Study of the photovoltaic properties of Cs and Cl co-doped FAPbI 3 based on first principles

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It has been found that doping with different kinds of elements at different sites can enhance its stability and improve the photoelectric conversion efficiency of solar cells. In this paper, the geometry, electronic structure and optical properties of FA 1 − x Cs x PbI 3−y Cl y were calculated using Cs and Cl co-doped with FAPbI 3 using the first nature principle. The analysis revealed that the Goldschmidt factors of the doped system were between 0.962 and 0.974, indicating that the system could maintain a stable chalcogenide structure, and the doped system had lower energy and more stable structure. By calculating the energy bands, it is found that the doped ions have a more pronounced effect on the increase of the dispersion at the bottom of the conduction band than the decrease of the dispersion at the top of the valence band of the system, and the reduction of the effective mass of carriers is more favorable for transport. As for the optical properties, the right amount of doping is favorable to the improvement of light absorption, while the excess doping shortens the light absorption range and weakens the light absorption effect, in which FA 0.875 Cs 0.125 PbI 2.958 Cl 0.125 has the largest light absorption coefficient. It is shown that the photoelectric properties of chalcogenide FAPbI 3 can be effectively modulated by the co-doping of Cs and Cl, which can provide theoretical reference for the precise preparation of more efficient solar cells experimentally. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction The development of economy and science and technology cannot be supported by energy sources, which are mainly non-renewable energy sources, such as oil, coal and natural gas. As more and more energy is used, there are few reserves of energy left on the earth, and the environmental problems caused by the use of non-renewable energy sources have also caused concern in many countries, so they hope to vigorously develop renewable and clean energy sources such as solar energy 1 – 5 . The conversion efficiency of solar cells depends largely on the photoelectric conversion of their photoabsorption layer, and the special properties of chalcogenide materials, such as direct and tunable band gap, high lattice defect tolerance, high usage efficiency of photogenerated carriers and high light absorption coefficient, are particularly suitable for use as a photoabsorption layer in solar cells 6 , 7 . The conversion efficiency of chalcogenide solar cells, first prepared in 2009 at 3.8% 8 has recently exceeded 25% after years of unremitting efforts 9 . Although the conversion efficiency has made great progress, however,chalcogenide solar cells are prone to react with water vapor in the air, causing structural instability,so stability is also a difficult point to overcome for chalcogenide solar cells 10 , 11 . The crystal structure of chalcogenide materials as light absorbing layers is ABX 3 type, with methylamine ions (MA + =CH 3 NH 3 ), formamidine ions (FA + =HC(NH 2 ) 2 + ), cesium ions (Cs + ), and rubidium ions (Rb + ) usually in the A site, lead ions (Pb 2 + ) and tin ions (Sn 2 + ) usually in the B site, and chloride ions (Cl - ), bromine ions (Br - ) and iodide ions (I - ) are usually in the X site. There are more reasons for their instability, such as external environment like temperature and humidity, and then intrinsic properties such as electron migration and ion migration, which are largely related to ion size 12 , 13 . Methylamine ions (MA + ), formamidine ions (FA + ) and also chloride ions (Cl - ) are large size ions with soft lattice, so they tend to react to temperature, humidity and also light, causing a decrease in stability 14 .The cubic phase band gap of FAPbI 3 is closer to the Shockley-Queisser limit of 1.34 eV than that of MAPbI 3 , which is more suitable for light absorbing materials, while FAPbI 3 is more likely to form the hexagonal phase at room temperature. To improve the performance of solar cells, researchers have tried to dope different sites of chalcogenide type crystals with different types of ions.MA x FA 1-x PbI 3 was prepared by Pellet et al 15 using a mixture of methylamine and formamidine ions at site A. The hybrid system exhibited better photovoltaic properties than the undoped system. In addition, Eperon et al 16 found that the diffusion length of carriers in the MA x FA 1-x PbI 3 system became longer, revealing the reason for the improved photoelectric conversion efficiency from the internal mechanism.Lee et al 17 use a small amount of Cs ions instead of FA ions, which makes the bond energy of the chemical bonds between ions larger and the internal defects smaller, and the thermal stability of the prepared Cs x FA 1–x PbI 3 system is improved.Hu et al 18 added 10% CsCl to FAPbI 3 was able to suppress the hexagonal phase of FAPbI 3 , making the cubic phase more stable and the system with the lowest density of film defects. Numerous studies have shown that the simultaneous addition of Cs and Cl to FAPbI 3 leads to the formation of FA 1-x Cs x PbI 3-y Cl y with better optoelectronic properties and stability than FAPbI 3 , however, the components of FA 1-x Cs x PbI 3-y Cl y cannot be precisely detected experimentally. In this paper, we calculate the stability, electronic structure and optical properties of Cs and Cl co-doped FA 1-x Cs x PbI 3-y Cl y by first nature principle in order to find the theoretically best performing chalcogenide FA 1-x Cs x PbI 3-y Cl y system. Results Experiments by Mark 19 et al showed that FAPbI 3 exhibits a cubic phase with lattice constant a = 6.3620Å and space group pm3m at 298 K. In this paper, the cubic phase FAPbI 3 model structure is optimized by taking a = 6.3620Å. The optimized lattice constants are a = 6.392Å, b = 6.473Å, c = 6.323Å,α = β = γ = 90°, because the symmetry of the structure is reduced due to the presence of organic molecules, so it becomes an orthorhombic crystal system after optimization. When calculating its energy band, the high symmetry K point is chosen according to the orthogonal crystal system. A 2×2×2 cubic phase FAPbI 3 supercell is shown in Fig. 1 (a). The calculated energy band structure is shown in Fig. 1 (b), and the calculated forbidden band width Eg = 1.40 eV, which is slightly smaller than the experimental value of 1.48 eV 20 . Figure.1(c) shows its total density of states and the density of fractional states. It can be seen that the conduction band bottom is mainly composed of Pb-6p orbitals and some I-5p orbital electrons hybridized, and the valence band top is mainly composed of I-5p orbital electrons. Charles et al 21 prepared Cs x FA 1-x PbI 3 at 300 K and obtained many stable cubic phases at x < 0.15. Cheng et al 22 prepared FAPbI 3-x Cl x (x = 0 ~ 0.4) planar heterojunction photovoltaic cells using a one-step solution method and found that the conversion efficiency did not increase linearly with increasing Cl content, the conversion efficiency was up to 17% at x = 0.2 and decreased with increasing Cl content, and the light absorption pattern also showed that the excess doping of chlorine shortens the light absorption range of the chalcogenide compound. So to keep the FA 1-x Cs x PbI 3-y Cl y system in cubic phase at room temperature, the amount of doped Cs should not exceed 15%, i.e., x should be less than 0.15. Because the excess Cl will shorten the light absorption range of the material, so for the proportion of doped Cl is between 0 and 0.4, i.e., y is between 0 and 0.4. Due to the limitation of calculation volume, this paper calculates the substitution of 1 of 8 FA ions by one Cs ion in 2×2×2 supercell FAPbI 3 (i.e., x = 0.125 < 0.15) and 1 to 9 of 24 I ions by Cl ions (i.e., y = 0.042, 0.083, 0.125, 0.167, 0.208, 0.250, 0.292, 0.333, 0.375) in terms of electronic structure and optical properties. To investigate the stability of the FA 1-x CsxPbI 3-y Cl y chalcogenide system, the Goldschmidt factor t of the system was calculated according to Eq. (1) and the individual ionic radii ( \({r}_{{FA}^{+}}\) =2.53 Å 23 , \({r}_{{Cs}^{+}}\) =1.67 Å, \({r}_{{Pb}_{2}^{+}}\) =1.2 Å, \({r}_{{I}^{-}}\) =2.20 Å, \({r}_{{Cl}^{-}}\) =1.81 Å), and it was found that all the Goldschmidt factors t were in the range 0.962~0.974, as shown in Figure.2(a), indicating that the system can maintain a stable cubic phase structure of chalcogenide. The variation of energy ∆E before and after Cs + and Cl - doping was further analyzed. As shown by the black dash in Fig. 2 (b), all ∆Es of the Cs + and Cl - co-doped FA 1-x Cs x PbI 3-y Cl y system are less than 0 eV, indicating that all crystal structures can remain stable. When x = 0.125 and y = 0.042, ∆E = -0.039 eV, corresponding to the most stable crystal structure of FA 0.875 Cs 0.125 PbI 2.958 Cl 0.042 . From the red dash in Figure.2(b), it can be seen that as the doping ratio becomes larger, the volume of the whole cell decreases. Because the radii of FA + , I - , Cs + and Cl - are 2.53Å, 2.20Å, 1.67Å and 1.81Å, respectively, the doping of Cs + and Cl - leads to a charge shift around Pb + and an increase in the chemical bonding energy between Cs-Pb, Cs-Cl, and Pb-Cl ions inside the crystal structure, resulting in a contraction and distortion of the octahedra, which further leads to a decrease in the lattice constant. The PBE generalized FA 1-x Cs x PbI 3-y Cl y system was used for energy band calculation, and it was found that when x = 0.125, y = 0.042, 0.125, 0.292, 0.333, the FA 1-x Cs x PbI 3-y Cl y system is the direct band gap, and the other doped ones are the indirect band gaps, and the indirect band gaps are not suitable to be used as light absorbing materials, which will increase the difficulty of interband electron leap, making the photoelectric conversion efficiency is greatly reduced. Therefore, we only discuss the electronic structure of the doped system with direct band gap. The average effective masses of the forbidden band width, electrons and holes of the FA 1-x Cs x PbI 3-y Cl y system when x = 0.125, y = 0.042, 0.125, 0.292, 0.333 were further calculated immediately. Table 1 Band gap and effective masses of electron and hole versus different Bromine content. Structure Band gap/eV \({m}_{e}^{\ast }\) / \({m}_{0}\) \({m}_{ℎ}^{\ast }\) / \({m}_{0}\) FAPbI3 1.40 3.84 0.52 FA0.875Cs0.125PbI2.958Cl0.042 1.73 1.56 0.85 FA0.875Cs0.125PbI2.875Cl0.125 1.77 1.61 0.88 FA0.875Cs0.125PbI2.708Cl0.292 1.97 2.22 1.17 FA0.875Cs0.125PbI2.667Cl0.333 2.00 2.31 1.45 As can be seen from Table 1 , the co-doped system has a larger forbidden band width compared to the pure FAPbI 3 system. From the experiments 24 , it is known that the forbidden band widths of the doped systems become larger mainly due to the doping of Cs ions. The average effective mass of electrons is reduced for all doped systems, which indicates that the doping of Cs ions and Cl ions increases the dispersion at the bottom of the conduction band, which facilitates the interband electron leap as well as the transport.while the average effective mass of holes in the doped system increases, indicating that the dispersion at the top of the valence band is reduced. It can be seen that the co-doping of Cs ions and Cl ions has a greater effect on the electron effective mass of the system, which leads to an increase in the hole effective mass but has a more obvious effect on the reduction of the electron effective mass. Overall, the co-doping of Cs ions and Cl ions is beneficial to the carrier leap and transport, which promotes the conversion efficiency of solar cells.When x = 0.125 and y = 0.042, the average effective masses of electrons and holes of the doped system are the smallest, 1.56m 0 and 0.85m 0 . The energy band diagrams in Fig. 3 show that the bottom of the conduction band and the top of the valence band are located at the same high symmetry point Γ, and the forbidden band widths are 1.73eV, 1.77eV, 1.97eV, and 2.00eV, respectively, which are all direct band gap semiconductors, indicating that the interband electron leap is favorable. Comparing the energy band diagrams before and after doping, it is still found that the dispersion at the bottom of the conduction band increases in the doped system compared with the undoped system, indicating that the effective mass of electrons in the energy band decreases, while the dispersion at the top of the valence band decreases in the doped system compared with the undoped system, indicating that the effective mass of holes in the energy band increases. To further analyze the electron occupation of molecular orbitals, the total and fractional densities of states of the corresponding systems are given in Fig. 4 . As known from Fig. 4 , the conduction band bottom of the undoped system consists of Pb-6p orbital and I-5p orbital electron hybridization, and the valence band top consists of I-5p orbital electrons. After doping with Cs + and Cl - , the Cl-3p orbital electrons interact with I-5p, Pb-6p and Cs-5p orbital electrons, causing the density of states peak of I-5p electrons at the top of the valence band to move toward the high energy region and the density of states peak of Pb-6p electrons at the bottom of the conduction band to move toward the low energy region, so that the forbidden band width becomes larger. The absorption coefficient is the characteristic that best reflects the optical properties of the material. The larger the absorption coefficient of the material used as the light absorbing layer of the solar cell, the more beneficial it is to improve the photoelectric conversion efficiency of the solar cell. As shown in Fig. 5 ,it is the calculated light absorption coefficient. It can be seen that in the wavelength range of 400nm-700nm,the FA 0.875 Cs 0.125 PbI 2.958 Cl 0.042 and FA 0.875 Cs 0.125 PbI 2.875 Cl 0.125 light absorption peaks have a significant red shift compared to the undoped system FAPbI 3 , where FA 0.875 Cs 0.125 PbI 2.875 Cl 0.125 has the highest absorbance intensity and possesses the highest light absorption coefficient. While the light absorption coefficients of FA 0.875 Cs 0.125 PbI 2.708 Cl 0.292 and FA 0.875 Cs 0.125 PbI 2.667 Cl 0.333 decreased a lot compared to the undoped system FAPbI3 and shortened the light absorption range visible. Although the proportion of doped ions is high, the effect on light absorption is not necessarily positive. Discussion In this paper, the geometry, electronic structure and optical properties of Cs + and Cl - co-doped FAPbI 3 to form FA 1-x Cs x PbI 3-y Cl y were investigated by first principle calculations, and firstly, all the doped systems were found to maintain a stable chalcogenide structure by the judgment of Goldschmidt factor, and further by analyzing the energy of the FAPbI 3 system before and after doping. The contrast shows that Cs + and Cl - doping makes the structure of chalcogenide system more stable, among which FA 0.875 Cs 0.125 PbI 2.958 Cl 0.042 is the most stable. The study of the energy band reveals that the forbidden band width of the system becomes larger as the amount of Cs + and Cl - doping increases. The increasing effect of dispersion at the bottom of the conduction band is stronger than the decreasing effect of dispersion at the top of the valence band, which is favorable to the carrier transport. The analysis of absorption spectra reveals that the light absorption coefficient of the system has a significant red-shift with a certain amount of Cl - doping, and the excess shortens the light absorption range of the material, and the light absorption of the doped system is best when x = 0.125 and y = 0.125. These findings help to provide theoretical guidance for the experimental preparation of efficient and stable solar cells. Discussion should be succinct and must not contain subheadings. Methods All calculations in this paper are performed in the VASP (Vienna ab initio Simulatioan Package) software package, where the first-nature principle is based on density generalized function theory, and the projective suffix plus plane wave pseudopotential is chosen to describe the interaction between the nucleus and the valence electron, and the generalized gradient approximation Perdew-Burke-Ernzerhof(PBE) generalized gradient approximation to describe the interaction-correlation energy of electron interactions. As we all know, when calculating the band gap of a semiconductor, the lack of spin-orbit coupling effect(SOC) usually overestimates the band gap, while the use of DFT(GGA) usually causes an underestimation of the band gap, and the two effects cancel each other and can yield results that are almost consistent with experimental data, so in this paper, the band gap of the system is calculated using the PBE generalized function. The k-point of the integral in the Brillouin zone is 4x4x4, 400eV is chosen as the plane wave truncation energy, and the total energy convergence criterion is 1x10-5eV/atom, and the maximum interaction force between atoms is 2x10-2eV/Å when structural optimization is performed. The structure of the chalcogenide crystal itself is one of the main factors affecting its stability, and the Goldschmidt factor t has been used to assess the stability of the ionic radius in relation to the chalcogenide structure since it was proposed 25 . Regarding the doped system FA 1-x Cs x PbI 3-y Cl y , the weights of the different types of atoms need to be measured, and the formula valid for calculating the Goldschmidt factor t is $${t}_{eff}=({r}_{eff1}+{r}_{eff2})/\sqrt{2}({r}_{{Pb}_{2}^{+}}+{r}_{eff2})$$ \({r}_{eff1}\) =(1-x) \({r}_{{FA}^{+}}+\) x \({r}_{{Cs}^{+}}\) \({r}_{eff2}\) =(1-y) \({r}_{{I}^{-}}+\text{y}{r}_{{Cl}^{-}}\) (1) \({r}_{eff1}\) is the effective radius of the mixture of FA and Cs, \({r}_{eff2}\) is the effective radius of the mixture of I and Cl, \({r}_{{Pb}_{2}^{+}}\) , \({r}_{{FA}^{+}}\) , \({r}_{{Cs}^{+}}\) , \({r}_{{I}^{-}}\) , \({r}_{{Cl}^{-}}\) is the radius of \({Pb}_{2}^{+}\) , \({FA}^{+}\) , \({Cs}^{+}\) , \({I}^{-}\) , \({Cl}^{-}\) respectively.For the Goldschmidt factor t, the crystals maintain a stable cubic phase structure of chalcocite when t is within 0.78 to 1.05. The effective mass of the photogenerated carriers is closely related to the second-order derivative of the energy band edge, and the effective mass of the carriers m* can be calculated by fitting the energy band edge according to the following equation: m*= \({\left(\frac{1}{ħ}\frac{{d}^{2}E}{d{K}^{2}}\right)}^{-1}\) (2) where E is the dispersion relation function obtained by fitting the energy band structure map and k is the inverse space vector, which is the approximate Planck constant. Declarations Data Availability Statement The data that support the findings of this study are available from the corresponding S-F.H., upon reasonable request. Author contributions statement The work was initiated by S-F.H. and H-X.L., with research ideas supplying by S-F.H., and H-X.L. during the work progresses. The simulation was performed by S-F.H. The data analyses were performed by S-F.H., J.L., J.T. This manuscript was written by S-F.H., and H-X.L. 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Advanced Energy Materials. 7. https://doi.org/10.1002/aenm.201601297 (2016). Weber, O. J., Charles, B., & Weller, M. T. Phase behaviour and composition in the formamidinium–methylammonium hybrid lead iodide perovskite solid solution. Journal of Materials Chemistry. 4, 15375-15382. https://doi.org/10.1039/C6TA06607K (2016). Liu, Na. et al. Theoretical study on the stability and photoelectric properties of APbI 3 perovskite. Acta Phys. Sin. 66, 057103. http://dx.doi.org/10.7498/aps.66.057103 (2017). Goldschmidt, V. M. Die Gesetze der Krystallochemie. Naturwissensenschaffen. 14, 477-485. https://doi.org/10.1007/BF01507527 (1926) Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2134630","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":142533604,"identity":"2d649a0e-25dd-4402-984b-191628291b8c","order_by":0,"name":"Shang-Fen Huang","email":"","orcid":"","institution":"Guilin University of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Shang-Fen","middleName":"","lastName":"Huang","suffix":""},{"id":142533605,"identity":"3fa78563-ceb7-4abc-b71b-5716fb711a59","order_by":1,"name":"Hai-Xia Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYBACfvmHjQ8kKv7Vz5c/fIA4LZINyc0GFmcOMG6cwZZAnBaDA+ltEpUtBxgbbvAYEOmyAwcbJG423GFmnN3z8cYbBjs53QYCOhgbGxsMZ+54xsYuc3az5RyGZGOzAwS0MDMzNiRLnmHmYWzI3SbNw3AgcRshLWxsjA2H/7YxSzAcyHlGnBYeHsbGBsm2wwYMN3LYiNMiIcHYzCBxJi3BsOeYseUcAyL8Yn+D/fkPiQqbBHn25oc33lTYyRHUgmol0VGDpIVUHaNgFIyCUTAiAABEWkdldVBixQAAAABJRU5ErkJggg==","orcid":"","institution":"Guilin University of Technology","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Hai-Xia","middleName":"","lastName":"Li","suffix":""},{"id":142533606,"identity":"8cfe3b41-0f4d-4563-b977-a0c0975485f9","order_by":2,"name":"Jun Liu","email":"","orcid":"","institution":"Guilin University of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Jun","middleName":"","lastName":"Liu","suffix":""},{"id":142533607,"identity":"8ba9edb2-16e7-4306-af9d-ddc4934fccc8","order_by":3,"name":"Jun Tao","email":"","orcid":"","institution":"Guilin University of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Jun","middleName":"","lastName":"Tao","suffix":""}],"badges":[],"createdAt":"2022-10-05 09:44:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2134630/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2134630/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":27639860,"identity":"a8fd7d45-6e21-4394-9c1a-2e3ec8205ca2","added_by":"auto","created_at":"2022-10-11 19:17:30","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":310925,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Pseudocubic crystal structures of α-FAPbI\u003csub\u003e3\u003c/sub\u003e with 2×2×2 supercell; (b) Band structure of α-FAPbI\u003csub\u003e3\u003c/sub\u003e calculated using 2×2×2 supercell; (c) DOS of α-FAPbI\u003csub\u003e3\u003c/sub\u003e calculated using 2×2×2 supercell.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2134630/v1/9cce9199cb7124e1f10022f7.jpeg"},{"id":27639858,"identity":"730fbf08-a86b-469e-9f0a-a20b1d2adc3d","added_by":"auto","created_at":"2022-10-11 19:17:30","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":122699,"visible":true,"origin":"","legend":"\u003cp\u003e(a)Goldschmidt factor t at different doping ratios,(b)Calculated total energy change ∆E and 2×2×2 supercell volume for different doping radios of Cs and Cl.\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2134630/v1/625d74d5fcef4bcab4fe2860.jpeg"},{"id":27640275,"identity":"1c0a3907-a278-498f-8781-7ef645067cf3","added_by":"auto","created_at":"2022-10-11 19:22:30","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":720748,"visible":true,"origin":"","legend":"\u003cp\u003eThe band structure of the (a) FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.958\u003c/sub\u003eCl\u003csub\u003e0.042\u003c/sub\u003e, (b) FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.875\u003c/sub\u003eCl\u003csub\u003e0.125\u003c/sub\u003e, (c) FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.708\u003c/sub\u003eCl\u003csub\u003e0.292\u003c/sub\u003e, (d) FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.667\u003c/sub\u003eCl\u003csub\u003e0.333\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2134630/v1/6069cb8d8356277562d48a33.jpeg"},{"id":27639859,"identity":"8888dc3e-d9e7-433f-9c28-97bb1f044e4a","added_by":"auto","created_at":"2022-10-11 19:17:30","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":434783,"visible":true,"origin":"","legend":"\u003cp\u003eThe total DOS and PDOS of the (a) FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.958\u003c/sub\u003eCl\u003csub\u003e0.042\u003c/sub\u003e, (b) FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.875\u003c/sub\u003eCl\u003csub\u003e0.125\u003c/sub\u003e, (c) FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.708\u003c/sub\u003eCl\u003csub\u003e0.292\u003c/sub\u003e, (d) FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.667\u003c/sub\u003eCl\u003csub\u003e0.333\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2134630/v1/97dc21bb490a9ff1440f971d.jpeg"},{"id":27639856,"identity":"4c2d088a-c8ea-4e7d-a157-e511bc99b2c7","added_by":"auto","created_at":"2022-10-11 19:17:30","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":20690,"visible":true,"origin":"","legend":"\u003cp\u003eAbsorption spectra of FA\u003csub\u003e1-x\u003c/sub\u003eCs\u003csub\u003ex\u003c/sub\u003ePbI\u003csub\u003e3-y\u003c/sub\u003eCl\u003csub\u003ey\u003c/sub\u003e\u003c/p\u003e","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-2134630/v1/4883ee538f6287e310e0342a.png"},{"id":28437586,"identity":"1b6fae75-031a-4349-9286-b87112ed31ea","added_by":"auto","created_at":"2022-10-31 06:29:38","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":606290,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2134630/v1/ce38af43-cc6a-48a9-b7d0-de3808a61098.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Study of the photovoltaic properties of Cs and Cl co-doped FAPbI 3 based on first principles","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe development of economy and science and technology cannot be supported by energy sources, which are mainly non-renewable energy sources, such as oil, coal and natural gas. As more and more energy is used, there are few reserves of energy left on the earth, and the environmental problems caused by the use of non-renewable energy sources have also caused concern in many countries, so they hope to vigorously develop renewable and clean energy sources such as solar energy\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3 CR4\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. The conversion efficiency of solar cells depends largely on the photoelectric conversion of their photoabsorption layer, and the special properties of chalcogenide materials, such as direct and tunable band gap, high lattice defect tolerance, high usage efficiency of photogenerated carriers and high light absorption coefficient, are particularly suitable for use as a photoabsorption layer in solar cells\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. The conversion efficiency of chalcogenide solar cells, first prepared in 2009 at 3.8%\u003csup\u003e8\u003c/sup\u003e has recently exceeded 25% after years of unremitting efforts\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. Although the conversion efficiency has made great progress, however,chalcogenide solar cells are prone to react with water vapor in the air, causing structural instability,so stability is also a difficult point to overcome for chalcogenide solar cells\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe crystal structure of chalcogenide materials as light absorbing layers is ABX\u003csub\u003e3\u003c/sub\u003e type, with methylamine ions (MA\u003csup\u003e+\u003c/sup\u003e=CH\u003csub\u003e3\u003c/sub\u003eNH\u003csub\u003e3\u003c/sub\u003e), formamidine ions (FA\u003csup\u003e+\u003c/sup\u003e=HC(NH\u003csub\u003e2\u003c/sub\u003e)\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e+\u003c/sup\u003e), cesium ions (Cs\u003csup\u003e+\u003c/sup\u003e), and rubidium ions (Rb\u003csup\u003e+\u003c/sup\u003e) usually in the A site, lead ions (Pb\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e+\u003c/sup\u003e) and tin ions (Sn\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e+\u003c/sup\u003e) usually in the B site, and chloride ions (Cl\u003csup\u003e-\u003c/sup\u003e), bromine ions (Br\u003csup\u003e-\u003c/sup\u003e) and iodide ions (I\u003csup\u003e-\u003c/sup\u003e) are usually in the X site. There are more reasons for their instability, such as external environment like temperature and humidity, and then intrinsic properties such as electron migration and ion migration, which are largely related to ion size\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. Methylamine ions (MA\u003csup\u003e+\u003c/sup\u003e), formamidine ions (FA\u003csup\u003e+\u003c/sup\u003e) and also chloride ions (Cl\u003csup\u003e-\u003c/sup\u003e) are large size ions with soft lattice, so they tend to react to temperature, humidity and also light, causing a decrease in stability\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e.The cubic phase band gap of FAPbI\u003csub\u003e3\u003c/sub\u003e is closer to the Shockley-Queisser limit of 1.34 eV than that of MAPbI\u003csub\u003e3\u003c/sub\u003e, which is more suitable for light absorbing materials, while FAPbI\u003csub\u003e3\u003c/sub\u003e is more likely to form the hexagonal phase at room temperature. To improve the performance of solar cells, researchers have tried to dope different sites of chalcogenide type crystals with different types of ions.MA\u003csub\u003ex\u003c/sub\u003eFA\u003csub\u003e1-x\u003c/sub\u003ePbI\u003csub\u003e3\u003c/sub\u003e was prepared by Pellet et al\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e using a mixture of methylamine and formamidine ions at site A. The hybrid system exhibited better photovoltaic properties than the undoped system. In addition, Eperon et al\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e found that the diffusion length of carriers in the MA\u003csub\u003ex\u003c/sub\u003eFA\u003csub\u003e1-x\u003c/sub\u003ePbI\u003csub\u003e3\u003c/sub\u003e system became longer, revealing the reason for the improved photoelectric conversion efficiency from the internal mechanism.Lee et al\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e use a small amount of Cs ions instead of FA ions, which makes the bond energy of the chemical bonds between ions larger and the internal defects smaller, and the thermal stability of the prepared Cs\u003csub\u003ex\u003c/sub\u003eFA\u003csub\u003e1\u0026ndash;x\u003c/sub\u003ePbI\u003csub\u003e3\u003c/sub\u003e system is improved.Hu et al\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e added 10% CsCl to FAPbI\u003csub\u003e3\u003c/sub\u003e was able to suppress the hexagonal phase of FAPbI\u003csub\u003e3\u003c/sub\u003e, making the cubic phase more stable and the system with the lowest density of film defects.\u003c/p\u003e \u003cp\u003eNumerous studies have shown that the simultaneous addition of Cs and Cl to FAPbI\u003csub\u003e3\u003c/sub\u003e leads to the formation of FA\u003csub\u003e1-x\u003c/sub\u003eCs\u003csub\u003ex\u003c/sub\u003ePbI\u003csub\u003e3-y\u003c/sub\u003eCl\u003csub\u003ey\u003c/sub\u003e with better optoelectronic properties and stability than FAPbI\u003csub\u003e3\u003c/sub\u003e, however, the components of FA\u003csub\u003e1-x\u003c/sub\u003eCs\u003csub\u003ex\u003c/sub\u003ePbI\u003csub\u003e3-y\u003c/sub\u003eCl\u003csub\u003ey\u003c/sub\u003e cannot be precisely detected experimentally. In this paper, we calculate the stability, electronic structure and optical properties of Cs and Cl co-doped FA\u003csub\u003e1-x\u003c/sub\u003eCs\u003csub\u003ex\u003c/sub\u003ePbI\u003csub\u003e3-y\u003c/sub\u003eCl\u003csub\u003ey\u003c/sub\u003e by first nature principle in order to find the theoretically best performing chalcogenide FA\u003csub\u003e1-x\u003c/sub\u003eCs\u003csub\u003ex\u003c/sub\u003ePbI\u003csub\u003e3-y\u003c/sub\u003eCl\u003csub\u003ey\u003c/sub\u003e system.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eExperiments by Mark\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e et al showed that FAPbI\u003csub\u003e3\u003c/sub\u003e exhibits a cubic phase with lattice constant a\u0026thinsp;=\u0026thinsp;6.3620\u0026Aring; and space group pm3m at 298 K. In this paper, the cubic phase FAPbI\u003csub\u003e3\u003c/sub\u003e model structure is optimized by taking a\u0026thinsp;=\u0026thinsp;6.3620\u0026Aring;. The optimized lattice constants are a\u0026thinsp;=\u0026thinsp;6.392\u0026Aring;, b\u0026thinsp;=\u0026thinsp;6.473\u0026Aring;, c\u0026thinsp;=\u0026thinsp;6.323\u0026Aring;,α\u0026thinsp;=\u0026thinsp;β\u0026thinsp;=\u0026thinsp;γ\u0026thinsp;=\u0026thinsp;90\u0026deg;, because the symmetry of the structure is reduced due to the presence of organic molecules, so it becomes an orthorhombic crystal system after optimization. When calculating its energy band, the high symmetry K point is chosen according to the orthogonal crystal system. A 2\u0026times;2\u0026times;2 cubic phase FAPbI\u003csub\u003e3\u003c/sub\u003e supercell is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a). The calculated energy band structure is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b), and the calculated forbidden band width Eg\u0026thinsp;=\u0026thinsp;1.40 eV, which is slightly smaller than the experimental value of 1.48 eV\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. Figure.1(c) shows its total density of states and the density of fractional states. It can be seen that the conduction band bottom is mainly composed of Pb-6p orbitals and some I-5p orbital electrons hybridized, and the valence band top is mainly composed of I-5p orbital electrons.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eCharles et al\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e prepared Cs\u003csub\u003ex\u003c/sub\u003eFA\u003csub\u003e1-x\u003c/sub\u003ePbI\u003csub\u003e3\u003c/sub\u003e at 300 K and obtained many stable cubic phases at x\u0026thinsp;\u0026lt;\u0026thinsp;0.15. Cheng et al\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e prepared FAPbI\u003csub\u003e3-x\u003c/sub\u003eCl\u003csub\u003ex\u003c/sub\u003e (x\u0026thinsp;=\u0026thinsp;0\u0026thinsp;~\u0026thinsp;0.4) planar heterojunction photovoltaic cells using a one-step solution method and found that the conversion efficiency did not increase linearly with increasing Cl content, the conversion efficiency was up to 17% at x\u0026thinsp;=\u0026thinsp;0.2 and decreased with increasing Cl content, and the light absorption pattern also showed that the excess doping of chlorine shortens the light absorption range of the chalcogenide compound. So to keep the FA\u003csub\u003e1-x\u003c/sub\u003eCs\u003csub\u003ex\u003c/sub\u003ePbI\u003csub\u003e3-y\u003c/sub\u003eCl\u003csub\u003ey\u003c/sub\u003e system in cubic phase at room temperature, the amount of doped Cs should not exceed 15%, i.e., x should be less than 0.15. Because the excess Cl will shorten the light absorption range of the material, so for the proportion of doped Cl is between 0 and 0.4, i.e., y is between 0 and 0.4. Due to the limitation of calculation volume, this paper calculates the substitution of 1 of 8 FA ions by one Cs ion in 2\u0026times;2\u0026times;2 supercell FAPbI\u003csub\u003e3\u003c/sub\u003e (i.e., x\u0026thinsp;=\u0026thinsp;0.125\u0026thinsp;\u0026lt;\u0026thinsp;0.15) and 1 to 9 of 24 I ions by Cl ions (i.e., y\u0026thinsp;=\u0026thinsp;0.042, 0.083, 0.125, 0.167, 0.208, 0.250, 0.292, 0.333, 0.375) in terms of electronic structure and optical properties.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo investigate the stability of the FA\u003csub\u003e1-x\u003c/sub\u003eCsxPbI\u003csub\u003e3-y\u003c/sub\u003eCl\u003csub\u003ey\u003c/sub\u003e chalcogenide system, the Goldschmidt factor t of the system was calculated according to Eq.\u0026nbsp;(1) and the individual ionic radii (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{{FA}^{+}}\\)\u003c/span\u003e\u003c/span\u003e=2.53 \u0026Aring;\u003csup\u003e23\u003c/sup\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{{Cs}^{+}}\\)\u003c/span\u003e\u003c/span\u003e=1.67 \u0026Aring;, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{{Pb}_{2}^{+}}\\)\u003c/span\u003e\u003c/span\u003e=1.2 \u0026Aring;,\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{{I}^{-}}\\)\u003c/span\u003e\u003c/span\u003e=2.20 \u0026Aring;, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{{Cl}^{-}}\\)\u003c/span\u003e\u003c/span\u003e=1.81 \u0026Aring;), and it was found that all the Goldschmidt factors t were in the range 0.962~0.974, as shown in Figure.2(a), indicating that the system can maintain a stable cubic phase structure of chalcogenide. The variation of energy ∆E before and after Cs\u003csup\u003e+\u003c/sup\u003e and Cl\u003csup\u003e-\u003c/sup\u003e doping was further analyzed. As shown by the black dash in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b), all ∆Es of the Cs\u003csup\u003e+\u003c/sup\u003e and Cl\u003csup\u003e-\u003c/sup\u003e co-doped FA\u003csub\u003e1-x\u003c/sub\u003eCs\u003csub\u003ex\u003c/sub\u003ePbI\u003csub\u003e3-y\u003c/sub\u003eCl\u003csub\u003ey\u003c/sub\u003e system are less than 0 eV, indicating that all crystal structures can remain stable. When x\u0026thinsp;=\u0026thinsp;0.125 and y\u0026thinsp;=\u0026thinsp;0.042, ∆E = -0.039 eV, corresponding to the most stable crystal structure of FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.958\u003c/sub\u003eCl\u003csub\u003e0.042\u003c/sub\u003e. From the red dash in Figure.2(b), it can be seen that as the doping ratio becomes larger, the volume of the whole cell decreases. Because the radii of FA\u003csup\u003e+\u003c/sup\u003e, I\u003csup\u003e-\u003c/sup\u003e, Cs\u003csup\u003e+\u003c/sup\u003e and Cl\u003csup\u003e-\u003c/sup\u003e are 2.53\u0026Aring;, 2.20\u0026Aring;, 1.67\u0026Aring; and 1.81\u0026Aring;, respectively, the doping of Cs\u003csup\u003e+\u003c/sup\u003e and Cl\u003csup\u003e-\u003c/sup\u003e leads to a charge shift around Pb\u003csup\u003e+\u003c/sup\u003e and an increase in the chemical bonding energy between Cs-Pb, Cs-Cl, and Pb-Cl ions inside the crystal structure, resulting in a contraction and distortion of the octahedra, which further leads to a decrease in the lattice constant.\u003c/p\u003e \u003cp\u003eThe PBE generalized FA\u003csub\u003e1-x\u003c/sub\u003eCs\u003csub\u003ex\u003c/sub\u003ePbI\u003csub\u003e3-y\u003c/sub\u003eCl\u003csub\u003ey\u003c/sub\u003e system was used for energy band calculation, and it was found that when x\u0026thinsp;=\u0026thinsp;0.125, y\u0026thinsp;=\u0026thinsp;0.042, 0.125, 0.292, 0.333, the FA\u003csub\u003e1-x\u003c/sub\u003eCs\u003csub\u003ex\u003c/sub\u003ePbI\u003csub\u003e3-y\u003c/sub\u003eCl\u003csub\u003ey\u003c/sub\u003e system is the direct band gap, and the other doped ones are the indirect band gaps, and the indirect band gaps are not suitable to be used as light absorbing materials, which will increase the difficulty of interband electron leap, making the photoelectric conversion efficiency is greatly reduced. Therefore, we only discuss the electronic structure of the doped system with direct band gap. The average effective masses of the forbidden band width, electrons and holes of the FA\u003csub\u003e1-x\u003c/sub\u003eCs\u003csub\u003ex\u003c/sub\u003ePbI\u003csub\u003e3-y\u003c/sub\u003eCl\u003csub\u003ey\u003c/sub\u003e system when x\u0026thinsp;=\u0026thinsp;0.125, y\u0026thinsp;=\u0026thinsp;0.042, 0.125, 0.292, 0.333 were further calculated immediately.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBand gap and effective masses of electron and hole versus different Bromine content.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStructure\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBand gap/eV\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({m}_{e}^{\\ast }\\)\u003c/span\u003e\u003c/span\u003e/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({m}_{0}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({m}_{ℎ}^{\\ast }\\)\u003c/span\u003e\u003c/span\u003e/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({m}_{0}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFAPbI3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFA0.875Cs0.125PbI2.958Cl0.042\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFA0.875Cs0.125PbI2.875Cl0.125\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.88\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFA0.875Cs0.125PbI2.708Cl0.292\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFA0.875Cs0.125PbI2.667Cl0.333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs can be seen from Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the co-doped system has a larger forbidden band width compared to the pure FAPbI\u003csub\u003e3\u003c/sub\u003e system. From the experiments\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e, it is known that the forbidden band widths of the doped systems become larger mainly due to the doping of Cs ions. The average effective mass of electrons is reduced for all doped systems, which indicates that the doping of Cs ions and Cl ions increases the dispersion at the bottom of the conduction band, which facilitates the interband electron leap as well as the transport.while the average effective mass of holes in the doped system increases, indicating that the dispersion at the top of the valence band is reduced. It can be seen that the co-doping of Cs ions and Cl ions has a greater effect on the electron effective mass of the system, which leads to an increase in the hole effective mass but has a more obvious effect on the reduction of the electron effective mass. Overall, the co-doping of Cs ions and Cl ions is beneficial to the carrier leap and transport, which promotes the conversion efficiency of solar cells.When x\u0026thinsp;=\u0026thinsp;0.125 and y\u0026thinsp;=\u0026thinsp;0.042, the average effective masses of electrons and holes of the doped system are the smallest, 1.56m\u003csub\u003e0\u003c/sub\u003e and 0.85m\u003csub\u003e0\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003eThe energy band diagrams in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e show that the bottom of the conduction band and the top of the valence band are located at the same high symmetry point Γ, and the forbidden band widths are 1.73eV, 1.77eV, 1.97eV, and 2.00eV, respectively, which are all direct band gap semiconductors, indicating that the interband electron leap is favorable. Comparing the energy band diagrams before and after doping, it is still found that the dispersion at the bottom of the conduction band increases in the doped system compared with the undoped system, indicating that the effective mass of electrons in the energy band decreases, while the dispersion at the top of the valence band decreases in the doped system compared with the undoped system, indicating that the effective mass of holes in the energy band increases.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo further analyze the electron occupation of molecular orbitals, the total and fractional densities of states of the corresponding systems are given in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. As known from Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the conduction band bottom of the undoped system consists of Pb-6p orbital and I-5p orbital electron hybridization, and the valence band top consists of I-5p orbital electrons. After doping with Cs\u003csup\u003e+\u003c/sup\u003e and Cl\u003csup\u003e-\u003c/sup\u003e, the Cl-3p orbital electrons interact with I-5p, Pb-6p and Cs-5p orbital electrons, causing the density of states peak of I-5p electrons at the top of the valence band to move toward the high energy region and the density of states peak of Pb-6p electrons at the bottom of the conduction band to move toward the low energy region, so that the forbidden band width becomes larger.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe absorption coefficient is the characteristic that best reflects the optical properties of the material. The larger the absorption coefficient of the material used as the light absorbing layer of the solar cell, the more beneficial it is to improve the photoelectric conversion efficiency of the solar cell. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e,it is the calculated light absorption coefficient. It can be seen that in the wavelength range of 400nm-700nm,the FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.958\u003c/sub\u003eCl\u003csub\u003e0.042\u003c/sub\u003e and FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.875\u003c/sub\u003eCl\u003csub\u003e0.125\u003c/sub\u003e light absorption peaks have a significant red shift compared to the undoped system FAPbI\u003csub\u003e3\u003c/sub\u003e, where FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.875\u003c/sub\u003eCl\u003csub\u003e0.125\u003c/sub\u003e has the highest absorbance intensity and possesses the highest light absorption coefficient. While the light absorption coefficients of FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.708\u003c/sub\u003eCl\u003csub\u003e0.292\u003c/sub\u003e and FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.667\u003c/sub\u003eCl\u003csub\u003e0.333\u003c/sub\u003e decreased a lot compared to the undoped system FAPbI3 and shortened the light absorption range visible. Although the proportion of doped ions is high, the effect on light absorption is not necessarily positive.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eIn this paper, the geometry, electronic structure and optical properties of Cs\u003csup\u003e+\u003c/sup\u003e and Cl\u003csup\u003e-\u003c/sup\u003e co-doped FAPbI\u003csub\u003e3\u003c/sub\u003e to form FA\u003csub\u003e1-x\u003c/sub\u003eCs\u003csub\u003ex\u003c/sub\u003ePbI\u003csub\u003e3-y\u003c/sub\u003eCl\u003csub\u003ey\u003c/sub\u003e were investigated by first principle calculations, and firstly, all the doped systems were found to maintain a stable chalcogenide structure by the judgment of Goldschmidt factor, and further by analyzing the energy of the FAPbI\u003csub\u003e3\u003c/sub\u003e system before and after doping. The contrast shows that Cs\u003csup\u003e+\u003c/sup\u003e and Cl\u003csup\u003e-\u003c/sup\u003e doping makes the structure of chalcogenide system more stable, among which FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.958\u003c/sub\u003eCl\u003csub\u003e0.042\u003c/sub\u003e is the most stable. The study of the energy band reveals that the forbidden band width of the system becomes larger as the amount of Cs\u003csup\u003e+\u003c/sup\u003e and Cl\u003csup\u003e-\u003c/sup\u003e doping increases. The increasing effect of dispersion at the bottom of the conduction band is stronger than the decreasing effect of dispersion at the top of the valence band, which is favorable to the carrier transport. The analysis of absorption spectra reveals that the light absorption coefficient of the system has a significant red-shift with a certain amount of Cl\u003csup\u003e-\u003c/sup\u003e doping, and the excess shortens the light absorption range of the material, and the light absorption of the doped system is best when x\u0026thinsp;=\u0026thinsp;0.125 and y\u0026thinsp;=\u0026thinsp;0.125. These findings help to provide theoretical guidance for the experimental preparation of efficient and stable solar cells. Discussion should be succinct and must not contain subheadings.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eAll calculations in this paper are performed in the VASP (Vienna ab initio Simulatioan Package) software package, where the first-nature principle is based on density generalized function theory, and the projective suffix plus plane wave pseudopotential is chosen to describe the interaction between the nucleus and the valence electron, and the generalized gradient approximation Perdew-Burke-Ernzerhof(PBE) generalized gradient approximation to describe the interaction-correlation energy of electron interactions. As we all know, when calculating the band gap of a semiconductor, the lack of spin-orbit coupling effect(SOC) usually overestimates the band gap, while the use of DFT(GGA) usually causes an underestimation of the band gap, and the two effects cancel each other and can yield results that are almost consistent with experimental data, so in this paper, the band gap of the system is calculated using the PBE generalized function. The k-point of the integral in the Brillouin zone is 4x4x4, 400eV is chosen as the plane wave truncation energy, and the total energy convergence criterion is 1x10-5eV/atom, and the maximum interaction force between atoms is 2x10-2eV/\u0026Aring; when structural optimization is performed.\u003c/p\u003e \u003cp\u003eThe structure of the chalcogenide crystal itself is one of the main factors affecting its stability, and the Goldschmidt factor t has been used to assess the stability of the ionic radius in relation to the chalcogenide structure since it was proposed\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. Regarding the doped system FA\u003csub\u003e1-x\u003c/sub\u003eCs\u003csub\u003ex\u003c/sub\u003ePbI\u003csub\u003e3-y\u003c/sub\u003eCl\u003csub\u003ey\u003c/sub\u003e, the weights of the different types of atoms need to be measured, and the formula valid for calculating the Goldschmidt factor t is\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$${t}_{eff}=({r}_{eff1}+{r}_{eff2})/\\sqrt{2}({r}_{{Pb}_{2}^{+}}+{r}_{eff2})$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({r}_{eff1}\\)\u003c/span\u003e \u003c/span\u003e=(1-x)\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{{FA}^{+}}+\\)\u003c/span\u003e\u003c/span\u003ex\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{{Cs}^{+}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({r}_{eff2}\\)\u003c/span\u003e \u003c/span\u003e=(1-y)\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{{I}^{-}}+\\text{y}{r}_{{Cl}^{-}}\\)\u003c/span\u003e\u003c/span\u003e (1)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({r}_{eff1}\\)\u003c/span\u003e \u003c/span\u003e is the effective radius of the mixture of FA and Cs, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{eff2}\\)\u003c/span\u003e\u003c/span\u003e is the effective radius of the mixture of I and Cl, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{{Pb}_{2}^{+}}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{{FA}^{+}}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{{Cs}^{+}}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{{I}^{-}}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{{Cl}^{-}}\\)\u003c/span\u003e\u003c/span\u003e is the radius of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Pb}_{2}^{+}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({FA}^{+}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Cs}^{+}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I}^{-}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Cl}^{-}\\)\u003c/span\u003e\u003c/span\u003erespectively.For the Goldschmidt factor t, the crystals maintain a stable cubic phase structure of chalcocite when t is within 0.78 to 1.05.\u003c/p\u003e \u003cp\u003eThe effective mass of the photogenerated carriers is closely related to the second-order derivative of the energy band edge, and the effective mass of the carriers m* can be calculated by fitting the energy band edge according to the following equation:\u003c/p\u003e \u003cp\u003em*=\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\left(\\frac{1}{ħ}\\frac{{d}^{2}E}{d{K}^{2}}\\right)}^{-1}\\)\u003c/span\u003e\u003c/span\u003e (2)\u003c/p\u003e \u003cp\u003ewhere E is the dispersion relation function obtained by fitting the energy band structure map and k is the inverse space vector, which is the approximate Planck constant.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eData Availability Statement\u0026nbsp;\u003c/h2\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding S-F.H., upon reasonable request.\u003c/p\u003e\n\u003ch2\u003eAuthor contributions statement\u003c/h2\u003e\n\u003cp\u003eThe work was initiated by S-F.H. and H-X.L., with research ideas supplying by S-F.H., and H-X.L. during the work progresses. The simulation was performed by S-F.H. The data analyses were performed by S-F.H., J.L., J.T. \u0026nbsp;This manuscript was written by S-F.H., and H-X.L. The results and their interpretation were collectively discussed by all authors.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003eCompeting interests\u003c/h2\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003eAdditional Information\u003c/h2\u003e\n\u003cp\u003ePublisher\u0026apos;s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional afliations.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eMiles, R.W., Hynes, K.M., \u0026amp; Forbes, I. Photovoltaic solar cells: An overview of state-of-the-art cell development and environmental issues. Progress in Crystal Growth and Characterization of Materials. 51, 1-42. \u0026nbsp; \u0026nbsp; https://doi.org/10.1016/j.pcrysgrow.2005.10.002 (2005).\u003c/li\u003e\n \u003cli\u003eMishima, T., Taguchi, M., Sakata, H., \u0026amp; Maruyama, E. Development status of high-efficiency HIT solar cells. Solar Energy Materials and Solar Cells. 95, 18-21. https://doi.org/10.1016/j.solmat.2010.04.030 (2010).\u003c/li\u003e\n \u003cli\u003eLuan, L. J., He, Y., Wang, T., Liu, Z. W. First-principles study of interface interaction and photoelectric properties of the solar cell heterojunction CdS/CdMnTe. Acta Physica Sinica. 70, 166302, doi:10.7498/aps.70.20210268 (2021).\u003c/li\u003e\n \u003cli\u003eY, M. et al. Energy, exergy, economic and environmental (4E) analysis of a novel power/refrigeration cascade system to recover low-grade waste heat at 90\u0026ndash;150\u0026deg;C[J]. Journal of Cleaner Production. 363, 132353. https://doi.org/10.1016/j.jclepro.2022.132353 (2022).\u003c/li\u003e\n \u003cli\u003eJu, F., Ke, M. The Spatial Spillover Effects of Environmental Regulation and Regional Energy Efficiency and Their Interactions under Local Government Competition in China. Sustainability. 14, 8753. \u0026nbsp;https://doi.org/10.3390/su14148753 (2022).\u003c/li\u003e\n \u003cli\u003eWang, S., Yang, F., Zhu, J. et al. Growth of metal halide perovskite materials. Sci. China Mater. 63, 1438\u0026ndash;1463. https://doi.org/10.1007/s40843-020-1300-2 (2020).\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eLIU, Y., DENG, Z. Fast Synthesis of Highly Luminescent Two-dimensional Tin-halide Perovskites by Anti-solvent Method. Chem. J. Chinese Universities. 42, 3774. https://doi.org/10.7503/cjcu20210358 (2021).\u003c/li\u003e\n \u003cli\u003eKojima, A., Teshima, K.,Shirai Y., \u0026amp; Miyasaka, T. Organometal halide perovskites asvisible-light sensitizers for photovoltaic cells[J].Journal of the American Chemical Society. 131, 6050-6051. https://doi.org/10.1021/ja809598r (2009).\u003c/li\u003e\n \u003cli\u003eNREL,National Renewable Energy Laboratory.Best Research-Cell Efficiencies,2021.\u003c/li\u003e\n \u003cli\u003eHonglei, W. et al. Two-Dimensional Perovskites and Their Applications on Optoelectronic Devices[J]. Progress in Chemistry. 29, 859-869. https://doi.org/10.7536/PC170512 (2017).\u003c/li\u003e\n \u003cli\u003eYao, X., Ding, Y-L., Zhang, X-D., Zhao, Y. A review of the perovskite solar cells. Acta Phys. Sin. 64, 038805. https://doi.org/10.7498/aps.64.038805 (2015).\u003c/li\u003e\n \u003cli\u003eZhang, Y., Zhou, H-P. Intrinsic stability of organic-inorganic hybrid perovskite. Acta Phys. Sin. 68, 158804. https://doi.org/10.7498/aps.68.20190343 (2019).\u003c/li\u003e\n \u003cli\u003eXiaohui, M. et al. All-Inorganic Perovskite Solar Cells: Status and Future[J]. Progress in Chemistry. 32, \u0026nbsp;1608-1632. https://doi.org/10.7536/PC200313 (2020).\u003c/li\u003e\n \u003cli\u003eHuidong, L., Hongjing, H., Jie, L. Simulation and property calculation for FA\u003csub\u003e1\u0026ndash;x\u003c/sub\u003eCs\u003csub\u003ex\u003c/sub\u003ePbI\u003csub\u003e3\u0026ndash;y\u003c/sub\u003eBr\u003csub\u003ey\u003c/sub\u003e:Structures and optoelectronical properties[J]. Acta Physica Sinica. 70, 199-207. https://doi.org/10.7498/aps.70.20201387 (2021).\u003c/li\u003e\n \u003cli\u003ePellet, N. et al. Mixed-organic-cation perovskite photovoltaics for enhanced solar-light harvesting. Angew Chem Int Ed Engl. 53, 3151-7. https://doi.org/10.1002/anie.201309361 (2014).\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eEperon, G. E. et al. Formamidinium Lead Trihalide: A Broadly Tunable Perovskite for Efficient Planar Heterojunction Solar Cells. Energy \u0026amp; Environmental Science. 7, 982-988. https://doi.org/10.1039/c3ee43822h (2014).\u003c/li\u003e\n \u003cli\u003eLee, J-W. et al. Formamidinium and Cesium Hybridization for Photo- and Moisture-Stable Perovskite Solar Cell. Advanced Energy Materials. 5. https://doi.org/10.1002/aenm.201501310 (2015).\u003c/li\u003e\n \u003cli\u003eHuyen, T. et al. Unraveling the influence of CsCl/MACl on the formation of nanotwins, stacking faults and cubic supercell structure in FA-based perovskite solar cells. Nano Energy. 87, 106226. https://doi.org/10.1016/j.nanoen.2021.106226 (2021).\u003c/li\u003e\n \u003cli\u003eWeller, M. T., Weber, O. J., Frost, J. M., \u0026amp; Walsh, A. Cubic Perovskite Structure of Black Formamidinium Lead Iodide, \u0026alpha;-[HC(NH\u003csub\u003e2\u003c/sub\u003e)\u003csub\u003e2\u003c/sub\u003e]PbI\u003csub\u003e3\u003c/sub\u003e, at 298K. Journal of Physical Chemistry Letters. 6, 3209-3212. https://doi.org/10.1021/acs.jpclett.5b01432 (2015).\u003c/li\u003e\n \u003cli\u003eStoumpos, C. C., Malliakas, C. D., Kanatzidis, M. G. Semiconducting tin and lead iodide perovskites with organic cations: phase transitions, high mobilities, and near-infrared photoluminescent properties. Inorg Chem. 52, 9019-9038. https://doi.org/10.1021/ic401215x (2013).\u003c/li\u003e\n \u003cli\u003eCharles, B. et al. Phase Behavior and Substitution Limit of Mixed Cesium-Formamidinium Lead TriIodide Perovskites. Chemistry of Materials. 32, 2282-2291. https://doi.org/10.1021/acs.chemmater.9b04032 (2020).\u003c/li\u003e\n \u003cli\u003eMu, C., Pan, J., Feng, S., Li, Q., \u0026amp; Xu, D. Quantitative Doping of Chlorine in Formamidinium Lead Trihalide (FAPbI\u003csub\u003e3\u0026minus;x\u003c/sub\u003eCl\u003csub\u003ex\u003c/sub\u003e) for Planar Heterojunction Perovskite Solar Cells. Advanced Energy Materials. 7. https://doi.org/10.1002/aenm.201601297 (2016).\u003c/li\u003e\n \u003cli\u003eWeber, O. J., Charles, B., \u0026amp; Weller, M. T. Phase behaviour and composition in the formamidinium\u0026ndash;methylammonium hybrid lead iodide perovskite solid solution. Journal of Materials Chemistry. 4, 15375-15382. https://doi.org/10.1039/C6TA06607K (2016).\u003c/li\u003e\n \u003cli\u003eLiu, Na. et al. Theoretical study on the stability and photoelectric properties of APbI\u003csub\u003e3\u003c/sub\u003e perovskite. Acta Phys. Sin. 66, 057103. http://dx.doi.org/10.7498/aps.66.057103 (2017).\u003c/li\u003e\n \u003cli\u003eGoldschmidt, V. M. Die Gesetze der Krystallochemie. Naturwissensenschaffen. 14, 477-485. https://doi.org/10.1007/BF01507527 (1926)\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-2134630/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2134630/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFormamidine lead iodide chalcogenide (FAPbI\u003csub\u003e3\u003c/sub\u003e) is often used as a light-absorbing layer in solar cells to alleviate the energy crisis because of its own good photovoltaic properties.however, the lack of stability is also an obstacle to the current development. It has been found that doping with different kinds of elements at different sites can enhance its stability and improve the photoelectric conversion efficiency of solar cells. In this paper, the geometry, electronic structure and optical properties of FA\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eCs\u003csub\u003ex\u003c/sub\u003ePbI\u003csub\u003e3\u0026minus;y\u003c/sub\u003eCl\u003csub\u003ey\u003c/sub\u003e were calculated using Cs and Cl co-doped with FAPbI\u003csub\u003e3\u003c/sub\u003e using the first nature principle. The analysis revealed that the Goldschmidt factors of the doped system were between 0.962 and 0.974, indicating that the system could maintain a stable chalcogenide structure, and the doped system had lower energy and more stable structure. By calculating the energy bands, it is found that the doped ions have a more pronounced effect on the increase of the dispersion at the bottom of the conduction band than the decrease of the dispersion at the top of the valence band of the system, and the reduction of the effective mass of carriers is more favorable for transport. As for the optical properties, the right amount of doping is favorable to the improvement of light absorption, while the excess doping shortens the light absorption range and weakens the light absorption effect, in which FA\u003csub\u003e0.875\u003c/sub\u003eCs\u003csub\u003e0.125\u003c/sub\u003ePbI\u003csub\u003e2.958\u003c/sub\u003eCl\u003csub\u003e0.125\u003c/sub\u003e has the largest light absorption coefficient. It is shown that the photoelectric properties of chalcogenide FAPbI\u003csub\u003e3\u003c/sub\u003e can be effectively modulated by the co-doping of Cs and Cl, which can provide theoretical reference for the precise preparation of more efficient solar cells experimentally.\u003c/p\u003e","manuscriptTitle":"Study of the photovoltaic properties of Cs and Cl co-doped FAPbI 3 based on first principles","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-10-11 19:17:28","doi":"10.21203/rs.3.rs-2134630/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ed673766-274f-4161-85f8-d213ed8ec061","owner":[],"postedDate":"October 11th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2022-10-31T06:29:31+00:00","versionOfRecord":[],"versionCreatedAt":"2022-10-11 19:17:28","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2134630","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2134630","identity":"rs-2134630","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}