High-Efﬁciency Electron Transport Layer-Free Perovskite/GeTe Tandem Solar Cell: Numerical Simulation

: The primary purpose of recent research has been to achieve a higher power conversion efﬁciency (PCE) with stable characteristics, either through experimental studies or through modeling and simulation. In this study, a theoretical analysis of an efﬁcient perovskite solar cell (PSC) with cuprous oxide (Cu 2 O) as the hole transport material (HTM) and zinc oxysulﬁde (ZnOS) as the electron transport material (ETM) was proposed to replace the traditional HTMs or ETMs. In addition, the impact of doping the perovskite layer was investigated. The results show that the heterostructure of n-p PSC without an electron transport layer (ETL) could replace the traditional n-i-p structure with better performance metrics and more stability due to reducing the number of layers and interfaces. The impact of HTM doping and thickness was investigated. In addition, the inﬂuence of the energy gap of the absorber layer was studied. Furthermore, the proposed PSC without ETL was used as a top sub-cell with germanium-telluride (GeTe) as a bottom sub-cell to produce an efﬁcient tandem cell and boost the PCE. An ETL-free PSC/GeTe tandem cell is proposed for the ﬁrst time to provide an efﬁcient and stable tandem solar cell with a PCE of 45.99%. Finally, a comparison between the performance metrics of the proposed tandem solar cell and those of other recent studies is provided. All the simulations performed in this study are accomplished by using SCAPS-1D. V were obtained. The use of ZnOS as the ETL in the cell structure is consistent with the performance estimation given in [27]. These output performance metrics are achieved when the conduction band offset (CBO) of the ETM is 0.3 eV higher than the corresponding band of CH 3 NH 3 PbI 3 − x CI x, which is within the optimal range [28,29]. ZnOS has a tunable energy gap and a high electron afﬁnity. Consequently, it is an excellent replacement for traditional ETMs such as titanium dioxide (TiO 2 ).


Introduction
Nowadays, the need for energy is increasing at a very fast rate [1]. Clean energy, especially solar energy, presents a promising solution [2]. Currently, the crystallized silicon solar cells in multi-crystalline and monocrystalline versions dominate the photovoltaic market. So far, the efficiency of crystalline silicon solar cells has surpassed 25% [3,4]. Copper indium gallium selenide (CIGS) solar cells are very competitive thin-film solar cells and have achieved a PCE of 23.35% [5]. Organic solar cells (OSCs) show promise for application in indoor solar cells [6]; however, their spectrally inefficient light absorption ability and photo-instability limit the performance of OSCs [7]. Consequently, indoor organic tandem cells could be used, with a PCE exceeding 16.4% with good photostability [8,9].
PSCs have also developed recently and have demonstrated rapid progress, thus providing new directions in photovoltaics. PSC devices now have a record efficiency of around 25% [10], and the development of PSC in recent years has produced simulation results of up to more than 30% [11]. Lower recombination rates, a broad absorption spectrum, long diffusion lengths, a high open-circuit voltage, and bandwidth adjustment are all factors that contribute to perovskite cells' improved performance.

Tandem Solar Cell
The top and bottom sub-cells are simulated separately while investigating the performance of tandem solar cells. According to the commonly used assumption in multi-junction simulation, the tunnel junction is perfect, and the optical and electrical losses in both interfaces are neglected [18][19][20][21][22].
The proposed tandem cell consists of a PSC as a top sub-cell and a GeTe as a bottom sub-cell, as shown in Figure 1a. The structure of the top sub-cell uses the perovskite material sandwiched between the hole transport layer (HTL) and ETL. The TCO functions as an optically transparent electrode, allowing photons to pass through the cell and deliver the produced electrons to the cell's external terminals. Before the absorber material, the bottom sub-cell consists of zinc oxide (ZnO) and cadmium sulfide (CdS). Due to its properties, especially the narrow E g , GeTe is a good choice as an absorber of the bottom sub-cell; besides, it provides a very high current [23,24].
work. Finally, Section 4 concludes our work.

Tandem Solar Cell
The top and bottom sub-cells are simulated separately while investigating the performance of tandem solar cells. According to the commonly used assumption in multijunction simulation, the tunnel junction is perfect, and the optical and electrical losses in both interfaces are neglected [18][19][20][21][22].
The proposed tandem cell consists of a PSC as a top sub-cell and a GeTe as a bottom sub-cell, as shown in Figure 1a. The structure of the top sub-cell uses the perovskite material sandwiched between the hole transport layer (HTL) and ETL. The TCO functions as an optically transparent electrode, allowing photons to pass through the cell and deliver the produced electrons to the cell's external terminals. Before the absorber material, the bottom sub-cell consists of zinc oxide (ZnO) and cadmium sulfide (CdS). Due to its properties, especially the narrow Eg, GeTe is a good choice as an absorber of the bottom subcell; besides, it provides a very high current [23,24].
The transmitted spectrum of the top sub-cell to the bottom sub-cell is given by Equation (1) [18]: and α is given by Equation (2) [18]:  The transmitted spectrum of the top sub-cell to the bottom sub-cell is given by Equation (1) [18]: and α is given by Equation (2) [18]: Crystals 2022, 12, 878 4 of 17

The Top Sub-Cell
The layers of the suggested top sub-cell design are a glass substrate, fluorine-doped tin oxide (FTO) as a transparent conducting oxide (TCO), ZnOS as the ETL, CH 3 NH 3 PbI 3−x CI x as an absorber layer, Cu 2 O as the HTL, and gold (Au) as a back contact. A common phenomenon of OSCs incorporating these metal-oxide electron extraction layers is the requirement to expose the devices to ultraviolet light to enhance the OSC performance, known as the "light soaking" issue. This issue can be avoided by using Al-doped ZnOS as electron extraction interlayers. Figure 1b,c illustrate the energy band diagrams of the top and bottom sub-cells, respectively. The conduction band minimums are the electron affinities (χ), and the valence band maximums (VBMs) are given by Equation (3).
The parameters of the materials used in the simulation are listed in Table S2. A flat band model was employed for the interfaces between the semiconductor, TCO, and metal. To address the practical concerns, a neutral defect with Gaussian distribution was used [25]. An illumination spectrum of air mass (AM 1.5) and a temperature of 300 K were utilized for all simulations. All materials' absorption coefficients (α) were calculated through Equation (2). The used pre-factor (A α ) was 10 5 cm −1 eV −1/2 [26]. Figure 2 depicts the output performance curves of the first proposed PSC using Cu 2 O as the HTL and ZnOS as the ETL. Figure 2a shows the JV curve of the initial PSC. The values of PCE, fill factor (FF), high short-circuit current (J SC ), and an open-circuit voltage (V oc ) of the initial PSC were extracted from the JV curve. The designed PSC achieved a promising output performance. A PCE of 29.34% with FF of 84.88%, J sc of 24.38 mA/cm 2 , and V oc of 1.42 V were obtained. The use of ZnOS as the ETL in the cell structure is consistent with the performance estimation given in [27]. These output performance metrics are achieved when the conduction band offset (CBO) of the ETM is 0.3 eV higher than the corresponding band of CH 3 NH 3 PbI 3−x CI x, which is within the optimal range [28,29]. ZnOS has a tunable energy gap and a high electron affinity. Consequently, it is an excellent replacement for traditional ETMs such as titanium dioxide (TiO 2 ).

The Top Sub-Cell
The layers of the suggested top sub-cell design are a glass substrate, fluorine-dope tin oxide (FTO) as a transparent conducting oxide (TCO), ZnOS as the ETL, CH3NH3Pb xCIx as an absorber layer, Cu2O as the HTL, and gold (Au) as a back contact. A commo phenomenon of OSCs incorporating these metal-oxide electron extraction layers is the r quirement to expose the devices to ultraviolet light to enhance the OSC performanc known as the "light soaking" issue. This issue can be avoided by using Al-doped ZnO as electron extraction interlayers. Figure 1b,c illustrate the energy band diagrams of the top and bottom sub-cells, r spectively. The conduction band minimums are the electron affinities (χ), and the valen band maximums (VBMs) are given by Equation (3).
The parameters of the materials used in the simulation are listed in Table S2. A fl band model was employed for the interfaces between the semiconductor, TCO, and met To address the practical concerns, a neutral defect with Gaussian distribution was use [25]. An illumination spectrum of air mass (AM 1.5) and a temperature of 300 K we utilized for all simulations. All materials' absorption coefficients (α) were calculate through Equation (2). The used pre-factor (Aα) was 10 5 cm −1 eV −1/2 [26]. Figure 2 depicts the output performance curves of the first proposed PSC using Cu2 as the HTL and ZnOS as the ETL. Figure 2a shows the JV curve of the initial PSC. Th values of PCE, fill factor (FF), high short-circuit current (JSC), and an open-circuit volta (Voc) of the initial PSC were extracted from the JV curve. The designed PSC achieved promising output performance. A PCE of 29.34% with FF of 84.88%, Jsc of 24.38 mA/cm and Voc of 1.42 V were obtained. The use of ZnOS as the ETL in the cell structure is co sistent with the performance estimation given in [27]. These output performance metri are achieved when the conduction band offset (CBO) of the ETM is 0.3 eV higher than th corresponding band of CH3NH3PbI3-xCIx, which is within the optimal range [28,29]. ZnO has a tunable energy gap and a high electron affinity. Consequently, it is an excellent r placement for traditional ETMs such as titanium dioxide (TiO2). The energy gap of ZnOS is in the range of 2.7-3.8 eV, which permits it to abso photons with higher energy and enhances the current density [30]. Moreover, ZnOS h good transparency, which enhances photons absorption in the CH3NH3PbI3-xCIx laye thus enhancing the output performance. Figure 2b shows the proposed PSCs' quantu efficiency (QE) curve. The QE is almost constant in the range from 350 nm to 590 nm an subsequently falls to 800 nm, when it disappears, as seen in the curve.  The energy gap of ZnOS is in the range of 2.7-3.8 eV, which permits it to absorb photons with higher energy and enhances the current density [30]. Moreover, ZnOS has good transparency, which enhances photons absorption in the CH 3 NH 3 PbI 3−x CI x layer, thus enhancing the output performance. Figure 2b shows the proposed PSCs' quantum Crystals 2022, 12, 878 5 of 17 efficiency (QE) curve. The QE is almost constant in the range from 350 nm to 590 nm and subsequently falls to 800 nm, when it disappears, as seen in the curve.
The conductivity of the materials in solar cells greatly influences the performance characteristics. The conductivity of solar cell materials can be controlled by doping, either n-type or p-type. The impact of doping concentrations on CH 3  The perovskite materials can be doped n-type or p-type [31]. The doping concentration can be practically adjusted between N A of 10 14 cm −3 and N D of 7.6 × 10 20 cm −3 [31]. The output performance metrics are constant in the N A range from 0 to 10 15 cm −3 . Figure 3 depicts the effect of the absorber layer's N D on the performance metrics. The output performance metrics are constant in the N D range from 0 to 10 15 cm −3 . This work suggests a reasonable value of 1 × 10 18 cm −3 for the perovskite layer's N D , with a PCE of 32.19%, as displayed in Figure 3a. The PCE is enhanced by 2.83% more than the initial design. This improvement is mainly due to the enhancement in the fill factor and V oc, as depicted in Figure 3b,d, respectively. The increase in FF is due to the decrease in the series resistance as the doping rises. Additionally, it can be seen from Figure 3c that J sc is almost constant with the variation in the doping level. The performance metrics, FF, Voc, and Jsc, when the N D of the perovskite layer is 10 18 cm −3 are 90.88%, 1.45 V, and 24.38 mA/cm 2 , respectively. The conductivity of the materials in solar cells greatly influences the performance characteristics. The conductivity of solar cell materials can be controlled by doping, either n-type or p-type. The impact of doping concentrations on CH3NH3PbI3-xCIx, ZnOS, and Cu2O is investigated through Sections 2.1.1 to 2.1.3 to enhance PCE.

Optimization of the Doping Concentration ND of CH3NH3PbI3-xCIx
The perovskite materials can be doped n-type or p-type [31]. The doping concentration can be practically adjusted between NA of 10 14 cm −3 and ND of 7.6 × 10 20 cm −3 [31]. The output performance metrics are constant in the NA range from 0 to 10 15 cm −3 . Figure 3 depicts the effect of the absorber layer's ND on the performance metrics. The output performance metrics are constant in the ND range from 0 to 10 15 cm −3 . This work suggests a reasonable value of 1 × 10 18 cm −3 for the perovskite layer's ND, with a PCE of 32.19%, as displayed in Figure 3a. The PCE is enhanced by 2.83% more than the initial design. This improvement is mainly due to the enhancement in the fill factor and Voc, as depicted in Figure  3b,d, respectively. The increase in FF is due to the decrease in the series resistance as the doping rises. Additionally, it can be seen from Figure 3c that Jsc is almost constant with the variation in the doping level. The performance metrics, FF, Voc, and Jsc, when the ND of the perovskite layer is 10 18 cm −3 are 90.88%, 1.45 V, and 24.38 mA/cm 2 , respectively.

Optimization of the Doping Concentration ND of ETM
The ETL does not affect the performance metrics once the absorber layer has been doped [30]. As a result, a PSC without ETL has been recommended to replace the conventional n-i-p PSC architecture with an n-p one to reduce the number of layers and interfaces. Table 1 compares the performance characteristics of the PSC with and without the ETL. Due to the imbalanced charge transfer rate and the lack of a permanent built-in field

Optimization of the Doping Concentration N D of ETM
The ETL does not affect the performance metrics once the absorber layer has been doped [30]. As a result, a PSC without ETL has been recommended to replace the conven-tional n-i-p PSC architecture with an n-p one to reduce the number of layers and interfaces. Table 1 compares the performance characteristics of the PSC with and without the ETL. Due to the imbalanced charge transfer rate and the lack of a permanent built-in field in the absence of an ETL, ETL-free perovskite solar cells suffer from significant hysteresis and unsteady stabilized-power output [32,33]. Surface modification of an FTO substrate with a self-assembled fullerene monolayer (SAM), on the other hand, can improve device performance and reduce PSC hysteresis [34,35]. FTO effects on cells can be treated by different methods, one of which was produced for PSCs in a simplified configuration of glass/FTO-TMAH/perovskite/spiro-OMeTAD/Au using a modified FTO surface with tetramethylammonium hydroxide (TMAH). The increased device performance may be attributed to the improved charge extraction/transport, lower trap density, and lower charge recombination rate at the FTO/perovskite interface and in the perovskite layer, which displays up to 20.1% efficiency experimentally [36].

Optimization of the Doping Concentration N A and Thickness of HTM
In a previous work, the doping concentration N A of Cu 2 O was increased from N A of 10 17 cm −3 to 10 20 cm −3 [37]. The performance metrics were low because of the high series resistance within the low doping concentration N A . When the doping in Cu 2 O is increased, the offset in energy bands between the perovskite layer and Cu 2 O layer increases, causing the diffusion current to increase due to the gradient of carrier concentrations and particles to flow from the highest concentration regions to the lowest according to random thermal motion which is known as Brownian Motion. Figure 4a depicts the effect of Cu 2 O N A on the PCE, while the rest of the performance parameters are illustrated in the Supplementary Materials, Figure S1. The highest PCE was achieved in the range of N A from 10 17 to 10 18 cm −3 , as shown in Figure 4a. As a result, keeping N A at a low level is preferable. Furthermore, high N A generates deep Coulomb traps and reduces hole mobility [38]. The performance metrics, PCE, FF, V oc , and J sc , when N A of Cu 2 O is 10 17 cm −3 are 32.19%, 90.84%, 1.45 V, and 24.41 mA/cm 2 , respectively. in the absence of an ETL, ETL-free perovskite solar cells suffer from significant hysteresis and unsteady stabilized-power output [32,33]. Surface modification of an FTO substrate with a self-assembled fullerene monolayer (SAM), on the other hand, can improve device performance and reduce PSC hysteresis [34,35]. FTO effects on cells can be treated by different methods, one of which was produced for PSCs in a simplified configuration of glass/FTO-TMAH/perovskite/spiro-OMeTAD/Au using a modified FTO surface with tetramethylammonium hydroxide (TMAH). The increased device performance may be attributed to the improved charge extraction/transport, lower trap density, and lower charge recombination rate at the FTO/perovskite interface and in the perovskite layer, which displays up to 20.1% efficiency experimentally [36].  [37]. The performance metrics were low because of the high series resistance within the low doping concentration NA. When the doping in Cu2O is increased, the offset in energy bands between the perovskite layer and Cu2O layer increases, causing the diffusion current to increase due to the gradient of carrier concentrations and particles to flow from the highest concentration regions to the lowest according to random thermal motion which is known as Brownian Motion. Figure 4a depicts the effect of Cu2O NA on the PCE, while the rest of the performance parameters are illustrated in the Supplementary Materials, Figure S1. The highest PCE was achieved in the range of NA from 10 17 to 10 18 cm −3 , as shown in Figure 4a. As a result, keeping NA at a low level is preferable. Furthermore, high NA generates deep Coulomb traps and reduces hole mobility [38]. The performance metrics, PCE, FF, Voc, and Jsc, when NA of Cu2O is 10 17 cm −3 are 32.19%, 90.84%, 1.45 V, and 24.41 mA/cm 2 , respectively.  Following that, the effect of the HTL thickness was investigated. Figure 4b depicts the effect of Cu2O thickness on the PCE, while the rest of the performance parameters are illustrated in Figure S2. It can be shown that as the thickness of Cu2O grows from 100 to 400 nm, the PCE is almost constant. The PCE is constant for thicknesses greater than 400 nm. As a result, a thickness of 400 nm with a PCE of 32.22%, Jsc of 24.44 mA/cm2, FF of Following that, the effect of the HTL thickness was investigated. Figure 4b depicts the effect of Cu 2 O thickness on the PCE, while the rest of the performance parameters are  Figure S2. It can be shown that as the thickness of Cu 2 O grows from 100 to 400 nm, the PCE is almost constant. The PCE is constant for thicknesses greater than 400 nm. As a result, a thickness of 400 nm with a PCE of 32.22%, Jsc of 24.44 mA/cm 2 , FF of 90.83%, and no change in Voc was chosen.
2.1.4. Impact of the E g and N t of CH 3 NH 3 PbI 3−x CI x The energy gap of the perovskite layer has a significant impact on the performance characteristics. PSCs benefit significantly from an adjustable energy gap. Figure 5a depicts the fluctuation in PCE caused by a change in E g from 1.5 to 1.63 eV [39,40]. Figure S3 illustrates the rest of the performance parameters. Reducing E g boosts carrier generation. As a result, the best performance was obtained at the lowest E g . When E g is 1.5 eV; the performance characteristics were as follows: PCE = 33.45%, FF = 90.58%, V oc = 1.40 V, and, J sc = 26.30 mA/cm 2 with a 3.12% increase in PCE. The energy gap of the perovskite layer has a significant impact on the performanc characteristics. PSCs benefit significantly from an adjustable energy gap. Figure 5a depict the fluctuation in PCE caused by a change in Eg from 1.5 to 1.63 eV [39,40]. Figure S3 illus trates the rest of the performance parameters. Reducing Eg boosts carrier generation. As result, the best performance was obtained at the lowest Eg. When Eg is 1.5 eV; the perfor mance characteristics were as follows: PCE = 33.45%, FF = 90.58%, Voc = 1.40 V, and, Jsc 26.30 mA/cm 2 with a 3.12% increase in PCE. The defect density has a great effect on the performance of the solar cell. Section 2.1. discusses the study of the defect density of the perovskite absorber layer on the main per formance parameters of the PSC. The defect density was studied in the range from 10 9 t 2 × 10 13 (1/cm 3 ). The results show that the PCE decreases at a high rate with an increase i the defect density, as shown in Figure 5b. The rest of the performance metrics with th variation in the defect density are illustrated in Figure S4. The chosen defect density fo our design was 2 × 10 11 (1/cm 3 ). The performance parameters at this value are: PCE i 33.45%, FF is 90.58%, JSC is 26.30 mA/cm 2 , and VOC is 1.40 V.

The Initial PSC vs. the Optimized One
Decreasing the recombination rate at the CH3NH3PbI3-xCIx/ETL interface is a good way to extract the carriers efficiently. To achieve this condition, the CBO of th CH3NH3PbI3-xCIx layer should be 0-0.3 eV lower than the corresponding band of the ETL The CBO is given by Equation (4) [41].
where is the affinity of the absorber layer and is the affinity of the ETL. Ac cording to the above equation and the affinity of CH3NH3PbI3-xCIx is 3.9 eV, the optimum affinity of the ETL is in the range of 3.9-4.2 eV. This condition is not satisfied with ZnO as an ETL because its affinity is 3.6 eV. The CBO after removing the ZnOS layer will be i the optimum range because the affinity of FTO is 4 eV, which illustrates the enhancemen of the performance metrics. As an additional physical explanation of the improvement o The defect density has a great effect on the performance of the solar cell. Section 2.1.4 discusses the study of the defect density of the perovskite absorber layer on the main performance parameters of the PSC. The defect density was studied in the range from 10 9 to 2 × 10 13 (1/cm 3 ). The results show that the PCE decreases at a high rate with an increase in the defect density, as shown in Figure 5b. The rest of the performance metrics with the variation in the defect density are illustrated in Figure S4. The chosen defect density for our design was 2 × 10 11 (1/cm 3 ). The performance parameters at this value are: PCE is 33.45%, FF is 90.58%, J SC is 26.30 mA/cm 2 , and V OC is 1.40 V.

The Initial PSC vs. the Optimized One
Decreasing the recombination rate at the CH 3 NH 3 PbI 3−x CI x /ETL interface is a good way to extract the carriers efficiently. To achieve this condition, the CBO of the CH 3 NH 3 PbI 3−x CI x layer should be 0-0.3 eV lower than the corresponding band of the ETL. The CBO is given by Equation (4) [41].
where χ abs is the affinity of the absorber layer and χ ETL is the affinity of the ETL. According to the above equation and the affinity of CH 3 NH 3 PbI 3−x CI x is 3.9 eV, the optimum affinity of the ETL is in the range of 3.9-4.2 eV. This condition is not satisfied with ZnOS as an ETL because its affinity is 3.6 eV. The CBO after removing the ZnOS layer will be in the optimum range because the affinity of FTO is 4 eV, which illustrates the enhancement of the performance metrics. As an additional physical explanation of the improvement of the performance metrics, Figure 6a,b illustrates the energy band diagrams of the initial PSC and the optimized PSC without ETL. As shown in Figure 6a, the initial PSC with ZnOS as an ETL has a conduction band spike, which results in lower PCE on the other hand, the optimized PSC without ETL has a conduction band cliff, as shown in Figure 6b. The variation in the performance metrics could be explained by the observation of the recombination rate before and after optimization. Figure 6c shows the recombination rates (in cm −3 s −1 ) as a function of the PSC distance. As can be seen, the highest recombination rate was at the interface between CH 3 NH 3 PbI 3−x CI x /ETL, which could be avoided in the optimized PSC without ETL. Moreover, the recombination rate at the interface between Cu 2 O/CH 3 NH 3 PbI 3−x CI x was also decreased. The results support our choice of removing the ETL from the PSC and show the importance of our optimization.
als 2022, 12, x FOR PEER REVIEW 8 of (in cm −3 s −1 ) as a function of the PSC distance. As can be seen, the highest recombinati rate was at the interface between CH3NH3PbI3-xCIx/ETL, which could be avoided in t optimized PSC without ETL. Moreover, the recombination rate at the interface betwe Cu2O/CH3NH3PbI3-xCIx was also decreased. The results support our choice of removi the ETL from the PSC and show the importance of our optimization.

Temperature Effect and Comparison of PCEs
The transition from traditional to clean energy, that is, solar cells, is associated wi a set of concepts. One of these concepts is to improve the unit durability to extend the lifetime [42]. PSCs still face significant commercialization challenges, including long-ter durability versus environmental triggers such as temperature [43]. The temperature s bility of the initial design and the optimized one were investigated from 280 to 360 K. T results show that the PCE of the optimized PSC without ETL is more stable and mo

Temperature Effect and Comparison of PCEs
The transition from traditional to clean energy, that is, solar cells, is associated with a set of concepts. One of these concepts is to improve the unit durability to extend their lifetime [42]. PSCs still face significant commercialization challenges, including longterm durability versus environmental triggers such as temperature [43]. The temperature Crystals 2022, 12, 878 9 of 17 stability of the initial design and the optimized one were investigated from 280 to 360 K. The results show that the PCE of the optimized PSC without ETL is more stable and more immune to temperature variations than the traditional PSC with a pin structure. Figure 7 illustrates the variation in the PCE of the proposed PSCs of the initial design and the optimized PSC without ETL with temperature. At the end of this section, a comparison between the PCE for single-junction PSCs of the initial design, the optimized PSC without ETL, and other researchers' work is shown in Table 2.

ETM/HTM PCE (%)
TiO2/CuI [44] 21.32 TiO2/CuI [45] 21.76 ZnOS/CuI [45] 26.11 ZnOS/Cu2O [11] 25.71 ZnOS/Cu2O [11] 30.82 PCBM/Cu2O [46] 19.61 PEDOT:PSS/HATNT [47] 18.1% PEDOT:PSS/TDTP [48] 18.2% TiO2/- [49] 25   Table S3. All materials' absorption coefficients (α) were calculated via Equation (2). The used pre-factor (Aα) was 10 5 cm −1 eV −1/2 [26]. The JV curve using AM 1.5 incident spectrum at 300 k is shown in Figure  8a. A PCE of 26.21% with FF of 81.92%, Jsc of 53.3 mA/cm 2 , and Voc of 0.6 V were achieved. The defect density effect on the GeTe bottom sub-cell performance was tested in the range of 10 12 to 10 16 (1/cm 3 ). The results show enhancement in the performance parameters with a decrease in the defect density but no significant decay below 10 14 (1/cm 3 ), as shown in Figure 8b of the PCE. The thickness of the GeTe layer is 2000 nm, which is quite a large thickness, to produce a defect-free film to be exploited in PV applications. Consequently, the chosen value of the designed GeTe sub-cell defect density was 10 14 (1/cm 3 ), which is a relatively high and more practical value.  19.61 PEDOT:PSS/HATNT [47] 18.1% PEDOT:PSS/TDTP [48] 18.2% TiO 2 /- [49] 25   Table S3. All materials' absorption coefficients (α) were calculated via Equation (2). The used pre-factor (A α ) was 10 5 cm −1 eV −1/2 [26]. The JV curve using AM 1.5 incident spectrum at 300 k is shown in Figure 8a. A PCE of 26.21% with FF of 81.92%, J sc of 53.3 mA/cm 2 , and V oc of 0.6 V were achieved. The defect density effect on the GeTe bottom sub-cell performance was tested in the range of 10 12 to 10 16 (1/cm 3 ). The results show enhancement in the performance parameters with a decrease in the defect density but no significant decay below 10 14 (1/cm 3 ), as shown in Figure 8b of the PCE. The thickness of the GeTe layer is 2000 nm, which is quite a large thickness, to produce a defect-free film to be exploited in PV applications. Consequently, the chosen value of the designed GeTe sub-cell defect density was 10 14 (1/cm 3 ), which is a relatively high and more practical value.

Optimizing Algorithm of the Absorber's thickness of the Top Sub-Cell to Achieve an Optimized Tandem Solar Cell
Two-terminal tandem solar cells have a restriction in regard to current density. The top and bottom sub-cells must have the same current density and the sub-cell with the minimum value (usually the bottom) will force the other sub-cell and the overall tandem cell to operate at its minimum current density. This, in turn, limits the overall performance of the tandem cell. The matching current density process of sub-cells is applied by changing the absorber's thickness of the top sub-cell, as the bottom sub-cell must be as thick as possible to absorb the transmitted spectrum from the top sub-cell after a part of it is already absorbed by the top sub-cell. This section shows the proposed modification of an algorithm that optimizes the top sub-cell absorber's thickness to get the best possible performance from the two-terminal tandem solar cells [46]. The previous algorithm uses one stage for the optimization of the thickness with one step (10 nm).
The proposed modified algorithm uses three steps: tcs (50 nm), tfs1 (20 nm), and the fine step, tfs2 (10 nm). The main difference between the proposed modified algorithm relative to the previous one is the ability to start from a high value rather than from zero, as the range of the optimum thickness range can be estimated for a tandem cell from the previous ones. Using this algorithm can decrease the number of steps to obtain the optimum thickness of the top sub-cell for the studied tandem cell, with the same accuracy of finding the thickness. This in turn decreases the processing time. The algorithm flowchart is shown in Figure 9a. It must be noted that the tandem structure's overall thickness should not be more than the diffusion length to ensure free charge transport to electrodes, 50 µm [50].

Optimizing Algorithm of the Absorber's Thickness of the Top Sub-Cell to Achieve an Optimized Tandem Solar Cell
Two-terminal tandem solar cells have a restriction in regard to current density. The top and bottom sub-cells must have the same current density and the sub-cell with the minimum value (usually the bottom) will force the other sub-cell and the overall tandem cell to operate at its minimum current density. This, in turn, limits the overall performance of the tandem cell. The matching current density process of sub-cells is applied by changing the absorber's thickness of the top sub-cell, as the bottom sub-cell must be as thick as possible to absorb the transmitted spectrum from the top sub-cell after a part of it is already absorbed by the top sub-cell. This section shows the proposed modification of an algorithm that optimizes the top sub-cell absorber's thickness to get the best possible performance from the two-terminal tandem solar cells [46]. The previous algorithm uses one stage for the optimization of the thickness with one step (10 nm).
The proposed modified algorithm uses three steps: t cs (50 nm), t fs1 (20 nm), and the fine step, t fs2 (10 nm). The main difference between the proposed modified algorithm relative to the previous one is the ability to start from a high value rather than from zero, as the range of the optimum thickness range can be estimated for a tandem cell from the previous ones. Using this algorithm can decrease the number of steps to obtain the optimum thickness of the top sub-cell for the studied tandem cell, with the same accuracy of finding the thickness. This in turn decreases the processing time. The algorithm flowchart is shown in Figure 9a. It must be noted that the tandem structure's overall thickness should not be more than the diffusion length to ensure free charge transport to electrodes, 50 µm [50].

The Optimized Tandem Solar Cell
Based on the previous results, the used top sub-cell consists of a glass substrate, TCO, N-type CH 3 NH 3 PbI 3−x CI x as an absorber layer, and Cu 2 O as the HTL, respectively. The output spectrum from the HTL of the top sub-cell is the incident spectrum to the bottom subcell. The used bottom sub-cell uses GeTe as an absorber layer. The GeTe chosen to be used in the bottom sub-cell shows a high current density; this impacts the overall performance of the tandem cell current density and the tandem cell power conversion efficiency.
The top sub-cell thickness optimization algorithm explained in Section 2.3 was used to find the optimum top sub-cell absorber thickness and the highest power conversion efficiency of the tandem cell. As shown in Figure 9b spectrum. The structure of the optimized tandem solar cell with complete details of the thickness and doping concentration for each layer is illustrated in Figure 10. The JV curves of both sub-cells and the tandem cell are shown in Figure 11a. Figure 11b illustrates the QE curves of both sub-cells and tandem cells. As shown in Figure 11b, the maximum light-harvesting of the tandem cell started at the wavelength of 360 µm and vanished after 1550 µm. Figure 11c shows the absorption coefficients of the materials used in the tandem cell using Equation (2), while Figure 11d shows the incident AM 1.5 with the absorbed spectrum of both sub-cells. The results show that using GeTe as a bottom sub-cell can absorb most of the transmitted spectrum up to 1540 nm. This is greater than most of the other materials that can be used as absorbers of the bottom sub-cell. This explains the improvement in the tandem cell performance.

The Optimized Tandem Solar Cell
Based on the previous results, the used top sub-cell consists of a glass substrate, TCO, N-type CH3NH3PbI3-xCIx as an absorber layer, and Cu2O as the HTL, respectively. The output spectrum from the HTL of the top sub-cell is the incident spectrum to the bottom sub-cell. The used bottom sub-cell uses GeTe as an absorber layer. The GeTe chosen to be used in the bottom sub-cell shows a high current density; this impacts the overall performance of the tandem cell current density and the tandem cell power conversion efficiency.
The top sub-cell thickness optimization algorithm explained in Section 2.3 was used to find the optimum top sub-cell absorber thickness and the highest power conversion of the tandem cell started at the wavelength of 360 µm and vanished after 1550 µm. Figure  11c shows the absorption coefficients of the materials used in the tandem cell using Equation (2), while Figure 11d shows the incident AM 1.5 with the absorbed spectrum of both sub-cells. The results show that using GeTe as a bottom sub-cell can absorb most of the transmitted spectrum up to 1540 nm. This is greater than most of the other materials that can be used as absorbers of the bottom sub-cell. This explains the improvement in the tandem cell performance. of both sub-cells and tandem cells. As shown in Figure 11b, the maximum light-harvesting of the tandem cell started at the wavelength of 360 µm and vanished after 1550 µm. Figure  11c shows the absorption coefficients of the materials used in the tandem cell using Equation (2), while Figure 11d shows the incident AM 1.5 with the absorbed spectrum of both sub-cells. The results show that using GeTe as a bottom sub-cell can absorb most of the transmitted spectrum up to 1540 nm. This is greater than most of the other materials that can be used as absorbers of the bottom sub-cell. This explains the improvement in the tandem cell performance.

Comparison with the Latest Published Results
This section outlines the recently reported results of tandem solar cells from the last few years. A comparison between this work and other published results is presented in Table 3. The proposed tandem cell has one of the highest efficiencies for double-junction tandem cells and even the more complex tandem cells with more than two junctions.

Conclusions
The performance of these tandem solar cells surpasses single-junction cells due to their ability to absorb a broader spectrum. The simulation of perovskite solar cells is presented in this work with ZnOS as the electron transport material and Cu2O as the hole transport material to introduce good candidates to replace the traditional materials. The perovskite solar cell without an electron transport layer was introduced to improve the stability of the top sub-cell. It has a simple design and shows excellent performance parameters. The main material parameters of the proposed Cu2O/MAPbI3-xClx perovskite solar cell without an electron transport layer were investigated to improve the performance metrics. The results obtained from the SCAPS-1D simulator show a higher open-circuit voltage of 1.404 V relative to the other recorded perovskite solar cells, which, in turn, improves the tandem cell's overall voltage. In addition, a proposed GeTe was used as the bottom sub-cell of the tandem cell as it shows a high current density, which allows the top

Comparison with the Latest Published Results
This section outlines the recently reported results of tandem solar cells from the last few years. A comparison between this work and other published results is presented in Table 3. The proposed tandem cell has one of the highest efficiencies for double-junction tandem cells and even the more complex tandem cells with more than two junctions.

Conclusions
The performance of these tandem solar cells surpasses single-junction cells due to their ability to absorb a broader spectrum. The simulation of perovskite solar cells is presented in this work with ZnOS as the electron transport material and Cu 2 O as the hole transport material to introduce good candidates to replace the traditional materials. The perovskite solar cell without an electron transport layer was introduced to improve the stability of the top sub-cell. It has a simple design and shows excellent performance parameters. The main material parameters of the proposed Cu 2 O/MAPbI 3−x Cl x perovskite solar cell without an electron transport layer were investigated to improve the performance metrics. The results obtained from the SCAPS-1D simulator show a higher open-circuit voltage of 1.404 V relative to the other recorded perovskite solar cells, which, in turn, improves the tandem cell's overall voltage. In addition, a proposed GeTe was used as the bottom sub-cell of the tandem cell as it shows a high current density, which allows the top sub-cell to operate at a higher current density and enhances the overall two-terminal tandem cell. An optimizing algorithm was used to find the optimum top sub-cell absorber thickness. All the proposed modifications on both the top and bottom sub-cells are reflected in the power conversion efficiency of the proposed tandem cell of 46%, with an open-circuit voltage of 2.02 V and a short-circuit current density of 26.44 mA/cm 2 . To consider the practical concerns, the impact of a neutral defect with Gaussian distribution was investigated. This density is higher than more complicated tandem cells. To our knowledge, the proposed tandem cell shows one of the best-recorded results of the tandem cells in literature, and it is simpler than many of them.  Table S1: Physical parameters of the incident, transmitted spectrum definitions, and their units; Table S2: Materials parameters of the top sub-cell used in SCAPS-1D simulator; Table S3: Materials parameters of the top bottom-cell used in SCAPS-1D simulator. References [3,25,30,31,45,46,[57][58][59][60][61][62]

Data Availability Statement:
No new data were created or analyzed in this study. Data sharing does not apply to this article.

Conflicts of Interest:
The authors declare no conflict of interest.