Design of a Novel Lead-Free Perovskite Solar Cell for 17.83% Efficiency

Lead halide perovskite solar cell shows an enormous potential for the next generation renewable energy, but it also offers some environmental hazards due to their inherent lead-based toxicity. On the other hand, if lead based perovskite is efficiently replaced by other non-toxic metal based perovskite then their toxicity can remarkably be reduced for photovoltaic applications. In this study, a novel lead free compound Cs2TiBr6 based photovoltaic device is proposed as Au/PEDOT:PSS/ Cs2TiBr6/TiO2/AZO, where each layer is optimized and analysed through a series of simulations for maximum power-conversion efficiency using SCAPS-1D software. Comprehensive optimization of the thickness and doping density of each layer leads to the maximum power-conversion efficiency up to 17.83% for our proposed solar cell. Therefore, we believe that these results will provide a route heading towards the progress of lead-free and highly efficient perovskite photovoltaic devices.


I. INTRODUCTION
Over the last few decades, researchers are very optimist about photovoltaic technology to replace the depleted fossilfuels for enormous energy demand in near future [1]. Despite the tremendous achievements, the demands of efficient, green, low-cost, and abundantly available material for solar cell technology is a challenging task [2]. Even with the higher processing cost, the crystalline silicon is still the most dominating material and have occupied a major chunk of current photovoltaic market [3]. Up till now the laboratory power-conversion efficiency is over 25%, while the commercial power conversion-efficiency of Si solar-cell modules have reached up to 18-22% under standard testing conditions [4]- [6].
Perovskite cover a broader range of compounds with formula ABX 3 , where A is an organic or inorganic cation, B is a divalent metal ion, and X is a halide anion. Perovskite solar cell has emerged as a new class with unprecedented The associate editor coordinating the review of this manuscript and approving it for publication was Xiao-Jun Yang . The authors acknowledge the use of SCAPS-1D program developed by Marc Burgelman and his colleagues at the University of Gent for all the simulations reported in this work. progress and their power-conversion efficiency has already reached up to 25% within very few years [6]. It offers various advantages such as low-cost, highly-efficient, thin-film deposition, simple fabrication process, tunability of parameters including energy bandgap and excellent electrical and optical properties. However, the most efficient perovskites are lead (Pb) based compounds (e.g. methylammonium lead trihalide, CH 3 NH 3 PbX 3 ). Lead is inherently a toxic material and poses some serious poisonous threat to the environment which is a crucial limitation for their photovoltaic applications [7]- [10].
To replace Pb, different researchers exploring various metal ions for efficient photovoltaic solar cell. Some schools of thought are convinced that tin (Sn) can replace the Pb due to their physical and electronic similarities, however till-now Sn based perovskite solar cells did not show acceptable power-conversion efficiency [11]. Consequently, other novel divalent metal combinations are also proposed to develop efficient and stable perovskite solar cells. Wu and his co-worker reported Cs 2 AgBiBr 6 as double perovskite solar cell [8]. Kang and his co-worker testified antioxidative stannous oxalate derived compounds for leadfree CsSnX 3 perovskite nanocrystals [12]. Liu et. al. has studied CsBi 3 I 10 complexes to figure out efficient Pb free perovskite materials [13]. Locardi and his co-worker investigated Cs 2 AgInCl 6 and Mn-doped Cs 2 AgInCl 6 [14]. Ito et. al. used the mixed tin and germanium-based compound for perovskite solar cell [15]. Lefanova and his co-worker studied (NH 4 ) 3 Sb 2 I x Br 9−x to replace Pb for perovskite solar cell [16]. Regardless of these massive efforts, we are still far away to discover new Pb free perovskite compound which are close to methylammonium lead trihalide (CH 3 NH 3 PbX 3 ) with respect to efficiency and as well as stability. Recently a novel perovskite compound Cs 2 TiBr 6 is reported, which shows an excellent stability response with very promising electrical and optical properties [17]- [19]. At this stage this perovskite compound is not comprehensively investigated, and little information is available, therefore wide-ranging efforts are desired [17], [18], [20].
The Cs 2 TiBr 6 is inherently poly-crystalline in nature which contains many crystalline domains at different directions but separated by some grain boundaries, the average grain-boundary size can be calculated with the help of SEM and XRD analysis. The effects of poly-crystalline grain-boundary size on the performance of photovoltaic response for perovskite materials are still not very clear. Some researchers believe that the perovskite grain size plays a lesser role on the performance of perovskite solar cell as compared to the other materials parameters (e.g. tunable energy bandgaps, quantity and quality of additive, type and nature of defect density etc). Recently, researchers discovered that the grain-size of perovskite might play a crucial role for the formation of ion migration channels. These channels help the intrinsic ions to migrate from one grain to other grain boundary inside perovskite thin film at lower activation energy for switchable photovoltaic response [21].
For comprehensive investigation, different approaches are reported in literature. Among these approaches, simulation and modelling of photovoltaic devices are exceedingly popular now a day's [22]. The simulation and modelling of solar cells are based on the theoretical models which are rigorously studied and now unanimously accepted. These theoretical models can be expressed by the series of mathematical equations govern by the substantial number of physical, electrical, and optical parameters to comprehensively define the operation of associated photovoltaic material and device.
In recent literature, numerous types of both open sources software e.g. gpvdm, wxAMPS, SCAPS-1D, PC-1D, AFORS-HET, AMPS-1D etc and commercially available software such as TCAD, COMSOL, Silvaco Atlas etc are available. Among these software SCAPS-1D (Solar Cell Capacitance Simulator -1 Dimension) is highly respected and reported for the simulation and modelling of various types of solar cell [23].
In this study we designed, proposed, and simulated Cs 2 TiBr 6 based efficient perovskite solar cell. For this purpose, we select and optimized the most appropriate electrontransport layer, hole-transport layer, mesoporous layer with respect to thickness and doping concentration and then finally optimized the absorber layer (Cs 2 TiBr 6 ) for efficient Pb free perovskite solar cell.

II. DESIGN OF NOVEL PEROVSKITE SOLAR CELL AND MATERIALS PARAMETERS
For solar cell the absorber layer is the main constituent of photovoltaic device to absorbs photons and generate electronshole pairs which in turn produces electricity. Theoretically, the absorber layer sandwiched between two electrodes is enough for the photovoltaic response, but the maximum photovoltaic response can only be achieved with the balanced distribution of electron and hole inside the solar cell [24]. Therefore, in order to get balanced charge distribution, the perovskite absorber is sandwiched between electrontransport layer (ETL) and hole-transport layer (HTL) for effective perovskite solar cell [25]. Where, the absorber layer we have already selected Cs 2 TiBr 6 due to the reasons as discussed above.
For the selection of other layers, both HTL and ETL have to perform three well-define tasks (i) extract hole/electron from absorber layer, (ii) block opposite charges to enter from the absorber layer to avoid recombinations, and (iii) collect holes/electrons from absorber layer and guided them towards their respective electrode [26], [27]. A large number of inorganic, organic and conjugate polymers HTL materials are reported such as CuI, CuSCN, NiO, Spirobifluorenes, Thiophenes, Triphenylamines, Triazatruxenes, Spiro-MeOTAD, DMeO-TPD, Tetrathiafulvalene (TTF), PEDOT: PSS, P3HT, PTAA etc [26], [27]. From efficiency point of view spiro-MeOTAD has been reported as the most appropriate HTL for perovskite solar cell. But, spiro-MeOTAD has some serious issues with respect to cost, stability, compatibility, and hysteresis [28].
Broadly speaking after spiro-MeOTAD, the polymer Poly (3,4-ethylenedioxythiophene): polystyrene sulfonate (PEDOT:PSS) is the most suitable hole-transport layer candidate for efficient perovskite solar cell. PEDOT:PSS deals with many advantages of stability, low cost, excellent electrical, optical and thermal properties [29]. Therefore, we opt PEDOT:PSS as hole-transport layer for this study.
There are three structural types exist such as (i) p-i-n, (ii) n-i-p, and (iii) mesoporous type for perovskite solar cells, where both p-i-n and n-i-p are considered as planar perovskite solar cell. It is remarkably noted that compared to the plannar type, the mesoporous architecture of perovskite solar cell was found more efficient [30]. In this type, generally a mesoscopic layer is used between ETL and absorber layer and TiO 2 is the most reported mesoporous layer for perovskite solar cell [31]. As, TiO 2 behaves n-type semiconducting material in nature therefore it provides inherent support for the extraction of electrons from perovskite absorber layer. Similarly, it also supports band-alignment, and reduction of hysteresis to boost the power-conversion efficiency and stability of the perovskite solar cell [31]. Therefore, we refer TiO 2 as mesoporous layer for our proposed perovskite solar cell. For ETL inorganic materials such as zinc oxide (ZnO), aluminium-doped zinc oxide (AZO), tin-oxide (SnO 2 ), alumina (Al 2 O 3 ), zirconia (ZrO 2 ), silica (SiO 2 ) and many other compounds are commonly reported for perovskite solar cell. Among these electron-transport materials, ZnO has many unique advantages of solution processing, excellent electrical properties and high mobility. However, frequent instabilities and poor device efficiency of perovskite solar cell with ZnO have already reported [32]. By using Al doped ZnO for electron-transport layer, excellent photovoltaic response and stability can be achieved due to improved conductivity, better work-function alignment, and acid resistance [33]. Therefore, in this study we prefer AZO (n-ZnO:Al) as electron-transport layer. Figure 1 shows the both (a) schematic and (b) energy band diagram of the proposed device used in this study as Au/PEDOT:PSS/ Cs 2 TiBr 6 /TiO 2 /AZO perovskite solar cell.

III. SIMULATION, MODELLING AND DESIGN PARAMETERS
As discussed above, the simulation in this study is employed with the help of SCAPS software version 3.3.07 which was developed by ELIS, University of Gent, Belgium and it is a one dimension (1-D) photovoltaic simulator [23]. The SCAPS software is versatile in nature and covers nearly all recommended electrical, optical and photovoltaic models, therefore it can be successfully used for the simulation of dye-sensitized solar cell [34], [35], graphene [36], CIGS materials [37], polymer [38], nanowire [39], perovskite and many other types of photovoltaic materials [40]. Kang et. al. reported the simulation analysis of graphene contact for perovskite solar cell [41]. Abdelaziz comprehensively investigated and reported the performance of tin-based perovskite solar cell by SCAPS device simulation [42]. On the other hand, the reasonable agreements of the experimental findings with SCAPS-1D simulation results [43], inspired us to use this open-source software for this work.
Fundamentally, SCAPS 1D execute four set of photovoltaic equations for both electron and hole carriers density separately [44]. These equations are 1) Poisson equation: where φ is the is the electrostatics potential, e is electronic charge, ε 0 is permittivity of vacuume, ε r is relative permittivity, N D is the shallow donor impurity density and N A is the shallow acceptor impurity density. Similarly ρ p is hole density distribution and ρ n is the electrons density distribution, while n(x) and p(x) are the the electron and hole density as a function of x respectively. 2) Continuity equation: where J n and J p are the electron and hole current densities, G is the generation rate and R is the recombination rate. 3) Charge transport equation: where D n and D p are the electron and hole diffusion coefficient respectively, µ n and µ p are the electron and hole mobility respectively. 4) Absorption coefficient equation: For the determination of the absorption coefficient α(λ), we use the following equation where A, B are constant, h is plank constant, ν is frequency of photons and E g is the band gap of the absorber layer. The band discontinuity between the interface of the different layers is presumed small and therefore can be neglected for simplicity. The ambient temperature 300 K and the solar spectrum AM.1.5 (1000 W /m 2 ) is used for this study. All physical and electrical parameters which are required by SCAPS 1D for each layer are extracted from scientific literature and are listed above in Table 1.

A. PEDOT: PSS THICKNESS OPTIMIZATION
The charge-transport process in PEDOT:PSS is not so efficient and offers high resistance in the presence of low conductive PSS contents [45]- [47]. Therefore, in order to simulate high resistive PEDOT:PSS we introduced some interface defects and detailed information can be found from Table 2. To optimize the PEDOT:PSS for this study, firstly  we optimized the thickness and then acceptor doping density for PEDOT:PSS layer. For this purpose, initially we used the Table 1 parameters and run the software for proposed device and obtained results are shown in Figure 2 [48]. As power-conversion efficiency is the resultant of all these factors, so it rises and reaches maximum (6.47%) at 80 nm and then start to decreases as a function of PEDOT:PSS layer thickness. Like many other conducting polymers, the charge transportation and recombination are very complex in nature and specially in the presence of traps distribution [49]- [53], so we can infer that all these factors are optimized at 80 nm thickness of PEDOT:PSS for our proposed solar cell.

B. PEDOT: PSS ACCEPTOR DENSITY OPTIMIZATION
Despite the numerous advantages, PEDOT: PSS shows inherently low conductivity and therefore the doping of PEDOT:PSS is essential for efficient photovoltaic applications. Doping is generally performed by introducing suitable amount of some compounds into the PEDOT:PSS aqueous solution, such compounds may be ionic, polar, organic, polymer anionic, and surfactant compounds. The conductivity of PEDOT:PSS can be further enhanced from two to three orders of magnitude by using proper doping compound under normal conditions [54]. It is experimentally noted that the successful doping beyond 10 20 cm −3 is not a conventional task and the conductivity of both organic semiconductor and inorganic semiconductor increase with doping up to a certain limit (10 20 cm −3 ) and then start to decrease [55]. It may be due to the carrier-carrier or may be carriermolecular orbital interactions, therefore in this study we analysed the photovoltaic response of ETL, HTL and mesoporous layer for our proposed device up to 10 20 cm −3 doping concentration [56].
In Figure 3a and 3b, firstly incorporated the optimize thickness of PEDOT:PSS (80 nm) and then we varied the shallow acceptor doping density (Na) inside by PEDOT:PSS from 10 11 to 10 20 cm −3 and different photovoltaic parameters such as (a) short-circuit current, open-circuit voltage, (b) fill-factor and power-conversion efficiency were calculated from the photovoltaic responses. Figures 3a and  3b demonstrate the similar trends, where open-circuit voltage, short-circuit current, and fill-factor are firstly increases sharply and then gradually increases. Similarly, the powerconversion efficiency is also increases sharply and then steadily with doping concentration and the maximum efficiency close to 8.3% is observed at most optimum doping 10 20 cm −3 for PEDOT:PSS for our proposed solar cell.

C. AZO THICKNESS OPTIMIZATION
The aluminium doped ZnO (AZO) plays two types of role, one as electron-transport layer and other as a transparent conductive oxide (TCO) for photovoltaic response, therefore their optimization is also very important for efficient solar cell. For thickness optimization, the photovoltaics  Figure 4a and 4b respectively. We observed that the effects of thickness on open-circuit voltage is nearly negligible, while shortcircuit current rises up to 400 nm and then start to decrease. Similarly, Fill-factor is continuously decreases with AZO thickness and power-conversion efficiency is very slightly decreases with AZO layer thickness. So on the basis of the results we can conclude that 100 nm (PCE 8.37%) is the most optimum thickness of AZO layer for efficient Au/PEDOT:PSS/Cs 2 TiBr 6 /TiO 2 /AZO solar cell.

D. AZO DONOR DENSITY OPTIMIZATION
The conductivity of AZO (n-ZnO:Al) is not comparable with other transparent conductive oxides (TCO) such as indium tin oxide (ITO) and fluorine tin oxide (FTO), which are frequently used for perovskite solar cell [57]. But the conductivity (σ , which is the inverse of resistivity ρ = 1 enµ ) can be increased by either increasing mobility and/or increasing free electron density. Doping is the easiest way to increase the free electron carrier density, but on the other side heavy doping degrades optical absorption, reflection and transmission for photovoltaic response. Similarly, higher donor doping can also degrade the electron mobility and hence it is very important to optimize the donor doping of AZO for highly optimized solar cell [58], [59].
For donor doping-density, the photovoltaics parameters such as (a) open-circuit voltage, (b) short-circuit current, (c) fill-factor and (d) power-conversion efficiency of Au/PEDOT:PSS/Cs 2 TiBr 6 /TiO 2 /AZO solar cell were examined by varying shallow donor doping from 10 11 to 10 20 cm −3 of AZO layer and the results are shown in Fig. 5a and 5b respectively. It is realized that all photovoltaic parameters are improved by doping concentration but with different rates. Short-circuit current is significantly increases while opencircuit voltage is nearly unaffected with increasing doping concentration. Power-conversion efficiency and fill-factor are sharply increased at early stage (up to 10 12 cm −3 ) and then increases very slightly. So, the optimum efficiency (8.42 %) of the device is achieved at the donor density of 10 20 cm −3 respectively.

E. TiO 2 THICKNESS OPTIMIZATION
The TiO 2 interaction with perovskite material is complex in nature and offers some unique behaviour such as high chemical reactivity, unwanted charge build-up, excessive recombination, and uncertainty under ultraviolet light, low mobility, non-uniform distribution of electronic trap states, and high density of these trap states [60].
Generally, it can be observed by both theoretically (e.g. DFT: density functional theory) and experimentally (e.g. XPS: X-ray photo-electron spectroscopy) that the inorganic perovskite material such as Cs 2 TiBr 6 offers a weak interface with inorganic metal oxide layer (e,g TiO 2 , ZnO etc) leading towards low power conversion efficiency. Such weaker contact is formed due to the non-existence of hydrogen bonds during the interfacial chemical reactions between metal oxide and perovskite layers compared to the organicperovskite interfaces. Therefore, numerous organic additives are reported for the formation of strong hydrogen bonding to improve the interfacial contact between perovskite and inorganic metal oxide layer but at the cost of thermal stability and hysterics for perovskite solar cell.
The photovoltaic parameter responses of the device are simulated when TiO 2 film thickness is varied from 10 to 100 nm as shown in Figure 6a and 6b respectively. Figure 6a shows the open-circuit voltage and short-circuit current behaviours as a function of TiO 2 film thickness. It is clear from the figure that the open-circuit voltage is very slightly increases (nearly constant), while short-circuit current of the device is very slightly decreases (nearly constant) as a function of TiO 2 film thickness, respectively. Similarly, Figure 6b shows the fill-factor and power-conversion efficiency response as a function of TiO 2 film thickness. It is also evident from the figure that the fill-factor's behaviour is very similar to short-circuit current, while power-conversion efficiency of the device is linearly decreases as a function of TiO 2 film thickness and maximum value is observed at 8.45% for 20 nm TiO 2 film thickness, respectively. As powerconversion efficiency is the prime parameter, therefore we can infer that the most optimum thickness of TiO 2 for proposed device is 20 nm.

F. TiO 2 DOPING OPTIMIZATION
Similarly, we also analysed the proposed device to determine the optimum donor density for TiO 2 layer. Very similar results for (i) open-circuit voltage, (ii) short circuit Current, (iii) fillfactor and (iv) power-conversion efficiency are observed as already shown in Figure 6. It is also noted that the maximum power-conversion efficiency 9.18% is achieved at donor doping 10 12 cm −3 for TiO 2 layer. Therefore, the TiO 2 doping density effects on photovoltaic responses are not shown here for simplicity.

G. THE ABSORBER Cs 2 TiBr 6 THICKNESS OPTIMIZATION
After incorporating the optimized thickness and doping density of PEDOT:PSS as hole-transport layer, TiO 2 as mesoporous layer and AZO as electron-transport layer, we are finally interested to determine the most optimum powerconversion efficiency of our proposed device. As we know that the power-conversion efficiency is related to the thickness of Cs 2 TiBr 6 absorber layer, therefore we analysed the photovoltaic parameters of the proposed device as a VOLUME 9, 2021 function of Cs 2 TiBr 6 layer thickness from 100 to 1000 nm and the results are given in Figure 7a and 7b respectively. In Figure 7a, it is observed that the short-circuit current is continuously increased but at later stage the rate of increment is very slow as a function of perovskite absorber layer thickness. As perovskite absorber thickness increases then more optical absorption can be taken place which in turn leads to the higher electron-hole pair generation and therefore shortcircuit current is constantly increases as shown in Figure 7a. On the other hand, open-circuit voltage is sharply dropped from 1.3 V to 1 V and then slightly decreases as the thickness increases of the absorber layer. Such open-circuit voltage losses in the proposed solar cell may be due to the accumulation of positive hole charges at the interface with Cs 2 TiBr 6 absorber layer as similar observations were already reported by many other studies [61]- [63]. Accumulation of interfacial charges causes to enhance charge carrier recombination and hence a significant drop of open-circuit voltage is observed.
Accumulation of interfacial charges also effects fill-factor and power-conversion efficiency as shown in Figure 7b. Therefore, more or less similar power-conversion efficiency and fill-factor responses are observed as both increase significantly at early stage and reached maximum value (power-conversion efficiency 10.62%) at 200 nm thickness then very steadily decreases with increasing absorber layer thickness. It may be the trade of balance between generation of free carriers, and interfacial recombination as a function of absorber layer thickness. Hence, based on these results and specially power-conversion efficiency we can infer that the best thickness is 200 nm for Cs 2 TiBr 6 absorber layer for our proposed solar device.

H. THE ABSORBER Cs 2 TiBr 6 DOPING OPTIMIZATION
The presence of inherent interfacial traps states of perovskite material causes to accumulate unwanted charge carriers which in turn trigger excessive recombination to degrade the photovoltaic response [64]. Perovskite materials are polycrystalline in nature and also have non-uniform bulk distribution of trap states, which further worsen the photovoltaic response of perovskite solar cell. As discussed above the doping is one of the most effective and easy solution to fill their surface traps, minimize unwanted charge accumulation and significantly enhance the electron injection efficiency to improve the photovoltaic response of perovskite solar cell [65], [66]. In order to determine the optimum doping density, the photovoltaic parameters of the proposed device are investigated by varying the absorber doping density from 10 11 to 10 20 cm −3 and the results are summarized in Figure 8a   current, and power-conversion efficiency of the proposed device are continuously increasing with shallow donor doping and power-conversion efficiency reached up to 17.83 % at 10 20 cm −3 doping of Cs 2 TiBr 6 absorber layer respectively. At higher doping the fill-factor follows complex response which may be due to higher leakage current at heavy doping [67]. Thus, the optimum doping of absorber layer is 10 20 cm −3 for the most efficient design of proposed solar cell.
Finally, we figure out the most optimum thickness and doping parameters of each layer of our proposed solar cell and listed in Table 3. As Cs 2 TiBr 6 is a novel perovskite material for photovoltaic response and little information is available in literature, therefore we compared our proposed photovoltaic device with other Cs 2 TiBr 6 based reported solar cell and it is found that the maximum power-conversion efficiency of our proposed solar cell is improved from 3% to 17.83% mainly due to the proper material selection, thickness and doping concentration of hole-transport, electron-transport, mesoporous and perovskite absorber layer [17]- [20].

V. CONCLUSION
In this study we firstly designed novel Cs 2 TiBr 6 based photovoltaic device according to the available literature information. We proposed highly suitable hole-transport layer (PEDOT:PSS), mesoporous layer (TiO 2 ) and electrontransport layer (AZO) as Au/PEDOT:PSS/Cs 2 TiBr 6 /TiO 2 / AZO, and simulated by SCAPS-1D software. To improve the power-conversion efficiency of the proposed lead-free perovskite solar cell, an effort has been made by optimizing the hole-transport layer, electron transport layer, mesoporous layer and then Cs 2 TiBr 6 absorber layer. After comprehensive optimization of each layer thickness, and doping density the maximum 17.83% power-conversion efficiency is achieved for the proposed device. It is further observed that the photovoltaic parameters of the perovskite solar-cell are significantly affected by the thickness and doping concentration of respective hole-transport layer, electron transport layer, and perovskite absorber layer. Therefore, not only the proper selection of materials but also the thickness and doping concentration play a vital role for an efficient perovskite solar cell. The overall outcomes of this study will not only help to understand the photovoltaic process but also provide a route heading towards the progress of lead-free and highly efficient photovoltaic devices.