We present a detailed first-principles analysis of the (001) surface of methylammonium lead triiodide (MAPbI3). With density functional theory, we investigate the atomic and electronic structure of the tetragonal (I4cm) phase of MAPbI3. We analyzed surface models with MAI-termination (MAI-T) and PbI2-termination (PbI2-T). For both terminations, we studied the clean surface and a series of surface reconstructions. We find that the clean MAI-T model is more stable than its counterpart, PbI2-T. For the MAI-T, reconstructions with added or removed units of nonpolar MAI and PbI2 are most stable. The corresponding band structures reveal surface states originating from the conduction band. Despite the presence of such additional surface states, our stable reconstructed surface models do not introduce new states within the bandgap.

Perovskite solar cells (PSCs) have attracted immense attention within the photovoltaic community due to their rapidly rising power conversion efficiency (PCE): it reached 25.5%1 only nine years after the invention of the state-of-the-art PSC architecture in 2012 (PCE ∼10%).2,3 The hybrid (organic–inorganic) halide perovskite (HP) methylammonium (MA) lead triiodide (CH3NH3PbI3 or MAPbI3) has been the most common PSC photoabsorber for a long time, and it is still a major focus of both experimental and theoretical studies, along with the rising isostructural material based on formamidinium (FA). HPs have also received significant recognition in luminescence and light detection.4–9 

To advance HPs for eventual use in large-scale commercial applications, further efforts in fundamental research are still necessary to enable materials and device engineering. Researching surface passivation is critical in this regard since defects at perovskite surfaces and grain boundaries are centers of nonradiative recombination, which is a major inhibitor to further PCE improvement.10–16 Additionally, organic components in hybrid HPs suffer from rapid degradation when exposed to moisture, heat, and oxygen,17–22 the effects of which can be reduced with proper surface passivation. To enhance the stability of HPs and enable large-scale applications, measures need to be taken to mitigate their instability with minimal compromise to PCE. Several proposals have addressed this challenge. Notable approaches include surface passivation via organic long-chain ligands,23–25 dimensionality reduction of perovskite active materials,26–31 protective coating with inorganic semiconductors or insulators,32–35 and A-site substitution with smaller monovalent ions.36–43 

The application of these proposed solutions requires an understanding of the surface properties and possible surface reconstructions of HPs. This includes several aspects, such as morphology control during the growth of the HP thin films, HP-interlayer interface engineering, and the passivation of intrinsic defects at the interfaces and grain boundaries. A comprehensive understanding of the atomic and electronic structure of MAPbI3 surfaces would advance the development of this class of novel materials and their applications. The surfaces of Pb-based perovskites have been extensively investigated theoretically and experimentally,4,44–61 but understanding of the non-pristine surfaces is still lacking. Most of the MA-perovskite surface studies are focused on the stability of the two main terminations of HP (001) surfaces: MAI- and PbI2-terminated (shortened as MAI-T and PbI2-T hereafter, respectively) with little to no consideration of possible surface reconstructions.

In our previous work, we investigated the atomic and electronic structure of (001) surfaces of cesium lead triiodide (CsPbI3) using first-principles density functional theory (DFT) calculations and surface phase diagram (SPD) analysis.49 For both cubic (α) and orthorhombic (γ) phases, we found that the CsI-termination is more stable than PbI2-termination, and the former class features a series of stable surface reconstructions with added or removed valence-neutral CsI and PbI2 units. Our previous study established a systematic method for understanding stable surface reconstructions with a representative HP and motivates the present work with regard to both materials engineering and theoretical methodology.

In this work, we present a comprehensive DFT study of the (001) surface of the room-temperature tetragonal phase of the more popular HP, MAPbI3. Haruyama et al. have carried out preliminary studies for this surface and identified some stable surface terminations dependent on growth conditions, with some of them beyond the regular “clean surface” models.44,45,48 Nevertheless, an extensive exploration of surface terminations and reconstructions with the addition or removal of constituent elements CH3NH2 (MeNH2), Pb, I, and their complexes is lacking. We aim to establish such a systematic theoretical description by means of DFT, ab initio thermodynamics,62–64 and SPD analysis.

It is worth noting that the unique charge state of the organic MA cation introduces additional complexity into this DFT study compared to our work on CsPbI3.49 Simply separating MAPbI3 into its constituents MA, Pb, and I in a way similar to the decomposition of CsPbI3 into Cs, Pb, and I2 is not thermodynamically sensible. The charge-neutral CH3NH3 radical is not stable on its own and far less suitable as a thermodynamic reference system than Cs is for CsPbI3. We, therefore, use the neutral CH3NH2 (MeNH2) and H2 molecules in this work. Similar to Ref. 49, we will classify the thermodynamic stability of considered MAPbI3 surfaces for different growth conditions and analyze their electronic structure.

The remainder of this paper is organized as follows: In Sec. II, we briefly outline the computational details of our DFT calculations and summarize the thermodynamic constraints for the growth of bulk MAPbI3, as well as the MAI-T and PbI2-T surfaces. In Sec. III, we first analyze the stability of the clean surface models (MAI-T and Pb2-T) and the reconstructed models with missing- and add-atoms and complexes. We then discuss the impact of surface reconstruction on both the atomic and electronic structure. Finally, we conclude with a summary in Sec. IV.

All DFT calculations were performed using the Perdew–Burke–Ernzerhof exchange–correlation functional for solids (PBEsol)65 implemented in the all-electron numeric-atom-centered orbital code FHI-AIMS.66–68 We chose PBEsol because it describes the lattice constants of MAPbI3 well at moderate computational costs.69,70 In our previous study on CsPbI3 surfaces,49 we also tested the PBE functional but found only negligible changes in the surface phase diagram. We expect the same to be true for MAPbI3. Scalar relativistic effects were included by means of the zeroth-order regular approximation.71 As with the PBE test, the inclusion of full spin–orbit coupling did not affect the conclusions of our CsPbI3 study49 and we expect the same for MAPbI3. Standard FHI-AIMS tier-2 basis sets were used in combination with Γ-centered 4 × 4 × 4 (bulk) and 4 × 4 × 1 (surfaces) k-point meshes. The bulk structures were optimized with the analytical stress tensor72 until forces were below 5.0 × 10−3 eV Å−1. For the surface slab models, we fixed the lattice constants and all atomic positions except for atoms in the top and bottom MAPbI3 units (the surface atoms). A surface-dipole correction73 was applied in all surface calculations.

In the interest of open science,74 we made all relevant calculations included in this work available on the Novel Materials Discovery (NOMAD) repository.75 

1. Bulk and surface structures

As experimentally reported, the tetragonal phase of MAPbI3 is stable from ∼160 to ∼330 K, including room temperature.76,77 The structure belongs to the polar space group I4cm (No. 108) as a result of its intrinsic polarization along the principal axis.76 Considering several possible disordered MA alignments,78,79 we constructed a series of 2 × 2 × 2 supercells with different MA orientations and optimized their structures with DFT. We then take the structure with the lowest energy. The lattice parameters of this structure (Fig. 1) are a = b = 12.40 Å and c = 12.68 Å. Figure 1 displays some disorder and an overall vertical (downward in the side view, i.e., [001̄]) net dipole, which is formed by the C–N dipoles of the MA cations. The horizontal, i.e., (001), component of the overall dipole moment within the model nearly vanishes.

FIG. 1.

Bulk geometry and band structure of the I4cm phase of CH3NH3PbI3 in the 2 × 2 × 2 supercell model. C, H, N, Pb, and I are colored in brown, light gray, light blue, black, and purple, respectively. The PbI6 octahedra are colored in dark gray. The valence band maximum is set to zero and depicted by the red line in the band structure plot.

FIG. 1.

Bulk geometry and band structure of the I4cm phase of CH3NH3PbI3 in the 2 × 2 × 2 supercell model. C, H, N, Pb, and I are colored in brown, light gray, light blue, black, and purple, respectively. The PbI6 octahedra are colored in dark gray. The valence band maximum is set to zero and depicted by the red line in the band structure plot.

Close modal

In this work, we focus on the (001) surfaces, which are the major facet of HPs44,45,80 and the most relevant surfaces of MAPbI3. Due to the polar bulk structure, it is not possible to build a surface supercell by repeating several bulk layers along the [001] direction as this would result in a polar surface model [see Fig. 2(a), left]. Such a model will induce artifacts into the calculated properties of the system such as the unphysical removal of band degeneracies and reduction of the bandgap [Fig. 2(a), right] and would ultimately lead to a polar catastrophe, in which the valence band at one end of the slab lies higher in energy than the conduction bands at the other end.

FIG. 2.

Construction of the nonpolar MAI-T slab model, with the [001] components of MA dipoles represented by blue arrows. (a) A polar slab model results from simple repetition of bulk unit cells. (b) By mirroring bulk structures around a central domain wall, the overall dipole vanishes. Also shown is how the surface dipoles on both sides of the slab reorient themselves during relaxation and point inwards as a result of hydrogen bonding with surface I ions. The band structure of each model is given in the right column.

FIG. 2.

Construction of the nonpolar MAI-T slab model, with the [001] components of MA dipoles represented by blue arrows. (a) A polar slab model results from simple repetition of bulk unit cells. (b) By mirroring bulk structures around a central domain wall, the overall dipole vanishes. Also shown is how the surface dipoles on both sides of the slab reorient themselves during relaxation and point inwards as a result of hydrogen bonding with surface I ions. The band structure of each model is given in the right column.

Close modal

To circumvent these artifacts, we constructed a symmetric slab model by introducing a “domain wall” in the slab. As sketched in the left image of Fig. 2(b), such a domain wall is a PbI2-containing (001) plane located at the center of the slab. The atomic structures on the opposite sides of the domain wall are mirrored with respect to this plane, so that the [001] components of the MA dipole moments on opposite sides cancel each other, giving rise to a nearly vanishing overall dipole moment. As a result, the polar artifacts vanish and the surface band structure [Fig. 2(b), right] exhibits a proper bandgap and the right degeneracies. Similar approaches have been successfully employed in previous studies.44,81

With the approach illustrated in Fig. 2(b), we constructed symmetric clean surface models in a way similar to our previous work on CsPbI3. Specifically, the MAI-T surface model consists of 6 MAI and 5 PbI2 layers alternately stacked along the [001] direction. Similarly, the PbI2-T surface model has 7 PbI2 and 6 MAI alternating layers. By inserting a 40 Å-thick vacuum layer to separate neighboring slabs along [001] and including a surface-dipole correction73 in the DFT calculations, we minimized the interaction between neighboring slabs.

Figure 3 depicts the optimized structures of both clean MAI-T and PbI2-T surfaces. The top views of both phases show a similar in-plane tilting pattern of PbI6 octahedra and in-plane alignment of MA dipoles as in the bulk. The side views demonstrate that the mirror symmetry of both slab models with respect to the domain wall is maintained after geometry optimization. We note that in MAI-T, MA dipoles at both top and bottom surfaces point inwards (sketched in Fig. 2) as a result of hydrogen bonding with the surface I ions.

FIG. 3.

Relaxed MAI-T and PbI2-T clean surface models. Depicted on the left is the MAI-T and on the right is the PbI2-T termination.

FIG. 3.

Relaxed MAI-T and PbI2-T clean surface models. Depicted on the left is the MAI-T and on the right is the PbI2-T termination.

Close modal

We studied various add- and missing-atom surface models based on both MAI-T and PbI2-T clean surfaces. All add-atom models (iX) were constructed by adding the atoms or atom-complexes X to the surface, while for missing-atom models (vX), atoms or complexes X were removed from the topmost X-containing layers. For MAI-T surfaces, as an example, vMeNH2, vH, vMA, vI, and vMAI were constructed by removing atoms from the topmost MAI layer, while vPb and vPbI2 indicate the removal of atoms from the PbI2 layer below the topmost MAI layer. For models with double missing- or add-atoms (i.e., v2X or i2X), we considered both line and diagonal modes that correspond to the reconstruction units distributed along the [100] or [110] directions, respectively. Only the more stable model will be presented and discussed in Sec. III. For instance, we find the line modes to be more stable in both v2MAI and i2PbI2. Table I lists all surface models considered in this paper.

TABLE I.

Reconstructed MAI-T and PbI2-T surface models of tetragonal MAPbI3 considered in this work.

MAI-TPbI2-T
vMeNH2 iMeNH2 vMeNH2 iMeNH2 
v2MeNH2 i2MeNH2 v2MeNH2 i2MeNH2 
vMA iMA vMA iMA 
v2MA i2MA v2MA i2MA 
v4MA iPb vPb iPb 
vPb i2Pb v2Pb i2Pb 
v2Pb iI v4Pb iI 
vI i2I vI i2I 
v2I iH v2I iH 
vH i2H vH i2H 
v2H i4H v2H i4H 
v4H iMAI v4H iMAI 
vMAI i2MAI vMAI i2MAI 
v2MAI i4MAI v2MAI i4MAI 
v4MAI iPbI2 vPbI2 iPbI2 
vPbI2 i2PbI2 v2PbI2 i2PbI2 
v2PbI2 i4PbI2 v4PbI2 i4PbI2 
MAI-TPbI2-T
vMeNH2 iMeNH2 vMeNH2 iMeNH2 
v2MeNH2 i2MeNH2 v2MeNH2 i2MeNH2 
vMA iMA vMA iMA 
v2MA i2MA v2MA i2MA 
v4MA iPb vPb iPb 
vPb i2Pb v2Pb i2Pb 
v2Pb iI v4Pb iI 
vI i2I vI i2I 
v2I iH v2I iH 
vH i2H vH i2H 
v2H i4H v2H i4H 
v4H iMAI v4H iMAI 
vMAI i2MAI vMAI i2MAI 
v2MAI i4MAI v2MAI i4MAI 
v4MAI iPbI2 vPbI2 iPbI2 
vPbI2 i2PbI2 v2PbI2 i2PbI2 
v2PbI2 i4PbI2 v4PbI2 i4PbI2 

We applied the grand potential analysis to investigate the stability of a variety of different surface reconstructions. Neglecting finite temperature contributions, the grand potential (Ω) is

formula
(1)

Here, ΔH indicates the standard formation energy of the model system, E is the total energy, is the chemical potential of species i in its most stable form, xi is the number of atoms of this species in the structure, and Δμi is the change in the chemical potential away from its value in the element’s most stable phase, . Δμi represents the control of experimental growth conditions and is both a meaningful and convenient parameter to vary in phase diagrams. The relative stability between two structures is determined by comparing their grand potentials, with the structure lower in grand potential considered to be more stable. Details of the grand potential analysis are described in our previous work on surface reconstruction of CsPbI3.49 

We first consider conditions for stable MAPbI3 in the bulk. In order to avoid the formation of elemental Pb and I, molecular MA (as a whole instead of elemental C, N, and H for simplicity), as well as bulk MAI and PbI2, the region of the phase diagram for stable MAPbI3 is determined by the inequalities,

ΔH(MAPbI3)ΔμMA0,ΔH(MAPbI3)ΔμPb0,ΔH(MAPbI3)3ΔμI0

and

ΔH(MAPbI3)ΔμMA+ΔμPb+3ΔμI,ΔμMA+ΔμIΔH(MAI),ΔμPb+2ΔμIΔH(PbI2).

However, due to the unstable radical nature of neutral MA ≡ CH3NH3 (the reaction CH3NH2+12H2CH3NH3 is endothermic), we use the sum () instead of , and similarly (ΔμMeNH2+ΔμH) instead of ΔμMA. The inequalities should then be rewritten as

ΔH(MAPbI3)ΔμMeNH20,ΔH(MAPbI3)ΔμH0,ΔH(MAPbI3)ΔμPb0,ΔH(MAPbI3)3ΔμI0;
(2)

and

ΔH(MAPbI3)ΔμMeNH2+ΔμH+ΔμPb+3ΔμI,ΔμMeNH2+ΔμH+ΔμIΔH(MAI),ΔμPb+2ΔμIΔH(PbI2).
(3)

The inequalities in Eq. (3) can be rearranged as

ΔH(MAPbI3)ΔH(MAI)ΔμPb+2ΔμIΔH(PbI2),ΔH(MAPbI3)ΔH(PbI2)ΔμMeNH2+ΔμH+ΔμIΔH(MAI).
(4)

Inequalities in Eq. (2) define the domains of variables μMeNH2, μH, μPb, and μI, and the inequalities in Eq. (4) define the region for the growth of “stable-bulk MAPbI3” in the phase diagram. , , , and can be calculated for the stable reference structures of MeNH2 (molecule), H (H2 molecule), Pb (P63/mmc), and I (I2 molecule) with DFT, respectively. Formation energies ΔH in Eq. (4) can be calculated with DFT, too.

Equations (2) and (4) only serve to determine the bulk stability. For the stability of (clean and reconstructed) surface models, we need to solve Eq. (1) to obtain the SPDs. Note that the bulk and surface are not in isolation from each other. The final surface stability is determined by the intersection of the SPD and the stable-bulk region.

In principle, we need to plot the SPDs in four dimensions (4D) as the grand potential of each surface is a function of four variables (ΔμMeNH2, ΔμH, ΔμPb, and ΔμI). In practice, however, such a 4D diagram is hard to draw and visualize, and we use three two-dimensional (2D) slices instead: the ΔμI/ΔμMeNH2 slice at ΔμPb = ΔμH = 0, the ΔμIμPb slice at ΔμMeNH2=ΔμH=0, and the ΔμIμH slice at ΔμPb=ΔμMeNH2=0.

The PBEsol-calculated formation energies of bulk MAPbI3, MAI, and PbI2 are −4.82, −2.30, and −2.47 eV, respectively. From Eq. (4), we can find the numerical values for thermodynamic growth limits of bulk MAPbI3 in its tetragonal phase,

2.53eVΔμPb+2ΔμI2.47eV,2.35eVΔμMeNH2+ΔμH+ΔμI2.30eV.

The energy required for tetragonal MAPbI3 to decompose into MAI and PbI2, i.e., the difference between the left and the right values of either inequality, is as small as 0.06 eV. Such a narrow stability region reflects the general instability of tetragonal MAPbI3.

SPD analysis helps in identifying the stability of the two considered surface terminations. Figure 4 shows that, at ΔμMeNH2=ΔμH=0, the MAI-T and PbI2-T clean surfaces are stable in the Pb-poor and Pb-rich limits, respectively. We consider MAI-T to be the more stable surface since the region for stable MAI-T covers a wider range of Δμk (k = Pb and I, as well as MeNH2 and H, which are not shown here). Furthermore and quite importantly, the stable-bulk region, shown by yellow shading in Fig. 4, intersects only the MAI-T surface. This finding agrees with previous theoretical results for MAPbI310,61,77,82–84 that claimed the stability of MAI-T over PbI2-T and is similar to the CsPbI3 surface properties that we reported earlier.49 Our discussions will, therefore, focus on MAI-T surfaces from here on. Data for PbI2-T surfaces, including the relaxed surface reconstructions and the SPDs, are given in the supplementary material.

FIG. 4.

Thermodynamic growth limit for MAI-T and PbI2-T surfaces in tetragonal MAPbI3. The yellow shaded regions depict the thermodynamically stable range for the growth of bulk MAPbI3.

FIG. 4.

Thermodynamic growth limit for MAI-T and PbI2-T surfaces in tetragonal MAPbI3. The yellow shaded regions depict the thermodynamically stable range for the growth of bulk MAPbI3.

Close modal

SPDs for the considered surface reconstructions of the MAI-T surfaces are shown in Fig. 5 (SPDs for the PbI2-T counterparts are available in Fig. S1 in the supplementary material). It is not surprising that the ΔμI/ΔμMeNH2 and ΔμIμH SPDs display similar features, as MeNH2 and H are closely related to each other through the organic MA component of the material. In these two SPDs, which are given in the Pb-rich limit (ΔμPb = 0), we observe the following stable surface structures: i4MAI (in the MeNH2- and H-rich limits), v4MAI (in the MeNH2- and H-poor limits), clean surface, vPbI2, v2PbI2, iPbI2, i2PbI2, i2MAI, and vMAI. The major difference in the appearance of these two phase diagrams lies with the v4H surface, which is observed in the H-poor and I-rich limits. With our choice of 2D slices, this surface reconstruction appears in one quadrant of only one of these two 2D phase diagrams.

FIG. 5.

2D slices through the 4-dimensional surface phase diagrams of MAI-T surfaces of tetragonal MAPbI3. The yellow regions in each panel mark the bulk stability region of MAPbI3.

FIG. 5.

2D slices through the 4-dimensional surface phase diagrams of MAI-T surfaces of tetragonal MAPbI3. The yellow regions in each panel mark the bulk stability region of MAPbI3.

Close modal

The MeNH2- and H-rich (thus MA-rich) limits (ΔμMeNH2=ΔμH=0) create a third 2D slice of the total phase diagram, shown on the right side of Fig. 5. In this SPD, we find i4MAI and v2PbI2 to be stable. Except for v4H, all the observed stable reconstructions are valence-neutral, i.e., with addition or removal of MAI or PbI2 units, net charges are not induced in the system, which is similar to what we previously found for the CsPbI3 surfaces.49 We notice that in the MeNH2-, H-, and Pb-rich limits, i4MAI dominates over PbI2-derived reconstructions. That is, on the MAI-termination layer at the MAPbI3 surface, the tendency for growing an extra MAI layer is greater than for the growth of PbI2 units, which would eventually transform the system into PbI2-T. This finding again verifies that MAI-T is more stable.

We are particularly interested in the most relevant reconstructions, which we define as those regions in the SPDs that intersect the stable-bulk region. It is these overlapping regions of bulk and surface stability that are viable standalone surfaces in the laboratory. These relevant models are the clean surface, vPbI2, v2PbI2, iPbI2, and i2PbI2 in the Pb-rich limit, and i4MAI in the MA-rich limit. Different from CsPbI3, for which we observe a relatively broad range in chemical potential for the clean surface, the range for its stability on MAI-T (001) at ΔμPb = 0 is very narrow in terms of ΔμMeNH2 and ΔμH. In addition, it is only stable in I-deficient growth conditions.

The optimized geometries of the most relevant surface models are given in Fig. 6 (relevant reconstruction models of PbI2-T are presented in Fig. S2 in the supplementary material). Because the surface atomic structure varies mainly to accommodate the absence or addition of atoms, our discussion of geometric rearrangement will be with reference to the clean surface in the following text. We observe that PbI2 removal causes noticeable atomic structure changes in the reconstructed surfaces. The topmost PbI2 layer of vPbI2 displays (PbI6)2(PbI5) polyhedra, while in v2PbI2, there are two isolated PbI5 polyhedra (Fig. 7). Interestingly, no migration of surface I anions occurs in v2PbI2, which is the main characteristic of the equivalent removal in α-CsPbI3.49 This is very likely due to the different A-site cations: the hydrogen bonding between the ammonium group and the surface I anions would stabilize the latter, so that the surface Pb–I units are relatively regularly distributed.

FIG. 6.

Atomic structures of the most relevant surface reconstruction models of tetragonal MAPbI3. The atomic color convention follows that of Fig. 1. The light gray shading depicts the octahedra in the topmost layer in the “top view” and sites with missing or add PbI2 units in the “side view.”

FIG. 6.

Atomic structures of the most relevant surface reconstruction models of tetragonal MAPbI3. The atomic color convention follows that of Fig. 1. The light gray shading depicts the octahedra in the topmost layer in the “top view” and sites with missing or add PbI2 units in the “side view.”

Close modal
FIG. 7.

Surface polyhedra in reconstructed models with missing and add PbI2 units.

FIG. 7.

Surface polyhedra in reconstructed models with missing and add PbI2 units.

Close modal

In iPbI2 and i2PbI2, each added PbI2 unit is linked to a surface I atom via Pb–I bonding, giving rise to a PbI3 tetrahedron that contains one Pb and three I atoms as its vertices (Fig. 7). Notably, the i2PbI2 reconstruction shows characteristic PbI5PbI3 polyhedra (Fig. 7), as previously reported by Haruyama et al.44 This asymmetric distribution of surface I atoms results from the removal of two linearly aligned PbI2 units, which is very different from the same surface reconstruction of α-CsPbI3 where the diagonal mode is more stable.

Finally, we find a relatively regular alignment of the added MAI units, forming a uniform sheet on the MAI-T surface in i4MAI. The C–N bonds of all added MA+ cations point toward the surface to form hydrogen bonds with the topmost I anions. The average shortest H(N)⋯I distance is 2.68 Å, a typical value for hydrogen bonding.85,86 The fact that extra MAI units can readily grow above the already existing MAI surface termination layer, as also indicated by the SPDs in Fig. 5, makes it very likely that MAI multilayers can grow on MAPbI3 surfaces in MAI-rich situations. This would be detrimental to device performance since MAI is very poor in transporting charge carriers.

In this section, we focus on the electronic properties of bulk MAPbI3 and the most relevant reconstructed MAI-T surface models. The band structures of the most relevant PbI2-T surface reconstructions are presented in Fig. S3 in the supplementary material.

1. Electronic properties of the bulk and the clean MAI-T surface

Figure 8 depicts the band structures of the bulk and the pristine MAI-T surface of MAPbI3. For the bulk, we adopt the high-symmetry k-point path of a simple-cubic lattice in the 2 × 2 × 2 supercell model for simplicity. Our plots show the band structure along M–X–Γ–M with M=12,12,0, X=0,12,0, and Γ = (0, 0, 0), i.e., within the a*b* plane of the Brillouin zone [identical to the ab = (001) plane in real space in our cases].

FIG. 8.

Band structures of bulk and clean MAI-T surface of tetragonal MAPbI3. Both bulk and surface band structures are calculated with a 2 × 2 in-plane supercell to share a common Brillouin zone and k-point path (far right). VBM is set to 0 as marked by the red horizontal line. In the surface band structure plots, the projected bulk band structure is shown as blue shading.

FIG. 8.

Band structures of bulk and clean MAI-T surface of tetragonal MAPbI3. Both bulk and surface band structures are calculated with a 2 × 2 in-plane supercell to share a common Brillouin zone and k-point path (far right). VBM is set to 0 as marked by the red horizontal line. In the surface band structure plots, the projected bulk band structure is shown as blue shading.

Close modal

The bulk band structure exhibits a direct bandgap at the Γ point. The element projected density of states (PDOS) in Fig. 9 reveals that the valence band (VB) is dominated by I-5p orbitals. The VB maximum (VBM) exhibits a noticeable contribution from Pb-6s, which gives rise to the well-known antibonding character, and thus, introduces the noticeable band dispersion at Γ (Fig. 8). The conduction-band minimum (CBM) consists mainly of Pb-6p orbitals. The MA cation shows no significant contributions at the band edges.

FIG. 9.

Density of states of the bulk and clean MAI-T surface of tetragonal MAPb3, showing the contributions of different atomic species. We scaled the Pb density of states by a factor of 5 (depicted by *5) to make it more visible. The arrow is indicative of the surface states at the edge of the CB in the clean surface.

FIG. 9.

Density of states of the bulk and clean MAI-T surface of tetragonal MAPb3, showing the contributions of different atomic species. We scaled the Pb density of states by a factor of 5 (depicted by *5) to make it more visible. The arrow is indicative of the surface states at the edge of the CB in the clean surface.

Close modal

Next, we investigate if our MAI-T surface model introduces surface or mid-gap states. The bands of the clean MAI-T surface are shown in the middle panel of Fig. 8. Both the VB and CB edges of the surface nearly align with the bulk bands at the M-point. The bandgap of the surface at M is slightly larger than the bulk, which could be a quantum confinement artifact of the slab model, but the bands themselves agree. At Γ and X, however, the CB of the clean surface extends below the CBM of the bulk. At these points, the shapes of the bulk and surface bands at Γ are different.

To understand the nature of these states, we first analyze the PDOS in Fig. 9. The PDOS verifies that the apparent bandgap of the clean surface is ∼0.2 eV less than the bulk, as already indicated by the band structure. We plot the charge densities of the lowest four CB states of our surface model in Fig. 10. We find that these states are surface states that come in nearly degenerate pairs, with the partners of each pair on opposite sides of the slab. The slight degeneracy lift in each pair is caused by a small relaxation induced structural asymmetry in the two bulk halves that make up our surface slab model (see Sec. II A 1). The characters of these band edge wave functions are the same as the ones we observed for the α phase of CsPbI3.49 

FIG. 10.

Charge distributions of the valence band maximum (VBM) and conduction band minimum (CBM) up to CBM +3 at Γ point for the clean surface.

FIG. 10.

Charge distributions of the valence band maximum (VBM) and conduction band minimum (CBM) up to CBM +3 at Γ point for the clean surface.

Close modal

The DOS of the clean surface in Fig. 9 is consistent with the interpretation of conduction band-derived surface states. The right panel exhibits small bumps as shown by the arrow in Fig. 9 (right panel) in the CB at ∼1.25 and 2.10 eV compared to the bulk, indicating the rearrangement of bands in the slab model.

The behavior of the VBM is a little different. It is pinned to the domain wall at the mid-plane of the slab model. This quasi-two-dimensional state is still dispersive and its band very closely matches that of the bulk, which provides good evidence for the quality of our slab model. The pinning of the state to the mid-plane is reasonable. The dipoles on either side of the domain wall point away from the mid-plane, lowering the energy of an electron residing on the mid-plane and pinning it there. Again, the lack of artifacts in the slab electronic structure and good agreement with the bulk support the quality of the model, even with the pinning of the VBM to the domain wall.

2. Electronic properties of the most relevant MAI-T surface models

The band structure and PDOS of the most relevant surface models observed in Fig. 5 (vPbI2, v2PbI2, iPbI2, i2PbI2, and i4MAI) are shown in Figs. 11 and 12, respectively. Similar to Fig. 8, the bulk band structure is included as the background for comparison in Fig. 11. We find that the band structures of two of the most relevant reconstructed surface models, vPbI2 and i4MAI, resemble the band structure of the clean MAI-T surface shown in Fig. 8.

FIG. 11.

Band structures of the most relevant surface reconstruction models in tetragonal MAPbI3. The bulk-projected band structure is depicted by the blue shading.

FIG. 11.

Band structures of the most relevant surface reconstruction models in tetragonal MAPbI3. The bulk-projected band structure is depicted by the blue shading.

Close modal
FIG. 12.

Density of states of the most relevant surface reconstruction models in MAI-T tetragonal MAPbI3. The VBM is set to zero and shown as a red dashed line.

FIG. 12.

Density of states of the most relevant surface reconstruction models in MAI-T tetragonal MAPbI3. The VBM is set to zero and shown as a red dashed line.

Close modal

For the others, there are flat bands near and below the bulk CB edges (CBEs), which are more pronounced at the M-point. They are most visible in iPbI2. In the iPbI2 and i2PbI2 surfaces, we observe increased intensities within the CB of the PDOS at ∼1.6 and ∼1.9 eV, which corresponds to the flat bands at the M-point in Fig. 11. These small peaks come from Pb states, suggesting that the flat bands are, indeed, due to the added PbI2 units. To confirm this, we plot the charge distribution of CBE at M for these two reconstructions in Fig. 13.

FIG. 13.

Charge distribution for v2PbI2, iPbI2, and i2PbI2 of the conduction band edges (CBEs) at the M-point. We also show CBE +5 v2PbI2 as well as CBE +2 for iPbI2 and i2PbI2.

FIG. 13.

Charge distribution for v2PbI2, iPbI2, and i2PbI2 of the conduction band edges (CBEs) at the M-point. We also show CBE +5 v2PbI2 as well as CBE +2 for iPbI2 and i2PbI2.

Close modal

Even though the CBE at M in these two reconstructions and in v2PbI2 belongs to a band that is flat across the entire Brillouin zone, the wave functions of these states (Fig. 13) still resemble the surface states of the pristine slab, especially for v2PbI2 and i2PbI2. This is somewhat surprising since the CBE states of the clean surface model belong to a dispersive band. The CBE states of the reconstructed surfaces in Fig. 13 still come in nearly degenerate pairs with each partner appearing on opposite sides of the slab, as for the clean surface. However, we can ignore the state at the bottom of the slab, since it corresponds to the clean and not the reconstructed surface. The states in iPbI2 and i2PbI2 at the top of the slab, on the reconstructed surface side, have considerable weight on the added PbI2 units. This wave function localization explains the flat character of the band.

In summary, we have investigated the stability and electronic structure of MAPbI3 surfaces in the tetragonal phase from first-principles. To circumvent the polar catastrophe in our supercell calculations, we build a slab geometry from two MAPbI3 bulk segments with opposite polarity, effectively introducing a domain wall in the middle of the slab. Our surface science study reveals that the methylammonium iodine (MAI) termination is more stable than the PbI2-termination. We further observe that the removal or addition of polar units that induce zero net charge in the system leads to more stable surface reconstructions. MAI-terminated surfaces introduce conduction band-derived surface states near the conduction band edge, which result in a surface bandgap that is slightly smaller than the bulk bandgap. The stable reconstructions do not introduce further surface states in the bandgap, which bodes well for the transport properties across interfaces with these reconstructions. Our study opens up future work on surface adsorbates, defects, and interfaces.

See the supplementary material for surface phase diagrams of PbI2-terminated models and crystal and electronic band structures of the most relevant reconstructed surfaces of PbI2-T models.

The authors acknowledge the computing resources from the CSC-IT Center for Science, the Aalto Science-IT project, and Xi’an Jiaotong University’s HPC Platform. The authors further acknowledge funding from the Väisälä Foundation, the Emil Aaltonen Foundation, and the Academy of Finland through its Key Project Funding scheme (Grant No. 305632) and postdoctoral Grant No. 316347.

The authors have no conflicts to disclose.

All authors contributed equally in this work.

The data that support the findings of this study are openly available in Novel Materials Discovery (NOMAD) repository at https://dx.doi.org/10.17172/NOMAD/2021.10.21-1.75 

1.
National Renewable Energy Laboratory: Best research-cell efficiencies, https://www.nrel.gov/pv/assets/pdfs/best-research-cell-efficiencies.20200311.pdf, 2020.
2.
H.-S.
Kim
,
C.-R.
Lee
,
J.-H.
Im
,
K.-B.
Lee
,
T.
Moehl
,
A.
Marchioro
,
S.-J.
Moon
,
R.
Humphry-Baker
,
J.-H.
Yum
,
J. E.
Moser
,
M.
Grätzel
, and
N.-G.
Park
, “
Lead iodide perovskite sensitized all-solid-state submicron thin film mesoscopic solar cell with efficiency exceeding 9%
,”
Sci. Rep.
2
,
591
(
2012
).
3.
M. M.
Lee
,
J.
Teuscher
,
T.
Miyasaka
,
T. N.
Murakami
, and
H. J.
Snaith
, “
Efficient hybrid solar cells based on meso-superstructured oraganometal halide perovskites
,”
Science
338
,
643
(
2012
).
4.
C.
Das
,
M.
Wussler
,
T.
Hellmann
,
T.
Mayer
,
I.
Zimmermann
,
C.
Maheu
,
M. K.
Nazeeruddin
, and
W.
Jaegermann
, “
Surface, interface and bulk electronic and chemical properties of complete perovskite solar cells: Tapered cross-section photoelectron spectroscopy, a novel solution
,”
ACS Appl. Mater. Interfaces
12
,
40949
409571
(
2020
).
5.
P.
Giulia
, “
Highly efficient perovskite LEDs
,”
Nat. Rev. Mater.
6
,
108
(
2021
).
6.
L.-Y.
Huang
and
W. R. L.
Lambrecht
, “
Lattice dynamics in perovskite halides CsSn X3 with X = I, Br, Cl
,”
Phys. Rev. B
90
,
195201
(
2014
).
7.
Q.
Lin
,
A.
Armin
,
D. M.
Lyons
,
P. L.
Burn
, and
P.
Meredith
, “
Low noise, IR-blind organohalide perovskite photodiodes for visible light detection and imaging
,”
Adv. Mater.
27
,
2060
2064
(
2015
).
8.
H.
Cho
,
S.-H.
Jeong
,
M.-H.
Park
,
Y.-H.
Kim
,
C.
Wolf
,
C.-L.
Lee
,
J. H.
Heo
,
A.
Sadhanala
,
N.
Myoung
,
S.
Yoo
,
S. H.
Im
,
R. H.
Friend
, and
T.-W.
Lee
, “
Overcoming the electroluminescence efficiency limitations of perovskite light-emitting diodes
,”
Science
350
,
1222
(
2015
).
9.
C.
Li
,
H.
Wang
,
F.
Wang
,
T.
Li
,
M.
Xu
,
H.
Wang
,
Z.
Wang
,
X.
Zhan
,
W.
Hu
, and
L.
Shen
, “
Ultrafast and broadband photodetectors based on perovskite/organic bulk heterojunction for large-dynamic-range imaging
,”
Light: Sci. Appl.
9
,
31
(
2020
).
10.
W.-J.
Yin
,
T.
Shi
, and
Y.
Yan
, “
Unusual defect physics in CH3NH3PbI3 perovskite solar cell absorber
,”
Appl. Phys. Lett.
104
,
063903
(
2014
).
11.
K. X.
Steirer
,
P.
Schulz
,
G.
Teeter
,
V.
Stevanovic
,
M.
Yang
,
K.
Zhu
, and
J. J.
Berry
, “
Defect tolerance in methylammonium lead triiiodide perovskite
,”
ACS Energy Lett.
1
,
360
366
(
2016
).
12.
A.
Walsh
,
D. O.
Scanlon
,
S.
Chen
,
X. G.
Gong
, and
S.-H.
Wei
, “
Self-regulation mechanism for charged point defects in hybrid halide perovskites
,”
Angew. Chem., Int. Ed.
54
,
1791
(
2015
).
13.
J.
Kim
,
S.-H.
Lee
,
J. H.
Lee
, and
K.-H.
Hong
, “
The role of intrinsic defects in methylammonium lead iodide perovskite
,”
J. Phys. Chem. Lett.
5
,
1312
1317
(
2014
).
14.
J. M.
Ball
and
A.
Petrozza
, “
Defects in perovskite-halides and their effects in solar cells
,”
Nat. Energy
1
,
16149
(
2016
).
15.
X.
Wu
,
M. T.
Trinh
,
D.
Niesner
,
H.
Zhu
,
Z.
Norman
,
J. S.
Owen
,
O.
Yaffe
,
B. J.
Kudisch
, and
X.-Y.
Zhu
, “
Trap states in lead iodide perovskites
,”
J. Am. Chem. Soc.
137
,
2089
2096
(
2015
).
16.
R.
Long
,
J.
Liu
, and
O. V.
Prezhdo
, “
Unravelling the effects of grain boundary and chemical doping on electron–hole recombination in CH3NH3PbI3 perovskite by time-domain atomistic simulation
,”
J. Am. Chem. Soc.
138
,
3884
(
2016
).
17.
G.
Niu
,
W.
Li
,
F.
Meng
,
L.
Wang
,
H.
Dong
, and
Y.
Qiu
, “
Study on the stability of CH3NH3PbI3 films and the effect of post-modification by aluminumoxide in all-solid-state hybrid solar cells
,”
J. Mater. Chem. A
2
,
705
(
2014
).
18.
G.
Niu
,
X.
Guo
, and
L.
Wang
, “
Review of recent progress in chemical stability of perovskite solar cells
,”
J. Mater. Chem. A
3
,
8970
(
2015
).
19.
J.
Huang
,
S.
Tan
,
P. D.
Lund
, and
H.
Zhou
, “
Impact of H2O2
,”
Energy Environ. Sci.
10
,
2284
(
2017
).
20.
G.-H.
Kim
,
H.
Jang
,
Y. J.
Yoon
,
J.
Jeong
,
S. Y.
Park
,
B.
Walker
,
I.-Y.
Jeon
,
Y.
Jo
,
H.
Yoon
,
M.
Kim
,
J.-B.
Baek
,
D. S.
Kim
, and
J. Y.
Kim
, “
Fluorine functionalized graphene nano platelets for highly stable inverted perovskite solar cells
,”
Nano Lett.
17
,
6385
(
2017
).
21.
I.
Mesquita
,
L.
Andrade
, and
A.
Mendes
, “
Perovskite solar cells: Materials, configurations and stability
,”
Renewable Sustainable Energy Rev.
82
,
2471
(
2018
).
22.
F.
Li
,
J.
Yuan
,
X.
Ling
,
Y.
Zhang
,
Y.
Yang
,
S. H.
Cheung
,
C. H. Y.
Ho
,
X.
Gao
, and
W.
Ma
, “
A universal strategy to utilize polymeric semiconductors for perovskite solar cells with enhanced efficiency and longevity
,”
Adv. Funct. Mater.
28
,
1706377
(
2018
).
23.
L. C.
Schmidt
,
A.
Pertegás
,
S.
González-Carrero
,
O.
Malinkiewicz
,
S.
Agouram
,
G. M.
Espallargas
,
H. J.
Bolink
,
R. E.
Galian
, and
J.
Pérez-Prieto
, “
Nontemplate synthesis of CH3NH3PbBr3 perovskite nanoparticles
,”
J. Am. Chem. Soc.
136
,
850
(
2014
).
24.
S.
González-Carrero
,
R. E.
Galian
, and
J.
Pérez-Prieto
, “
Maximizing the emissive properties of CH3NH3PbBr3 perovskite nanoparticles
,”
J. Mater. Chem. A
3
,
9187
(
2015
).
25.
H.
Dong
,
J.
Xi
,
L.
Zuo
,
J.
Li
,
Y.
Yang
,
D.
Wang
,
Y.
Yu
,
L.
Ma
,
C.
Ran
,
W.
Gao
,
B.
Jiao
,
J.
Xu
,
T.
Lei
,
F.
Wei
,
F.
Yuan
,
L.
Zhang
,
Y.
Shi
,
X.
Hou
, and
Z.
Wu
, “
Conjugated molecules ‘bridge’: Functional ligand toward highly efficient and long-term stable perovskite solar cell
,”
Adv. Funct. Mater.
29
,
1808119
(
2019
).
26.
L. N.
Quan
,
M.
Yuan
,
R.
Comin
,
O.
Voznyy
,
E. M.
Beauregard
,
S.
Hoogland
,
A.
Buin
,
A. R.
Kirmani
,
K.
Zhao
,
A.
Amassian
,
D. H.
Kim
, and
E. H.
Sargent
, “
Ligand-stabilized reduced-dimensionality perovskites
,”
J. Am. Chem. Soc.
138
,
2649
(
2016
).
27.
L.
Dou
, “
Emerging two-dimensional halide perovskite nanomaterials
,”
J. Mater. Chem. C
5
,
11165
(
2017
).
28.
C.
Ran
,
J.
Xi
,
W.
Gao
,
F.
Yuan
,
T.
Lei
,
B.
Jiao
,
X.
Hou
, and
Z.
Wu
, “
Bilateral interface engineering toward efficient 2D-3D bulk heterojunction tin halide lead-free perovskites solar cells
,”
ACS Energy Lett.
3
,
713
(
2018
).
29.
Z.
Wang
,
A. M.
Ganose
,
C.
Niu
, and
D. O.
Scanlon
, “
First-principles insights into tin-based two-dimensional hybrid halide perovskites for photovoltaics
,”
J. Mater. Chem. A
6
,
5652
(
2018
).
30.
C.
Liu
,
W.
Huhn
,
K.-Z.
Du
,
A.
Vazquez-Mayagoitia
,
D.
Dirkes
,
W.
You
,
Y.
Kanai
,
D. B.
Mitzi
, and
V.
Blum
, “
Tunable semiconductors: Control over carrier states and excitations in layered hybrid organic-inorganic perovskite
,”
Phys. Rev. Lett.
121
,
146401
(
2018
).
31.
C.
Ran
,
W.
Gao
,
J.
Li
,
J.
Xi
,
L.
Li
,
J.
Dai
,
Y.
Yang
,
X.
Gao
,
H.
Dong
,
B.
Jiao
,
I.
Spanopoulos
,
C. D.
Malliakas
,
X.
Hou
,
M. G.
Kanatzidis
, and
Z.
Wu
, “
Conjugated organic cations enable efficient self-healing FASnI3 solar cells
,”
Joule
3
,
3072
(
2019
).
32.
F.
Matteocci
,
L.
Cinà
,
E.
Lamanna
,
S.
Cacovich
,
G.
Divitini
,
P. A.
Midgley
,
C.
Ducati
, and
A.
di Carlo
, “
Encapsulation for long-term stability enhancement of perovskite solar cells
,”
Nano Energy
30
,
162
(
2016
).
33.
R.
Cheacharoen
,
N.
Rolston
,
D.
Harwood
,
K. A.
Bush
,
R. H.
Dauskardt
, and
M. D.
McGehee
, “
Design and understanding of encapsulated perovskite solar cells to withstand temperature cycling
,”
Energy Environ. Sci.
11
,
144
(
2018
).
34.
R.
Cheacharoen
,
C. C.
Boyd
,
G. F.
Burkhard
,
T.
Leijtens
,
J. A.
Raiford
,
K. A.
Bush
,
S. F.
Bent
, and
M. D.
McGehee
, “
Encapsulation for long-term stability enhancement of perovskite solar cells
,”
Sustainable Energy Fuels
2
,
2398
(
2018
).
35.
A.
Seidu
,
L.
Himanen
,
J.
Li
, and
P.
Rinke
, “
Database-driven high-throughput study of coating materials for hybrid perovskites
,”
New J. Phys.
21
,
083018
(
2019
).
36.
J. H.
Noh
,
S. H.
Im
,
J. H.
Heo
,
T. N.
Mandal
, and
S. I.
Seok
, “
Chemical management for colourful, efficient, and stable inorganic-organic hybrid nanostructured solar cells
,”
Nano Lett.
13
,
1764
(
2013
).
37.
C.
Yi
,
J.
Luo
,
S.
Meloni
,
A.
Boziki
,
N.
Ashari-Astani
,
C.
Grätzel
,
S. M.
Zakeeruddin
,
U.
Röthlisberger
, and
M.
Grätzel
, “
Entropic stabilization of mixed A-cation ABX3 metal halide perovskites for high performance perovskite solar cells
,”
Energy Environ. Sci.
9
,
656
(
2016
).
38.
Y.
Zhou
,
Z.
Zhou
,
M.
Chen
,
Y.
Zong
,
J.
Huang
,
S.
Pang
, and
N. P.
Padture
, “
Doping and alloying for improved perovskite solar cells
,”
J. Mater. Chem. A
4
,
17623
(
2016
).
39.
H.
Tan
,
A.
Jain
,
O.
Voznyy
,
X.
Lan
,
F. P. G.
de Arquer
,
J. Z.
Fan
,
R.
Quintero-Bermudez
,
M.
Yuan
,
B.
Zhang
,
Y.
Zhao
,
F.
Fan
,
P.
Li
,
L. N.
Quan
,
Y.
Zhao
,
Z.-H.
Lu
,
Z.
Yang
,
S.
Hoogland
, and
E. H.
Sargent
, “
Efficient and stable solution-processes planar perovskite solar cells via contact passivation
,”
Science
355
,
722
(
2017
).
40.
A.
Ciccioli
and
A.
Latini
, “
Thermodynamics and the intrinsic stability of lead halide perovskites CH3NH3PbX3
,”
J. Phys. Chem. Lett.
9
,
3756
(
2018
).
41.
W.
Gao
,
C.
Ran
,
J.
Li
,
H.
Dong
,
L.
Zhang
,
X.
Lan
,
X.
Hou
, and
Z.
Wu
, “
Robust stability of efficient lead-free formamidinium tin iodide perovskite solar cells realized by structural regulation
,”
J. Phys. Chem. Lett.
9
,
6999
(
2018
).
42.
J.-P.
Correa-Baena
,
A.
Abate
,
M.
Saliba
,
W.
Tress
,
T. J.
Jacobsson
,
M.
Grätzel
, and
A.
Hagfeldt
, “
The rapid evolution of highly efficient perovskite solar cells
,”
Energy Environ. Sci.
10
,
710
(
2017
).
43.
A. M.
Ganose
,
C. N.
Savory
, and
D. O.
Scanlon
, “
Beyond methylammonium lead iodide: Prospects for the emergent field of ns2 containing solar absorbers
,”
Chem. Commun.
53
,
20
(
2017
).
44.
J.
Haruyama
,
K.
Sodeyama
,
L.
Han
, and
Y.
Tateyama
, “
Termination dependence of tetragonal CH3NH3PbI3 surfaces for perovskite solar cells
,”
J. Phys. Chem. Lett.
5
,
2903
2909
(
2014
).
45.
J.
Haruyama
,
K.
Sodeyama
,
L.
Han
, and
Y.
Tateyama
, “
Surface properties of CH3NH3PbI3 for perovskite solar cells
,”
Acc. Chem. Res.
49
,
554
561
(
2016
).
46.
A.
Akbari
,
J.
Hashemi
,
E.
Mosconi
,
F.
De Angelis
, and
M.
Hakala
, “
First principles modelling of perovskite solar cells based on TiO2 and Al2O3: Stability and interfacial electronic structure
,”
J. Mater. Chem. A
5
,
2339
(
2017
).
47.
L.
Zhang
,
X.
Liu
,
J.
Su
, and
J.
Li
, “
First-principles study of molecular adsorption on lead iodide perovskite surface: A case study of halogen bond passivation for solar cell application
,”
J. Phys. Chem. C
120
,
23536
23541
(
2020
).
48.
R.
Ohmann
,
L. K.
Ono
,
H.-S.
Kim
,
H.
Lin
,
M. V.
Lee
,
Y.
Li
,
N.-G.
Park
, and
Y.
Qi
, “
Real-space imaging of the atomic structure of organic-inorganic perovskite
,”
J. Am. Chem. Soc.
137
,
16049
16054
(
2015
).
49.
A.
Seidu
,
M.
Dvorak
,
P.
Rinke
, and
J.
Li
, “
Atomic and electronic structure of cesium lead triiodide surfaces
,”
J. Chem. Phys.
154
,
074712
(
2021
).
50.
J.
Hieulle
,
S.
Luo
,
D.-Y.
Son
,
A.
Jamshaid
,
C.
Stecker
,
Z.
Liu
,
G.
Na
,
D.
Yang
,
R.
Ohmann
,
L. K.
Ono
,
L.
Zhang
, and
Y.
Qi
, “
Imaging of the atomic structure of all-inorganic halide perovskites
,”
J. Phys. Chem. Lett.
11
,
818
823
(
2020
).
51.
S.
Wang
,
W.-b.
Xiao
, and
F.
Wang
, “
Structural, electronic, and optical properties of cubic formamidinium lead iodide perovskite: A first-principles investigation
,”
RSC Adv.
10
,
32364
(
2020
).
52.
J.
Xue
,
J.-W.
Lee
,
Z.
Dai
,
R.
Wang
,
S.
Nuryyeva
,
M. E.
Liao
,
S.-Y.
Chang
,
L.
Meng
,
D.
Meng
,
P.
Sun
,
O.
Lin
,
M. S.
Goorsky
, and
Y.
Yang
, “
Surface ligand management for stable FAPbI3 perovskite quantum dot solar cells
,”
Joule
2
,
1866
(
2018
).
53.
Y.
Fu
,
T.
Wu
,
J.
Wang
,
J.
Zhai
,
M. J.
Shearer
,
Y.
Zhao
,
R. J.
Hamers
,
E.
Kan
,
K.
Deng
,
X.-Y.
Zhu
, and
S.
Jin
, “
Stabilization of the metastable lead iodide perovskite phase via surface functionalization
,”
Nano Lett.
17
,
4405
(
2017
).
54.
Q.
Jiang
,
Y.
Zhao
,
X.
Zhang
,
X.
Yang
,
Y.
Chen
,
Z.
Chu
,
Q.
Ye
,
X.
Li
,
Z.
Yin
, and
J.
You
, “
Surface passivation of perovskite film for efficient solar cells
,”
Nat. Photonics
13
,
460
(
2019
).
55.
P.
Chen
,
Y.
Bai
,
S.
Wang
,
M.
Lyu
,
J.-H.
Yun
, and
L.
Wang
, “
In situ growth of 2D perovskite capping layer for stable
,”
Adv. Funct. Mater.
28
,
1706923
(
2018
).
56.
Y.
Cho
,
A. M.
Soufiani
,
J. S.
Yun
,
J.
Kim
,
D. S.
Lee
,
J.
Seidel
,
X.
Deng
,
M. A.
Green
,
S.
Huang
, and
A. W. Y.
Ho-Baillie
, “
Mixed 3D–2D passivation treatment for mixed-cation lead mixed-halide perovskite solar cells for higher efficiency and better stability
,”
Adv. Energy Mater.
8
,
1703392
(
2018
).
57.
M.
Saliba
,
T.
Matsui
,
J.-Y.
Seo
,
K.
Domanski
,
J.-P.
Correa-Baena
,
M. K.
Nazeeruddin
,
S. M.
Zakeeruddin
,
W.
Tress
,
A.
Abate
,
A.
Hagfeldt
, and
M.
Grätzel
, “
Cesium-containing triple cation perovskite solar cells: Improved stability, reproducibility and high efficiency
,”
Energy Environ. Sci.
9
,
1989
(
2016
).
58.
M.
Saliba
,
S.
Orlandi
,
T.
Matsui
,
S.
Aghazada
,
M.
Cavazzini
,
J.-P.
Correa-Baena
,
P.
Gao
,
R.
Scopelliti
,
E.
Mosconi
,
K.-H.
Dahmen
,
F.
De Angelis
,
A.
Abate
,
A.
Hagfeldt
,
G.
Pozzi
,
M.
Grätzel
, and
M. K.
Nazeeruddin
, “
A molecularly engineered hole-transporting material for efficient perovskite solar cells
,”
Nat. Energy
1
,
15017
(
2016
).
59.
M.
Saliba
,
T.
Matsui
,
K.
Domanski
,
J.-Y.
Seo
,
A.
Ummadisingu
,
S. M.
Zakeeruddin
,
J.-P.
Correa-Baena
,
W. R.
Tress
,
A.
Abate
,
A.
Hagfeldt
, and
M.
Grätzel
, “
Entropic stabilization of mixed A-cation ABX3 metal halide perovskites for high performance perovskite solar cells
,”
Science
354
,
206
(
2016
).
60.
L.
Qiu
,
S.
He
,
L. K.
Ono
, and
Y.
Qi
, “
Progress of surface science studios on ABX3-based metal perovskite solar cells
,”
Adv. Energy Mater.
10
,
1902726
(
2020
).
61.
J.
He
,
D.
Casanova
,
W.-H.
Fang
,
R.
Long
, and
O. V.
Prezhdo
, “
MAI termination favours efficient hole extraction and slow charge recombination at the MAPbI3/CuSCN heterojunction
,”
J. Chem. Phys.
11
,
004481
(
2020
).
62.
K.
Reuter
and
M.
Scheffler
, “
First-principles atomistic thermodynamics for oxidation catalysis: Surface phase diagrams and catalytically interesting regions
,”
Phys. Rev. Lett.
90
,
046103
(
2003
).
63.
K.
Reuter
,
C.
Stampf
, and
M.
Scheffler
, in
Handbook of Material Modeling
, edited by
S.
Yip
(
Springer Dordrecht
,
2005
), p.
149
.
64.
K.
Reuter
and
M.
Scheffler
, “
Composition and structure of the RuO2(110) surface in an O2 and CO environment: Implications for the catalytic formation of CO2
,”
Phys. Rev. B
68
,
045407
(
2003
).
65.
J. P.
Perdew
,
A.
Ruzsinszky
,
G. I.
Csonka
,
O. A.
Vydrov
,
G. E.
Scuseria
,
L. A.
Constantin
,
X.
Zhou
, and
K.
Burke
, “
Restoring the density-gradient expansion for exchange in solids and surfaces
,”
Phys. Rev. Lett.
100
,
136406
(
2008
).
66.
V.
Blum
,
R.
Gehrke
,
F.
Hanke
,
P.
Havu
,
V.
Havu
,
X.
Ren
,
K.
Reuter
, and
M.
Scheffler
, “
Ab initio molecular simulations with numeric atom-centered orbitals
,”
Comput. Phys. Commun.
180
,
2175
(
2009
).
67.
V.
Havu
,
V.
Blum
,
P.
Havu
, and
M.
Scheffler
, “
Efficient O(N) integration for all-electron electronic structure calculation using numeric basis functions
,”
J. Comput. Phys.
228
,
8367
(
2009
).
68.
S. V.
Levchenko
,
X.
Ren
,
J.
Wieferink
,
R.
Johanni
,
P.
Rinke
,
V.
Blum
, and
M.
Scheffler
, “
Hybrid functionals for large periodic systems in an all-electron, numeric atom-centered basis framework
,”
Comput. Phys. Commun.
192
,
60
69
(
2015
).
69.
R. X.
Yang
,
J. M.
Skelton
,
E. L.
da Silva
,
J. M.
Frost
, and
A.
Walsh
, “
Spontaneous octahedral tilting in the cubic inorganic cesium halide perovskites CsSnX3 and CsPbX3 (X = F, Cl, Br, I)
,”
J. Phys. Chem. Lett.
8
,
4720
(
2017
).
70.
M.
Bokdam
,
J.
Lahnsteiner
,
B.
Ramberger
,
T.
Schäfer
, and
G.
Kresse
, “
Assessing density functionals using many body theory for hybrid perovskites
,”
Phys. Rev. Lett.
119
,
145501
(
2017
).
71.
E.
van Lenthe
,
E. J.
Baerends
, and
J. G.
Snijders
, “
Relativistic regular two-component Hamiltonians
,”
J. Chem. Phys.
99
,
4597
(
1993
).
72.
F.
Knuth
,
C.
Carbogno
,
V.
Atalla
,
V.
Blum
, and
M.
Scheffler
, “
All-electron formalism for total energy strain derivatives and stress tensor components for numeric atom-centered orbitals
,”
Comput. Phys. Commun.
190
,
33
(
2015
).
73.
J.
Neugebauer
and
M.
Scheffler
, “
Adsorbate-substrate and adsorbate-adsorbate interactions of Na and K adlayers on Al(111)
,”
Phys. Rev. B
46
,
16067
(
1992
).
74.
L.
Himanen
,
A.
Geurts
,
A. S.
Foster
, and
P.
Rinke
, “
Data-driven materials science: Status, challenges, and perspectives
,”
Adv. Sci.
6
,
1900808
(
2019
).
75.
A.
Seidu
,
M.
Dvorak
,
J.
Jarvi
,
P.
Rinke
, and
J.
Li
, “
MAPbI3 surface models
,”
Novel Materials Discovery Repository
(
2021
), .
76.
C. C.
Stoumpos
,
C. D.
Malliakas
, and
M. G.
Kanatzidis
, “
Semiconducting tin and lead iodide perovskites with organic cations: Phase transitions, high mobilities, and near-infrared photoluminescent properties
,”
Inorg. Chem.
52
,
9019
9038
(
2013
).
77.
T.
Baikie
,
Y.
Fang
,
J. M.
Kadro
,
M.
Schreyer
,
F.
Wei
,
S. G.
Mhaisalkar
,
M.
Graetzel
, and
T. J.
White
, “
Synthesis and crystal chemistry of the hybrid perovskite (CH3NH3)PbI3 for solid-state sensitised solar cell applications
,”
J. Mater. Chem. A
1
,
5628
(
2013
).
78.
J.
Lahnsteiner
,
G.
Kresse
,
A.
Kumar
,
D. D.
Sarma
,
C.
Franchini
, and
M.
Bokdam
, “
Room-temperature dynamic correlation between methylammonium molecules in lead-iodine based perovskites: An ab initio molecular dynamics perspective
,”
Phys. Rev. B
94
,
214114
(
2016
).
79.
J.
Li
,
J.
Järvi
, and
P.
Rinke
, “
Multiscale model for disordered hybrid perovskites: The concept of organic cation pair modes
,”
Phys. Rev. B
98
,
045201
(
2018
).
80.
P.
Schulz
,
D.
Cahen
, and
A.
Kahn
, “
Halide perovskites: Is it all about the interfaces?
,”
Chem. Rev.
119
,
3349
(
2019
).
81.
V.
Roiati
,
E.
Mosconi
,
A.
Listorti
,
S.
Colella
,
G.
Gigli
, and
F.
De Angelis
, “
Stark effect in perovskite/TiO2 solar cells: Evidence of local interfacial order
,”
Nano Lett.
14
,
2168
(
2014
).
82.
C.
Caddeo
,
A.
Filippetti
, and
A.
Mattoni
, “
The dominant role of surfaces in the hysteretic behavior of hybrid perovskites
,”
Nano Energy
67
,
104162
(
2020
).
83.
A.
Mirzehmet
,
T.
Ohtsuka
,
S. A. A.
Rahman
,
T.
Yuyama
,
P.
Krüger
, and
H.
Yoshida
, “
Surface termination of solution-processed CH3NH3PbI3 perovskite film examined using electron spectroscopy
,”
Adv. Mater.
33
,
e2004981
(
2021
).
84.
W.
Geng
,
C.-J.
Tong
,
Z.-K.
Tang
,
C.
Yam
,
Y.-N.
Zhang
,
W.-M.
Lau
, and
L.-M.
Liu
, “
Effect of surface composition on electronic properties of methylammonium lead iodide perovskite
,”
J. Materiomics
1
,
213
(
2015
).
85.
J.
Li
and
P.
Rinke
, “
Atomic structure of metal-halide perovskites from first-principles: The chicken-and-egg paradox of the organic-inorganic interactions
,”
Phys. Rev. B
94
,
045201
(
2016
).
86.
J.
Li
,
M.
Bouchard
,
P.
Reiss
,
D.
Aldakov
,
S.
Pouget
,
R.
Demadrille
,
C.
Aumaitre
,
B.
Frick
,
D.
Djurado
,
M.
Rossi
, and
P.
Rinke
, “
Activation energy of organic cation rotation in CH3NH3PbI3 and CD3NH3PbI3: Quasi-elastic neutron scattering measurements and first-principles analysis including nuclear quantum effects
,”
J. Phys. Chem. Lett.
9
,
3969
(
2018
).

Supplementary Material