sights into tin-based two-dimensional hybrid halide perovskites for photovoltaics †

Xi'an Jiaotong University, Center of Nanom Lab of Electrical Insulation and Power Equ 99 Yanxiang Road, Xi'an 710054, China Department of Chemistry, University Coll WC1H 0AJ, UK. E-mail: d.scanlon@ucl.ac.u Thomas Young Centre, University College L UK Diamond Light Source Ltd., Diamond H Campus, Didcot, Oxfordshire OX11 0DE, UK † Electronic supplementary informa 10.1039/c8ta00751a Cite this: J. Mater. Chem. A, 2018, 6, 5652


Introduction
2][3] Since the rst reports of solid-state hybrid perovskite solar cells in 2012, 4 power conversion efficiencies (PCEs) have increased dramatically up to 22.1%. 5Despite the rapid rise in efficiencies of the hybrid lead perovskite such as CH 3 NH 3 PbI 3 (MAPbI 3 ), their poor long-term stability 6,7 and the toxicity of water-soluble lead compounds, 8 necessitates the development of alternative lead-free halide perovskite materials with improved moisture tolerance.
found the 2D perovskites to be more resistant to moisture than their 3D analogues, 9 owing to the hydrophobicity of the organic cation 16 and van der Waals interactions between the organic molecules and the surface of the inorganic framework. 17,18esides enhanced moisture tolerance, 2D perovskites also present other prospective benets.For example, the inorganic framework provides the potential for high carrier mobilities, whereas the organic moiety can enable intense photoluminescence (PL), owing to the quantum connement effect. 19,20Compared with the 3D hybrid perovskites, the 2D conguration provides greater exibility for morphology and electronic structure engineering.This has been exemplied in the L 2 (BX 3 ) nÀ1 BX 4 series (where L ¼ octylammonium, butylammonium; B ¼ Sn, Pb; X ¼ Cl, Br, I), in which choice of alkyl chain length and perovskite-like layer thickness play a crucial role in controlling platelet size and band gap. 213][24] The band gaps of the 2D series generally decrease monotonically with increasing perovskite-like layer thickness, nally tending to that of corresponding 3D perovskite. 25,26In this way, the 2D hybrid perovskites have attracted increasing attention and witnessed a sharp rise in efficiency over the past two years, 27 with champion devices (containing (PEA) 2 (MA) 59 Pb 60 I 181 ) showing efficiencies of 15.3%. 12espite these recent improvements, most devices containing 2D perovskites show efficiencies below 5%, due to the increase in band gap associated with moving from a 3D connected metalhalide framework to one with 2D connectivity. 9,10,26,28Based on the well-known Shockley-Queisser limit, 29 a solar absorber should possess a band gap between 1.0 and 1.5 eV (ref.30) to maximise its efficiency.This limits the applicability of the butylammonium containing layered perovskites, (BA) 2 (MA) nÀ1 Pb n I 3n+1 , which possess band gaps of 2.43, 2.17 and 2.03 eV for the n ¼ 1, 2, and 3 compositions, respectively. 10Similar to the reduction in band gap seen when moving from MAPbI 3 (1.55 eV) to MASnI 3 (1.2eV), the band gaps of the Sn-based butylammonium layered perovskites are smaller than to their Pb analogues. 26As recently demonstrated by Cao et al., the (BA) 2 (MA) nÀ1 Sn n I 3n+1 series are semiconductors with band gaps decreasing from 1.83 eV (n ¼ 1), to 1.64 eV (n ¼ 2), and 1.50 eV (n ¼ 3). 26articularly in the case of the n ¼ 3 composition, these band gaps are closer to the ideal specied by the Shockley-Queisser limit and should enable increased efficiencies.Furthermore, it has been suggested that the Sn-based iodide perovskites possess much lower exciton binding energies than their lead counterparts, due to their larger dielectric constants, and should therefore show reduced open-circuit voltage losses.Thus, the low n tin-based 2D perovskites should possess the best of both worlds, with optimal band gaps and improved moisture stability.
In 2017, the n ¼ 3 and 4 structures of the (BA) 2 (MA) nÀ1 Sn n I 3n+1 series were fabricated into heterojunction solar cell devices, using mesoporous TiO 2 as an electron-accepting layer. 26espite growing the 2D perovskites with the sheets aligned perpendicular to the electrodes (as shown to be necessary in highly efficient 2D perovskite devices), 10 the devices showed poor efficiencies of 1.94% (n ¼ 3) and 2.53% (n ¼ 4).This was, in part, due to low ll factor and small open-circuit voltages (V oc ) of 382 mV (n ¼ 3) and 229 mV (n ¼ 4), well below the optical band gaps of the materials.Importantly, however, the stability of the devices was drastically improved, with 90% of the initial efficiency retained aer 1 month, in contrast to comparable MASnI 3 lms which deteriorated to 0% efficiency in a similar timeframe.Despite poor efficiencies, this series shows promise for the future of lead-free perovskite solar cells, with the authors highlighting a clear path to improve efficiencies, through use of alternative electron contact materials to enable higher V oc .
In this paper, we investigate the optoelectronic properties of a series of Sn containing layered hybrid perovskites, (BA) 2 (MA) nÀ1 Sn n I 3n+1 (n ¼ 1, 2 and 3), using relativistic hybrid density functional theory.We systematically assess the relationship between crystal structure and electronic properties, in particular the effect of octahedral distortions.Lastly, evaluation of the thin-lm photovoltaic ability of the series, indicates promising applications in the future of lead-free perovskite solar cells.

Computational methodology
2][33][34] The interactions between core and valence electrons were described via the projector augmented-wave (PAW) method. 35,36The plane wave cut-off energy was set to 580 eV, with a G-centered 3 Â 3 Â 1 kpoint mesh employed for the unit cells of the n ¼ 1 and n ¼ 3 structures, and a G-centered 3 Â 3 Â 2 used for the unit cell of the n ¼ 2 composition, of which structures are shown in Fig. S1 and the lattice parameters are provided in Table S1 of the ESI.† These parameters were necessary to converge the total energy of each system to within 1 meV per atom.
Based on previous studies on the hybrid perovskites, we tested lattice relaxations using two functionals: [37][38][39] the Perdew-Burke-Ernzerhof functional 40 (PBE), with dispersion interactions included via Grimme's D3 dispersion correction 41 (PBE-D3), and the PBEsol functional, 42 a version of PBE revised for solids.Both functionals have been shown to accurately reproduce the structural parameters of layered materials and those containing weak van der Waals' type forces. 43,44During geometry optimisation, the atomic positions, lattice shape and cell volume were allowed to relax, until the forces on each atom totalled less than 0.02 eV ÅÀ1 .
In order to obtain an accurate description of the electronic structure of our systems, hybrid density functional theory was employed.Here, we used the Heyd-Scuseria-Ernzerhof (HSE) functional 45,46 incorporating 43% Hartree-Fock exact exchange a and 100% of the correlation energy from PBE.This has been shown to reproduce the band gap of MAPbl 3 , 47 and therefore we expect that it will perform well here.To properly account for the relativistic effects present on the heavy elements Sn and I, [48][49][50][51] all electronic structure calculations explicitly included spin-orbit coupling (SOC).This combination of HSE43 + SOC was used for all band structure, density of states, optical absorption and charge density calculations.The high-frequency dielectric response was calculated from the optical transition matrix elements within the transversal approximation. 52,53The ionic dielectric contribution was calculated using density functional perturbation theory (DFPT), 54 using the PBE-D3 functional.Crystal Orbital Hamilton Population (COHP) analysis was performed using the LOBSTER program 55,56 based on wavefunctions calculated using HSE43.Due to constraints of the LOBSTER program, spin-orbit effects were not included in the COHP analysis, however, we note that while SOC introduces a slight spin-splitting of the band edges, the orbital nature of the bands is expected to remain unchanged.

Results and discussion
Geometric structure 2 and 3) are members of the layered perovskite family adopting the Ruddlesden-Popper type crystal structure, where n is the number of anionic perovskite-like layers, comprising 2D sheets of cornersharing SnI 6 4À octahedra (Fig. 1). 57The layers are separated from one another by organic butylammonium (BA) cations.The molecule acts to maintain charge neutrality and stabilises the perovskite structure., respectively, with the lowtemperature phase possessing greater tilting of the octahedra.The low temperature structure was found to be marginally lower in energy by 2.3 meV per atom.
Geometry relaxations were trialled using both PBEsol and PBE-D3, with the full results provided in Table S2 of the ESI.† Overall, the PBE-D3 lattice constants showed greater agreement with experiment (Table 1) and, as such, these structures were employed for the rest of this report.We note that the b parameter of the n ¼ 2 structure increased upon lattice relaxation, likely due to the xed orientations of the organic cations which will show signicant exibility in the room temperature structure.All other lattice parameters showed acceptable agreement with the experimental values.

Electronic properties
The fundamental band gaps of the series, calculated using HSE43 + SOC, are listed in Table 2.In all cases, the band gaps are larger than that of MASnI 3 (1.3 eV). 22As expected, the band gaps decrease monotonically as the thickness of the perovskite layer increases (Fig. 1), 24,61,62 from 1.85 eV (n ¼ 1), to 1.50 eV (n ¼ 2), and 1.38 eV in the n ¼ 3 case.These are in good agreement with ultraviolet-visible spectroscopic measurements, which show band gaps of 1.83, 1.64 eV, and 1.50 eV for the n ¼ 1, 2, and 3 structures, respectively. 26imilar to MASnI 3 , 49 the upper valence band of the series is determined by Sn 5s and I 5p anti-bonding orbitals, with the lower conduction band composed entirely of Sn 5p antibonding orbitals (Fig. 2), both of which give rise to excellent band dispersion.The antibonding character of these states is demonstrated by the Crystal Orbital Hamilton Population (COHP) analysis provided in Fig. S2 of the ESI.† Because the states of the organic cations are several eV away from the band edges, they will not play a role in determining the electron and hole transport properties.The HSE43 + SOC calculated band structures for the series are plotted in Fig. 2. The results indicate that all systems possess direct fundamental band gaps with the valence band minimum (VBM) and conduction band maximum (CBM) situated at the G point (0.0, 0.0, 0.0).
Both the VBM and CBM are dispersive along the directions parallel to the perovskite-like layers (Y-G and G-X), while they are at in the perpendicular direction (G-Z), due to the 2D connectivity of the tin iodide octahedra.As a result, the calculated effective masses are nearly innite in the perpendicular direction, indicating carriers will be immobile across the layers (Table 2).Accordingly, any devices containing these systems should possess [Sn n I 3n+1 ] (1+n)À slabs that are oriented perpendicular to the device contacts, allowing for efficient extraction of charge carriers to the electrodes.This has recently been demonstrated experimentally for the (BA) 2 (MA) nÀ1 Sn n I 3n+1 series, in which judicial choice of solvent enables control over the orientation of the perovskite-like layers. 26wing to the dispersive VBM and CBM, the series display light hole and electron effective masses in the directions  parallel to the 2D sheets (in all cases below 0.2m 0 ).Moving across the series, the carrier effective masses decrease as the thickness of the inorganic layer increases.In particular, the n ¼ 3 composition possesses light hole and electron effective masses of 0.13m 0 and 0.13m 0 , respectively, smaller than those of MAPbI 3 (0.25m 0 and 0.19m 0 ) and comparable to the effective masses of MASnI 3 (0.13m 0 and 0.28m 0 ) calculated by GW + SOC. 48In general, the series shows slightly larger masses than their lead analogues, such as (BA) 2 PbI 4 (0.14m 0 and 0.08m 0 ), (BA) 2 (MA) 2 Pb 3 I 10 (0.14m 0 and 0.10m 0 ), (BA) 2 (MA) 3 Pb 4 I 13 (0.15m 0 and 0.09m 0 ), as calculated by Stoumpos et al. 25 We note that the calculations performed by Stoumpos et al. did not include the effects of spin-orbit coupling, and may therefore not accurately represent the true properties of the systems.Previous reports have indicated the Sn-I-Sn bond angle (: SnIsn ) as a primary factor in the controlling electronic properties of lead and tin based layered perovskites. 24,61,62This bond angle quanties the degree of distortion in the SnI 6 4À octahedra, with a value of 180 indicating the ideal (undistorted) structure.This distortion can be further broken down into its in-plane (: k SnISn ) and out-of-plane (: t SnISn ) components.Analysis of the distortion angle provides an explanation for the discrepancy in band gap between room temperature and low temperature n ¼ 1 structures (Table 2).The greater distortion in the Sn-I-Sn bond angle of (BA) 3 ), and is therefore likely responsible for the variation in band gap.We note, that in general our results contrast previous reports, which suggest the in-plane distortion plays a greater role in tuning the band gap. 61,62In reality, as both distortions occur simultaneously, the effect of the distortions will be cooperative and should be considered at the same time, as quantied by the overall Sn-I-Sn bond angle.For the n ¼ 2 and 3 structures, the tilting angles were found to be close to the ideal (168.3 and 168.2 ), indicating relatively little structural distortion.a Thickness: 0.5 mm.The charge density isosurfaces shown in Fig. 3, provide an explanation for the effect of Sn-I-Sn bond angle on electronic properties.Due to the structural distortion, the in-plane I atoms are displaced such that they do not sit directly between two adjacent Sn atoms.As demonstrated in the inorganic perovskite, CsPbI 3 , 61,62 greater distortion results in a reduction of the in-plane orbital overlap of the states that comprise the upper valence band (Sn 5s and I 5p), producing larger hole effective masses and a narrower valence band width.Likewise, a similar effect is found on the lower conduction band overlap (composed of Sn 5p and a small contribution from the I 5p), which increases its band width and results in greater electron effective masses.For example, within the n ¼ 1 structures, the greater distortion of (BA) 2 SnI 4 lt (149.6 ) compared to (BA) 2 SnI 4 rt (153.5 ), results in a wider band gap (2.13 eV), larger effective masses of electrons (0.20m 0 ) and holes (0.18m 0 ), and reduced valence (0.95 eV) and conduction band widths (1.53 eV).Further analysis of the charge density isosurfaces in the two n ¼ 1 structures (Fig. S3 of the ESI †), indicates the conduction band minima are derived mainly of Sn 5p x and p y orbitals, with the p z orbital showing very little contribution.For this reason, the outof-plane distortion will have a reduced impact on the electronic properties of the conduction band, compared with the in-plane distortion, explaining the limited variation in electron effective masses and conduction band widths between the two structures.For the n ¼ 2, and 3 structures, the minimal distortion further produces optimal optoelectronic properties, such as small band gaps very light hole and electron effective masses.

Optical properties
In comparison to the 3D hybrid perovskites, the unique layered conguration introduces a directional dependence into the dielectric constants and optical response.2D perovskites can be regarded as quantum-well-like structures, of which the inorganic sheets ("wells") are more polarisable, and the organic layers ("barriers") are less polarisable. 63,64Previous computational studies have shown that in the 2D hybrid perovskites, the dielectric constant of the inorganic component is signicantly greater than that of the organic layer. 65,66Since the bulk dielectric response calculated here corresponds to an average over both the inorganic and organic components, those compounds with thicker inorganic layers should possess greater dielectric constants.This is in agreement with our results, which show that both the in-plane (3 k r ) and out-of-plane (3 t r ) dielectric constants increase as the thickness of the perovskite-like layer increases.For the n ¼ 1 (BA) 2 SnI 4 rt structure, the in-plane and out-of-plane dielectric constants are 21.24 and 4.36, respectively, which increase to 34.05 and 11.71 for the n ¼ 2 structure, and 47.99 and 9.77 in the n ¼ 3 case.As n decreases, the negative charge arising from the perovskite-like surface is distributed over a decreasing number of Sn and I ions.This has the effect of making these ions less positive, in turn reducing their polarisability and thus their ability to screen charge, as evidenced by the reduction in their Born effective charge (provided in Table S3 of the ESI †).In general, the dielectric constants for the direction perpendicular to the perovskite sheets are much smaller than those in the parallel directions.Again, the Sn-I-Sn bond angle plays an important role, with the low temperature, more distorted structure ((BA) 2 SnI 4 lt ) actually showing larger in-plane and out-of-plane dielectric constants (31.87 and 5.19, respectively) than the room temperature compound.
As discussed in the introduction, one of the advantages of the tin layered perovskites over their lead analogues is that their fundamental band gaps are closer to the optimum value for a single junction solar cell. 30The optical response for the series, calculated using HSE43 + SOC, is provided in Fig. 4. Similar to other layered perovskites, 11,12,25 an increase in the perovskitelike layer thickness causes a red shiing of the absorption edge.In all cases, the optical absorption edges of the (BA) 2 (MA) nÀ1 Sn n I 3n+1 (n ¼ 1, 2 and 3) series are located at the fundamental band gaps, indicating that the fundamental band gap transitions are symmetry allowed.All four perovskites studied exhibit strong optical absorption, with the absorption coefficient reaching 10 5 cm À1 within $1 eV of the band edge.The strength of optical absorption is dependent on the thickness of the inorganic component-as the number of layers increases, the optical absorption gets stronger.This is to be expected as the organic cations do not contribute to the optical response until larger excitation energies.
In the Shockley-Queisser limit, 29 the efficiency of an absorber is dependant solely on its band gap.In practice, however, strong visible light absorption as well as a fundamental allowed band gap transition are also critical for achieving high efficiency cells.In a real solar cell, the maximum efficiency is also determined by the thickness of the absorber layer.Aer taking all the above factors into consideration, the maximum photovoltaic efficiency of an ideal absorber thin lm can be simulated using the spectroscopic limited maximum efficiency (SLME) metric proposed by Yu and Zunger. 67The SLME metric improves on the Shockley-Queisser limit in a number of ways: rstly, the non-radiative recombination rate is approximated, based on the difference between the lowest allowed optical transition and the fundamental band gap; secondly, the frequency dependant absorption coefficient of the material is taken into account; lastly, the thin-lm thickness is also considered.The full details of how the SLME is calculated are provided in the ESI.† In order to evaluate the photovoltaic performance of these 2D perovskites, the SLMEs, computed based on a thin lm thickness of 0.5 mm, are listed in Table 2.The n ¼ 3 composition possesses the highest efficiency (24.6%) as expected based on it's high optical absorption coefficient and favourable band gap (1.38 eV), which is close to the optimal value based on the Shockley-Queisser limit.The predicted SLME values are signicantly higher than efficiencies of the devices produced by Cao et al., 10 highlighting the potential of further device engineering.The high SLME of (BA) 2 (MA) 2 Sn 3 I 10 is comparable to that of many state-of-art solar cell absorbers, such as CdTe (24.85%) and CuZnSnS (25.71%), and even greater than that of MAPbI 3 (22.1%),further conrming its potential as a lead-free replacement to the 3D hybrid perovskites. 68

Conclusion
In summary, we have shown that the layered lead-free perovskites (BA) 2 (MA) nÀ1 Sn n I 3n+1 (BA ¼ CH 3 (CH 2 ) 3 NH 3 + , MA ¼ CH 3 NH 3 + , n ¼ 1, 2 and 3) exhibit intrinsic properties that are well suited for solar cell applications, including band gaps close to the ideal indicated by the Shockley-Queisser limit and strong optical absorption.Furthermore, both electrons and holes show small effective masses in the directions parallel to the perovskite-like sheets.We have further elucidated the role that structural distortions, in the form of octahedral tilting, play in determining the optoelectronic properties of the series.Impressively, the champion absorber, (BA) 2 (MA) 2 Sn 3 I 10 (n ¼ 3), displays a high spectroscopic limited maximum efficiency greater than 24%.Based on these properties, the structures where n # 2, are promising candidates for top cells in tandem devices, whereas the n ¼ 3 composition is expected to perform well in a heterojunction solar cell in its own right.Despite the low power conversion efficiencies previously demonstrated by Cao et al., 26 our results indicate a signicant scope for improvement and suggest further device engineering and optimisation may be fruitful.

2
SnI 4 lt (149.6 ) gives rise to an increased band gap of 2.13 eV, compared with a band gap of 1.85 eV for the room temperature structure (153.5 ).The Sn-I-Sn angle, when decomposed into it's out-of-plane and in-plane contributions, indicates the in-plane distortion remains similar (26.4 vs. 21.3 ), whereas the out-of-plane distortion is signicantly greater in the tilted structure (22.3 vs. 2.

Fig. 2
Fig. 2 HSE43 + SOC calculated band structures and density of states (DOS) for the layered tin hybrid perovskites: (a) (BA) 2 SnI 4 rt , (b) (BA) 2 SnI 4 lt , (c) (BA) 2 (MA)Sn 2 I 7 , and (d) (BA) 2 (MA) 2 Sn 3 I 10 .The valence band maximum is set to 0 eV.Valence and conduction bands indicated by blue and orange lines, respectively.Red and green circles indicate the position of the valence band maximum and conduction band minimum.

Fig. 3
Fig. 3 Charge density isosurfaces of the VBM (above) and CBM (below), pictured along the (001) direction, for the layered tin hybrid perovskites: (BA) 2 SnI 4 rt , (BA) 2 SnI 4 lt , (BA) 2 (MA)Sn 2 I 7 and (BA) 2 (MA) 2 Sn 3 I 10 , where the Sn and I atoms are shown in light grey and purple, with the Sn-I-Sn bond angles of each compound indicated.The organic cations have been removed for clarity.
58For the n > 1 structures, methylammonium (MA) cations are present in the interstitial site at the centre of the perovskite cage.A larger value of n indicates a thicker perovskite-like component, with n ¼ N equivalent to the 3D perovskite, MASnI 3 .

Table 1
Lattice parameters of (BA) 2 (MA) nÀ1 Sn n I 3n+1 conventional cells, calculated using the PBE functional with Grimme's D3 dispersion correction, in comparison with experiment.Lattice lengths given in Å and lattice angles given in

Table 2
Band gaps (E g ), Sn-I-Sn bond angles (: SnISn ), hole (m k h ) and electron (m k e ) effective masses, dielectric constants (3 r ), and SLMEs of the series (BA) 2 (MA) nÀ1 Sn n I 3n+1 (n ¼ 1, 2 and 3).Hole and electron effective masses are averaged for the directions parallel to the perovskite layer.Superscripts k and t indicate properties parallel (in-plane) and perpendicular (out-of-plane) to the 2D perovskite sheets, respectively.Band gaps given in eV, bond angles given in , effective masses given in units of electron rest mass (m 0 ), and SLME given in %