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Perspective

Quantum Dynamics of Photogenerated Charge Carriers in Hybrid Perovskites:Dopants, Grain Boundaries, Electric Order and Other Realistic Aspects

Joanna Jankowska, Run Long, and Oleg V. PrezhdoACS Energy Lett., Just Accepted Manuscript • Publication Date (Web): 31 May 2017

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Quantum Dynamics of Photogenerated Charge Carriers in Hybrid

Perovskites: Dopants, Grain Boundaries, Electric Order and Other Realistic

Aspects

Joanna Jankowska1,2

, Run Long3, Oleg V. Prezhdo

1

1Department of Chemistry, University of Southern California, Los Angeles, California 90089,

United States

2Institute of Physics, Polish Academy of Sciences, Warsaw, 02-668, Poland

3College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of

Ministry of Education, Beijing Normal University, Beijing, 100875, P. R. China

ABSTRACT: Dissipation of photon energy to heat and recombination of photogenerated charge

carriers are among the main factors limiting the efficiency of solar-light harvesting devices. The

dynamics of excited electrons and holes depend critically on the microscopic structure of a

material, including dopants, defects, grain boundaries, crystallinity and electric order. The

perspective summarizes recent findings and suggests directions for improvement of hybrid

organic-inorganic perovskite materials, established by means of non-adiabatic dynamics

(NAMD) simulations. Combined with real-time time-dependent density functional theory,

NAMD provides an ab initio description of the photo-initiated processes that occur far from

thermodynamic equilibrium. It includes realistic aspects of material’s structure and gives unique

atomistic insights into the photo-active material properties.

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Because of their outstanding optical and electronic properties on the one hand, and low

production costs on the other, hybrid organic-inorganic perovskites (HOIP) have been

recognized as highly promising materials for photovoltaic applications1–6

. Intense research

efforts led to an unprecedented progress in the perovskite solar cells efficiency, recently reported

to exceed 22%.7 From the materials science perspective, photogenerated charge losses due to

electron-hole recombination are among the major factors setting limits upon this value. The

unwanted charge recombination may be realized through different mechanisms,8–12

including

non-radiative, radiative, trap-assisted and Auger-assisted recombinations. The two-body non-

radiative charge recombination occurs even in high quality, defect-free materials exposed to

moderate-to-high illumination. Often, the recombination occurs on sub-nanosecond timescales,

inevitably competing with charge carrier diffusion within the active medium towards the electron

and hole transporting layers and, thus, reducing the charge extraction efficiency.

Experimental lifetimes of electrons and holes in hybrid perovskites range from several

nanoseconds to microseconds, depending on numerous material- and environment-related

factors5,13–17

. Here, we overview recent theoretical studies concerning charge relaxation and

recombination in hybrid perovskites, performed with non-adiabatic molecular dynamics

(NAMD) and steady-state Fermi-golden-rule approach. The discussion focuses on realistic

aspects of HOIP geometric and electronic structure, and includes hot carrier cooling, photo-

induced charge transfer between perovskite and electron-accepting material, doping and grain-

boundary effects, consequences of material exposure to moisture, influence of electric order, and

modification of the electronic structure near the bandgap edges by spin-orbit coupling. All these

phenomena are ubiquitous in HOIP materials, constantly affecting their photovoltaics properties.

At the same time, their individual contributions are hard to extract from the experimental data.

For that, quantum dynamics simulations constitute a unique and extremely valuable tool to study

the exact mechanisms of energy loss and charge recombination, significantly advancing our

fundamental understanding of these processes.

Non-adiabatic molecular dynamics generates time-domain atomistic insights into far-from-

equilibrium evolution of electrons and nuclei

Mixed quantum-classical methodologies provide an affordable and sufficiently accurate

approach to real-time dynamic simulations of chemical and physical processes in condensed

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phases.18

Within the quantum-classical picture the nuclear degrees of freedom are treated

classically and follow the Newton equation of motion, while the quantum electronic subsystem

evolves by the time-dependent Schrödinger equation (TDSE). Typically, the electronic wave

function, ��,���, is expressed in the basis set of all possible electronic adiabatic states,

�����; �������,

��,��� = � ����������; ��������

where ���� and ���� are the coordinates of n electrons and N nuclei. With subsequent insertion of

the expanded wave function into the TDSE, one arrives at time-evolution relation for the

electronic wave function expansion coefficients

�ℏ ������� = � ���������� +����

�

where �� is the energy of the adiabatic state k, and ��� is the non-adiabatic coupling between

states k and j. The non-adiabatic coupling is created by atomic motions and reflects the strength

of electronic response to nuclear vibrations. ��� can be calculated numerically as an overlap of

orbitals j and k at sequential dynamics time steps:

��� = −�ℏ��� ∇"��#$ ��% ∙ �����

�� = −�ℏ '��( ��� (��)

In the surface hoping realization of non-adiabatic dynamics, the system undergoes

transitions (hops) between electronic states. A variety of surface hopping algorithms have been

developed to address particular types of systems and processes.19

The calculated evolution is

typically averaged over a large number of classical nuclear trajectories and surface-hopping

stochastic realizations to give high quality time-dependent picture of the systems dynamics.

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In the following sections of the Perspective we discuss several case-studies covering

different realistic aspects of the photodynamics in hybrid perovskites in the context of their

photovoltaic performance.

Halide mixing can slow down hot-carrier intraband relaxation.

In order to maximize power extraction from a solar cell, one needs to capture and

transform into electric energy as much of the incident energy carried by absorbed photons as

possible. On the one hand, this means that the active-material bandgap should match the near

infrared light frequencies corresponding to the lower bound of the high-intensity solar spectrum

reaching the Earth surface, since all higher-energy photons should be still absorbed by dense

manifold of states building up the valence and conduction bands. On the other hand, the same

dense structure of the bands facilitates an ultrafast excited carrier cooling to the band edges,

following directly the absorption process. The relaxation results in significant energy losses and

limits solar cell voltage. The power leakage could be avoided by extracting hot carriers before

they cool down. Although such hot carrier collection is experimentally challenging, theoretical

investigations based on time-dependent methods can guide future experimental research by

providing insights into the cooling process. The issue has been recently investigated by Madjet et

al.20

for a set of hybrid halide perovskites, in the wider context of the role of halogen mixing for

the cooling process dynamics.

The NAMD simulations were employed to investigate the interstate non-adiabatic

coupling within the valence and conduction bands to model the energy relaxation of the hot hole

and hot electron. This approach allows for both direct identification of the cooling timescales and

assignment of the lattice vibrational motions having most pronounced impact on the process. In

the case of the reference CH3NH3PbI3 (MAPbI3) system in its room-temperature stable tetragonal

phase, it was found that the intraband electron cooling, depending on the initial excess of the

excitation energy, occurs within 350-850 fs, which stays in line with the recent experimental

findings9,11,21

. The hot-hole relaxation is even faster than the hot-electron relaxation, and is

predicted to complete during first 700 fs after the excitation for the highest 1 eV over-bandgap

initial hole energy. The difference in the cooling rate for the electrons and holes is rationalized in

terms of lower density of states (DOS) observed in the conduction band, in which the relaxation

of hot electrons occurs. The calculations show that both cooling processes are driven mostly by

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the inorganic-lattice vibrations, with certain effects arising from the lattice coupling with the

organic-moiety modes. The importance of the organic subsystem has been established recently

by numerous studies as crucial for correct understanding of the hybrid perovskites electronic

properties22–25

.

The NAMD charge-cooling study demonstrated an interesting impact of halogen mixing

on the carrier relaxation. This effect was modeled through 8% replacement of the iodine atoms

with bromine and chlorine. As a result of the replacement, a factor of two retardation of the

cooling is observed for the chlorine substitution. It is explained by a partial charge localization

on the substituted atoms and the consequent decrease of the interstate non-adiabatic couplings.

Such an effect, however, was not observed for bromine. Thus, in addition to the detailed

understanding of the hot-carrier cooling dynamics, the discussed NAMD investigation sets up a

possible direction for experimental efforts towards efficient hot carrier extraction from the hybrid

perovskites materials, proposing chlorine doping as a structural modification of choice.

Effects of dopants and interfacial interactions on charge separation and recombination.

The interplay between dopants and host lattice often change geometric and electronic

structures of parent materials and affects excited-state properties in solar cell systems.

Experiment showed that non-radiative electron-hole recombination in solar cells composed of

TiO2 sensitized with MAPbI3 reduces when iodides are substituted with chlorines or bromines. In

contrast, the recombination increases when lead is replaced with tin.13,26–28

These findings are

rather unexpected and would have been hard to predict a priori, in particular since all three

dopants are lighter than the atoms they substitute, and since higher frequency vibrations

introduced by lighter atoms might be expected to accelerate the recombination.

Ab initio NAMD simulations performed on pristine and doped MAPbI3(100)/TiO2

anatase (001) interfaces establish the mechanisms of the energy and charge losses, and suggest

practical means for controlling the interfacial electron-hole recombination.29

The simulations

support the experimental observations that doping with Cl and Br reduces the recombination rate,

while doping with Sn increases the rate, Figure 1 a. The established results are rationalized by a

combination of three factors. First, Cl and Br decrease the MAPbI3/TiO2 bonding interaction,

while Sn increases the bonding. Second, Cl and Br diminish the donor-acceptor and non-

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adiabatic coupling, while Sn enhances the coupling. Third, Cl and Br accelerate loss of quantum

coherence, while Sn leaves the decoherence time largely unchanged. Similar dopant effect was

also observed in the theoretical study on pristine MAPbI3.30

The recombination is driven by

coupling of the electronic subsystems to low-frequency bending and stretching modes of I-Pb

bonds in perovskite and acoustic modes in TiO2. The obtained time scales agree well with the

time-resolved experimental data31,32

. The study characterizes the fundamental mechanisms lying

behind the energy losses, such as wave function overlap and quantum coherence, and provides

practical guidelines, such as specific suggestions for rational choice of dopants, for reducing

charge recombination and designing higher efficiency perovskite solar cells.

Interestingly, another recent NAMD study on the photophysics at the perovskite/TiO2

interface has uncovered that, in the presence of strong, covalent-like interaction between the

perovskite and electron-accepting component, an ultrafast electron transfer may occur on a sub-

100 fs timescale.33

The strong, finite-temperature-induced interactions facilitate number of

pathways for the electron to be transferred, including direct inter-component excitation,

adiabatic, and non-adiabatic mechanisms, Figure 1 b. The ultrafast interfacial injection

guarantees efficient photo-induced charge separation that creates favorable conditions for

operation of perovskite solar cells.

Figure 1. a. Left: Simulation cell of the MAPbI3(100)/TiO2 anatase (001) interface. Right:

Energy level diagram. The electron-hole recombination occurs by electron transfer from the TiO2

conduction band minimum to the perovskite valence band maximum. Replacement of I with Cl

or Br reduces electron-hole recombination, while substitution of Pb with Sn accelerates this

process. b. Scheme of the photoinduced electron transfer (ET) mechanism. Adiabatic ET occurs

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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), creating a charge separated state. Adapted from Ref.29

(a.) and Ref.33

(b.).

Grain boundaries accelerate charge recombination in the CH3NH3PbI3 perovskite.

MAPbI3 perovskites unavoidably contain grain boundaries (GBs) that affect the excited

state lifetime and solar cell performance. First-principles calculations predicted that MAPbI3

GBs are benign because no deep trap states are found.34,35

However, factors other than the state

energy, in particular, the NA coupling and quantum coherence time, influence the nonradiative

electron-hole recombination significantly. Even though shallow defects have only a minor

influence on the bandgap, they can affect strongly elastic (coherence) and inelastic (NA

coupling) electron-phonon scattering. According to the energy gap law, the recombination rate is

approximately linear in the energy gap. According to Fermi’s golden rule, the rate is proportional

to the NA coupling squared, and depends strongly on the decoherence time, which enters the rate

expression through the Franck-Condon factor. The dependence on the energy gap is weakest

among the three factors, and the influence of decoherenece is the subtlest. Therefore, it is hard to

predict a priori by static electronic structure calculations whether defects accelerate charge

recombination or decelerate it; to approach this problem thoroughly, one requires more advanced

NAMD simulations to determine directly the nonradiative decay dynamics.

Experiments contradict the static electronic structure prediction34,35

and show that GBs

notably degrade the film optoelectronic properties.15,36,37

Tosun and co-authors demonstrated that

annealing perovskite films in the presence of MAI vapor increases grain size and results in

longer excited-state lifetime.37

Bischak et al. reported significant differences in non-radiative

recombination rates from grain to grain within MAPbI3 films using cathodoluminescence

microscopy.36

Snaith and co-authors showed that the electron-hole recombination rate

significantly increases in the presences of GBs, while it is reduced with Cl doping.15

The discrepancy between the experiment and theory motivated the ab initio NAMD

simulations focusing on electron-hole recombination in pristine MAPbI3 and MAPbI3 containing

GB with and without Cl passivation.38

The NAMD study demonstrated that GBs strongly

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accelerate the electron-hole recombination relative to the bulk MAPbI3, while introduction of

substitutional Cl dopants at the boundary reduces the recombination,38,39

Figure 2. The

acceleration of the charge recombination at GBs is attributed to three major effects. First, GBs

introduce trap states, reducing the electron-hole energy gap and bringing the electronic and

vibrational quanta closer to resonance. Second, GBs increase the non-adiabatic electron-phonon

couplings between the electron and hole wave functions by localizing the wave functions at the

boundary, and by creating additional phonon modes that couple to the electronic subsystem.

Third, the phonon-induced decoherence time remains largely unchanged because no foreign

atoms are incorporated into the lattice. Once lighter chlorines substitute heavier iodines at the

GB, they introduces higher-frequency vibrations and accelerates quantum coherence loss.

Further, in contrast to I, the Cl dopants do not contribute to the hole wave function, thus,

eliminating some of the wave function overlap, reducing the non-adiabatic electron-phonon

coupling, and restoring its value close to that for the pristine MAPbI3. Both factors arising from

the doping compete successfully with the reduced bandgap relative to the pristine MAPbI3, and

slow down the electron-hole recombination. The discussed NAMD results show excellent

agreement with experiment,31,32

establishes how GBs and chlorine dopants affect electron-hole

recombination in perovskite solar cells, and suggest a valuable route to increasing photon-to-

electron conversion efficiency through rational GB passivation.

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Figure 2. Top: Simulation cell of the MAPbI3 grain boundary system. Bottom: Energy level

diagram. The nonradiative charge recombination occurs by interaction of an electron from the

conduction band minimum with a hole at the valence band maximum of the perovskite. Grain

boundary accelerates the recombination, while replacing the I atoms by the Cl atoms at the grain

boundary slows down it. Adapted from Ref.38

.

Moderate humidity slows down electron-hole recombination at the CH3NH3PbI3 surface.

The effect of humidity on the HOIP properties can be either positive40,41

or negative,42,43

having a strong impact on the solar cells performance, as reported by different experiments. On

the one hand, some measurements demonstrate that humidity increases the excited-state lifetime

of MAPbI3 and improves the solar cells performance.40

On the other hand, some experiments

show that moisture accelerates the electron-hole recombination in MAPbI3 and degrades the

solar cell quality.42

Because halide perovskites are highly-polar salts, they are prone to

dissociation in water, and the resulting structure modification affects the photovoltaic

performance. Macroscopically, it has been suggested that humidity level influences crystalline

grain size. However, the presence of water affects not only grain size of films, but also the

electronic structure. The microscopic origin of the positive or negative impact of humidity on

perovskite solar cells is unclear. In particular, the influence of relative humidity on non-radiative

electron-hole recombination remains unknown.

Motivated by the experiments,40–43

ab initio NAMD simulations were performed to

investigate the non-radiative electron-hole recombination at the MAPbI3 (001) surface covered

by a varying number of water molecules44

. The study indicated that exposure to small amounts

of water can slow down electron-hole recombination, while large water amounts accelerate the

recombination. In small quantities, water molecules perturb the surface layer and localize the

photo-excited electron close to the surface, Figure 3. Importantly, the localized state does not

create a deep electron trap. As a result, the electron-hole overlap decreases, and the quantum

coherence time decreases as well. Both factors reduce the electron-hole recombination and

increase the excited-state lifetime. In large quantities, water molecules prefer to accumulate on

the MAPbI3 surface and form stable hydrogen-bonded networks. Water molecules aggregated

into a continuous film need to overcome a higher barrier to break the film and enter MAPbI3. A

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water film has little influence on charge localization, and the electron-hole overlap is not

affected, compared to the bare surface, Figure 3. At the same time, the NA coupling grows in

MAPbI3 covered by a water film due to participation of high frequency water vibrations, and the

excited state lifetime shortens. The obtained electron-hole recombination timescales show good

agreement with the available experimental data.31,32

The discussed study reveals the importance of relative humidity on the excited-state

lifetime of MAPbI3 perovskite, highlights the factors affecting the electron-hole recombination,

and provides insights that can be used to improve the performance of perovskite solar cells. In

particular, the short-range chemical and long-range electrostatic mechanisms of perovskite-water

interaction are identified to provide control over charge localization and recombination.

moreover, the simulations suggest that different solvents can have different effects on the

electron-hole recombination, depending on the relative strength of the solvent-solvent and

solvent-perovskite interactions.

Figure 3. Electron-hole recombination between the conduction band minimum and valence band

maximum of the perovskite depends of the relative humidity. Small amounts of water extend the

exited-state lifetime, while large quantities of water molecules decrease the lifetime compared to

bare perovskite. Adapted from Ref.44

.

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Local electric order inhibits non-radiative electron-hole recombination.

The outstanding photovoltaic and synthetic properties of HOIP materials stem from a

beneficial combination of features of their both components. In particular, the organic

component is responsible for controlling the inorganic-part dimensionality which further

influences the bandgap size and exciton binding energy. Until recently the understanding of the

role of electrostatic interactions between the organic and inorganic layers has been limited to

recognition of their mutual structure-stabilizing effects. The experimental and theoretical results

reported lately have changed this point of view dramatically, suggesting the fundamental

connection of the dynamic interaction between the organic and inorganic components to such

crucial photovoltaic features as material bandgap,24,45

photogenerated charge localization and

electrostatic screening25,45–48

.

The effect of a local electric-dipole order of organic cations on the non-radiative hole-

electron recombination was investigated by NAMD for a hybrid perovskite exhibiting room-

temperature stable ferroelectric phase.49

Focusing on the (benzylammonium)2PbCl4 system,

Figure 4 a., chosen for its proven stable polar C-N bonds orientation50

, it was demonstrated that

electrostatic interactions within the organic component have a significant impact on the excited

state lifetime. Depending on the alignment pattern of the polar C-N groups, Figure 4 b., the non-

adiabatic coupling between the band edge states of electron and hole may change its value by

more than 20%, enhancing or suppressing charge recombination. Ferroelectric, ordered

arrangement of polar organic groups is found to slow down bandgap energy vibrations, which

can be noticed in the calculated power spectrum, Figure 4 c.. This results in the inhibition of the

non-radiative electron-hole recombination. This local effect, working hand-in-hand with the

field-induced long-range effects, such as electron-hole separation and improved carriers

mobility51–53

leads to prolonged charge-carrier lifetimes. The slowdown of the photogenerated

hole-electron recombination due to the locally ordered ferroelectric alignment is predicted at the

order of ca. 20%.

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Figure 4: a. Structure of stable room-temperature ferroelectric phase of (benzyl-

ammonium)2PbCl4. Pb is grey, Cl is green, N is dark blue, C is orange, and H is turquoise. Purple

arrows indicate the aligned C-N bonds responsible for the cell dipole moment. b. Top view of

crystal cells chosen to model the ferroelectric (ferro) and paraelectric (anti-ferro, mixed) material

phases. Black dots mark the Pb atoms positions, and polygons illustrate the network of the in-

plane Cl atoms occupying the polygons corners. Polygon color marks the micro-domain

polarization: purple/green is used for ferroelectric/paraelectric dipole moment alignment,

respectively. Red and dark-blue arrows show the dipole moment orientation for the upper and

lower organic layers. Black dashed-line squares mark the bc-plane cross-section of the unit cell.

c. Power spectra (continuous solid lines) and low-energy IR vibrational spectra (vertical ticks)

for ferro (black), anti-ferro (red) and mixed (green) forms. The gray ticks in the background

mark frequencies of all modes calculated for a particular form. Adapted from Ref.49

.

Electron-hole recombination is slowed down by the Rashba effect.

Exceptionally long lifetimes of photogenerated charge carriers are among recognized

crucial features of hybrid perovskite materials leading to their excellent photovoltaic

performance. The reason for their slow charge recombination rate, usually characterized by

nanosecond and longer lifetimes, has not been unequivocally determined, though. Among

possible explanations one may consider ultrafast quantum decoherence suppressing the non-

adiabatic dynamics of the charges,29,39,45,49

as has been already pointed out in the previous

sections. Another cause could be dynamic charge localization and screening due to rotations of

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the polarized molecular cations24,45–48

or effective charge separation at the bulk ferroelectric

domains walls52

. Recently another explanation for this ultra-long carriers lifetime, based on the

Rashba effect, has been proposed.54–58

In the presence of electric field, systems exhibiting strong spin-orbit coupling experience

lift of the spin degeneracy within their electron bands, Figure 5 a.. Known as the 3D Rashba

phenomenon, the splitting leads to spin-allowed and spin-forbidden transitions in materials that

contain heavy atoms and, at the same time, exhibit bulk ferroelectricity. Hybrid perovskites can

satisfy these two conditions due to the presence of Pb (or I, Br) atoms that are known to show

strong relativistic effects,59,60

and the possibility of domain polarization by local alignment of

the organic moieties.49–53

Since the intra-band hole and electron cooling are much faster than the

charge recombination, the electrons and holes recombine from the edges of the conduction and

valence bands. The Rashba splitting may lead to various spin patterns at the band edges,

resulting in some cases, in a mismatch between the lowest conduction and highest valence state

spin orientations. Such mismatch would slow down the charge recombination stemming from

low probability of spin flip. Moreover, upon the splitting, the conduction and valence band edges

experience slight shifts in the k-space. The shifts change the bandgap character from direct to

indirect, further retarding the recombination process, since now it requires not only energy but

also momentum transfer. The exact pattern of the state spin orientations depends on the details of

material structure. The direct-to-indirect bandgap transition in HOIP was recently observed in

experiments,12

rationalizing the thermally enhanced, long, secondary charge recombination

pathways.

It was recently reported by Zheng and co-authors54

for the MAPbI3 perovskite in its

typical cubic and tetragonal phases that a slight shift of the Pb atom is required for the Rashba

splitting to occur and to exhibit the spin mismatch between the valence and conduction band

edge states, Figure 5 b. & c.. Such distorted structures have been predicted to be thermally

accessible in room-temperature conditions and to be further stabilized by the aligned molecular

cations orientation. The exact charge-lifetime enhancement depends on the Rashba-induced

energy splitting between the states and, for the splitting of 0.1 eV, it is expected to reach a factor

of 10 as was estimated within the Fermi’s golden rule approach.54

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Figure 5. a. Diagram of Rashba bands and the electron transport path. The cyan and orange

arrows show the directions of the spins. The spin texture χ indicates spin vortex direction with its

signs characterizing spin rotation in “clockwise” (χ = −1) and “counterclockwise” (χ = +1)

directions. Photo-excited electrons in conduction bands Cχ=+1 and Cχ=−1 quickly relax to the

Cχ=−1 band minimum due to the inelastic electron-phonon scattering. Similarly, the holes

quickly relax to the Vχ=+1 band maximum. The radiative recombination of Cχ=−1 → Vχ=+1 is

spin-forbidden. Moreover, the Cχ=−1 band minimum and the Vχ=+1 band maximum are located

in different points in the Brillouin zone, creating an indirect bandgap that further slows down the

recombination. b. Schematic showing Pb and I displacement in pseudocubic MAPbI3. Pb is grey.

I is indigo. Broken circles are original high-symmetry positions. Organic molecules are not

shown. c. Phase diagram of splitting energy and spin texture for structures with different Pb and

apical I displacements in pseudocubic MAPbI3. The color is the minimum value between the

averaged splitting energy of two Rashba conduction bands and two valence bands. The spin

texture phase boundaries are indicated by the solid red lines. When the structure transforms from

a favorable to an unfavorable spin texture region, the two Rashba valence bands or conduction

bands exchange, creating a negative splitting energy. The dashed lines indicate the areas with

energy cost less than 25 meV (equivalent to thermal energy at room temperature) to distort Pb

and I. The red circle marks the distortions with the lowest total energy. Adapted from Ref.54

.

Concluding remarks.

We have discussed recent advances in the field of ab initio modeling of quantum

dynamics of photogenerated charge carriers in hybrid perovskites, with special emphasis on the

realistic aspects of perovskite atomistic and chemical structure. The considered examples show

a great potential of atomistic time-domain simulations for predicting properties and explaining

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mechanisms governing efficiencies of active materials for photovoltaics. The simulations

generate unique opportunities to separate the effects of various physical, chemical and structural

factors. Such knowledge is essential for understanding of complex photo-physical properties of

the hybrid perovskite systems. The reported dynamics studies formulate detailed conclusions

which may further guide technological efforts towards design of optimal perovskite materials for

photovoltaic purposes.

The photoinduced charge carrier cooling timescales for a popular hybrid perovskite,

MAPbI3, have been reported by Madjet et al. The calculations reproduced the experimental

timescales and identified the phonon modes responsible for the relaxation. The predicted

slowdown of carrier dynamics upon chlorine doping and the established mechanism of this effect

facilitate the efforts for hot charge carrier extraction.

Long et al. analyzed realistic structural aspects governing performance of perovskite

solar cells, including grain boundaries, dopants, surfaces and interfaces with charge acceptors

and water. It was found that strong interactions between perovskite and TiO2 facilitate ultrafast

photoinduced charge transfer, that Cl and Br doping reduces losses of the photogenerated

charges, that grain boundaries provide a major pathway for the charge recombination, and that

perovskite interaction with water depends strongly on the amount of water on the perovskite

surface. The predicted changes in the charge and energy transfer and relaxation processes arise

due to a complex interplay of charge localization, trapping, elastic and inelastic electron-phonon

interactions, and thermal disorder.

Jankowska and Prezhdo studied the effect of electric order among the organic cations on

electron-hole recombination. The ferroelectric phase demonstrated slower recombination than

the paraelectric phase, rationalizing the experimentally observed improved performance of

ferroelectric perovskites. The effect was explained by slow, collective oscillations of the polar

organic groups in the ferro form.

Zheng et al. demonstrated an interesting possibility for enhancement of charge-carrier

lifetimes due to the relativistic Rashba effect. The spin-orbit interaction and out-of-plane

displacements of the heavy Pb atoms were found to induce internal electric fields that lifted spin

degeneracy of the band-edge states and could lead to an indirect bandgap. The arising necessity

of a spin-flip and momentum transfer inhibit charge recombination.

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The great progress in the light-to-current conversion efficiency encourages

commercialization of hybrid organic-inorganic perovskite solar cells. At the same time, one

should be well aware of the major stability concerns of perovskite cells subjected to humidity40–

43, electric field

61 and irradiation by light

62, having strong negative effects on the solar cell

performance. The degradation due to exposure to moisture can be partially avoided via device

engineering and advanced fabrication techniques by covering the perovskite with other materials,

such as graphene63

, or replacing the organic cation with the Cs atom on the material surface64

.

Interaction between perovskite and electric field, leading to material polarization, and in

particular ion diffusion, as well as the photo-degradation problem, require resolution for real

device applications, because they undermine the solar cells performance in the long run. The

two-dimensional perovskites incorporated in the Ruddlesden-Popper solar cell have shown great

stability against humidity and photo-irradiation65

. The issue of stability under polarization

remains largely unsolved and needs further investigation.

The time-domain atomistic simulations of charge carrier dynamics, mimicking directly

numerous time-resolved pump-probe experiments provide unique insights into the atomistic

mechanisms of the far-from-equilibrium processes taking place in hybrid organic-inorganic

perovskites and other solar cells materials. The number of theoretical papers is orders of

magnitude smaller than the number of the corresponding experimental publications. In addition

to the optical laser experiments probing the dynamics of valence electrons and vibrational modes

at the visible, ultra-violet and infrared frequencies that are most relevant for solar energy

harvesting, other approaches, such as the terahertz spectroscopy66

, and the emerging techniques,

including time-resolved X-ray67

and attosecond68,69

spectroscopies, can provide additional

insights into the coupled evolutions of electrons and nuclei. For instance, terahertz measurements

characterize changes in electrical conductivity upon photo-excitation. Time-resolved X-ray can

probe directly structural re-arrangements, such as ion diffusion that occurs in perovskites subject

to electric fields. Attosecond time-resolution is required to study short-lived quantum coherences

that are formed during the initial photo-excitation and the subsequent quantum transitions.

The discussed theoretical studies of quantum dynamics focus largely on the non-

radiative, phonon-induced electron-hole recombination, and provide only a glimpse of the

capabilities of time-domain atomistic simulations. Future work should incorporate a broader

range of perovskites, more complex systems including interfaces of perovskites with various

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charge extracting materials70,71

, coupling of charge dynamics with ionic transport, longer time-

scales, larger systems and other phenomena, e.g. Auger-type charge scattering72,73

. It is

important to sample appropriately structural changes associated with long time events induced by

polaron formation, ion diffusion, surface degradation and electric phase transitions, in order to

investigate how such changes influence charge-phonon dynamics. Non-adiabatic molecular

dynamics simulations of three and two-dimensional inorganic and hybrid perovskites can

characterize in detail the highly non-equilibrium evolutions initiated in the perovskite materials

by light absorption and involving various degrees of freedom. Such studies generate valuable

knowledge that can form the fundamental basis for improving the performance of perovskite

solar cells and related systems.

Biographies

JJ received her Ph.D. in physical chemistry from the University of Warsaw and is currently a

postdoctoral associate at the University of Southern California. Her research focuses on

theoretical photochemistry and photophysics, including studies on molecular photoswitches,

excited state proton transfer, and charge and energy dynamics in hybrid perovskite materials.

RL obtained his Ph.D in atomic and molecular physics from Shandong University and is

currently a professor of chemistry at the Beijing Normal University. Dr. Long’s research

interests are focused on excitation dynamics in nanoscale systems, in particular energy and

charge transfer dynamics in condensed phase and at interfaces.

OVP is a Professor of Chemistry, Physics and Astronomy at the University of Southern

California. He is Editor for Journal of Physical Chemistry Letters, Journal of Physical Chemistry

and Surface Science Reports. His research interests range from fundamental aspects of

semiclassical physics to excitation dynamics in nanoscale and biological systems.

Acknowledgements

R. L. is grateful to the National Science Foundation of China, Grant No. 21573022, the

Fundamental Research Funds for the Central Universities, the Recruitment Program of Global

Youth Experts, and the Beijing Normal University Startup Package. O. V. P. acknowledges

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support of the U.S. Department of Energy, Grant No. DE-SC0014429 and U.S. National Science

Foundation, Grant No. CHE-1565704, and thanks the Photochemistry Center of the Russian

Science Foundation, project No. 14-43-00052, for hospitality during manuscript preparation.

Theoretical Models

NAMD simulations have been carried out with use of the mixed quantum-classical

approaches: fewest switches surface hopping (FSSH)74

in the case of carrier relaxation20

;

decoherence-corrected FSSH75

for effects of grain boundaries38

and chemical doping29

on

electron-hole recombination studies; and decoherence induced surface hopping (DISH)76

for

influence on humidity44

and local electric order49

on charge recombination. In all cases, the

classical path approximation (CPA) was used77

. The FSSH and DISH calculations have been

performed with the PYthon eXtension for the Ab Initio Dynamics software (PYXAID)77,78

. The

decoherence-corrected FSSH calculations have been done using the original codes75,79

. The

Rashba-effect on the inelastic phonon scattering rate for electrons and holes has been

investigated using Fermi’s golden rule approach54

. The geometric and electronic structure of the

analyzed systems have been calculated using ab initio density functional theory with the Perdew-

Burke-Ernzerhof (PBE)80,81

exchange-correlation functional, including the Grimme DFT-D2

correction82

for the van der Waals interactions.

Although it is acknowledged that hybrid functionals, such as HSE0683

increase the

accuracy of the non-covalent interactions description, they also significantly increase the

computational cost and are generally not affordable for NAMD simulations of the larger HOIPs

systems. The chosen PBE functional is widely accepted as one of the best parameter-free density

functionals satisfying the key physical and mathematical requirements of DFT. In particular,

PBE obeys the Lieb-Oxford bound,84

and leads to smooth pseudopotentials.80,81

Combined with

the correction for the van der Waals interactions implemented within the Grimme DFT-D2

method, the PBE functional gives reasonable description of intra- and inter-material interactions

within the studied systems.

With the exception of the Rashba-effect study, the spin-orbit coupling (SOC) effects have

not been included explicitly during the electronic structure calculations. The scalar-relativistic

correction is included in the used pseudopotentials. SOC is recognized to cause a down-shift of

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the lowest conduction-band state energies in HOIPs.85–87

The resulting reduction in the HOIP

bandgap is captured fortuitously by the self-interaction error present in PBE and other pure DFT

functionals. Please refer to the cited original papers for further methodological details.

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