Efficient electron extraction of SnO2 electron transport layer for lead halide perovskite solar cell

SnO2 electron transport layer (ETL) has been spotlighted with its excellent electron extraction and stability over TiO2 ETL for perovskite solar cells (PSCs), rapidly approaching the highest power conversion efficiency. Thus, how to boost the performance of ETL is of utmost importance and of urgent need in developing more efficient PSCs. Here we elucidate the atomistic origin of efficient electron extraction and long stability of SnO2-based PSCs through the analysis of band alignment, carrier injection, and interfacial defects in the SnO2/MAPbI3(MA = CH3NH3+) interface using unprecedentedly high level of first-principles calculations at the PBE0 + spin-orbit-coupling + dispersion-correction level for all possible terminations and MA directions. We find that Sn-s orbital plays a crucial role in carrier injection and defect tolerance. SnO2/MAPbI3 shows favorable conduction band alignments at both MAI- and PbI2-terminations, which makes the solar cell performance of SnO2/MAPbI3 excel that of TiO2/MAPbI3. Different electron transfer mechanisms of dipole interaction and orbital hybridization at the MAI- and PbI2-terminations indicate that post-transition metal (sp valence) oxide ETLs would outperform transition metal (d valence) oxide ETLs for PSCs.


INTRODUCTION
Recently, lead halide perovskite (LHP) solar cells (PSCs) based on ABX 3 [A = Cs + , CH 3 NH 3 + (MA + ), CHN 2 H 4 + (FA + ), B = Pb 2+ , Sn 2+ , Ge 2+ , X = I − , Br − , Cl − ] have become one of the most promising large-scale photovoltaic materials by achieving the power conversion efficiency over 25% [1][2][3][4][5][6][7] . The electron transport layer (ETL) plays a crucial role in extracting and transporting photogenerated electron carriers and serves as a hole-blocking layer by suppressing charge recombination as one of the most important components for photovoltaic devices 8 . The physical properties of the ETL, including charge mobility, energy level alignment, defect states, morphology, and related interfacial properties, are significant for the photovoltaic performance 9 . Until now, TiO 2 has been widely used as the ETL material for organic/inorganic PSCs 10,11 . However, TiO 2 shows some limitations as a stable and efficient ETL for PSCs [12][13][14][15][16]20 . The conduction band minimum (CBM) of TiO 2 is slightly higher than that of MAPbI 3 17 , which hinders the electron extraction from ETL 20 . TiO 2 decomposes under the exposure to ultraviolet (UV) for a long time, which is not suitable for commercialization of PSCs [12][13][14] . High temperature annealing for processing TiO 2 also hampers elaborate device fabrication 15 . Defect trap states such as oxygen vacancy in TiO 2 increases non-radiative loss and degrade the device performance 16 .
Many experimental efforts have been paid to overcome the limitations of TiO 2 and to find novel ETL materials, including SnO 2 18 , La-doped BaSnO 3 19 , and ZnO 20 . Among many candidates, SnO 2 has shown an excellent chemical stability, UV-resistance, superior band alignment, high charge extraction, and less photocatalytic activity compared with TiO 2 or other ETLs [21][22][23][24][25][26]28,29 . SnO 2 has shown a favorable CBM alignment to LHP, allowing minimum loss of open-circuit voltage 21 . UV spectroscopy and femtosecond transient absorption measurement showed that SnO 2 exhibits the better electron extraction than TiO 2 21 . Since SnO 2 has a large band gap (E g ) 22~3 .6 eV (vs. E g (TiO 2 )~3.0 eV) 23 , most of visible lights pass through SnO 2 24 . SnO 2 prohibits absorption of UV because of the large E g , protecting from UV exposure 25,26 . In addition, the bulk electron mobility in SnO 2 is two orders of magnitude higher than that of TiO 2 27 . SnO 2 is easily processed at low-temperature, which is suitable for large-scale commercialization 28,29 .
Although SnO 2 has been used as an alternative ETL for PSCs till now, the electron extraction mechanism of SnO 2 -based PSCs has not been studied yet. Here, we show a comparative study of rutile SnO 2 /MAPbI 3 and rutile TiO 2 /MAPbI 3 interfaces to uncover the mechanism behind the superior SnO 2 -based PSCs by employing first-principles calculations at the hybrid Perdew-Burke-Ernzerhof (PBE0) + spin-orbit-coupling (SOC) + Tkatchenko-Scheffler (TS) dispersion correction (PBE0-SOC-TS) level. Because the electronic structure of the interface is largely affected by the termination type and the alignment of organic A-site cation MA 1 (Fig. 1a) and TiO 2 /MAPbI 3 (Fig. 1d) (Fig. 1c) and TiO 2 /MAPbI 3 (Fig. 1f)  We note that the interfacial binding energy at the SnO 2 /MAPbI 3 interface (Fig. 1a-c) is larger than that at TiO 2 /MAPbI 3 (Fig. 1d-f) for both MAI-and PbI 2 -terminations (Table 1). For the MAItermination, the larger binding energy of SnO 2 /MAPbI 3 interface can be explained with the stronger SSHB at the interface. The binding energy of the interface A/B is calculated by the formula   (Table 1). The SSHB distance between hydrogen and oxygen atoms at the interface is shorter at the SnO 2 /MAPbI 3 interface (d(O ··· HN) = 1.54 Å) than at the TiO 2 / MAPbI 3 interface (d(O ··· HN) = 1.60 Å). Accordingly, the interaction energy of the SSHB, defined as the energy difference between the structure with and without HB between MA and interfacial O at SnO 2 /MAPbI 3 (ΔE = 0.52 eV/unit-cell) is almost twice stronger than that at TiO 2 /MAPbI 3 (ΔE = 0.27 eV/unit-cell). The SSHB stabilizes the oxygen dangling bond and enhances the binding energy of interface. For the PbI 2 -termination, E b (SnO 2 /MAPbI 3 ) is 3.00 eV/ unit-cell, much stronger than E b (TiO 2 /MAPbI 3 ) = 2.40 eV/unit-cell.
At the PBE-SOC-TS level (Supplementary Figs. 5, 6 and Supplementary Table 2), we note that the band gaps of materials are severely underestimated, resulting in misleading band alignments. For example, at the MAI-terminated SnO 2 /MAPbI 3 interface with the SSHB (Supplementary Fig. 3c), the CBM of Sn is much lower than the CBM of Pb, indicating a significant open circuit voltage loss of the device. Also, the charge transfer cannot be described accurately within the PBE-SOC-TS level, which results in a fictitious vacuum level shift because of wrong band alignments. Because we need to use the same level of theory to compare two interfaces, we investigated the band gap errors under various DFT functionals (PBE, PBE0, and HSE06) and GW approximation (Supplementary Tables 2, 3, and Methods). We find that the PBE0-SOC-TS shows the lowest average band gap error for the SnO 2 (TiO 2 )/MAPbI 3 interface system.
Quarti et al. showed that the band alignment is significantly influenced by the surface termination type 30 . We find that the band alignment mechanisms are related to the dipole polarization and orbital hybridization 31-34 at MAI-termination and PbI 2termination, respectively. In order to analyze the band alignment of SnO 2 /MAPbI 3 and TiO 2 /MAPbI 3 at each termination, we plot the partial density of states (PDOS) of the SnO 2 /MAPbI 3 and TiO 2 / MAPbI 3 interfaces at MAI-termination and PbI 2 -termination (Fig. 2). Although the contribution of interfacial atoms is significant for the electron extraction, we included whole atoms in the PDOS diagram, because atoms at bulk also contribute to the VB and CB edges, which is verified by the layer resolved DOS (Supplementary Figs. 7 and 8) 35 .
At the MAI-termination, the energy shift is governed by the MA dipolar polarization via the SSHB at the interface, largely affecting the band alignment. The interfacial CBM of SnO 2 is slightly lower (by 0.23 eV) than that of MAPbI 3 when the interfacial SSHB exists ( Fig. 2a and Supplementary Fig. 9a). Without the SSHB, the band alignment of CBMs becomes unfavorable, as the interfacial CBM of SnO 2 is 0.65 eV higher than that of MAPbI 3 ( Fig. 2b and Supplementary Fig. 9b), indicating a crucial role of the SSHB for CBM energy shift at the interface. On the contrary, the CBM of TiO 2   Supplementary Fig. 9c). However, such a small misalignment still allows the electron extraction 11,21 . The CBM misalignment at the TiO 2 /MAPbI 3 interface ( Fig. 2f and Supplementary Fig. 9f layers is also overestimated as −1.03 eV compared with the converged CBO (−0.68 eV) of the interface with nine MAPbI 3 layers or more. The minus sign indicates that the CBM of SnO 2 is lower than that of MAPbI 3 . Therefore, we note that at least nine layers of MAPbI 3 is required for eliminating the quantum confinement effect of the interface. However, the PBE0 + SOC + TS calculations of the interfaces with nine MAPbI 3 layers with a huge vacuum (~40 Å) are computationally too demanding even for thestate-of-the-art supercomputers. Therefore, our calculation result focuses on qualitative comparison of the CBO between two interfaces at both terminations. Also, at PbI 2 -termination, the orbital hybridizations of interfacial atoms are significant that the CBM has both Pb (MAPbI 3 ) and Sn (SnO 2 ) orbital characters (Figs. 2c, f and Supplementary Fig. 12), as Sn and Pb atom makes very similar behavior near the CBM, which contributes to highly efficient electron extraction ( Fig. 2c and Supplementary Fig. 12). This large orbital hybridization is manifested in the bonding population analysis based on crystal orbital Hamiltonian population (COHP) (Fig. 3b), which will be elaborated later.
The band gap of bulk SnO 2 and (001) surface has a significant difference (Supplementary Table 5). The calculated band gap (at PBE0-SOC-TS level) of the (001) surface of SnO 2 is 2.92 eV which is much lower than that of bulk SnO 2 (3.58 eV). In contrast, the calculated band gap (at PBE0-SOC-TS level) of the (001) surface of TiO 2 is 3.96 eV which is similar with that of bulk TiO 2 (4.09 eV). This is because of the multivalent property of Sn atom. The surface Sn atoms are reduced from Sn 4+ to Sn 2+ , resulting in SnO-like environment at the surface. This reduction makes the Sn-5s state filled with electrons near the valence band edge, which reduces the band gap ( Supplementary Fig. 13) 36,37 . Thus, a band gap of 2.68 eV (2.65 eV) for SnO 2 (in Supplementary Fig. 9a, c) is not so much underestimated as that of the (001) surface of SnO 2 (2.92 eV).
The band gap difference between MAPbI 3 for MAI-termination with the SSHB (1.95 eV, Supplementary Fig. 9a) and without the SSHB (1.55 eV, Supplementary Fig. 9b) is explained by the presence of the SSHB that significantly affects the band alignments of MAI-terminated interface. The SSHB (between interfacial O of SnO 2 and H of MA) stabilizes the dangling bond of interfacial O of SnO 2 , which in turn lowers the CBM of SnO 2 . While this interfacial SSHB stabilizes SnO 2 , it destabilizes MAPbI 3 , even though the interface is stabilized overall. The interfacial MAPbI 3 has three pairs of hydrogen bonding between I and H of MA. However, these hydrogen bonds inside MAPbI 3 are broken in the favor of the SSHB between O of SnO 2 and H of MA. And, this enhances the CBM level of MAPbI 3 and increases the band gap (Supplementary Table 6) 38 .
The COHP elements at the SnO 2 (TiO 2 )/MAI-terminated MAPbI 3 and SnO 2 (TiO 2 )/PbI 2 -terminated MAPbI 3 interfaces show that the interfacial atom-pairs form dominant antibonding states at both interfaces at the conduction bands (Fig. 3). The off-diagonal elements of COHP spanned by local orbital pairs can provide the covalent contributions (or orbital hybridization) of the bonds and in turn the carrier injections between interfacial atoms. As mentioned, the hybridization is an order of magnitude larger at the PbI 2 -termination than the MAI-termination (Figs. 3a, b). This affirms that the orbital hybridization is a dominant mechanism for the band alignment in the PbI 2 -termination. Though the hybridization at the MAI-termination is weaker than at the PbI 2termination, we observe a trend where the off-diagonal COHP elements of conduction bands of SnO 2 /MAPbI 3 interfacial atoms are larger than those of TiO 2 /MAPbI 3 by averaging 14 atom-pairs within 2.0-9.0 Å (Fig. 3a). In the PbI 2 -terminated MAPbI 3 interface, the COHP elements of the conduction bands at SnO 2 /MAPbI 3 interface are twice larger than those of TiO 2 /MAPbI 3 interface by averaging 19 atom-pairs within 2.0-5.0 Å. The result clearly indicates the larger orbital hybridization of interfacial atoms and larger electron carrier injection at the SnO 2 /MAPbI 3 interface (Fig.  3b). The CBMs of SnO 2 , TiO 2 , and MAPbI 3 are mostly composed of Sn-5s, Ti-3d, and Pb-6p, respectively. Thus, the CBM orbital hybridizations occur between Sn-5s and Pb-6p orbitals at the SnO 2 /MAPbI 3 interface and between Ti-3d and Pb-6p at the TiO 2 / MAPbI 3 interface. This large orbital hybridization could be also verified by the atomic orbital PDOS ( Supplementary Fig. 12) in that behavior of Sn-5s orbital and Pb-6p orbital at the CBM is similar. In general, d-orbitals do not strongly hybridize with sor p-orbital and the COHP results show that the orbital hybridizations in the SnO 2 /MAPbI 3 interface are larger than in the TiO 2 /MAPbI 3 interface ( Fig. 3c and Supplementary Fig. 14). Since the orbital hybridization is directly related to the carrier injection at the interface, this can qualitatively explain the reason for the superior carrier injection in SnO 2 /MAPbI 3 interface which contributes to the high efficiency of PSCs.
Defects are one of the main setbacks for an efficient photovoltaic device, which generate shallow donor/acceptor levels and deep recombination centers around the gap 39,40 . The defect in the ETL hampers the performance of PSC devices because of generation of trap states. Although, defects in the LHP only generates the shallow defect levels close to the band edges which does not damage the electron extraction from LHP to ETL 41 , Azpiroz et al. showed that defect migration can hamper the electron extraction at the interface which contributes to the hysteresis of PSC devices 42 .
In this work, we mainly focus on how defect states in ETL affect the SnO 2 /MAPbI 3 and TiO 2 /MAPbI 3 interface. We study the neutral oxygen vacancy V o 0 and the Sn(Ti) interstitial Sn i 0 (Ti i 0 ) at the surface or interface, which are known to be dominant defects in rutile SnO 2 43,44 and TiO 2 45,46 by employing the supercell layers of SnO 2 /TiO 2 (Supplementary Figs. 15 and 16). In pristine TiO 2 , both V o 0 and Ti i 0 generate deep levels below the CBM ( Supplementary  Fig. 16e, f), which is consistent with bulk TiO 2 47-49 . For pristine SnO 2 , the V o 0 (bridging) and Sn i 0 levels are different in the surface and the bulk. For the bulk SnO 2 , the V o 0 creates a shallow level below the CBM in the bulk 37,50 . We find that the interfacial bridging V o 0 defect forms a SnO-like defect states near the VBM in SnO 2 surface (Supplementary Fig. 16b) by a strong 5s-5p rehybridization, which is consistent with the previous experiment 51 . We confirm this hypothesis by observing a significant reduction of Sn 4+ → Sn 2+ from the Bader charge analysis (Supplementary Tables 7 and 8) 52 . For both MAI-and PbI 2termination, the charge difference of Sn2 atom is the most significant among tin atoms near the V o 0 (Sn1-Sn4), indicating that charge is localized on Sn2 atom due to V o 0 . Since both surface tin and (Sn2) oxygen have threefold coordination, their charge should be equal with opposite sign. From this, we can confirm the surface is reduced to SnO composition (Sn 2+ O 2− ), which means the charge of surface tin atom near V o 0 is reduced from Sn 4+ to Sn 2+ . This reduction makes the Sn-5s state filled with electrons and results in strong 5s-5p rehybridization. This unique interfacial defect property, derived from the multi-valency of Sn, creates a favorable electronic environment for the electron transfer between MAPbI 3 and SnO 2 . While Sn i 0 forms a shallow level below the CBM (Supplementary Fig. 16c) at SnO 2 surface, bulk Sn i 0 is a shallow donor inside the CBM in bulk SnO 2 53 . The interfacial V o 0 at SnO 2 /MAPbI 3 interface shows the consistent defect states near VBM for MAI- (Fig. 4a) and PbI 2 -terminations (Fig.  4c). The band structure of these configurations (Fig. 4a, c) are also calculated ( Supplementary Fig. 17a, b), indicating that the occupied 5s state of Sn at the surface lies slightly above the top of the valence band. This state does not show any flat dispersion, indicating that this state is due to the multivalence of Sn. Therefore, these SnO-like defect states near the VBM in the SnO 2 /MAPbI 3 interface (Fig. 4a, c and Supplementary Fig. 17) does not affect the electron extraction process at the CBM. The interfacial Sn i 0 generates a shallow level near VBM at both MAI-and PbI 2 -termination (Fig. 4b, d). On the contrary, the interfacial V o 0 and Ti i 0 of TiO 2 create the Ti mid-gap deep level trap states at the MAI-and PbI 2 -terminated TiO 2 /MAPbI 3 interfaces (Fig. 4-h). Therefore, the SnO 2 /MAPbI 3 interface has the superior defect tolerance to the TiO 2 /MAPbI 3 interface at both terminations for all dominant defect types.
In summary, we studied the theoretical origin of high electron extraction of SnO 2 ETL for PSCs at the PBE0-SOC-TS level by comparing the SnO 2 /MAPbI 3 and TiO 2 /MAPbI 3 interfaces. We calculated the binding energy, band alignment, carrier injection, and the interfacial defect levels at various terminations with different MA directions. We unveil crucial distinction of the conduction band electron transfer mechanisms at the MAItermination (dipole polarization) and the PbI 2 -termination (orbital hybridization) in the SnO 2 (TiO 2 )/MAPbI 3 interface. We explicitly showed that SnO 2 exhibits favorable band alignments to MAPbI 3 at both MAI-and PbI 2 -terminations over conventional TiO 2 ETL. The carrier injection of the SnO 2 /MAPbI 3 is larger than that of the TiO 2 / MAPbI 3 because of strong Sn-5s and Pb-5p/I-6s orbital hybridizations. Also, the interfacial V o 0 and Sn i 0 defect levels in SnO 2 do not form deep recombination centers unlike TiO 2 interface. Given that one of the crucial parts of PSC device is ETL, this understanding of electron transfer mechanism in the SnO 2 /MAPbI 3 interface can pave a way to design better ETL materials for PSCs.

METHODS
We performed the noncollinear density functional theory (DFT) calculations with the hybrid PBE0 functional 54 including TS dispersion correction 55 using Vienna Ab initio Simulation Package 56 with dipole corrections. This is because the PBE0 functional can describe the band alignment of our system very well. In order to choose a suitable exchange-correlations, we performed band gap calculation for bulk SnO 2 , TiO 2 , and MAPbI 3 with different exchange-correlations, such as PBE, PBE0, and HSE06, including spin-orbit coupling (Supplementary Table 2). For SnO 2 , the PBE0-SOC-TS gives the most similar band gap to experiment, whereas the HSE06-SOC-TS gives the most similar band gap to experiment for TiO 2 . For MAPbI3, both the PBE and the PBE0-SOC-TS give similar band gaps to experiment. We noted that regardless of exchange-correlation, theoretical band gap is larger in TiO 2 , whereas experimental band gap is larger in SnO 2 . The same trend is also noted in the GW calculation of bulk SnO 2 and TiO 2 (Supplementary Table 3). Therefore, instead of choosing different exchange-correlation for SnO 2 /MAPbI 3 and TiO 2 / MAPbI 3 interface, we selected only one potential for the whole interface calculations which can minimize the average band gap error. Since the PBE0-SOC-TS gives the minimum band gap error compared with the experimental band gap, we choose the PBE0-SOC-TS exchange-correlation. In order to check surface properties, we also calculated the band gap of (001) surface of SnO 2 and TiO 2 at the PBE0-SOC-TS level (Supplementary Table 4). We used PAW pseudopotentials of Ti(3s 2 3p 6 3d 2 4s 2 ), Sn(4d 10 5s 2 5p 2 ), O(2s 2 2p 4 ), Pb(5d 10 6s 2 6p 2 ), and I(5s 2 5p 5 ). We employed Γ-centered (4 × 4 × 1) k-mesh for sampling the Brillouin zone and 560 eV energy cutoff for the planewave basis. Structural geometry optimization was performed with energy convergence and force convergence of 10 −6 eV and 0.02 eV/Å, respectively ( Fig. 1 and Supplementary Table 9). The COHP analysis was done using LOBSTER v.3.1.0 57 . COHP is a theoretical bond-detecting tool for solids, which partitions the band-structure energy into orbital-pair interactions.
In order to obtain the quantitative band alignments ( Supplementary Fig.  9), we extracted the band alignment from the PDOS of bulk-like regions of the respective layers (L3 for SnO 2 (TiO 2 ) and L2 for MAPbI 3 in Supplementary  Figs. 7 and 8). Also, in order to show the PDOS method is reliable, we calculated the CBO for MAI-termination with SSHB and PbI 2 -termination of SnO 2 /MAPbI 3 interface ( Supplementary Fig. 18) by using an alternative method called Hartree potential alignment. In order to obtain the CBO of the interface A/B by using Hartree potential alignment, we need the Hartree potentials (VH) of the interface (A/B) and its corresponding A and B structure with the lattice parameter of the interface (or constrained bulk systems from the geometry of the interface). Then, the Hartree potentials of A and B are vertically shifted to be overlapped with the Hartree potential of the interface (A/B), where A and B are SnO 2 and MAPbI 3 in our system, respectively. Here, we obtain the shifts of the Hartree potential VH A/B-A (energy shift between the interface A/B and A) and VH A/B-B (energy shift between the interface A/B and B) ( Supplementary Fig. 18a, b). The CBO is calculated by CBO = (CB B + can be used to obtain band alignments, assuming the interface is thick enough to have bulk-like properties and dense k-points are used 35 . For MAI-termination with SSHB of SnO 2 /MAPbI 3 interface, we obtain the CBO of −0.23 eV from the PDOS method ( Supplementary Fig. 9a), as compared with the CBO of −0.29 eV from the Hartree potential alignment ( Supplementary Fig. 18c). For PbI 2 -termination of SnO 2 /MAPbI 3 interface, similarly, we obtain the CBO of +0.17 eV from the PDOS method ( Supplementary Fig. 9c), as compared with the CBO of +0.11 eV from the Hartree potential alignment (Supplementary Fig. 18d). The plus/minus sign of the CBO indicates that the CBM of SnO 2 is higher/lower than that of MAPbI 3 . For both terminations, the CBO difference between the PDOS method and the Hartree potential alignment is within 60 meV, indicating that the results of our PDOS method are reliable 58 . Therefore, we used this PDOS method for the analysis of whole systems.

DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.