Simulation of Perovskite Solar Cells Optimized by the Inverse Planar Method in SILVACO: 3D Electrical and Optical Models

Abstract

In recent years, perovskite solar cells (PSCs), often referred to as the third generation, have rapidly proliferated. Their most prominent deficiencies are their low efficiency and poor stability. To enhance their productivity, a combination of silicon and perovskite is employed. Here, we present a 3D simulation analysis of various electrical and optical properties of PSCs using the SILVACO simulation software. Using the inverted planar method with inorganic transport materials and the proper selection of anti-reflective coatings with a back contact layer increases the efficiency of PSCs to 28.064%, and enhances their stability without using silicone composites. Several materials, including CaF₂, SiO₂, and Al₂O₃, with various thicknesses have been employed to investigate the effect of anti-reflective coatings, and to improve the efficiency of the simulated PSC. The best thickness of the absorbent layer is 500 nm, using a CaF₂ anti-reflective coating with an optimal thickness of 110 nm. A polymer composition of Spiro-OMeTAD and inorganic materials Cu₂O and NiOx was used as the hole transport material (HTM) and inorganic ZnO was employed as the electron transport material (ETM) to optimize the solar cell efficiency, and an optimized thickness was considered for these materials. Yields of 29.261, 28.064 and 27.325% were obtained for Spiro-OMeTAD/ZnO, Cu₂O/ZnO and NiOx/ZnO, respectively. Thus, Spiro-OMeTAD yields the highest efficiency. This material is highly expensive with a complex synthesis and high degradability. We proposed to employ Cu₂O to alleviate these problems; however, this reduces the efficiency by 1.197%. As a graphene connector has high flexibility, reduces cell weight, and is cheaper and more accessible compared to other metals, it was regarded as an optimal alternative. The simulation results indicate that using the inverted planar method with inorganic transport materials for graphene-based PSCs is highly promising.

1. Introduction

Perovskite solar cells (PSCs) have garnered extensive attention worldwide owing to their fast development, extremely high efficiency, and easy and low-cost manufacturing process. In recent years, many studies have been conducted on PSCs, which has led to a power conversion efficiency (PCE) of 25.2% in 2019 [1]. In contrast to early research on the structure of conventional PSCs, the inverted planar structures (n-i-p or p-i-n) have been investigated owing to their ease of manufacturing, low-temperature and low-cost processing, and compatibility with flexible beds in PSC [2,3,4]. According to several studies, inverted planar devices have shown efficiency of above 20% for producing conventional structures, which is very promising [5,6]. To the best of our knowledge, despite recent advances in PSCs, inverted planar PSCs have garnered less attention and only a few studies have been conducted in this field. Accordingly, many studied are needed to improve and maximize their performance at the same levels as their counterparts compared to conventional structures.

In this study, we have followed two fundamental principles. First, some of the existing studies have focused on inverted planar PSCs, which have resulted in using specific metals (silver and gold as the back contact, Spiro-OMeTAD polymer material as the hole transport, and improper anti-reflective coatings on the cell surface) [7,8,9,10,11]. We addressed these issues by (a) the use of graphene back contact instead of metal, (b) proposing an inverted planar PSC with all inorganic material and (c) selecting calcium fluoride (CaF₂), for the first time, in PSCs as the best anti-reflection material. Second, one of the most important disadvantages of inverted planar solar cells is their low efficiency, which requires new and developed techniques, such as CIGS, a-si, and c-si pairing, to be used to improve productivity [12,13,14]. The use of the inverted planar method with inorganic transport materials and properly selected anti-reflective coatings with a back contact layer to achieve an efficiency of 28.064% without the presence of a pair facilitates various types of techniques. Solar cells (tandem) with a two-terminal structure are difficult to use in building high-efficiency solar modules because the different materials used in the solar cell must be adjusted and coordinated in such a way as to prevent them from limiting each other’s performance under certain light conditions. If this problem is solved, PSCs can be lighter and cheaper, owing to the elimination of two transparent connections, and potentially one layer [15].

One of the important factors affecting the conversion efficiency of solar cells is the reflection losses of the light hitting the solar cell surface. To reduce light reflectance losses, often a single anti-reflective coating or several coatings are placed on the solar cell surface. Because anti-reflective coatings can enable the light to enter into the active parts of the device, they play an important role in increasing the conversion efficiency of solar cells. The anti-reflective coating is usually composed of one or several dielectric layers. Its thickness is a quarter of the wavelength of the light, which reduces reflection owing to the phenomenon of interference [16,17]. Accordingly, Hiroyuki Kanda et al. acquired the best results from aluminum oxide (Al₂O₃) by studying several elements as anti-reflective coatings [18]. According to [19], a few other elements were investigated as anti-reflective coating, and silicon dioxide (SiO₂) was selected as the best anti-reflective element.

Two major problems is encountered in large-scale production of PSCs: First, using a hole-transporting material considerably increases the cost and decreases the effective lifespan of the cell. Second, expensive metals are applied as the counter electrode in these cells. These two problems limit the production of low-cost solar cells. Despite significant progress, some problems, such as the reduced lifespan of perovskite (because of the high degradability of Spiro-OMeTAD [2,2′,7,7′-Tetrakis (N,N-di-pmethoxyphenylamino)-9,9′-spirobifluorene], the dominant hole-transporting material in perovskite), the complex synthesis, and the high cost of Spiro-OMeTAD, will pose potential obstacles to commercializing PSC in the future [20,21,22,23,24,25,26]. Furthermore, the Spiro-OMeTAD layer should aid electrode polarization and play a major role in the hysteresis phenomenon of current density–voltage (J–V), which will affect the stability of the device [27]. For PSCs with conventional structures, using organic hole transport materials and metal electrodes is an important reason for the reduced lifespan of the PSC [28]. In recent studies, using pin-holes in the HTL has resulted in poor stability of PSCs. Oxygen and moisture in the environment can penetrate through pin-holes and degrade the perovskite absorbent layer; however, the reason for producing pin-holes in HTL is still unclear [29]. To solve this problem, many studies have focused on developing efficient PSCs and new types of hole-transport materials as an alternative to Spiro-OMeTAD [30], or HTL-free PSCs, which are appropriate for simplifying the optimal process of the device, preventing perovskite degradation, and reducing the costs [31].

One of the largest hurdles in commercializing PSCs is using expensive metals, such as gold and silver, as back contacts [32]. Employing expensive metals as the counter electrode in these cells is obviously costly and challenging because the perovskite reacts with metal electrodes, including silver, copper, aluminum and gold [33,34,35,36]. In addition, layer deposition of these materials, which is performed via methods such as vacuum evaporation, is costly as well. One of the unique features of perovskite-based solar cells is their flexibility. Using gold or silver as the back connector reduces the flexibility and increases the cell weight, which has always been one of the challenges. In this study, by using graphene instead of gold or silver, the flexibility of the PSC is increased, and its weight is reduced owing to the light weight of graphene compared to metals, which prevents the perovskite layer from degrading and makes producing large-scale cells economical [37].

This study aimed to simplify PSC manufacturing technology, reduce its production costs, and enhance its performance as much as possible. Therefore, the 3D analysis of a PSC associated with the solution of an electro-optical profile is presented. The use of proper all-inorganic transport materials in the construction of solar cells, and using graphene as a back contact instead of metals, significantly reduces the production costs and instability of PSCs, and increases their flexibility. In addition, the high efficiency resulting from employing the inverted planar method without the need for silicon compositions and the proper selection of anti-reflective coatings in their construction can result in a wider range of applications in the industry. Here, the simulation results of conversion efficiency, open circuit voltage, short-circuit current density, electrical power, fill factor, and quantum efficiency are compared numerically and graphically using the results obtained from SILVACO.

2. Modeling Inverted Planar Solar Cell

In this study, to investigate the effects of inorganic transport layers along with graphene back contact on the function of inverted planar PSC, the ATLAS-SILVACO software was used. In the simulation via the ATLAS module, the transfer matrix method is used as an optical model to calculate the production rate of carriers. The SILVACO software package [38] is a simulation software tool targeting the area of electronic design. This software has the ability to simulate the manufacturing process of semiconductor devices, such as oxidation, diffusion, ion implantation, removal, coating, lithography, etc. This is a large suite of highly sophisticated tools—among which is ATLAS—that aid in the design and development of all types of semiconductor and VLSI devices. This module is capable of simulating different pieces of semiconductor equipment, including MOSFETs, HEMTs and solar cells, in 2D and 3D manners. These simulations are considerably cheaper and faster than experiments, and provide precise information regarding the performance of solar cells. These simulations follow the principles of semiconductor physics, and have a satisfactory level of accuracy. The major radiation and optical parameters required for ATLAS modeling include the energy band gap, the density of electron states, the carrier mobility of electrons and holes, electrical permeability, electron continuity, and open rate composition. However, solar cell manufacturers and researchers have not adequately attempted to utilize this powerful tool for modeling advanced solar cells. Numerical simulation in ATLAS-SILVACO is based on the numerical solution of three basic equations of charge transport in semiconductors, including Poisson’s equation, the load carrier continuity equation, and the drift diffusion equation for electrons and holes, which are obtained via three types of iterations, including GUMMEL, NEWTON, and BLOCK, respectively [39].

Poisson’s equation:

$$\frac{{\partial }^2\phi }{\partial x^2}=\frac{q}{\epsilon }\left(n-p\right)$$

(1)

Load carrier continuity equation:

$$\frac{\partial n}{\partial t}=\frac{1}{q}\frac{\partial J_n}{\partial x}+G-R,\frac{\partial p}{\partial t}=-\frac{1}{q}\frac{\partial J_p}{\partial x}+G-R$$

(2)

Drift diffusion equation:

$$J_n=q{D}_n\frac{\partial n}{\partial x}-q{\mu }_{n}n\frac{\partial \phi }{\partial x},J_p=-q{D}_p\frac{\partial p}{\partial x}-q{\mu }_{p}p\frac{\partial \phi }{\partial x}$$

(3)

where φ: electric potential; ε: the permittivity; q: electron charge; J_n: electron current density; J_p: hole current density; G: generation rate; R: recombination rate; D_n: electron constant diffusion; D_p: hole constant diffusion; μ_n: electron mobility; μ_p: hole mobility.

In many studies, two-dimensional (2D) simulation is performed via free software, such as SCAPS or AFORS-HET. These pieces of software do not have the unique features of the commercial ATLAS-SILVACO software, such as identifying structural defects [40] and impurities [41], and possessing a 3D device simulator [42]. SILVACO is able to predict the electrical and optical behavior of specific semiconductor structures, and calculate through electromagnetic modules, semiconductors and electron–hole pair transitions for a fine mesh structure. The structure of an inverted planar PSC simulated in ATLAS is plotted in Figure 1. In this structure, the anode and cathode are located at the top and bottom of the plot, respectively.

Three-dimensional meshing in the direction of the y, x, and z axes is the first determined factor in the simulation. The absence of 3D meshing in 2D simulations is one of the most significant structural defects of 2D simulations. Despite its considerable complexity compared to 2D meshing, 3D meshing helps in exploring the behavior of the device using more parameters. For example, the doping process depends on the location of the lattice and its distance. Hence, the number of nodes in the lattice has a direct effect on the accuracy and timing of the simulation. The ATLAS module calculates the parameters of current, voltage, etc., at any point in the mesh. The smaller the mesh size, the more precise the results are. Thus, 3D meshing offers accurate analysis and modeling. The utility of such an exact analysis for solving many real problems is dependent on how they are actually constructed [43]. In addition, impurities may have a significant effect on the performance of MAPbI3 solar cells by introducing deep levels as nonradiative recombination centers, compensating the built-in electric field, changing the band offset at interfaces, creating shunting paths, etc. The unintentional incorporation of impurities in MAPbI3 could lead to significant device degradation [44]. Figure 2a shows a 3D mesh of the inverted planar PSC structure. In this structure, there are 147,325 grid points in the 3D mesh. The net-doping of this structure is also shown in 3D in Figure 2b. In addition, Figure 1 shows the solar cell components from top to bottom, which are described as follows:

• Creating an anti-reflective coating on the surface of this type of structure is the most important method for light trapping to compensate for the current reduced by the reflection of surface photons. Thus, in this section, by employing several different materials, including CaF₂ [45], SiO₂ [46] and Al₂O₃ [47], it can work as an anti-reflective layer in the device between the air and the front electrode layer, as an optical trap which reduces the reflection and strengthens the photon transfer to the absorbent layer. The highest efficiency is obtained for CaF₂ with an optimal thickness of 110 nm, the results of which are fully described in Section 4.1;
• The next layer of indium tin oxide (ITO) with a thickness of 45 nm is used as a transparent front contact in this solar cell. The low thickness of this material can lead to an increased optical clarity and higher electrical conductivity [48];
• NiO_x is used as the hole transport layer in this study. Of the notable features of these inorganic materials, we can mention suitable energy levels compared to perovskites, as well as uniformity, compression, proper electrical properties, abundance, and cost-effectiveness, which could greatly reduce the cost of solar cell production. Therefore, in this research, these inorganic materials are used as an alternative to expensive organic hole transporters [30,49].
• The main layer of this solar cell is a layer known as perovskite, which is composed of several organic mineral halides PSC_S and methyl ammonium lead halide (CH3NH3PbI3), and works as the absorbent layer [50];
• A zinc oxide (ZnO) layer is considered as the electron transport material (buffer) with a thickness of 300 nm between the perovskite layer and graphene. ZnO-based PSCs have interesting advantages over titanium dioxide (TiO₂). For example, large exciton of 60 MeV, high optical efficiency, high mechanical and thermal stability, and radiation hardening are other features of this material. Additionally, the higher electron mobility of ZnO than TiO₂ makes it an ideal choice for the ETL layer [51];
• In particular, we used graphene (as a carbon derivative) instead of gold or silver as the back contact. Graphene is widely used in electronics, owing to its extraordinary transparency and some unique physical properties. Among these properties, the mobility of charged particles in graphene, which is denoted by μ, is highly important. The mobility value for graphene is 10,000 cm²/V s. All these properties have raised the potential of graphene as a potent conductor for electronic applications, including inverted planar PSCs. Given the availability of this material, as well as its ability to reduce manufacturing costs as one of the most large-scaled flexible lightweight solar cells, it can be considered the most efficient, leading to wide use of this solar cell in the industry [52];
• To achieve the maximum current, all layers must have the same structure. Otherwise, it leads to structural failure and increases the recombination rate. Therefore, the loss of photo-generated minority carriers increases, and the efficiency decreases [53].

The difference in the energy state of different materials in the conduction and valence bands is depicted in Figure 3. Provided that the type of material varies from one layer to another and the electronegativity of each material is a constant value and independent of the amount of impurities, the areas differed in electronegativity, which resulted in discontinuity in the structure of the energy bar. As the Spiro-OMeTAD, Cu₂O and NiO_x areas have p-type impurities, their Fermi level alignment was close to the valence band, as also evident in Figure 3. The reason for the proximity of the Fermi level alignment to the conduction band in the fifth layer is that ZnO has n-type impurities. In effect, these findings confirm the accuracy of the simulated energy bar chart.

Table 1. Electrical parameters used to simulate the inverted planar PSC.

Parameter	Anti-Reflection	ITO	Spiro-OMeTAD	Cu2O	NiOx	MAPbI3	ZnO	Back Contact Graphene
Thickness (nm)	110	45	12	12	12	500	300	200
Acceptor Con NA (cm−3)	-	-	-	-	-	1.8e15	-	-
Donor Con ND (cm−3)	-	-	1e15	-	-	-	2e20	1e14
Electric resistance	80	80	20	80	80	45	80	100
Band gap (eV)	-	-	2.45	1.42	3.76	1.6	3.37	1.07
Con Band Density NC (cm−3)	-	-	2e17	-	-	2e17	-	1e14
Val Band Density NC (cm−3)	-	-	1e18	-	-	1.7e17	-	1e15
Electron affinity (eV)	-	-	4	3.2	2.2	4.58	4.54	4.42
Defect type	Neutral	Neutral	Neutral	-	-	Neutral	-	Neutral

lists the electrical parameters used to simulate the inverted planar PSC.

3. Results and Discussion

3.1. Effect of Absorbent Layer Thickness Variation (CH3NH3PbI3) on Inverted Planar PSC

One of the parameters affecting the efficiency of the PSC is the absorbent layer’s thickness. For the complete and comprehensive review of using inorganic materials ZnO/Cu₂O as ETM/HTM, as well as the effect of graphene back contact on solar cell performance, acquiring the optimal thickness of the perovskite layer is necessary.

In organic solar cells, a boost in the thickness of the active layer has two different effects. Regarding the optical properties, by increasing the thickness, the absorption capacity enhances, current density diminishes, and the maximum efficiency of solar cells experiences an upward trend. Furthermore, owing to the increased thickness, the ohmic resistance of cells boosts, and when the resistance of cells increases, the efficiency of cells undergoes a downward trend.

The effects of these two factors (ohmic resistance and absorption) act in opposite directions until, at a certain thickness, the ohmic resistance is higher than light absorption, current density undergoes a downward trend, and the efficiency of cells decreases. Figure 4 and

Table 2. Effect of perovskite layer thickness variation (CH3NH3PbI3) on the efficiency of the inverted planar perovskite solar cell.

Thickness of Perovskite	Jsc (mA/cm2)	Voc (V)	FF (%)	Eff (%)
200	25.0556	1.62791	86.3937	25.526
400	24.9564	1.62791	86.3938	25.425
500	27.5356	1.62601	86.3939	28.064
600	26.7772	1.62791	86.3938	27.28
700	26.415	1.62791	86.3938	26.911

show that considering absorption and ohmic resistance, an increase in the perovskite layer thickness to 500 nm results in the highest absorption at the wavelength of 750 nm, which increases the efficiency to 28.064%. Eventually, by increasing the thickness of the active layer to over 500 nm, the current density declines, and the ohmic resistance becomes high enough to overcome light absorption, which leads to a decrease in the efficiency of cells.

Figure 5 shows the external quantum efficiency (EQE). In the active area, any point with the highest absorption has the maximum value of EQE. The optimum thickness of the inverted planar PSCs was 500 nm, and a maximum EQE of 93.36% was obtained with this thickness. The simulation results are in good agreement with the experimental results presented in the existing studies. The simulation results reveal that the solar cells have the highest absorption capacity in the wavelength range of 450–750 nm, and the maximum value of EQE is obtained within this wavelength range. For the thickness of 500 nm, the maximum wavelength is estimated to be 750 nm. Ultimately, through the absorption of photons with a very low energy at a wavelength of over 750 nm, the absorption drastically decreases until it reaches a value of zero at a wavelength of 800 nm.

Figure 6 shows the photon absorption in the inverted planar PSC for the anti-reflective coating of CaF₂. The lowest photon absorption was obtained for the perovskite layer with a thickness of 200 nm. The increased thickness of the absorbent layer increases the photon absorption at longer wavelengths. Therefore, a wider absorption range absorbs higher-energy photons in the ultraviolet region and emits fluorescence at wavelengths between 450 and 750 nm, where the quantum efficiency of the solar cell is higher. Finally, increased fluorescence intensity increases the short-circuit current density, followed by an improved efficiency in this solar cell.

When the thickness of the anti-reflective coating of CaF₂ is greater than the input wavelength, it prevents their entry into the cell. Accordingly, the highest increase in photon absorption occurs as a result of optimizing the thickness of the anti-reflective coating of CaF₂ to 110 nm. It could be concluded that the anti-reflective coatings in solar cells are applied based on a certain refractive index and thickness. The lower the refractive index of the anti- reflective layer, the thicker the layer would be. Thus, the thickness of CaF₂ as a reflection reduction coating depends on its refractive index. To achieve the lowest reflection, the ideal thickness is obtained using $d_{ARC} = \lambda /4n_{ARC}$, where $d_{ARC}$ is the thickness of the anti-reflective coating and $n_{ARC}$ is the refractive index of the anti-reflective coating.

3.2. Performance Parameters

The performance of a solar cell can be shown based on its parameters. These parameters will be presented below.

3.2.1. Short-Circuit Current (I_SC)

Dark- and light-generated currents are the two types of currents in solar cells. Dark current is a current that is derived from a pn current in the absence of light. The light-generated current (I_L) is a current that is generated by a pn junction in the presence of light. The total current (I_total) is equal to the sum of these two currents [54].

$$I_{total}=I_O\left[\exp \left(\frac{qv}{nKT}\right)-1\right]-I_L$$

(4)

$$I_{SC}=-I_L$$

(5)

where I_SC denotes the short-circuit current density (mA/cm²).

Here, Spiro-OMeTAD, Cu₂O and NiO_x are replaced as the HTM. When the Spiro-OMeTAD material is added to the device, a higher current density is obtained from Cu₂O and NiO_x, owing to the more suitable glass transition temperature, solubility, ionization potential, and transparency in the range of the visible spectrum of the Spiro-OMeTAD layer. In particular, it is owing to the increased recombination between the interfaces, which improves the performance of the solar cell and yields the highest efficiency.

However, after determining the highest efficiency for the Spiro-OMeTAD polymer composition, the highest efficiency and current density of inorganic materials Cu₂O and NiO_x are obtained. Therefore, inorganic materials can provide a successful path to achieve higher efficiencies for PSCs based on Cu₂O or other inorganic transport materials, owing to their acceptable conductivity, simple methods of layer deposition, and high stability. Figure 7 and

Table 3. Effect of using different materials as an HTM on the efficiency of an inverted planar perovskite solar cell.

Wavelength (nm)	Spiro-OMeTAD	Cu2O	NiOx
700	26.73	25.73	25.99
710	27.47	26.39	26.45
720	28.10	26.95	26.84
730	28.69	27.48	27.18
740	29.05	27.85	27.32
750	29.26	28.06	27.30
760	28.47	27.38	26.26
770	25.36	24.62	23.45
780	20.74	20.52	19.93
790	16.26	16.48	16.54

show the results obtained for Spiro-OMeTAD, Cu₂O, and NiO_x. Consequently, the presence or absence of this layer has a significant effect on the overall efficiency of the solar cell.

3.2.2. Open-Circuit Voltage (V_OC)

The maximum voltage of the solar cell terminals is obtained at I = 0. By substituting this into Equation (4), the V_OC is obtained as follows [54]:

$$V_{OC}=\frac{nKT}{q}\ln \left(\frac{I_L}{I_O}+1\right)$$

(6)

3.2.3. Fill Factor (FF)

Fill factor indicates the maximum power extracted from a solar cell in relation to the ideal power, in a percentage [54]:

$$FF=\frac{V_{OC}-L_n\left(V_{OC}+0.72\right)}{V_{OC}+1}$$

(7)

3.2.4. Efficiency (η)

Solar cell efficiency is defined as the ratio of the maximum electrical power output (P_out) to the power input (P_in) in a percentage, and is expressed as follows [54]:

$$\eta =\frac{P_{out}}{P_{in}}=\frac{V_m{I}_m}{P_{in}}$$

(8)

4. Performance Comparison

There are significant drawbacks to Spiro-OMeTAD that mean it cannot be considered as the best and only HTM in PSCs. The use of Spiro-OMeTAD reduces the stability of a solar cell in the long term [55], thus preventing its use in the photovoltaic industry. If Spiro-OMeTAD is primitive, natural and intact, it has a relatively low hole mobility and conductivity (hole mobility of 1.67 × 10⁻⁵ cm²·V⁻¹·s⁻¹ and conductivity of 3.45 × 10⁻⁷ s cm⁻¹) [56]. Therefore, we need p-dopant additives and chemicals to increase the conductivity of the hole many times, and consequently, to increase the conversion efficiency of PSCs. The p-dopants commonly used in Spiro-OMeTAD solution are lithium bis (trifluoromethanesulfonyl), imide salt (LiTFSI) [57], 4-tert-butylpyridine (TBP) [57] and cobalt (III) compositions such as tris(2-(1H-pyrazol-1-yl)-4-tert-butylpyridine) cobalt (III) tri[bis(trifluoromethane)sulfonimide] (Co[t-BuPyPz]3[TFSI]3), which is abbreviated as FK 209 [58]. The use of dopants results in a higher conductivity and better electron injection by Spiro-OMeTAD, and is important in retarded recombinations; however, the use of these compounds has a negative effect on the stability of the solar cell [59].

Recently, a wide range of minerals, such as HTM and ETM, has become increasingly prevalent in PSCs owing to their low manufacturing costs. However, only a handful of samples have been able to achieve a PCE of 25.05% [60,61,62,63]. There is no limit to the minerals that can be used in solar cells to reach efficiencies similar to those obtained using Spiro-OMeTAD as the hole transfer layer. Here, we studied the voltage and current properties of inverted flat PSCs with Spiro-OMeTAD organic and inorganic substances, including Cu₂O and NiO_x, used as HTM and inorganic substances, respectively, including using ZnO as ETM. The simulation results are presented in Figure 8, Figure 9 and Figure 10; the best I–V was obtained by using Spiro-OMeTAD for Cu₂O, and finally for NiO_x.

The use of a Cu₂O inorganic hole transporter, which is semiconductive, informal, low cost, and available, in addition to being able to solve the stability problems of Spiro-OMeTAD, eliminates the need for complex purifications. Furthermore, the use of inexpensive reagents has reduced the price to approximately 14.686 USD/g. While the cost of the employed Spiro-OMeTAD material is approximately 300 USD/g, the cost of multi-stage synthesis, which requires a low temperature (−78 °C), is high; there is also the sensitive reagent n-butyllithium or Grignard, and an aggressive reagent (Br₂), in the chemical composition [64], and the sublimation step, which is required for purification, is costly [65]. In this study, we achieved a reduction of 1.197%; this reduction applies to five grams of Spiro-OMeTAD, which costs USD 1500. Accordingly, the price of five grams of Cu₂O will be USD 73.43, which shows that USD 1426.57 is saved for every five grams of Cu₂O.

Figure 8 shows the AM 1.5G spectrum, which is commonly referred to terrestrial-use solar cells undergoing non-concentrated sunlight spectrum measurements. The solar spectrum ranges widely from 250 to 2500 nm. The majority of the light absorption occurs on the absorption layer with a 1.6 eV bandgap and at a wavelength of 400 to 800 nm, which covers a large part of the visible range of light (indicated in the turquoise blue color). In addition, Figure 8 shows that the maximum absorption point in the turquoise blue region, at a wavelength of 750 nm, is important for this solar cell. According to Table 2, the best efficiency under conditions of a wavelength of 750 nm and a thickness of 500 nm is 28.064%.

The characteristic I-V curve for the three different HTMs of Spiro-OMeTAD, Cu₂O and NiO_x is shown in Figure 9a. Given the advantages of the Cu₂O material, despite a slightly lower current, it could be a suitable alternative for the hole transport layer of Spiro-OMeTAD in the PSCs. This degree of decrease in the current density in the inorganic material Cu₂O is because of either the poor photon absorption or the poor separation, transfer, and electric charge collection. The lowest current density for the inorganic material NiO_x is obtained by HTM for this structure. The optical response shows that HTM significantly affects the short-circuit current of the solar cells. In

Table 4. Performance parameters of the p-i-n perovskite solar cell structures for three HTMs.

Structure	Jsc (mA/cm2)	Voc (V)	FF (%)	Eff (%)
With Spiro-OMeTAD	28.7217	1.62609	86.3938	29.261
With Cu2O	27.5356	1.62601	86.3939	28.064
With NiOx	26.8218	1.62596	86.3936	27.325

, the results of the proposed solar cell’s open-circuit voltage (Voc), short-circuit current density (Jsc), fill factor (FF), and efficiency (η) are shown for comparison.

Figure 9b demonstrates the power curve for three different HTMs of Spiro-OMeTAD, Cu₂O and NiO_x. The power curve is influenced by the maximum power that can be extracted from a solar cell. The maximum power P_max is calculated as the product of the maximum voltage V_m and maximum current I_m. The power curve values of the inverted planar PSC for Spiro-OMeTAD, Cu₂O, and NiO_x are 4.0395 × 10⁻¹⁰, 3.8742 × 10⁻¹⁰ and 3.7723 × 10⁻¹⁰, respectively, under the same conditions and with the same thickness.

4.1. Effect of Different Anti-Reflective Coatings on the Efficiency of Inverted Planar PSC by Graphene Contact

Anti-reflective coatings play a major role in improving the performance of inverted planar PSCs, with a decrease in surface photon reflection and an increase in photon absorption, because the loss of reflection will reduce the efficiency of the solar cell. Furthermore, anti-reflective coatings can improve mechanical, electrical, optical, and other physical properties [18]. The anti-reflective coating is added to the surface of the inverted PSC with specific values of refractive index and a certain thickness so that the air passes towards the sublayer and the refractive index varies gradually. Therefore, the most important factor affecting the reflection reduction of the anti-reflective material is the refractive index, as well as the thickness of anti-reflective layer; as such, the optimal limit for each of these parameters is determined, and the conditions to access the lowest reflection and the highest light transfer are provided [66,67].

Figure 10a–c illustrates the total conversion efficiency, quantum efficiency and reflection in the inverted planar PSC with three anti-reflective coatings, respectively. Accordingly, the total conversion efficiency of a solar cell with an anti-reflective coating of CaF₂ is greater than that with the anti-reflective coatings of SiO₂ and Al₂O₃. According to Figure 10c, this result can be attributed to the trapping of photons in each of the three anti-reflection coatings of the inverted planar PSC.

Accordingly, the highest conversion and quantum efficiencies of 28.064 and 93.36%, respectively, for the structure with an anti-reflective coating of CaF₂ with a thickness of 110 nm are approximately identical to the conversion and quantum efficiencies—27.92 and 93.18%, respectively—of a solar cell with an anti-reflective coating of SiO₂ with a thickness of 110 nm. This is because the refractive index ($n_{ARC}$= 1.43) of CaF₂ is approximately similar to the refractive index ($n_{ARC}$ = 1.45) of SiO₂. Moreover, the lowest conversion efficiency and quantum efficiency for a device with an anti-reflective coating of Al₂O₃, a refractive index of $n_{ARC}$= 1.76 and thickness of 110 nm are 27.70 and 92.94%, respectively. Finally, the highest efficiencies for the proposed PSC with the two anti-reflective coatings (SiO₂ and Al₂O₃) are 27.92 and 27.70%, respectively, which are lower than those of the inverted planar PSC with an anti-reflective coating of CaF₂.

Among the conventional anti-reflective materials, CaF₂ has low refractive index properties and a favourable thermal stability. SiO₂ has desirable durability and a better refractive index than Al₂O₃. Therefore, CaF₂, SiO₂ and Al₂O₃ are used as anti-reflective coatings to investigate their effect on the solar cell performance. According to the results in

Table 5. Effect of using various materials as an anti-reflective coating on the efficiency of the inverted planar perovskite solar cell.

Wavelength (nm)	CaF2	SiO2	Al2O3
710	26.39	26.72	27.07
720	26.95	27.20	27.41
730	27.48	27.61	27.64
740	27.85	27.86	27.70
750	28.06	27.92	27.53
760	27.38	26.90	26.06
770	24.62	23.80	22.54
780	20.52	19.67	18.44
790	16.48	16.00	15.29

, the most appropriate anti-reflective material, CaF₂, and the worst anti-reflective material, Al₂O₃, are identified. This is owing to the low refractive index and transparent nature of CaF₂ compared to that of Al₂O₃, which improves the optical absorption of the solar cell.

5. Conclusions

In this study, a 3D design and related simulations were conducted using minerals for both low-cost ETM and HTM in an inverted planar PSC (MAPbI₃), via the ATLAS-SILVACO software. The simulations gave highly accurate results for the properties of the transporter material that determine the main functions of PSCs. First, the effect of the thickness of the absorbent layer on the quantum efficiency and photon absorption process in an inverted planar PSCs was investigated. When the layer’s thickness was less or more than 500 nm, the efficiency of the PSC decreased; therefore, the best results were obtained at a thickness of 500 nm.

Subsequently, CaF₂, SiO₂ and Al₂O₃ were applied as anti-reflective coatings. The highest efficiency was achieved for CaF₂ with a wavelength of 750 nm. Furthermore, the polymer compositions of Spiro-OMeTAD with Cu₂O and NiO_x as HTM and ZnO as ETM were examined for all structures. The highest efficiency was obtained with ZnO/Spiro-OMeTAD (29.261%). The simulation results showed that although Cu₂O—an inorganic material—decreases efficiency by 1.197%, it is a cheap and available HTM; hence, it is an appropriate alternative to expensive organic materials. Moreover, we proposed to use inorganic materials, such as Cu₂O, because they help achieve approximately similar efficiencies compared to solar cells with Spiro-OMeTAD—an organic material—used as HTM.

Finally, this type of solar cell is flexible and inexpensive. In addition, the use of a metallic connector diminishes the flexibility and increases the cell weight and costs. Therefore, using a graphene connector in place of a metallic connector in PSCs provides highly flexible and light solar cells with a significantly cost-effective manufacturing process.