Structures and Electronic Properties of Different CH3NH3PbI3/TiO2 Interface: A First-Principles Study

Methylammonium lead iodide perovskite, CH3NH3PbI3, has attracted particular attention due to its fast increase in efficiency in dye sensitization TiO2 solid-state solar cells. We performed first-principles calculations to investigate several different types of CH3NH3PbI3/TiO2 interfaces. The interfacial structures between the different terminated CH3NH3PbI3 and phase TiO2 are thoroughly explored, and the calculated results suggest that the interfacial Pb atoms play important roles in the structure stability and electronic properties. A charge transfer from Pb atoms to the O atoms of TiO2 lead to the band edge alignment of Pb-p above Ti-d about 0.4 eV, suggesting a better carries separation. On the other hand, for TiO2, rutile (001) is the better candidate due to the better lattice and atoms arrangement match with CH3NH3PbI3.

layers, therefore, the (001) slab of perovskite owns two types of surfaces based on the different terminations: the MAI termination (MAI-T) with MA + and I − ions, and the PbI 2 termination (PbI 2 -T) with Pb 2+ and I − ions. Here both terminations are considered, and seven-layer slabs is used to mimic the surface, which is thick enough to represent the surface as shown in the previous work 31 .
In the reality, the TiO 2 is substrate to grow perovskite, therefore we use the optimized TiO 2 cell parameters to build our supercells. Among many possible combinations between TiO 2 and perovskite surfaces, the interfaces between rutile (001), anatase (001) and CH 3 NH 3 PbI 3 (001) have the relatively small lattice mismatch between TiO 2 and CH 3 NH 3 PbI 3 , thus we mainly consider the above two types of interfaces. The rutile (001) slab is represented with four layer, and the anatase (001) is consistent with five layer rotated 26.565˚ × 5 5 anatase surface. Coincidentally, both slabs contain 20 TiO 2 unit, namely 120 atoms. The corresponding lattice mismatch between rutile and perovskite are − 3.97%, and between anatase and perovskite are 4.56%, respectively.
The TiO 2 /perovskite interfaces is built by connecting TiO 2 slabs with seven layers MAI-T (four MAI and three PbI 2 layers) or PbI 2 -T (four PbI 2 and three MAI layers) slabs, as mentioned above, leaving 20 Å vacuum along the nonperiodic direction orthogonal to the surface direction. In some case, perovskite slabs were slightly shifted to avoid interaction between anion-anion, namely I-O. The system is full relaxed, and the optimized four types of interface configurations are shown in Fig. 1: Fig. 1a. MAI-T/anatase (MAI/A), Fig. 1b. PbI 2 -T/anatase (PbI/A), Fig. 1c. MAI-T/rutile (MAI/R) and Fig. 1d. PbI 2 -T/rutile (PbI/R).
As shown in Fig. 1a, the interaction between the perovskite and TiO 2 is mainly through perovskite I atoms and under-coordinated Ti atoms of the TiO 2 surface. The detailed bonding situation of CH 3 NH 3 PbI 3 perovskite/TiO 2 interface are shown in Table 1. The proportion of perovskite surface ions bonded to TiO 2 are 50% (the bond number of one kind of atom are defined as the surface chemical bond/surface atoms number), with the bond length of 2.98 (I-Ti) and 1.73 (H-O) Å, respectively. It is also observed some structure distortion arises on the interface, for example, the shift of interlayer under-coordinated I atoms lead to the distortion of surface PbI6 octahedron. The PbI6 octahedron framework is the skeleton of CH 3 NH 3 PbI 3 perovskite, and the bond angle between the PbI6 octahedrons (Pb-I-Pb) is rather flexible, which could decrease to 150˚ to stabilize the structure under phase change 28 ; while the bond angle in the PbI6 octahedron (I-Pb-I) is rigid and always around 180˚. Here the angle of interface I-Pb-I decrease to about 174˚ relative to 176˚ in the tetragonal phase bulk, confirming the interaction of the interface. In addition, some interfacial O atoms of the TiO 2 rise slightly with broken of original O-Ti bond to  For PbI/A system, the formation of interfacial I-Ti bond and Pb-O bond with bond length of 3.28 and 2.33 Å. The proportion of bonded atoms for perovskite surface are 50%, which are same as MAI/A system. The interaction between them leads to a large distortion of the original surface, for example, equatorial I-Pb-I angle decrease, and partly O-Ti bond are broken. For MAI/R system, the interfacial bond types are same as MAI/A system. However, the bond lengths are slightly shorter than the MAI/A system, more importantly, all the perovskite interfacial atoms are involved in chemical bonding, indicating a better atom arrangement match between rutile (001) and perovskite than that of anatase (001). For PbI/R system, interestingly, it is observed the formation of O-Pb-O bond without the breaking of O-Ti bond. The interfacial Pb atoms obviously move towards the pervoskite, and the corresponding bond lengths of Pb-O and I-Ti are 2.4 Å and 2.9 Å, respectively. The relative shorter interfacial bond lengths indicate a strong interaction between the two surfaces. In the interfacial region, the surface PbI6 of perovskite are seriously distorted, and the opposite I-Pb-I bond angle sharply decrease to 152˚.
The calculated binding energies of the different interfaces as listed in Table 2 together with lattice mismatch and Bader charges. The binding energies of the composites were calculated by the equation: where the E total , E p , and E sub denote the total energy of the perovskite/TiO 2 system, isolated perovskite, and TiO 2 substrate, respectively, especially, the E p , were calculated with allowing the cell parameter relaxation, hence the strain energy of the CH 3 NH 3 PbI 3 slabs have been taken into account the binding energies. It is not surprising that the interfaces with PbI 2 -T slab are 0.86 and 2.82 eV more stable than the corresponding MAI-T slab for the anatase (001) and rutile (001), respectively. The reason should be that the interaction between MA ions of the MAI-T with other ions is through either van der Waals (vdW) or hydrogen bond, which is rather weak. The interaction between the Pb atom with PbI 2 -T with the other atoms is chemical bonding, which connects TiO 2 and perovskite as a bridge.
On the other hand, the interface with rutile (001) are thermodynamically more stable than the corresponding of anatise (001) for both terminations. As shown in Table 2, the calculated binding energy of PbI/R is about 3.21 eV larger than the one of the corresponding PbI/A. The corresponding lattice mismatch between TiO 2 and perovskite are 4.56% for anatase and − 3.97% for rutile, respectively. Thus the different binding energy should come from the different lattice match between rutile and anatase TiO 2 with perovskite (001). The lattice mismatch is relatively large between the CH 3 NH 3 PbI 3 and TiO 2 is relatively large, thus the strain may affect the interfacial stability between CH 3 NH 3 PbI 3 and TiO 2 . The calculated E b is negative, which suggests that the interaction between the interface atoms could compensate the mismatch energy. Mosconi et al. calculated the perovskite and anatase (101) interface, and they found that the lattice mismatch of pseudocubic phase perovskite with anatase (101) were small (0.75 and − 1.85%) but that of tetragonal phase were large (− 6.4% and − 13.52%) 31 . Here we consider the tetragonal phase, which is stable under room temperature, and found the better lattice match for tetragonal phase perovskite (001) with anatase (001) as well as rutile (001).
In order to check whether the seven layer is thick enough, we also examined the binding energy with nine layers for both terminations, and the calculated E b are within 3% compared with the one with seven layers, which indicates seven layers is thick enough to represent the properties of (001) slab of MAPbI 3 perovskite. To summarize, the interfaces are strongly stabilized by interaction with rutile (001) than anatase (001) as well as, with interfacial Pb atoms leading to additionally higher binding energy to TiO 2 in PbI 2 -T surface compared to that of MAI-T surface. This stability is primarily due to the presence of the oppositely charged attractive interfacing ions.
To analyze the interactions, we have calculated the electron localization function (ELF), which can effectively reveal the nature of different chemical interactions directly from the charge localization between individual atoms. Figure 2 shows the ELF contour plots with color scheme for the four optimized CH 3 NH 3 PbI 3 perovskite/ TiO 2 systems interfaces. The value of the ELF ranges from 0 to 1, where red color represents the electrons that are highly localized, blue color signifies electrons with almost no localization and green color with value of 0.5 corresponds to the electron-gas-like pair probability as in metallic bonds. Here, we see that in all the systems, the electros around H atoms of MA ions, I atoms and O atoms are more localized, while the electros around Pb and Ti atoms show an electron-gas-like feature. The blue color between interface anions and caions suggest the chemical interactions between them mainly origins from electrostatic interaction. Comparing Fig. 2a,c, the PbI 2 -T systems show more electron-gas-like in the interface, means a better charge transfer feature in the surface.
The left panel of Fig. 3 displays the difference charge density plot, i.e., the difference between the density of the perovskite/TiO 2 system and its individual constituent, and the right panel of Fig. 3 show the plane-averaged electrostatic potential of the four structures to estimate the electronic level positions. When the TiO 2 and perovskite forms the interface, electrons transfer from perovskite slab to TiO 2 slab due to the Fermi level difference,  therefore, it generate a built-in electric field from perovskite to TiO 2 slab to against the charge transfer, then the interface is under equilibrium. To clarify quantitatively the charge transfer between perovskite and TiO 2 , we calculated Bader charge and which of perovskite fragment as shown in Table 2. The calculated Bader charge of perovskite fragment are − 0.11, − 0.07, − 0.19 and − 0.22 e for the four systems respectively, negative value means electron transfer from perovskite to TiO 2 . The direction of charge transfer are same for all the systems, but the charge transfer of rutile interface are larger than that of anatase. As shown in the right panel of Fig. 3, for perovskite slabs, the electrostatic potential of MAI layers are higher than that of PbI 2 slayers. The average potential of TiO 2 slab is lower than that of perovskite slab, suggesting a charge transfer from perovskite to TiO 2 in line with above results. The potential difference between rutile and perovskite slabs are relatively larger than that of anantase systems, therefore, charge transfer amount for rutile systems are larger. Since the potential of MAI layers are higher than that of PbI 2 slayers, potential drop on the interface of PbI 2 -T systems are deeper than that of MAI-T, large amount of electrons can be accumulated to the TiO 2 side, suggesting a better separation of electron-hole in the solar cells.
The built-in electric field behavior widely exists in the metal/semiconductor systems, the charge transfer situations of the perovskite/TiO 2 systems are more complicated due to the variety of interface atoms arrangement. To know the details of charge transfer behavior of the perovskite/TiO 2 systems, we draw the difference charge density plots, in which the blue color represents charge accumulation, while the red color represents charge depletion. In Fig. 3a,c, the blue color mainly distributes on the middle of I and Ti atoms, around O atoms, while the red color distributes around Ti atoms and H atoms of NH 3 . In Fig. 3b,d, the charge redistribution led by I-Ti interaction is In order to further understand the electronic properties of the TiO 2 /perovskite interfaces, the partial density of states (PDOS) is calculated. As shown in Fig. 4, the conduction band minimum (CBM) of TiO 2 is obviously lower than that of perovskite. Considering the bandgap of perovskite is smaller than that of TiO 2 , the electron should excite from valence band (VB) of perovskite (I-p and partly Pb-s orbital) to conduction band (CB) of perovskite (Pb-p), and then transfer to CB of TiO 2 (Ti-d). Therefore, the energy difference between I-p and Pb-p decided the photo absorption efficiency, and the difference between Pb-p and Ti-d decided the efficiency of charge transfer cross the interface. Generally speaking, electron injection to a state lead to the left shift relative to the Fermi level, and the electron outflow are contrary. As shown in Fig. 4, the calculated band gap of PbI 2 -T is slightly smaller than that of MAI-T, because the electron outflow from the Pb atoms lead to the left shift of Pb states lower the gaps. The perovskite CB edge, contribution main from Pb-p, is calculated to lay about 0.7, 0.3, 0.1 and 0.2 eV above the TiO 2 CB edge respectively for the MAI/A, PbI/A, MAI/R and PbI/R. It is noted that the band offset of MAI/A system is obviously larger than the others. This value is in line with Mosconi et al. calculated result of 0.8 eV obtained from a similar system of combine anatase (101) and MAI terminated perovskite (110) by GGA-DFT including SOC (spin orbit coupling) 31 . While the value of MAI/R system is slightly underestimated compared to experimental result. The PbI 2 -T systems agrees well with experimental result of 0.4 eV, which come from Lindblad et al. directly measuring the occupied energy levels of the MAPbI 3 and the underneath TiO 2 34 . It is well-known that the spin-orbit coupling (SOC) effect has great effect on the calculated band gap, as shown in the previous work 20 . In order to check the effect of the SOC, we check the SOC effect on the band gap of bulk CH 3 NH 3 PbI 3 . The calculated band gap is 0.60 eV, which is obviously smaller than the one with pure PBE and experimental results 3 . Therefore, we retain the PBE calculated of the electronic structure of the investigated interfaces, which was shown to qualitatively give the same trend as experiment.

Discussion
In summary, we have performed first-principles calculations to study the structure and electronic properties of the interface between CH 3 NH 3 PbI 3 and TiO 2 including four types structures: MAI/A, PbI/A, MAI/R and PbI/R. The calculated results suggest the PbI 2 -T surface of CH 3 NH 3 PbI 3 interact with TiO 2 stronger due to the formation of the bridge bond. Rutile (001) surface has better lattice and atoms arrangement match with CH 3 NH 3 PbI 3 . The charge transfers from CH 3 NH 3 PbI 3 to TiO 2 are observed for all the four systems. The different band edge alignment show the PbI 2 -T surface and rutile (001) are better candidate for the charge separation.

Methods
The DFT calculations were performed using the Vienna Ab Initio Simulation Package (VASP) code 35,36 . The electron-ion interaction was described by the projector augmented wave (PAW) method [37][38][39] . Electronic orbitals 5d6s6p, 5s5p, 2s2p, 2s2p and 1s were considered as valence orbitals for Pb, I, C, N and H atoms, respectively. The cutoff energy for basis functions was 400 eV, and the k-space integration was done with a 4 × 4 × 1 k-mesh in the Monkhorst-Pack scheme 40 . Further increasing the energy cutoff and k-points showed little difference on the results. All the structures considered in this study were relaxed with conjugate-gradient algorithm until the forces on the atoms were less than 0.01 eV/Å. Periodic boundary conditions were applied in all three dimensions. Due to large sizes of Pb and I ions, cages formed by four PbI 6 octahedron are large enough to accommodate MA + ions and there is no obvious chemical bond formation between MA + ions and the inorganic matrix. Therefore, non-local density functional, vdW-DF 41 , was employed to take into account the weak interaction in the system, as implemented in VASP by J. Klimeš et al. 42,43 . In this method, the exchange-correlation energy takes the form of