Comprehensive Computational Study of Partial Lead Substitution in

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Comprehensive Computational Study of Partial Lead Substitution in Methylammonium Lead Bromide Arun Mannodi-Kanakkithodi, Ji-Sang Park, Nari Jeon, Duyen H. Cao, David J Gosztola, Alex B. F. Martinson, and Maria K. Y. Chan Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b04017 • Publication Date (Web): 19 Mar 2019 Downloaded from http://pubs.acs.org on March 20, 2019

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Chemistry of Materials

Pb

M

Br

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All substituents selected for this study.

H

Mid-gap energy levels.

Li Be

Energetically favorable substitution.

Na Mg K

Ca Sc Ti

Rb Sr

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Lanthanides

MAPbBr3

MAPb0.87M0.13Br3

ACS Paragon Plus Environment

Actinides

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Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr

Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te

Cs Ba Lu Hf Ta W Re Os Fr Ra Lr

He

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Pt Au Hg Tl Pb Bi Po At Rn Uun Uuu Uub

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La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Ac Th Pa

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MAPbBr3

MAPb0.87Sc0.13Br3

MAPb0.87Ti0.13Br3

MAPb0.87Co0.13Br3

MAPb0.87Ni0.13Br3

MAPb0.87Zr0.13Br3

MAPb0.87Bi0.13Br3

MAPb0.87Hf0.13Br3

MAPb0.87Sb0.13Br3



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Calculated Property

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-1/-2 0/-1 +1/0 +2/+1 Ef Ionization Energy Valence Electron Affinity Density Melting Point Atomic Radius Electronegativity Specific Heat Heat of Fusion Thermal Conductivity y from MBry MBry Direct Gap MBry Indirect Gap MBry Form. En. MBry Avg. Bond Length MBry CN of M MBry Poly. Dist. Index MAMBr3 VBM MAMBr3 CBM MAMBr3 Mix. En. MAMBr3 Form. En. MAMBr3 lattice constant MAMBr3 CN of M MAMBr3 Sum_inv_bonds MAMBr3 Oct. Dist. Index

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Chemistry of Materials 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

Comprehensive Computational Study of Partial Lead Substitution in Methylammonium Lead Bromide Arun Mannodi-Kanakkithodi,∗,† Ji-Sang Park,‡ Nari Jeon,¶ Duyen H. Cao,¶ David J. Gosztola,† Alex B. F. Martinson,¶ and Maria K. Y. Chan† †Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL 60439, USA ‡Department of Materials, Imperial College London, London SW7 2AZ, United Kingdom ¶Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA E-mail: [email protected] Abstract Impurities in semiconductors, for example lead-based hybrid perovskites, have a major influence on their performance as photovoltaic (PV) light absorbers. While impurities could create harmful trap states that lead to non-radiative recombination of charge carriers and adversely affect PV efficiency, they could also potentially increase absorption via mid-gap energy levels that act as stepping stones for transitioning photons, or introduce charge carriers via doping. To unearth trends in impurity energy states, we use first principles density functional theory calculations to extensively study partial substitution of Pb in methylammonium lead bromide (MAPbBr3 ), a representative lead-halide perovskite. Investigation of the density of states and energy levels related to the transition of the substitutional defect from one charged state to another reveals that several elements create mid-gap energy states in MAPbBr3 . We machine learned trends and design rules from the computational data and discovered that a

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few easily-computed properties of the bromide compounds of any element can be used to predict the energetics and energy levels of the substitutional defect related to that element. The calculated Fermi level dependent defect formation energies lead to the observation that substitution by transition metals Zr, Hf, Nb and Sc, and group V element Sb, can shift the equilibrium Fermi level and change the perovskite conductivity as determined by the dominant intrinsic point defects. Lastly, metal substitutedMAPbBr3 compounds of Bi, Sc, Ni and Zr were experimentally investigated, and while there was an improvement in thin film morphology and enhancement in charge carrier lifetimes, no clear evidence of sub-gap absorption features owing to the substituent being incorporated in the MAPbBr3 lattice could be seen.

Introduction Organic-inorganic halide perovskites have desirable optoelectronic properties such as optimal band gaps, high absorption coefficients, and long carrier lifetimes, which puts them at the forefront of research for emerging photovoltaics. 1–24 From their earliest reported solar cell efficiencies of ∼ 4% in 2009 to ∼ 22% from latest estimates, 1,25 hybrid perovskites have come a long way thanks to concerted experimental and computational efforts. 26–45 The versatility of the ABX3 perovskite structure in terms of the compositional choices makes this class of materials of great interest and the resulting chemical space quite vast. Most commonly, X is a halogen atom — iodine(I), bromine (Br) or chlorine (Cl), A is methylammonium (MA), formamidinium (FA) or Cs, and B is Pb, forming hybrid lead halide perovskites.

Methylammonium lead iodide (MAPbI3 ) and methylammonium lead bromide (MAPbBr3 ) are the most commonly-studied hybrid perovskites so far, and while the latter shows lower device efficiencies compared to the former, MAPbBr3 is environmentally more stable, leads to higher open circuit voltages, and shows respectably high absorption coefficients and long carrier lifetimes owing to optoelectronically benign intrinsic defects. The band gap of MAPbBr3 2



is optimal for application in tandem and triple junction solar cells. 46 MAPbBr3 is also conducive to property manipulation via partial substitution at the A, B or X sites. 21,40 For instance, mixed halide compositions have been used to control the electronic band structure and band gap; replacing a fraction of Br with I decreases the band gap whereas replacement by Cl increases it. 27,31,40 Changing the cation A from MA to FA or Cs has been used to alter the thermal stability and photo-stability of the perovskite. 39,47

Point defects in semiconductors, whether intrinsic or extrinsic, play a major role in determining their electrical properties, such as the type and concentration of charge carriers and their recombination behavior. Defect energy levels well within the band gap (referred to as “deep” levels) can be exploited for intermediate-band photovoltaics (IBPVs), potentially leading to improved PV efficiencies via absorption of multiple sub-gap photons. 48–60 This effect was investigated in a recent study where we performed density functional theory (DFT) calculations on MAPbBr3 with partial substitution of Pb sites by the transition metal Co, which revealed mid-gap density of states belonging to Co and Br that were further experimentally shown to create sub-gap absorption peaks. 40 However, having deep defect levels is a double-edged sword, as they could prove to be catastrophic for PV performance by acting as non-radiative recombination centers for minority charge carriers. 20,61 It is thus crucial to be able to predict intrinsic and extrinsic point defect formation energies and energy levels in hybrid perovskites. Experimentally probing defect levels and determining the origin of such levels is challenging, 62,63 making computational approaches valuable for studying defects. Furthermore, a substantial defect dataset provides the opportunity for learning trends and identifying descriptors that influence a semiconductor’s defect properties, possibly enabling accelerated future predictions of trap states.

While there are numerous examples of partial substitution of Pb in MAPbI3 leading to changes in electronic structure, creation or suppression of defect states, and improvements

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in solar cell efficiency, 26,31,36,37,42–45 such studies are limited when it comes to MAPbBr3 . 40,41 In this work, we swept across the periodic table for possible substituents and conducted an extensive DFT study of partial Pb-substitution in MAPbBr3 . Group I, II, III, IV, V and VI elements with known positive oxidation states, as well as all 3d, 4d and 5d transition metals (resulting in a total of 55 substituents) were each simulated. Fig. 1 (a) shows the MAPbBr3 unit cell that contains 12 atoms, and the 2×2×2 supercell with 96 atoms where one out of 8 Pb atoms is replaced by substituent M. We present the DFT-computed electronic structures and formation energies of the various extrinsic substitutional defects in MAPbBr3 in different relevant charged states. All elements that were studied as Pb-substituents are highlighted in color in Fig. 1(b). The defect energy states or trap levels created by the substituent are probed in two different ways: from the electronic density of states (DOS), 40 and from the charge transition levels 20 obtained from the DFT energies of the charged systems. Further, we calculated the formation energies of the substituents as a function of the system net charge, the Fermi level as it changes from the MAPbBr3 valence band maximum (VBM) to the conduction band minimum(CBM), and the chemical potential of all relevant species. 64–66

Our computations reveal interesting trends across the periodic table in the change in structure and energetics for different substitutional defects, which help understand the feasibility of incorporation of any element as a dopant in MAPbBr3 , as well as in the energy levels created by these defects relative to the MAPbBr3 band edges. In Fig. 1(b), all the elements that create mid-gap energy states are highlighted in blue, providing both a list of promising substituents for IBPVs as well as a list of potential impurity states in the MAPbBr3 band gap that could act as harmful traps. Further, shown in green are the substitutional defects with lower formation energy than the dominant intrinsic defects in MAPbBr3 , which allows them to shift the equilibrium Fermi level and change the electrical conductivity of the semiconductor. The computational data was mined to extract chemical and physical rules that determine the energetics of substitution as well as the location of any substituent transition

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level relative to the MAPbBr3 VBM. Different descriptors ranging from elemental properties of the substituent M to electronic and structural properties of its compounds are used for this purpose, revealing that the formation energy and the q/q − 1 transition level could be reasonably predicted using just a few easily-attainable descriptors. Further, four of the candidates identified from our computations as creating mid-gap states, MAPb0.875 M0.125 Br3 (M = Bi, Sc, Ni, and Zr), were experimentally studied to evaluate changes in optoelectronic properties resulting from substitution.

Methodology Computational Methods In this work, DFT was used to obtain the crystal structure, total energy, and electronic structure information for M-substituted (where M is one of the 55 elements chosen as substituents) supercells of MAPbBr3 in the neutral state and charged states of +2, +1, -1 and -2, leading to systems with the formula unit MA8 Pb7 MBr24 . All calculations were performed using the Vienna ab-initio Simulation Package (VASP) employing the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional and projector-augmented wave (PAW) atom potentials. The kinetic energy cut-off for the planewave basis set was 500 eV, and all atoms were relaxed until forces on each were less than 0.05 eV/˚ A. Brillouin zone integration was performed using 3×3×3 Monkhorst-Pack meshes for structure optimization and using 6×6×6 meshes for calculation of absorption coefficients. For transition metals, the PBE+U functional was used to take into account the effects of on-site Coulomb interaction using a Hubbard-like U term. Although the appropriate value of U for each element should be determined by calibrating to experimental reaction energies or other properties, we fixed the value of U for all transition metals to be 3 eV based on prior work. 40

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The MAPbBr3 structure that served as the starting point for this work was obtained from ref. 40, and has a pseudo-cubic structure with lattice constants of 6.03, 6.04 and 6.12 ˚ A calculated at the PBE level of theory. The PBE functional is used in this work for all calculations despite the calculated band gap of ∼ 2 eV being underestimated by about 0.3 eV compared to experiments, 67 because of the computational expense and minimal improvement obtained by using hybrid functionals or incorporating spin-orbit coupling. 23,40 For every neutral state calculation on an MA8 Pb7 MBr24 system, the volume is allowed to relax along with all the atoms, and the change in the pseudo-cubic lattice constant is tracked. For the charged calculations, the optimized neutral state volume is kept fixed. Further, the density of states obtained from every neutral state calculation is analyzed to locate the electronic states belonging to the impurity (substituent) atoms.

Equations 1 and 2 are used to calculate the formation energies and charge transition levels associated with the substitution of M in different charged states, respectively:

E f (S q , EF ) = E(S q ) − 8E(M AP bBr3 ) + µP b − µM + qEF + Ecorr ǫ(q1 /q2 ) =

E f (S q1 ) − E f (S q2 ) q2 − q1

(1) (2)

In equation 1, E f (S q , EF ) is the energy of formation of MA8 Pb7 MBr24 in an overall charge state q at Fermi level EF (referenced to the VBM of bulk MAPbBr3 ), µP b and µM are the chemical potentials of Pb and M respectively, and Ecorr is the correction energy term calculated using Freysoldt’s correction scheme 68,69 to account for periodic interaction between the charge and its image. If the chemical potentials of Pb and M are fixed, Ef (Sq ) can be calculated as a function of EF as it moves from the VBM to the CBM. For the special case of a neutral substitution of Pb by M, q = 0 and the Fermi level and correction energy terms vanish.

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The chemical potential ranges are constrained by the stability of various compounds in the phase diagram. In the Supporting Information, Fig. S1 shows different regions of stability for MAPbBr3 and the bromides of MA and Pb based on their respective calculated formation energies for different chemical potential choices; µBr , µP b and µM A are referenced to Br2 molecule, Pb-fcc and MA-bcc structures respectively. We select µ values from three distinct points in the shaded red region where MAPbBr3 exists in thermodynamic equilibrium, namely Br-rich, moderate, and Pb-rich conditions. In the shaded red region, all µBr , µP b , µM A and µM (referenced to the known elemental standard state of M obtained from the Materials Project 70 ) values satisfy appropriate equality and inequality conditions (discussed in the SI) to ensure thermodynamic equilibrium for MAPbBr3 , and to prevent the formation of MABr, PbBr2 and MBry (the known, stable, lowest formation energy bromide of element M obtained from Materials Project 70 ). Equation 2 is used to calculate the charge transition level ǫ(q1 /q2 ), which is the Fermi level where charge states q2 and q1 are energetically equivalent. For all 55 substituents, we calculated the relevant charge transition levels for charge states +2, +1, 0, -1 and -2, referenced against the VBM of MAPbBr3 .

Experimental Methods CH3 NH3 Br, PbBr2 , BiBr3 , NiBr2 were purchased from Sigma Aldrich, and used as received. ZrBr4 and ScBr3 were purchased from Alfa Aesar, and used as received. Mixed powders of the desired stoichiometry were ground in a mortar for approximately 15 minutes, followed by annealing at 200 ◦ C for 2 hours in an N2 glovebox. Precursor solutions for thin films were prepared by dissolving powder materials in a mixed 5:2 v/v DMSO:DMS solvent to obtain 0.67 M concentration. The solution was stirred at 100 ◦ C for 30 min, and filtered with 0.2 µm filters. After that, the solution was dropped on a glass substrate and the substrates were spun at 3,000 rpm for 30 seconds, followed by annealing at 100 ◦ C for 1 hour. The entire process from the solution preparation to annealing was performed in an N2 glovebox. For 7


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the substituted samples, the substitution level was fixed to 12.5% for both powder and thin film samples.

Reflectance and transmittance spectra were measured by using a Cary 5000 photospectrometer with an integrating sphere. The absorbance spectra of thin film samples were corrected with the reflectance data. The absorbance spectra of powder samples were calculated from reflectance spectra, which were measured from compressed powder by two glass slides, with assumption of 0% transmission. SEM images were acquired at an accelerating voltage of 10-15 kV using a Hitachi S-4700 instrument equipped with a Quanta EDS detector. X-ray diffraction (XRD) patterns were collected using a Rigaku Miniflex 600 X-ray diffractometer with Cu Kα source. Steady-state and time-resolved photoluminescence spectra of perovskite thin films were collected at room temperature using a 410 nm pulsed diode laser with repetition rate of 5 MHz. The PL decay was fitted to a bi-exponential function y = Baseline + A1 exp(−(t − t0 )/τ1 )) + A2 exp(−(t − t0 )/τ2 ).

Results and Discussion Structure and Energetics In order to understand the feasibility of incorporation of any element M in the perovskite environment, we calculated the Goldschmidt tolerance and octahedral factors 71 based on tabulated values of cation and anion radii. 72 In Fig. S2, we plotted the calculated tolerance and octahedral factors for each of the 55 elements studied here, showing the acceptable regions of perovskite stability. 40,71 It can be seen that while the tolerance factor criterion is generally satisfied by all elements, a slight relaxation of the octahedral factor criterion would lead to all except the early Group III, IV, V and VI elements being suitable for perovskite environment insertion. Regardless, we decided to study all 55 elements in partial substitu8



tion of Pb in MAPbBr3 , but keep these stability factors in mind while determining a final list of energetically favorable substituents that create energy levels in the band gap.

How well a substituent fits in the perovskite lattice can be further understood by looking at how the lattice parameters change, and the energetics based on DFT total energies. The percentage change in (pseudo-cubic) lattice constant of the MAPbBr3 supercell owing to partial substitution of Pb by any element M has been plotted for elements period-wise in Fig. 2. We further calculated the formation enthalpy of incorporating M in the MAPbBr3 lattice against bromide formation (the known stable bromide compound for any M obtained from Materials Project 70 ) by considering the neutral version of equation 1 (with q = 0) at Br-rich chemical potential, which reduces to equation S1. The calculated formation enthalpy is also plotted period-wise for all the elements in Fig. 2. It can be seen that the percentage change in lattice constant is 1% or lower for all the cases, while the formation enthalpy is generally positive and below 0.5 eV.

It is seen that there is no clear correlation between the formation enthalpy and the change in lattice constant. Further, these calculated properties are not directly correlated with the tolerance and octahedral factors. As an example, let us examine Ta and W in Fig. 2 (d), both of which have particularly high formation enthalpy and change in lattice constant. But Fig. S2 shows that both Ta and W comfortably meet the tolerance factor criterion and are right on the boundary of the octahedral factor lower limit, so one would have expected a lower formation enthalpy and a smaller change in lattice constant. This indicates that there are other factors at play dictating the feasibility of incorporating an element in the perovskite environment, such as affinity for Br and preferred bromide coordination environment. Both Ta and W, for instance, are known to create square pyramidal MBr5 environments in their experimentally known bromide compounds, 73,74 leading to some amount of distortion in the MBr6 octahedron relative to the PbBr6 octahedron in the MA8 Pb7 MBr24 lattice. This oc-

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tahedral distortion further leads to changes in the perovskite electronic structure and the creation of impurity levels.

It should be noted that although the formation enthalpies for incorporating certain elements are rather high when considering the neutral substitution, they could be more stable in a different charged state, and thus cannot be dismissed as unsuitable substituents for Pb in MAPbBr3 . Ta and W are known to adopt oxidation states of 4+ and higher (and the corresponding ionic radii are used in Fig. S2), and are not suited to replace Pb in a 2+ oxidation state. Further, as explained in more detail in the coming sections, we observe that for certain elements such as Zr and Hf which have positive formation energies, the energetics of different charged states are more favorable, thanks to the proclivity of said elements for the 4+ and 3+ oxidation states. In the next section, we present the impurity energy levels calculated for all the substitutional defects starting from the optimized MA8 Pb7 MBr24 structure as discussed here.

Impurity Levels We estimated the impurity levels created by the partial substitution of Pb in MAPbBr3 by an element M in two ways: by examining the electronic density of states of MA8 Pb7 MBr24 , and by calculating the charge transition levels from different charged calculations on MA8 Pb7 MBr24 , using equation 2. In Fig. 3, we show the DOS for MAPbBr3 and 8 selected substituents. In pure MAPbBr3 , the VBM is primarily composed of Br p states while the CBM consists of Pb p states, as has been previously documented. 23,24,40 Upon partial substitution of Pb sites, the VBM and CBM are shifted by very minor amounts, such that the parent band gap of the material remains ∼ 2 eV. The substituent, however, sometimes creates isolated energy levels within the band gap, which might act as harmful recombination centers or as stepping stones for additional photon transitions between the VBM and CBM. In the case of transi10



tion metals such as Sc, Co, Zr and Nb, these sub-gap energy levels are primarily composed of states from substituent d orbitals with some amount of mixing from Br p orbitals.

The transition levels calculated using equation 2 correspond to substituent energy levels in the electronic structure of the material. They provide an alternative method of probing impurity states from the same DFT computations; whereas the DOS is obtained from the energy eigenvalues, transition levels depend on the total DFT energies of the relevant systems. Fig. 4, shows the calculated transition levels for all substituents divided according to the period they occupy in the periodic table. The +2/+1, +1/0, 0/-1, and -1/-2 transition levels are observed for most of the substituents, with the occasional presence of a +2/0, +1/-1 and 0/-2 transition. Also shown in Fig. 4 are the substituent energy states as estimated from the DOS.

It can be seen that certain transition levels overlap with, or can be correlated with, substituent density of states. The existence of the DOS substituent levels at those locations can be explained by the appropriate charge transition that takes place. For instance, the Sc mid-gap states in MA8 Pb7 ScBr24 that occur around 1.7 eV above the VBM correspond to a +1/0 charge transition; this means Sc exists in a 3+ oxidation state in the substituted system until 1.7 eV from the VBM, then transforms to a 2+ oxidation state, creating an overall neutral system. Similarly, Co mid-gap states are found in MA8 Pb7 CoBr24 around 0.2 eV below the CBM, corresponding to a 0/-1 transition level as Co goes from a 2+ to 1+ oxidation state.

Fig. 4 shows that most of the transition metals create mid-gap transition levels or density of states. This is not surprising as transition metals are known to adopt a wide range of valences and have a strong tendency to form coordination complexes with halogen atoms. Among period II and III elements shown in Fig. 4(a), Al is the only electropositive atom that creates mid-gap states, but is likely an unsuitable substituent owing to the large size

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difference between Al3+ and Pb2+ ions. Further, it can be seen that none of the alkali or alkaline earth metals create mid-gap states; the former exist in a -1 charge state in the gap owing to their preferred 1+ oxidation state while the latter are stable in the neutral state because of their preference for 2+ oxidation.

From Fig. 4(b), some trends in the energy levels created by 3d transition metals are evident. The +1/0 transition levels occur within the band gap for Sc and Ti, owing to their known stabilities in the 3+ oxidation state, but go further down into the valence band upon moving along the period to the right. The 0/-1 transition also moves down as we go from Sc to Zn, and it is seen that for Co, Ni and Cu, it lies in the band gap and thus corresponds to mid-gap states. Ga and As also create mid-gap states due to their stability in the 1+ to 3+ oxidation states.

Fig. 4(c) shows that all 4d transition metals except Y create mid-gap energy states. In a trend similar to the 3d transition metals, Zr, Nb and Tc show states corresponding to +2/+1 transition, which goes further down into the valence band upon moving to the right of the period. The stability of the early 4d metals in the 4+ as well as 3+ oxidation states lead to these transition levels. The +1/-1 charge transition is shown by all elements from Zr to Ag, but it goes down towards the valence band as one moves across the row. For Ru, Rh, Pd and Ag, +1/-1 transition corresponds to mid-gap substituent energy levels. Further, both In and Sb create mid-gap states owing to their stability in 3+ to 1+ states. Sn, which belongs to the same group as Pb, having similar ionic radii and oxidation states compared to Pb, creates a stable neutral system in the band gap but no mid-gap states. Indeed, Sn-based iodide and bromide hybrid perovskites have already been studied, 75–77 as have Sn-Pb mixed cation hybrid perovskites. 78,79 It can also be seen from Fig. 4(d) that all of the 5d transition metals from Hf to Hg show mid-gap energy states and transition levels, with trends very similar to the 4d transition series. These mid-gap levels are owed to the

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+2/+1 transition for the early members of the series and +1/-1 transition for later members.

This extensive study of impurity levels created by partial substitution at the Pb-site has revealed the various ways in which substituents create energy states in the band gap. While the presence of such energy states could prove beneficial in beyond-Shockley-Queisser photovoltaic designs, 60 it is important to note that they may very well act as detrimental impurity traps in conventional single junction solar cells in which they serve no purpose. In previous works, 20,61 it has been reported that low formation energy defect levels deep within the band gap could correspond to traps that cause nonradiative recombination of charge carriers which brings down the minority carrier concentration, changes the absorption characteristics and decreases the photovoltaic efficiency. It should be noted that allowing volume relaxation of the supercell is not standard practice in charged defect calculations; however, the current study is geared towards a substantial incorporation of substituents, such as necessary in IB applications. Nonetheless, we observe that there is a very small lattice constant change of less than 1% throughout the dataset, and we also observe that there is a good match between charge transition levels computed by fixed or relaxed volumes (Table S2). Further, the charge transition levels would change if we take spin-orbit coupling (SOC) into account or use hybrid functional or GW corrections. For three selected substituents, we computed charge transition levels using PBE, PBE+SOC, and HSE06 and present these results in Table S3. It can be seen that although the actual transition levels differ from each other, each theory predicts the same states to be in the band gap, at a similar relative position (i.e., as a fraction of the gap above the VBM). While band gap and band edge position corrections are important, there is a fortuitous cancelation of errors that means our conclusions are not affected significantly.

Given the importance of predicting and understanding the origin of impurity levels, the computational data generated here provides the opportunity to extract trends and unearth

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the chemical descriptors that explain the positioning of defect levels. In the next section, we explore this avenue by applying machine learning techniques.

Machine Learning Trends in Impurity Levels Over the last few years, there has been a rise in the application of modern machine learning and data mining techniques in materials science, leading to the efficient design of new materials. 80–99 The availability of sufficient quantity and diversity of data, whether computational or experimental, is necessary for such an approach. Machine learning in materials science is typically intended to solve the material → property problem; extracting physical and chemical design rules from data can lead to quantitative or qualitative predictive models. 85 Such models have been applied in the past for predicting electronic band gaps, 80,81,87,95 determining forces and energies, 82,96–98 classifying material phases, 84 predicting defect behavior, 91 and guiding successful experimental discovery. 86,89,90

In this work, we have generated a computational dataset of electronic and defect properties of substituents in MAPbBr3 , and have an opportunity to mine this data to obtain crucial insights. The first step towards addressing this problem is determining appropriate descriptors 85,93 for the system that correlate with the properties of interest, namely the formation energy of, and the transition levels introduced by, the substituents. Here, we apply descriptors belonging to three different categories: 1. Elemental properties of substituent M, e.g. first ionization energy, electronegativity and ionic radius. 2. Computed structural and electronic properties of MBry , the most stable known bromide of M obtained from the Materials Project. 70 3. Computed structural and electronic properties of MAMBr3 , the 12-atom perovskite 14



unit cell optimized with complete substitution of Pb in MAPbBr3 by M. Here, DFT calculations were performed for all 55 MAMBr3 unit cells using the same calculation parameters as before. A detailed description of each descriptor is provided in the Supporting Information. In Fig. 5, the Pearson coefficient of linear correlation 100 (r) between 5 properties (formation energy and 4 transition levels relative to the VBM) and several descriptors has been plotted; a darker color indicates a high (positive or negative) correlation whereas a lighter color is an indication of a lack of correlation between the two quantities. It can be seen that the formation energy (Ef ) of creating a neutral MP b substitutional defect in MAPbBr3 is highly correlated with the MAMBr3 formation energy (r = 0.91), meaning the energetics of the MAMBr3 unit cell estimated from a cheaper DFT calculation is a useful predictor of the stability of MP b in MAPbBr3 . Curiously, there is little or no correlation between Ef and the atomic radii or electronegativity of M (r < 0.2), whereas Ef has a stronger correlation (r > 0.64) with the melting point and heat of fusion of elemental M, proving that there is much more than just the size and Br affinity of the element M that dictates its stability in the perovskite environment.

When it comes to the charge transition levels, the -1/-2 level shows correlation with the (first) ionization energy (r = 0.65) and electronegativity (r = 0.57) of M, while the +2/+1 level is correlated with the melting point (r = 0.65) and heat of fusion (r = 0.58). These observations can be explained in the following manner: a large ionization energy and high electronegativity indicates an element that prefers a negative oxidation state. This brings down the -1/-2 transition level, possibly to within the band gap as can be seen for the case of Sulfur in Fig. 4 (a). A larger melting point and heat of fusion are characteristic of transition metals. This coupled with the fact that many of these elements prefer the 4+ or 3+ oxidation states brings the +2/+1 transition level higher, and even within the band gap as is the case with several 4d and 5d transition metals in Fig. 4 (c) and (d). 15


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However, the strongest correlations for the transition levels appear to be between the +1/0 and 0/-1 levels and the MAMBr3 VBM (r = 0.84) and CBM (r = 0.92), respectively (the band edges of MAMBr3 are aligned with respect to the 1s core levels of nitrogen from a reference MAPbBr3 calculation). This is not surprising as the +1/0 and 0/-1 levels are the energy levels which would roughly correspond with the perovskite valence and conduction band edges. The shift in band edges in MA8 Pb7 MBr24 compared to pure MAPbBr3 is a direct consequence of the distinct electronic behavior of the MBr6 octahedron, which can be approximated from the electronic structure calculated for the MAMBr3 unit cell. The band edges from this cheap DFT calculation (it should be noted that many of them correspond to a band gap of 0 eV) are thus a good predictor for the +1/0 or 0/-1 transition levels (and in many cases, the +1/-1 transition level, where the +1/0 and 0/-1 levels coincide with each other), which correspond to most of the mid-gap energy states shown in Fig. 4.

A correlation analysis as presented here helps one identify the common descriptors that can be used to move a particular transition level up or down. However, something of far greater value would be a predictive model to quantitatively locate where any transition level would lie relative to the VBM of MAPbBr3 , using a minimum number of easily attainable material attributes or descriptors. We applied an extended linear correlation analysis based on “compound functions” generated by combinations of primary descriptors. 87,92 We consider functions such as x 2 , x3 , x−1/2 and ex (10 functions in total) to generate new features from the set of 30 primary descriptors (properties of M, MBry and MAMBr3 ), leading to a set of 300 total features. By taking each of these 300 features one at a time as well as the products between any two features, we obtain 45450 compound features, and calculate linear correlation coefficients between the 5 properties of interest and every compound feature. By selecting compound functions with maximum magnitude of correlation with any transition level, we determine some simple but very useful functions that only take any two descriptors

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at a time to make a prediction with a mean absolute error (MAE) between 0.2 and 0.4 eV.

In Fig. 6, we present predictive models for the formation energy, +1/0 transition and 0/-1 transition level respectively, based on simple functions of the calculated band edges, bond lengths and lattice constants of MAMBr3 and MBry . The formation energy can be predicted with an MAE of 0.32 eV using an exponential functions of two descriptors: the average M-Br bond length in MBry , and the formation energy of MAMBr3 . Whereas the +1/0 transition can be predicted with an MAE of 0.38 eV using the MAMBr3 VBM and lattice constant, the CBM and M-Br bond lengths (specifically, the inverse sum of all M-Br bond lengths) in MAMBr3 can be used to predict the 0/-1 transition with a much lower MAE of 0.22 eV. While correlations between the +1/0 and 0/-1 transitions and the band edges of MAMBr3 are evident from Fig. 5, the relationships in Fig. 6 (b) and (c) follow with additional information about the MAMBr3 optimized structure making for more accurate predictions than using band edges alone.

The simplicity and reasonable accuracy of these models mean that with simply a DFT calculation on the MAMBr3 unit cell and the known stable bromide MBry , the energy of formation as well as two of the most important charge transition levels (which constitute a majority of the substituent mid-gap states highlighted in Fig. 4) created by a defect MP b in MAPbBr3 can be predicted. The consequence of such an insight is two-fold: (a) we have identified the crucial features of element M in a halide perovskite environment that contribute to the energetics and transition levels of M in MAPbBr3 , and (b) such models could potentially be extended to the screening of energetically favorable substituents with or without mid-gap states in other MAPbX3 halide perovskites (X = Cl, I or some combination of Cl, Br and I). It should be mentioned that the predictive models trained in this work can most likely be improved by using more advanced regression techniques, by expanding on the set of descriptors, and by expanding the dataset.

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Fermi Level Tuning by Substitutional Defects In the total absence of external impurities, the electrical properties of a semiconductor, for example the electrical conductivity, is determined by the dominant intrinsic defects. In order to understand how the conductivity changes (induced by a shift in the equilibrium Fermi level, calculated here by taking into account charge carrier neutrality conditions 101 ) in the presence of substitutional defects, we used equation 2 to calculate the Fermi level, charge and chemical potential dependent formation energies of all 55 substitutional defects and 12 possible intrinsic point defects, namely vacancy, self-interstitial and anti-site defects. The formation energy of all intrinsic defects is plotted for Br-rich, Pb-rich and moderate chemical potential conditions in Fig. S3. The slopes of different Ef vs EF plots reveal the preferred charged states of the defects from the VBM (EF = 0 eV) to the CBM (EF ∼ 2 eV), and the charge transition levels indicate probable energy trap states.

Our calculated results are consistent with reported energetics and transition levels of intrinsic defects in MAPbBr3 in the literature. 20,65 Some of the potential anti-site defects would create deep levels, but are not active because of their high formation energies. The three vacancy defects, VBr , VM A , and VP b , yield the lowest formation energies of all intrinsic defects and create shallow levels close to the band edges. While VBr is the dominant donor type intrinsic defect under all chemical potential conditions, VM A is generally the dominant acceptor type defect and along with VBr , pins the equilibrium Fermi level inside the VB for Br-rich conditions (leading to highly p-type conductivity), about 0.3 eV above the VBM for moderate conditions (leading to slightly p-type conductivity), and in the middle of the band gap for Pb-rich conditions (leading to intrinsic conductivity). VP b shows lower formation energy than VM A in some cases closer to the CBM; thus, we consider the three vacancy defects as the dominant intrinsic point defects and compare their energetics with that of the 18



extrinsic substitutional defects.

The formation energies of stable charged states of selected substitutional defects are shown in Fig. 7, along with the formation energies of VBr , VM A , and VP b , for Br-rich, moderate and Pb-rich chemical potential conditions. It can be seen that several MP b defects show lower formation energy than the vacancy defects, and would thus change the equilibrium Fermi level. Under Br-rich conditions, Zr, Hf, Sc, Nb and Sb create donor-type defects (in the charged state +2 or +1) with lower energy than VBr , shifting the equilibrium EF away from the VBM and making the conductivity less p-type. All of these substituents have lower energies than VBr under moderate chemical potential conditions as well, again moving the equilibrium EF away from the VBM and placing it around the middle of the band gap, making the conductivity intrinsic. Only Zr creates a low-energy substitutional defect under Pb-rich conditions and moves the equilibrium EF 0.5 eV below the CBM, resulting in slightly n-type conductivity.

The consequence of the results shown in Fig. 7 is that under certain chemical potential conditions, certain substituents create defects of sufficiently low energy that override the influence of dominant intrinsic defects. Zr, Nb, Hf, Sc and Sb all have been identified in the previous sections as substituents that create mid-gap energy levels in the electronic structure, and here it has been shown that they can create dominant defects and change the electrical properties of MAPbBr3 . The calculated transition levels for these 5 substituents, including the levels located within the band gap, are listed in Table 1.

In terms of practical applicability of these results, it is important to determine the appropriate growth (or chemical potential) conditions that ensure stability of a desired substitution. It can be seen from Fig. 7 that under Br-rich and moderate chemical potential conditions, VM A and VP b are likely to form spontaneously owing to their generally nega-

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Table 1: The calculated +2/+1, +1/0 and 0/-1 transition levels for substituents Sb, Sc, Zr, Nb and Hf in MAPbBr3 . The parent perovskite VBM is set at 0 eV and CBM is set at 1.97 eV. The levels shown in bold correspond to deep mid-gap energy states created by the substitutional defect. Substituent Sb Sc Zr Nb Hf

+2/+1 Transition (eV) -1.1 -1.3 1.1 0.5 1.1

+1/0 Transition (eV) 1.3 1.7 2.2 2.0 1.8

0/-1 Transition (eV) 2.0 2.5 2.2 2.0 2.5

tive formation energies, making such conditions unsuitable for growth and manipulation of MAPbBr3 . There is some evidence in the literature of Pb precipitates being detected during the synthesis of MAPbBr3 , and measured charge carrier density being in the intrinsic range. 102 This makes Pb-rich conditions of most relevance in the current work. It can be seen that ZrP b is the only substitution defect with a lower formation energy than VBr under these conditions, and would thus be the most promising case to pursue experimentally for energetically favorable intermediate band formation. With energetic concerns and likelihood of mid-gap energy states in mind, we pursued synthesis and characterization of a few promising substitutional defects; the results are presented in the next section.

Experiments on Selected Substituents (Bi, Sc, Ni, and Zr) Following the computational insights in the previous sections, a few elements were selected to be studied experimentally for partial substitution of Pb in MAPbBr3 . The factors used for this selection included but were not limited to: tolerance and octahedral factors (Fig. S2), formation enthalpy (Fig. 2), mid-gap impurity energy levels (Fig. 4), defect formation energies (Fig. 7), synthetic feasibility and availability of raw materials. While the requirement of mid-gap energy states reduces the suitable pool of substituents, the current computational approach can be extended to more generalized studies of partial substitution of Pb in halide 20



perovskites. Substitution by 4 elements—Bi, Sc, Ni and Zr—was attempted in powder and thin film samples. The absorption spectra of MAPbBr3 with a number of substitutional defects were calculated from DFT and are presented in Fig. S4 and Fig. 8(a). It can be seen from the computed spectra that certain substituents such as Hf, Zr, Bi and Sb show very pronounced sub-gap absorption peaks between 0.5 eV and 1 eV, consistent with the mid-gap energy states observed for these substituents from the computed DOS. Among the four substituents experimentally studied, Bi and Zr show the most striking sub-gap absorption feature (Fig. 8(a)) while Sc induces a small additional absorption, and none is observed in the Ni-substituted system.

The experimental absorption spectra of the parent MAPbBr3 and all substituted powder samples are shown in Fig. 8(b). The mid-IR absorption features (between 0.50 and 0.75 eV) seen in all samples most likely originate from the overtones of vibrational modes of the organic sub-lattice. 103–105 For the Bi-substituted system, a red shift in the absorption onset is observed which is in agreement with previous reports. 105 By combining UV-VIS absorption and spectroscopic ellipsometry measurements, Nayak et al. 105 determined that this red shift is due to defect states and sub-gap states, rather than bandgap narrowing. The Ni-substituted powder sample shows additional absorption features from ∼ 1.1 to 1.6 eV. However, these features are also observed in the starting material, NiBr2 , used in our synthesis (Fig. 8(c)), implying that Ni may not be incorporated in the MAPbBr3 lattice after all.

The fabrication of Sc, Ni, and Zr-substituted MAPbBr3 thin films is challenging due to the low solubility of their commercially available bromide salts in the mixed DMF:DMSO solvents. For instance, less than 1 mol % of Zr bromide salt can be solubilized to react with the parent MAPbBr3 compound. Other solvents such as N-Methyl-2-pyrrolidone (NMP) and Gamma Butyrolactone (GBL) were also tried but the solubility of metal salts could not

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be enhanced. Photographs of MAPbBr3 and Zr-substituted MAPbBr3 precursor solutions are shown in Fig. S5, showing an apparent color change from colorless to light yellow in the presence of Zr2+ /Zr4+ salt, despite at a small concentration. XRD pattern of the resulting Zr-substituted film (Fig. S6) reveals a small shift for the characteristic 15 deg peak of MAPbBr3 (0.03 deg), which would correspond to a roughly 0.2% lattice constant change, which is similar to the change calculated for MA8 Pb7 ZrBr24 from DFT and plotted in Fig. 2.

Shown in Fig. S7 is the comparison between absorption features of Sc, Ni, Zr, and Bisubstituted MAPbBr3 thin films and that of the parent MAPbBr3 film. The absorption onset of Bi-substituted red-shifts similarly to the powder sample, and no additional optical transitions is detected, which could be due to the relatively small intensity calculated for these transitions compared to the intensity of fundamental band gap transitions. The low substitution concentration of Sc, Ni, and Zr results in no obvious change in their absorption responses relative to that of MAPbBr3 .

Interestingly, the morphology and PL kinetics of the MAPb1−x Zrx Br3 thin film are much enhanced compared to the pure MAPbBr3 film. Top-view SEM images (Figure 7 (a) and (b)) illustrate that the discrete crystalline islands in the pure MAPbBr3 film are fused upon the introduction of ZrBr4 salt, forming a much smoother surface and thus improving the film morphology. As shown in Fig. 9 (c) and (d), the better film morphology in turn translates to enhanced charge carrier lifetimes from

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