Nature of the Electronic and Optical Excitations of Ruddlesden

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Energy Conversion and Storage; Plasmonics and Optoelectronics

On the Nature of the Electronic and Optical Excitations of Ruddlesden--Popper Hybrid Organic--Inorganic Perovskites: the Role of Many-Body Interactions Giacomo Giorgi, Koichi Yamashita, and Maurizia Palummo J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b02653 • Publication Date (Web): 22 Sep 2018 Downloaded from http://pubs.acs.org on September 22, 2018

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The Journal of Physical Chemistry Letters

On the Nature of the Electronic and Optical Excitations of Ruddlesden–Popper Hybrid Organic–Inorganic Perovskites: the Role of the Many-Body Interactions Giacomo Giorgi,† Koichi Yamashita,‡ and Maurizia Palummo∗,Π †Dipartimento di Ingegneria Civile e Ambientale, Universitá di Perugia (DICA), Via G. Duranti, 93 - 06125 - Perugia, Italy ‡Department of Chemical System Engineering, School of Engineering, The University of Tokyo, Tokyo, Japan & CREST-JST, Tokyo, Japan ΠDipartimento di Fisica and INFN, Universitá di Roma ”Tor Vergata” Via della Ricerca Scientifica 1, Roma, Italy E-mail: [email protected],[email protected]

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Abstract The knowledge of the exact nature of the electronic and optical excitations of Ruddlesden–Popper organic–inorganic halide perovskites (RPPs) is particularly relevant in view of their usage in optoelectronic devices. By means of parameter-free quantum-mechanical simulations we unambiguously demonstrate the dominant role of many-body Coulomb interaction, as recently proposed by Blancon et al.. Indeed, focusing on the first two terms (n=1,2) of the Pb–based buthylammonium series, both in the form of isolated nanosheet and repeated bulk–like quantum–well, we observe large band-gap renormalization and strongly bound excitons with binding energies up to about 1 eV in the thinnest isolated nanosheet. Notably, taking into account electronic correlation beyond DFT, we obtain exciton reduced masses similar to the corresponding 3D bulk counterpart and large Rashba splitting of the same order of the value reported by Zhai et al. in a recent experimental work.

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In the last decade the scientific community has faced the raise of Hybrid OrganicInorganic halide Perovskites (OIHPs) as leading materials in the realm of low–cost photovoltaics (PV). 1 The relevance of these materials, whose archetypal compound is represented by MAPbI3 (hereafter also MAPI, where MA=CH3 NH3 + , methylammonium), stems from a long list of striking properties in the photoconversion process. 2–9 There remain anyway some detrimental shortages that make OIHP devices yet unsuitable for solar device mass production. The major is the instability over heat, light, and moisture: the presence of the organic moiety highly reduces the durability of 3D OIHPs solar cells. 10 To overcome this issue the scientific community has focused its attention on more efficient alternatives, finding as ideal candidates the so–called Ruddlesden–Popper perovskites (hereafter also RPPs), 11 a mixed 2D/3D class of materials which has been recently successfully applied both in PV 12–14 and, due to their intense photoluminescence that persists also at RT, also in light emitting diodes (LED) applications. 14,15 In these layered structures of general stoichiometric relation (RNH3 )2 An−1 Mn I3n+1 (n = 1, 2, 3,...), layers of [MX6 ]4− (M=Pb2+ , Sn2+ ; X=halide) semiconductors form quantum wells (QWs) of different thickness (n). Their cavities are filled with a small organic cation (usually MA) and are separated by a long chain organic cation. The presence of the latter ones in the structure highly increases the hydrophobicity of the RPPs and also minimizes the environmental risk due to the presence of Pb. The case n=1 corresponds to the more general case of pure 2D OIHPs, materials already investigated at the end of the nineties for their possible optoelectronic applications. 16 n–butylammonium (BA=CH3 (CH2 )3 NH3 + ) is the aliphatic most studied organic spacer, 12,14 while 2–phenylethylammonium (PEA=C6 H5 (CH2 )2 NH3 + ) is the aromatic most studied one. 17–21 Although works focusing on the electronic and optical properties of such materials have been recently published, 22–28 to the best of our knowledge an unbiased theoretical analysis based on parameter-free excited state methods is yet unavailable. Moreover, recent experimental works 29 demonstrated that by means of a solution–based process it is possible to grow and characterize not only QWs but also isolated nanosheets (NS-RPPs),

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which offer extreme mechanical flexibility and strong optical tunability that varies as function of the halide anions. It is then important to compute the excited-state properties of isolated NS and periodic QW-RPPs including many-body effects beyond the mean-field Density Functional Theory (DFT). Ideally continuing our research on layered materials with optoelectronic applicability, 30–35 we here investigate (BA)2 (MA)n−1 Pbn I3n+1 n=1, 2 RPPs, i.e. those which show intense room–temperature photoluminescence, and accordingly better suitable for LED applications. 12,20 Starting from few available experimental data 14,29 we obtain fully optimized atomic structures both in the form of isolated nanosheet (NS) and bulk quantum-well (QW) structures. All the computational details and a detailed analysis of the structural data are reported in the S.I. section (see text and Table S1). The NS and QW structures for n = 1 are reported in Fig. S1 in S.I., while those for n = 2 are reported in Fig. 1. Larger geometrical distortions in the latter ones (see S.I. section) are associated with a larger Rashba–Dresselhaus splitting, as discussed in the following. We initially focus on the electronic properties, showing in Fig. 2 the DFT-KS (dashed black curve) and the GW (red solid curve) bandstructure of n=1 (top panels), n=2 (bottom panels) NS (left) and QW-RPPs (right). Notably, the inclusion of the quasi-particle selfenergy largely renormalizes the DFT-KS electronic gap, increasing the band dispersion and thus reducing the effective masses. For the NS (QW)-RPP the KS gap increases of ∼ 2.1 (1.5 eV) in n=1 and of ∼ 1.8 eV (1.3 eV) in n=2 RPPs. 36 It is worth noting that for n=1 NS, the QP gap is larger than that recently obtained by Ma et al. 37 by means of a hybrid exchange-correlation functional. Concerning the hole (electron) effective mass along t df t the X→Γ direction we obtain mdf = 0.26) at the DFT-KS level and mgw h = 0.37 (me h =

0.34 (mgw e = 0.19 ) at the GW level, which result lighter than the effective masses reported in the same reference. 37 Interestingly, the GW calculated exciton reduced masses, both for the QW (0.12) and the NS (0.11), are of the same order of magnitude of that predicted in bulk tetragonal MAPI, 38 at the same level of theoretical approximation, and also very close to the value reported by Kanatzidis et al. 14 for bulk QW (BA)2 (MA)n−1 Pbn I3n+1 RPPs.

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Figure 1: (a) lateral view and (b) top view of the n=2 sheet (NS-RPP) optimized structure. Same (c, d) for the bulk QW (QW-RPP). [Grey: Pb; Purple: I; Brown: C; Light blue: N; White: H atoms] The large influence of spin-orbit coupling in 3D-OIHPs bandstructure is well documented in the literature, 8,39 nevertheless the importance of local or extended inversion symmetry breaking, leading to Rashba-Dresselhaus (RD) effect, is still under debate. 40,41 Due to the layered structure, RPP OIHPs are more prone to a break of symmetry and then manifest this exotic effect. Indeed, a recent experimental work, supported by DFT calculations, reported the presence of a giant Rashba splitting in a RPP using PEA as spacer. 42 Notably, all the atomic structures calculated here, except the n=1 NS-RPP, show the presence of RD splitting in their bandstructure. In particular, for n=2 NS-RPP, quite large RD parameters, 5



comparable to values reported in ref. [39], are obtained at the GW level of approximation, being about αc,v ' 1 eV ˚ A, along the Γ →S direction. Indeed, in Fig.3 the expectation value (red (blue) color indicate negative(positive) numbers) of the three spin-components (Sx , Sy , Sz from left to right) along the −0.25S → Γ → 0.25S directions is reported. To gain better understanding of the origin of the valence and conduction band, the projected density of states (PDOS) have been calculated for the n=1 case (see Fig.S2 in the S.I. section). The corresponding data for n=2 are qualitatively similar and are not reported. We found, consistently with what observed in bulk MAPI, 8,39 that near the gap the conduction states are mainly due to p orbital of Pb-atoms, while valence band stems from the anti–bonding overlap between p (s) orbitals of I (Pb) atoms. The states associated to the RPP organic components are far from the gap region and are not reported for clarity. Similarly, the PDOS for the bulk n=1 QW structure confirms the presence of an isolated and localized CB peak, feature previously observed at the pure DFT level of theory 14 and that is mainly formed by Pb p 3/2 orbitals. 43 Once determined the QP bandstructures, we solved in a fully ab-initio way the Bethe-Salpeter Equation to look at the role played by excitons in the optical response of both isolated NS and QW structures. In Fig. 4 we report the optical spectra of NS (left) and QW (right) for n=1 (top panels) and n=2 RPP (bottom panels). The blue arrows indicate the position of the minimum direct electronic gap as obtained by means of GW calculations. For the QW-RPPs, the experimental curves obtained from ref. [22,23] are also reported. The good agreement between experimental and unbiased theoretical BSE curves, definitively confirms that the first optical peaks are due to strongly bound excitons, as reported by Blancon et al. 22,23 using optical spectroscopy joined to a simplified exciton model. Due to a lower dielectric screening the exciton binding energy of the isolated NS is more than three times larger than that of the corresponding QW. Nevertheless, as observed in several other two-dimensional materials, 31,32,34,44 a large compensation of the electronic self-energy blue-shift and e-h interaction red-shift, makes the energetic position of the first optical peak quite similar in the NS and

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Figure 2: DFT-KS (dashed) and GW (red, solid) Bandstructure of the Pb-based single sheet (left) and QW (right) with n=1 (top panels) and n= 2 (bottom panels)

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Figure 3: Expectation values of Sx , Sy ,Sz (left,center,right) for the n=2 NS–RPP. (Bands are plotted here at the DFT-PBE level of approximation ) QW (for NS we observe a slight blue-shift in agreement with experimental data of Dou et al. 29 ). For n=1 (n=2) NS and QW, the estimated exciton binding energies are about 950 (650) and 300 (260) meV, respectively. It is worth to point out that while the exciton binding energy obtained for the n=2 QW-RPP is in quite good agreement with data of ref., 23 the corresponding value for n=1 QW is smaller than that reported in the same reference. The role played by the electron-phonon interaction and polarons on the opto-electronic properties of hybrid halide perovskites is an highly debated topic in the literature, 45–48 then it is important to underline that our present theoretical analysis does not take into account this aspect but we plan to include it a near future. Nevertheless, the good agreement between our unbiased BSE optical spectra and the experimental curves, seems to suggest that the role of polarons in these specific layered hybrid halide perovskites with short organic spacers, could be negligible, as also suggested by the very small Stock-shifts observed at experimental 8


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level. 23 Longer organic spacers 49 or different sample dimensionality 50 certainly change the scenario as demonstrated by several recent works. Very delocalized excitons (∼ 20-50 ˚ A) 51–53 along with their very small binding energies (reported values from 6 to 50 meV), 51–53 characterize the optical properties of the 3D counterpart. Such values stress the intriguing and still debated dual free-carrier 54–56 vs. exciton bound behavior of bulk MAPbI3 , regimes that co–exist at room temperature (kB T ∼ 25 meV, where kB is the Boltzmann constant). 3,57,58 As illustrated before, the reduced dielectric screening and spatial quantum-confinement of RPPs induce the formation of strongly bound excitons whose spatial localization is completely different from what expected in the 3D bulk counterpart. Fig. 5 shows the side view of the spatial distribution of the first bright exciton for n=1 (left) and n=2 (right) NS. Notably, in both cases, the exciton is localized only in the inorganic parts of the RPP, but for n=2 NS it has a more delocalized lateral spatial distribution compared to n=1 . Indeed, a non–zero probability to find the electron quite far from the fixed hole position (red cross in the plots) and in both adjacent inorganic layers, is observed. The exciton spatial localization in the QW–RPPs does not change substantially and for this reason it is not reported: when fixing the hole position in one of the two PbI4 planes the exciton is spread in the same plane for n=1, while for n=2 there is the non–zero probability to find the electron also in the other PbI6 layer for n=2. This suggests that the large spatial delocalization characteristic of the first optical excitation in the corresponding perovskite bulk should be rapidly recovered, favoring the e–h separation and supporting the experimental observation of an increase of photo-conversion efficiency for n > 2. 22 On the other hand the larger e-h overlap in n = 1 RPPs clearly explains why the experimental photoluminescence efficiency increases reducing the index n 23 and is very high in isolated nanosheets with n = 1. 29 To summarize, starting from the few available structural experimental data we have investigated the role of many-body effects, such as e–e and e–h interactions, on the electronic and optical properties of the first two terms (n=1, 2) of (BA)2 MAn−1 Pbn I3n+1 Ruddlesden–

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Figure 4: Optical spectra of Pb-based single sheet (left) and QW (right) with n=1 (top panels) and n= 2 (bottom panels)

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Figure 5: Side view of the first bright exciton for the isolated Pb-Based RPP sheet n=1 (left) and n=2 (right). Hole position is represented by the red cross Popper hybrid organic–inorganic halide perovskites. The confined geometries in the form of isolated nanosheets clearly show the presence of strongly bound excitons, which remain present even in the repeated quantum–well structures, a feature ascribed to the low dielectric screening of the organic parts of the RPPs. For the n=1 NS, the electron-hole spatial distribution tends to be extremely localized, i.e. both the hole and electron forming the first bright exciton resides in the same semiconductor PbI6 octahedral layers. This tendency which could be expected in the isolated sheet holds in a similar way also for the corresponding bulk quantum–well structure. Notably, in the n=2 structures the excitonic spatial distribution is more spread laterally and is non zero in both the two adjacent PbI6 semiconductor layers, even if the hole position is fixed in one of the two layers. This observation clearly suggests that in these layered materials the delocalized nature of the exciton observed in 3D hybrid perovskites should be rapidly recovered increasing n. Interestingly an evident Rasbha splitting is found in the n = 2 nanosheet confirming the interest of these novel layered materials for spintronics applications.

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Acknowledgments M.P. and G.G. acknowledge MIUR for FFABR funds. M.P. acknowledges INFN for financial support through the National project Nemesys and for allocated computational resources at Cineca with the project INF16-nemesys and the EC for the RISE Project No. CoExAN GA644076. G.G acknowledges PRACE for awarding us access to resource Marconi based in Italy at CINECA (Grant No. Pra14 3664). G.G. is similarly grateful to CARIT project ”Progetto per l’ applicazione delle attivitá di ricerca pubblica nell’ area di crisi complessa ternana. Valutazione della possibilitá di utilizzo di materiali metallici innovativi per applicazioni antisismiche, automobilistiche ed energetiche” (ref. FCARITR17FR) for supporting this research. K.Y. thanks the supported by MEXT as ”Priority Issue on Post-K computer”(Development of new fundamental technologies for high-efficiency energy creation, conversion/storage and use).

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(a) lateral view and (b) top view of the n=2 sheet (NS-RPP) optimized structure. Same (c, d) for the bulk QW (QW-RPP). [Grey: Pb; Purple: I; Brown: C; Light blue: N; White: H atoms] 280x323mm (120 x 120 DPI)


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DFT-KS (dashed) and GW (red, solid) Bandstructure of the Pb-based single sheet (left) and QW (right) with n=1 (top panels) and n= 2 (bottom panels). 161x205mm (120 x 120 DPI)



Expectation values of Sx, Sy,Sz (left,center,right) for the n=2 NS{RPP. (Bands are plotted here at the DFT-PBE level of approximation ). 219x138mm (120 x 120 DPI)


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Optical spectra of Pb-based single sheet (left) and QW (right) with n=1 (top panels) and n= 2 (bottom panels). 164x218mm (120 x 120 DPI)



Side view of the first bright exciton for the isolated Pb-Based RPP sheet n=1 (left) and n=2 (right). Hole position is represented by the red cross. 241x89mm (120 x 120 DPI)


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Nature of the Electronic and Optical Excitations of Ruddlesden

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