The (001) surface of the emerging photovoltaic material cesium lead triiodide (CsPbI3) is studied. Using first-principles methods, we investigate the atomic and electronic structure of cubic (α) and orthorhombic (γ) CsPbI3. For both phases, we find that CsI-termination is more stable than PbI2-termination. For the CsI-terminated surface, we then compute and analyze the surface phase diagram. We observe that surfaces with added or removed units of nonpolar CsI and PbI2 are most stable. The corresponding band structures reveal that the α phase exhibits surface states that derive from the conduction band. The surface reconstructions do not introduce new states in the bandgap of CsPbI3, but for the α phase, we find additional surface states at the conduction band edge.

In recent years, perovskite solar cells (PSCs) have generated increased attention within the photovoltaic community. The most common PSC photoabsorbers are hybrid organic-inorganic halide perovskites (HPs) with an ABX3 structure, where A is an (organic) monovalent cation, B is either Pb or Sn, and X is a halogen. Among the HPs, the most widely studied materials are methylammonium (MA) lead iodide (CH3NH3PbI3 or MAPbI3) and formamidinium (FA) lead iodide [HC(NH2)2PbI3 or FAPbI3]. HPs are the most promising materials for next-generation photovoltaic technologies, as reflected by their rapidly rising power conversion efficiency (PCE): It reached ∼25%1 only seven years after the invention of the state-of-the-art PSC architecture in 2012 (PCE ∼10%).2,3 HPs are also promising for light emitting diodes, lasers, and photodetectors.4–6 Their outstanding properties for optoelectronic applications include optimal bandgaps, excellent absorption in the visible range of the solar spectrum, exceptional transport properties for both electrons and holes, flexibility of composition engineering, and low cost in both materials and fabrication.7–12 

Despite the rapid PCE improvement in the laboratory, stability issues limit the development and commercialization of HPs for real photovoltaic applications. Especially, the organic components in hybrid perovskites are susceptible to ambient conditions such as moisture, oxygen, and heat, and exposure leads to rapid performance degradation.13–19 Several approaches have been proposed to solve these pressing stability problems, including surface protection with organic long-chain ligands,20–22 synthesis of quasi-two-dimensional perovskites,23–28 protective coating with inorganic semiconductors or insulators,29–32 and A-site substitution with smaller monovalent ions.18,33–39

In the context of A-site substitutions, the all-inorganic perovskite CsPbI3 and its mixed-halide derivatives have emerged as a promising alternative to the hybrid MA- and FA-based perovskites. CsPbI3 has a similar structure and slightly closer Pb–I packing and higher thermal and chemical stabilities than MAPbI3 and FAPbI3.11,40 The latest PCE of CsPbI3-based PSCs has already reached 18%,41 but more material design and device engineering are needed to increase the conversion efficiency and the operational stability. This applies to several aspects, such as morphology control of the HP thin films, interface engineering between CsPbI3 and interlayer materials, and the passivation of intrinsic defects at the interfaces and grain boundaries, which act as nonradiative recombination centers, thus degrading the device efficiency. A comprehensive understanding of the atomic and electronic structure of CsPbI3 surfaces would advance its development as a PSC photoabsorber. The surfaces of MA- and FA-based perovskites have been investigated theoretically42–45 and experimentally.46–51 For CsPbI3, however, we are only aware of bulk defect studies.52–55 The surfaces and interfaces of CsPbI3 have not yet been considered.

In this work, we present first-principles density functional theory (DFT) calculations for the reconstructed surfaces of the photovoltaic-active α (cubic) and γ (orthorhombic) phases of CsPbI3. Starting from the pristine (clean) surface models with CsI- and PbI2-terminations (denoted by CsI-T and PbI2-T, respectively), constituent elements (Cs, Pb, and I) as well as their complexes (CsI, PbI, and PbI2) were added to or removed from the surface. The thermodynamic stability of these surface models will be investigated with surface phase diagram (SPD) analysis for different chemical environments by means of ab initio thermodynamics.56–58 For the stable surface models, we calculated their electronic structure and elucidated changes in their electronic properties in comparison to the clean surfaces.

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 CsPbI3 as well as the CsI-T and PbI2-T surfaces. In Sec. III, we first analyze the stability of the clean-surface models (CsI-T and Pb2-T) and the reconstructed models with missing- and add-atoms (and their complexes). We then discuss changes in crystal structures due to missing- and add-atoms with focus on their stability and their atomic and electronic structures. Finally, we conclude with a summary in Sec. V.

All DFT calculations were performed using the Perdew–Burke–Ernzerhof exchange-correlation functional for solids (PBEsol)59 implemented in the all-electron numeric-atom-centered orbital code FHI-AIMS.60–62 We chose PBEsol because it describes the lattice constants of CsPbI3 well at moderate computational cost.63,64 Scalar relativistic effects were included by means of the zeroth-order regular approximation.65 We used standard FHI-AIMS tier two basis sets for all calculations, in combination with a Γ-centered 4 × 4 × 4 and a 4 × 4 × 1 k-point mesh for the bulk materials and the surface calculations with a slab model, respectively. The bulk structures were optimized with the analytical stress tensor.66 For the slab models, we fixed the the lattice constants and all atomic positions except for atoms in the top and bottom CsPbI3 units (the surface atoms). Surface-dipole correction67 was used in all surface calculations.

1. Bulk and surface structures

In this work, we considered two experimentally accessible photovoltaic-active perovskite phases of CsPbI3: the α (cubic) phase with space group Pm3̄m and the γ (orthorhombic) phase with space group Pnma. For each phase, we constructed and optimized a 2 × 2 × 2 bulk supercell with DFT (structures shown in Fig. 1). The lattice parameters of our optimized α phase are a = b = c = 12.47 Å and α = β = γ = 90°. For the γ phase, the lattice parameters are a = b = 12.21 Å, c = 12.35 Å, and α = β = 90°, γ = 85.8°.

FIG. 1.

Bulk crystal structures of the α (cubic) and the γ (orthorhombic) phases of CsPbI3. Cs, Pb, and I are colored in green, black, and purple, respectively. The PbI6 octahedra are colored in dark gray.

FIG. 1.

Bulk crystal structures of the α (cubic) and the γ (orthorhombic) phases of CsPbI3. Cs, Pb, and I are colored in green, black, and purple, respectively. The PbI6 octahedra are colored in dark gray.

Close modal

For each phase, we constructed the surface models by inserting a vacuum region in the [001] direction of the investigated system. With a 30 Å vacuum thickness and the inclusion of surface-dipole correction,67 we minimized the interaction between neighboring slabs. In this work, we focused on the (001) surfaces, which are the major facet of halide perovskites42,43,68 and the most relevant surfaces of CsPbI3. We carried out DFT calculations for CsPbI3 surfaces with symmetric slab models for CsI-T and PbI2-T surfaces. As depicted in Fig. 2, the CsI-T surface model consists of five CsI and four PbI2 layers alternatively stacked along the [001] direction. Similarly, the PbI2-T surface model has five PbI2 and four CsI alternating layers. To remove quantum confinement effects from the band structure, we performed slab-model calculations with up to 5 additional CsPbI3 layers before and after relaxation.

FIG. 2.

Relaxed CsI-T and PbI2-T clean-surface models of the α and the γ phases. Depicted are the CsI-T on the left and the PbI2-T termination on the right.

FIG. 2.

Relaxed CsI-T and PbI2-T clean-surface models of the α and the γ phases. Depicted are the CsI-T on the left and the PbI2-T termination on the right.

Close modal

For both CsI-T and PbI2-T surface models, we studied different missing- and add-atom reconstructions. The missing- and add-atoms are labeled as vX and iX, respectively, with X indicating the atoms or their complexes. All add-atoms and their complexes were added to the surfaces, while missing-atoms were removed from the topmost layers containing those atoms. For instance, vCs, vI, and vCsI of CsI-T surfaces were constructed by removing atoms from the topmost CsI layer, while vPb, vPbI, and vPbI2 indicate the removal of atoms from the PbI2 layer below the topmost CsI layer.

The 2 × 2 surface unit cell allows us to study 26 reconstructed surface models each for CsI-T and PbI2-T. In detail, these amount to 13 missing-atom or missing-complex models and 13 add-atom or add-complex structures, as listed in Table I. For double missing- and add-atoms (i.e., v2X and i2X), we considered both line and diagonal options (i.e., removing two iodine atoms along the [100] or [110] directions for v2I). We found no significant total-energy differences between these two modes. Hence, we only present results from the diagonal modes in this paper.

TABLE I.

CsI-T and PbI2-T surface models in the α and the γ phases.

CsI-TPbI2-T
vCs iCs vCs iCs 
v2Cs i2Cs v2Cs i2Cs 
v4Cs iI vI iI 
vI i2I v2I i2I 
v2I iPb vPb iPb 
vPb i2Pb v2Pb i2Pb 
v2Pb iCsI v4Pb iCsI 
vCsI i2CsI vCsI i2CsI 
v2CsI i4CsI v2CsI iPbI 
vPbI iPbI vPbI i2PbI 
v2PbI i2PbI v2PbI iPbI2 
vPbI2 iPbI2 vPbI2 i2PbI2 
v2PbI2 i2PbI2 v2PbI2 i4PbI2 
CsI-TPbI2-T
vCs iCs vCs iCs 
v2Cs i2Cs v2Cs i2Cs 
v4Cs iI vI iI 
vI i2I v2I i2I 
v2I iPb vPb iPb 
vPb i2Pb v2Pb i2Pb 
v2Pb iCsI v4Pb iCsI 
vCsI i2CsI vCsI i2CsI 
v2CsI i4CsI v2CsI iPbI 
vPbI iPbI vPbI i2PbI 
v2PbI i2PbI v2PbI iPbI2 
vPbI2 iPbI2 vPbI2 i2PbI2 
v2PbI2 i2PbI2 v2PbI2 i4PbI2 

In pursuit of open materials science,69 we made the results of all relevant calculations available on the Novel Materials Discovery (NOMAD) repository.70 

For a system in contact with a particle reservoir and neglecting finite temperature contributions, the thermodynamic stability of a structure is obtained from the grand potential, Ω,

ΩEixiμi.
(1)

Here, μi is the chemical potential of species i and xi is the number of atoms of this species in the structure. The sum over i runs over all elements in the compound. The relative stability between two systems in contact with the same particle reservoir is determined by differences in Ω with ΩA < ΩB indicating that phase A is more stable than phase B. A special case of Ω is when a system is in contact with its constituent species in their most stable phase. This defines the standard formation energy, which is denoted by ΔH hereafter,

ΔH=Eixiμio.
(2)

Here, μio indicates the chemical potential of species i in its most stable form. The thermodynamic stability condition ΔH < 0 states that the system’s total energy must be lower than the sum of its constituents’ chemical potentials, each in their most stable phase.

The chemical potentials μi are set by environmental conditions. We apply a simple transformation to the chemical potentials,

Δμi=μiμio,
(3)

to introduce the parameter Δμi. Δμi is the change in the chemical potential away from its value in the element’s most stable phase, μio. Δμi represent environmental growth conditions and are a convenient parameter to vary in order to map phase diagrams. The grand potential can be rewritten as

Ω=EixiμioixiΔμi.
(4)

The relative stability condition between phases A and B is then

ΩA<ΩB,
(5)

which can be rearranged as

EAixiAμioEBixiBμio<i(xiAxiB)Δμi.

We recognize ΔH for phases A and B,

ΔHAΔHB<i(xiAxiB)Δμi.
(6)

The inequality given in Eq. (6) is the basis for the phase diagram, including the SPDs in this work. We calculate ΔH using the DFT total energy of the surface for E and the DFT total energy per species unit for μio. For the specific case of a surface formation energy, ΔH reduces to

ΔHsurf=EsurfEbulkEads
(7)

for surface total energy Esurf, bulk total energy Ebulk, and the total energy of any adsorbants Eads. With the various total energies tabulated from DFT calculations, we plot an SPD based on the inequalities in Eq. (6) as a function of the parameters Δμi.

We first consider conditions for stable CsPbI3 in the bulk. In order to avoid the formation of elementary Cs, Pb, and I as well as bulk CsI and PbI2, the region of the phase diagram for stable CsPbI3 is determined by the inequalities,

ΔH(CsPbI3)ΔμCs0,ΔH(CsPbI3)ΔμPb0,ΔH(CsPbI3)3ΔμI0
(8)

and

ΔH(CsPbI3)ΔμCs+ΔμPb+3ΔμI,
ΔμCs+ΔμIΔH(CsI),
(9)
ΔμPb+2ΔμIΔH(PbI2).

The inequalities in Eq. (9) can be rearranged as

ΔH(CsPbI3)ΔμCs+ΔμPb+3ΔμI,
ΔH(CsPbI3)ΔH(CsI)ΔμPb+2ΔμIΔH(PbI2),
(10)
ΔH(CsPbI3)ΔH(PbI2)ΔμCs+ΔμIΔH(CsI).

μCso, μPbo, and μIo are calculated for the stable structures of Cs (I43̄m), Pb (P63/mmc), and I (I2 molecule). Equations (8) and (10) are the conditions for stable CsPbI3. Formation energies ΔH for Eqs. (8) and (10) are calculated with DFT. Varying the three parameters ΔμCs, ΔμPb, and ΔμI maps the bulk stability region.

To compare the stability of two surfaces, we solve Eq. (6) to obtain the SPDs. Equation (6) is a condition for surface stability in addition to Eqs. (8) and (10), which are only for the bulk. The bulk and surface are not in isolation from each other. For this reason, the final surface stability is determined by overlaying the SPD on the bulk stability region. We consider the overlap of the stable bulk region with the SPD to be the predictor of a viable bulk and surface together.

In this section, we present the results from our thermodynamic analysis, compare the stability of our surface termination models (CsI-T vs PbI2-T), and analyze the most relevant terminations using SPDs. We conclude the section with the electronic properties of the bulk and most relevant reconstructed surface models.

The PBEsol-calculated formation energies of bulk CsI, PbI2, α-CsPbI3, and γ-CsPbI3 are −3.40, −2.47, −5.89, and −6.02 eV, respectively. From Eq. (10), the thermodynamic growth limits for bulk CsPbI3 in the α and the γ phases at ΔμCs = 0 then are

2.49 eVΔμPb+2ΔμI2.47 eV forα,2.62 eVΔμPb+2ΔμI2.47 eV forγ.
(11)

Similarly, the growth limits for bulk CsPbI3 at ΔμPb = 0 in the α and the γ phases are

3.42 eVΔμCs+ΔμI3.40 eV forα,3.55 eVΔμCs+ΔμI3.40 eV forγ.
(12)

The small difference between the left and the right values of these inequalities indicates the narrow stability region of bulk CsPbI3. The stability window in the α phase is especially small, only ∼0.02 eV. For each phase, the width of this region equals the energy required for CsPbI3 to decompose into CsI and PbI2. Therefore, the narrow energy range for the growth of bulk CsPbI3 reflects the instability and ease of dissociation of CsPbI3 into CsI and PbI2, as alluded to in Sec. I.

Figure 3 depicts the SPDs for the CsI-T and PbI2-T clean surfaces in the α and the γ phases at ΔμCs = 0. The stable bulk region is represented with the yellow shading. The CsI-T and PbI2-T surfaces are stable in different regions. Since the CsI-T surface intersects the stable bulk region, we consider it more stable in conditions for bulk growth. Additionally, we observe stable CsI-T surfaces across a wider range of Δμk (k = Cs, Pb, I) than PbI2-T surfaces. The results of Fig. 3 are similar to the findings of previous theoretical studies for MAPbI342,43,71,72 on the stability of methylammonium-iodide terminated over PbI2-T surfaces. Our discussions will therefore focus on CsI-T surfaces from here on. The data for PbI2-T surfaces including the relaxed surface-reconstruction structures and the SPDs are given in the supplementary material.

FIG. 3.

Thermodynamic growth limit for CsI-T and PbI2-T surfaces in the α and the γ phases at ΔμCs = 0. The yellow shaded regions depict the thermodynamically stable range for the growth of bulk CsPbI3.

FIG. 3.

Thermodynamic growth limit for CsI-T and PbI2-T surfaces in the α and the γ phases at ΔμCs = 0. The yellow shaded regions depict the thermodynamically stable range for the growth of bulk CsPbI3.

Close modal

1. Surface phase diagrams of CsI-T surface models

Figure 4 shows the SPDs for the considered surface reconstructions of the CsI-T surfaces (SPDs of PbI2-T reconstructed models are given in Fig. S5 of the supplementary material). In principle, we need to plot the SPD in three dimensions (3D) because it depends on three chemical potentials: ΔμCs, ΔμPb, and ΔμI. Since such a 3D diagram is hard to visualize, we present two 2D slices instead, one ΔμIμCs slice at ΔμPb = 0 and one ΔμIμPb slice at ΔμCs = 0. The left side of Fig. 4 shows the SPDs at ΔμPb = 0, and the right side shows ΔμCs = 0. The vertical panels show the α and the γ phases, respectively. ΔμI is plotted on the vertical axis, and the other chemical potential is plotted on the horizontal axis. The colored regions and their labels indicate the most stable surface at that pair of chemical potentials. The yellow shaded region again depicts the growth limit for stable bulk CsPbI3, which serves as our reference to determine the most relevant surface models. We have also performed reference calculations with the PBE functional73 (see Fig. S1 of the supplementary material). The SPDs in PBE and PBEsol are almost identical, which demonstrates that PBEsol is appropriate for surface reconstructions.

FIG. 4.

Surface phase diagrams of reconstructed CsI-T surfaces with missing- and add-atoms as well as their complexes (upper panel for the α phase and lower panel for the γ phase). The yellow regions depict the thermodynamically stable range for the growth of bulk CsPbI3.

FIG. 4.

Surface phase diagrams of reconstructed CsI-T surfaces with missing- and add-atoms as well as their complexes (upper panel for the α phase and lower panel for the γ phase). The yellow regions depict the thermodynamically stable range for the growth of bulk CsPbI3.

Close modal

For the α phase (Fig. 4 upper panel), we find the following stable surface structures at some point in the phase diagram in the Pb-rich limit (ΔμPb = 0): v4Cs, vCsI, v2CsI, vPbI2, v2PbI2, i4CsI, iPbI2, i2PbI2, and the clean surface. In the Cs-rich limit (ΔμCs = 0), we instead find v2PbI2 and i4CsI. The situation for the γ phase is very similar. The extent of some of the stability regions changes slightly from α to γ, and the vCsI reconstruction disappears from the phase diagram (lower panel of Fig. 4).

With the exception of v4Cs, all the observed reconstructions are valence-neutral, i.e., with addition or removal of valence-neutral units such as CsI or PbI2. Here, valence-neutral units refer to added or removed complexes that do not induce “net charges” on CsPbI3 as a whole. The addition or removal of valence-neutral units is energetically more favorable than that of single atoms or non-valence-neutral complexes because it does not introduce free charge carriers, as we will demonstrate in Sec. III B. As expected, we observe Cs-deficient reconstructed models (v4Cs, vCsI, v2CsI) for low ΔμCs and Cs-rich ones (i4CsI) at the high ΔμCs region. A similar trend is observed for low and high Pb chemical potentials. A notable exception is the stability of i4CsI in the Pb-rich region in the upper right panel. Since the Cs chemical potential is at a maximum, the Cs-rich, i4CsI reconstruction dominates over Pb add-atom structures.

Of particular relevance to us are the surface reconstructions that intersect the bulk stability region (yellow region). These stable reconstructions that intersect the bulk region are the same for the α and the γ phases. In addition to the clean CsI-T surface, we find only the valence-neutral surface reconstructions v2PbI2, v2PbI2, iPbI2, i2PbI2, and i4CsI. It is noteworthy that although the clean surface occupies quite a broad stability region for ΔμPb = 0, it is only stable if the growth conditions are I-deficient and not at all in Cs-rich conditions.

2. Atomic structures of the most relevant surface reconstructions

Figure 5 shows the relaxed geometries of the most relevant surface models (clean, vPbI2, v2PbI2, iPbI2, i2PbI2, and i4CsI) for the α and the γ phases. The remaining surface structures are shown in Fig. S2. The clean surface does not exhibit any significant deviations from the bulk atomic positions after relaxation. Hence, all changes in the reconstructed structures will be discussed with reference to the clean surface hereafter.

FIG. 5.

Atomic structures of the most relevant surface reconstructions for the α phase (upper panel) and the γ phase (lower panel). The surface Pb and I atoms that exhibit pronounced displacements are highlighted by red and blue colors, respectively. The pink circles denote added Cs atoms.

FIG. 5.

Atomic structures of the most relevant surface reconstructions for the α phase (upper panel) and the γ phase (lower panel). The surface Pb and I atoms that exhibit pronounced displacements are highlighted by red and blue colors, respectively. The pink circles denote added Cs atoms.

Close modal

In all reconstructions, we observe changes in the surface layer that translate into slight tilting of the surface octahedra. For instance, the surface octahedra in vPbI2 for both phases tilt to account for the missing PbI2 units. Similarly, the surface octahedra of iPbI2 and i2PbI2 tilt to accommodate the added PbI2. In addition to the tilting, other slight changes in the atomic positions are observed. For example, the Cs–I bond lengths in the surfaces of i4CsI for both phases vary by ∼0.1 Å. To highlight the changes in atomic positions, Cs, Pb, and I atoms of interest in Fig. 5 are depicted in pink, red and blue, respectively.

A more drastic change occurs for v2PbI2 in the α phase. The migration of I atoms within the surface layer leads to an asymmetric distribution of them, causing the formation of separate PbI5 and PbI4 polyhedra in the surface layer. This structure is similar to the findings of Haruyama et al. for MAPbI3,42,43,74 in which they observed the formation of PbI3–PbI5 polyhedra upon the removal of “one-half” of the PbI2 units from the PbI2-T surfaces. Interestingly, we do not see the same atomic rearrangement for v2PbI2 in the γ phase. Instead, we find a relatively symmetric I distribution and two isolated PbI4 polyhedra. The different behavior in the α phase is likely due to the larger lattice constant, which results in a larger Cs–Cs distance and a weaker binding of I atoms.

I migration is also observed in the i2I reconstruction of both phases and v4Cs of the γ phase (see Fig. S2 of the supplementary material). In each case, two I atoms move close to each other such that their distance is close to that of an I2 molecule.75 Specifically, the I–I distance in v4Cs is reduced to ∼2.9 Å. Similarly, the I–I distance of the added I atoms in i2I reduces to ∼2.9 Å in the α phase and ∼2.8 Å in the γ phase. These values are close to the experimental bond length (∼2.67 Å) of the I2 molecule in the gas phase,75 albeit a bit larger since the surface I atoms are bound to other surface atoms such as Cs and Pb, thus reducing the bond strength of I–I. Experimentally, the formation of I2 on the surface facilitates the degradation of MAPbI3 and FAPbI3,76,77 while its effect on the stability of CsPbI3 is yet unknown.

In this section, we discuss the electronic properties of bulk CsPbI3, the clean surfaces in the α and the γ phases, and the relevant reconstructions reported in Figs. 4 and 5.

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

Figure 6 depicts the band structures of the bulk and the clean CsI-T surfaces of the α and the γ phases. For the bulk of both phases, we adopt the high-symmetry k-point path in the Brillouin zone for a simple-cubic lattice of the 2 × 2 × 2 supercell model for simplicity. In addition, we only 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]. Accordingly, we plot the band structure of the 2 × 2 surface unit cells of both phases along the same high-symmetry k-point path for an easy comparison. The valence band maximum (VBM) in all plots is set to zero. In the band structure plots of the surface models, the projected bulk band structure is included as a blue-shaded background to help identify possible surface states.78,79

FIG. 6.

Band structures of bulk CsPbI3 and the clean surfaces (with and without geometry relaxation) in the α (upper panel) and γ (lower panel) phases. 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. As shown in the Brillouin zone (far right), the in-plane k-point path for the bulk is the same as the surface. The 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. 6.

Band structures of bulk CsPbI3 and the clean surfaces (with and without geometry relaxation) in the α (upper panel) and γ (lower panel) phases. 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. As shown in the Brillouin zone (far right), the in-plane k-point path for the bulk is the same as the surface. The 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

In both phases, bulk CsPbI3 exhibits a direct bandgap at the Γ point. The charge densities (shown in Fig. 7) reveal that the VBM of CsPbI3 in both phases is dominated by I-5p orbitals with a noticeable contribution from the Pb-6s orbitals, which gives rise to the well known antibonding character.42,43,53,80 The conduction band maximum (CBM) mainly consists of Pb-6p orbitals.

FIG. 7.

Charge distribution of the VBM and CBM of bulk CsPbI3 and the CsI-T clean surfaces for (a) the α and (b) the γ phase.

FIG. 7.

Charge distribution of the VBM and CBM of bulk CsPbI3 and the CsI-T clean surfaces for (a) the α and (b) the γ phase.

Close modal

Next, we investigate if the CsI termination introduces surface states. The middle panels of Fig. 6 show the band structure of the two unrelaxed CsI-T models. The bands of the supercell coincide with the projected bulk band structure, which indicates that no surface states appear. However, upon relaxation, the bottom of the conduction band is pulled into the bulk bandgap for the α phase but not for the γ phase, as can be seen in the right most band structure panels in Fig. 6. The clean surface of the α phase therefore exhibits a surface state that derives from the CsPbI3 conduction band. This is further evidenced in Fig. 7, which shows that the lowest conduction band resides at the surface and has a Pb-6p character. In contrast, the corresponding state in the γ phase is quite clearly a bulk state and not a surface state.

2. Electronic properties of most relevant reconstructed CsI-T surface models

Figure 8 shows the band structures of the most relevant surface models observed in Fig. 4, i.e., vPbI2, v2PbI2, i4CsI, iPbI2 and i2PbI2. Similar to Fig. 6, the bulk band structure is included as the background for comparison.

FIG. 8.

Band structures of the most relevant reconstructed CsI-T surface models in the α and the γ phases. The legends follow Fig. 6.

FIG. 8.

Band structures of the most relevant reconstructed CsI-T surface models in the α and the γ phases. The legends follow Fig. 6.

Close modal

Figure 8 displays a similar pattern as Fig. 6, i.e., the most notable changes in the band structure of the surface models appear for the α phase near the bottom of the conduction band. For neither phase, do we observe perturbations of the VBM region. Further inspection of the charge distributions of the valence-band-edge states shown in Fig. S3 of the supplementary material confirms that the VBM retains its bulk character for all relevant surface reconstructions.

For the reconstructed surface models of the α phase, we observe the same surface states as in the clean-surface model (Fig. 6). In addition, flat bands appear near or below the conduction band edge, which are most notable around the M-points of the band structure. The only exception is i4CsI, for which the surface band structure strongly resembles that of the clean CsI-T surface. The flat bands are especially pronounced in the vPbI2 and v2PbI2 models. Correspondingly, the states near the conduction band edge of these two surface reconstructions exhibit a more localized character than for the clean surface (compare the upper panel of Fig. S3 of the supplementary material with Fig. 7). For these surface models, the reconstruction therefore introduces additional surface states to the ones of the clean surface.

Our results offer guidance for growing favorable CsPbI3 surfaces. By favorable, we here imply surface reconstructions that have a bulk-like band structure and no additional states in the bandgap or perturbations of the band edges that might adversely affect the transport properties. Our analysis of Sec. III B 2 suggests that the γ phase of CsPbI3 is generally more suited for this purpose, as all of its stable surface reconstructions are free of band edge perturbations.

For the α phase, the objective would be to avoid both PbI2 deficient (vPbI2 and v2PbI2) and rich (iPbI2 and i2PbI2) reconstructions. Fortunately, the clean surface is stable across a wide range of the bulk stability region, as our surface phase diagram analysis shows. For Cs rich growth conditions, the i4CsI phase dominates the phase diagram. This phase provides a good alternative to the clean surface since its band structure resembles that of the clean surface closely.

In summary, we have studied the surface atomic and electronic structure of CsPbI3 from first-principles. For both the α (cubic) and the γ (orthorhombic) phases, we have considered the clean-surface models and a series of surface reconstructions. Surface phase diagram analysis indicates that the CsI-terminated (001) surface is more stable within a large range of allowed chemical potentials for both phases. In addition, several CsI and PbI2 rich and deficient surface reconstructions are stable. These surface reconstructions do not induce deep energy levels in the bandgap. Nevertheless, the removal of PbI2 units in the CsI-terminated α-CsPbI3 surface has noticeable effects on the material’s electronic structure, especially close to the conduction band edge. Combining our surface-phase diagram and electronic structure analysis allows us to recommend growth regimes for CsPbI3 surfaces with favorable transport properties. Our work highlights the complexity of CsPbI3 surfaces and provides avenues for future surface science and interface studies.

See the supplementary material for CsI-T SPDs computed with PBE, charge density plots of all relevant surface models with CsI-termination, surface phase diagrams of PbI2-terminated models, crystal structures of studied surface models in both CsI-T and PbI2-T (that are not included in the main text), the formation energies of all surface models, and the evaluation of the effect of spin–orbit coupling.

We acknowledge the computing resources by the CSC-IT Center for Science, the Aalto Science-IT project, and Xi’an Jiaotong University’s HPC Platform. An award of computer time was provided by the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program. This research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract No. DE-AC02-06CH11357. We further acknowledge funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 676580 [The Novel Materials Discovery (NOMAD) Laboratory], the Väisälä Foundation as well as the Academy of Finland through its Centres of Excellence Programme (Grant No. 284621), its key project funding scheme (Grant No. 305632), and Project No. 316347.

The data that support the findings of this study are openly available in the Novel Materials Discovery (NOMAD) repository.70 

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