First-Principles Study of Enhanced Out-of-Plane Transport Properties

Letter Cite This: J. Phys. Chem. Lett. 2019, 10, 3670−3675

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First-Principles Study of Enhanced Out-of-Plane Transport Properties and Stability in Dion−Jacobson Two-Dimensional Perovskite Semiconductors for High-Performance Solar Cell Applications Zhuo Xu,†,# Ming Chen,†,# and Shengzhong Frank Liu*,†,‡

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†

Key Laboratory of Applied Surface and Colloid Chemistry, National Ministry of Education; Shaanxi Key Laboratory for Advanced Energy Devices; Shaanxi Engineering Lab for Advanced Energy Technology; Institute for Advanced Energy Materials; School of Materials Science and Engineering, Shaanxi Normal University, Xi’an 710119, China ‡ State Key Laboratory of Catalysis, Dalian National Laboratory for Clean Energy, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China S Supporting Information *

ABSTRACT: Two-dimensional (2D) perovskites have attracted much attention in research for solar cell applications because of their increased stability. The versatile structures of 2D perovskites enable fine-tuning of their optoelectronic properties. Newly reported Dion−Jacobson (DJ) perovskites have shown superior out-of-plane charge transport properties and better stability than the Ruddlesden−Popper (RP)-type perovskites because of their freedom from weak van der Waals interactions between adjacent layers. Tunable band gaps of 2D AMX4 can be achieved by alternatively substituting the corresponding compositions at A, M, and X sites, and significantly enhanced stability is observed because of the two hydrogen bonds formed at both ends of the divalent organic cation. Enhanced interlayer charge transport properties are found in DJ perovskites because of the short apical I−I distance in AMX4 perovskites, especially for PDAPbI4 and PDASnI4 perovskites. These findings provide us effective ways to tune the stability and optoelectronic properties of 2D perovskites.

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mental stability and intriguing optoelectroic properties compared with their 3D counterparts.22−27 The hydrophobic cations can significantly improve their stability to moisture, and the van der Waals interaction between +1 cations leads to more flexible layer stacking in RP perovskites.28−34 The efficiency of RP 2D perovskite solar cells is currently over 15%,29 with much improved stability compared to their 3D counterparts. However, because of the large interlayer distance and weak van der Waals interaction between +1 cations in RP perovskites, the conductivity between layers is severely hindered, and the stability of these materials under harsh conditions still needs to be further improved. In DJ perovskites, replacement of two 1+ hydrophobic cations by one 2+ hydrophobic cation and disappearance of the van der Waals gap is supposed to introduce fewer degrees of freedom into the structure, making the inorganic layers closer to each other. Additionally, with the two hydrogen bonds formed at both ends of the divalent cation, DJ perovskites are expected to show much improved optoelectronic properties and stability.35−41 Perovskite solar cells based on benzene dimethanammonium cation have just achieved an

ybrid metal halide perovskites have been broadly recognized as promising candidates for next-generation photovoltaic (PV) and optoelectronic (OE) devices because of their excellent optoelectronic properties,1,2 including suitable optimal band gaps for solar light absorption,3−5 high absorption coefficients,6,7 steep absorption onsets, tunable band gaps,8 small exciton binding energies,9 high charge carrier mobilities,10,11 and long diffusion lengths (100−1000 nm) and carrier lifetimes.6,12,13 The power conversion efficiencies (PCEs) of solar cells based on perovskites have reached 24.2% within only a few years; further, they still have comparatively huge potential for improvement.14 Despite the high photovoltaic efficiency of perovskite solar cells, degradation of both MAPbI3 and FAPbI3 can be easily caused by moisture,15 oxidation,16 thermal stress,17 light,18 and ion migration,19 which urgently needs to be solved before their large-scale commercial application. Recently, cation engineering-induced dimensionality reduction of perovskites has emerged as an effective way to construct new alternatives with intrinsically improved stability.20,21 Two-dimensional (2D) perovskites with general formula A′2(A)n−1MnX3n+1 or A′(A)n−1MnX3n+1 (A′ = 1+ or 2+ hydrophobic cations; A = 1+ cation; M = Pb2+, Sn2+, Ge2+, Cu2+, Cd2+, etc.; X = Cl−, Br−, and I−), which are also known as Ruddlesden−Popper (RP) or Dion−Jacobson (DJ) perovskites, exhibit higher environ© 2019 American Chemical Society

Received: May 13, 2019 Accepted: June 17, 2019 Published: June 17, 2019 3670

DOI: 10.1021/acs.jpclett.9b01360 J. Phys. Chem. Lett. 2019, 10, 3670−3675

Letter

The Journal of Physical Chemistry Letters

Å for experimental results; a = 8.523, b = 8.750, and c = 10.760 Å for theoretical results), the slight differences are most likely caused by the temperature influence.38 In DJ perovskites, the divalent organic cation induces fewer degrees of freedom in the structures compared to the RP phase, making the inorganic layers closer to each other because of the elimination of the van der Waals gap. Thus, the inorganic layers in DJ perovskites stack almost right on top of each other with a significantly reduced apical I−I distance, as shown in Table S1. As the size of the divalent organic cation decreases, the apical I−I distance further decreases with a mismatch between neighboring inorganic layers. As for EDAMX4 perovskites, with a further reduced apical I−I distance, the repulsive force between the apical I−I will cause a more severe mismatch between neighboring inorganic layers. Moreover, different divalent organic cations will introduce different hydrogen bonding with the inorganic MI6 octahedron, which have an important effect on the in-plane distortion, and in turn on the electronic properties. The band structures of 2D AMX calculated using the PBE schemes are displayed in Figures S1−S3, as well as the results considering the spin−orbit coupling (SOC) effect, which is critical to account for the relativistic effects in the Sn, Pb, and I p orbitals. The calculated band gap of BDAPbI4 in the PBE scheme is consistent with previous results (2.08 eV in this work and 2.13 eV in previous work)42 and very close to the experimental values.38,40 Cancellation of the errors arising from an underestimation in the standard DFT band gap calculation and an overestimation due to the neglect of the SOC effects in the heavy element, such as lead or bismuth, is responsible for this agreement.43 However, neither PBE or PBE+SOC can produce accurate band gaps. Therefore, for further benchmarking purposes, we calculate the band structures with the HSE06 functional including the SOC effect; here, the parameter α = 43% is used separately because it can produce more reasonable values with experimental ones. The results are all shown in Table 1, and we found that the band gaps of PDAPbI4 and BDAPbI4 calculated using the HSE06α=43+SOC scheme match very well with the experimental values. Hereafter, the HSE06α=43+SOC scheme is used for computing the band gaps of all structures. As shown in Table 1, we observed that Sn- and I-based 2D perovskites have the smallest band gaps, while the Pb- and Brbased 2D perovskites have the largest band gaps. Usually, the band gaps of semiconductors decrease with increasing atomic

efficiency of 15.6%, which was one of the highest reported values for low-dimensional perovskites.41 These inspiring results indicate the huge potential of DJ perovskites for photovoltaic and other optoelectronic applications. However, the superior optoelectronic properties of DJ perovskites have not been elaborated thoroughly. In this work, we investigate the structural, electronic, and excitonic properties of 2D DJ AMX4 perovskites (A = EDA, PDA, BDA; M = Ge, Sn, Pb; X = Br, I) based on density functional theory (DFT) (see more computational details in the Supporting Information). We find that the band gaps of 2D-AMX4 perovskites can be tuned through substitution of different components, and desirable values for solar cell application between 1.5 and 2.0 eV are accessible through structural engineering, which is enlightening for experiments toward the fabrication of 2D perovskite materials suitable for high-performance OE or PV applications. Furthermore, significantly improved charge transport properties along the out-of-plane direction are observed because of the strong interlayer I−I interaction, indicating the superior PV performance of this kind of material. The structural configurations of EDAPbI4, PDAPbI4, and BDAPbI4 are shown in panels a, b, and c of Figure 1,

Figure 1. Different side views of the structural configurations of (a) EDAPbI4, (b) PDAPbI4, and (c) BDAPbI4 hybrid DJ perovskites.

respectively. The optimized lattice constants of 2D AMX4 based on the PBE+D3 method are listed in Table S1. We found the PBE+D3 method can yield reasonable lattice constants for 2D BDAPbI4 that are in good agreement with the experimental results (a = 8.481, b = 8.847, and c = 11.203

Table 1. Computed Band Gaps (eV) for the Single-Layer Hybrid Perovskites AMI4 (A = BDA, PDA, and EDA) and APbBr4 Using the PBE, PBE+SOC, and HSE06α=43 + SOC schemes PBE BDAPbBr4 BDAGeI4 BDASnI4 BDAPbI4 PDAPbBr4 PDAGeI4 PDASnI4 PDAPbI4 EDAPbBr4 EDAGeI4 EDASnI4 EDAPbI4

2.581 1.456 1.260 2.081 2.668 1.524 1.366 2.159 2.723 1.784 1.550 2.363

(G−Z) (G−Z) (G−Z) (G−Z) (G−Z) (G−Z) (G−Z) (G−Z) (Z−Z) (G−Z) (Z−Z) (Z−Z)

PBE+SOC 1.841 1.335 1.035 1.342 1.942 1.362 1.160 1.437 1.984 1.672 1.316 1.581

(Z−Z) (G−Z) (G−Z) (Z−Z) (Z−Z) (G−Z) (G−Z) (Z−Z) (Z−Z) (G−Z) (Z−Z) (Z−Z)

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HSE06α=43+SOC 3.166 2.281 1.874 2.368 3.300 2.307 2.033 2.491 3.366 2.736 2.229 2.685

(Z−Z) (G−Z) (G−Z) (Z−Z) (Z−Z) (G−Z) (G−Z) (Z−Z) (Z−Z) (G−Z) (Z−Z) (Z−Z)

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2.3738

2.4636

DOI: 10.1021/acs.jpclett.9b01360 J. Phys. Chem. Lett. 2019, 10, 3670−3675

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Figure 2. (a) Brillouzin zone and k-path illustration of PDAPbI4, where Z(0.0, 0.0, 0.5), X(0.5, 0.0, 0.5), M(0.5, 0.0, 0.0), Γ(0.0, 0.0, 0.0), Q(0.0, 0.5, 0.5), and N(0.0, 0.5, 0.0). (b) HSE06a=43 + SOC band structure of single-layer PDAPbI4. Side (upper panel) and top views (lower panel) of decomposed charge densities of (c) CBM and (d) VBM (isovalue = 0.002 e Å−3).

number according to Ge → Sn → Pb, which is indeed the case for Ge- and Sn-based 2D perovskites. The exception in Pbbased 2D perovskites is mainly due to the higher binding energy of Pb 6s orbitals, which are stabilized because of relativistic contraction of the s shell and thus lower the level of the valence band maximum (VBM). Additionally, the higher binding energy of Br 4p states compared to I 5p states can further reduce the Fermi level and result in larger band gaps of Br-based perovskites. We also found the band gaps of AMX4 increase according to BDA → PDA → EDA. This dependence of electronic properties on interlayer cations mainly originates from the impact of different hydrogen-bonding behaviors on the Pb−I−Pb bond angle in different 2D perovskites.39 In BDAMX4, the BDA cation forms weak hydrogen bonding with terminal I−, which has a small effect on the in-plane Pb−I−Pb angles because of their indirect contribution to the in-plane distortion, whereas the hydrogen bonding is formed with the bridging I− anions deeper inside the layers in PDAMX4 and EDAMX4, which amplifies the in-plane distortion, as shown in Table S1. We also notice that there is much more apparent distortion of the MI6 octahedra in Ge-based perovskites than in Sn- and Pb-based perovskites, as shown in Table S1. This is because group IVA divalent cation M2+ has a lone pair of nonbonding electrons, which usually lowers the coordination symmetry around the cation. Two distinct categories of inplane Ge−I bonds and intermediate out-of-plane Ge−I bonds in Ge- and I-based perovskites are observed, along with I−Ge− I and Ge−I−Ge bond angles that deviate very severely from the ideal 90°. The larger Pb−I−Pb bond angles always indicate more overlap of metal s and halide p orbitals, whose strong antibonding interaction then pushes up the VBM, thus resulting in a decreasing band gap of 2D perovskites according to EDA → PDA → BDA because of the more linear Pb−I−Pb angles in 2D PDAMX4 and BDAMX4. It has been indicated

that the thickness of the inorganic layer also has an impact on the band gap because of the dimension reduction.29,39 To conclude this aspect, the band gaps of BDA(MA)n−1MnX3n+1 with different thicknesses (n = 2, 3, 4) are also calculated using the PBE functional. The variations of band gaps with thickness n are displayed in Figure S4. We find that the band gaps decrease as n increases, which is due to the dimension reduction-induced weakened quantum well effect; however, the reduction caused by n is very limited. The projected density of states (PDOS), crystal orbital Hamilton population (COHP), and band-decomposed charge density analyses are performed to better illustrate the band compositions and bonding characters in these 2D perovskites. The upper valence band of the series is dominated by metal shalide p antibonding orbitals, resulting in a tremendously dispersive VBM, which is responsible for the small in-plane hole effective masses in these systems, whereas the lower conduction band is determined by metal p−halide s and metal p−halide p antibonding orbitals (Figures S5−S7). The antibonding character of these states is demonstrated by the results of the COHP analysis provided in Figures S8−S10. Therefore, the electronic properties of these 2D AMX4 perovskites are mainly affected by the halide and metal. The bonding character of the in-plane Ge−I bonds in the COHP analysis of Ge-based 2D perovskites are found to be distinct from each other, while the bonding characters of in-plane Pb− Br, Pb−I, and Sn−I bonds are almost identical. These findings are consistent with the severe distortion in Ge-based perovskites. As illustrated previously, the aligned perovskite layer stacking and reduced apical I−I distances in DJ perovskites allow for a better interlayer electronic coupling through I−I interactions.39 Our COHP analysis indicates the apical I−I contacts participate in antibonding interactions, which may be 3672

DOI: 10.1021/acs.jpclett.9b01360 J. Phys. Chem. Lett. 2019, 10, 3670−3675

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The Journal of Physical Chemistry Letters responsible for the dispersive VBM along the Γ−Z direction in the Brillouin zone as compared to the almost flat band dispersion perpendicular to the layer plane in RP perovskites.44 This distinctive band structure feature indicates a reduction of the quantum well effect in these 2D perovskites and considerable enhancement of charge transport between adjacent inorganic layers, which has been pointed out in experimental adsorption and photoluminescence (PL) spectra.37 The COHP analysis results in Figures S8−S10 also demonstrate that the antibonding I−I interactions in 2D BDAMX4 are weaker than those in 2D PDAMX4 and EDAMX4 because shorter I−I distances in 2D PDAMX4 and EDAMX4 are observed. Additionally, the strongest antibonding I−I interactions are usually found in Pb- and I-based 2D perovskites for each kind of 2D perovskite. The HSE06α=43+SOC band structure of PDAPbI4, in which the severest apical I−I antibonding interaction has been observed, is shown in Figure 2b. Decomposed charge densities corresponding to the conduction band minimum (CBM) and VBM are also provided in Figure 2c,d as an alternative way to understand the bonding character in these 2D perovskites; obvious Pb p states and antibonding Pb s and I p states can be observed in panels c and d of Figure 2, respectively. To verify the stability of these studied systems, we calculate the decomposition energy according to the decomposition path: AMI4 → AI2 + MI2 to assess their thermodynamic stability.45 The calculated values are listed in Table S2, as well as the one of MAPbI 3 for comparison. The small decomposition energy of MAPbI3 indicates the instability of MAPbI3, which is consistent with many theoretical studies and experiments, while decomposition energies of AMX4 are all negative (the more negative of the energies, the more stable of the structures) except for EDAGeI4 and EDAPbI4, and the relative stabilities are found to decrease along BDA → PDA → EDA; this is mainly due to the increasing repulsive force between the apical I−I from BDA → PDA → EDA as mentioned previously. We also calculated the exfoliation energy (ΔE) according to the equation ΔE = (2Einl + Eoc − Ebulk)/2A (Einl, energy of the inorganic layer; Eoc, energy of the interlayer organic cation; Ebulk, energy of the bulk 2D perovskite; A, the surface area parallel to the layer plane). The calculated exfoliation energies of each case are shown in Figure S11b, the magnitude of which are a dozen times higher than those of the corresponding 2D BA2MX4 RP perovskites,46 indicating the excellent stabilities of these DJ perovskites. This enhanced stability can be attributed to the two hydrogen bonds formed at both ends of the divalent organic cation. Figure S11b also indicates PDAMX4 has the highest exfoliation energies, with slightly lower energies for BDAMX4 because of its larger interlayer distance. Because of the strong repulsive force, the lowest exfoliation energies are found in EDAMX4. The performance of optoelectronic devices based on these 2D DJ perovskites also depends on the excitonic properties of the base materials. First, the effective masses of carriers are estimated according to the band structures calculated considering the SOC method. Here, we use the equation m* = ℏ2/(∂2E/∂2k) to calculate the curvature effective masses of carriers (where ℏ is the reduced Planck constant and k is the magnitude of the wave vector in momentum space).47 The calculated effective masses corresponding to the VBM and CBM are summarized in Figure 3; we found that ASnI4 or AGeI4 mostly have the smallest in-plane effective masses, and APbBr4 mostly have the largest in-plane effective masses.

Figure 3. Effective masses of holes and electrons for single-layer APbBr4 and AMI4 in the in-plane Z−X, Z−Q, and out-of-plane Z-Γ directions in the Brillouzin zone.

Additionally, BDAMX4 have smaller effective masses than the other two cases because of the stronger antibonding interaction of metal s and halide p orbitals. Significantly reduced effective masses compared to 2D RP perovskites are estimated in the out-of-plane situation, and this can be attributed to the apical I−I antibonding interaction. Furthermore, the out-of-plane effective masses of BDAMX4 and EDAMX4 are larger than that of PDAMX4 because of the long apical I−I distance in BDAMX4 and mismatched layer stack in EDAMX4. Finally, the out-of-plane effective masses are smaller in APbI4 cases than in other structures because of the strongest antibonding I−I interaction in these structures. These results suggest that the general transport properties of PDAPbI4 are superior to those of the other cases. Next, the Wannier−Mott exciton binding energies (Eb) are estimated based on the effective mass theory using a modified hydrogen-atom-like Bohr model as Eb = μe4/2ℏ2ε2, where ε is the high-frequency dielectric constant, μ the reduced effective mass of the exciton calculated according to μ = me*mh*/(me* + mh*), and e is the charge of an electron.48 From the expression of Eb, a smaller effective mass and a larger dielectric constant will lead to a smaller exciton binding energy. As shown in Table S3, the dielectric constants of AGeI4 and ASnI4 have much larger values than those of APbBr4 and APbI4. With the small in-plane effective masses of AGeI4 and ASnI4, small in-plane exciton binding energies are expected in these structures, indicating easier separation of photoexcited excitons into free carriers and potential use in solar cell applications, whereas a strong exciton effect in APbBr4 and APbI4 may enable enhanced PL quantum efficiency at room temperature. However, the out-of-plane exciton binding energies are much larger than the in-plane exciton binding energies, indicating a poor charge transport property in the out-of-plane direction. Nevertheless, relatively small out-of-plane exciton binding 3673

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energies are observed in PDAPbI4 and PDASnI4, indicating much improved transport properties along the out-of-plane direction in these structures compared to other DJ perovskites and RP perovskites. Therefore, promising solar cell performance can be expected using PDAPbI4 or PDASnI4 as the absorber layers. In conclusion, we have investigated the electronic and charge transport properties of the DJ perovskites AMI4 and APbBr4 (A = BDA, PDA, and EDA; M = Ge, Sn, and Pb). We find that tunable band gaps of 2D AMX4 can be achieved by alternatively substituting the A, M, and X sites, and desirable 1.5−2.0 eV band gaps for solar cells can be obtained. The outof-plane transport properties are found significantly improved compared to RP perovskites because of the short apical I−I distance in AMX4. Relatively small effective masses and exciton binding energies are found in PDAPbI4 and PDASnI 4 perovskites, which may lead to high-performance solar cells. The results indicate the use of a divalent cation is an effective way to promote the photovoltaic properties and stability of 2D perovskites and holds great promise for obtaining higher solar cell PCEs. Furthermore, our findings also provide effective ways to tune the stability and optoelectronic properties of 2D perovskites by adjusting the interlayer interactions, which can be achieved through introducing additives.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.9b01360. Computational details; structural parameters; excitonic properties; band structures; project density of states; crystal orbital Hamilton populations; variation of band gaps of BDA(MA)n−1MnI3n+1 and BDA(MA)n−1PbnBr3n+1 with n = 1, 2, 3, and 4; decomposition energies and exfoliation energies (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Shengzhong Frank Liu: 0000-0002-6338-852X Author Contributions #

Z.X. and M.C. contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by the National Key Research and Development Program of China (2017YFA0204800/ 2016YFA0202403), National Natural Science Foundation of China (91733301/61704098/61604091), the DNL Cooperation Fund CAS (DNL180311), the 111 Project (B14041), the Changjiang Scholar and Innovative Research Team (IRT_14R33), and the China Postdoctoral Science foundation (2018M633455). All calculations are supported by the Key Laboratory for Macromolecular Science of Shaanxi Province, School of Chemistry and Chemical Engineering, Shaanxi Normal University. 3674

DOI: 10.1021/acs.jpclett.9b01360 J. Phys. Chem. Lett. 2019, 10, 3670−3675

Letter

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DOI: 10.1021/acs.jpclett.9b01360 J. Phys. Chem. Lett. 2019, 10, 3670−3675