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Strong Interaction at the Perovskite/TiO Interface Facilitates Ultrafast PhotoInduced Charge Separation: A Nonadiabatic Molecular Dynamics Study Run Long, Wei-Hai Fang, and Oleg V. Prezhdo J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b12921 • Publication Date (Web): 07 Feb 2017 Downloaded from http://pubs.acs.org on February 8, 2017

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The Journal of Physical Chemistry

Strong Interaction at the Perovskite/TiO2 Interface Facilitates Ultrafast Photo-Induced Charge Separation: A Nonadiabatic Molecular Dynamics Study Run Long,1* Wei-Hai Fang,1 Oleg V. Prezhdo2† 1

College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing, 100875, P. R. China

2

Department of Chemistry, University of Southern California, Los Angeles, CA 90089, USA

ABSTRACT: Interfacial electron transfer (ET) plays a key role in the operation of solar cells based on TiO2 sensitized with organohalide perovskites, since it leads to separation of the photo-generated electrons and hole into different materials. The reported experimental ET times range by over three orders of magnitude, from sub-200 fs to over 300 ps. Using nonadiabatic molecular dynamics combined with ab initio time-domain density functional theory, we demonstrate that ET at a CH3NH3PbI3/TiO2 interface can be complete within 100 fs, indicating that the longer time scales reflect other processes, such as charge and exciton diffusion in perovskite bulk. The electron injection is fast because the interaction between the donor and acceptor species is strong at ambient conditions. Photoexcitation directly at the interface can create a charge separated state. Electrons generated farther away inject by a combination of adiabatic and nonadiabatic mechanisms. Thermally activated low frequency vibrational motions at the interface modulate the CH3NH3PbI3/TiO2 separation, creating opportunities for chemical bonding and generating channels for adiabatic ET. Higherfrequency modes create large nonadiabatic coupling. The interaction between perovskite and TiO2 is purely van der Waals at 0 K, whereas at ambient temperatures I-Ti covalent bonds

* †

Corresponding author, E-mail: [email protected] Corresponding author, E-mail: [email protected]

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can form transiently at the interface. The covalent bonding is particularly important for photo-excitation of charge-separated states and adiabatic ET. The ET occur prior to nonradiative electronic energy losses that can lead to charge trapping and recombination. The ultrafast interfacial charge separation contributes to the high efficiencies of perovskitesensitized TiO2 solar cells. The reported simulations provide a detailed time-domain atomistic description of the interfacial ET and advance our understanding of carrier dynamics in perovskite solar cells.


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1. INTRODUCTION Bringing

ideas

from

dye-sensitized

solar

cells,1

organohalide

perovskite

(CH3NH3PbI3)-sensitized TiO2 solar cells have been attracting intense attention in the past several years due to its rapidly increasing power conversion efficiency: starting at 3.8 % of the first perovskite solar cells,2 and reaching3-7 and exceeding 20%8-10 within five years. Low charge recombination rates, high charge-carrier mobilities, and long electron and hole diffusion lengths are believed to be responsible for the high performance of perovskite solar cells.11-28 In particular, the excited state lifetime in the CH3NH3PbI3 perovskite can last from several nanoseconds29 to several microseconds,30 and it further increases in the CH3NH3PbI3/TiO2 system.31-33 Slow electron-hole recombination reduces electronic energy dissipation into phonons and enhances photon-to-electron conversion efficiency. Realistic factors such as defects and environment, such as moisture, have a complicated influence on the electron-hole recombination. Local microstructures decrease excited electronic state lifetimes and deteriorate solar cells quality, while surface passivation can have a significant positive effect.34-35 Rational choice of dopants can control electron-hole recombination in pristine CH3NH3PbI336 and at the CH3NH3PbI3/TiO2 interface.37 Low humidity delays electron-hole recombination in CH3NH3PbI3 perovskites, while heavy humidity accelerates the recombination.38 The photo-induced interfacial electron transfer (ET) constitutes the initial step of conversion of solar energy into electrical or chemical energy, leading to generation of free charge carriers. Rapid charge separation is usually favorable, since separated charges cannot recombine easily. Further, if charges can separate before relaxing to their lowest energy states, they are less likely to get trapped at interfacial defects. Figure 1 shows the energy diagram of the CH3NH3PbI3/TiO2 interface. Photoexcitation of CH3NH3PbI3 promotes an electron from its ground state into its excited state that is located energetically within the TiO2 conduction 3 ACS Paragon Plus Environment


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band (CB). The electron is subsequently injected into the TiO2 CB. Since the CB minimum (CBM) of perovskite CH3NH3PbI3 is higher than the CBM of TiO2, the electron can be efficiently injected into the TiO2 CB even if it relaxes rapidly down to the band edge of perovskite. This is because the excited electron requires several nanoseconds to recombine with the hole, needing to pass across a wide energy gap.31-33 The non-radiative electron-hole recombination is a high order process requiring excitation of many phonons.

Figure 1. Energy diagram for the photoinduced electron injection from CH3NH3PbI3 into a TiO2 surface. An absorbed photon promotes an electron from the valence band (VB) to the conduction band (CB) in CH3NH3PbI3, putting it in resonance with the TiO2 CB. Then, the excited electron is injected into the TiO2 CB.

Interestingly, experiments showed a variety of time scales of electron injection from CH3NH3PbI3 into TiO2, ranging from sub-200 fs to 300 ps, as measured by different techniques.39-43 Zhu et al. reported the injection times of 260-307 ps.41 Insertion of a layer of ultrathin graphene quantum dots between perovskite and TiO2 accelerates ET to 90-106 ps.41 Using time-resolved terahertz and microwave conductivity measurements, Ponseca and coauthors suggested that ET from CH3NH3PbI3 into TiO2 occurs within 2 ps.40 These ET time scales are several orders of magnitude longer than intraband carrier cooling.24 Sum et al. 4 ACS Paragon Plus Environment

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pointed out that band bending due to strong interfacial dipoles may result in a barrier for ET between CH3NH3PbI3 and TiO2.44 The longer ET times can be attributed to electron diffusion inside perovskite, rather to the interfacial ET itself. More recently, Piatkowski and coauthors reported the photoinduced ultrafast ET from CH3NH3PbI3 into TiO2 to occur within 200 fs.39 Such rapid ET competes successfully with the electron-phonon energy relaxation inside CH3NH3PbI3,26 demonstrating that hot electrons can be efficiently extracted from the photosensitizer. The broad range of the experimental ET times reported for the CH3NH3PbI3-TiO2 system motivates theoretical investigations, which can separate the interfacial ET process from charge diffusion to and from the interface. By mimicking most directly the timeresolved experiments, ab initio time-domain simulations also establish the ET mechanisms, which have qualitatively different dependence on system properties, such as donor-acceptor coupling and local densities of states. The simulations identify the phonon modes that participate in the ET process. An ab initio atomistic description captures the realistic aspects of the CH3NH3PbI3/TiO2 interface, including the possibilities of chemical interactions, formation of defects, thermally induces disorder, charge trapping, etc. As demonstrated with the studies of TiO2 surfaces sensitized with molecule chromophores,45-51 water,52 semiconducting53-55 and metallic56 nanoparticles, and graphene,57 an atomistic description complements phenomenological models and provides many valuable and often critical insights into the photoinduced electron-vibrational dynamics.58 Presently, we report simulations of the photoexcited ET and related processes at the CH3NH3PbI3/TiO2 interface, using a combination of nonadiabatic molecular dynamics (NAMD) with real-time time-domain density functional theory (TDDFT).59-60 The simulations demonstrate that the photo-excited (PE) electron can be efficiently extracted by TiO2 within 100 fs, competing successfully with electron-phonon relaxation inside the 5 ACS Paragon Plus Environment


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CH3NH3PbI3. The ET is ultrafast due to strong interaction between CH3NH3PbI3 and TiO2. The strong donor-acceptor coupling creates the possibility of optical excitation of chargeseparated states, if photoexcitation occurs near the interface. PE electrons generated farther from the interface inject with nearly equal probability by both adiabatic and nonadiabatic mechanisms. Several scenarios for individual ET events can be observed.

Thermally

activated low-frequency vibrational motions modulate chemical bonding at the interface and affect the donor-acceptor coupling strength. Higher frequency modes create large nonadiabatic coupling. The strong chemical-like donor-acceptor interaction at the CH3NH3PbI3/TiO2 interface favors ultrafast ET, which contributes to the observed high power conversion efficiency of solar cells based on perovskite sensitized TiO2.

2. METHODS The simulations of ET dynamics are performed using the mixed quantum-classical approach61 implementing NAMD59,

62-64

within TDDFT65-67 in the Kohn-Sham (KS)

representation.68 The faster and lighter electrons are treated quantum mechanically, while the slower and heavier nuclei are classical. The computational procedure is outlined below. A detailed description of this approach can be found in ref.59-60, 69-70

2.1 Time-Dependent Kohn-Sham Theory for Electron-Nuclear Dynamics The ET dynamics including the nonadiabatic effects71 are described by real-time TDDFT59-60 within the Kohn-Sham (KS)68 framework. The electron density, , , is expressed by the sum of the densities of the occupied time-dependent single-electron KS orbitals, , , Ne

ρ (r, t ) = ∑ | ϕ p (r, t ) |2

(1)

p =1


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The evolution of the electron density is determined by the time-dependent variational principle, leading to a set of single-electron equations for the evolution of the KS orbitals:

ih

∂ϕ p (r, t ) ∂t

= H (r, R, t )ϕ p (r, t ); p = 1,2,..., Ne

(2)

The single-electron equations are coupled, because the Hamiltonian H depends on the electron density. The electron-vibrational interaction enters the Hamiltonian H through the external potential generated by the atomic motions. The time-dependent single-electron orbitals in eq 2 are expressed in the basis of the adiabatic KS orbitals, ϕ% p (r, R (t )) , which are calculated for the current atomic positions R. The adiabatic representation of the time-dependent KS orbital occupied by the PE electron is given in eq 3

ϕ PE (r , t ) = ∑ ck (t )ϕ%k (r; R (t ))

(3)

k

Inserting eq 3 into eq 2 gives the equation for evolution of the expansion coefficients.

ih

∂ c j (t ) = ∑ ck (t )(ε kδ jk + d jk ) ∂t k

(4)

where ε k is the energy of the adiabatic state k, and d jk is the nonadiabatic coupling between states k and j. The nonadiabatic coupling is created by atomic motions and reflects the strength of electron-vibrational interaction. It is calculated numerically as the overlap of orbitals j and k at sequential time steps

d jk = −ih < ϕ% j | ∇ R | ϕ%k > • ≈−

dR ∂ = −ih < ϕ% j | | ϕ%k > dt ∂t

ih (< ϕ% j (t ) | ϕ%k (t + ∆t ) > − < ϕ% j (t + ∆t ) | ϕ%k (t ) >) 2∆t


(5)


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2.2 Electron Transfer Mechanisms: Adiabatic, Nonadiabatic and Direct by Photoexcitation The extent of ET from CH3NH3PbI3 into the TiO2 surface is computed by integrating the PE electron density over the region of the simulation cell occupied by CH3NH3PbI3, Figure 2.

∫

CH3 NH3 PbI3

ρPE (r, t )dr = ∫

CH3 NH3 PbI3

= ∑ ck* (t )c j (t )∫

| ϕPE (r, t ) |2 dr

CH3 NH3 PbI3

k, j

ϕ%k* (r, R(t ))ϕ% j (r, R(t ))dr

(6)

The time-derivative of eq 6 gives the contributions of the adiabatic and nonadiabatic ET components: d ∫ CH 3 NH 3 PbI 3 ρ PE (r , t ) d r dt

=

* d ∫ CH 3 NH 3 PbI 3 φi*φ j d r   d ( ci c j ) * * φ φ + d r c c  i j i j ∫CH 3 NH 3 PbI3 dt  dt 

∑ k, j

The first term has fixed localizations of adiabatic states, ∫

CH 3 NH 3 PbI 3

φi*φ j dr , but changing

expansion coefficients, ci*c j . The second term has fixed adiabatic state occupations, but changing localizations. The first and second terms represent nonadiabatic ET and adiabatic ET, respectively. The adiabatic ET proceeds by a change in the localization of the adiabatic state occupied by the electron from CH3NH3PbI3 to TiO2, induced by atomic motions. To undergo a nonadiabatic transfer, the PE electron has to hop into a TiO2 state, causing a change in the state occupations. If the donor-acceptor coupling is very strong, photoexcitation can directly promote an electron from the donor state to an acceptor state, corresponding to the direct ET mechanism. Typically, nonadiabatic ET operates when the donor-acceptor coupling is weak , whereas adiabatic and direct ET require strong coupling. Adiabatic and nonadiabatic ET are typically described by different analytic expressions, in particular, the Marcus theory and the Fermi’s golden rule, respectively. Therefore, establishing the ET mechanism is of both fundamental and practical importance. A more 8 ACS Paragon Plus Environment

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detailed discussion of the ET mechanisms can be found in our recent work49, 53, 56-57 and reviews.70, 72

2.3 Characterization of Active Phonon Modes: Autocorrelation Function and Fourier Transform Analysis of fluctuations of the electronic energy caused by atomic motions allows one to characterize the phonon modes that couple to the electronic subsystem, promote charge transfer and are responsible for electron-phonon energy relaxation. The autocorrelation function (ACF), defined as (8)

= 〈0〉

indicates how many vibrational modes are coupled to the electronic degrees of freedom. Here, the brackets indicate canonical averaging. A rapidly decaying ACF suggests participation of many vibrations, while a periodically oscillating ACF shows that few vibrations influence the electronic subsystem. The energy ACF describes how the energy at a particular time depends on its value at earlier times. Generally, poorly correlated random motions make ACFs decay rapidly from 1 to 0. Well-correlated periodic vibrations result in ACFs that oscillate between 1 and −1. Often, the ACF is normalized (9)

= 〈0〉 / 〈 0〉

by its initial value 0 = 〈 0〉 . The square root of this value gives the average energy fluctuation. Replacing the energy by localization in eqs. 8 and 9, gives ACF of the PE state localization, which is defined in eq. 6. Fourier transforms (FT) of the energy and localization ACFs characterize the phonon modes that couple to the electronic subsystem. The modes are identified by their frequencies. 9 ACS Paragon Plus Environment


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The electron-phonon coupling strength for the mode of a particular frequency is reflected in the magnitude of the FT signal at that frequency

2.4 Simulation Details The simulation cell, shown in Figure 2, contains a 150-atom anatase TiO2-(5 × 5) (001) surface interfaced with 108-atom CH3NH3PbI3 (3×3)(100) surface terminated with the organic cation CH3NH3. We also considered a CH3NH3PbI3/TiO2 interface terminated with PbI2, and the calculation showed it to be unstable.37 The lattice mismatch between the two slabs is only 0.01Å in both x and y direction. The system is separated from its image along the surface normal by a vacuum region of 20 Å. Additional calculations are performed with the simulation cell having a twice thicker perovskite layer, Figure S1 of Supporting Information (SI). The interfacial interaction between the perovskite and TiO2 subsystems includes the long-range van der Waals force described by the DFT-D2 method of Grimme.73 The geometry optimization, adiabatic MD, and nonadiabatic couplings are obtained using the Vienna ab initio simulation package (VASP).74 The electronic exchange and correlation energies are described by the Perdew-Burke-Ernzerhof (PBE) functional75 under generalized gradient approximation. The valence electron-ion interaction is treated by the projector augment wave method.76 It is important to note that spin-orbit interactions affect significantly the electronic structure of CH3NH3PbI3 due to presence of the heavy Pb atoms. It has been shown77-78 that DFT calculations using PBE and other generalized gradient approximation (GGA) functionals without spin-orbit interactions give a good agreement with the experimental band gap of the CH3NH3PbI3 perovskite,11,

24, 79

allowing one the use of these cost-efficient

functionals for exploring novel effects. 10 ACS Paragon Plus Environment

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After relaxing the geometry at 0 K, the CH3NH3PbI3/TiO2 system is heated up to 300 K using repeated velocity rescaling, corresponding to the temperature in the experiment.39 After that, a 3 ps adiabatic MD simulation is performed in the microcanonical ensemble with a 1 fs atomic time-step. The adiabatic state energies and nonadiabatic couplings are calculated for each step of the MD run. To simulate the photoinduced ET dynamics, 500 initial system geometries are selected randomly from the 3 ps adiabatic MD trajectory. The KS orbital corresponding to the PE state is chosen by considering optically active transitions near the perovskite band gap. In particular, excitations between pairs of KS orbitals from the valence and conduction are selected within the energy range from the perovskite band gap to 0.25 eV above it, and the excitation with the largest transition dipole moment is found. The energy fluctuation of the PE state is on the order of 100 meV. The inhomogeneous distribution of the photoexcited state energies due to thermal fluctuations is significantly smaller than the perovskite and the TiO2 band gaps; however, it has an influence on the position of the donor state with respect to the acceptor state due to frequent energy levels crossings. An electron is placed into the PE state orbital, and its evolution is tracked by solving the TDKS equation, eq 4, using the second-order differencing scheme and a 10-3 fs electronic time-step. This procedure is applied to study the ET dynamics within the manifold of CH3NH3PbI3 and TiO2 conduction band states.

3. RESULTS AND DISCUSSION 3.1 Geometric Structure Figure 2 presents the top (top panels) and side (bottom panels) views of the optimized geometry at 0 K (left panels) and a typical geometry form the MD simulation at 300 K (right panels). At 0 K, the TiO2 slab remains nearly intact, and all CH3NH3+ cations point in the 11 ACS Paragon Plus Environment


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same direction, confirmed by both the side and top views. The distances between the I and Pb atoms and the cation orientations determine the globally stable geometry. The interaction between TiO2 and CH3NH3PbI3 is purely van der Waals. At ambient temperature, both CH3NH3PbI3 and TiO2 geometries change significantly. In particular, thermal fluctuations allow formation of several I-Ti covalent bonds at the interface. The chemical bonding enhances the donor-acceptor coupling and accelerates ET. The largest movement on the TiO2 surface is associated with surface bridging oxygen atoms approaching the CH3NH3PbI3 slab (side view). The motion of the bridging oxygens acts to reduce the donor-acceptor separation, and further enhances the donor-acceptor coupling. The organic groups do not directly participate in the interfacial bonding, rather, they affect the donor-acceptor interaction electrostatically. Generally, strong covalent bonds result in adiabatic ET,49,

53

while weak van der

Waals interaction leads to nonadiabatic ET.56-57 For instance, the adiabatic ET mechanism is dominant in a broad range of systems including TiO2 surface sensitized with the molecular chromophore49 and the semiconducting quantum dot53 due to covalent bonds. The nonadiabatic ET mechanism is dominant in the graphene/TiO257 and Au20/TiO256 systems, which predominantly interact by van der Waals forces. If the donor-acceptor interaction is sufficiently strong, the PE electron can be promoted directly from donor to acceptor as the photon is being absorbed. In the present CH3NH3PbI3/TiO2 system, the interfacial I-Ti covalent bonds and reduced donor-acceptor separation facilitate charge delocalization and are beneficial for both direct and adiabatic ET. The simulation cell with a thicker perovskite layer is shown in Figure S1 of SI. The strong perovskite/TiO2 interaction is seen at room temperature, similarly to that in the smaller simulation cell, Figure 2.


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Figure 2. Top and side views of the simulation cell showing geometry of the CH3NH3PbI3 (100)-TiO2 anatase (001) interface at 0 K (left panels) and 300 K (right panels). Thermal fluctuations influence the system geometry and, hence, its electronic structure. A larger simulation cell is shown in Figure S1.

3.2 Electronic Structure The electronic interaction between the donor and acceptor subsystems mixes their orbital densities. Generally, the stronger is the interaction, the more significant is the mixing. Photoexcitation of an electron from a localized donor state into a state that exhibits a significant delocalization onto the acceptor results in partial ET by the direct photoexcitation mechanism. In the present system, both donor and acceptor energy levels are continuous bands, the PE state is delocalized between CH3NH3PbI3 and TiO2, and the direct mechanism contributes significantly to the overall ET event. Figure 3 presents the charge densities of the donor and acceptor levels. The electron donor state is delocalized significantly between CH3NH3PbI3 and TiO2 from, Figure 3a. 13 ACS Paragon Plus Environment


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Within the CH3NH3PbI3 slab, the electron density is mostly localized on the surface Pb atoms and interfacial I atoms. The mixing is extremely strong at the covalent I-Ti bonds regions. In particular, about half of the PE electron is delocalized into TiO2 slab, indicating that the direct ET mechanism is responsible for nearly 50% of the overall injection event. The electron acceptor state is mostly localized within the TiO2 slab, and the tail of the wave function extends onto interfacial the I-Ti covalent bonding region, Figure 3b. Direct chemical-like bonding between CH3NH3PbI3 and TiO2 produces a strong donor-acceptor coupling, resulting in mixing of the donor and acceptor orbital densities.

Figure 3. Charge densities of (a) donor and (b) acceptor states of the CH3NH3PbI3-TiO2 system. Not only the photoexcited donor state is delocalized significantly into the TiO2 slab, but also the final acceptor state at the TiO2 conduction band edge is delocalized into the interfacial region. The latter fact is unexpected since the TiO2 conduction band edge resides in the CH3NH3PbI3 band gap. The wave function delocalization between the donor and acceptor materials leads to rapid electron transfer from CH3NH3PbI3 into TiO2. The projected density of states (PDOS) of the combined system, separated into the contribution from CH3NH3PbI3 (red line) and TiO2 (black line), is shown in the top panel of Figure 4. The perovskite band gap calculated for the optimized geometry of around 1.5 eV in agreement with the experimental value11, 24, 79 and previous DFT calculations.77-78 Doubling the thickness of the perovskite layer gives similar band gap and PDOS, compare Figure S2 of 14 ACS Paragon Plus Environment

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SI with top panel of Figure 4. These results indicate that our simulation cell is able to capture the key electronic properties of the perovskite/TiO2 interface. The PDOS illustrates that that the CH3NH3PbI3 CB is well inside the TiO2 CB. The high density of TiO2 acceptor states facilitates efficient ET and favours the nonadiabatic ET mechanism. The bottom panel of Figure 4 shows the distribution of PE state energy and its localization. The two properties exhibit no correlation.

Figure 4. Top panel: Projected density of states (PDOS) of the CH3NH3PbI3 (100) / TiO2 anatase (001) interface, separated into contributions from CH3NH3PbI3 (red line) and TiO2 (black line). The Fermi level is set to zero. Bottom Panel: TiO2 PDOS in the excitation



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energy range (black line) and localization of the photoexcited state on CH3NH3PbI3 (red squares). About 50% of the photoexcited state density delocalizes onto TiO2 on the average. The PE state localization varies little around 0.5 and remains almost constant in the excitation energy region (red dots), indicating that photoexcitation of CH3NH3PbI3 creates a state that is already about 50% delocalized onto the TiO2 acceptor. The local dip in the DOS correlates to the t2g–eg splitting of the Ti 3d orbitals that form the TiO2 CB.80 In the region of decreased DOS, the CH3NH3PbI3 interacts with fewer TiO2 CB states, and therefore, the interface properties become less averaged. Higher TiO2 DOS tends to average out the properties of the interface. The differences between the average behaviour and individual members of the canonical ensemble of CH3NH3PbI3/TiO2 systems are emphasized further in the ET dynamics section.

3.3 Electronic-Vibrational Interactions The atomic motions affect the energy and localization of the PE state, create an ensemble of initial conditions for the photoinduced ET, and to a large extent, determine whether the ET proceeds by the adiabatic or nonadiabatic mechanism. Nuclear fluctuations generate the nonadiabatic coupling, causing hops between adiabatic states: the nonadiabatic coupling is directly proportional to the nuclear velocity dR/dt. Nuclear motions also influence localization of adiabatic state densities: a shift of the density of the state occupied by the electron from donor to acceptor gives adiabatic ET. FTs of the evolving PE state energy and localization are shown in Figure 5. The normalized ACFs of the PE state energy and localization are presented in the insets. The FTs characterize the phonon modes that couple to electronic subsystem and promote the ET. The coupling is directly correlated to the second derivative of the energy along the nuclear 16 ACS Paragon Plus Environment

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trajectory.81 Therefore, the vibrational modes that most strongly modulate the energy levels also create a large coupling.

Figure 5. Fourier transforms of phonon-induced fluctuation of the photoexcited state (a) energy and (b) localization. The insets show autocorrelation functions of these fluctuations. The FTs show that low-frequency vibrational modes couple to the electronic subsystems more strongly than high-frequency modes, Figure 5. Phonon modes with frequencies less than 200 cm-1 dominate both PE state energy and localization spectra. In addition to the largest amplitude at 100 cm-1, notable contributions from vibrations between 400 and 800 cm-1 are seen in the localization spectral density. The strongest peak at 100 cm-1 seen in both energy and localization spectra can be assigned to the I-Pb stretching mode at 94 cm-1.82 The peak can also be attributed to the librations of the organic cations at 119 cm-1.82 The organic group cations contribute to the ET by affecting the donor-acceptor interaction



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electrostatically. Rotation of organic groups brings notable changes of the electrostatic field.83-84 The small peak at 200 cm-1 can be assigned to the Eg mode of TiO2 at 198 cm-1.85 A more accurate mode assignment requires a full normal mode analysis, which is quite expensive for systems of this size. Note that not only normal modes themselves but also electron-phonon coupling for each mode would need to be obtained. The phonon modes seen in the power spectra of the PE localization show significant differences from those of the PE state energy, in particular in the middle to high-frequency region. The localization is sensitive to changes in the wave function, while energy is computed by averaging over the entire wave function. Therefore, the localization shows many more frequencies in the power spectrum. Shown in Figure 5b, the peaks at 400 cm-1, 500 cm-1 and 615 cm-1 can be assigned to the 409 cm-1, 515 cm-1 and 633 cm-1 modes of anatase TiO2,85-86 respectively. The higher frequencies above 600 cm-1 are associated with fast motions of surface oxygen atoms. Because the electron donor state is shared by the CH3NH3PbI3 sensitizer and the TiO2 substrate, Figure 3a, its wave function is more sensitive to low-frequency phonons involving both subsystems. High-frequency CH and NH stretching modes of CH3NH3 molecules are not detected in the FTs, because these moieties do not contribute to the donor wave function, Figure 3a. As shown in the insets of Figure 5, the PE state energy ACF decays quite slowly. It reaches zero at approximately 100 fs and then rebounds to 30% of its initial magnitude at 300 fs. In comparison, the PE state localization ACF decays much faster and shows no significant rebounds. The difference is rationalized by the difference in the power spectra: the localization is sensitive to many more phonon modes than the energy.

3.4 Electron Transfer Dynamics 18 ACS Paragon Plus Environment

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The canonically averaged photo-induced ET dynamics from the CH3NH3PbI3 sensitizer into the TiO2 substrate is demonstrated in Figure 6a. The ET coordinate starts at 0.5 at t=0, indicating that absorption of a photon at the CH3NH3PbI3/TiO2 interface has a 50% probability of creating a charge transfer excited state. The remaining 50% of the ET events occur by both adiabatic and nonadiabatic mechanisms. The ET coordinate is defined by integrating the PE electron density over the region of the simulation cell occupied by the electron acceptor, i.e., TiO2, eq. 6. The relative amounts of adiabatic and nonadiabatic ET are calculated by separating the overall evolution of the ET coordinate into the contributions due to the changes in the localization and occupation, respectively, eq. 7. The schematic of Figure 6b illustrates the three ET mechanisms. A photon can promote an electron directly from donor to acceptor. This mechanism requires strong donoracceptor coupling.

Adiabatic ET also operates in the strong donor-acceptor interaction

regime. Nonadiabatic ET does not require strong donor-acceptor interaction and, thereby, occurs in a broader range of systems. The strong interaction between CH3NH3PbI3 and the TiO2 surface favors both direct and adiabatic ET, while the high density of TiO2 acceptor states facilitates nonadiabatic ET. All ET mechanisms lead to ultrafast electron injection. The total ET line is fitted to a bi-exponential function. The faster ET component arises almost entirely from the adiabatic mechanism. It can be assigned to a rapid shift of the electron density from the donor to the acceptor through the regions of strong chemical interaction, most notably I-Ti chemical bonds, Figures 2 and S1. The slower ET component reflects transfer of the electron that is localized in CH3NH3PbI3, corresponding to the experimental sub-200fs time scale.39 The CH3NH3PbI3 layer used here is very thin compared to experiment, and therefore, one can expect that the slower ET component obtained in the calculation dominates the experimental data.



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Figure 6. (a) Average ET dynamics. The solid black, dashed blue, and dotted red lines represent the contributions from total, adiabatic and nonadiabatic ET, respectively. The open circles give a bi-exponential fit with the time scales shown. 50% of ET at the interface occurs by direct electron photoexcitation into TiO2. Photo-excited electrons generated inside perovskite transfer to TiO2 by an approximately equal combination of adiabatic and nonadiabatic mechanisms. (b) Schematic of the photoinduced ET mechanism. Adiabatic ET occurs by passing over a transition state barrier (curved red arrow). Non-adiabatic ET occurs via a hop between donor and acceptor states (downward blue arrow). Photoexcitation can promote the electron directly from the donor material to a state that is localized on the acceptor (upward green arrow).


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Figure 7. Examples of individual ET events. The lines have the same meaning as in Figure 6a. (a) Adiabatic ET with a small nonadiabatic component. (b) Nonadiabatic ET with a small adiabatic contribution. (c) ET with equal adiabatic and nonadiabatic contributions. The adiabatic component exhibits a sequence of forward and backward transfer events due to several re-crossings of the transition state, Figure 6b. (d) An initial delay, associated with search for a transition state, is followed by rapid adiabatic ET. Figure 6 represents the average behavior of the system during the ET process. A more detailed picture is presented in Figure 7, which shows examples of individual ET events. The examples demonstrate interesting interplay between adiabatic, nonadiabatic, and direct ET mechanisms, and exhibit a broad range of possibilities for the ET dynamics. Figure 7a displays a rapid adiabatic ET without a nonadiabatic contribution. Figure 7b shows an example dominated by the nonadiabatic ET, which starts after a short initial delay. The example of Figure 7c demonstrates ET exhibiting a complex interplay of adiabatic and nonadiabatic contributions. The adiabatic component exhibits a sequence of forward and backward transfer events due to several transition state re-crossings. The oscillation in the 21 ACS Paragon Plus Environment


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total ET process is driven by atomic motions that produces the re-crossings of the adiabatic ET barrier. Finally, Figure 7d demonstrates an initial delay, associated with search for a transition state, followed by rapid adiabatic ET. On the short time scale, the ET is driven entropically, by the larger density of TiO2 acceptor states within the relevant energy window, compared to the than CH3NH3PbI3 states state density, Figure 4. In the long time limit, prior to the electron-hole recombination,17, 37 the electron relaxes to the TiO2 CB minimum, which is lower than the CH3NH3PbI3 CB minimum. The energy difference between the CH3NH3PbI3 and TiO2 CB minima constitutes the main driving force for the photo-induced charge separation. The individual ET events shown in Figure 7 represent examples of electron injection that can be detected by single-molecule spectroscopies. Despite the diversity in the ET dynamics,

the

average

ET

is

straightforward.

Photoexcitation

of

the

CH3NH3PbI3/TiO2 interface has a high probability of creating a charge separated state. Electrons generated inside CH3NH3PbI3 transfer into TiO2 by the adiabatic mechanism if they are located in regions of chemical-like CH3NH3PbI3-TiO2 interaction facilitated by I-Ti bonds, or by the nonadiabatic mechanism if such interaction is absent.

4. CONCLUSIONS We have used real-time TDDFT combined with NAMD to simulate photo-induced ET at the CH3NH3PbI3/TiO2 interface. Showing good agreement with the experimental time scale,39 the reported study mimics the observed time-resolved ET process, establishes the mechanisms responsible for the electron injection, characterizes the atomic motions that participate in the movement of charge in this system, and generates a detailed understanding of the ET dynamics. 22 ACS Paragon Plus Environment

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The simulation shows that the ET occurs on an sub-100 fs time scale in the presence of a strong interaction between CH3NH3PbI3 and TiO2. Photon absorption near the interface has a high probability of creating a charge-separated state. Electrons approaching the interface from CH3NH3PbI3 bulk can transfer to TiO2 by both adiabatic and nonadiabatic mechanisms. Thermal fluctuations of atoms of the donor and acceptor materials create opportunities for transient chemical bonding across the interface, notably, formation of I-Ti bonds. The bonding is not seen at 0K. The strong donor-acceptor coupling generated through such bonds makes charge transfer excitations optically active. It is also responsible for the adiabatic ET mechanism. In the absence of the strong donor-acceptor coupling, the ET is nonadiabatic. Because the interfacial chemical bonding is not seen at 0K, one expects primarily nonadiabatic ET at lower temperatures. The nonadiabatic mechanism also produces fast ET due to high density of acceptor states, and therefore, only a weak temperature dependence in the ET time can be expected. Adiabatic ET is often viewed as a thermally activated process.87 Transient formation of I-Ti bonds induced by thermal nuclear fluctuations can be regarded as part of the activation. The situation differs from ET at molecule/TiO2 interfaces,

45-51

where donor-acceptor chemical bonds are much more stable

and exist both at zero and ambient temperatures. The electron couples primarily to lower frequency vibrational motions including both I-Pb stretching mode and librations of the organic cations. These motions generate an inhomogeneous distribution of initial conditions for the photoinduced ET, modulate the donor-acceptor separation, and create nonadiabatic coupling. The higher frequency Ti-O vibrations available at the CH3NH3PbI3/TiO2 interface have a smaller influence on the ET dynamics. They shift the electronic density between the donor and acceptor species and facilitate adiabatic ET. The complex interplay of the electron transfer mechanisms, donoracceptor and electron-phonon interactions, and phonon dynamics creates a variety of 23 ACS Paragon Plus Environment


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individual electron injection scenarios. All ET mechanisms seen in the simulations lead to ultrafast ET, indicating that the broad range of the reported experimental ET times is associated with charge and exciton diffusion in perovskite, rather than the interfacial dynamics. The ultrafast interfacial injection guarantees efficient photo-induced charge separation that creates favorable conditions for operation of perovskite solar cells.

Supporting Information. Geometric structure and projected density of states for the CH3NH3PbI3/TiO2 system with a twice thicker perovskite layer. These materials are available free of charge via the Internet at http://pubs.acs.org.

Acknowledgements R.L. is grateful to the National Science Foundation of China, Grant no. 21573022, the Recruitment Program of Global Youth Experts, and the Beijing Normal University Startup package. W.H.F. thanks the National Science Foundation of China, Grant nos. 21520102005 and 21421003. O.V.P. acknowledges support of the U.S. National Science Foundation, Grant no. CHE-1565704.


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