Atomic structure and electronic properties of lead and tin based hybrid halide perovskite surface for photovoltaic applications

Organic-inorganic hybrid halide MABX₃ perovskites (MA/methylammonium = CH₃NH₃; B = Sn or Pb; X = I, Br, or Cl) have recently emerged as one of the most promising materials for photovoltaic technology.^1,2 The power conversion efficiency (PCE) of these halide perovskite has risen from 3.8% to 24.2%,^2–6 since the first use of halide perovskite as a light absorber in solar cells.⁷ Beside the PCE, MABX₃ family of perovskites also exhibit remarkable photovoltaic features compared to conventional solar absorbers like CdTe, and amorphous Si. The unique features of halide perovskite includes its band gap (≈2 eV), greater optical absorption spectra (up to a wavelength of ∼800 nm) compared to the conventional thin-film solar cell absorber (about ∼600 nm wavelength),^1,8–10 high carrier mobility and long (>1μm) electron-hole diffusion length.¹¹ Further, in the hybrid halide perovskite, most of the defects are formed in the valence band or the conduction band making them less likely to form deep trap defects within the band gap.¹² 

In a typical perovskite-based solar cell, photo-active perovskite layer is interfaced with an electron transport layer (ETL) comprising of materials^13–16 such as C₆₀, PCBM, TiO₂ and hole transport layer (HTL). The atomic structure and electronic property of the perovskite/ETL (or HTL) interface arise from the individual atomic structure of perovskite and ETL (or HTL) surface layers as well as by the unique structures produced when the ETL (or HTL) is formed on the perovskite surface. Consequently, it is the surface and interface which play a key role in the performance of perovskite solar cells. For example, different electronic trap states are known to form on perovskite surface with point defect depending on surface terminations.¹² Thus, facets within perovskite solar cells may have a direct consequence on the power conversion efficiency,¹⁷ due to the facet-dependent density of trap states.

Numerous theoretical studies up-to-date have been devoted to the study of the properties of bulk perovskite materials. However, our understanding of the surface and interface structure and properties of perovskite/ETL systems are still at the nascent stage. The surface structure for limited number of perovskite systems such as lead iodide and bromide has been explored so far.^13,18–24 The structure and properties of some of the common halide perovskite such as lead-chloride, tin-bromide, and tin-chloride are still unclear. It is notable that in bulk form lead- and tin-based halide perovskite was found to exhibit significantly distinct electronic properties.^9,25,26 For instance, MASnI₃ exhibit smaller band gap than that of MAPbI₃ (1.2 vs. 1.6 eV, respectively).²⁷ Likewise, the choice of halides in MAPbX₃ can modify the band gap of the perovskite. In that case, it is expected the surface structure, and electronic properties of individual halide perovskite surface will be unique.

In this paper, we aim to develop a more comprehensive understanding of the surface structure and electronic properties of MABX₃ for different B site and halide composition. In particular, we will present electronic structure calculations of the surface atomic structure and electronic properties of tetragonal MABX₃, with B=Pb or Sn, and X=I, Br, or Cl. It should be pointed out that both theory and experiment have confirmed that (110) and (001) charge neutral surfaces are stabilized in the tetragonal phase of the perovskite.^18,28 In this study, we restrict our computations to more commonly observed (001) surface. The orientation of polar ion (⁠$CH3NH3+$⁠), the metal-halide interatomic distance, B-X-B angle as well as band gap are compared between the surface with their corresponding bulk structures, to gain a thorough understanding of the change in properties from bulk to surface. Further, we have highlighted the importance of the crystal symmetry and size of the halide atom and its bond distance with B atom as factors responsible for reduction of band gap at the surface compared to the bulk counterpart. Understanding of the surface structures will form the preliminary basis to comprehend the more complex interfacial atomic structure and properties.

We performed density functional theory (DFT)^29,30 calculations using the Vienna ab initio simulation package (VASP).^31,32 The electron-ion interaction is described by the projector-augmented wave (PAW) method.^33,34 The exchange-correlation interaction between electrons is treated by the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional.³⁵ To describe the interaction between MA⁺ ions and the inorganic matrix, the van der Waals (vdW) correction,³⁶ vdW-DF, as implemented in VASP, is employed. The cutoff energy of 500 eV is used for the plane-wave basis set in all calculations. We have taken only the scalar-relativistic effect in our calculations, as discussed in details later in the manuscript.

Experimental lattice parameters are chosen as starting lattice parameters,^26,37 when it is available. For each bulk structure, lattice parameter and position of atoms are optimized until the force on each atom is below 0.02 eV/Å. For surface calculations, the slab models are constructed from the corresponding optimized bulk perovskite structures. For all six compositions, neutral (001) surfaces with two possible surface termination of slabs, i.e., MAX- and BX₂- surface terminations are considered. Our BX₂- and MAI-terminated (001) slab models have nine and eleven alternating MAX and BX₂ layers, respectively, while a 2×2 in-plane periodicity is maintained perpendicular for each surface structure.^13,38 We maintained the same supercell volume for both MAX and BX₂ terminations for a given composition. Resulting vacuum thickness used was about 25 Å and 35 Å for MAX and BX₂ terminations, respectively to avoid any interaction between the slab and its periodic image. Finally, all slabs models are relaxed for their atomic position with (4 × 4 × 1) Monkhorst-Pack k-point grids with the same force convergence criteria as the bulk.

For direct comparison of the surfaces across the different compositions, we limit our study on the surfaces to those of tetragonal perovskite structures. Within the tetragonal phase, we performed calculations on P4/mmm space group for all compositions, except MAPbI₃. For MAPbI₃ we used structures in I4/mcm space group. Experimentally both MAPbI₃ and MAPbBr₃ has been observed in I4/mcm, at different temperature ranges.^26,37 Hence, the additional structure of MAPbBr₃ in I4/mcm was also included in the calculation. In case of MASnBr₃ and MASnCl₃, there are no experimentally reported tetragonal structures^39–41 to best of our knowledge. Hence, we modeled tetragonal MASnBr₃ and MASnCl₃ structures by replacing I of MASnI₃ P4/mmm structure with Br and Cl atoms respectively and optimizing the structure with the DFT.⁴² Typical examples of tetragonal bulk structures in space group I4/mcm and P4/mmm are shown in Fig. 1 (a) and (b), respectively.

To understand bulk vs. surface properties, first we have analyzed the atomic structure of both MAX and BX₂ terminated surfaces of different crystal symmetry and composition, and compared them with their corresponding bulk structures, Fig 1. Fig. 2 shows the optimized slab models of the MAX surface termination. In all MAX surface terminations, ions $CH3NH3+$ that lies on the surface have more free volume available compared to the bulk and has relatively more freedom in adjusting its orientation at the surface. For reference, the atomic structure of the bulk can be visualized from the inner layers of the surface structures. However, the bulk values presented in the manuscript are from the true bulk structures as presented in Fig. 1. It can be seen from Fig. 2 (a) and (b) surfaces of the perovskites, MAPbI₃ and MAPbBr₃, belonging to the same space group I4/mcm, shows different orientation of $CH3NH3+$ after optimization. In case of the MAPbI₃, $CH3NH3+$ of the outermost layers rotates so that CH₃ is pointing towards the surface in both the top and bottom surfaces in Fig. 2 (a). While the orientation of $CH3NH3+$ in MAPbBr₃ remains unchanged compared to bulk after the optimization, i.e., CH₃ and NH₃ are pointing towards the surface at opposite ends, Fig. 2 (b). For other perovskite compositions, that belong to the space group P4/mmm, in all MAX surface terminations, $CH3NH3+$ cations aligned with the CH₃ pointing towards the surface (at both ends), except for the case of MASnBr₃ and MASnCl₃ perovskites, Figures 2 (f) and (g), respectively. In both perovskites MASnBr₃ and $MASnCl3CH3NH3+$ show similar orientation as in I4/mcm - MAPbBr₃, where CH₃ and NH₃ are pointing towards the surface at opposite ends.

Fig. 3 shows the optimized slab models of BX₂ terminations. In BX₂ surface terminations, $CH3NH3+$ is shielded from the outer surface by BX₂ atomic layer. The surface of the perovskite MAPbI₃ and MAPbBr₃ belonging to space group I4/mcm does not show significant reorientation of $CH3NH3+$ compared to the bulk structure after optimization, Figures 3 (a) and (b), respectively. It is notable that P4/mmm structures have a more symmetric arrangement of atoms as angle joining two polyhedra (the B-X-B angle) shown in Fig. 1 are closer to linear angle i.e., 180° in comparison to I4/mcm, where it deviates more from 180°. Details of the B-X-B angles in each structure are given later in the manuscript (see Table I). With the increased symmetry in the space group P4/mmm, $CH3NH3+$ reorientates compared to the bulk during optimization for the BX₂ surface termination of MAPbBr₃, MAPbCl₃ and MASnI₃, Fig. 3(c)–(e). For these structures, during optimization $CH3NH3+$ rotated in such a way that NH₃ points towards the surface (angles that C-N bonds make at two ends of the slab are different for MAPbBr₃ and MAPbCl₃). Further, for the BX₂ surface terminations of both MASnBr₃ and MASnCl₃, $CH3NH3+$ does not show significant reorientation during optimization similar to the MAX surface terminations of these perovskites.

In the hybrid organic-inorganic halide perovskite methylammonium (⁠$CH3NH3+$⁠) ions are located in the octahedron volume formed by B-X bonds, i.e., BX₆ (see Fig. 1). In general, the reduced symmetry in the space group I4/mcm (based on B-X-B angles, Table I) leads to decrease in octahedron volume formed by BX₆ compared to structures in the space group P4/mmm. However, for perovskite structures in P4/mmm the smaller interatomic distances of Sn-Br (2.86 Å) and Sn-Cl (2.82 Å) in MASnBr₃ and MASnCl₃, respectively compared to other perovskite structures (e.g., MASnI₃) with B-X interatomic distance > 3 Å will also result in a decrease in octahedron volume formed by BX₆. Eventually, the decreased volume will be the limiting factor for free rotation of the $CH3NH3+$⁠. Symmetric arrangement of polyhedra and the larger B-X distance will allow $CH3NH3+$ to reorient in slab structures. Clearly, both surface terminations (MAI and SnI₂) of MASnI₃ perovskite shows the most symmetric orientation of $CH3NH3+$ at both ends of the slab, Fig. 2 (e) and 3 (e). MASnI₃ belongs to the space group P4/mmm, and Sn-I distance is the largest inter-atomic distance compared to other metal-halide distances within the same space group, Fig. 4. For comparison, in the optimized bulk perovskite the values of B-X distances are 3.05 Å for Sn-I; 2.95 Å for Pb-Br; 2.84 Å for Pb-Cl; 2.86 Å for Sn-Br; and 2.82 Å for Sn-Cl. Reorientation of the MA cation in the perovskite structure (MAPbI₃) was reported previously,⁴³ and the rotation/relaxation of MA cation contributes to the dielectric constants.⁴⁴ The static permittivity, ϵ_stat, in bulk MAPbX₃ was found to have a magnitude of 62 for the iodide, 58 for the bromide, and 45 for the chloride below 1 GHz at room temperature,⁴⁴ i.e., higher the reorientation of MA lesser the permittivity. Also, it was confirmed that reorientation of the $CH3NH3+$ cation could be captured only when van der Waals interaction for the description of the MA cation is properly included in the calculations¹³ as it was done in the present work. The asymmetric orientation of the polar $CH3NH3+$ ion in different layers may lead to accumulation of bound charges giving rise to surface states in the electronic structure, which will be discussed in the section Electronic Structure.

Contribution at the band edges and hence the transport attributes in hybrid halide perovskites arises mainly from the bonding between metal B and the halide X.²⁷ To investigate the changes in metal halide bonding characteristics from bulk to the surface, we have analyzed the metal halide, B-X, distances, and B-X-B angles. The average B-X distances in optimized bulk and the two (BX₂ and MAX) surface terminations for different perovskite composition is depicted in Fig. 4. The atoms on each side of the slab, which lie in the outermost BX₂ layer, and MAX layers next to the BX₂ above and below if any, were considered as the surface atoms. In other words, for the BX₂ surface termination, the surface atom will be atoms on the outermost BX₂ layer and one MAX layer below it, i.e., atoms inside rectangles in Fig. 2 (a). Similarly, the MAX surface termination will have atoms on the BX₂ layer together with one MAX layer above and below it, atoms inside rectangles in Fig. 3 (b). In Pb-based perovskites, generally, the average Pb-X distances for the surface atoms remain close to the bulk values. The maximum deviation from the bulk value is less than 2.5% for both MAX and PbX₂ surface terminations, Fig. 4. Further, there is no significant difference in the variation of the distances of the atoms on the surface from the bulk interatomic distances for the two space groups I4/mcm and P4/mmm. While for the Sn-based perovskite, deviation in the Sn-X distance from the bulk increases with the decrease (increase) in size (electronegativity) of the halide, size of the halide follows I > Br > Cl. The electronegativity has the opposite trend to size, i.e., I < Br < Cl. The deviation of the surface Sn-X distance from the bulk is 2.62% for Sn-I, 3.15% for Sn-Br and 6.77% for Sn-Cl in the MAX surface termination, SnX₂ surface terminations follows the similar trend with slightly less deviation from the bulk compared to MAX surface terminations, Fig. 4. However, in Pb-based perovskite surface, Pb-X distances deviate less (<2.5%) from the bulk. There is no specific trend observed across the different halides in Pb-based perovskite. In Pauling scale electronegativity of Pb and Sn are 2.33 and 1.96, respectively. Because of the larger electronegativity of Pb, compared Sn, Pb-X bonds would have higher covalent nature than Sn-X bond. The less deviation of surface Pb-X distance could be due to the more covalent nature of Pb-X bond making all in-plane Pb-X distances more or less equal.

Further, deviation in the bond distances in surface structures from the bulk may lead to change in bond angles resulting in the polyhedra distortion.⁴⁵ Hence, we have calculated the bond angles (B-X-B) between the surface atoms and the ranges of angles are listed on the Table I. In general, from the Table I it can be seen that for the structures in the space groups I4/mcm have relatively more significant octahedral distortion than that of the structures in the space group P4/mmm, due to the deviation of the angle from 180°. Whereas from the comparison of surface and the bulk B-X-B angles, it is seen that structure in the space group I4/mcm shows the least deviation in angle from their bulk values, which is less than 2%. For the structure that belongs to P4/mmm, the deviation in B-X-B angle from the bulk is ≈ 3 to ≈ 5% with no specific trend across the composition, Table I. The less distortion on I4/mcm could be due to already distorted polyhedra (deviated from 180°) in bulk compared to P4/mmm structures. Both deviation in the distance and the angle from their bulk values should be due to the reconstruction of the surface, which leads to distortion in the polyhedra. Effects of the atomic reconstruction on the electronic structure will be discussed in the next section.

The band gap is one of the essential material properties for photovoltaic applications. Hence, we have calculated the band gap of the various perovskite surfaces and compared them with the bulk values. It is notable that although, the combination of spin orbit coupling (SOC) and quasi-particle approximations (GW) can reproduce the experimental band gap, but SOC or the advanced DFT methods like quasi-particle approximations (GW) alone fails to reproduce experimental band gap (See supplementary material).^9,23,27,46 Combined SOC+GW approach is highly computationally expensive in the present case, because of the size of the models studied. On the contrary, the scalar-relativistic DFT calculation at GGA level (presented in this work), predicts the band gap of Pb-based perovskite correctly due to the fortuitous cancellation of errors between the relativistic spin-orbit coupling and the GGA.^46,47 In the case of Sn-based perovskites, effects due to spin-orbit interaction are relatively less. The band gaps of Sn-based perovskites are underestimated due to deficiency of the GGA method (See supplementary material).^9,48,49 In any case, we expect the role of different approaches on the relative change in band gap for different surface terminations compared to bulk perovskites will be relatively nominal. Further, it is worth mentioning that previous reports already established that the use of SOC+GW or SOC has a negligible effect on the structural features such as lattice parameters, metal-halide distances, and angles. However, the same reports found that the van der Waals (vdW) corrections play a critical role in the atomic structure of the MA⁺ ions.^13,46,50 Overall, the use of simple DFT with vdW corrections without the inclusion of SOC as it is done in our calculations was found to produce reasonable electronic structures and the structural features.^51–54 

Fig. 5 shows the band gap for the bulk perovskites and their two different surface terminations. The band gap of the surfaces that belongs to the space group I4/mcm is reduced from the bulk value for both MAX and BX₂ terminations. Moreover, BX₂ surface termination shows a smaller band gap compared to MAX surface terminations for all the compositions with B=Pb. For the perovskite of the space group P4/mmm, different perovskite compositions have different band gap characteristics compared to their bulk values. For MAPbCl₃, the band gap for both surface terminations remains close to bulk value, with a slight fluctuation of ≈ 0.03 eV, whereas the MABr (PbBr₂) surface termination shows increase (similar) band gap values with their bulk MAPbBr₃ values, Fig. 5. In Sn-based perovskite, the band gap increases from their bulk values for both surface terminations, except for MASnCl₃. The reduced band gap in MASnCl₃ surfaces from its bulk value is an exception to all other perovskite compositions in the space group P4/mmm. Further, in contrast to Pb-based perovskite, where band gap remains equal or smaller for the PbX₂ surface terminations than that of the MAX surface terminations, in the Sn-based perovskite, SnX₂ surface termination always shows a higher band gap compared to MAX surface terminations.

The reduction in band gap compared to bulk values in the space group I4/mcm can be understood from layer resolved density of state, Fig. 6(a), and the charge density plotted at the band edges, namely conduction band minimum (CBM) and valence band maximum (VBM) of MAPbI₃ Fig. 6 (c) and (d), respectively. For MAPbI₃ and MAPbBr₃ the CBM is located at the BX₂ layer on which NH₃ are facing, while valence VBM is located at the BX₂ layer on which CH₃ is pointing. The asymmetric position of the metal cation and orientation of the dipole $CH3NH3+$ from the adjacent layers results in the accumulation of excess positive and negative charge on the surface layers. The excess charge can shift the CBM down and the VBM up in energy depending upon the magnitude of charge, which will reduce the band gap. For the structure in space group P4/mmm, MAX surface terminations of MAPbBr₃, MAPbCl₃ and MASnI₃, Fig. 2 (c)–(e) and SnI₂ surface terminations in Fig. 3 (e) have a more or less symmetric orientation of the dipole $CH3NH3+$ on both sides of the slab, for all of these slabs CBM and VBM located at the same energy level for the top and bottom end of the slabs as shown in Fig. 6 (b). While for MAX surface terminations of MASnBr₃ and MASnCl₃ (Fig. 2 (f) and (g)) and all BX₂ surface terminations, except SnI₂ (Fig. 3 (b), (c), (f) and (g)), their top and bottom layers have an asymmetric location of VBM and CBM, Fig. 6 (b).

Further, change in the octahedral geometry at the surface compared to bulk can also be responsible for the change in the band gap between surface and bulk. In hybrid halide perovskite, VBM consists of the antibonding combinations of metal B s and halide X p orbitals, whereas CBM consists of mainly metal p orbitals.^39,55 It was found that octahedral distortion can reduce the overlap between metal s and halide p orbitals leading to wider band gap.^56,57 Hence, an increase in the band gap of the P4/mmm structures should be due to polyhedral distortion resulting from surface terminations. MASnCl₃ is an exception to the structures in the space group P4/mmm in which band gap decreases compared to the surface. A possible reason for the decreased band gap in MASnCl₃ could be the drastic change in the bond distance in the slab model, where an average Sn-Cl distance is increasing by more than 6% compared to bulk. The strong equatorial Sn-Cl bonds lead to the weakening of another equatorial Sn-Cl bond causing one out of four equatorial distances greater than 3.24Å compared to rest of the equatorial distances ≈ 2.6Å i.e., Cl-Sn⋯ Cl interaction. Formation of the nonuniform Sn-Cl bond during the phase transition was also discussed in previous studies.^41,51 At a considerable distance, overlap of Sn s and Cl p orbitals may vanish completely causing unsaturated bond, leading to a reduction in the band gap.

In summary, the band gap at the perovskite surface results from competition between two phenomena. First, accumulated bound charge due to the orientation of the $CH3NH3+$ or unsaturated bonding leading to the downshift of the CBM and up shift of VBM in energy resulting in a reduced band gap (MAPbI₃, MAPbBr₃, MASnCl₃). Second, octahedral distortion, which lessens overlap of halide p orbitals and metal s orbitals leading to a larger band gap (MASnI₃, MASnBr₃). Moreover, in all surface terminations studied surface states appear in the band edges, and no midgap states are being formed in the perovskite surfaces. It should be pointed out that our results on the atomic structure for free surfaces of perovskite (interfacing with vacuum) can provide an initial understanding of the more complex atomic structures of perovskite surfaces during solution-based deposition of perovskite. The structural complexity of perovskite surface for such solution based-processes can be understood as a combined effect of surface structure with a vacuum (presented in this work) and the complex interactions between the solvent molecules and the perovskite surface. We plan to address such the complex, dynamic mutual interactions between solvent molecules, ETL/HTL molecules, and perovskite surface using adaptive biasing force (ABF) approach in our future publication.⁵⁸ 

DFT calculations were performed to investigate (001) surfaces of the tetragonal Pb- and Sn-based hybrid-halide perovskite structures. Reconstruction of the atoms in the surface structures leads to the reorientation of $CH3NH3+$ ion. The degree of reorientation of the $CH3NH3+$ ion depends on the availability of the volume created by BX₆ octahedral. The octahedral volume depends on the crystal symmetry and the size of the halide atom. Further, in comparison to Pb-based perovskite Sn-based perovskite surface shows significant variations in the metal halide distances compared to their bulk values. In the space group, P4/mmm departure in the octahedral angle from the bulk is higher, compared to the I4/mcm structures. Reorientations of the MA may cause an accumulation of charges resulting in the narrowing of the band gap, whereas the octahedral distortion arising from the deviation in angle (B-X-B) and the distance (B-X) leads to the opening of the band gap. Importantly, the hybrid halide perovskite considered in this study were found to produce no mid-gap surface states, which reduces the chance of trap state formation in perovskite surfaces. Our finding suggests that any of these perovskite composition could be used to create the interface free from mid-gap states to achieve optimal performance in the photovoltaic applications.

See supplementary material for the comparison of band gap of halide perovskites from different DFT approach.

This research made use of the resources at the High Performance Computing Center at Idaho National Laboratory, which is supported by the Office of Nuclear Energy of the U.S. Department of Energy under Contract No. DE-AC07-05ID14517. Publication of this article was funded by the University of Idaho Open Access Publishing Fund.