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First Principles Study of Electron Injection and Defects at the TiO/CHNHPbI Interface of Perovskite Solar Cells 2

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Jun Haruyama, Keitaro Sodeyama, Ikutaro Hamada, Liyuan Han, and Yoshitaka Tateyama J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b02622 • Publication Date (Web): 12 Nov 2017 Downloaded from http://pubs.acs.org on November 13, 2017

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The Journal of Physical Chemistry Letters

First Principles Study of Electron Injection and Defects at the TiO2/CH3NH3PbI3 Interface of Perovskite Solar Cells Jun Haruyama,*,† Keitaro Sodeyama,‡,⊥ Ikutaro Hamada,† Liyuan Han,‖ and Yoshitaka Tateyama*, ‡, § †

Global Research Center for Environment and Energy Nanoscience (GREEN), and §International

Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan ‡

Center for Materials Research by Information Integration (CMI2), Research and Services

Division of Materials Data and Integrated System (MaDIS), and ‖Research Network and Facility Services Division, National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan ⊥

PRESTO, Japan Science and Technology Agency (JST), 4-1-8 Honcho, Kawaguchi, Saitama

333-0012, Japan AUTHOR INFORMATION Corresponding Author *Email: [email protected] *Email: [email protected]

ACS Paragon Plus Environment

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ABSTRACT We investigated electron injection rates and vacancy defect properties by performing first-principles calculations on the interface of an anatase-TiO2(001) and a tetragonal CH3NH3PbI3(110) (MAPbI3(110)). We found that the coupling matrix element between the lowest unoccupied molecular orbital of MAPbI3 and the TiO2 conduction band (CB) minimum is negligibly small, the indication being that electron-injection times for low-energy excited states quite long (> several tens of picoseconds). We also found that higher-lying CB states coupled more strongly; injection was expected to take place on a femtosecond time scale. Furthermore, we found that vacancy defects in the TiO2 layer produced undesired defect levels that caused hole traps and recombination centers. Whereas most of the vacancy defects in the MAPbI3 layer produced no additional states in the MAPbI3 gap, a Pb vacancy (VPb) at the interface created an energy level below the MAPbI3 CB edge and had a lower energy of formation than the VPb defect in bulk because of the interaction with the TiO2 surface.

TOC GRAPHICS Energy Diagram at TiO2/MAPbI3 interface Energy

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CBM LUMO large Γ (~0.3eV)

small |Vda| (< 1meV) VO defect levels

TiO2

Energy loss

MAPbI3


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The conversion of solar energy to electrical power is one of the most important renewable energy technologies being considered to address problems associated with global warming, the depletion of fossil fuels, and the instability of nuclear power generation. The power conversion efficiencies (PCEs) of perovskite solar cells (PSCs) based on methylammonium lead iodide (MAPbI3) and its derivatives have increased dramatically in recent years. The PCE, first reported to be 3.8%1, has increased to over 22% in the past 6–7 years.2–10 Although the practical applications of PSCs are still constrained by the short-term stability of the metal halide perovskites, a detailed analysis of PSC modules indicates that they can become a cost-effective alternative to traditional energy sources in the near future.11 The great progress with PSCs has been due largely to several exclusive properties of the characteristic absorbing layer, MAPbI3. One of the outstanding properties of MAPbI3 is its very long diffusion paths for both photo-excited holes and electrons. The path lengths range from subµm12–14 to a hundred µm15. The high mobility and slow recombination rate of excited carriers16–18 are indicative of effective carrier transport from the photo-absorbing MAPbI3 layer to the attached charge-extracting layer, i.e., the electron-transport layer (ETL) or hole-transport layer (HTL). This remarkable ability of photo-excited carriers is theoretically explained by the low effective masses of both carriers19–21 and the shallow defect levels in bulk.22–25 Even at their surfaces, the stable structures of MAPbI3 have almost no midgap state.26–29 In particular, the absence of midgap states leads to a few carrier traps and nonradiative recombination centers, the result being long diffusion lengths. The photo-excited carriers in the MAPbI3 layer are expected to reach the ETL or HTL with negligible energy loss, and interfaces between photo-absorbing perovskites and charge-extracting layers have therefore attracted considerable attention.


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Here we consider TiO2/MAPbI3 as the most representative ETL/perovskite interface, and we focus on electron injection from the MAPbI3 layer to the TiO2 scaffold. Many experimental studies have applied time-resolved techniques to unravel ultrafast events such as charge separation and recombination at interfaces16–18,30–33 because the quantum yield for electron injection can be determined from the relationships between the magnitudes of the rates of electron injection, radiative and nonradiative decay, and all possible quenching pathways. Although knowledge of the charge-separation rates is essential for establishing the architecture of the PSC interface, a wide range of values (nanosecond to sub-picosecond timescales) has been reported.30–33 From the standpoint of unravelling energy loss processes, the precise role of TiO2/MAPbI3 interface in PSC is still unclear, in contrast with the well-established knowledge of its role in dye-sensitized solar cells (DSSCs).34 A clear understanding of carrier reaction dynamics at the TiO2/MAPbI3 interface will be necessary to further improve of PSCs. De Angelis and co-workers have conducted density functional theory (DFT) calculations35–39 to intensively study anatase TiO2 (aTiO2) and tetragonal MAPbI3 (tMAPbI3) interfaces. They have calculated the atomic and electronic structures of aTiO2(101)/tMAPbI3(110) and aTiO2(101)/tMAPbI3(001) interfaces and have found that the interface of tMAPbI3(110) is more stable than that of tMAPbI3(001).37 Those studies revealed that interfacial chlorine atoms tended to locate at the TiO2 interfaces, a tendency consistent with the observation of high chlorine concentrations at the TiO2/MAPbI3 interface.38 In a subsequent study, they reported a strong interfacial modification associated with the PbI2-terminated interface.39 First-principles investigations

dealing

with

aTiO2(001)/MASnxPb1-xI3,

rutile-TiO2(110)/MAPbI3-xClx,

amorphous-Al2O3/MAPbI3, and time-domain studies at aTiO2(001)/MAPbI3(100) have also been reported by several authors.40–44


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In this letter, we focused on the carrier-transport dynamics at the interface of aTiO2(001)/tMAPbI3(110) and conducted first-principles calculations. Similar to previous investigators, we calculated the atomic and electronic structures at the interface. Next, we estimated the rates of electron injection at the interface from the coupling matrix elements between the conduction band (CB) states of TiO2(001) and MAPbI3(110). We further investigated the electronic structures in the presence of vacancy defects. Based on the calculated electronic densities of states (DOSs), we suggest that certain defects should be avoided when fabricating each component layer. In addition, we discuss the Hubbard U and spin-orbit coupling (SOC) effects on the behavior of electron injection and defect levels. Figure 1 shows the most stable structure of the aTiO2(001)/tMAPbI3(110) interfaces. The relaxed structures of all the aTiO2(001)/tMAPbI3(110) interfaces considered in this work are shown in Figure S5. Some of the Pb atoms on the MAPbI3 surfaces showed large structural changes, in contrast with the negligible deformation of aTiO2 layers. The strong Pb–O interactions at the interfaces pulled Pb atoms from the surfaces, and some of the PbI5 polyhedrons were broken. The fact that the interfacial atomic bonds were quite incomplete compared with the oxide/oxide interface, however, reflects the large difference between the cell parameters (or bond lengths) of oxide and iodide. In addition, Ti–I interactions were relatively weak, and there were only a few Ti–I bonds at the constructed aTiO2/tMAPbI3 interfaces. We note here that simple bond counting at the interfacial region is useful for qualitative estimation of electronic couplings.


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b c

O1 Ti1 I1

Pb1

Pb2

MA1

Figure 1. Optimized interface structure of aTiO2(001)/tMAPbI3(110). The H, C, N, O, Ti, I, and Pb atoms are depicted as white, brown, light blue, red, blue, purple, and black spheres, respectively. Blue and black polyhedrons represent TiO6 (or TiO5) and PbI6 (or PbI5) complexes, respectively. The atomic sites near the interface are labeled for vacancy calculations.

Table S3 lists the relative energies, cell parameters, and adhesion energies of the relaxed structures for our constructed interface models. All of these results were calculated with the vdW functional and U = 0. The energy differences between the relaxed interfaces were ~2 eV. The optimized in-plane lattice constants (a’s) of our interface supercells were close to that of aTiO2

(for 3.784 × 7 = 26.488 Å) for each model, whereas the b’s were consistently shorter. This

shrinkage resulted from the small slab size of aTiO2(001), because the cell parameters of the aTiO2(001)/tMAPbI3(110) interfaces were almost the same as those of the surface slab of aTiO2(001) containing four Ti layers (see Table S1). The one-sided deformation of the MAPbI3


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layer may reflect the fact that the oxides were rigid enough to keep their atomic structures, whereas the soft iodide materials were influenced by the interface interactions and modified their structures to fit the oxide scaffolds. The distortions themselves turned out to have little effect on the electronic structures. The formation energies of interface defects, however, were modified by interface interactions, as discussed below. The

adhesion

energies

(i.e.,

the

binding

energies

per

unit

area)

of

the

aTiO2(001)/tMAPbI3(110) interfaces exceeded 6 eV/nm2. Mosconi et al. have obtained a similar energy of ~4 eV/nm2 for their aTiO2(101)/tMAPbI3(110) interface.37 The difference can be attributed to the different lattice parameters and terminations among the surfaces of aTiO2(001), aTiO2(101), MA-terminated tMAPbI3(110), and PbI2-terminated tMAPbI3(110). A previous experiment indicated that the facets of aTiO2(001) are more effective than those of (101),45 and we could therefore expect that the small lattice distortion of the tMAPbI3(110) layer contributed to the high solar cell efficiencies. However, it is difficult to explain the efficiency of aTiO2 surfaces on the basis of nothing more than structural properties; electron-injection times, defect or trap states, and recombination rates at aTiO2 interfaces should also be investigated. Hereafter, we focus for simplicity on the most stable interface. The electronic structures of the interfaces were investigated by calculating the PDOS shown in Figure 2. The upper part of the VB consisted mainly of I-5p and Pb-6s orbitals, as was the case for MAPbI3 bulk22,25 (n.b., the surface states of the MAPbI3 layer are located at the top of the VB26). The O-2p and the small amount of Ti-3d character (i.e., the VB of the TiO2 layer) was located at an energy 1.7 eV. The CB offset (~1 eV) was overestimated compared with the offsets of previous


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experiments (0.07–0.4 eV46,47). Because the energy gaps of the TiO2 and MAPbI3 layers were almost the same as those of the surface slabs (see Tables S1 and S2), more accurate descriptions (especially of CB levels) will be necessary for correct evaluation of band alignments. In spite of the bond breaking and deformation at the interface, no midgap level appeared, and reasonable band alignment was obtained. These properties of the electronic structure were consistent with previous DFT calculations.35–37

Density of states (states/eV)

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Total Ti O Pb I MA

500 400 300 200 100 0 -4

-2

0

2

4

Energy (eV)

Figure 2. PDOS of the aTiO2(001)/tMAPbI3(110) interface. The black, blue, red, green, purple, and yellow lines represent the PDOS of the total interface, Ti, O, Pb, I atoms, and MA molecules, respectively. The dotted line indicates the Fermi level. The zero points of energy were set at the top of the occupied band.

The coupling strength between the electronic states of the TiO2 and MAPbI3 layers could be estimated roughly by broadening the PDOS. Figure S6 (d) shows the enlarged PDOS. In the VB and CB offset regions, the Ti-3d and O-2p character spreads out, and the Pb-6p and I-5p character deviates downward, respectively. This behavior indicates the strong coupling between the layers and reflects the character of the Pb–O bonds. We can thus infer that electron injection


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was fast in these broadening regions, as already discussed qualitatively in a previous DFT calculation.37 Quantitative estimation of electron injection rates is enabled by evaluating the coupling matrix elements |Vda|, as discussed below. Figure 3 shows the coupling matrix elements |Vda| between donor (the diabatic MAPbI3 LUMO) and a wide range of acceptor states (diabatic TiO2 CB) as a function of the acceptor energy levels. Together with the energy of the donor state (ELUMO), the spectral function Γ(E) in eq (3) is also depicted. The |Vda| elements were calculated from eq (1) by adopting the PDOS coefficients shown in Figure 2. In the partitioning procedure, we were then able to obtain wellseparated DOSs attributable to the MAPbI3 and TiO2 states (Figure S7 (a)). Calculation of the coupling matrix elements revealed two main characteristics of electron injection.

Γ(E) |Vda|

0.3

Γ(E), |Vda| (eV)

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ELUMO 0.2

0.1

0 0

1

2

3

Energy (eV) Figure 3. Spectral function Γ(E) (black line) and coupling matrix |Vda| between the diabatic MAPbI3 LUMO (donor) state, and TiO2 CB (acceptor) states (green impulses). The energies of the diabatic MAPbI3 LUMO state (ELUMO) are indicated by red lines.

First, the spectral function Γ(E) (E < 1 eV) showed no structure, although the state of the diabatic TiO2 CB minimum (CBM) was located at 0.79 eV. The value of |Vda| between the


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MAPbI3 LUMO state and the TiO2 CBM state was less than 1 meV, see Table1. This small coupling reflects the following facts. In the aTiO2(001)/tMAPbI3(110) interface, interface electronic interactions were largely associated with the Pb–O bonds. The TiO2 CBM consisted mostly of Ti-3d orbitals and showed a negligible contribution from the O-2p orbital. The MAPbI3 LUMO (Pb-6p) and the TiO2 CBM (Ti-3d) could therefore not interact with each other, the result being quite small values for |Vda|. In contrast, the value of |Vda| between the MAPbI3 LUMO (Pb-6p) and the TiO2 VB maximum (VBM) was relatively large because of the O-2p character of the TiO2 VB. We expect that the electron injection time was longer than several tens

of picoseconds in the excited low-energy region (E = 0.5–1 eV) based on the relation = ℏ/Γ, although the estimation of Γ in eq (3) depends on the broadening parameter.

Table 1. The values of the coupling matrix |Vda| between the diabatic MAPbI3 LUMO (donor) state and the TiO2 (acceptor) states. These results were calculated with U = 0 condition. Acceptor state

Energy level of

∣Vda∣ [meV]

acceptor state [eV] VBM

-1.97

5.37

CBM

0.79

0.53

Second, the coupling elements were much larger in the high-energy region (E = 1–2 eV) than in the low-energy region (E < 1 eV). The maximum value of Γ (~0.3 eV) was comparable to the Γ’s of dye-sensitized solar cells calculated in previous studies.48–50 Because the TiO2 CB states in the high-energy region showed a small O-2p contribution (see Figure 2), they coupled strongly with the MAPbI3 LUMO state. The sub-eV magnitude of the Γ function therefore indicated a short electron injection time (femtosecond range). We note that, in the evaluation of the injection


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times, the exciton separation dynamics were not taken into account; only the injection times from already-separated electronic (MAPbI3 CB) states to ETL (TiO2 CB) states were considered. Nonetheless, our simple estimate provides possible explanations for the controversial electroninjection times observed in experiments; low-energy excited states inject slowly, and highenergy excited states inject very rapidly. However, to fully understand the injection properties, an extensive study of injection rates at various interfaces with different facets or terminations would be required. In addition, to obtain a reliable Γ value requires a high precision spectral function, the more accurate description is to directly calculate the injection and recombination times using Marcus theory or time-domain stimulations.43,44 We here briefly discuss the effects of Hubbard U and SOC. Figure S6 shows the PDOSs and coupling matrix elements calculated by including these effects. Inclusion of Hubbard U (= 3 eV) caused the energy levels of the TiO2 CB to show a small upward shift, and the energy gap increased from 0.76 to 1.1 eV. In contrast, inclusion of SOC effects caused the energy levels of the MAPbI3 CB to show a large downward shift ( ~1 eV), a result consistent with bulk MAPbI3 calculations.19–21,51,52 All of the PDOSs show reasonable band alignments; the VBM of TiO2 was lower than that of MAPbI3, whereas the CBM of MAPbI3 was higher than that of TiO2. Figure S7 and Tables S4 show the coupling matrix elements, including cases with U = 3 eV or with SOC. Despite the band shifts due to the different computational setups, the spectral function Γ(E) showed almost the same shape as the Γ(E) corresponding to U = 0. Furthermore, the values of |Vda| for the low-energy TiO2 CB state showed similar values (at least the magnitude was

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