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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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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] 11
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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