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Instability and Efficiency of Mixed Halide Perovskites CHNHAI Cl (A=Pb and Sn): a first principles, computational study x
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Yuping He, and Giulia Galli Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.6b04300 • Publication Date (Web): 14 Dec 2016 Downloaded from http://pubs.acs.org on December 16, 2016
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Chemistry of Materials
Instability and Efficiency of Mixed Halide Perovskites CH3 NH3 AI3−x Clx (A=Pb and Sn): a first principles, computational study Yuping He∗,† and Giulia Galli∗,‡,¶ Sandia National Laboratories, Livermore, California 94551-0969, United States, The Institute for Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, United States, and Argonne National Laboratory, Lemont, Illinois 60439, United States E-mail:
[email protected];
[email protected] Abstract We carried out calculations based on density functional theory to investigate the electronic, vibrational and dielectric properties of mixed halide perovskites CH3 NH3 AI3−x Clx with A=Pb and Sn. Computed free energies indicated that Cl mixed systems may be formed only for Cl concentrations not exceeding 1019 cm−3 , and phonon calculations showed that the disorder induced in the host lattice by the presence of a smaller halogen is responsible for mechanical instabilities. However we found that the presence of chloride may be beneficial to the electronic properties of the perovskites. Chloride anions cause the organic cations to be displaced from the center of the cage; such a displacement induces preferential orientations of the cation dipole, which in turn are responsible for notable changes in the dielectric properties of the material, ∗
To whom correspondence should be addressed Sandia National Laboratories, Livermore, California 94551-0969, United States ‡ The Institute for Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, United States ¶ Argonne National Laboratory, Lemont, Illinois 60439, United States †
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and possibly for the formation of local ferroelectric domains. The latter are instrumental in separating electron hole pairs and hence in contributing to long charge carrier diffusion lengths, in spite of polarons being more likely formed in mixed perovksites than in CH3 NH3 AI3 .
Introduction Organohalide metal perovskite solar devices have attracted much attention in the photovoltaic (PV) community, due to their efficiency in converting solar energy into electricity, which reached up to 21.6% in the last five years , 1–9 and to low fabrication costs. In particular, mixed halide perovskites MAPbI3−x Clx (MA=CH3 NH3 )have been shown to play a crucial role in the high performance of perovskite PV devices, 4,5,7,10 most likely due to their charge carrier diffusion length, notably larger than that of MAPbI3 . 11–15 It is now established that mixed organic-inorganic perovskites may be formed with Cl incorporated in their lattice. 16 However, whether Cl− is present as an interstital for I− or at grain boundaries or interfaces, and how Cl− affects the morphology and electronic properties of perovskites are still issues under debate. Dar et al.
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compared the morphology of
perovskite samples grown with different precursors, with and without Cl; they found that the presence of Cl improved the growth of the material, but they could not detect any signal of its incorporation in the material. Eventually the authors used the formula MAPbI3−x Clx to simply indicate the uncertainty on the Cl content. 18 Ndione et al. 19 investigated the role of Cl in the stability of perovskite MAPb(I1−x Clx )3 films with x=0,0.05 and 0.1 by using grazing incidence X-ray diffraction. They found that both stability and efficiency of Cl mixed perovskites depend on the concentration of the chlorine: the mixed perovskites with 10% Cl yielded the highest efficiency (i.e. 15.7%), although they turned out to be less stable than those with 5% Cl. Recently, a (110)-oriented MAPbI3−x Clx thin film was synthesized, 16 with some of the experimental results indicating that Cl may substitute I. Many studies have appeared in the literature aimed at understanding the observed long carrier diffusion length in CH3 NH3 PbI3−x Clx . For example, Wehrenfennig et al. investigated 2
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the carrier recombination rates and mobilities in both solution processed 14 and vapour deposited
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mixed halide perovskite samples, by using transient and time resolved THz spec-
troscopy. They found that the carrier mobilities of mixed halide perovskites (MAPbI3−x Clx ) were similar to those of the trihalide (MAPbI3 ); however, the defect induced carrier recombination rates and electron-hole recombination rates in mixed halide perovskites were much smaller than those of tri-halides. Long carrier diffusion lengths may also be related to the existence of polarons in hybrid perovskites, and recent experiments suggested that the influence of polarons on light absorption and carrier transport 20–22 should be taken into account. Indeed, the relative high ionicity and large difference between static and high frequency dielectric constants of perovskites indicate that polarons may form in these materials. 8 This in turn raises the question of how polarons might be altered in mixed halide perovskites, i.e. CH3 NH3 PbI3−x Clx , with respect to configurations they attain in CH3 NH3 PbI3 . In this paper, we report the results of ab initio density functional theory calculations of the vibrational, electronic and dielectric properties of mixed halide perovskites, and we discuss the origin of their mechanical and thermodynamic instabilities; we also suggest possible reasons for their high PV efficiency, by assuming chloride substitutes iodine in the lattice, and discuss the role of polarons in Cl mixed perovskites.
Results Thermodynamic and mechanical instabilities We first studied the dependence of the thermodynamic stability of the perovskites on the Cl concentration. Using density functional theory and the PBE functional, we computed the free energies (T=0) of formation of tri-halide solids described by 1x1x1, 2x2x1 and 2x2x2 supercells containing one Cl atoms, corresponding to the following concentrations of Cl : 4x1021 cm−3 (x=1), 9x1020 cm−3 (x=0.25), and 7x1019 cm−3 (x=0.125) (See Table SI). These supercells were obtained by repeating the coordinates of a fully relaxed unit cell, which were further optimized after substituting one Cl atom. The free energies of formation indicates that CH3 NH3 PbI3−x Clx could be formed only x 250 cm−1 ) pertain to the motion of the organic molecular cations; there are also several flat bands at low frequencies, arising from the organic molecular cation (i.e. C, N and H atoms) (see Fig.1). These flat bands, similar to those of rattling modes found in clathrates semiconductors, 28 are coupled to the acoustic modes of the inorganic framework, leading to a significant decrease of the group velocity of the lattice vibrations of the host lattice. This is likely responsible, at least in part, for the recently observed ultra-low thermal conductivity in MAPbI3 (i.e. 0.5 W/mK) , 29,30 indicating that the organohalide metal perovskites could potentially be materials for thermoelectric applications. 31 As shown in Fig. 2, in the tri-halides (i.e. MAPbI3 and MASnI3 ), the soft modes arise mainly from the motion of I atoms. Substituting Cl atoms changes only slightly the high frequency phonon modes (Fig. 1), but significantly influences the modes at low frequencies (Fig. 2). The density of unstable modes in MASnI2 Cl is largely increased with respect to that of MASnI3 , and these unstable modes arise not only from I atoms, but also from Sn, C and H atoms. Interestingly we found that N atoms do not contribute to any unstable mode. The partial phonon density states arising from C and N sites before and after substituting Cl atoms is shown in Fig 3a and 3b. In the absence of Cl, the vibrational modes of both C and N atoms are within a similar frequency range and all positive. After substituting Cl in the host lattice, the vibrational modes of N are shifted to higher frequency, and those of C to lower frequency and they become unstable.
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Figure 1: Phonon dispersion curves along directions spanning Γ, X, M and R symmetry points, and partial phonon density of states of MAPbI3 (a and b), MASnI3 (c and d) and MASnI2 Cl (e and f) with the MA dipole oriented along the < 100 > direction, as obtained using DFT-PBE calculations without spin-orbit coupling, and a grid of q-points =6x6x6. The low frequency spectrum is also presented in Fig.2. 5
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Figure 2: Partial phonon density of states at low frequency of MAPbI3 (a), MASnI3 (b) and MASnI2 Cl (c) (see Fig.1 for the full spectrum) with the MA dipole oriented along the < 100 > direction, as obtained using DFT-PBE calculations without spin-orbit coupling, and a grid of q-points =6x6x6.
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Overall, the comparison of phonon density of states of the tri-halides and the Cl mixed halide perovskites indicates that mixing Cl and I atoms induces some degree of mechanical instability by creating structural disorder. To further understand the effect of substituted Cl atoms, we calculated the electronic charge density distribution of MA cations in both MASnI3 and MASnI2 Cl. In the absence of Cl atoms, the organic molecular cations (MA) are approximately located at the center of the cages formed by the SnI6 framework. The electronic charge density of hydrogens belonging to the MA is overlapping with those of all neighbor I atoms(See Fig. 3c). When Cl substitutes some of the I atoms, the position of the MA cations significantly deviates from the center, and the network of bonds between I and the MA is broken (See Fig. 3d). Indeed, the MA cation has a dipole with positive charge on N (N+ ) and negative charge on C (C− ); both Cl− and I− have negative charges, hence attracting N+ . However Cl− has a larger electronegativity and smaller ionic radius than those of I− ; the electronegativity is responsible for N being pulled away from the cage center, towards the smaller anion; the smaller radius is responsible for inducing a certain degree of disorder in the cage. In addition, the electron density of hydrogens closest to N overlaps with neighboring Cl atoms, while there is hardly any electron density overlap between hydrogens bonded to C and their neighboring Cl atoms; hence the CH groups can freely vibrate due to the absence of constraints and behave as rattling centers, as mentioned above. The vibrations of the rattling centers interact with those of the MX6 framework, leading to unstable modes in MASnI2 Cl contributed from most atoms (i.e. Sn, I, and C). Electronic structure properties The results presented above indicate that the presence of Cl is not beneficial to the mechanical stability of perovskites. However several experiments indicated that it may increase the efficiency of these materials in solar energy conversion, therefore we investigated their electronic properties. To understand how substituting Cl with I affects the value of the band gap, we generated eight cubic organohalide metal perovskites (i.e. MAPbI3 , MAPbI2 Cl, MAPbICl2 , MAPbCl3 , MASnI3 , MASnI2 Cl,
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Figure 3: Upper panels: partial vibrational density of states (vDOS) contributed from Carbon and Nitrogen atoms:(a) MASnI3 and (b) MASnI2 Cl. Lower panels: (c) the electronic charge density difference ∆n=n(MASnI3 )-n(SnI3 ), (d) ∆n=n(MASnI2 Cl)-n(SnI2 Cl), where n denotes the electronic charge density and n(SnI3 ) and n(SnI2 Cl) were computed at the geometry of MASnI3 and MASnI2 Cl, respectively. Purple,red, green, black and blue spheres represent I, Sn, Cl, C, and N atoms, respectively. Hydrogen atoms were omitted for clarity.
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Table 1: The high frequency (ǫ∞ ) and static (ǫ0 ) dielectric constant, and polarizability volume (χ) in unit ˚ A3 of both MASnI3 and MASnI2 Cl with MA along , and directions, calculated by using DFPT-PBE. Ave represents the average value of dielectric constants over X,Y,Z directions and over all MA orientations.
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100 Y 9.05 148.37 167.13 7.76 127.16 134.80
Z 8.49 67.84 155.51 7.28 50.18 125.14
110 Y 8.96 28.27 161.03 8.27 62.2 135.26
X 8.96 28.27 161.04 3.75 3.87 51.15
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Figure 4: Band structures of MAPbI2 Cl (a) and MASnI2 Cl (b) with the dipole of MA oriented along the < 100 > direction and Cl atoms substituted in three different sites, denoted by three different colors (black, red and blue), respectively. Band structure were obtained at the DFT-PBE level, including spin-orbit coupling, and band gap values were corrected using G0 W0 results (see text).
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MASnCl3 and MASnI2 Br). These compounds are described by the formula AMX3−x Bx ( here A=CH3 NH3 , M=Pb or Sn, X=I, and B= Br or Cl). As in the previous section, for reasons of computational simplicity, we used cubic structures for all solids. Since the size of A relative to that of the cages in the MX6 framework may affect the phase stability of perovskites, to insure that all perovskites studied here may indeed exist in cubic phases, we used the Goldschmidt’s tolerance factor of 0.78 < t < 1.05 for cubic perovskites 32 to estimate √ their stability: t = (rA + rB )/ 2(rM + rX ), rA , rB , rM and rX are the ionic radii of A, B, M and X, respectively. We found that the value of the estimated size of CH3 NH3 (∼ 2.5 ˚ A, corresponding to the largest distance between two hydrogen atoms in the optimized MA structure) is within the ranges of A for which all perovskite systems may be stable in the cubic phases.(See Fig. S1). We then carried out a series of electronic structure calculations on all perovskite systems using DFT and the semi-local functional PBE, including spin orbit coupling (SOC) (see method section). Since band gaps are known to be underestimated when using gradient corrected functionals, we corrected PBE values using the results of many body perturbation theory calculations at the G0 W0 level reported in Ref.26. In particular, we applied a rigid shift of 1.07 eV and 0.97 eV for Pb- and Sn-solids, based on the difference between DFT and G0 W0 results obtained for MAPbI3 33,34 and MASnI3 33 (see Table SII). Hereafter, we use corrected band gaps to analyze our results. In our previous work, we showed that the orientation of the organic cation MA has a negligible effect on the band structure of MAPbI3 perovskites . 31 Therefore here we chose all perovskites with MA oriented along the < 100 > direction for the calculations of band structures. We started from perfect cubic structures (Pm¯3m) for all samples, which became pseudo-cubic after optimization, with different values of lattice constants (See Table SII). We found that the values of the band gap depend on the concentration (see Table SII) and location of the substituted halogen. Given a specific substitution site, in the case of systems with Sn, the value of the band gap increased in the order of MASnI3 (1.12 eV)< MASnI2 Br (1.50 eV)
