Stress and Defect Effects on Electron Transport Properties at SnO2/Perovskite Interfaces: A First-Principles Insight.

The structural and electronic properties of interfaces play an important role in the stability and functionality of solar cell devices. Experiments indicate that the SnO2/perovskite interfaces always show superior electron transport efficiency and high structural stability even though there exists a larger lattice mismatch. Aiming at solving the puzzles, we have performed density-functional theory calculations to investigate the electronic characteristics of the SnO2/perovskite interfaces with various stresses and defects. The results prove that the PbI2/SnO2 interfaces have better structural stability and superior characteristics for the electron transport. The tensile stress could move the conduction band minimum (CBM) of CH3NH3PbI3 upward, while the compressive stress could move the CBM of SnO2 downward. By taking into account the stress effect, the CBM offset is 0.07 eV at the PbI2/SnO2 interface and 0.28 eV at the MAI/SnO2 interface. Moreover, our calculations classify VI and Ii at the PbI2/SnO2 interface and Sn-I, Ii and Sni at the MAI/SnO2 interface as harmful defects. The Ii defects are the most easily formed harmful defects and should be avoided at both interfaces. The calculated results are in agreement with the available experimental observations. The present work provides a theoretical basis for improving the stability and photovoltaic performance of the perovskite solar cells.

Introduction

Perovskites have been emerging as one of the important candidate materials for new photovoltaic cells because they possess superior photovoltaic performance of high light absorption coefficient, large carrier mobility, and long electron–hole diffusion length and also are easy to prepare in various synthetic methods with low manufacturing cost.[1−4] Perovskite organic metal halides were employed as a light harvester for the perovskite solar cells (PSCs) by Kojima et al. in 2009.[5] With the efforts of many researchers, the efficiency of perovskite-based solar cells has increased from 3.8% to 25.5%.[5−8] PSCs are generally composed of the transparent conductive electrodes, electron transport layers (ETLs), perovskite light absorption layers, hole transport layers (HTLs), and metal electrodes.[9] These layers are stacked together, and many interfaces are formed between the layers, all of which will affect the charge transport of the device. The bonding and defect properties of the interfaces play an important role in the interfacial stability and functionality. Therefore, it is very important to study the characteristics of the interfaces, which will help researchers overcome the shortcomings at the interfaces and continuously improve the efficiency of PSCs.

Electron transport layers are an important part of PSCs, which are responsible for transferring electrons to the electrodes. Electrons excited by light in the perovskite layer must transfer through the perovskite/ETL interfaces and then be collected by the ETL. Meanwhile, electrons and holes might recombine at the interfaces, which often affects the power conversion efficiency (PCE) of the device. TiO2 is the most popular ETL used in PSCs because of its suitable conduction band minimum (CBM) and the history of being used as an ETL in dye sensitized solar cells.[10,11] The PCE of TiO2-based PSCs has exceeded 25%.[12] However, the development of TiO2 is limited by a serious disadvantage, that is, its electron transport speed is very low, only 0.1–0.4 cm2 V s–1 and electrons are easy to accumulate at the TiO2/perovskite interfaces.[13] Many other materials such as ZnO,[14] Zn2SnO4,[15] BaSnO3,[16] SrTiO3,[17] CdS,[18] CdSe,[19] WO3,[20] In2O3,[21] Nb2O5,[22] and CeO[23] have been investigated as ETL with different strengths and weaknesses. In comparison, SnO2 as the promising ETL has attracted wide attention in recent years, and the PCE of SnO2-based PSCs has also exceeded 25%.[24]

SnO2 has superior physical properties for being used as an ETL. Its electron transfer efficiency is much higher, reaching 240 cm2 V s–1,[13] although it has a cell and band structure similar to those of TiO2. The CBM of SnO2 is lower than TiO2, which is favorable for electronic transport.[25] Also, the larger band gap of SnO2 makes it less susceptible to ultraviolet rays.[26] Moreover, SnO2 can be prepared at low temperatures, which is more convenient and can be used in flexible solar cells.[27] In 2015, Li et al. were the first batch to use mesoporous SnO2 films as ETL and got a PCE of 10.18%.[28] Ke et al. prepared SnO2 thin films by thermal decomposition of SnCl2·2H2O precursor on fluorine doped tin oxide (FTO), and the yield PCE reached 17.21%.[29] Anaraki et al. obtained 20.7% PCE by the spin coating and chemical bath deposition method.[30] Jiang et al. fabricated planar PSCs with a certificated PCE of 23.32% by using the organic halide salt phenylethylammonium iodide (PEAI) to passivate the surface defects of HC(NH2)2–CH3NH3 mixed perovskite films.[31] Recently, Yoo et al. tuned the chemical bath deposition of SnO2 and got better ETL with ideal film coverage, thickness, and composition, which could be beneficial for the interface properties, and thus a certified PCE of 25.2% was finally obtained.[24]

Many experimenters have reached a consensus on the excellent performance of SnO2 as an ETL and they have employed a lot of approaches to improve the properties of the SnO2/perovskite interfaces.[32−35] Yang et al. found that the recombination rate of quantum dot SnO2/perovskite interfaces is less than that of nanocrystalline SnO2/perovskite interfaces.[26] Zhang et al. used density functional theory (DFT) and experiments to comprehensively investigate the interface structures and transport properties of the CH3NH3PbI3/SnO2 interfaces and found that the interface contacted by the PbI2 layer is more stable than that contacted by the CH3NH3I layer.[34] In order to adjust the interfacial stress caused by the lattice mismatch, Du et al. introduced the amino acid self-assembled layer as the buffer layer, which improved the quality of perovskite films, enhanced the charge transfer/extraction at the interfaces, and finally made it achieve a PCE of 20.68%.[35] Kim et al. studied the orbital hybridization and the effects of O vacancy and Ti/Sn interstitial at TiO2/perovskite and SnO2/perovskite interfaces and indicated that SnO2 is better than TiO2 as an ETL material.[36] Until now the understanding of the influences of the microstructures on the performance of the SnO2/perovskite interfaces, such as the stress produced by the mismatch and the defect effects, is far from enough. So in this paper, we will carry out a systematic study on the structural and electronic properties of the SnO2/perovskite interfaces. The remainder of the paper is organized as follows. In Section , the theoretical methods and the computational details are described. Section presents the interfacial properties of the clean heterointerfaces, and the stress and defect effects on the electron transport at the interfaces are explored. Finally, a short summary is given in Section .

Computational Methods

The first-principles calculations in the framework of DFT were performed using Vienna ab initio Simulation Package (VASP).[37,38] The electron–ion interaction was described using the projector augmented wave method.[39,40] The energy cutoff for the plane wave basis set was 500 eV for all calculations. In the simulation, an empirical pairwise correction proposed by Grimme in terms of the DFT+D2 scheme had also been included for more precisely depicting the dispersion interactions in the systems.[41] For both bulk and interface systems, their structures were optimized by using the generalized gradient approximation (GGA) in the Perdew–Burke–Ernzerhof (PBE) form.[42] For the accuracy of the band alignment and electronic transport properties at the interfaces, the electronic properties were calculated using the Heyd–Scuseria–Ernzerhof screened Coulomb hybrid functional (HSE06).[43] The supercell parameters and the atomic positions were allowed to relax until the forces on all atoms were converged to 0.05 eV/Å.

The calculated parameters of bulk tetragonal CH3NH3PbI3 (MAPbI3) perovskites are a = 8.69 and c = 12.80 Å, which match well with the previous DFT calculations and experimental observations.[44−46] In order to build a typical SnO2/perovskite interface, we also optimized the lattice constants of SnO2 to be a = 4.83 and c = 3.24 Å, which are in good agreement with other researches.[47,48] Then, we constrained the lattice constants of the perovskite slab with these of the SnO2 slab, which is always employed as the substrate in experiments. Haruyama et al. listed all possible surface of tetragonal CH3NH3PbI3, and we chose the (001) surface to stack interface models because the (001) surface has the best match with the SnO2 lattice.[49] Due to the structural characteristics of the (001) slab of perovskites, we produced two kinds of interfaces based on the different terminations: the MAI termination with MA+ and I– ions and the PbI2 termination with Pb2+ and I– ions, as shown in Figure . The heterointerfaces were built by connecting the five-layer SnO2 slabs with seven-layer perovskite slabs together and left 20 Å vacuum along the nonperiodic direction. The SnO2 slab contains 10 SnO2 units, namely, 60 atoms. The perovskite slab contains 6.5 MAPbI3 units with 78 atoms for PbI2 termination, and 7.5 MAPbI3 units with 90 atoms for MAI termination. The bottom atoms of the SnO2 substrate were fixed to keep the bulk environment. The corresponding k-point mesh was 4 × 4 × 1.

Figure 1

Optimized stable geometrical structures of SnO2/perovskite interfaces: (a) PbI2/SnO2; (b) MAI/SnO2.

Results and Discussion

Stability and Bonding Characteristics of SnO2/Perovskite Interfaces

In order to evaluate the stability of the SnO2/perovskite interfaces, we calculate the interfacial adhesion energy (Ead), which is defined aswhere Einterface, ESnO, and Eperovskite denote the total energies of the heterointerface supercell, the SnO2 substrate and the perovskite slab, respectively and S is the area of the interfaces. The slabs of SnO2 and perovskite are constrained to match the lattice constants at the interfaces. A positive interfacial adhesion energy implies that it is energetically favorable to form the interface.

By using eq , we have obtained that the PbI2/SnO2 interfaces have higher interfacial adhesion energy of 1.22 J/m2 as shown in Table . For the MAI/SnO2 interfaces, it is only 0.66 J/m2. These results show that the PbI2/SnO2 interfaces are more stable than the MAI/SnO2 interfaces. Since perovskites are supposed to grow on the SnO2 surface in experiments, their lattice constants parallel to the interface are compressed to match SnO2. Then, we calculated the lattice mismatch of the SnO2/perovskite heterointerfaces to be about 11% (Table ), larger than that (7.35%) of TiO2/perovskite heterointerfaces. However, compared to the stable PbI2/TiO2 interfaces (0.93 J/m2), the SnO2/perovskite interface is energetically more stable even though it has a large mismatch.[50] But when referred to the heterointerfaces of traditional CZTS/CdS solar cells (3.05 J/m2), it can be deduced that the binding at the SnO2/perovskite interfaces is still relatively weak.[51]

Table 1

Calculated Interfacial Adhesion Energy, Lattice Mismatch and Bader Charge of Different SnO2/Perovskite Interfaces

interface	interfacial adhesion energy (J/m2)	lattice mismatch (%)	Bader charge (e)
PbI2/SnO2	1.22	11	0.74
MAI/SnO2	0.66	11	0.54

In order to study why the stability of the PbI2/SnO2 interface is better, we continue to study the bonding characteristics at SnO2/perovskite interfaces from the atomic and electronic levels. First, the analyses of Bader charge are listed in Table to address the interactions between two slabs. It shows that for the PbI2/SnO2 interfaces, the perovskite slab lost more electron (0.74 e) than the MAI/SnO2 interfaces (0.54 e). With more electron transfer between the two slabs, the binding of the PbI2/SnO2 interfaces might be stronger.

Second, the proportion of bonded atoms of the perovskite surface and bond length of the interface structures are obtained in Table . The bonding ratio of one kind of bond is defined as the surface chemical bond/surface atom number (O and Sn). In the PbI2 termination, the bonding ratio of Pb–O bonds is 50%, and the bond length of Pb–O is 2.29 Å. For Sn–I bonds, the bonding ratio is 100% and the bond length is 2.82–2.94 Å. In the MAI termination, H–O and Sn–I bonds dominate the stability of the interfaces, and the bonding ratios (bond length) are 37.5% (1.41–1.63 Å) and 50% (2.87 Å), respectively. On the basis of the above analyses of the atomic structures at the interfaces, we can conclude that the PbI2/SnO2 interfaces not only have more atoms bonded but also contain some Pb–O bonds with high strength when compared to the MAI/SnO2 interfaces, which can be considered another strong evidence for its high interfacial adhesion energy.

Table 2

Proportion of Bonded Atoms of the Perovskite Surface and Bond Length of Interface Structures

	bond (Pb–O or H–O)		bond (Sn–I)
interface	bond number (%)	band length (Å)	bond number (%)	bond length (Å)
PbI2/SnO2	50	2.29	100	2.82–2.94
MAI/SnO2	37.5	1.41–1.63	50	2.87

Furthermore, the charge density differences at the interfaces are given to clarify the interactions of different atoms. Figure depicts the charge density differences (left panels) and planar-averaged charge density differences (right panels) of the two interfaces. We can clearly observe the strong Pb–O and Sn–I coupling at the PbI2/SnO2 interfaces, while only some Sn–I coupling at the MAI/SnO2 interfaces. Electrons are favorable to accumulate around O and I atoms (yellow region) and deplete around Sn and Pb atoms (green region). The weak charge transfer at the MAI/SnO2 interfaces can also be quantitatively described by the planar-averaged charge density differences along the Z direction. The charge distribution at the interfaces could form an internal electric field to affect the charge transport properties of the solar cells. Thus, more stable PbI2/SnO2 interfaces are supposed to cause a stronger internal electric field and make the electron–hole pairs separate more easily at the interfaces.[52] We can speculate that the PbI2/SnO2 interfaces could be easier to form during the device manufacturing process as evidenced by experiments,[53] and it is beneficial to the performance improvement of the electron transport.

Figure 2

Main views of the 3D charge density differences (left panels) and planar-averaged charge density differences (right panels) along the Z direction of the (a) PbI2/SnO2 and (b) MAI/SnO2 interfaces, respectively. The location of two different defects I-1 and I-2 at the latter interfaces are also marked. The yellow region denotes the electron accumulation, and the green region represents the electron depletion.

Characteristics of the Electron Transport at SnO2/Perovskite Interfaces

The electrical properties at the interfaces are closely related to the electron transport at the interfaces. In order to understand the electrical properties of SnO2/perovskite interfaces, we first resorted to the partial density of states (PDOSs) of the interfaces, as shown in Figure . It can be seen from Figure that the CBM of SnO2 at two different interfaces are all significantly lower than that of perovskites. Because with a proper band gap, perovskites always act as the light absorption layer, electrons should be excited from the top of the valence band maximum (VBM) (I-p and Pb-s orbitals) of perovskites to the conduction band minimum (CBM) of perovskites (Pb-p orbitals) and then transferred from the conduction bands of the perovskites to the conduction bands of SnO2 (Sn-s orbitals). It also clearly shows that MA molecules have little effect on CBM and VBM at the interfaces and almost no participation in electron transport. By comparing the band gaps of the two interfaces by the HSE06, it can be found that that the band gap of the PbI2/SnO2 (1.76 eV) interface is slightly smaller than that of the MAI/SnO2 interface (2.26 eV). This is because the outflow of electrons from the Pb atoms causes the Pb states to shift to the left, thereby reducing the band gap.[54] The band gap of the PbI2/SnO2 interfaces is closer to the ideal one of single-junction solar cells, which indicates that the PCE of the PbI2/SnO2 interfaces might be higher. Moreover, the rate of electron transport at the interfaces can be determined by the CBM difference between the perovskite and SnO2 layers. A larger energy difference could accelerate the electron transport. Thus, comparing the positions of Pb-p and Sn-s orbitals in Figure , we can safely say that the electron transport at the MAI/SnO2 interfaces could have a higher efficiency. To deeply understand the characteristics of the electronic transport at the interfaces, the stress and defect effects will be further discussed in the following.

Figure 3

Partial density of states (PDOSs) for the upper and lower two-layer atoms at the (a) PbI2/SnO2 and (b) MAI/SnO2 interfaces.

Stress Effect on the Electronic Transport at SnO2/Perovskite Interfaces

Because of the lattice mismatch between the perovskite and SnO2 layers, there necessarily exists stress at the interfaces. The stress could have a nonnegligible impact on the electron transport at the interfaces and therefore should be taken into account. Figure shows the CBM and VBM of the perovskite and SnO2 layers under different deformation rates, where positive and negative values indicate that the material bears tensile stress and compressive stress, respectively. We considered the following situations: (1) all the deformation caused by the lattice mismatch occurred on the perovskite layer and it was subjected to tensile strain at the deformation rate of 9%; (2) all the deformation was applied on the SnO2 layer and it was subjected to compressive strain at the deformation rate of −8.28%; (3) the deformation was equally applied to the perovskite and SnO2 layers, and the deformation rate of the perovskite and SnO2 layers is 4.5% and −4.14%, respectively. The deformation rate here refers to the degree of deformation of the matched lattice constant at the interfaces relative to the initial lattice constant. The cell volume remains unchanged under different conditions of deformation. The core level alignment method has been employed to obtain the band alignment of two different SnO2/perovskite interfaces by using the PBE-HSE functional.[55,56] From Figure , we can see for both PbI2/SnO2 and MAI/SnO2 interfaces, the CBM of perovskite is uplifted gradually under the tensile stress and the corresponding band gap increases; the CBM of SnO2 is decreased gradually under the compressive stress with a reduced band gap. When the deformation at the interfaces mainly occurs on the perovskite layer, the CBM difference between the perovskite and SnO2 is relatively small, i.e., 0.07 eV at PbI2/SnO2 interfaces and 0.28 eV at MAI/SnO2 interfaces, which could be beneficial to improve the PCE of the PSCs;[57,58] when the SnO2 layer carries all the deformation at the interfaces, the CBM difference between the two layers could be enlarged, i.e., 0.55 eV at PbI2/SnO2 interfaces and 0.76 eV at MAI/SnO2 interfaces, which is conducive to improve the electron transport efficiency at the interfaces.[54,59] From Figure , it can be also found that the CBM offset between the two layers at the MAI/SnO2 interfaces is greater than that at the PbI2/SnO2 interfaces, indicating that the MAI/SnO2 interfaces might be more suitable for electron transport. As in the preparation process of PSCs, MAPbI3 always grows on the SnO2 layer, the perovskite layer is supposed to withstand the major deformation caused by the lattice mismatch at the interfaces. By considering the stress effect, we find that for the PSCs the CBM offset at the PbI2/SnO2 interfaces is close to 0.07 eV, and at the MAI/SnO2 interfaces is approximately 0.28 eV. There are many researchers measuring the CBM offset at perovskite/SnO2 interfaces in the experiments. For example, Park et al. and Chen et al. measured the optical properties of SnO2/CH3NH3PbI3 heterojunction by the ultraviolet–visible spectrophotometer, and they both showed the difference was 0.27 eV.[60,61] Yang et al. measured the Fermi level by Kelvin probe force microscopy (KPFM) and obtained the value of 0.10 eV,[62] and Xiong et al. measured the VBM and CBM of SnO2 by the UV photoelectron spectroscopy (UPS) and speculated it to be 0.30 eV.[63] The predicted values by the high accurate HSE06 method are very consistent with the experimental results, and our theoretical calculations have proved that the stress can be used to adjust the PCE and the electron transport efficiency at the interfaces.[64,65]

Figure 4

CBM and VBM of the (a) PbI2/SnO2 and (b) MAI/SnO2 interfaces with their deformation rates in brackets below.

Defect Effect on the Electronic Transport at SnO2/Perovskite Interfaces

Defects are more likely to occur at the interfaces, and the produced defects are likely to affect the electron transport properties at the interfaces. Therefore, we have studied the formation of several defects that may occur at the two types of interfaces and analyzed their influence on the electron transport properties at the interfaces. The formula for calculating defect formation energy is shown in eq .Ed and ESC are the total energies of the defect system and defect-free supercell structure, respectively. μi and ni are the chemical potentials and the number of defect species i that have been added to (ni > 0) or removed from (ni < 0) the supercell structure. When the number of all the species in the supercell does not change, such as antisite substitutions, then ni = 0.

The formation energies of defects depend on the chemical potentials (μi) of the constituent elements in preparation environments. In this work, we use the chemical potentials at the point B (ΔμPb = −1.06 eV, Δμ = −0.6 eV, ΔμMA = −2.41 eV) mentioned by Yin’s work as a reference, which is an intermediate state for the growth of the perovskites.[66] Δμi and μi are linked bywhere μiref is the chemical potential of the most stable elemental phase.

For the defects related with SnO2, the relevant chemical potentials μSn and μO can be determined by the following formula:where ΔH(SnO2) is the formation enthalpy of SnO2. Here, we continue to employ an intermediate state (Δμomed and ΔμSnmed) as the growth condition, which is the average value of the two extreme environments, namely, O-richest (Sn-poorest) and O-poorest (Sn-richest) conditions. In the former case, Δμorich = 0, and the corresponding Sn-poorest chemical potential ΔμSnpoor can be obtained by eq . In the latter case, the O-poorest chemical potential Δμopoor can be obtained through eq by setting ΔμSnrich = 0. On the basis of the above, we compute Δμomed = −1.19 eV and ΔμSnmed = −2.39 eV, for the intermediate state. Therefore, the related defect formation energies by using the chemical potentials (Δμomed and ΔμSnmed) can be derived.

In previous studies, Yin et al.’s DFT calculations demonstrated that VPb, VI, Ii, VMA and MAPb defects with low formation energies have transition levels less than 0.05 eV above (below) VBM (CBM) in CH3NH3PbI3.[66] Freeman et al. found that the point defects in SnO2 are mainly Schottky defects, and the interstitial defects Sni and Oi are easily formed.[67] Noh et al. found there are a lot of oxygen vacancies in SnO2 films.[68] Shi et al. indicated that there might be some element exchanges at the interfaces.[69] On the basis of these results, we have considered all these possible point defects that might be easily formed at the CH3NH3PbI3/SnO2 interfaces, including four vacancies (VO, VPb, VI, VMA), three interstitials (Sni, Oi, Ii), one cation substitution (MAPb), and two antisite substitutions (Sn–I, Pb–O). Table lists the formation energies of ten possible defects at the PbI2/SnO2 interfaces. Among these defects, these five types of defects, such as VI, VO, Ii, MAPb, and Sni are more likely to form at the interfaces with a formation energy less than 1 eV. VO has a low formation energy of 0.10 eV, which is consistent with the previous experiments’ observations that O vacancy can easily form at the interface.[68,69] For VI and Ii, their formation energies at the interface are 0.37 and 0.26 eV, respectively, relatively smaller when compared to the bulk. It can be attributed to the bonding environment at the interface that the lattices of the perovskites are expanded by the tensile stress, which weakens the bond strength of Pb–I bonds and enlarges the interstice space. Therefore, VI and Ii become easily formed at the interface. For the MAPb, the formation energy at the interface is largely reduced to −0.60 eV. By checking the bonding characteristics, we can observe that the MA loses an H to form CH3NH2, and the H preferably passivates the dangling bonds of O atoms at the interface, which largely reduces the formation energy of MAPb. [See Figure S1.] Similarly, one interstitial Sn atom could form two strong Sn–O bonds at the interface, which makes the formation energy of Sni much lower than the bulk. However, it is worth noting that the free volume and the dangling O atoms might be exhausted by a small content of defects, and then the interstitial defects could become hard to form.

Table 3

Defect Formation Energies at the PbI2/SnO2 Interfaces

	defect
	Sn–I	VI	VMA	VO	Ii	MAPb	Oi	Pb–O	Sni	VPb
formation energy (eV)	2.20	0.37	1.58	0.10	0.26	–0.60	1.37	2.69	–0.21	3.60

In order to address the impact of the defects on the electron transport efficiency at the PbI2/SnO2 interface, the PDOSs of these five defect systems by the HSE06 method have been depicted in Figure . From Figure a, we can see the formation of VI at the interfaces causes Pb-p states slightly shift to the left, which reduces the band gap and makes the CBM of CH3NH3PbI3 significantly lower than that of SnO2. Therefore, the electron transport from CH3NH3PbI3 to SnO2 becomes denpendent on thermal effects. For VO at the interface, it almost has little effect on the band gap, VBM and CBM (Figure b), which demonstrates that a small amount of oxygen vacancies at the interface might be acceptable. As for Ii at the interface, it causes I-p states to shift slightly to the left (Figure c), which is close to or just below the CBM of SnO2. To some extent, it could also affect the electron transport mechanism at the interface. For Sni at the interfaces, we can observe a shallow defect level (Sn-s) lying at E = −0.7 eV below the VBM (Figure d). The shallow defect level caused by Sni could not become the recombination center of electrons and holes and might not be harmful for the electron transport at the interfaces. The formation of MAPb at the interface causes the Pb-p states slightly shift to the right (Figure e); this does not affect the transport mechanism of electrons but may cause electrons accumulation at the interface. This change could increase the open circuit voltage of the PSCs, which finally affects the PCE of solar cells.[70]

Figure 5

PDOSs for the upper and lower two-layer atoms at the PbI2/SnO2 interfaces with different defects: (a) I vacancy, (b) O vacancy, (c) I interstitial, (d) Sn interstitial, and (e) MAPb cation substitution.

As for the MAI/SnO2 interfaces, we have also chosen several possible point defects including five vacancies (VO, VPb, VI-1, VI-2, VMA), three interstitials (Sni, Oi, Ii), one cation substitution (MAPb), and one antisite substitution (Sn–I).[66−69]Table lists the corresponding formation energies of these possible defects. Due to the different bonding environments at the MAI/SnO2 interfaces, two different iodine atoms labeled as I-1 and I-2 in Figure are involved in this study. Among these ten defects, eight types of defects have a formation energy less than 1 eV, namely, Sn–I, VI-1, VI-2, VO, Ii, MAPb, Oi, and Sni. Obviously, compared to the defects at the PbI2/SnO2 interfaces, Sn–I, VO, Ii, Oi, and Sni at the MAI/SnO2 interfaces are favorable to form with a relatively smaller formation energy. We can attribute these to the poor stability and bonding characteristics of the MAI/SnO2 interfaces. The Sn–I antisite substitution becomes easily formed at this weak-binding interface with the formation energy of 0.89 eV. For the defect of I vacancy, the formation energy of VI-2 (0.33 eV) is less than that of VI-1 (0.63 eV), because the strength of Sn–I bonds is weaker than that of Pb–I bonds. VO has a low formation energy of 0.01 eV at the MAI/SnO2 interfaces, which is similar to that for the PbI2/SnO2 interfaces and consistent with experimental observations.[67,68] Compared with the PbI2/SnO2 interfaces, the formation energies of Ii and Oi are becoming lower. This is because the MAI/SnO2 interfaces have larger interstice space at the interfaces. For MAPb at the MAI/SnO2 interfaces, its formation energy becomes larger due to that the MA molecule replacing a Pb atom is far away from the SnO2 layer and could not be bonded to the dangling O atom. As for Sni at the MAI/SnO2 interfaces, we could also observe the similar phenomenon as the PbI2/SnO2 interfaces. It has very low formation energy of −0.32 eV because of the free volume and the dangling O atoms. [See Figure S2].

Table 4

Defect Formation Energies at the MAI/SnO2 Interfaces

	defect
	Sn–I	VI-1	VI-2	VMA	VO	Ii	MAPb	Oi	Sni	VPb
formation energy (eV)	0.89	0.63	0.33	1.91	0.01	0.11	0.17	0.79	–0.32	1.86

For these defects that might form at the MAI/SnO2 interfaces, we also give the PDOSs in Figure for further discussing their effects on the electron transport. From Figure a, it is noticed that there appear I-p and O-p levels near the middle of the band gap for the Sn–I antisite substitution defect. The deep levels in the band gap produced by the defect could attract electrons/holes and act as Shockley–Reid–Hall nonradiative recombination centers, which could adversely affect the efficiency of the solar cells. On the other hand, the band edges of VBM and CBM are totally changed, which are not conducive to electron transfer from CH3NH3PbI3 to SnO2. In Figure b, VO creates a defect level (Sn-s) at E = −0.4 eV, where the level is located just above the VBM of CH3NH3PbI3. Because the electronic transport path does not involve the VBM of SnO2, the production of an oxygen vacancy could have no impact on the electron transport properties at the interfaces. From Figure c,d, we can see I-1 and I-2 vacancy defects have slightly moved the CBM of SnO2 upward and have little effect on the electron transport process at the interfaces. For Sni and Ii defects, they both create defect levels near the middle of the band gap. As shown in Figure e,f, the defect levels are composed of Sn-s, Sn-p, O-p, and I-p at E = 0.5 eV for Sni and I-p and Pb-p at E = 1.1 eV for Ii, respectively. Thus, Sni and Ii can be classified as harmful defects and the deep levels might become recombination centers for electrons and holes. Besides, Sni makes the Pb-p shift to the CBM edge, which seriously influences the electron transfer from CH3NH3PbI3 to SnO2. Unlike other defects, Oi at the interfaces does not create any defect levels but narrows the band gap of SnO2 to 1.58 eV as observed from Figure g. The reduced band gap could decrease the open circuit voltage of PSCs and therefore affects the PCE of the solar cells.[70] As for MAPb at the interfaces, it creates a defect level (Pb-p) at E = 3.2 eV (Figure h). As the defect level is just located above the CBM of CH3NH3PbI3, the effects on the electron transport can be neglected.

Figure 6

PDOSs for upper and lower two-layer atoms at the MAI/SnO2 interfaces with different defects: (a) Sn–I antisite substitution, (b) O vacancy, (c) I-1 vacancy, (d) I-2 vacancy, (e) I interstitial, (f) Sn interstitial, (g) O interstitial, and (h) MAPb cation substitution.

In general, VI and Ii can be classified as the harmful defects, and VO, Sni, and MAPb are the benign defects at the PbI2/SnO2 interfaces. At the MAI/SnO2 interfaces, Sn–I, Ii, and Sni are harmful, and VO, VI, Oi, and MAPb are benign. Obviously, harmful defects are more easily formed at the MAI/SnO2 interfaces. Ii is the most easily formed harmful defect at both PbI2/SnO2 and MAI/SnO2 interfaces, which is consistent with the previous calculations and experimental results.[71−73] The harmful defects affect the transport of electrons from CH3NH3PbI3 to SnO2 or create deep levels that could become the recombination center of electrons/holes, thereby injuring the performance of PSCs. Therefore, minimizing the formation of the MAI/SnO2 interfaces and avoiding the harmful defects could be beneficial to achieve high-performance and stable PSCs.

Conclusion

In this paper, first-principles calculations have been performed to study structural and electronic properties of CH3NH3PbI3/SnO2 interfaces by involving two different terminations (PbI2 and MAI). It is expected that the PbI2/SnO2 interfaces have a high interfacial adhesion energy of 1.22 J/m2 due to the interfacial Pb–O and Sn–I bonding as well as a stronger internal electric field for the electron–hole pairs separation. The effects of the stress and defects at the interfaces on the electron transport are also thoroughly addressed. The tensile stress could move the CBM of CH3NH3PbI3 upward, and the compressive stress could move the CBM of SnO2 downward. By considering the stress effect, the CBM offset at the PbI2/SnO2 interfaces is close to 0.07 eV, and at the MAI/SnO2 interfaces is approximately 0.28 eV. Moreover, according to our research on possible interface defects, VI, and Ii can be classified as the harmful defects at the PbI2/SnO2 interfaces, and Sn–I, Ii and Sni are harmful at the MAI/SnO2 interfaces. The harmful defects affect the transport of electrons from CH3NH3PbI3 to SnO2 or create deep levels that could become the recombination center of electrons/holes. For both PbI2/SnO2 and MAI/SnO2 interfaces, Ii is the most easily formed harmful defect and should be avoided in experiments. These results might contribute to the understanding of the CH3NH3PbI3/SnO2 interfaces and provide some references for finding ways to improve the stability and photovoltaic performance of the PSCs.