Perovskite Solar Cell with Added Gold/Silver Nanoparticles: Enhanced Optical and Electrical Characteristics

Different perovskite materials, such as methylammonium lead triiodide MAPbI3, exhibit many outstanding and desirable properties in solar energy harvesting. In this paper, the enhancement of perovskite solar cells’ both optical and electrical characteristics through adding either gold (Au) or silver (Ag) nanoparticles (NPs) using different simulations was studied. The used plasmonic nanoparticles were found to be able to compensate for the low absorption of MAPbI3 in the visible with optical coupling resonance frequencies close to that spectrum. Optimal diameters of Au and Ag NPs were found and simulated, and their impact on different parameters such as transmission, absorption, reflection, external quantum efficiency (EQE), open circuit voltage, short-circuit current density, fill factor, and most importantly, efficiency of the perovskite solar cell, have been investigated.


Introduction
Solar photovoltaic (PV) is one of the world's best renewable energy sources, having experienced exponential growth over the last several years [1], with an expected installed capacity of 1 terawatt (TW) by 2022-2023 [2]. One prominent emerging type of solar cells is perovskite solar cells. Even though perovskites had a weak start in photovoltaic applications in 2009, with power conversion efficiency as little as 3.8% [3], their efficiencies have skyrocketed to 14% in 2013 and to~23% in 2018 [4]. Additionally, as of June 2018, thin-film perovskite technologies have exceeded all other thin-film solar cell technologies, including cadmium telluride (CdTe) and Copper Indium Gallium Selenide (CIGS), proving to be a strong candidate to the future of solar PV.
One of the most promising perovskite materials is methylammonium lead triiodide (MAPbI 3 or MAPI), exhibiting many outstanding and desirable properties. Its electrical properties include: a direct bandgap [5] with a value around 1.6 eV with shallow defect levels [6], tunable bandgap (up to 2.25 eV) [7], a large open circuit voltage of 1.07 [8], and a relatively high short-circuit current density. Not only does MAPbI 3 excel electrically, but it also possesses some appealing optical properties, such as high carrier mobilities [9], high absorption coefficient [10,11], and long diffusion lengths [12][13][14]. All these exceptional and advantageous properties are important metrics for high performance solar cells [15], making MAPbI 3 one of the top contenders in perovskite solar cell technology.
One of the ways to enhance the performance of perovskite solar cells is by the addition of plasmonic NPs to the cell. Plasmonic NPs, known for their very useful and interesting properties, have become the subject of many scientific applications over the past decade [16]. More importantly, metallic NPs have attracted the most attention due to their optical properties, allowing their applications to vary from biology, to photothermal imaging and therapy, to solar cells and much more. Many metallic NPs exhibit high absorption in the visible electromagnetic spectrum range, but only Au, Ag, and copper (Cu) NPs exhibit surface plasmon resonance (SPR) effect in that visible region too [16]. SPR is a phenomenon in which polarized light hits a metallic film at the interface of media with different refractive indices which causes the collective oscillation of free electrons, known as surface plasmons. These plasmons can be set to resonate with light, resulting in high absorption of light [17]. This SPR effect is particularly effective in solar cell applications due to the great absorption of light NPs have to offer, especially Au and Ag. This improvement in absorption can lead to an improved power conversion efficiency which we aspire to achieve. Over the last few years, there have been some recent experimental works of embedding plasmonic nanostructures, such as both Ag and Au NPs, within perovskite solar cells to enhance the power conversion efficiency (PCE). The experimental synthesized plasmonic-perovskite cell improved PCE from 15.4% up to 17.3% when adding both blended Ag and Au nanocrystals of 1 vol.%. However, the design technique is still dependent on blending the plasmonic nanocrystals within the perovskite layer of the cell [18][19][20].
In this paper, the enhancement of perovskite solar cells through the addition of Au and Ag NPs is studied. This enhancement is analyzed both optically and electrically. Our aim is to demonstrate the effect of these NPs to the optical and electrical characteristics of the cell through different simulations. It is shown that plasmonic NPs are able to compensate for the low absorption of MAPbI 3 in the visible spectrum by adding NPs with resonance frequencies close to that spectrum [15]. Optimal diameters of Au and Ag NPs are found and simulated, and their impact on different parameters such as transmission, absorption, reflection, external quantum efficiency (EQE), open circuit voltage (V oc ), short-circuit current density (J sc ), fill factor (FF), and most importantly, efficiency (η) of the perovskite solar cell, is investigated. Through our work, the plasmonic layer of NPs is added to the rear side of the solar cell. That configuration is proven to be more effective in enhancing the photocurrent [21,22].

Optical Modeling
Stanford University McGehee Group's Transfer Matrix Optical Modeling software was used to optically simulate and model our cell. The software utilizes the transfer matrix method (TMM) which solves Maxwell's equations at the layers' interfaces to optically model the thin-film layer stacks [23]. Stanford's TMM code uses complex refractive index and the thickness of each layer as input, and outputs the absorbance, reflectance, electric field intensity, and photogeneration rate of each layer, along with the overall optical short circuit current density.

Silvaco TCAD-ATLAS (Electrical Modeling)
A Silvaco ATLAS technology computer-aided design (TCAD) simulation was used to model the electrical behavior of our cell. ATLAS is a 2D and 3D device simulator based on finite element analysis that performs DC, AC, and transient analysis for numerous material-based devices and enabling the characterization and optimization of semiconductor devices for a wide range of technologies [24]. Its working principle is based on solving Poisson's equations, charge carrier continuity equations, and charge transport of drift-diffusion equations for electrons and holes [25,26]; allowing the generation of the desired J-V curves and the extraction of: J sc , V oc , FF, and the η of the cell.

Case Study
The cell under study is a semitransparent perovskite solar cell with an n-i-p architecture: TCO/ETL/Perovskite/HTL/TCO. For the transparent conductive oxide (TCO), a 140 nm thick indium-tin oxide (ITO)-coated glass substrate as front electrode and 50 nm thick ITO as the back electrode. The electron transport layer (ETL) consists of 5 nm thick SnO 2 combined with 15 nm thick phenyl-C61-butyric acid methyl ester (PCBM) bilayer. The perovskite material used in this study is a 372 nm thick MAPbI 3 followed by a 250 nm thick 2,2',7,7'-tetrakis[N,N-di(4-methoxyphenyl)amino]-9,9'-spirobifluorene (Spiro-OMeTAD) as hole transport layer (HTL). Roughness layers for front ITO, MaPbI 3 , and rear ITO were added to simulate experimental irregularities with thicknesses of 4 nm, 50 nm, and 10 nm, respectively. Both Au and Ag NPs will be applied to the rear of the perovskite solar cell, and their effect on the performance of the solar cell will be studied both optically and electrically. The model of the cell is illustrated in the schematic in Figure 1.

Case Study
The cell under study is a semitransparent perovskite solar cell with an n-i-p architecture: TCO/ETL/Perovskite/HTL/TCO. For the transparent conductive oxide (TCO), a 140 nm thick indiumtin oxide (ITO)-coated glass substrate as front electrode and 50 nm thick ITO as the back electrode. The electron transport layer (ETL) consists of 5 nm thick SnO2 combined with 15 nm thick phenyl-C61-butyric acid methyl ester (PCBM) bilayer. The perovskite material used in this study is a 372 nm thick MAPbI3 followed by a 250 nm thick 2,2',7,7'-tetrakis[N,N-di(4-methoxyphenyl)amino]-9,9'spirobifluorene (Spiro-OMeTAD) as hole transport layer (HTL). Roughness layers for front ITO, MaPbI3, and rear ITO were added to simulate experimental irregularities with thicknesses of 4 nm, 50 nm, and 10 nm, respectively. Both Au and Ag NPs will be applied to the rear of the perovskite solar cell, and their effect on the performance of the solar cell will be studied both optically and electrically. The model of the cell is illustrated in the schematic in Figure 1.

Simulation Procedure
The optical and electrical simulations are mainly focused on studying the effect of adding either Au or Ag NPs to the rear end of a semitransparent perovskite solar cell. The optical simulation started by using the Effective Medium Theory (EMT) to approximate the NP spheres and represent them with a planar stack of changing refractive index. Then, the TMM was used with the derived effective refractive index from EMT to represent the Au and Ag NPs. In the TMM, the diameters of these NPs were varied in order to find the optimum thickness which yields the highest optical Jsc. Photogeneration files corresponding to the optimum NPs thickness from the optical TMM simulations were used in the electrical simulation via Silvaco ATLAS to investigate the effect of Au and Ag NPs on the electrical performance of the perovskite solar cell.

Planarization of the Au and Ag NPs Using EMT Method
The EMT was used to model NPs at the rear side of our cell. Being suspended at the rear of the cell, these nanospheres form a graded refractive index at the air/NP interface from either side. For periods smaller than λ/(2n), n being the refractive index of the NP, the propagation of light can be

Simulation Procedure
The optical and electrical simulations are mainly focused on studying the effect of adding either Au or Ag NPs to the rear end of a semitransparent perovskite solar cell. The optical simulation started by using the Effective Medium Theory (EMT) to approximate the NP spheres and represent them with a planar stack of changing refractive index. Then, the TMM was used with the derived effective refractive index from EMT to represent the Au and Ag NPs. In the TMM, the diameters of these NPs were varied in order to find the optimum thickness which yields the highest optical J sc . Photogeneration files corresponding to the optimum NPs thickness from the optical TMM simulations were used in the electrical simulation via Silvaco ATLAS to investigate the effect of Au and Ag NPs on the electrical performance of the perovskite solar cell.

Planarization of the Au and Ag NPs Using EMT Method
The EMT was used to model NPs at the rear side of our cell. Being suspended at the rear of the cell, these nanospheres form a graded refractive index at the air/NP interface from either side. For periods smaller than λ/(2n), n being the refractive index of the NP, the propagation of light can be Energies 2020, 13, 3854 4 of 14 explained using the EMT [27,28] by approximating the spheres and representing them with a planar stack of changing refractive index [29], as shown in Figure 2.
Energies2020, 10, x; doi: FOR PEER REVIEW 4 of 14 explained using the EMT [27,28] by approximating the spheres and representing them with a planar stack of changing refractive index [29], as shown in Figure 2. The effective refractive index of each of the layers can be expressed by the following formula, Equation (1) [30]: where n1 and n2 are the refractive indices of the incident medium and the metallic NPs, respectively, and f(z) being the volume ratio as a function of the height of the structure, z. The volume ratio can be expressed as ( ) = ( )/ , where Agrid is the area of the nanospheres arrangement grid, which is circular in our case, and An(z) is the cross-sectional area of the sphere at a height z. Hence, the effective refractive index, Equation (1), can be simplified to Equation (2): where rb is the base radius of the grid and AHF(z) being the area height factor, ranging from 0 to 1. By substituting, a generalized formula for the effective refractive index with a circular grid is derived and expressed in Equation (3): For spheres, see Figure 3, it was derived that the ( ) = 1 − , with h being the height or half the thickness of the sphere, yielding a final expression for effective refractive index for spheres, Equation (4): Transmitted Light Transmitted Light The effective refractive index of each of the layers can be expressed by the following formula, Equation (1) [30]: where n 1 and n 2 are the refractive indices of the incident medium and the metallic NPs, respectively, and f(z) being the volume ratio as a function of the height of the structure, z. The volume ratio can be expressed as f (z) = A n (z)/A grid , where A grid is the area of the nanospheres arrangement grid, which is circular in our case, and A n (z) is the cross-sectional area of the sphere at a height z. Hence, the effective refractive index, Equation (1), can be simplified to Equation (2): where r b is the base radius of the grid and AHF(z) being the area height factor, ranging from 0 to 1. By substituting, a generalized formula for the effective refractive index with a circular grid is derived and expressed in Equation (3): For spheres, see Figure 3, it was derived that the AHF(z) = 1 − z h 2 , with h being the height or half the thickness of the sphere, yielding a final expression for effective refractive index for spheres, Equation (4): Utilizing the equation above (Equation (4)), we converted each sphere into a one-dimensional multilayer stack in the z-direction. The effective refractive index of the stacks was varied according to the equation, from z = h, the top of the sphere, to z = −h, the bottom of the sphere; see Figure 3. This resulted in an effective sweep of the refractive index, from n air (z = h) to n Au and n Ag at the base of the sphere (z = 0), and back to n air , at the bottom of the sphere (z = −h), for each structure. A plot of normalized height versus effective refractive index shows the refractive index profile of the graded index for both Au and Ag NPs; see Figure 4.

Optimization of the Au and Ag NPs Size Using TMM
This part of the optical simulation was performed using the Stanford TMM MATLAB code, where the layers were added as shown in the schematic of Figure 1. The complex refractive index of each material was added to the software's refractive index library file and renamed accordingly. All the complex refractive index values were obtained from literature and referenced [31][32][33][34][35]. The thickness of each layer was also set according to Figure 1. To obtain precise and accurate results, the wavelength range was set from 300 nm to 1200 nm with a small step size increment of 1 nm. MAPbI3 was selected as the active material in the cell, where photocurrent will be generated.
To find the optimum thickness for the Au and Ag NPs, the diameter was swept from 0 to 300 nm and the optical Jsc was observed and recorded for each thickness. Figure 5 shows the diameter optimization for Au and Ag NPs. A maximum Jsc of 20.25 mA/cm 2 was reached at a diameter size of 153 nm for the Au nanospheres. For Ag, a higher Jsc of 20.38 mA/cm 2 was reached at a lower nanosphere size of 135 nm. Furthermore, photogeneration plots and files, versus the depth of the perovskite material were created at each of these optimum Au and Ag diameters, as seen in Figure 6.

Optimization of the Au and Ag NPs Size Using TMM
This part of the optical simulation was performed using the Stanford TMM MATLAB code, where the layers were added as shown in the schematic of Figure 1. The complex refractive index of each material was added to the software's refractive index library file and renamed accordingly. All the complex refractive index values were obtained from literature and referenced [31][32][33][34][35]. The thickness of each layer was also set according to Figure 1. To obtain precise and accurate results, the wavelength range was set from 300 nm to 1200 nm with a small step size increment of 1 nm. MAPbI3 was selected as the active material in the cell, where photocurrent will be generated.
To find the optimum thickness for the Au and Ag NPs, the diameter was swept from 0 to 300 nm and the optical Jsc was observed and recorded for each thickness. Figure 5 shows the diameter optimization for Au and Ag NPs. A maximum Jsc of 20.25 mA/cm 2 was reached at a diameter size of 153 nm for the Au nanospheres. For Ag, a higher Jsc of 20.38 mA/cm 2 was reached at a lower nanosphere size of 135 nm. Furthermore, photogeneration plots and files, versus the depth of the perovskite material were created at each of these optimum Au and Ag diameters, as seen in Figure 6.

Optimization of the Au and Ag NPs Size Using TMM
This part of the optical simulation was performed using the Stanford TMM MATLAB code, where the layers were added as shown in the schematic of Figure 1. The complex refractive index of each material was added to the software's refractive index library file and renamed accordingly. All the complex refractive index values were obtained from literature and referenced [31][32][33][34][35]. The thickness of each layer was also set according to Figure 1. To obtain precise and accurate results, the wavelength range was set from 300 nm to 1200 nm with a small step size increment of 1 nm. MAPbI 3 was selected as the active material in the cell, where photocurrent will be generated.
To find the optimum thickness for the Au and Ag NPs, the diameter was swept from 0 to 300 nm and the optical J sc was observed and recorded for each thickness. Figure 5 shows the diameter optimization for Au and Ag NPs. A maximum J sc of 20.25 mA/cm 2 was reached at a diameter size of 153 nm for the Au nanospheres. For Ag, a higher J sc of 20.38 mA/cm 2 was reached at a lower nanosphere size of 135 nm. Furthermore, photogeneration plots and files, versus the depth of the perovskite material were created at each of these optimum Au and Ag diameters, as seen in Figure 6. It can be seen that the cells with the Au and Ag nanospheres mostly have higher photogeneration rates throughout the depth of the MAPI material than the semitransparent cell, with the Ag cell slightly outperforming the Au cell at certain depths.
It can be seen that the cells with the Au and Ag nanospheres mostly have higher photogeneration rates throughout the depth of the MAPI material than the semitransparent cell, with the Ag cell slightly outperforming the Au cell at certain depths.

Electrical Simulation
The electrical simulations were performed using Silvaco ATLAS. The device dimensions were first meshed accordingly and optimized to yield the most accurate results. Next, the material layers were added as to the previous suggested structure and doped accordingly. Material parameters were specified for each material according to Table 1 [36][37][38], selected and cited from experimental and theoretical data. Recombination models were then set for the ETL, HTL, and the perovskite. These models are essential to correctly model the behavior of the cell, especially when we have both organic and inorganic materials in the cell, which is why Silvaco ATLAS was chosen to accurately model and simulate our cell. For the ETL, the carrier concentration dependent mobility and Shockley-Read-Hall (SRH) recombination were set. For the perovskite, the Poole-Frankel field dependent mobility model, SRH, and Langevin recombination were set. As for the HTL, the Poole-Frankel field dependent  It can be seen that the cells with the Au and Ag nanospheres mostly have higher photogeneration rates throughout the depth of the MAPI material than the semitransparent cell, with the Ag cell slightly outperforming the Au cell at certain depths.

Electrical Simulation
The electrical simulations were performed using Silvaco ATLAS. The device dimensions were first meshed accordingly and optimized to yield the most accurate results. Next, the material layers were added as to the previous suggested structure and doped accordingly. Material parameters were specified for each material according to Table 1 [36][37][38], selected and cited from experimental and theoretical data. Recombination models were then set for the ETL, HTL, and the perovskite. These models are essential to correctly model the behavior of the cell, especially when we have both organic and inorganic materials in the cell, which is why Silvaco ATLAS was chosen to accurately model and simulate our cell. For the ETL, the carrier concentration dependent mobility and Shockley-Read-Hall (SRH) recombination were set. For the perovskite, the Poole-Frankel field dependent mobility model, SRH, and Langevin recombination were set. As for the HTL, the Poole-Frankel field dependent

Electrical Simulation
The electrical simulations were performed using Silvaco ATLAS. The device dimensions were first meshed accordingly and optimized to yield the most accurate results. Next, the material layers were added as to the previous suggested structure and doped accordingly. Material parameters were specified for each material according to Table 1 [36][37][38], selected and cited from experimental and theoretical data. Recombination models were then set for the ETL, HTL, and the perovskite. These models are essential to correctly model the behavior of the cell, especially when we have both organic and inorganic materials in the cell, which is why Silvaco ATLAS was chosen to accurately model and simulate our cell. For the ETL, the carrier concentration dependent mobility and Shockley-Read-Hall (SRH) recombination were set. For the perovskite, the Poole-Frankel field dependent mobility model, SRH, and Langevin recombination were set. As for the HTL, the Poole-Frankel field dependent mobility model and Langevin recombination were specified, as found in the literature [39]. The photogeneration rate from the optical TMM simulation was then used as an input file. With this file, ATLAS can perform all the necessary calculations and solve all the equations necessary to extract the required electrical Energies 2020, 13, 3854 7 of 14 parameters. Silvaco ATLAS was then finally ready to solve the solar cell. The voltage was swept from 0 to 1.1 V with increments of 0.01 V to ensure accuracy. It then extracted all the required electrical parameters including V oc , J sc , FF, and η.
To ensure the reliability of the simulator, a series of calibration simulations were first performed to match the experimental results of a semitransparent perovskite solar cell provided by the Interuniversity Microelectronics Centre (IMEC) [40]. Figure 7 shows the simulated IV curve closely matched with the experimental curve with some small deviation. The electrical parameters extracted from both simulated and experimental IV curves as shown in Table 2. From the table, you can see a strong agreement between the simulated and experimental results. mobility model and Langevin recombination were specified, as found in the literature [39]. The photogeneration rate from the optical TMM simulation was then used as an input file. With this file, ATLAS can perform all the necessary calculations and solve all the equations necessary to extract the required electrical parameters. Silvaco ATLAS was then finally ready to solve the solar cell. The voltage was swept from 0 to 1.1 V with increments of 0.01 V to ensure accuracy. It then extracted all the required electrical parameters including Voc, Jsc, FF, and η.
To ensure the reliability of the simulator, a series of calibration simulations were first performed to match the experimental results of a semitransparent perovskite solar cell provided by the Interuniversity Microelectronics Centre (IMEC) [40]. Figure 7 shows the simulated IV curve closely matched with the experimental curve with some small deviation. The electrical parameters extracted from both simulated and experimental IV curves as shown in Table 2. From the table, you can see a strong agreement between the simulated and experimental results.

Results and Discussion
With the simulator calibrated, J-V curves were produced for our semitransparent cell with and without the optimally sized Au and Ag NPs. Figure 8 show a comparison between the three J-V curves along with a summary of the extracted electrical parameters in Table 3. It is clear that the

Results and Discussion
With the simulator calibrated, J-V curves were produced for our semitransparent cell with and without the optimally sized Au and Ag NPs. Figure 8 show a comparison between the three J-V curves along with a summary of the extracted electrical parameters in Table 3. It is clear that the added NPs have a direct effect on the enhancement of the J sc , with an increase of 1.45 mA/cm 2 and 1.58 mA/cm 2 for Au and Ag NPs, respectively. This may be due to the improvement in the EQE Energies 2020, 13, 3854 8 of 14 of the cell. However, this had minimal-to-negligible effect on V oc ; which almost remained constant. The FF, however, decreased, as expected, by~1% with the addition of the Au and Ag NPs at the rear side. This can be explained due to the increased value of the cell's sheet resistance. Overall, an improvement of~1% on the conversion efficiency was achieved by adding either Au or Ag NPs at the rear-side of a semitransparent MAPbI 3 perovskite solar cell with Ag slightly outperforming Au.   To further investigate the reason behind the slight improvement in performance of Ag NP over the Au NP, and to gain a clear-cut understanding, three optical analyses are considered in this paper:

Solar-Weighted Reflectance
The solar-weighted reflectance (SWR) is a measure of reflectivity over the entire solar spectrum weighted by the intensity of sunlight of each wavelength. Since the reflection plots produced were a function of wavelength, it is sometimes difficult to determine which reflection curve results in lower or higher overall reflection. The SWR provides a more tangible measure of reflectance by providing a single numerical expression for the reflectance rather than a function of wavelength. It is expressed in Equation (5) by the following expression [44]: where is the wavelength, R( ) is the reflection of the cell, and .
is the AM1.5G solar spectrum. Integrations were performed from 300 nm to 800 nm, which is the interval of interest in  To further investigate the reason behind the slight improvement in performance of Ag NP over the Au NP, and to gain a clear-cut understanding, three optical analyses are considered in this paper:

Solar-Weighted Reflectance
The solar-weighted reflectance (SWR) is a measure of reflectivity over the entire solar spectrum weighted by the intensity of sunlight of each wavelength. Since the reflection plots produced were a function of wavelength, it is sometimes difficult to determine which reflection curve results in lower or higher overall reflection. The SWR provides a more tangible measure of reflectance by providing a single numerical expression for the reflectance rather than a function of wavelength. It is expressed in Equation (5) by the following expression [44]: where λ is the wavelength, R(λ) is the reflection of the cell, and ϕ AM 1.5G is the AM1.5G solar spectrum. Integrations were performed from 300 nm to 800 nm, which is the interval of interest in our perovskite solar cell. A summary of the results is provided in Table 4. With the SWR calculations, it can be seen Energies 2020, 13, 3854 9 of 14 that the addition of the NPs has a clear and significant impact on the overall reflection of the cell, resulting in an increase of~3.5% with the Au NPs and~4% with the Ag NPs. This may cause photon recycling, and therefore, increase the probability of absorption in the perovskite layer which causes an increase in the external quantum efficiency of the solar cell. As a result, a slight increase in J sc. with Ag NPs over Au NPs can be seen.

Solar Absorptance Enhancement
Similar to SWR, the solar absorptance enhancement (SAE) also provides a better understanding and interpretation of one of the most important optical parameters, absorption. The SAE translates the absorption vs. wavelength into a numeric ratio which indicates the degree in absorption enhancement. The SAE is expressed in Equation (6) by the following expression [45]: where A is the total absorption of the cell (i.e., A = EQE perovskite + A parasitic ), A reference represents the absorption of the semitransparent cell with no NPs, whereas A structure represents the absorption of the cell with the added NPs. A value of SAE > 1 implies a positive effect or an enhancement and SAE < 1 implies a negative effect or a deterioration, whereas SAE = 1 implies no enhancement or deterioration in absorption. Integrations were performed from 300 nm to 800 nm, which is the interval of interest in our perovskite solar cell. Calculations were performed on three different kinds of absorptions: the total cell absorption, perovskite absorption, and parasitic absorption. A summary of the results is provided in Table 5. With the SAE calculations, it can be seen that the addition of the plasmonic NPs has a clear and significant impact on the overall absorption enhancement of the cell, with Au NPs resulting in just a minor fraction more total absorption enhancement than the Ag NPs. However, this extra absorption is being squandered on parasitic absorption, as the NPs resulted in an SAE value of 1.956 and 1.83 for Au and Ag NPs, respectively. Thus meaning, the Ag NPs contributed more to the perovskite absorption (i.e., EQE), with an SAE value of 1.084 as opposed by 1.077 for the Au NPs, resulting in higher photocurrent; see Figure 9.

Current Density Loss (Jloss) Analysis
Reflection, transmission, and absorption are essential parameters that optically characterize a solar cell. They can provide a definite indication on the performance of the cell and ultimately translate into optical current. In order to calculate the current density loss due to reflection, transmission, and parasitic absorption, current loss analysis was carried out to investigate the effect of Au and Ag NPs on the performance of the semitransparent perovskite solar cell, by using TMM simulations. At the device front, part of the light is lost due to external reflection. These reflection losses (i.e., J reflection-loss) are calculated by integrating the reflection spectrum on the front side of the cell according to Equation (7) [15]. Moreover, at the device rear, part of the light is lost due to transmission, where long wavelength light is transmitted through the transparent rear ITO. This external loss is calculated by integrating the transmission curve of the cell according to Equation (8) [15]. Finally, the current loss due to parasitic absorption (i.e., Jparasitic-loss) is calculated using Equation (9) [15], by integrating the area between the EQE and the absorbance curves over the AM1.5G solar spectrum for the wavelength region of interest.
= q hc λ·Φ(λ)·R(λ)·dλ (mA/cm ) = q hc λ·Φ(λ)·T(λ)·dλ (mA/cm ) Furthermore, the total Jsc which can be produced by the solar cell for each specific NP can be expressed in Equation (10) as: where q is the elementary charge, h is Planck's constant, c is the speed of the light, R is the reflection of the cell, T is the transmission of the cell, and A is the absorption of the cell. A summary of the results can be found in Table 6. It can be shown that + + + = 27.28 mA/cm for all structures, which is approximately 27.3 mA/cm 2 , the Shockley-Quiesser Jsc limit for a 1.55 eV bandgap material [46]. For the semitransparent cell, much of Parasitic Absorption (a.u)

Wavelength (nm)
No NPs Au NPs Ag NPs Figure 9. Parasitic absorption plot for the cell with and without Au and Ag NPs.

Current Density Loss (J loss ) Analysis
Reflection, transmission, and absorption are essential parameters that optically characterize a solar cell. They can provide a definite indication on the performance of the cell and ultimately translate into optical current. In order to calculate the current density loss due to reflection, transmission, and parasitic absorption, current loss analysis was carried out to investigate the effect of Au and Ag NPs on the performance of the semitransparent perovskite solar cell, by using TMM simulations. At the device front, part of the light is lost due to external reflection. These reflection losses (i.e., J reflection-loss) are calculated by integrating the reflection spectrum on the front side of the cell according to Equation (7) [15]. Moreover, at the device rear, part of the light is lost due to transmission, where long wavelength light is transmitted through the transparent rear ITO. This external loss is calculated by integrating the transmission curve of the cell according to Equation (8) [15]. Finally, the current loss due to parasitic absorption (i.e., J parasitic-loss ) is calculated using Equation (9) [15], by integrating the area between the EQE and the absorbance curves over the AM1.5G solar spectrum for the wavelength region of interest.
Furthermore, the total J sc which can be produced by the solar cell for each specific NP can be expressed in Equation (10) where q is the elementary charge, h is Planck's constant, c is the speed of the light, R is the reflection of the cell, T is the transmission of the cell, and A is the absorption of the cell. A summary of the results can be found in Table 6. It can be shown that J parasitic + J transmission + J re f lection + J sc = 27.28 mA/cm 2 for all structures, which is approximately 27.3 mA/cm 2 , the Shockley-Quiesser J sc limit for a 1.55 eV bandgap material [46]. For the semitransparent cell, much of that current is lost due to transmission losses and only a little is lost due to parasitic absorption and reflection. Adding the Au and Ag seems to mitigate these transmission losses and improve the J sc by 7.76% and 8.44%, respectively; however, the parasitic and reflection losses have also increased unfavorably as depicted by the SWR and SAE calculations. The J reflection increased by~1 mA/cm 2 and 1.1 mA/cm 2 while the J parasitic increased by 1.73 mA/cm 2 and 1.5 mA/cm 2 with the addition of Au and Ag NPs, respectively. Overall, the addition of these NPs resulted in a positive impact. J sc also had a direct improvement due to the increase in the EQE of the cell. It should be noted that silver resulted in better overall characteristics than gold with higher absorption, EQE and reflection, along with lower transmission and parasitic absorption. An illustration of these optical parameters can be shown in Figure 10. The magnitude of each parameter is illustrated by the area it covers at its pertinent wavelength region. It can be noticed from Figure 10 that the EQE was also enhanced at wavelength range close to the plasmonic resonance frequency. This enhancement is due to the improvement in the absorption and the entrapment of the reflected photoelectrons [15]. However, the overall parasitic absorption also increased absorption and reflection at the resonance frequency. that current is lost due to transmission losses and only a little is lost due to parasitic absorption and reflection. Adding the Au and Ag seems to mitigate these transmission losses and improve the Jsc by 7.76% and 8.44%, respectively; however, the parasitic and reflection losses have also increased unfavorably as depicted by the SWR and SAE calculations. The Jreflection increased by ~1 mA/cm 2 and ~1.1 mA/cm 2 while the Jparasitic increased by 1.73 mA/cm 2 and 1.5 mA/cm 2 with the addition of Au and Ag NPs, respectively. Overall, the addition of these NPs resulted in a positive impact. Jsc also had a direct improvement due to the increase in the EQE of the cell. It should be noted that silver resulted in better overall characteristics than gold with higher absorption, EQE and reflection, along with lower transmission and parasitic absorption. An illustration of these optical parameters can be shown in Figure 10. The magnitude of each parameter is illustrated by the area it covers at its pertinent wavelength region. It can be noticed from Figure 10 that the EQE was also enhanced at wavelength range close to the plasmonic resonance frequency. This enhancement is due to the improvement in the absorption and the entrapment of the reflected photoelectrons [15]. However, the overall parasitic absorption also increased absorption and reflection at the resonance frequency.

Conclusions
This work shows the enhancement of both optical and electrical properties of a semitransparent perovskite solar cell by the addition of either Au or Ag NPs of different diameters. Optical simulations show that these nanoparticles have improved the external quantum efficiency of the perovskite solar cell at certain parts of the spectrum and in turn, the short-circuit current density. J sc has increased by 1.45 mA/cm 2 (7.76%) and 1.58 mA/cm 2 (8.44%), with the addition of the optimally sized Au and Ag NPs, respectively. On the other hand, electrical simulations showed little-to-no changes in both V oc and FF, but an improvement in the efficiency due to the enhancement of the J sc . The efficiency, η, has increased by~0.98% and~1.07% with the addition of the optimally sized Au and Ag NPs, respectively.
Additional optical analysis tools and methods were also considered including: Solar-Weighted Reflectance (SWR), Solar Absorptance Enhancement (SAE), and Current Density Loss (J loss ) analysis. SWR calculations show that the overall reflection of the cell increased by~3.5% with the Au NPs and 4% with the Ag NPs. SAE calculations show that the Au NPs have increased the total absorption slightly more than the Ag NPs, but this increase was mostly wasted on parasitic absorption rather than the perovskite, unlike the Ag NPs. J loss analysis showed the exact distribution of light in terms of current density. Due to the increase in reflection and parasitic absorption in the cell, J reflection and J parasitic have also increased. The J reflection increased by~1 mA/cm 2 and~1.1 mA/cm 2 while the J parasitic increased by 1.73 mA/cm 2 and 1.5 mA/cm 2 with the addition of Au and Ag NPs, respectively. J transmission underwent the biggest improvement, dropping from 4.24 mA/cm 2 , down to 0.09 mA/cm 2 and 0.07 mA/cm 2 for Au and Ag NPs, respectively.