, cylindrical, and cube showed overall enhancement in short circuit current up to 8.9% and 9%, 3.5%, respectively. Titanium dioxide
(b)
(a)
20
2
Jsc (mA/cm )
Jsc (mA/cm 2)
15
10
5
0 0
15
10
5
Planar Simulation Planar Measured 0.2
0.4
0.6
0.8
0 0
1
Planar Simulation Ag Sphere (R = 125nm, Pitch = 650nm) Ag Cylindrical (R = 150nm, Pitch = 900nm) Ag Cube (L = 200nm, Pitch = 900nm) TiO2 Sphere (R = 125nm, Pitch = 650nm) TiO2 Cylindrical (R = 190nm, Pitch = 600nm)
0.2
0.4
0.6
0.8
1
Voltage (V)
Voltage (V)
Fig. 11. (a) Comparison between measured and simulated perovskite solar cells, (b) J-V characteristics of the solar cells with the optimum dimensions and pitch length of the proposed silver and dielectric antireflection nanostructured coatings. 812
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nanostructured coatings showed better enhancement than the silver counterparts, due to their larger scattering cross-section and smaller absorption cross-section over the wideband. The use of TiO2 sphere and cylindrical resulted in an overall increase in the short circuit current up to 12.8% and 15%, respectively. The fabrication of the proposed nanostructures on perovskite surface can be achieved using a plethora of fabrication methods such as optical interference lithography (Henzie et al., 2007), atomic layer deposition (Standridge et al., 2009), focused ion beam lithography (Langford et al., 2007), electron-beam lithography (Broers et al., 1976), template stripping (Nagpal et al., 2009), soft lithography (Lindquist et al., 2012; Kumar and Whitesides, 1993), and electrospinning (Abdellah et al., 2018). Integrating the proposed optimally TiO2 nanostructures with perovskite solar cells would enhance light absorption in the cell and increase the overall efficiency of perovskite solar cells. The proposed method can be extended for any substrate or solar cell type. Applying this method when designing antireflection coating for many optoelectronic devices would limit the computational efforts exerted to select optimum dimensions.
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