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Theoretical study of Ag and Au triple core-shell spherical plasmonic nanoparticles in ultra-thin film perovskite solar cells

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Abstract

This work demonstrates the enhancement of the power conversion efficiency of thin film organic-inorganic halide perovskites solar cells by embedding triple-core-shell spherical plasmonic nanoparticles into the absorber layer. A dielectric-metal-dielectric nanoparticle can be substituted for embedded metallic nanoparticles in the absorbing layer to modify their chemical and thermal stability. By solving Maxwell's equations with the three-dimensional finite difference time domain method, the proposed high-efficiency perovskite solar cell has been optically simulated. Additionally, the electrical parameters have been determined through numerical simulations of coupled Poisson and continuity equations. Based on electro-optical simulation results, the short-circuit current density of the proposed perovskite solar cell with triple core-shell nanoparticles consisting of dielectric-gold-dielectric and dielectric-silver-dielectric nanoparticles has been enhanced by approximately 25% and 29%, respectively, as compared to a perovskite solar cell without nanoparticles. By contrast, for pure gold and silver nanoparticles, the generated short-circuit current density increased by nearly 9% and 12%, respectively. Furthermore, in the optimal case of the perovskite solar cell the open-circuit voltage, the short-circuit current density, the fill factor, and the power conversion efficiency have been achieved at 1.06 V, 25 mAcm-2, 0.872, and 23.00%, respectively. Last but not least, lead toxicity has been reduced due to the ultra-thin perovskite absorber layer, and this study provides a detailed roadmap for the use of low-cost triple core-shell nanoparticles for efficient ultra-thin-film perovskite solar cells.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Increasing global warming and the depletion of fossil fuels have led to the use of photovoltaic systems becoming more prevalent [1]. After conversion by the inverter, the DC power provided by photovoltaic devices is available as AC power [24]. Metal halide perovskites, such as methylammonium lead triiodide (MAPbI3), were first synthesized in 1978, and are promising candidates for photovoltaic applications [5]. The unique optoelectronic properties of perovskite (CH3NH3PbI3) such as direct band gap, high absorption coefficient, low exciton binding energy, tunability of bandgap, long carrier diffusion length, and convenient manufacturing process, have led to its rapid growth in the past decade [6]. From 2009 to 2021, the power conversion efficiency (PCE) of perovskite solar cell (PSC) has rapidly increased from 3.8% to over 24% [7,8]. A major reason for the limited use of solar cells is their high final fabrication cost. As a result, they are made as thin layers in order to reduce the overall cost on a large scale. There are many challenges associated with reducing the thickness of solar cells and limiting their active regions, including limited sunlight absorption, unbalanced and low mobility of charge carriers, and short exciton diffusion lengths, but on the other hand, charge carrier separation is relatively easily available in PSC, which improves transparency. Even though reducing the thickness of the absorber in PSCs reduces the toxicity of lead, effective photon management is still required for optimal performance.

Plasmonic nanoparticles (NPs) are one of the most well-known methods for increasing solar cell absorption while maintaining a constant thickness [9]. The plasmonic nanoparticles have attracted considerable interest in nanoscience and nanotechnology in recent decades due to their unique characteristics, including their ability to localize light in the nanometer regime and to overcome the diffraction limit. As a result, it is widely used in applications such as biosensors, nano-imaging, Terahertz sensors, modulators, power splitters, and solar cells. There have been numerous applications for coinage metals (Ag and Au) in the field of plasmonics [1014]. NPs in different geometries (spherical, cylindrical, cubic, and pyramidal) have been widely investigated in second-generation solar cells [1517]. Moreover, over the past few years, this process has been applied to PSCs, organic solar cells (OSCs), and dye-sensitized solar cells (DSSCs) [1822].

The photovoltaic device can be optimized using localized surface plasmon resonance (LSPR) effects when metallic NPs are embedded in the semiconductor layer. This results in enhanced carrier generation rates as well as greater sunlight absorption. In spite of the fact that metallic NPs embedded in the photoactive region absorb light, this absorption does not lead to the generation of electron-hole pairs in the semiconductor. Through the use of two methods of absorption spectroscopy including Photothermal Deflection Spectroscopy (PDS) and Fourier Transform Photocurrent Spectroscopy (FTPS), parasitic absorption in the absorber layer can be separated from useful absorption [23]. Therefore, the cost of absorption spectroscopy must be added to the final manufacturing cost of plasmonic solar cells in order to estimate optical losses (parasitic absorption). There have been a number of previous studies in which optical losses in PSC have not been calculated [2428]. As an example, in an experimental study, silver NPs were embedded in the perovskite layer using the vapor phase deposition method, improving the efficiency of PSC by about 15% [29]. In another study, with two gold NPs at the top and backside of the photoactive region with thickness of 1200 nm, the short-circuit current density or photocurrent improved from 18 mAcm-2 to 21 mAcm-2 [30].

Basically, when sunlight reaches the absorbing material of solar cells with NPs embedded within their absorbing material, a strong interaction occurs between the sunlight and the free electrons of the metals, leading to a local field (far field and near field) occurring as a result of the oscillation of free electrons. Due to the local field enhancement caused by plasmonic NPs, photocurrent, absorption, and efficiency are improved. All of these plasmonic phenomena are explained by classical physics. While optical losses are one of the challenges associated with the use of NPs, the next set of challenges is directly related to the material used for the absorber.

As we know, perovskite is easily decomposed and has corrosive properties. Moreover, after the interaction between sunlight and free electrons of metallic NPs, the electrons that do not affect the absorption process and remain on the surface of NPs, lead to the heating of surface NPs during phonon radiation and relaxation processes [31]. This eventually leads to NPs acting as recombination exciton centers [32]. In addition, the decomposition of NPs decreases the efficiency of the PSC [33]. A dielectric material with high stability, such as silica (SiO2), is used around NPs and pure metallic NPs are changed into core-shell NPs to overcome this challenge. By using this model, NPs are more thermally and chemically stable. Therefore, dielectric materials act as shields to prevent direct contact between semiconductors and metals [33,34]. The experimental study that was recently published regarding thermal stability demonstrated that SiO2 nanoshells were able to maintain and stabilize the structure at a temperature of approximately 700°C [35]. In various PSC, metal-dielectric NPs have been used. A related study reported an increase of approximately 2% (from 14.5% to 16.3%) in PCE with Au/SiO2 core-shell NPs [36]. In another study, it was shown that the combination of gold and silver NPs with silica dielectric can lead to high absorption of 50% in sunlight [37].

It should be noted, however, that in this category of NPs (metal-dielectric), the metal forms a large part of the NPs and contributes to optical losses. There is generally a direct correlation between optical losses in NPs and metal size, which can be ignored in very small NPs. Triple dielectric-metal-dielectric NPs have a very thin metal layer. Thus, one of the advantages of using these NPs is that parasitic absorption is not considered. There have been previous studies that have provided details regarding the synthesis of triple core-shell NPs [3840]. Thin-layer PSCs have a low absorber layer thickness, leading to decreased near-infrared absorption. In contrast, for efficient PSCs, it is the first condition of high light harvesting in the entire wavelength range. The optimal state of the NPs can enhance the absorption spectrum without affecting the open circuit voltage adversely.

Throughout this research, we aim to compare gold and silver NPs and calculate their optical losses in PSC in order to increase absorption in the photoactive region. In comparison with pure metallic NPs of the same size, dielectric-metal-dielectric NPs demonstrate excellent absorption and thermal stability for PSC. Using triple core-shell nanoparticles for efficient PSC, the results of this study provide a detailed roadmap for high-efficient PSC. The continuation of the paper is as follows: In the second section, the details of the proposed structure is presented. The third section includes physical modeling, mathematical relationships, and solution methods related to the proposed structure. The fourth section analyzes the simulation results. Finally, the conclusion is presented in the fifth section.

2. Proposed structure of PSC

In this study, the PCE of ultra-thin film PSC has been enhanced by embedding triple-core-shell spherical NPs into the absorber layer. The proposed PSC structure consists of six layers, including SiO2, fluorine-doped tin oxide (FTO), Titanium dioxide (TiO2), methylammonium lead triiodide (perovskite), Spiro-OMeTAD and gold (Au). A 3D schematic of the unit cell of the proposed structure is depicted in Fig. 1. To prevent contamination of the surface by the environment, a top layer of SiO2 with a thickness of hAR1, is utilized as an anti-reflection coating (ARC). There are various transparent conductive oxides (TCOs) used in PSC, including FTOs and Indium-doped tin oxides (ITOs). Whenever comparing two TCO materials, FTO is a superior choice due to two factors. First, indium, the main component of ITO, is quite rare. Second, FTO has better stability than ITO. As the second component of the anti-reflection coating, FTO material was used with a thickness of hAR2 [41]. As the third layer Tio2 has the thickness of hETL. A layer of this type plays two roles due to the minima of its conduction band and maxima of its valence band, which are 4.4 eV and 7.63 eV, respectively. The first function of this layer is to extract electrons from the perovskite layer, and the second one is to block holes at the interface between perovskite and FTO layers [42]. There is a perovskite layer with a thickness of hAbs in the absorber region of the proposed solar cell structure. The next layer is the hole transport layer (HTL) with a thickness of hHTL. Spiro-OMeTAD is one of the most widely used materials for blocking the path of electrons and extracting holes. The addition of low-cost materials such as alkyl thiol to the spiro-OMeTAD increases the performance stability of PSC [43]. The bottom layer of the proposed PSC structure is Au with a thickness of hbc. This layer reflects part of the sunlight into HTL and the absorber region of PSC. The thickness of all the materials used in the proposed PSC is listed in Table 1.

 figure: Fig. 1.

Fig. 1. 3D schematic of proposed structure ultra-thin-film halide PSC with four models NP

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Table 1. The simulation parameters

A perovskite material can absorb sunlight in the range of 300-800 nm according to its bandgap energy [44,45]. However, the absorption decreases from about 600 nm, which results low absorption in the near-infrared region. As an alternative, plasmonic NPs may be embedded in the absorber region to achieve plasmonic properties. Consequently, NPs can be utilized in the photoactive region to enhance the absorption capability of the PSC in the near-infrared region. It has been demonstrated that exposure of electromagnetic fields to NPs can enhance PCE due to improvement of the absorption spectrum by four different mechanisms. Radiative effects include near-field coupling and far-field scattering. Hot electron transfer (HET) and plasmon resonance energy transfer (PRET) are non-radiative effects. Radiative effects are considered in this study.

3. Modeling and simulation methods

To understand electromagnetic fields in PSCs, solving Maxwell's equations is required. The 3D-FDTD method solves Maxwell's equations in specific boundary conditions. The electric field intensity ${\vert E(r, \lambda)\vert}$ can be determined by solving Maxwell's equations. The total absorption spectrum for the perovskite absorber per unit volume is calculated according to Eq. (1):

$$A(r,\omega ) = \frac{1}{2}\frac{{\omega {\varepsilon _0}{\mathop{\rm Im}\nolimits} ({\varepsilon (r,\omega )} ){{|{E(r,\omega )} |}^2}}}{{{P_{in}}}}.$$

In this equation, ω is the angular frequency and r represents specific locations, ${\varepsilon _0}$ and $\varepsilon$ are the dielectric constants of the environment and the electric permittivity of the vacuum, respectively. The power of incident light is indicated by Pin and according to the standard conditions of AM 1.5, it is equal to 1000 wm-2. Besides, the parasitic absorption for Au and Ag NPs per unit volume is calculated by this Equation. Net absorption is obtained by subtracting the parasitic absorption from the total absorption, according to Eq. (2):

$${A_{net}}(\lambda ) = \int\limits_{{V_{absorber}}} {A(r,\lambda )dV} - \int\limits_{{V_{nanoparticles}}} {A(r,\lambda )dV.}$$

To evaluate and analyze the performance of the proposed NPs in the PSC, the photocurrent is calculated as

$${J_{SC}} = \int\limits_{300nm}^{800nm} {\textrm{A(}\lambda \textrm{)}} \textrm{.AM1}\textrm{.5D(}\lambda \textrm{)d}\lambda$$

Exciton generation rate values are a function of four variables, variables $({x,y,z,\lambda } )$, calculated by Eq. (4):

$$G({x,y,z,\lambda } )= \frac{{{\varepsilon _0}}}{{2\hbar }}\frac{{lm({\varepsilon (r,\lambda )} ){{|{E(r,\lambda )} |}^2}}}{{{P_{in}}}}$$

As it is clear from Eq. (4), the exciton generation rate is directly related to ${|{E(r,\lambda )} |^2}$. Additionally, the total number of excitons generated at each point is obtained by Eq. (5). Finally, the photocurrent is obtained from the excitons generation rate according to Eq. (5).

$$G(x,y,z,\lambda ) = \int {G(x,y,z,\lambda )d\lambda }$$

To understand electrical characteristics in PSCs, Poisson equation are solved. Equation (6) shown this equation, here in, E is electric field, $\rho$ is space charge density, $\psi$ and ${\varepsilon _S}$ are the electrostatic potential and static materials permittivity. elementary charge is q in this equation equal to 1.6 x10−19 (C). NA and ND are ionized acceptor and donor densities, respectively.

$$\frac{{{\partial ^2}\psi }}{{{\partial ^2}x}} ={-} \frac{{\partial E}}{{\partial x}} ={-} \frac{\rho }{{{\varepsilon _S}}} = \frac{q}{{{\varepsilon _S}}}[p - n + {N_D}(x) - {N_A}(x) \pm {N_{def}}(x)]$$

Besides, Eqs. (7) and 8 describes the carrier continuity at steady state for electron and hole.

$$\frac{{\partial {J_n}}}{{\partial x}} + G - {U_n}(n,p) = 0$$
$$- \frac{{\partial {J_p}}}{{\partial x}} + G - {U_p}(n,p) = 0$$
where Jn is current density of electron, Jp is current density of hole carriers, G is the electron-hole generation rate, Up and Un are the net recombination rates. Finally, Drift diffusion equations (9-10) are solved.
$${J_n} = qp{\mu _n}E + q{D_n}\frac{{\partial n}}{{\partial x}}$$
$${J_p} = qp{\mu _p}E + q{D_p}\frac{{\partial n}}{{\partial x}}$$
where q is the elementary charge, ${\mu _n}$ and ${\mu _p}$ are the electron and hole mobility carrier, respectively. Dn and Dp are the diffusion coefficients of electron and hole, respectively.

4. Simulation results and discussion

As mentioned, metallic NPs can manipulate and control absorption spectra. The increase in the absorption spectrum leads to the enhancement of PCE in perovskite absorber performance. The surrounding electromagnetic fields of the NPs play the main role in increasing the optical path and absorption. The analyses of the optical behavior of NPs inside the absorber material, such as the absorption spectrum, numerical value of photocurrent, the profile of the exciton generation rate, and electrical field distribution, were performed by the 3D-FDTD method of the commercial Lumerical software package. The plane-wave source is located on the top of the PSC structure, which emits sunlight towards the structure under standard AM1.5 conditions. Although the wavelength spectrum of AM1.5 is from approximately 300 nm to 2000nm, the length of the perovskite absorption spectrum was considered from 300 nm to 800 nm due to perovskite band gap (about 1.5 eV). Perfectly matching layer (PML) boundary conditions were used in the direction of sunlight and periodic boundary condition (PBC) were used in other directions. Refractive index (n) and extinction coefficient (k) for FTO, TiO2, and Spiro-OMeTAD materials are taken from previous studies [33,46,47]. Additionally, optical constants for MAPbI3, SiO2, Au, and Ag materials are taken [4749].

In the first step, a unit cell with a volume of 615 nm × 200 nm × 200 nm was considered. To achieve maximum light harvesting and the maximum numerical value of photocurrent, NPs must be swept. Pure Au and Ag NPs were swept in the range of 40 nm to 60 nm. For both metals, the maximum photocurrent is available with radius of 50 nm. The photocurrent for the PSC with embedded spherical Au NPs is 23.38 mAcm-2 and the photocurrent for the PSC with spherical Ag NPs is 23.55 mAcm-2. Considering the optical losses, the net photocurrent value for the PSC with embedded Au and Ag spherical NPs is 21.10 mAcm-2 and 21.69 mAcm-2, respectively. Therefore, optical losses lead to a decrement in photocurrent of 9.76% (2.35 mAcm-2) for Au spherical NPs and 7.9% (1.86 mAcm-2) for Ag spherical NPs. Calculating the optical losses of NPs reduces the costs of spectroscopy. Another important note in the use of metals on a large scale is their final cost. The cost of plasmonic metals such as Au NPs is about 50 times higher than Ag NPs per ounce [50].

Optical losses of NPs must be considered in different material semiconductors that are used as solar cell absorbers. On the other hand, in PSCs that are easily decomposed, there are other challenges such as thermal and chemical instability of NPs. Triple core-shell NPs were chosen to overcome existing challenges. In this type of nanoparticles, utilize of a metal nanoshell between two dielectric layers reduces the thickness of the metal. The radius of the dielectric core (SiO2) added to the metal shell of the triple shell NPs was designed to be the same as the radius of pure metal NPs (50 nm). In addition, the thickness of the metal nanoshell (Au or Ag) and the outer dielectric layer (SiO2) is between 1 nm to 20 nm. After optimization, SiO2/Au/SiO2 triple core-shell NPs was chosen as best case. Radius of Au nanoshell is 20 nm and the SiO2 outer dielectric layer radius is 5 nm, photocurrent value is 24.18 mAcm-2.

According to study [51], the hot electron does not overcome the Schottky barrier for SiO2 with a thickness of more than 3 nm, so the hot electron is not injected into the perovskite conduction band and the hot electron transfer (HET) process is canceled. Unlike the first non-radiative effect (HET), the SiO2 layer cannot hinder the plasmon resonant energy transfer (PERT) process. This process happens as long as there are strong fields around the metal NPs inside the perovskite material and there is a spectral overlap between perovskite absorption and LSPR. The last proposed NPs model is the SiO2/Ag/SiO2 triple core-shell NPs, which has a photocurrent of 24.89 mAcm-2 in the optimal state. In this case, the thickness of the Ag nanoshell and the outer SiO2 thickness are 20 nm and 5 nm, respectively. This scenario was repeated for NPs with a radius of 40 nm and 60 nm, and the results of the numerical values of the photocurrent are shown in the bar graph of Fig. 2. The cut line in this figure shows the photocurrent value of the PSC without NPs. The net photocurrent for Au and Ag NPs is shown in this bar graph. Despite the proposed NPs, fundamental limitations for perovskite with a thickness of 200 nm haven’t been broken. According to previous studies [52], The Shockley-Queisser photocurrent limit for perovskite (methylammonium lead iodide) with a thickness of 200 nm is about 25.5 mAcm-2. Furthermore, PCE, open-circuit voltage and fill factor are approximately 29.5%, 1.28 V and 90.2 respectively.

 figure: Fig. 2.

Fig. 2. Bar graph of the photocurrent value for the Ag NPs, Au NPs, SiO2/Au/SiO2 NPs and SiO2/Ag/SiO2 NPs in the radius of 40 nm, 50 nm and 60 nm

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To have a better view of the difference in the numerical values of the photocurrent in different models, the absorption diagram, generation rate, and electrical distribution are obtained and analyzed. Figure 3 shows the absorption spectrum diagram for pure metal NPs and triple core-shell NPs. Figure 3(a), illustrates the total absorption of spherical Au NPs, showing that the total absorption spectrum is improved, but by subtracting the optical losses from the total absorption, it is clear that the absorption length spectrum of the absorber material is improved for wavelengths higher than 700 nm. SiO2/Au/SiO2 triple core-shell NPs perform better than spherical Au NPs in the entire wavelength and specifically increase the absorption in the range above 450 nm. Figure 3(b), displays that spherical Ag NPs have improved entire wavelengths like spherical Au NPs, the difference between the two net absorption diagrams for Ag and Au indicates that the parasitic absorption of spherical Ag NPs is lower than that of spherical Au NPs, especially in the wavelengths of 450 nm to 600 nm. SiO2/Ag/SiO2 triple core-shell NPs significantly increase the spectra above 450 nm compared to the net absorption of spherical Ag NPs. In addition, in the range of 400 nm to 650 nm, it has a better performance than SiO2/Au/SiO2 triple core-shell NPs depicted in Fig. 3(c).

 figure: Fig. 3.

Fig. 3. (a) Absorption spectrum diagram of perovskite absorber with Ag spherical NPs and triple core-shell NPs (b) Absorption spectrum diagram of perovskite absorber with spherical Au NPs and triple core-shell NPs (c) Absorption spectrum diagram for the proposed PSC with four NPs models in the best case (d) Bar chart of numerical photocurrent values of proposed PSC without NPs and PSC Whit Ag NPs, Au NPs, SiO2/Au/SiO2 NPs and SiO2/Ag/SiO2 NPs

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Commonly, the perovskite material has good absorption in the wavelength range of 300-650 nm. After the embedding triple core-shell NPs in photoactive area, incident light hits the triple core-shell NPs, very strong local fields are formed around them. Far and near field effects causes the light with high albedo to be emitted to the surrounding environment and absorbed by the semiconductor. This scenario causes about 80% of the incident light to be uniformly absorbed by the semiconductor in the wavelength of 400-800 nm, seen in Fig. 3(c). The bar chart in Fig. 3(d) shows the numerical values of the photocurrent for the PSC without NPs and with Au NPs, Ag NPs, SiO2/Au/SiO2 NPs, and SiO2/Ag/SiO2 NPs.

The absorption of each photon by perovskite leads to the generation of an exciton, so the efficiency of solar cells is proportional to the rate of exciton generation rate. According to the standard conditions of AM1.5, the power of sunlight (1000 wm-2) is not in the range of non-linear propagation. Thus, the photon absorption process by perovskite results in the generation of only an exciton. Figure 4 shows the exciton generation rate for four models of spherical NPs. Exciton generation rate of spherical Au NPs is higher than Ag NPs, this exactly approves the value of photocurrent and total absorption without considering optical losses which has been depicted in Fig. 4 (a)-(b). In the triple shell-core models for Au and Ag illustrated in Fig. 4 (c)-(d), the exciton generation rate values are higher than pure metal NPs.

 figure: Fig. 4.

Fig. 4. Exciton Generation rate for perovskite absorber with, (a) Au spherical NPs (b Ag spherical NPs (c) SiO2/Au/SiO2 NPs (d) SiO2/Ag/SiO2 NPs

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The direct contact of the strong local fields around Au or Ag spherical NPs with excitons causes excitons recombination on the surface of spherical NPs. For this reason, a layer of SiO2 is used to barricade direct contact of the excitons with NPs like a shield. The highest rate of exciton generation rate is related to SiO2/Ag/SiO2 triple core-shell NPs. In other words, the exciton generation rate and the absorption spectrum diagram confirm the numerical values of the photocurrent as the best-proposed structure. In the next step, the electric field distribution in the best model is analyzed.

As mentioned earlier, strong local fields are formed around NPs. These local fields depend on the shape, size of the NPs, and the surrounding environment. In addition, the local field distribution is not the same at entire wavelengths. To have a clear view of distribution of electric fields in different wavelengths, electrical fields distribution profile in several wavelengths for SiO2/Ag/SiO2 triple core-shell NPs is analyzed from the cross-sectional view, shown in Fig. 5. The perovskite absorber has good absorption in the primary wavelengths. The scattering effects can be seen in the wavelength of 300 nm (Fig. 5(a)). In other words, there is no interaction between light and NPs during the primary wavelengths, and the incident light is reflected after hitting SiO2/Ag/SiO2 triple core-shell NPs. After a short period of time, free electron of metal oscillation, the near and far field effects can be seen at the wavelength of 407 nm (Fig. 5(b)). The near fields effect increases in wavelengths of 625 nm and the scattering effects decrease, demonstrated in Fig. 5(c). At the wavelength of 759 nm, significant near fields effect can be seen in Fig. 5(d).

 figure: Fig. 5.

Fig. 5. The distribution of electric field for the best-proposed structure with SiO2/Ag/SiO2 NPs at different wavelengths (a) λ=300 nm, (b) λ=407 nm, (c) λ=625 nm, and (d) λ=759 nm (cross-section view of the PSC)

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Therefore, thanks to the strong localization, SiO2/Ag/SiO2 triple core-shell NPs can be considered as a secondary incident light source by photon flux recharge in different wavelengths, and this helps to transfer electrons from the valance band to the conduction band. Furthermore, Strong electromagnetic fields around NPs enhancement the mobility of charge carriers and overcome the binding energy of excitons [53], so that an effective PSC is available. It is noteworthy that triple NPs do not have optical losses and have a better plasmon hybridization mechanism than pure metallic spherical NPs. It is also important to mention that based on the effective medium theory and according to the Yablonovitch limit (also called the 4n2 limit), Plasmonic NPs are capable of increasing the refractive index in the active layer of the solar cell, in turn increasing the broadband solar cell absorption, which has been discussed in previous studies [5458]. In the final section, the exciton generation rate as an input Solar Cell Capacitance Simulator (SCAPS-1D) software is used for electrical calculations [59]. All parameters required for electrical simulation are taken from previous studies are shown in Table 2 [6064]. Also, Au is defined in the electrical simulation with a work function of 5.1(eV) [65]. J-V characteristics for all proposed PSC, illustrated in Fig. 6. Triple core-shell Au and Ag NPs have better performance than pure Au and Ag NPs as demonstrated in Fig. 6 (a)-(b). In addition, in Fig. 6(c), it is clear that the best performance of the PSC will be available with SiO2/Ag/SiO2 triple core-shell NPs.

 figure: Fig. 6.

Fig. 6. J-V characteristics for proposed PCS (a) Au NPs and (SiO2/Au/SiO2) NPs (b) Ag NPs and (SiO2/Ag/SiO2) NPs (c) (SiO2/Au/SiO2) NPs and Ag (SiO2/Ag/SiO2) NPs

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Table 2. Electrical simulation parameters used for PSC

Furthermore, FF, and PCE values were calculated for all proposed models and listed in Table 3. As shown in Table 3, the SiO2/Ag/SiO2 triple core-shell NPs with photocurrent 24.89 mAcm-2, open-circuit voltage 1.06 v, fill factor 0.872, and power conversion efficiency 23.00%, are best choice. Finally, the numerical values of photocurrent, Voc, FF, and PCE for SiO2/Ag/SiO2 triple core-shell NPs are listed in Table 2 to compare with other PSC studies. It should be noted that optical losses have not been calculated in most studies [24,25,30,36,66,67]. Photocurrent improvement was 28.96% compared to without NPs. Besides, the PCE increased by 49.35% compared to previous studies [67]. Moreover, the PCE grows by 37.06% compared to similar recent study [66]. In the Table 4, there is an increment in PCE compared to more similar recent studies in the “Increase” column.

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Table 3. Electrical characteristics of the proposed PSC with Au NPs, Ag NPs, SiO2@ Au@SiO2 and SiO2@ Ag@SiO2 NPs

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Table 4. Compare the proposed PSC and similar studies

5. Conclusion

In this research, the PCE enhancement of a thin-film organic-inorganic halide PSC has been investigated by embedding triple core-shell spherical metallic-dielectric NPs into the absorber layer. An electro-optical simulation revealed that the short-circuit current density generated by triple core-shell metallic-dielectric NPs embedded in the absorber layer can be nearly 2.5 times greater than that generated by pure metallic NPs. A short-circuit current density of the proposed PSC based on dielectric-gold-dielectric and dielectric-silver-dielectric NPs has been improved by approximately 25% and 29%, respectively, in comparison with a conventional PSC. Further, the use of low-cost triple core-shell NPs provides thermal and chemical stability, as well as reducing the spectroscopic costs associated with the use of pure metallic NPs. Based on the optimal design of the proposed PSC, the open-circuit voltage, the short-circuit current density, the fill factor, and the PCE were achieved at 1.06 V, 25mAcm-2, 0.872, and 23.00%, respectively. Finally, by reducing the thickness of the perovskite absorber, lead toxicity can be decreased. The findings of this study provide a detailed roadmap for the development of an efficient and cost-effective PSC with high absorption, which paves the way for the production of solar cells with high efficiency and cost-effectiveness.

Disclosures

The authors declare that they have no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (6)

Fig. 1.
Fig. 1. 3D schematic of proposed structure ultra-thin-film halide PSC with four models NP
Fig. 2.
Fig. 2. Bar graph of the photocurrent value for the Ag NPs, Au NPs, SiO2/Au/SiO2 NPs and SiO2/Ag/SiO2 NPs in the radius of 40 nm, 50 nm and 60 nm
Fig. 3.
Fig. 3. (a) Absorption spectrum diagram of perovskite absorber with Ag spherical NPs and triple core-shell NPs (b) Absorption spectrum diagram of perovskite absorber with spherical Au NPs and triple core-shell NPs (c) Absorption spectrum diagram for the proposed PSC with four NPs models in the best case (d) Bar chart of numerical photocurrent values of proposed PSC without NPs and PSC Whit Ag NPs, Au NPs, SiO2/Au/SiO2 NPs and SiO2/Ag/SiO2 NPs
Fig. 4.
Fig. 4. Exciton Generation rate for perovskite absorber with, (a) Au spherical NPs (b Ag spherical NPs (c) SiO2/Au/SiO2 NPs (d) SiO2/Ag/SiO2 NPs
Fig. 5.
Fig. 5. The distribution of electric field for the best-proposed structure with SiO2/Ag/SiO2 NPs at different wavelengths (a) λ=300 nm, (b) λ=407 nm, (c) λ=625 nm, and (d) λ=759 nm (cross-section view of the PSC)
Fig. 6.
Fig. 6. J-V characteristics for proposed PCS (a) Au NPs and (SiO2/Au/SiO2) NPs (b) Ag NPs and (SiO2/Ag/SiO2) NPs (c) (SiO2/Au/SiO2) NPs and Ag (SiO2/Ag/SiO2) NPs

Tables (4)

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Table 1. The simulation parameters

Tables Icon

Table 2. Electrical simulation parameters used for PSC

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Table 3. Electrical characteristics of the proposed PSC with Au NPs, Ag NPs, SiO2@ Au@SiO2 and SiO2@ Ag@SiO2 NPs

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Table 4. Compare the proposed PSC and similar studies

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

A ( r , ω ) = 1 2 ω ε 0 Im ( ε ( r , ω ) ) | E ( r , ω ) | 2 P i n .
A n e t ( λ ) = V a b s o r b e r A ( r , λ ) d V V n a n o p a r t i c l e s A ( r , λ ) d V .
J S C = 300 n m 800 n m A( λ ) .AM1 .5D( λ )d λ
G ( x , y , z , λ ) = ε 0 2 l m ( ε ( r , λ ) ) | E ( r , λ ) | 2 P i n
G ( x , y , z , λ ) = G ( x , y , z , λ ) d λ
2 ψ 2 x = E x = ρ ε S = q ε S [ p n + N D ( x ) N A ( x ) ± N d e f ( x ) ]
J n x + G U n ( n , p ) = 0
J p x + G U p ( n , p ) = 0
J n = q p μ n E + q D n n x
J p = q p μ p E + q D p n x
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