Role of Lead Vacancies for Optoelectronic Properties of Lead-Halide

This work presents spin-polarized and. 18 non-collinear spin ground state ... DFT is a typical work-. 52 horse implemented into electronic structure s...
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Role of Lead Vacancies for Optoelectronic Properties of Lead-Halide Perovskites Dayton Jonathan Vogel, Talgat M Inerbaev, and Dmitri S. Kilin J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b05375 • Publication Date (Web): 18 Dec 2017 Downloaded from http://pubs.acs.org on December 19, 2017

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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.

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Role of Lead Vacancies for Optoelectronic Properties of Lead-Halide Perovskites

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Dayton J. Vogel,a Talgat M. Inerbaev,b,c Dmitri S. Kilina,d,*

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a

Department of Chemistry, University of South Dakota, Vermillion, SD 57069 b

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L.N. Gumilyov Eurasian National University, Astana 010008, Kazakhstan

c

National University of Science and Technology MISIS, Moscow, 119049 Russian Federation

d

Department of Chemistry and Biochemistry, North Dakota State University, Fargo, ND, 58108

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Corresponding author: [email protected]

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Methylammonium lead iodide perovskite materials have been shown to be efficient in

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photovoltaic devices. The current fabrication process has not been perfected, leaving defects

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such as site vacancies, which can trap charge and have a detrimental effect on photo-generated

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charge carriers. Here, focus is placed on the effect a Pb site vacancy has on the and charge carrier

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dynamics following photoexcitation. Electronic structure of materials with vacancies are often

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found in open shell configurations with unpaired electrons in the conduction/valence bands. To

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accurately describe unpaired electrons, spin-polarized and non-collinear spin calculations are

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performed on both neutral and charged vacancy systems. This work presents spin-polarized and

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non-collinear spin ground state electronic structures, non-radiative rates of charge carrier

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relaxation, and introduces an extension to a novel procedure to compute photoluminescence

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spectra for open shell models. This study describes non-adiabatic dynamics of MAPbI3 models

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within a Redfield formalism focusing on the role of a Pb vacancy defect on electronic relaxation

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processes. Results show the vacancy of the Pb ion introducing a new energy state within the

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unblemished material band gap region. This additional unoccupied state is expected to increase

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the non-radiative relaxation lifetime of the excited electron, allowing for a longer lifetime of the

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charge carrier and increased opportunity for secondary relaxation mechanisms or collection to

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take place.

Abstract

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1.Introduction

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The introduction of methylammonium lead halide perovskite materials into photovoltaic

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devices in 2009 has resulted in an increased interest in the material’s wide range of applications.1

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A large factor increasing interest in the material is that PV device efficiency has now been

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increased up to 22.1%.2 Photoinduced processes within MAPbI3 are fundamentally important to

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optoelectronic applications and have been experimentally observed through a range of optical

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and spectral monitoring techniques.3 Within the available optical characterization data,

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photoluminescence signatures can provide keen insight into specific photoexcited processes and

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the corresponding material composition giving rise to unique findings. As the synthesis of

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MAPbI3 materials has been developed as a low cost solution based processes, it is not

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uncommon to find material defects and impurities.4,5 These defects can range from surface

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defects, interstitial positioning, ion migration, antisite populations, and vacancies.6,7,8,9 Each type

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of material defect has an impact on the electronic structure of the MAPbI3, with vacancies and

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surface defects providing possible locations for charge carrier recombination and trapping

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states.10 Depending on the target application of the material and its desired properties, these

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defects can be unwanted or intentionally manufactured by choice of precursor ratios.11,12

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A removal of a positive atomic species from a hybrid organic-inorganic perovskite

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material induces a localized charge due to electrons left at the defect site. The excess charges

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need to be accounted for as the number of charges will modify the HOMO/LUMO energy levels

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and the resulting band gap energy. In the situation where there is excess charge it should be

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noted that open shell electronic configurations are possible and must be taken into consideration.

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Open shell systems require spin-polarized calculations which has been readily applied to systems

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with heavy elements and high spin multiplicities. The “spin-polarized” DFT is a typical work-

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horse implemented into electronic structure software packages allowing qualitative analysis of

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electronic properties. The explicit description of spin components has been shown to be of

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importance within MAPbI3 materials.13,14 While spin-polarized approach provide a basis for

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qualitative analysis, the non-collinear spin approach helps to build complete picture.

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In order to assess and minimize the suppressive influence of defects onto optoelectronic

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properties of MAPbI3, nonadiabatic dynamics may be used to highlight fundamentally important

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mechanisms that pertain to (a) the relative change in electronic structure across models

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representing multiple possible defect environments and (b) their respective excited state

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relaxation mechanisms, and (c) a protocol to convert general quantum state dynamics into

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observables. Such modeling can be completed through a range of methods and approaches, with

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each unique defect condition necessitating the level of methodology needed.

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(a) Initial comparisons of ground state electronic structure are calculated using DFT15,16

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and used to highlight changes due to a specific defect and to show the necessity of

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spin-polarized calculations17,18,18 or non-collinear spin calculations. Electron dynamic

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calculations begin with molecular dynamic calculations, providing modeling of

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atomic positions under specific conditions. Interesting insights on the thermally

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induced re-structurization and photoexcitation induced processes can be obtained by

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nonadiabatic molecular dynamics19 excited state molecular dynamics20 or time-

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dependent excited state molecular dynamics.21

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(b) The excited state dynamics is critically needed to assess the ability of material with

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defect to emit light. Photoemission can be computationally modeled by a synergy of

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radiative and nonradiative processes following a photoexcitation. The nonradiative

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dissipative dynamics of excited states primarily originates from interaction with

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thermalized nuclear degrees of freedom and can be modeled by a range of

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approaches. Most of atomistic approached to nonradiative dynamics rest on the time

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dependent electronic structure monitored along an adiabatic MD trajectory, allowing

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for computation of the “on-the-fly” nonadiabatic couplings.22,23 The time propagation

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of the excited state can be pursued by multiple spawning methods,24 a family of

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methods based on surface hopping approach.25,26 Another option for modeling time-

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evolution of the excited state stems from density matrix approach,27,28 that has been

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recently implemented in a form appropriate for atomistic modeling of closed and

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open shell configurations.29,30 Nonradiative relaxation rate calculations in any of these

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methods are facilitated by atomic motion.

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(c) Observables indicating excited state phenomena, such as an excited state or a pair of

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hot carriers (electron and hole), can be calculated to follow charge carrier migration

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through a material and the multiple processes that may occur. Photoluminescence is

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dependent on the spatial and energetic location of the charge carriers, which is

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calculated through electron dynamics.31 Along the dynamic trajectory all possible

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emission events may be explored following a specific initial excitation. This work

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also reports an adaptation of spin-polarized non-adiabatic dynamics codes for

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computing photoluminescence of open shell species. This can provide insight into

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spin-polarized systems and unique PL spectral features previously unattainable

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through closed shell theoretical methods. This methodology is critically needed to

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computationally assess optical trends in open shell electronic configurations, radicals, and dilute magnetic semiconductors.

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In this work, a single Pb point defect (VPb) is created within bulk cubic MAPbI3 to

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monitor the resulting changes in electronic structure. To study a single VPb this study is

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conducted computationally using ab initio DFT and non-adiabatic formalism to study electronic

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structure, molecular dynamics, and non-adiabatic transitions relating to the resulting optical

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properties. The importance of material defects in MAPbI3 have been extensively covered through

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various ground state electronic structure calculations. With each type of defect there can be

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changes to both the morphology and electronic relaxation channels within the material. Studying

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a single isolated point defect, and the resulting optical properties, can be a challenging task for an

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experiment.

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This work focuses to accurately study the effect of a VPb and the resulting electronic

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structure, charge carrier dynamics, and emission mechanisms in three bulk cubic MAPbI3

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  systems. The systems provide a pure MAPbI3 material,  ,  , and  . The charge

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system provides an opportunity to computational model conditions representing open shell

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electronic systems due to excess charge. The use of approximations within this computational

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study allow for strong qualitative trends to be found regarding spin-polarized calculations.

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Computed data, even for simplistic atomistic models, can provide qualitative insight to others

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researching MAPbI3 materials. An important issue facing theoretical modeling of MAPbI3

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materials is the necessity to include SOC due to the heavy Pb and I elements. The largest

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constraint for results accounting for SOC is the computational time required. Therefore, in this

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work, very basic data in presence of SOC are provided SOC is not explicitly treated. However,

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the meticulous development and testing of incorporating SOC into non-adiabatic dynamics has

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been applied to lanthanide doped systems.32

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2.Methods

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2.a.Theoretical Approaches

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Accurate analysis of the open shell system requires the use of spin polarized DFT or non-

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collinear spin DFT calculations. Non-collinear spin DFT as implemented in VASP has been used

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to calculate the effects of spin orbit coupling upon the ground state electronic structure of the

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modeled systems.33-35 This methodology has been detailed in previous work.32 The relativistic

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Hamiltonian, includes scalar relativistic and spin-orbit terms. These corrections are added to self-

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conistent

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 "## ∑,! −  ∇ +     =   , with   =   $&

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spin DFT procedure provides components of spinor orbitals, which represent two-component

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vectors, (  = )

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"## ! ≠ 0, while for the spin-polarized approach ! = 0, and only diagonal densities take non-

Kohn-Sham

equation

in

non-collinear

%$''

spin .

basis

The non-collinear

  * , | | + ,! , = 1. Note that for non-collinear spin approach, ! 

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zero values: 0  → 0 , 0!!  → 0! .36 Solution of the spin polarized ground state

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electronic structure are calculated according to the single electron Kohn-Sham equation with the

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solutions provided in the basis of Kohn-Sham orbitals, ( , and energies, ( , where 2 = 3, 4

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( 6 specifies spin up or spin down. The spin-resolved densities 0 5 = ∑7 ,, , and 0! 5 =

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8 ( ∑7 ,,! ,

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are parameterized by total number of electrons 9∝ , 9! with 3, 4 (+1/2 and -1/2)

values of spin projections. A constraint to the sum 9 = 9 + 9! and difference, ∆9= 9 − 9!

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of these parameters allow to describe broad variety of charged species and non-singlet electronic

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configurations. 37 For example, in one of the created open-shell systems, it is found that there is

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one more alpha electron than beta, ∆9 = 9 − 9! = 1, yielding a doublet multiplicity with

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