Performance evaluation of free hole-transport layer CsPbI3 perovskite solar cells

Stable inorganic cesium lead iodide (CsPbI3)-based perovskite solar cells received intensive research in the last 2 decades. Several experimental and simulation studies have been performed on CsPbI3 solar cells to achieve high efficiency. However, the usage of the hole-transport layer (HTL) has a good impact on the solar cell’s power conversion efficiency (PCE); HTL layer usage increases the cost of the cell. In this work, a SCAPS-1D simulation study is performed on HTL-free CsPbI3 perovskite solar cells to enhance the device performance. The optical refractive index and reflectivity of CsPbI3 are calculated with density functional theory. The solar cell device structure is investigated and optimized by changing parameters like metal back contact work function, absorber thickness, acceptor density, and defect density. It is found that the optimized solar cell device achieved a PCE of 17.2% with Selenium (Se) as a back metal contact. The optimized absorber thickness for the best PCE is 2000 nm, doping density concentration of 1 × 1019 cm−3, and defect density concentration of 2 × 1012 cm−3. A PCE of 24.5% is achieved using these parameters of the CsPbI3 absorber. The simulation study may guide the fabrication of low-cost and highly efficient HTL-free inorganic CsPbI3 solar cells.


Introduction
The energy supply is one of the most targeted goals for the sustainable development. The traditional sources of energy are based on burning fuels which results in harmful carbon gas evolution and global warming climate change. Renewable energy, like solar energy, is considered a practical energy source candidate. The solar cell device converts solar energy to electricity via the photoelectric effect. Perovskites are emerging materials in photovoltaic applications. Perovskite materials can capture solar light efficiently, and their bandgap can be tuned [1][2][3]. The first time used perovskite material was inorganic-organic metal halide CH3NH3PbI3 and CH3NH3PbBr3 as a photosensitizer [4]. After that, metal halide perovskites were used in solar cell devices. CH 3 NH 3 ? (MA) ? or HC(NH 2 ) 2 (FA) ? in the perovskite halide compound are organic degradable materials and this affects the stability of the cell [5,6]. The organic cation can be replaced by metal cations like Cs ? or Rb ? [7,8]. Recently, cesium lead triiodide CsPbI3 material received much attention.
CsPbI3 is a perovskite material with a bandgap of * 1.7 eV [9]. The material is extensively studied theoretically and experimentally [9][10][11][12][13][14][15]. For the solar cell device scale, the conventional planar perovskite solar cell comprises an FTO layer followed by ETL, the main perovskite layer, and an HTL layer. The commercialization of PSC faces many obstacles: One of these is the costly, most used conventional spiro-OMeTAD HTL material. Also, Spiro-OMeTAD material is an organic degradable material that affects the device's stability [16]. TiO 2 , as an ETL material, has the problem of decreasing the solar cell device stability. TiO2 is sensitive to ultra-violet light of the spectrum and needs high annealing temperature [17,18]. The formation of CsPbI3 on the TiO2 ETL layer is at a temperature of 190°C [18]. On the other hand, ZnO material has many advantages as an ETL material for CsPbI3. ZnO has high electron mobility [19], a good lattice match with CsPbI3 [15], and allows for low-temperature preparation with CsPbI3 at 120°C [20]. A carbon-based perovskite solar cell offers a cost-effective solution for the PSC. The C-PSC is a solar cell structure of FTO/ETL/ Perovskite/Carbon. The optimization of CsPbI 3 HTL-free performance can be explored by device simulation. Solar cell device simulation will help in (i) analyzing the performance of CsPbI 3 HTL-free solar cell device; (ii) Identifying the prospects that affect the efficiency of the cell; (iii) Offering alternatives for material selection like metal back contacts.
In this study, a DFT study is conducted on CsPbI3 cubic perovskite. The aim of the DFT study is to explore the optical and electronic properties of the material. A theoretical investigation, for the first time, of the optical refractive index and reflectivity is done. CsPbI3 HTL-free-based perovskite solar cell device performance is optimized by numerical simulation using SCAPS-1D. The ETL material is ZnO. The impact of metal back contact work function, CsPbI3 thickness, concentration doping, and defect density on PCE are studied. The results offer a guide for designing high-performance HTL-free-based inorganic CsPbI3 perovskite solar cells.

Computational study
DFT study is conducted on cubic perovskite CsPbI3 (Pm-3 m, 221) structure. The study intends to calculate the band structure, density of states, and optical properties (refractive index and reflectivity) of CsPbI 3 . Cambridge Sequential Total Energy Package (CASTEP) [21] was used in the DFT study. The Generalized Gradient Approximation-Perdew-Burke-Ernzerhof (GGA-PBE) functional was used to study the exchange-correlation between electrons for the CsPbI3 cubic structure [22]. GGA-PBE functional estimated the bandgap of CsPbI3 close to experimental. Ultra-soft pseudopotential was used with a Brillion k-point set of 3 9 3 9 3 and cut-off energy of 700 eV. The Broyden--Fletcher-Goldfarb-Shanno (BFGS) algorithm was used to relax the atom positions of the CsPbI 3 perovskite. A medium convergence tolerance was used with an energy of 2 9 10 -5 eV/atom, a maximum force of 0.05 eV/A°, and a maximum displacement of 0.002 A°. The optimization steps were set to be 1000 iterations. The selfconsistent field (SCF) tolerance was set to be 2 9 10 -6 eV/atom. Table 1 shows the calculated values of lattice constant, bandgap, and the real part of the refractive index of CsPbI3 material using GGA-PBE functional versus the experimental ones. The calculated and the experimental values of the lattice constant of CsPbI3 are 6.3 A°and 6.4 A°, respectively. The calculated bandgap of CsPbI3 equals 1.6, while the experimental equals 1.67. The real part of the refractive index n at a wavelength of 435 nm equals 2 using GGA-PBE theoretical calculations and 2.46 for experimental measures [12]. Figure 1a shows the calculated band structure of CsPbI3. The material is a direct bandgap semiconductor with a calculated bandgap value of 1.6 eV using GGA-PBE functional. The total density of states (DOS) and partial density of states (PDOS) calculations are shown in Fig. 1b. It is shown that the valence band dominance is by p states from Pb-I states. The dominance in the conduction band is by s states for Cs and p states for Pb-I states. Figure 2a shows the optical refractive index as a function of wavelength (real n and imaginary k). It is  [12] shown that the CsPbI3 perovskite material has relatively low values of the refractive index compared to other semiconductor materials, like Si and GaAs [24,25]. These low values of n are helpful for the device scale fabrication by avoiding losing light by reflection. On the other hand, the k (extinction coefficient) values of CsPbI3 material are relatively higher than those of the organic metal halide perovskite such as CH3NH3PbBr3 in the visible range of light [26,27]. The CsPbI3 is opaque to light in the visible range of light. Figure 2b shows the reflectivity versus wavelength for the CsPbI3 perovskites. The reflectivity is used to study the surface properties of a material, which is equal to the ratio of the reflection to the incident power. CsPbI 3 material shows low reflectivity in the first half of the solar spectrum, but the reflectivity increases for the second half of the solar spectrum for k [ 550 nm.

Device structure numerical simulation study
All simulations are done using SCAPS-1D simulator [28]. As shown in Fig. 3a, CsPbI3 HTL-free PSC consists of FTO/ETL/CsPbI3/Carbon. The bandgap alignment between CsPbI3 and ZnO is shown in Fig. 3b. The physical parameters of used materials are shown in Table 2, which are collected from the experimental and the theoretical studies previously published. In the table, NC and NV correspond to effective conduction and valence band density, Eg denotes bandgap, NA and ND denote acceptor and donor density, lp (ln) stands for hole (electron) mobility, Nt is the defect density, v is electron affinity, and er is relative permittivity. To consider the effect of interface recombination between ETL and CsPbI 3 , a 5 nm thin interface defect layer (IDL) is assumed in the ETL/CsPbI 3 interface. The IDL layer has the same physical parameters as CsPbI 3 material. The thermal velocity of the hole and the electron is 10 7 cm/s. The back contact work function is 5 eV as carbon.
3 Results and discussion  [19]. This structure is used as a reference for the solar cell further performance evaluation and investigation.

Impact of different metal back contacts
Different metals are simulated as back contact to study the performance of solar cell devices. The work functions of metals are carbon C (5 eV) [33], gold Au (5.1 eV) [34], platinum Pt (5.65 eV) [35], and selenium Se (5.9 eV) [36]. Figure 5a shows the J-V diagram of   Fig. 5c, d, respectively. The band diagram of the cell is overlapped using Se back contact compared to C and a high V bi is achieved. The high V bi results in a high electric field across the cell. The Schottky barrier for holes also decreases with high work function value of Se as shown in the dotted rectangle, Fig. 5d, and high Voc value is obtained.

Impact of CsPbI3 thickness
The engineering of perovskite layer thickness impacts the solar cell device performance. The layer thickness of CsPbI 3 is varied from 400 to 4000 nm to measure the J-V, quantum efficiency (QE) diagrams, and the solar cell parameters. Figure 6a shows the J-V diagram of FTO/ZnO/CsPbI 3 /Se structure. The solar cell parameters increase with thickness from 400 to 2000 nm. Then, carriers' recombination rate increases and causes decreased current density and PCE values. The QE is shown in Fig. 6b. The QE values are increased gradually until the 2000 nm thickness of CsPbI 3 is due to the increased photon absorption. The QE values saturate for thicknesses larger than 2000 nm. Table 3 shows the solar cell parameters with different CsPbI 3 thickness. With an absorber thickness of 2000 nm, the device achieves a high PCE of 20.6%. Therefore, the 2000 nm thickness of CsPbI 3 is the best value of perovskite layer thickness for high performance.

Impact of CsPbI3 doping concentration
In the present investigation, the acceptor density (NA) in CsPbI3 varies from 10 15 to 10 20 cm -3 . The J-V curves and PCE with varying NA are shown in Fig. 7. As shown, the Jsc values are identical for acceptor densities values from (10 15 cm -3 -10 19 cm -3 ). However, when the NA is 10 20 cm -3 , the JSC decreases, and VOC increases. The Voc values are increased gradually with higher doping NA. The increment in Voc can be explained by Eqs. (1) and (2) as follows: where I 0 is the dark saturation current, q is the electron charge, n i is the intrinsic carrier concentration. D n and D p are the diffusivities of electrons and holes. L n and L p are the diffusion length of electrons and holes. N A and N D are the acceptor and donor concentrations. KT/q is the thermal voltage that equals 0.02569 V at 25°C.
Increasing NA decreases the dark saturation current I0 and Jsc. The decrement of I0 improves the Voc values. The best NA value for the best device performance is shown in Fig. 7b, a maximum conversion efficiency of 24% can be obtained when NA is 10 19 cm -3 .  Furthermore, to interpret the band-to-band recombination defect in the ETL/CsPbI 3 interface, Fig. 8 shows the energy band diagrams of the solar cell device with low and high values of N A . For small values of N A , a high electric field is generated across the CsPbI3 material as photogenerated carriers are depleted and allow for the separation and collection of carriers to generate an electric field as shown Fig. 8a (N A =10 15 cm -3 ), leading to a high Jsc. However, under a high NA such as10 20 cm -3 , Fig. 8b), the depleted region became small, and the electric field is compressed to the interface between CsPbI3 and ETL. This causes an obstacle to carrier collection and separation and in turns, affects the Jsc value.

Effect of CsPbI3 defect density variation
The impact of absorber defect density Nt is simulated and shown in Fig. 9. The J-V characteristic diagram is shown in Fig. 9a. The Nt values have no impact on Jsc but have an impact on Voc values. The decrease of Nt values causes an increase of Voc values, which affects the PCE of the cell. Figure 9b shows the relationship between PCE and different defect densities. As shown, when Nt is lower than 2 9 10 12 cm -3 , the PCE shows few changes. However, when Nt goes beyond 2 9 10 15 cm -3 , the PCE becomes small. Therefore, controlling the Nt under * 10 12 cm -3 may enhance the PCE of CsPbI3 HTL-free PSCs. At this Nt value, an optimized PCE of 24.5% can be achieved for FTO/ZnO/CsPbI3 (2000 nm)/Se all-inorganic PSCs.

The simulated optimized structure
The optimized structure of CsPbI3 HTL-free-based perovskite solar cell can be assumed from the simulation study as FTO/ZnO/CsPbI3 (2000 nm)/Se. The doping acceptor concentration of the CsPbI3 layer can be estimated to be 10 19 cm -3 , and the best defect density concentration level Nt of 2 9 10 12 cm -3 . Figure 10a shows the J-V characteristics diagram of the optimized perovskite solar cell structure. The device has a Jsc of 20.82 mA/cm 2 , Voc of 1.35 V, PCE  Figure 10b shows the QE values of the optimized structure of the perovskite solar cell, which are high all over the spectrum.

Conclusion
In this work, a hybrid DFT and numerical simulation studies are executed on CsPbI3-based perovskite solar cells. The DFT study verified the experimentally measured optical refractive index and bandgap. The CsPbI3 material has the advantage of minimum reflection of light. The reference simulated solar cell device structure is based on ZnO as an ETL layer and carbon as a back contact. The SCAPS-1D numerical simulator shows that replacing metal back contact with low-cost abundant Se gives the device the optimum PCE. The optimized performance solar cell structure is (FTO/ZnO/CsPbI3/Se) with a PCE of 24.5%. The numerical simulation optimization results show that the optimum thickness of CsPbI3 is 2000 nm with an acceptor concentration of 10 19 cm -3 , and the best defect density concentration is 2 9 10 12 cm -3 .

Author contributions
HHA contributed to data acquisition, design, analysis, and drafted the manuscript. HHA contributed to conception, data interpretation, and the final revision of the manuscript. The author gave final approval and agreed to be accountable for all aspects of the work

Data availability
All the simulation data in this research article are available in the manuscript.

Declarations
Conflict of interest The author declares that no financial or non-financial support was received for this work..