1. IntroductionThe limited supply of fossil fuels is bound to come to an end, and using solar cells to turn the energy of sunlight into electricity is expected to become a main renewable energy source.[1–3] In the first generation of solar cells, single crystal silicon was used as the main raw material.[4] The disadvantage is that the consumption of silicon material is large, the production cost is high, the conversion efficiency is close to the theoretical limit, and the room for further development is limited. The second-generation solar cells are mainly based on thin-film solar cells, which greatly reduce production costs and save silicon material.[5–8] Large-area panels can also be made if needed, but the conversion efficiency is low and the stability is poor.
The dye-sensitized tandem solar cells, as third-generation solar cells, have the advantages of simple production process and abundant source of battery materials. Therefore, they can be a trend for future development.[9–13] Since the first application in 2009, perovskite solar cells (PSCs) have developed rapidly in just a few years.[14] Up to now, the reported power conversion efficiency (PCE) of the perovskite-based solar cells is over 20%.[15,16] Designated as perovskite is a material that has a general structure of ABX3, where A and B are two cations and X is an anion that bonds to both.[17] Koliogiorgos et al.[18] discussed the hybrid halide perovskites MABX3 (MA = methylammonium) replaced by MAGeCl3 and MAGeBr3; reference[19] reported that the Sr replacement for Pb in MAPbI3 leads to an energy gap doubling the initial one and thus cannot serve as photovoltaic (PV) applications, and they expected to find lead-free perovskites that can be used in energy technology such as solar cells and optoelectronics. Metal halide perovskites FAPbX3 (FA = formamidinium) possess an efficiency of 20.3% for solar cells.[20] And FAPbI3 has aroused intensive interest in its diverse optoelectronic applications. However, there is no research on the analysis of its working mechanism based on the band theory and spectral absorption theory. Here in this work, we calculate the energy band structure, density of states (DOS), and partial DOS (PDOS) of the hydrazine-iodide lead halide by the first-principles. Then, we theoretically analyze a design scheme for perovskite solar cell materials, published in Ref. [20], with the photoelectric conversion efficiency that can reach 20.3%, and explore the energy band structure, lattice constant, light absorption efficiency, etc., after the Ca, Zn, Ge Sr, Sn, and Ta atoms have replaced lead. The relevant factors affecting the photoelectric conversion efficiency are analyzed, and also we use non-toxic elements to replace lead in FAPbI3 without affecting its photoelectric conversion efficiency.
2. Results and discussionThe calculations are performed within the framework of the density functional theory (DFT). With this theory we investigate FAPbI3 structure crystal of the organic–inorganic perovskites and the doping crystal of it. The band structure and optical properties are calculated with the cambridge sequential total energy package (CASTEP)[21] code using the Perdew–Burke–Ernzerh of (PBE) version of the generalized gradient approximation (GGA).[22] The exchange–correlation functional is norm conserving pseudopotential with a cutoff energy of 310 eV. All the geometries of the unit cell of these materials with ultrasoft pseudopotentials and the atomic positions and lattice parameters are relaxed until atomic forces are converged to a value smaller than 10−5 eV/atom. We build the FAPbI3 crystal structure and obtain the energy band structure, DOS, and PDOS of it; then we replace the Pb atom with Ca, Zn, Ge, Sr, Sn, and Ta atoms separately, and use the functional hybrid HSE06 to obtain its reflection spectrum and absorption spectrum.
Also, we build the doped supercells with 2×2×1 mesh for FA0.75Cs0.25Sn0.5Pb0.5I3 cells, and 3×2×1 mesh for FA0.83Cs0.17Pb(I0.5Br0.53 cells. The plane-wave cutoff energy for wave function is taken to be 310 eV. The Gaussian smearing is well optimized under sufficient convergence criterion (0.05 eV/Å) for all the calculations. With the above calculation results, we can analyze the mechanism of achieving a very high photoelectric conversion efficiency for FA0.75Cs0.25Sn0.5Pb0.5I3 and FA0.75Cs0.25Sn0.25Ge0.75I3.
2.1. Model of FAPbI3
Recently, many researchers[23–27] have paid attention to the cubic structure model for FAPbI3 with space group symmetry, and they uses this structure of perovskite material to increase the photoelectric conversion efficiency of solar cells by 22%. In Ref. [28], a variety of lattice constants and energy band gaps of MAGeCl3 and MAGeBr3 were reported, the mixed hybrid halide perovskites were discussed, and the values of the energy gap were obtained although no simplified pattern exists. The formamidinium lead iodide (FAPbI3) has the potential to achieve higher performance than the established perovskite solar cells like methylammonium lead iodide (MAPbI3),[27] while maintaining a higher stability. In this work, we focus on the cubic FAPbI3,[29] and the hybrid halide perovskites crystallized into a cubic structure are shown in Fig. 1.
We create the cubic FAPbI3 model based on the previously reported results[20] with the crystal of FAPbI3 that has a=6.41 Å, b=6.34 Å, c=6.26 Å, α=90°, β=90°, γ=89.9°, and the space group of Pmm2. The atomic position of the FA cation within this cubic framework is confirmed by total energy calculations. As shown in Fig. 2, the band gap and DOS of FAPbI3 are calculated by the GGA method, presenting an underestimation relating to the available experimental value 1.344 eV, which is in agreement with the result in Ref. [29]. And its corresponding absorption edge reaches 923 nm, which is superior to that of MAPbI3 (1.59 eV) in the sense of serving as a light harvester.
The constituent elements and groups are FA, Pb, and I. We analyze their PDOS, as shown in Fig. 3, which contributes to the DOS that contributes to the s and p electrons of iodine, and s, p, and d electrons of lead atoms. The covalent bond of FA is strong, and the electron density of I exceeds the Fermi level, showing that the metallity is stronger. Because lead is a metal, its s and p orbital electrons all cross the Fermi level, which conforms to reality. It can also be seen that the FA group has a greater influence on the energy band distribution of the perovskite.
In this subsection, we also construct the approximate area of the solar spectrum[30] and introduce the calculated absorption spectra in the same coordinate system. From the point of view of the light absorption spectrum, it can be seen from Fig. 4 that most of the absorption peaks are very few distributed in the visible region when the crystal FAPbI3 is undoped. Most of them are distributed in ultraviolet and other areas.
2.2. Mixed halide perovskitesIn order to study the effect of crystal doping on its photoelectric conversion performance, we build a supercell crystal with 2×2×1 mesh in this subsection. And then we discuss FAPbI3 where FA is replaced with Cs atom at 25%, 50%, 75%, and 100%, and obtain the band gap and its absorption. The crystal structure of FA0.75Cs0.25PbI3 is shown in Fig. 5.
Comparing the band structure and optical absorption spectra of Figs. 6–10, we find that as the doping ratio increases, the bandgap first increases, and when the ratio exceeds 50%, the bandgap becomes significantly smaller. When the doping is 100%, it shows a distinct metal property. One of the spectral lines spans the Fermi level due to doping atoms. We know that the light radiated from the sun to the earth surface accounts for about 50% in the visible light region, and about 43% in the infrared light region and the ultraviolet light region. Although the band gap is 1.344 eV, theoretically it can absorb the sunlight at wavelengths less than 923 nm. According to the spectral distribution of sunlight radiation to the earth surface, solar cell light-sensitive material hardly covers the visible light and infrared light regions. The band structure and absorption spectrum properties of the doped perovskite material FAPbI3 are ideal for light absorption when the doping Cs structure is 25%.
2.3. Theoretical analysis of design scheme for perovskiteEperon and Leijtens[20] made mechanically stacked four-terminal tandem cells and obtained an efficiency of 20.3% with the materials of FA0.75Cs0.25Sn0.5Pb0.5I3 and FA0.83Cs0.17Pb(I0.5Br0.53. They discussed the FA0.75Cs0.25Sn0.5Pb0.5I3 that can deliver an efficiency of 14.8%. By combining this material with a wider-band gap FA0.83Cs0.17Pb(I0.5Br0.53 material, they achieved a monolithic two-terminal tandem efficiency of 17.0% with
open-circuit voltage. However, there is no relevant research on the photoelectric conversion working mechanism from the perspective of density functional theory. Therefore, we use the first-principles calculations to explore the relevant properties of these two structures. The structure models are shown in Figs. 11 and 12.
We use the controlled variable method to study the effect of doping on crystal band structure and absorption spectrum. After doping Cs and Sn according to Ref. [20], the crystal structures are of FAxCs1−xSn0.5Pb0.5I3 and FA0.75Cs0.25Sn1−yPbyI3. Using first-principles calculations, the energy bands of various crystals are given in Table 1. According to the relevant quantum mechanics theory, the electrons absorbing the photons to achieve energy level transition must comply with the selection rules in quantum mechanics, i.e.,
the absorption wavelength of the solar light can reach 1238 nm. The absorption spectra of FAxCs1−xSn0.5Pb0.5I3 and FA0.75Cs0.25Sn1−yPbyI3 are shown in Fig. 13. Comparison of the absorption lines of various doped crystal structures shows that both the band gap structure and the light absorption performance of FA0.75Cs0.25Sn0.5Pb0.5I3 are better than those of others. So this structure of perovskite material conduces to the increase of the solar photoelectric conversion efficiency. It is worth noting that FA0.75Cs0.25Sn0.25Pb0.75I3 should also be a good photovoltaic material.
Table 1.
Table 1.
 Table 1.
Band gaps of various crystals of FAxCs1−xSn0.5Pb0.5I3 and FA0.75Cs0.25Sn1−yPbyI3.
.
|
FAxCs1−xSn0.5Pb0.5I3
|
|
FA0.75Cs0.25Sn1−yPbyI3
|
| Value of x
|
1 |
0.25 |
0.5 |
0.75 |
0 |
Value of y
|
0 |
0.5 |
0.75 |
1 |
| Band gap/eV |
0.806 |
0.877 |
0.907 |
1.003 |
0.862 |
Band gap/eV |
0.642 |
1.003 |
1.122 |
1.401 |
| Wavelength/nm |
1538 |
1413 |
1367 |
1236 |
1438 |
Wavelength/nm |
1931 |
1236 |
1105 |
885 |
| Table 1.
Band gaps of various crystals of FAxCs1−xSn0.5Pb0.5I3 and FA0.75Cs0.25Sn1−yPbyI3.
. |
To achieve a better understanding of the optic properties of hybrid organic–inorganic halide perovskites with formamidinium lead iodide, we discuss another FAPbI3 doped perovskite material FA0.83Cs0.17Pb(I0.5Br0.5)3. Its crystal structure is shown in Fig. 14, and the band gap is 1.987 eV calculated by first principles, which is slightly larger than the bandgap of 1.6 eV given in Ref. [20], where this material was used to coordinate with FA0.75Cs0.25Sn0.5Pb0.5I3 to make the p–i–n structure to obtain a larger open circuit voltage and substantial photocurrent, for it has a large band gap.
2.4. Comparing optical properties of another perovskiteTo further explore the effects of doping other non-toxic atoms on their opto–electronic properties, we discuss another FAPbI3 where Pb is replaced separately with the Ca, Zn, Ge, Sr, Sn, and Ta atom, then use ultra-soft pseudo potentials and the valence configuration 1s1 for H, 2s22p2 for C, 2s22p3 for N, 5s25p5 for I, and other atoms as shown in Table 1. Further, we get the parameters corresponding to the doping crystal as shown in Table 2 and Fig. 15.
Table 2.
Table 2.
Table 2.
Calculation results of various crystal parameters.
.
|
FACaI3
|
FAZnI3
|
FAGeI3
|
FASrI3
|
FASnI3
|
FATaI3
|
FAPbI3
|
| Band gap/eV |
4.384 |
0.371 |
1.426 |
4.403 |
0.441 |
0 |
1.344 |
| Final energy/eV |
−2709 |
−2986 |
−1813 |
−2551 |
−1803 |
−1842 |
−3379 |
| Valence configuration |
3s23p64s2
|
3d104s2
|
4s24p2
|
4s24p65s2
|
5s25p2
|
5d36s2
|
5d106s26p2
|
| Toxicity |
nontoxic |
nontoxic |
nontoxic |
nontoxic |
nontoxic |
nontoxic |
toxic |
| Table 2.
Calculation results of various crystal parameters.
. |
The band gap Eg is the lower limit of the incident spectrum into the battery. A small bandgap width can broaden the absorption of solar light by the battery, but the decrease of Eg makes the concentration index of the intrinsic carrier increase. As a result, the saturated dark current increases greatly and the open circuit voltage decreases. So a small Eg causes the output voltage to decrease, an excessively wide band gap makes the absorption spectrum narrower, renders the excitation of carriers lower, and reduces the photocurrent. Thus, the bandgap that is too wide or too narrow will cause the efficiency to drop. References [31] and [32] show that the bandgap width is in a range of 1.1–1.3 eV, which is an index of good sensitizing dye solar material. By analyzing the data in Table 2 and Fig. 15, we find that FAGeI3 possesses the best optoelectronic performance and a band gap of 1.426 eV that is slightly larger than that of FAPbI3, and the peak of the absorption spectrum is slightly lower than that of FAPbI3. Comparing with the spectral distribution of the solar spectrum, it can be found that the light conversion efficiency of FAGeI3 is lower than that of FAPbI3, but Pb is toxic. If we consider this factor, the Ge atom can be used as an alternative substance for Pb.
2.5. Exploring one of non-toxic perovskite materialsIn order to use the Ge atom to replace Pb atom and obtain the corresponding perovskite structure, we calculate the energy band and absorption spectra of two Ge-doped perovskite crystals. Then we consider that in the crystal of the material FA0.75Cs0.25Sn0.5Pb0.5I3 structure, the Pb atom is replaced with Ge atom, and the corresponding bandgap structure and absorption spectrum characteristics are calculated, as shown in Figs. 16 and 17.
The result shows that the band gap and absorption spectrum of FA0.75Cs0.25Sn0.25Ge0.75I3 are close to that of FA0.75Cs0.25Sn0.5Pb0.5I3 properties according to the bandgap and the optical absorption spectrum. If experimental conditions are permitted in the future, the structure of these perovskite materials can be experimentally obtained to replace the crystal FA0.75Cs0.25Sn0.5Pb0.5I3.
3. ConclusionIn this work, we use the first-principles to calculate the atomic structure and optoelectronics properties of hybrid organic–inorganic halide perovskites with formamidinium lead iodide. To attempt to identify new lead-free halide perovskites, we use CASTEP to obtain the band structure and absorption spectrum curve. Firstly, we study the energy band structure, the PDOS curve, and the absorption spectrum of the FAPbI3. And then, we discuss the lattice doped with CS atom at 25%, 50%, 75%, and 100%, separately. The result shows that as the doping ratio increases, the band-gap increases; when the doping ratio exceeds 50%, the bandgap becomes significantly smaller. When the doping is 100%, it shows a distinct metal property. From Fig. 9, we can find that one of the spectral lines spans the Fermi level due to doping atoms. A perovskite material with high photoelectric conversion efficiency is reported based on Ref. [20], and we explain the reason for the higher energy absorption band and the band structure.
To further explore the effects of doping other non-toxic atoms on their optoelectronic properties, we discuss the properties of materials obtained by replacing Pb in FAPbI3 with Ca, Zn, Ge, Sr, Sn, and Ta atoms, respectively. The related factors affecting the photoelectric conversion efficiency are analyzed. As is well known, the electrons absorbing the photons to achieve energy level transition must comply with the selection rules in quantum mechanics, i.e.,
. The wide band gap will result in less absorption of sunlight and low photoelectric conversion efficiency. But if the band gap is too narrow, the carrier kinetic energy generated when absorbing photons with high energy is very large. In this case, downloaded carriers can easily interact with the lattice and then transfer energy to lattice vibration to lose that energy. At the same time, it is easy to form dark current and reduce the photoelectric conversion efficiency. Comparison of the spectral distributions of the solar spectrum shows that FAGeI3, FASnI3, and FAZnI3 have better absorbance characteristics in the solar spectral range. If the band gap structure is taken into account, FAGeI3 will become an ideal material to replace FAPbI3 although its performance is slightly lower than FAPbI3. And considering the toxicity of Pb, the Ge element can be used as an alternative substance for Pb. Moreover, we explore one of the perovskite materials, i.e., FA0.75Cs0.25Sn0.25Ge0.75I3 whose photovoltaic properties are close to those of FA0.75Cs0.25Sn0.5Pb0.5I3, but the former does not contain toxic atoms. Our results pave the way for further investigating the applications of these materials in relevant technologies.
