Chapter 4. Theoretical Study on Crystallinity of α-Phase Perovskite Structure for High
4.3 Results and Discussion
To understand the improvement of physical properties and efficiencies of α-phase FAPbI3
perovskite films, the DFT calculation was performed (Computational Details). We investigated the roles of MACl additive on the formation of α-phase FAPbI3 perovskite crystal structure from three points of view; effects of Cl and MA, and concentration effect of MACl on the thermodynamic stability of α-phase FAPbI3 perovskite structure.
4.3.1 Role of Cl on stability of α-phase FAPbI3 perovskite structure
Firstly, to understand the role of Cl on the thermodynamic stability of perovskite crystal structure, we calculated the formation energies of α-phase FAPbI3 perovskite structure and that including Cl, MA, or MACl (Figure 4.2) from model systems in Figures 4.3 and 4.4. The formation energies showed that Cl improved the thermodynamic stability of the perovskite structure compared to the case of system without Cl.
Figure 4.2. Formation energies of bare α-phase FAPbI3 perovskite structure and that with Cl, MA, or MACl.
Figure 4.3. Model systems of the α-phase FAPbI3 perovskite structure and Cl or MACl additive- incorporated α-phase FAPbI3 perovskite structures. (a) The 3 ´ 3 ´ 1 superlattice of the FAPbI3
perovskite structure. Based on the system (a), all possible configurations of the systems including Cl or MACl additive were screened for obtaining the representative system for each case, which had the most stable system energy and maintained the α-phase. The system energies are plotted on the right-hand sides of (b) and (c) based on the Cl sites, which are described as A, B, and C aligned along the x, y, and z-axes, respectively.
Figure 4.4. Model systems of reference state used to calculate the formation energy.
Note that the formation energy (ΔEf) of the α-phase FAPbI3 perovskite structure prepared with chloride, cation, or cationic chloride was calculated using the following equation,
– – – – –
system FA I cation
f Pb Cl
E E nE mE lE kE tE
D =
(4.1)where, Esystem is the total energy of the chloride, cation, or cationic chloride-incorporated perovskite system. EFA, EPb, EI, Ecation, and ECl are the energies per unit of the reference states, which are the FA, Pb, I2, cation, and Cl, respectively. n, m, l, k, and, t are the number of atoms in the system.
To deep understand the role of Cl in electronic properties, we calculated highest occupied molecular orbital (HOMO) of perovskite structure (Figure 4.5). Generally, FA cation has a weak interaction with I of a cubo-octahedral structure favored by Pb and I in the α-phase FAPbI3 and it results in decreasing the stability of perovskite structure.48 Interestingly, our calculated results showed that Cl induced p orbital localization of I (red dashed circle in the Figure 4.5). Furthermore, the results of projected density of states (PDOS) showed that Cl enhanced the intensity of p orbital of I near the Fermi level (Figure 4.6). Consequently, the interactions between FA and I can be enhanced by the above- mentioned Cl effects, which improve the thermodynamic stability of the FAPbI3 perovskite structure.
Figure 4.5. Highest occupied molecular orbitals (HOMOs) of bare α-phase FAPbI3 perovskite structure and that with Cl, MA, or MACl. Note that the isosurface value of the HOMO was 0.01 e/Å3.
Figure 4.6. (a) Projected density of states (PDOS) of α-phase FAPbI3 perovskite structure including MA or MACl. (b) PDOS of an α-phase FAPbI3 perovskite structure (bare) and that including Cl. Note that for the system including MA, the p orbital of I is considered except for one I, which occupies the Cl site in the system including the MACl. For the bare system, the p orbital of I is considered except for one I, which occupies the Cl site in the system including the Cl.
4.3.2 Role of MA on stability of α-phase FAPbI3 perovskite structure
Secondly, the effects of MA cation incorporated into the perovskite structure were investigated.
The previous study reported that the incorporation of Cs cation at the site of FA cation improved the stability of the perovskite by enhancing the interactions between FA and I through the volume shrinkage of the cubo-octahedral structure.48 Based on this report, we also confirmed the total volume shrinkage in the MA cation-incorporated systems compared to the bare α-phase FAPbI3 perovskite system (i.e.,
~0.57% in Figure 4.7). The main contribution of this volume shrinkage was caused by the contraction of MA cation-included cubo-octahedral structure compared to the bare system (i.e., ~0.89% in Figure 4.8). Moreover, we predicted that the dipole effect of the MA cation was another factor of more favorable formation energy of MA cation-incorporated system (Figure 4.2) because the dipole moment of MA cation was 10 times higher than FA cation.74 Our calculations also showed that the localization of p orbital of I in the MA-incorporated system resulted from the dipole effect of MA cation (blue dashed circle in Figure 4.5). The PDOS results of MA cation-incorporated system showed that the intensity of p orbital of I near the Fermi level was higher than the bare α-phase FAPbI3 perovskite structure (Figure 4.9).
Therefore, we conclude that the effects of volume shrinkage and the dipole moment of MA cation enhance the interactions between FA and I and it results in improving the thermodynamic stability of perovskite structure. It indicates that the volume shrinkage and the dipole moment of A-site cation can also play an important role in the thermodynamic stability of perovskite structure.
Figure 4.7. Total volume and cubo-octahedral structure of the bare α-phase FAPbI3 perovskite structure and that prepared with MA.
Figure 4.8. Volume of cubo-octahedral site of (a) bare α-phase FAPbI3 perovskite structure and (b) MA included structure. Note that the volume of cubo-octahedral site is calculated by Connolly surface method.73 The radius of probe atom is 1 Å. Each cubo-octahedral site is denoted by number. Calculated Connolly surfaces of cubo-octahedral site 5 of bare and MA systems are described by blue and pink colors, respectively.
Figure 4.9. PDOS of the bare α-phase FAPbI3 perovskite structure and that prepared with MA.
4.3.3 Concentration effect of MACl additive
Lastly, in the experimental results, the crystallinity of α-phase FAPbI3 perovskite structure was changed according to the concentration of MACl (Figure 4.10). The high crystallinity was obtained in 40% MACl concentration and it showed the highest device performance (i.e., 24.02%max and 23.93%certification). To understand the appropriate concentration of MACl additive for obtaining high crystallinity of α-phase FAPbI3 perovskite structure, we investigated the concentration effect of MACl.
For this investigation, we constructed four types of concentration system (Figure 4.11).
Figure 4.10. (a) XRD spectra of perovskite films prepared with different amounts, pristine, MA-10, MA-20, MA-30, MA-40, and MA-50. (b) Reciprocal FWHM obtained from films prepared with different additive concentrations at the diffraction peak 13.9° for the α-phase perovskite.
Pristine MA-10 MA-20 MA-30 MA-40 MA-50
6 8 10 12 14
Reciprocal of FWHM
(
degree-1)
10 12 14 16 18 20
2 Theta (degree)
In te n s it y ( a .u .)
MACl-50 MACl-40 MACl-30 MACl-20 MACl-10 Pristine
(a)
(b)
Figure 4.11. Model systems of α-phase FAPbI3 perovskite structure incorporated with (a) one MACl (11% concentration), (b) two MACl (22% concentration), and (c) three MACl (33% concentration) additives to construct the systems included with two, three, and four additives, which describe the 22%, 33%, and 44% concentration systems incorporated additives, respectively. Based on 11%, 22%, and 33%
concentration systems (left hand side) obtained from Figures 4.3(c), 4.11(a), and 4.11(b), all possible configurations, which the MACl can incorporate into the perovskite structure, are screened for obtaining the representative system for each concentration system, which has the most stable system energy and maintains the α-phase (right hand side). The sites of Cl and MA are described as A and C, respectively.
In order to investigate the effect of the concentration of cationic chloride additive on the crystallinity of the α-phase FAPbI3 perovskite structure, we have theoretically tested the α-phase perovskite structure, which described the system before (pre-annealing) and after (post-annealing) a thermal annealing, based on the model systems of Figure 4.11. Through these systems, we calculated the formation energy (Figure 4.4) and the doping formation energy (Figure 4.12).
Figure 4.12. Model systems of reference state for calculating the doping formation energy.
Doping formation energy was calculated to investigate the formation energy to dope the α-phase perovskite structure with additive. In this calculation, we considered one formation step of α-phase perovskite structure with cationic chloride additive; α-phase perovskite structure incorporated cationic chloride additive before annealing process (pre-annealing step). In the pre-annealing step of α-phase FAPbI3 perovskite structure, the doping formation energy of cationic chloride additive into the perovskite structure (ΔEd) was calculated by using the following equation,
(
A out A in) (
C out C in)
d cation Cl doping non doping
E E
-E
-n m
-m m m
-m
D = + +
(4.2)where Ecation Cl doping is the total energy of perovskite system incorporated cationic chloride. Enon-doping is the total energy of the system that does not incorporate the cationic chloride. μA out (μC out) and μA in (μC in) are the chemical potentials of anions (cations), which are deleted from or inserted to the perovskite structure with cationic iodide and cationic chloride. n and m are the number of anions and cations, respectively.
In Figure 4.13, the doped model systems are described, which are at their most stable states, over the concentration range of 11% to 44%. Note that in the pre-annealing step, the α-phase perovskite is doped with cationic chloride as an additive, and in the post-annealing step, the α-phase perovskite is doped with I, which occupies the Cl site through anionic exchange. We found that the formation energy decreased as the MACl concentration increased at the pre-annealing step (Figure 4.13a), implying that the performance of materials increased from their increased structural stabilities. But, one can readily expect that there exists a limit of the additive concentration effect to increase the performance since the doping formation energy increases (Figure 4.13a). Thus, we examined the formation energy at the post- annealing step, where I was substituted with Cl through the annealing process (Figure 4.13b). Moreover, we found that the formation energy was stabilized between 33% and 44%, which corresponded to the best performance shown in the experiment (i.e., 40%).
Figure 4.13. (a) Formation energy of α-phase FAPbI3 perovskite structure including MACl and doping formation energy of MACl into the α-phase FAPbI3 perovskite structure at the pre-annealing step. (b) Formation energy of α-phase FAPbI3 perovskite structure including MAI at the post-annealing step.
Note that model systems of α-phase FAPbI3 perovskite structure including (a) MACl or (b) MAI are described according to their concentration from 11% to 44%. Red colored regions indicate the doped sites of MA cation.
Our theoretical prediction was in good agreement with experimental observation. The optimal concentration of MACl additive was caused by the doping formation energy of MACl into the α-phase FAPbI3 perovskite structure in the pre-annealing step and the formation energy of the perovskite structure including MAI in the post-annealing step. Especially, the formation energy was stabilized between 33% and 44%, which corresponded to the best performance shown in the experiment (i.e., 40%). Overall, we can understand that the role of MACl additive in the formation of perovskite structure through three points of DFT calculation.