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Surface Termination, Morphology and Bright Photoluminescence of Cesium Lead Halide Perovskite Nanocrystals Stephanie ten Brinck, and Ivan Infante ACS Energy Lett., Just Accepted Manuscript • DOI: 10.1021/acsenergylett.6b00595 • Publication Date (Web): 15 Nov 2016 Downloaded from http://pubs.acs.org on November 16, 2016

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Surface Termination, Morphology and Bright Photoluminescence of Cesium Lead Halide Perovskite Nanocrystals Stephanie ten Brinckv and Ivan Infante*,v

v

Department of Theoretical Chemistry, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands

AUTHOR INFORMATION Corresponding Author Email: [email protected]

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Colloidal cesium lead halide perovskite nanocrystals (CsPbX3 PNC, X=Cl, Br, I) exhibit important optoelectronic properties that make them amenable for a plethora of applications. The origin of these properties, even for as-synthesized and unpurified PNCs, is however largely unknown. Electronic structure calculations are therefore essential to understand with atomistic detail the properties of these nanomaterials, however finding a model for PNCs that resembles the experiments is a challenging task.

Essentially, the main problem is how to correctly

terminate the PNC surface that comprises of a large fraction of the atoms that compose the nanocrystal and of ligands employed in the synthesis. Here, we construct nominally trap-free models for PNCs taking into account experimental conditions. With density functional theory we analyze the effect of size, shape and halide composition on the electronic structure of PNCs. We confirm that the PNC crystalline core exhibits an orthorhombic structure and we demonstrate that PNCs are robust light emitters even when a large number of ligands is displaced from the surface.

TOC GRAPHIC


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In early 2015 Protesescu et al.1 synthesized for the first time colloidal Cesium Lead Halide Perovskite nanocrystals (CsPbBr3 PNCs), which have emerged as a new class of nanomaterials with exceptional properties like very high photoluminescence quantum yield (PLQY) up to 90%, a tunable and narrow emission bandwidth in the visible spectrum and a high defect tolerance.1–7 For these reasons, PNCs show great promise in optoelectronic applications like sensing, lasing,8 photovoltaics9 and light-emitting devices (LED).7 Since their discovery, however, it is still not clear why these nanocrystals, even as-synthesized and unpurified, present such outstanding properties, especially when we compare them to their analogous colloidal semiconductor nanocrystals. The latter usually present very low PLQY when synthesized presumably for the presence of defects at the surface that create trap states and render these materials rather inefficient.10 Only after adding a shell of a different material, for example in a core-shell configuration like CdSe/ZnS, or by improving the surface passivation11 it is possible to increase their PLQY beyond 90%.12 For some materials, like lead chalcogenides, it is still difficult to achieve PLQY greater than 20%.13 To understand the properties of CsPbBr3 PNCs it is thus paramount to look at their electronic structure by performing quantum chemical simulations. The importance of theory has been demonstrated by the tremendous effort spent in recent years to analyze in atomistic detail the properties of thin films methylammonium perovskite materials,14–17 which have been remarkably successful in the photovoltaic field, reaching power conversion efficiencies above 21%.18 These theoretical works have shed light in the compositions and defect behavior of these films and helped in improving their optoelectronic performance.19–22 Unlike in thin films, however, there are few theoretical works that address the structural and optical properties of PNCs.23,24 The main reason to this is the lack of knowledge on the


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composition of the PNC surface, a very complex region to model. Several conditions need indeed to be satisfied to correctly describe the surface: (i) preservation of a charge neutral PNC, with the inorganic atoms composing the PNC conserving their thermodynamically preferred oxidation state; (ii) a low density, if not the lack, of defects/traps to explain the high PLQY; (iii) inclusion of the ligands employed in the synthesis like oleylamine and oleate; (iv) exposure of the same facets and crystalline structure observed in the experiment. Maintaining all these conditions when building a structural model is thus a challenging task. If not done correctly, the models for the PNCs employed in theoretical calculations could be severely limited and hinder a full understanding of their optoelectronic properties. In this work, we prepare models for PNCs akin to experimental procedures that take into account all conditions indicated above. These PNC models are nominally free of traps states, in agreement with high PLQY, preserve charge neutrality and are terminated with both oleylamine and oleate. We also discuss the effect of size, shape and halides in the electronic structure. Finally, we demonstrate that removal of ligands from the surface affects the electronic structure of these materials only slightly, indicating an unexpected robustness towards degradation of the material. This likely explains why PNCs maintain high PLQY in sub-optimal conditions.

Building models for CsPbBr3 nanocrystals. In Table 1, we present different sizes and atomic compositions of CsPbBr3 PNCs models obtained by cutting the bulk in the cubic phase (space group 𝑃𝑚3𝑚). Note that cleaving the bulk in a given phase does not ensure that the final relaxed structure will converge to the same crystalline configuration (vide infra). As a start we cleaved the bulk in two ways along the (001) directions: the first leaves only Cs and Br at the PNC surface, and the second leaves only Pb and Br (Figure S1). For a given PNC size, this leads


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to different stoichiometric proportion between the different ions in the crystal, as shown in Table 1. Note also that at lower PNC sizes the increased surface-to-volume ratio leads to a significant deviation from the typical 1:1:3 ratio.

Table 1. The atomic composition of different CsPbBr3 PNCs models used in the study for different sizes, along with the ratios of cesium to lead and bromide to lead. The overall excess charge of the PNCs is computed by assuming the following oxidation states: MA+, Cs+, Pb2+ and Br–. A complete table including the total number of atoms for each nanocube is provided in the Supporting Information, Table S1. As-cut from the bulk along the (001) direction

Size (nm)

With Cs and Br exposed Cs : Pb : Br

Excess

With Pb and Br exposed Cs : Pb : Br

Charge

Excess

With 50% Cs+ and 50% MA+ at the surface

With excess Br to compensate charge

With less MA+ to compensate charge

With Cs and Br exposed



Cs : Pb : Br

Cs : Pb : Br

Cs : Pb : Br

Charge

Excess Charge

1.74

2.4 : 1 : 4.0

+10

0.4 : 1 : 2.3

+11

1.3 : 1 : 4.0

+10

1.3 : 1 : 4.4

1.3 : 1 : 4.0

2.32

2.0 : 1 : 3.8

+13

0.5 : 1 : 2.4

+14

1.2 : 1 : 3.8

+13

1.2 : 1 : 4.0

1.2 : 1 : 3.8

2.90

1.7 : 1 : 3.6

+16

0.6 : 1 : 2.5

+17

1.1 : 1 : 3.6

+16

1.1 : 1 : 3.7

1.1 : 1 : 3.6

3.48

1.6 : 1 : 3.5

+19

0.6 : 1 : 2.6

+20

1.1 : 1 : 3.5

+19

1.1 : 1 : 3.6

1.1 : 1 : 3.5

…

…

…

…

…

…

…

…

…

8.12

1.2 : 1 : 3.2

+43

0.8 : 1 : 2.8

+44

1.0 : 1 : 3.2

+43

1.0 : 1 : 3.2

1.0 : 1 : 3.2

Experiments 3.6

Not measured: 1 : 3.55a

7.8

0.97: 1 : not measuredb

7.8

1.0 : 1 : 3.2c

Bulk

1.0 : 1 : 3.0

a.

Pb:Br Ratio measured on CH3NH3PbBr3 PNCs: ref. [4] ; b. Taken from ref. [25] ; c. Taken from ref. [2]


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Experimentally, Feng Zhang et al4 observed a Br:Pb molar ratio of 3.55 for 3.3 nm CH3NH3PbBr3 PNCs, suggesting that methylammonium (MA) and Br are exposed at the surface. For larger PNCs, at sizes typically obtained in the experiments (i.e. 8 nm), a Br:Pb molar ratio of 3.2 was observed by Song Wei et al2 for 7.8 nm CsPbBr3 PNCs. Both these data strongly suggest that experimental CsPbBr3 PNCs likely present excess Cs and Br at the surface rather than Pb and Br, despite that the synthesis is usually carried out in excess of PbBr2. The main difference between our data in Table 1 and the experiments is in the Cs:Pb molar ratio. Our value of 1.2 is larger than the 0.97 estimated by Wei using XPS spectroscopy2 and the 1.0 obtained by de Roo et al25 using Rutherford Back Scattering (RBS) measurements. Although we could expect this discrepancy stemming from the experimental error bar, our understanding is that many of the surface Cs atoms are in fact replaced by oleylammonium (OA) ions to maintain colloidal stability of the PNCs. The presence of oleylammonium at the PNC surface is indeed confirmed experimentally by IR spectra and NMR studies25,26. For this reason, in building our model we decided to remove enough Cs atoms at the surface to obtain Cs:Pb ratio close to 1.0, and replace these atoms with methylammonium (MA) moieties. We noticed that about half of the Cs ions at the surface have to be removed to satisfy this condition. In our models we use MA instead of OA because it is more advantageous computationally. A summary of the new atomic compositions for different sizes, including MA, is shown in Table 1. In semiconductor metal chalcogenide colloidal nanocrystals, the surface usually presents an excess of metal cations that is charge compensated by organic ligand anions to preserve charge neutrality of the nanocrystal.27,28 In case of PNCs, we make the same assumption. Considering the relatively mild conditions in which the PNC synthesis takes place and the fact that the precursors already keep the PNC elements in their thermodynamically favored oxidation state,


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i.e. MA as +1, Cs as +1, Pb as +2 and Br as -1, we expect that our models of nanocubic PNCs shown in Table 1 present an excess of positive charge that depends on the size. To neutralize this excess charge there are two options: (i) by adding anions, as Br– or oleate, or (ii) by removing excess cations, either as Cs+ or MA+ or a mixture of the two. For the former case, we prepared a 2.9 nm CsPbBr3 PNC and we added enough Br– anions to compensate the excess charge. We then relaxed the geometry and computed the electronic structure as shown in Figure 1a (model 1). Each molecular orbital (MO) was further analyzed in terms of its atomic component orbitals and categorized according to the atomic composition and represented by a colored segment. The length of the colored section represents the fractional contribution of that element to the MO. The eye-catching feature is the presence of a large number of states just above the valence band (VB). Inspection of these states show that these are mostly localized on the 4p orbitals of the Br ions added to compensate the excess charge of the PNC (Figure 2a). It is likely that these states would act as localized traps and provide a clear pathway to non-radiative exciton recombination. This would then lead to a low PLQY that is in clear contrast with experimental evidence. Based on this, we then decided to compensate the CsPbBr3 PNC excess charge by removing cations from the surface (model 2). We did this by removing enough MA+ to neutralize the overall charge and we then optimized the geometry and calculated the electronic structure. In this case, the PNC exhibit a band gap without trap states as also evidenced by the HOMO plot in Figure 1c that exhibit a clear delocalized composition.


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Figure 1. (a) Computed electronic structure of the CsPbBr3 PNC at the DFT/PBE level of theory. Each line corresponds to a molecular orbital (MO). Each color indicates the contribution of a type of atom (or moiety) for a given MO. All these models include half Cs+ and half MA+ at the surface as shown in Table 1. From left to right: (1) Model in which the excess of positive charge is compensated by adding Br– ions; (2) Model in which the excess of positive charge is compensated by removing excess MA+ from the surface; (3) Same model as (2), with some of the Br– replaced by formate moieties, which emulates the


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oleate used in the synthesis; (4) Same model as (2), but starting from an orthorhombic configuration exposing both (001) and (110) facets; (5) Same model as (4) but starting from a cubic crystal structure; (b) Highest Occupied Molecular Orbital (HOMO) for the system compensated with excess Br ions. The HOMO is localized on Br ions; (c) HOMO state for the system where excess MA+ is removed. This state is delocalized and the PNC is trap-free.

Finally, to correctly terminate the surface of our models, we decided to take into account the experimental conditions for the PNC synthesis, which takes place in an ambient in excess of PbBr2, oleic acid and oleylamine. The presence of oleate (OE) at the PNC surface as an oleylammonium oleate (OA+OE-) ion-pair was confirmed by Roo et al.25, and more recently by Pan et al.26 As a consequence, we decided to include formate ligands in our PNC models that emulate the carboxylate group (oleate) anchored to the NC surface. To maintain charge neutrality, we removed some of the surface Br ion and replaced them with formates. We carefully maintained a Br:Pb ratio of about 3.5-3.4 for the 2.9 nm PNC by replacing 20-30 Br ions with formates. As in the case of MA, the positions of the formates are chosen randomly, but we distributed them evenly among each facet of the nanocube, about 4-5 on each side. The computed electronic structure after geometry relaxation is shown in Figure 1a (model 3). It is possible that the presence of the formate does not affect the energy levels much. Localized states are still absent and the band gap remains substantially unchanged.

Orthorhombic vs Cubic. In recent reports, there has been some debate on the correct crystal structure of CsPbBr3 PNCs whether it is cubic or orthorhombic. Using pair distribution functions (PDF) and Rietveld refinement, Cottingham et al.29 have demonstrated unambiguously that CsPbBr3 PNCs are orthorhombic. For this reason, we decided to build also model 4, which is


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obtained by carving the bulk in the orthorhombic phase (space group Pnma), to retrieve a pseudo-cubic structure of 2.4 nm. With this procedure we obtained a nanocrystal exposing six facets: two of those exposing Cs and Br at the surface in a similar fashion to the (001) facets in the nanocube, and four facets exposing Pb and Br at the surface resembling the (110) planes in the nanocube. Note that in recent reports, TEM images reveal that CsPbBr3 PNCs could exhibit indeed both these planes.26 For comparison we have also built model 5, stoichiometric with model 4, which is obtained from a starting cubic crystalline structure cut along the (001) and (110) directions. By passivating the surface of these models with half Cs and half MA at the surface and compensating the charge by removing excess bromine, we recovered a molar ratio of 1:1:3.2, close to the bulk value. We then performed a structural relaxation at the DFT/PBE level of theory for both models and we obtained also in this case nominal trap-free nanocrystals. Notably, these two models converge to two almost identical structures, separated by only 0.15 eV in energy, both exhibiting an orthorhombic phase (Figure 2a). Presumably, when we start from a cubic conformer, the lattice exerts a strain on the Pb-Br bonds that leads to a tilting of the octahedrons from the 90 degrees position. This effect is usually explained by the presence of a strong Pauli repulsion between the occupied 6s Pb orbitals and the 4p orbitals of the nearby Br ions. The presence of an orthorhombic phase is further confirmed by computing PDFs of the BrBr bonds for the starting and relaxed PNC structures of model 4 and 5 as depicted in Figure 2b. Clearly, the relaxed structure of our model 4 (green line) and model 5 (orange line) are in better agreement with the unrelaxed orthorhombic phase (red line) than the unrelaxed cubic one (black line).


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Note that also model 2 and model 3, which are carved from the bulk and expose only the (001) facets, converge to an orthorhombic phase once they are relaxed to their most stable conformation.

Figure 2. (a) Model 4 (orthorhombic) and Model 5 (cubic) unrelaxed structures of 2.4 nm CsPbBr3 nanocrystals as cut from the bulk. Both systems present the same number of atoms. The relaxed structures of Model 4 and Model 5, computed at the DFT/PBE level of theory, both exhibit an orthorhombic configuration; (b) PDFs of the Br-Br distance computed for the unrelaxed cubic structure of Model 4 (black line), the unrelaxed orthorhombic structure of Model 5 (red line), the relaxed structure of Model 4 and after 5 ps of AIMD simulation (blue line). (c) Time evolution of the HOMO-LUMO gap computed


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for Model 4. Blue line represents the HOMO-LUMO gap oscillation over time; red line is a linear regression of the computed HOMO-LUMO gap that indicates the stability of this variable throughout the simulation time.

To further assess the structural and energetic stability of our systems over time we performed a set of ab-initio molecular dynamics (AIMD) simulations. We computed the PDFs of model 4 after equilibrating it for 2 ps and performing a production run of 5 ps at room temperature (298 K). In this framework, model 4 retains the orthorhombic structure (blue line in Figure 2b). The effect of including methylammonium at the surface seems to be negligible in the morphology of these systems. Additionally, we also analyzed the evolution of the band gap of these materials over time (Figure 2c). The electronic structure of this system is very stable as evidenced by the regression line plotted against the HOMO-LUMO gap. The average band gap for these small 2.4 nm NCs is 1.82 eV, which is somewhat lower than the experiment for larger nanoparticles (2.39 eV for > 10 nm PNC). This discrepancy stems from our computational DFT approach that uses a pure exchange-correlation functional, i.e. PBE, which has been widely demonstrated to lead to an underestimation of the band gap for similar perovskite bulk systems.20,30 Size and Halide Effects. We analyzed the electronic structure of PNCs at different sizes and by changing the composition of the halide element, varying it from Cl to I. For these calculations we took the nanocubic model 2 of Figure 1a as a benchmark system. As depicted in Figure 3, increasing the size reduces the band gap as expected for strongly quantum-confined inorganic nanocrystals.


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Figure 3. Effect of size on the electronic structure of trap-free CsPbBr3 PNC nanocrystals computed at the DFT/PBE level of theory. Each line corresponds to a molecular orbital (MO) where each color indicates the contribution of a type of atom (or moiety) for a given MO.

On the other hand, changing the type of halides from Cl to I reduces the band gap in agreement with the experiments1–4 as shown in Figure 4. To provide further insights on the interaction between halide and lead atoms, we computed the crystal orbital overlap populations (COOP). In other words, we weighted the composition of each MO with the overlap between all lead atomic orbitals and all halides atomic orbitals. In this framework, large negative and positive values indicate large antibonding and bonding contributions between the two species, respectively. Values close to 0 indicate non-bonding interactions. As depicted in Figure 4 and explained elsewhere for bulk CsPbI3,31 the MOs close to the VB are formed by antibonding contribution between the Pb(6s) and halide(np). The strength of this antibonding interaction is largest with I even though the width of the antibonding region is larger for Cl. It is interesting to note that going deeper in the VB, this antibonding contribution tend to fade, forming a sort of non-


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bonding region of halide np orbitals, before it forms a bonding combination. This non-bonding region is shifted closer to the VB moving from Cl to I.

Figure 4. Effect of the halide X (X = Cl, Br, I) on the electronic structure of trap-free PNC nanocrystals computed at the DFT/PBE level of theory. All PNCs present the same number of atoms. Each line corresponds to a MO where each color indicates the contribution of a type of atom (or moiety) for a given MO. Next to each MO, we plotted the crystal orbital overlap (COOP) contribution. This term indicates the type (bonding, antibonding, non-bonding) and strength of the interaction between Pb and X atoms.

CsPbBr3 PNCs as Robust Light Emitters. Since the discovery of PNCs, several reports have highlighted how the surface plays a pivotal role in maintaining colloidal stability, structural integrity and stable optical properties.4,25,26,32 These reports suggest that these nanocrystals present a very ionic crystalline structure and it is thus expected that PNCs could lose many of their


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attractive optoelectronic properties, for example, during the purification procedures, especially with polar solvents. The polar solvent could indeed remove some of the labile ligands at the surface, likely as ion pairs, and introduce some defects that reduce their optoelectronic performance. For example, Pan et al.26 demonstrated that washing with polar solvents like acetone removes all oleylammonium from the surface of the PNC, presumably as bromide oleylammonium. A similar effect was also qualitatively demonstrated by de Roo et al25. They both show how the integrity of the PNC is degraded, along with the PLQY, when several washing cycles are carried out to remove surfactants from the PNC surface. To simulate the effect of washing on the electronic structure of CsPbBr3 PNCs, we performed a few geometry optimizations on our benchmark model 2 of Figure 1a. In a first step we removed all MA ions from the PNC surface in the form of Br–MA+ ion pairs as suggested by Pan et al.26 Then, we stripped 16 Cs+Br– ion pairs. This corresponds to removing about 20% of Cs at the surface. Despite these substantial displacements of ligands from the nanocrystal surface the PNC maintains both structural and electronic integrity with trap-free band gaps (Figure 5). We can conclude by saying that the high PLQY shown by these nanocrystals could be attributed to a high tolerance of these PNCs electronic structure towards degradation, and that the loss of PLQY obtained after washing could be tentatively attributed to aggregation and precipitation rather than the introduction of defects at the nanocrystal surface.


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Figure 5. Electronic structure of CsPbBr3 PNCs obtained before and after removing ligands from the surface. All structures have been computed at the DFT/PBE level of theory. Each line corresponds to a MO where each color indicates the contribution of a type of atom (or moiety) for a given MO.

Theoretical Methodology. We have carried out atomistic simulations at the Density Functional Theory level using the PBE exchange-correlation functional33 and a double-zeta basis-set plus polarization functions on all atoms as implemented in the CP2K 3.0 code.34 All structures have been optimized in vacuum. Scalar relativistic effects have been incorporated as effective core potential functions in the basis-set. Spin-orbit coupling effects have not been included, however their impact on the relaxed structural properties has been demonstrated to be negligible for similar systems. This indicates that scalar relativistic effects are sufficient to


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describe the equilibrium geometries of these materials. On the other hand, as also pointed out in the text, the HOMO-LUMO gap energy is strongly influenced by the exchange-correlation functional and the inclusion of spin-orbit coupling. Unfortunately, due to the large size of the systems presented in this work (more than 10000 basis functions on average), hybrid functionals and spin-orbit coupling effect could not be included in our calculations. Molecular dynamics simulations were carried at the DFT/PBE level of theory and the same basis-set employed for the static calculations. The dynamics employed an integration timestep of 1 fs and a constant temperature of 298 K was maintained using a velocity-rescaling thermostat. Canonical NVT simulations were run for 7 ps, with the first 2 ps discarded as an equilibration step. Further details on how we obtained the various nanocrystal structures are provided in the main text.

ASSOCIATED CONTENT Further details are provided in the Supporting Information. AUTHOR INFORMATION Corresponding Author Email: [email protected] Notes The authors declare no competing financial interests. ACKNOWLEDGMENT


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Ivan Infante and Stephanie ten Brinck would like to thank the Netherlands Organization of Scientific Research (NWO) for providing financial support within the Innovational Research Incentive (Vidi) Scheme (Grant No. 723.013.002). This work was carried out on the Dutch national e-infrastructure with the support of SURF Cooperative. Supporting Information Available: Cubic CsPbBr3 with the (001) facets exposed as Cs and Br, or as Pb and Br (Figure S1), atomic composition of the CsPbBr3 PNC models (Table S1), electronic structure of an n-doped CsPbBr3 PNC (Figure S2)

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