Hole Transfer in Dye-Sensitized Cesium-Lead-Halide Perovskite

Subscriber access provided by UNIVERSITY OF ADELAIDE LIBRARIES

Article

Hole Transfer in Dye-Sensitized Cesium-Lead-Halide Perovskite Photovoltaics: Effect of Interfacial Bonding Aaron Forde, and Dmitri S. Kilin J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b04961 • Publication Date (Web): 09 Aug 2017 Downloaded from http://pubs.acs.org on August 10, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

2

Hole Transfer in Dye-Sensitized Cesium-Lead-Halide Perovskite Photovoltaics: Effect of Interfacial Bonding

3

Aaron Forde, Dmitri Kilin*

4 5

Department of Materials Science and Nanotechnology, North Dakota State University, Fargo, North Dakota 58102, United States

6 7

*Department of Chemistry and Biochemistry, North Dakota State University, Fargo, North Dakota 58102, United States

8

*Corresponding Author

9

Email: [email protected]

1

10 11

Abstract

12

Lead halide perovskites have gained attention as an active material in solid state dye-sensitized

13

photovoltaics due to its high absorption of visible light and long charge transport lengths. In perovskite

14

based dye-sensitized photovoltaic architectures the perovskite material is typically paired with a hole

15

transport material, such as spiro-OMeTAD, which extracts a hole from the photo-excited perovskite to

16

generate free charge carriers. In this study, we explored two competing charge transfer pathways at the

17

interface between lead halide perovskite and spiro-OMeTAD: “though-bond” and “though-space”. For

18

the through-bond pathway we use a segment of spiro-OMeTAD which contains methoxy linker groups,

19

which will be referred to as “dye with methoxy linker groups” (DML). For the through-space pathway we

20

use a segment of spiro-OMeTAD and remove the linker groups, which will be referred to as “dye”. Four

21

atomistic models were studied: (I) A periodic cesium lead iodide (CsPbI3) perovskite nanowire (NW) that

22

is paired with the dye molecule. (II) A periodic CsPbI3 perovskite NW paired with the DML molecule

23

where the linker groups form coordination bond to the surface of the nanowire. (III) CsPbI3 perovskite

24

thin-film (TF) paired with the dye molecule. (IV) CsPbI3 perovskite TF paired with the DML molecule.

25

Charge transfer dynamics, providing rates of electron/hole relaxation and relaxation pathways, are

26

calculated using Reduced Density Matrix formalism using Redfield theory. It was found that the terminal

27

surface of the perovskite (Pb-I vs Cs-I) has important implications for energetic alignment at the

28

perovskite-dye interface due to band-bending. Computed charge transfer rates match well with upper

29

and lower bound of reported experimental results where “fast” picosecond rates correspond to

30

through-bond pathway and “slow” nanosecond rates correspond to through-space.

1

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

I.

Introduction

2

Solar cells have shown to convert sunlight into electrical energy, but as of 2015 they

3

account for less than 0.1% of total electricity production in the United States 1. One factor for

4

this is the high manufacturing cost of conventional 1st generation p-n junction based silicon

5

wafer solar cells2. Even though they can obtain high efficiencies of 20% they are costly to

6

manufacture due to high temperature thermal processing 3. 2nd generation thin-film solar cells

7

and 3rd generation emerging technologies, such as dye-sensitized solar cells (DSSC), organic

8

solar cells 4, and quantum dot (QD) solar cells, are popular areas of research but each pose their

9

own unique difficulties for commercialization.

10

DSSC’s, first produced by Gratzel, use molecular dyes as the light absorber and a

11

nanostructured TiO2 film to extract photoexcited electrons from the dye. The original Gratzel

12

cell displayed an 7.1-7.9% efficiency in under solar illumination5. One of the main drawbacks of

13

the original Gratzel cell is that it utilizes liquid electrolyte as a hole conductor where the liquid

14

electrolyte is prone to poor thermal and chemical stability 6. Research has gone into replacing

15

the liquid electrolyte with solid state hole transport materials which would employ enhanced

16

stability.

17

Lead halide perovskites have shown great promise as a material for next generation

18

photovoltaic (PV) solar cells. Its high absorption of visible light makes it potentially useful as an

19

optical absorber and its ability to transport charges over long distances as a solid state charge

20

transport material make it versatile to use in PVs. Initial studies in 2009 of using lead halide

21

perovskites in dye-sensitized solar cells utilized the perovskite as the sensitizer, replacing the

2


Page 2 of 41

Page 3 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

dye molecule, showed modest efficiencies of 3.2% but displayed instability due the liquid

2

electrolyte dissolving the lead halide perovskite.

3

architecture, replaced the liquid electrolyte with the solid state hole transport material (HTM) 2

4

,2’,7,7’-tetrakis(N,N-di-p-methoxyphenylamine)-9,9’-spirobifluorene

(spiro-OMeTAD)

5

showed an improved efficiency of 9.7% with increased stability.

8

6

constructed a thin-film PV cell which used the lead-halide perovskite as both the optical

7

absorber and electron transport material (ETM) by replacing the conventional TiO2 with an

8

insulating “scaffolding” and using spiro-OMeTAD as the HTM.9 This cell showed an improved

9

power conversion efficiency of 10.9%. Over the last five years there has been great

10

developments in improving the efficiency of lead halide perovskite based PVs, with multiple

11

reports of achieving efficiencies above 20%. 10, 11

7

In 2009 Kim et. al., using a thin-film PV

which

In 2012 Snaith et. al.

12

Many of the early investigations into lead halide perovskite based PVs focused on

13

organic-inorganic hybrid methylammonium (MA) lead halide where MA plays the role of the

14

charge stabilizing cation. Stability of the MA cation has shown to be a hindrance towards

15

commercial development due to degradation upon contact with moderate concentration of

16

moisture along with thermal degradation threshold of 85 C, which is low for commercial

17

processing practices. 12-13,14 Although there have been reports15 and supporting evidence16 for

18

small amounts of moisture improving performance in MA lead halide perovskite based PVs

19

there is still motivation to research alternative charge stabilizing cations. Cesium has been

20

found to adequately replace the MA cation in the lead halide perovskite crystal structure while

21

retaining its useful electrical properties for PVs to have increased moisture stability.17 Thus, the

22

inorganic cesium lead halide perovskite shows promise as an alternative material for PV’s.

3



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

There has also been an interest in utilizing nanostructured lead halide perovskite materials to

2

optimize performance in PVs. Nanostructured materials allow for greater control over the

3

bandgap of the material, greater interfacial surface area which is beneficial for surface area

4

limited processes such as light absorption, and increase charge transfer rates which lowers

5

probability of charge recombination.18,19 Additionally, unique properties such as size tenability

6

and multiple exciton generation were recognized for semiconductor quantum dots,20

7

nanowires,21,22 and thin films. Later on, lead halide perovskite QDs23, nanowires (NW) 24, and

8

thin-films (TF)7,8,9,10,11 have been successfully utilized for PVs.

9

One of the physical processes that impacts the power conversion efficiency in PVs is the

10

ability to spatially separate electron-hole pairs to decrease the probability of recombination.

11

This provides a challenge in generating fast electron-hole separation and slow recombination to

12

maximize PV performance. One method to achieve this is to ensure that the optical absorber

13

and the ETM/HTM have an energetically favorable offset where the ETM has a conduction band

14

minimum lower in energy than the absorber and the HTM has a valence band maximum higher

15

in energy than the absorber. This energy offset provides the necessary driving force to produce

16

charge transfer. Then after a photo-excitation the electron will thermally relax to the ETM and

17

the hole to the HTM by utilizing non-radiative relaxation though electron-phonon interactions,

18

as depicted in Figure 1. There is also the possibility of a “hot” charge carrier being extracted

19

before thermalization to band edges which would increase the rate of charge transfer.25

20

Experimentally using femto-second resolved spectroscopy it has been observed that hole

21

injection rates from lead halide perovskites into spiro-OMeTAD occur at rates spanning the

22

range of ~1ps to 16 ns. 8,27,28,29,30 Reported electron injection rates from lead halide perovskite

4


Page 4 of 41

Page 5 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

into TiO2 are on a wider timescale range of sub-200 fs to 7 ns with recombination occurring.

2

26,27,28,29,30

Numerous computational studies have been conducted on elucidating the mechanisms

3

11 ,31,32,33,34,35,36,37,38

4

behind the electronic properties of lead halide perovskites.

But there has

5

been limited account of investigation into the interfacial dynamics between lead halide

6

perovskites and ETM/HTM. Ab initio dynamics simulations have the opportunity to investigate

7

the physical mechanisms behind experimentally observed charge transfer rates between lead

8

halide perovskites and ETM/HTM. Dynamics of electronic transitions39 has shown to be effectively modeled using a range

9

40

10

of methods: (i)Time propagation of wavefunction,

11

originally developed for describing dye-to-semiconductor interface.25,41 (iii) time-dependent

12

density functional theory recently used to describe electron injection at the interface of the

13

cyaniding dye and titania nanowire.42 (iv)Tully’s surface hopping,

14

implemented for atomistic calculations of molecular systems 44, semiconductor nanostructures

15

45

16

been discussed as a promising tool to describe relaxation in multi-level systems.

17

Recently, the density matrix method has been implemented on a first principles level where

18

“on-the-fly” electron-to-nuclear motion couplings are processed as second order perturbation

19

and parametrize the Redfield tensor.52 This methodology rests on finding eigenvalues and

20

eigenvectors of the Redfield superoperator.53 Not long ago, this methodology was applied for

21

investigation of the photoinduced hole transfer at the interface of a titania NW and caffeic acid

22

molecule where the NW was the hole donor and the molecule was the hole acceptor. 54

, and dye-to-semiconductor interfaces.

46 ,47

(ii) Survival probability method that was

43

that was successfully

. (v) Density matrix method

5


48

has historically 49 ,50, 51


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

The nonadiabatic molecular dynamics with time dependent density functional theory

2

was recently used to study charge transfer between TiO2 and lead halide perovskite to show

3

ultrafast electron injection (sub 100 fs) into the TiO2.

4

experimental studies showing sub picosecond electron injection into TiO2. To our knowledge,

5

there have not been any studies examining dynamics of hole transfer from lead halide

6

perovskite to a HTM, such as the popular organic molecule spiro-OMeTAD.

55

This provides support to the

7

In this paper we use Redfield theory in density matrix method formalism to model the

8

charge transfer dynamics between nanostructured cesium lead iodide NW/TF paired with

9

organic dye molecules benzenamine and benzenamine, 3-methoxy-N-(3-methoxyphenyl)-N-

10

phenyl, which will be referred to as dye and dye with methoxy linker (DML), respectively. DML

11

is chosen since it is a segment of the spiro-OMeTAD molecule and provides an approximation to

12

the interfacial mechanisms between spiro-OMeTAD and lead halide perovskite, as shown in

13

Figure 2(a,b). The dye molecule is similar to DML except it does not contain methoxy linker

14

groups, as seen in Figure 2c. This allows for investigation of though-bond versus though-space

15

charge transfer pathways. We hypothesize that utilizing the through-bond pathway of the DML

16

bonded to the perovskite surface will provide faster charge transfer than though-space

17

mechanism of dye molecule due to enhanced coupling of the bridging electron density that the

18

methoxy linker group provides.

19

In this work, we use the PBE functional for ground-state electronic structure and to

20

generate non-adiabatic couplings, which are needed to compute charge transfer rates. GGA

21

functionals, such as PBE, lack the ability to describe long-range exchange and correlation

22

effects. This deficiency can result in two unphysical phenomena: (I) Orbitals become more 6


Page 6 of 41

Page 7 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

delocalized due to neglecting exchange interactions. (II) GGA calculations may predict artificial

2

charge transfer states. To describe exchange-correlation effects in a rigorous manner a long-

3

range hybrid functional, such as HSE06 or CAM-B3LYP, should be used. Although a hybrid

4

functional would provide more accurate electronic structure calculations than PBE the

5

computational cost would also increase greatly to generate non-adiabatic couplings. Aside from

6

explicitly using a hybrid functional, methods have been developed to approximate the accuracy

7

of long range hybrid functionals while still using a cost effective GGA functionals. Some of these

8

methods would include constrained DFT56, using alternative electron densities57 , and scaling

9

methods 58. For this study, we find that PBE acts as a suitable approximation to describe hole

10

transfer between the perovskite and dye/DML molecule with its use being justified throughout

11

the rest of the manuscript.

12

The manuscript is organized as follows: Our methodology is overviewed in Section II

13

which focuses on the theory of general electronic structure and non-radiative relaxation, along

14

with relevant computational details. Section III provides results of bonding stability, electronic

15

structure as a function of the perovskite surface composition, and relaxation dynamics. Section

16

IV concludes the paper with summary of results.

17 18

II.

Methods

19

Theory. Electronic structure of the perovskite – organic dye system is found from solving

20

the fictitious one electron Kohn-Sham (KS) equation59 from density function theory60 to

21

construct the total density:

7



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

ℏ

− ∇ + ( , [( )] ) ( ) = ( )

( ) = ( )∗ ( )

2

Page 8 of 41

(1)

(2)

3

More generally, ( ) = ∑ ( ) ( )∗ . Equations (1) and (2) are solved in a self-

4

consistent manner, where electron density ( ) is is refined until reaching total energy

5

convergence. After solving equations (1) and (2) one can compute several observables of the

6

system. Below we describe how to compute binding energies, density of states, and absorption

7

spectra from KS orbitals .

8 9 10

When we covalently bond the DML molecule to the surface of the perovskite we consider bonding stability. Binding energy is calculated using the equation below EBinding= ETotal(perovskite + molecule) – [ETotal(perovskite) + ETotal(molecule)]

(3)

11

A negative EBinding corresponds to a favorable bonding configuration while a positive value

12

means the bonding is unfavorable. We allow the perovskite-dye assembly to obtain a geometry

13

optimized structure and run single point calculations of the perovskite and dye, respectively.

14

This provides the three terms needed for equation (3) to compute binding energy.

15 16 17

18

Density of states (DOS) is found by counting the number of energy states that are available per energy level and is computed using: n() = ∑ δ( - )

8


(4)

Page 9 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

Here n() is the DOS, is an argument, is the energy of the ith KS orbital, and δ( - ) is a

2

Dirac delta function which is modeled using a Lorentzian distribution to provide broadening due

3

to thermal fluctuations. DOS is computed for the perovskite-dye assembly, perovskite, and dye

4

respectively.

5 6 7

The absorption spectrum of the perovskite-dye assembly is computed using the independent orbital approximation (IOA),61 by using the equations below:

8

"(#) = ∑ $ δ( ℏω − ℏ# )

9

$ =

&'( )*+ ,- .

1 | |0

1 〉 = 4 5 6 〈0

10

(5)

(6)

(7)

11

1 > is the Here "(#) is the absorption spectrum, $ is the oscillator strength, and < 0

12

transition dipole moment. The oscillator strength acts as probability of an electronic transition

13

occurring between state i and j corresponding to the angular frequency # of the incident light.

14

The transition dipole represents the spatial overlap between electronic states i, j. In equation 5

15

the delta function is approximated as a Lorentzian distribution to account for thermal

16

fluctuations.

17 18

To explore charge transfer dynamics in the perovskite-dye assemblies we implemented

19

adiabatic molecular dynamics with non-adiabatic couplings between nuclear and electronic

9



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 41

1

degrees of freedom where the couplings provide dissipative transitions. Non-adiabatic

2

couplings are computed “on-the-fly” as 9 (:) = −;ℏ

>?

= @

(8)

4

The nonadiabatic couplings are used to parameterize the Redfield approach to dynamics

5

of excited state. Here we briefly overview the Redfield treatment for dissipative dynamics.

6

Readers are directed to other works for more in-depth presentation of the theory implemented

7

here.52 ,53

8

62

. ,63 Processing of the non-adiabatic couplings is done using the autocorrelation

9

functions, which provide the first non-vanishing perturbative contribution to the equation of

10

motion for electronic degrees of freedom.64 A Fourier transform of the autocorrelation function

11

provide components for Redfield tensor. These components are summed together to generate

12

the time independent Redfield tensor which controls the dissipative dynamics of the density

13

matrix. 50 The Redfield tensor provides probabilities of transition rates for dissipative electronic

14

transitions.52

15

density matrix

,53

Dissipative electronic transitions are used to propagate the time evolution of

>A*+ >?

>A*+

16

>?

B

=

B

∑D(CD D − D CD ) + ℏ

>A*+ >?

>EE

(9)

∑D(CD D − D CD ) corresponds to the energy conserving Liouville - von

17

The first term

18

Neumann equation and

19

due to electron-phonon interactions. The iterative solution of equation 9 along the MD

ℏ

>A*+ >?

>EE provides electronic energy dissipation due to a heat bath

10


Page 11 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

trajectory provides the dynamic observables used to characterize charge transfer in this system.

2

The observables we describe are dynamic charge density distribution, rate of transitions

3

between electronic energy states, and rate of charge transfer. The non-equilibrium charge

4

distribution which is a function of time and energy is given by

5

F" (, :) = ∑ (:)H( − )

(10)

6

where F" (, :) is the non-equilibrium charge distribution. The change in occupancy of electronic

7

state populations from the equilibrium distribution is ∆F(, :) = F" (, :) − FJ ()

8

(11)

9

where FJ () is the equilibrium charge distribution. Using equation 11 to track the occupation

10

of KS orbitals over time we can track the changes in electron charge distribution over the

11

system as

12

(N,O) KFLM (P, , :) = ∑,

TLM

(:) 5 6Q6R(S ( ) ∗ S ( ))

(12)

13

where we project the KS orbitals in the conduction band onto the z-axis by integrating over x-

14

components and y-components. Changes in hole charge distribution can be found by

15

considering states in the valence band.

16

The energy expectation values of excited state electrons are given by

17

〈∆ 〉(:) = ∑UVW (:) (:)

18

< X > (:) = Y∆Z ([(])BY∆Z( [(\)

Y∆Z [(?)BY∆Z [(\) (

(

11


(13)

(14)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1 2

Page 12 of 41

Assuming a single exponential fit of energy dissipation the rate of relaxation of nonequilibrium electrons found as < X > (:) = expa−b :c

3

?"

(15) Be

4

b = ad cBe = f5?J < X > (:)6:g

5

Typically, t’=0, t”= ∞. Up to this point the implementation of the equations of Redfield

6

theory and corresponding observables detailed in equations 4-16 have been successfully used

7

to analyze excited state dynamics in other nanomaterials. In this study, we found multi

8

exponential decay to occur and need to determine the relaxation time for each of the individual

9

relaxations. For multi exponential decay the total charge transfer rate is found by (i) identifying

10

pronounced stages, (ii) identifying individual rates of these stages, and (iii) taking the inverse of

11

the sum of the lifetimes for each relaxation stage.

12

b = a∑ie(d )i cBe

(16)

(17)

13

Each lifetime (d )i is found analogously to equations 15-16, with integration times t’ and t”

14

being updated for each stage.

15 16 17

Energy expectations and relaxation rates for holes are found in an equivalent manner utilizing equations 13-17 by considering states in the valence band.

18

Computational Details. The perovskite TF of has a stoichiometry of Cs8Pb8I24 which is

19

subject to periodic boundary conditions along x-axis and y-axis. The thickness of the C8Pb8I24 TF

20

is 8.99 angstroms. Two types of perovskite NW models were considered: an iodide terminated

21

surface NW with stoichiometry Cs7Pb16I30 and a lead terminated surface NW with stoichiometry

22

Cs22Pb32I42. Both NW models are periodic along the crystallographic direction. The iodide

23

terminated NW Cs7Pb16I30 has a diameter of 16.25 angstrom and the lead terminated nanowire

12


Page 13 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

Cs22Pb32I42 with a diameter of 18.25 angstroms. Details of location, orientation, and bond

2

distances of the dye and DML molecules to the perovskite NW/TF can be found in Figure S1.

3 4

Ground state electronic structure and geometry are computed using VASP software65-66

5

with PBE functional67 in a plane-wave basis set along with PAW pseudopotentials68. K-point

6

sampling was done along the x-axis for the perovskite NW and along the x-axis and y-axis for

7

the perovskite TF. For dynamics, the models were heated to a thermostat and implemented

8

molecular dynamics at 300K. Charge transfer dynamics are calculated using Reduced Density

9

Matrix formalism. Adiabatic molecular dynamics with on-the-fly non-adiabatic couplings

10

between nuclear and electronic degrees of freedom provide components for the Redfield

11

tensor followed by propagating the electronic populations with Redfield equations. Electron

12

dynamics are run only for the gamma point. The perovskite TF is a direct bandgap

13

semiconductors at the gamma point whereas the perovskite NW is an indirect semiconductor

14

where the valence band has a maximum at the gamma point as shown in Figure S2. The

15

dispersion curve for the conduction band of the perovskite NW is essentially flat, so it is a

16

reasonable approximation to run electron dynamics at gamma point.

17

Knowing the deficiencies of PBE, which were described in the introduction, we have to

18

carefully consider the impact of using it as an approximation to a hybrid functional on our

19

results. For ground-state electronic structure calculations PBE can be used as a substitute for a

20

hybrid functional as long as they both describe charge transfer states in a similar manner (i.e.

21

state swapping does not occur). For non-adiabatic couplings, it has been found that the PBE

13



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 41

1

functional, compared to HSE06, will tend to overestimate non-adiabatic couplings since PBE

2

underestimates electronic gaps between states59. So as a first order approximation our

3

computed electronic transition from the perovskite to the dye would be faster than what would

4

be computed using a long-range hybrid functional. The magnitude of overestimation depends

5

on several factors, such as the degree of coupling between the donor and acceptor and the size

6

of the system. In the electron dynamics section, we provide a qualitative description of the

7

overestimation for each perovskite-dye assembly.

8

III.

Results

9

Bonding Stability. Here we analyze the bonding stability of the DML molecule explicitly

10

coordinated to the surface of the perovskite NW and TF. We try to identify the correlation

11

between terminal surface composition of the perovskite NW/TF and the value of binding

12

energy. The NW perovskite morphology can have either a Cs-Pb terminated surface or Cs-I

13

terminated surface while the TF has a Pb-I surface. For the TF morphology the DML linker

14

groups are coordinated to two terminal Pb atoms or two terminal I atoms. For the NW

15

perovskite morphology DML linker groups were coordinated to either a crystallographic corner

16

or face of the Cs-Pb terminated or Cs-I terminated surface. The binding energy of the dye

17

molecule to the surface of the perovskite was calculated using equation 3 where a negative

18

value corresponds to a stable bond and a positive value corresponds to an unstable bond. As

19

seen in Table S1 the binding of the linker group is more stable when they are coordinated to

20

terminal I atoms than when bonded to terminal Pb atoms.

14


Page 15 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

From an electrostatics point of view, it would be thought that binding of the methoxy group

2

to terminal lead atoms would be more stable due to physical charge interactions of the ionic

3

lead and dipole moment of the methoxy linker group.69 Our results suggest that the binding of

4

the methoxy group to the perovskite surface is covalent in nature. The valent shell of I and Pb

5

in perovskites are 5-p and 6-s orbitals, respectively.70 This seems to indicated that the methoxy

6

linker group is able to hybridize more effectively with the iodide 5-p orbitals than the lead 6-s

7

orbitals. Based on this analysis we will conduct further investigation of the DML linker groups

8

coordinated to Cs-I terminated NW and Pb-I terminated TF.

9

In what follows we investigate the electronic structure and electron dynamics for four

10

perovskite-dye assemblies, which are shown in Figure 3. Panels (a)-(b) in Figure 3 show a dye

11

molecule above the surface of the CsPbI3 perovskite NW. The orientation of the benzene rings

12

on the dye molecule towards the surface of the NW allows for π-stacking interactions. Panels

13

(c)-(d) show a DML molecule that has the same physical orientation in respect to the surface of

14

the NW as the dye molecule in panels (a)-(b) and also has its linker group forming coordination

15

bond to the surface of the NW. This allows for comparison between though-bond and though-

16

space hole transfer pathways between assembly (1) and assembly (2). Panels (e)-(f) show a dye

17

molecule that is oriented normal to the surface of the CsPbI3 perovskite TF. In this arrangement,

18

the dye molecule does not experience any π-stacking interactions with the TF surface which

19

represents a case of minimal interaction between the dye and perovskite. Panels (g)-(h) show a

20

DML molecule that is oriented normal to the surface of the TF and has its linker groups

21

coordinated to the surface of the TF. This allows for though-bond versus though-space hole

22

transfer between assembly (3) and assembly (4).

15



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 41

1

Electronic structure. The density of states (DOS) of the perovskite-dye assemblies were

2

computed using equation 4. For all models 0 eV represents the Fermi level of the respective

3

perovskite-dye assembly where the Fermi level is defined as EFermi = [E(HO) + E(LU)] / 2. Figure

4

3(a,c,e,g) shows the DOS partitioned between the dye/DML molecule (blue) and perovskite

5

(red) and Figure 3(b,d,g,h) shows DOS of the perovskite – dye assemblies (green).

6

The bandgaps of the perovskite NW and TF show the expected characteristic of the NW

7

having a larger bandgap of 2.60 eV than the TF which has a band gap of 1.89 eV due to

8

quantum confinement effects. These values reflect closely to experimentally determined

9

bandgaps for ultrathin 20 nm diameter nanowires (2.71 eV) and 400 nm thick thin films (1.73 71-72

10

eV) in the cubic phase

. It should be noted that in Pb containing materials spin-orbit

11

coupling effects should be considered for accurate bandgaps, but bandgaps computed on the

12

PBE level show roughly accurate values with negligible differences compared to spin orbit

13

coupling calculations.31

14

Absorption spectra of the perovskite-dye assemblies were computed using equations 5-

15

7 and are shown in Figure 4. For each spectrum, we show the two most probable excitations,

16

based on oscillator strengths, and their corresponding transition energy, which is shown in

17

Table 1. Transition energies up to 3.50 eV were considered since there will be negligible

18

contributions of higher energy photons due to absorption of high energy photons in the

19

atmosphere. Due to the large bandgaps of assemblies (1) and (2) the onset of light absorption

20

does not occur until after assembly (3) and (4).

16


Page 17 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

An interesting aspect of the computed DOS is the alignment of the dye/DML electronic

2

states in assemblies (1) and (2) compared to assemblies (3) and (4). From Figure 3(a,c) we see

3

that for assemblies (1) and (2) the HO of the dye/DML molecule and the HO of the perovskite

4

NW are degenerate εHO(Dye) ≈ εHO(Perovskite) and from Figure 3(e,g) we see that the HO of the

5

dye/DML is roughly 0.70-0.80 eV higher in energy than the HO of the perovskite TF εHO(Dye) >

6

εHO(Perovskite). To understand the origin of the differences in band alignment between assemblies

7

(1,2) and (3,4) we perform single point calculations on the dye/DML molecule and perovskite

8

NW/TF separately. This represents a case where the dye/DML and perovskite NW/TF are

9

infinitely far apart and do not influence one another. Then we align the Fermi levels of the

10

dye/DML molecule and perovskite NW/TF to replicate the computed DOS in Figure 3.

11 12

It was found that aligning the Fermi levels of the perovskite NW/TF with the dye/DML

13

was not sufficient to reproduce any of the DOS of the perovskite-dye assembly from Figure 3.

14

This indicates the effect of band bending occurring at the perovskite – dye/DML interface.

15

Supplementary Table S2 shows the values of the Fermi levels for each model and the change in

16

HO and LU energies due to band bending. It shows that for assembly (1) and (2) there is no

17

change in the perovskite conduction band and increases in energy of the dye/DML valence

18

band by 0.17 eV/0.18 eV, respectively. For assemblies (3) and (4) we see the perovskite

19

conduction band decreases in energy of 0.23 eV/0.40 eV, respectively, and increase in energy of

20

the dye/DML valence band of 0.75 eV/0.95 eV, respectively. We suspect the terminal surface of

21

the perovskite NW/TF plays a significant role in the observed band bending trend. The same

22

trend has been observed at a MAPbI3 – TiO2 interface where the Pb-I terminal surface showing 17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

significant band bending in the conduction and valence band while the MA-I terminal surface

2

showed band bending only in the valence band.

Page 18 of 41

73

3

To better understand the trends noted above we explore the frontier orbitals of the

4

perovskite NW and TF. For the perovskite NW the HO is located on terminal I atoms. This means

5

the HO state is able to interact with electronic states of the dye/DML since they are on the

6

surface of the NW. The LU states are located on Pb atoms which are on the interior of the

7

perovskite NW. This implies the LU state is not able to interact with the dye/DML molecule. For

8

the perovskite TF the HO is located on terminal I atoms and the LU is located on Pb atoms, but

9

in the TF morphology the Pb atoms are exposed on the surface allowing for them to interact

10

with the dye/DML molecule. A visual demonstration of this is shown in SI Figure S2 which

11

shows the ground-state frontier KS orbitals for each model. We suspect that the exposed Pb

12

atoms on the perovskite TF surface add additional electronic dipole interactions that

13

significantly influence the electronic states of the dye/DML molecule. This would help to explain

14

the differences in the band alignment of the dye/DML molecules in assemblies (1,2) and

15

assemblies (3,4). As a note going forward, we will see that the band alignment of the dye/DML

16

relative to the perovskite NW/TF has important implications for hole transfer rates.

17 18

CT state analysis. The ability for the perovskite-dye assembly to spatially separate

19

charges was characterized by the location of frontier orbitals on the perovskite-dye assembly.

20

Ideally, one would like to achieve maximal spatial separation between the photo-induced

21

electron and hole to minimize the probability of recombination. Upon phonon-assisted

18


Page 19 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

thermalization of the electron to the LU and the hole to the HO, the frontier orbitals are being

2

populated by the electron and hole, respectively. Thus, to achieve maximal spatial separation

3

the LU should be localized on the perovskite and the HO localized on the dye/DML molecule.

4

Figure 5 shows the frontier KS orbitals for the ground-state perovskite-dye assemblies.

5

Assemblies (1) and (2) showed partial charge separation where the HO was delocalized over

6

both the dye/DML molecule and perovskite NW while the LU was localized on the perovskite

7

NW. Assembly (3) and (4) showed complete spatial charge separation where the HO was

8

localized on the dye/DML molecule and LU on the perovskite TF. Thus, it appears that the

9

perovskite TF is able to spatially separate the electron and hole better than the perovskite NW.

10

This can be attributed to the large energy offset between the perovskite TF HO and dye/DML

11

HO, as seen in Figure 3(e,g).

12

We note that these electronic states where computed using a PBE functional, which can

13

provide incorrect charge transfer states. To confirm that the identified charge transfer state is

14

real we computed the electronic structure of each assembly using HSE06 functional and

15

compared the pDOS obtained with the PBE and HSE06 functionals, which are shown in Figure

16

S4. It is found that the location of the dye electronic states relative to the perovskite electronic

17

states are the same, indicating that hole transfer would occur as described above.

18

Relaxation Dynamics.

Relaxation dynamics were computed using equations 8-17.

19

Figure 6 shows the relaxation of a photo-excited electron and photo-induced hole charge

20

density distribution as a function of energy and position using a logarithmic time scale. Figure

21

6(a,c,e,g) illustrate dynamics of density distribution energy where there is an initial steady-state

22

excitation hv that populates an electronic state LU+y in the conduction band and introduces a 19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 41

1

hole state HO-x in the valence band, under IOA.61 The excitation source is then turned off. We

2

observe the photo-excited electron relax from LU+y to LU and the hole relax from HO-x to HO

3

by utilizing electron-phonon coupling to dissipate energy. The horizontal dashed line and solid

4

line indicate energy expectation values for excited-state electrons and holes, respectively.

5

Vertical dashed lines are associated with (Ke)-1 and (Kh)-1 which signify relaxation times of the

6

electron and hole to LU and HO, respectively. Figure 6(b,d,f,h) illustrates dynamics of the

7

spatial density distribution where the KS orbitals are projected onto the z-axis. Change in the

8

spatial distribution as the electron/hole relax to the LU and HO, respectively. Charge density

9

features at spatial regions above +5 Å indicate charge localization on the dye molecule and

10

features below +5 Å indicate charge localization on the perovskite. The arrows indicate change

11

in spatial distribution of the hole after time (Kh)-1.

12

Rates of non-radiative relaxation for the three most probable excitations for each

13

assembly are shown in Table 2. Comparing the hole relaxation rates for assemblies (1) and (2),

14

it is seen that the bonded arrangement provides an order of magnitude faster hole transfer rate

15

than the unbonded arrangement. The same trend can be seen when comparing assemblies (3)

16

and (4) where the bonded arrangement shows three orders of magnitude quicker rate than the

17

unbonded arrangement. Qualitatively, this suggests that the methoxy linker group provides a

18

“through-bond” pathway which facilitates quicker hole relaxation rates.74 For the rest of this

19

section we will look in-depth at the computed hole relaxation rates and analyze why the

20

though-bond pathway provided faster hole relaxation than though-space. It should be noted

21

that since we used PBE functional to compute these rates they will generally be overestimated

20


Page 21 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

on an absolute scale compared to a hybrid functional, but relative to each other the trends

2

observed are expected to hold as they each carry the same systematic error.

3

Here we provide a general framework to interpret the computed rates. Generally, non-

4

adiabatic transitions between electronic states are convenient to analyze in terms of Fermi’s

5

golden rule.75 The coupling between electronic and nuclear degrees of freedom drive the

6

transition rates for electron relaxation from LU+y to LU and hole relaxation from HO-x to HO. A

7

general equation to describe these transitions is bl =

8

qr

Hole Transfer in Dye-Sensitized Cesium-Lead-Halide Perovskite

Recommend Documents