Putting the Squeeze on Lead Iodide Perovskites: Pressure-Induced Effects To Tune Their Structural and Optoelectronic Behavior.

Lattice compression through hydrostatic pressure has emerged as an effective means of tuning the structural and optoelectronic properties of hybrid halide perovskites. In addition to external pressure, the local strain present in solution-processed thin films also causes significant heterogeneity in their photophysical properties. However, an atomistic understanding of structural changes of hybrid perovskites under pressure and their effects on the electronic landscape is required. Here, we use high level ab initio simulation techniques to explore the effect of lattice compression on the formamidinium (FA) lead iodide compound, FA1-x Cs x PbI3 (x = 0, 0.25). We show that, in response to applied pressure, the Pb-I bonds shorten, the PbI6 octahedra tilt anisotropically, and the rotational dynamics of the FA+ molecular cation are partially suppressed. Because of these structural distortions, the compressed perovskites exhibit band gaps that are narrower (red-shifted) and indirect with spin-split band edges. Furthermore, the shallow defect levels of intrinsic iodide defects transform to deep-level states with lattice compression. This work highlights the use of hydrostatic pressure as a powerful tool for systematically modifying the photovoltaic performance of halide perovskites.

Introduction

Organic–inorganic perovskite solar cells have shown an unprecedented increase in power conversion efficiency, exceeding 23% over the past few years.[1−9] The most common three-dimensional lead iodide perovskites have the composition APbI3, where A is a monovalent cation (e.g., methylammonium CH3NH3+ (MA+), formamidinium CH(NH2)2+ (FA+), or cesium Cs+), which fills the cuboctahedral cage formed by corner-sharing PbI6 octahedra. Various compositional engineering approaches, particularly alloying differently sized organic and inorganic cations, significantly enhance the stability of these solar cells.[10−16] In this regard, the substitution of Cs+ cations (up to 25%) for the relatively larger FA+ cations in FAPbI3 stabilizes the perovskite phase, increasing its resistance to chemical degradation.[11,13−16] Because of their enhanced structural stability, as well as improved photovoltaic properties, these mixed-cation perovskites are currently the most promising materials for perovskite solar cells.

Recently, the application of hydrostatic pressure has emerged as an effective means of tuning the structural phases and photovoltaic properties of hybrid perovskites.[17−23] Under pressure, the crystal structure of these materials evolves through several structural phases that are inaccessible by temperature variation. In addition, applied pressure reveals novel properties of halide perovskites by influencing their energetic landscapes and charge-carrier dynamics. The optimized band gap, increased charge-carrier lifetimes, reduced trap-state densities, and tuned carrier conductivities collectively result in improved photovoltaic performance in compressed halide perovskites.[20−22] Solution-processed polycrystalline thin films of halide perovskites often experience significant local strain.[24,25] The experimentally observed spatial heterogeneity of the optoelectronic and photoluminescence properties of these films are speculated to be closely connected to the local strain in the perovskites.[26−29] It is clear, however, that an in-depth atomistic understanding of the structural and optoelectronic properties of lead halide perovskites under pressure has yet to be established.

Our recent studies have focused on defect migration, compositional engineering, and environmental stability of hybrid halide perovskites.[30−39] Here we investigate the structural, optoelectronic, and defect properties of FAPbI3 and the mixed-cation FA0.75Cs0.25PbI3 under hydrostatic pressure using ab initio simulation methods. Our study shows that the valence band maxima shift to a higher energy with applied pressure, indicating improved energetic alignment between the perovskite absorber and the hole collecting organic layers, which would improve solar cell performance. Conversely, under high pressure the iodide vacancies can form deep trap levels, limiting the efficiency of the cell. Our results highlight that applied pressure can be an effective tool to tune electronic landscapes and access novel optical properties in these hybrid perovskites, which would otherwise be unachievable at ambient conditions.

Methods

Density functional theory (DFT)-based ab initio simulations were performed using the Vienna Ab Initio Simulation Package (VASP).[40,41] The generalized gradient approximation (GGA) was considered with the Perdew–Burke–Ernzerhof functional (PBE) form.[42] The plane-wave basis set, scalar relativistic pseudopotentials, and projected augmented wave (PAW)[43] methods were employed for all simulations. The nonlocal exchange-correlation functionals optB86b-vdW[44] and a 3 × 3 × 3 Γ-centered Monkhorst–Pack[45] sampling mesh with a plane wave cutoff of 520 eV were considered for structural optimizations, where all interatomic forces were <0.01 eV Å–1. These perovskite lattices were further optimized under static hydrostatic pressures of up to 3 GPa, which are typical experimental values.[17−23] A 2 × 2 × 2 (8 A cations) supercell of the parent FAPbI3 was considered for all the simulations. A 6 × 6 × 6 Γ-centered k-point mesh with a Gaussian smearing of 0.01 eV was used for Brillouin zone integrations for the electronic structure calculations. The electronic structure was further corrected by introducing spin–orbit coupling (SOC) and screened hybrid functionals, as implemented by Heyd–Scuseria–Ernzerhof (HSE06) self-consistently.[46] The HSE06 functionals include 25% of Hartree–Fock exchange with the empirical range-separation parameter ω = 0.11 bohr–1. For the band structure calculations, only SOC corrections have been considered as HSE functionals have an insignificant effect on band-edge dispersion.[47] The frequency-dependent dielectric function was calculated within the random phase approximation with a Γ-centered 4 × 4 × 4 k-point mesh.[48] The imaginary part of this function was used to evaluate the optical response of the materials. The defect formation energies and transition levels were calculated using a 4 × 4 × 1 supercell (16 A cations) while keeping all other relevant computational parameters unchanged. The Python Materials Genomics (Pymatgen)[49] and Python Charged Defect Toolkit (PyCDT) codes[50] libraries were used for input preparation and data analysis. Further computational details are included in the Supporting Information (section S1).

To explore the effects of external pressure at room temperature, ab initio molecular dynamics simulations were performed as implemented in the CP2K package.[51] To investigate structural dynamics reliably, a large cell of 64 units (4 × 4 × 4 supercell) of FAPbI3 was considered. The dispersion corrections, as formulated by Grimme (DFT-D3),[52] and the QUICKSTEP module[53] with analytical dual-space pseudopotentials[54] were employed. The Nosé–Hoover thermostat and barostat[55] were used to evaluate the equilibrium dynamics under the NPT ensemble. The dynamics were performed for 40 ps with a time step of 1 fs where the first 5 ps was considered as the equilibration time.

Results and Discussion

Structural Distortion and Dynamics

The fully optimized structure of FAPbI3 deviates from the high-symmetry cubic phase and exhibits a tetragonal distortion with an elongated c lattice parameter (see section S2 of the Supporting Information for a detailed discussion). A-cation mixing in FA0.75Cs0.25PbI3 causes further tetragonal distortion due to the internal chemical pressure creating lattice strain that arises from the FA/Cs ion size mismatch. Structural modifications to the parent lattice with A-cation mixing is consistent with previous experimental and computational studies.[14,15,31,39] By investigating the mechanical properties, we find that FAPbI3 has a bulk modulus (K0) of 16.5 GPa, indicating a much softer lattice than typical ceramic oxide perovskites (K0 > 100).[56] Notably, in FA0.75Cs0.25PbI3, the lattice stiffens with an increase of K0 to 20 GPa. Such lattice stiffening by A-cation mixing has been found to reduce nonradiative carrier recombination in MAPbI3 doped with FA and guanidinium cations.[57]

Recent in situ synchrotron X-ray diffraction-based studies report the loss of crystallinity and amorphization of FAPbI3 under hydrostatic pressure >4 GPa.[22] Thus, we restrict our study to values up to 3 GPa. Under pressure, the FA0.75Cs0.25PbI3 lattice contracts in volume with an isotropic reduction in all lattice parameters, as shown in Figure a. This contraction leads to a distortion of PbI6 octahedra through an isotropic shortening of the Pb–I bonds in all three Cartesian planes (Figure b). Unlike the bond lengths, the average Pb–I–Pb bond angles are anisotropic across different planes (Figure c). The PbI6 octahedra in the tetragonally distorted FA0.75Cs0.25PbI3 rotate primarily along the c-axis, and the Pb–I–Pb bond angles show a maximum deviation in the ab-plane from 180°. In response to hydrostatic pressure, the octahedral tilting along the c-axis increases, and this consequently introduces greater anisotropic angle distortion (Figure c). The PbI6 octahedra adjacent to each other tilt in the same direction, showing an “in-phase” rotation.[58] The anisotropic distortions of bond angles under pressure from our simulations are in good agreement with the in situ synchrotron X-ray diffraction study of FAPbI3.[22] Detailed comparisons between available experimental and computational data are given in the Supporting Information (Table S1). Therefore, the PbI6 octahedral rotation, rather than Pb–I bond contraction, results in the internal anisotropy in these compressed perovskite structures. We note that there are limited experimental reports on pressure-induced structural changes or phase transitions of FAPbI3. X-ray diffraction studies of Liu et al.[21] reported no evidence of a phase transition in FAPbI3 up to 7 GPa pressure. More recent studies[22,59] report phase transitions of FAPbI3 from cubic to other phases under pressure. However, the crystal systems under high pressure differ between these two studies; Wang et al.[22] find cubic to orthorhombic phase (Imm2 and then Immm) transitions whereas Jiang et al.[59] report tetragonal (P4/mbm) and cubic phases (Im3̅) at high pressures. Therefore, there is a significant degree of uncertainty and complexity regarding the exact high-pressure structures of FAPbI3. This has resulted in our initial focus on the structural and electronic properties of the observed tetragonally distorted structure as a representative model phase; we recognize that other reported crystal structures at high pressure warrant future detailed investigation.

Figure 1

Pressure-induced structural distortions in FA0.75Cs0.25PbI3: (a) lattice parameters, (b) averaged Pb–I bond distances, and (c) Pb–I–Pb angles averaged over three Cartesian planes, with a schematic of the angles shown in the inset. Interpolated dotted lines in the plots are guides for the eye. Key: lead (brown) and iodine (pink).

Recent studies report strong correlation between the lattice dynamics and photovoltaic properties of these materials.[60−62] To probe the effect of external pressure only, we chose to focus on the dynamics of FAPbI3. Our recent work[31,39] and other studies[63,64] have investigated A-cation dynamics and their interactions with the inorganic Pb/I frame to find their combined effect on the structural phase stability and solar cell device performance. To explore the influence of external pressure on such dynamics, we calculate the vector reorientational autocorrelation function of the cations from ab initio molecular dynamics trajectories (Figure a). The molecular axis is defined between the two nitrogen atoms of an FA cation (inset of Figure a). Reorientation of the molecular axis represents a slow “jumplike” rotation of FA cations among several equilibrium conformations.[65] This autocorrelation function evaluates the probability of the molecular axis remaining self-correlated over time. Thus, the fast decrease of the autocorrelation function of the N–N molecular axis indicates a rapid reorientation of the FA cations inside the Pb/I frame. Several techniques, such as solid-state nuclear magnetic resonance, quasi-elastic neutron scattering, and polarization-resolved two-dimensional spectroscopy, have been used to investigate these reorientational cation dynamics.[65−67]

Figure 2

Cation dynamics in FAPbI3. (a) Vector autocorrelation function of FA+ exhibiting the time correlation of the molecular vector (shown in the inset with a red arrow) of the cation and (b) different vibrational modes of N–H bonds of FA+. (c) Bending and (d) symmetric and asymmetric stretching of N–H bonds. Inset of (d) shows the shift in the vibrational peaks upon lattice compression more clearly. Key: hydrogen (white), carbon (cyan), and nitrogen (blue).

As shown in Figure a, the autocorrelation function for FA+ decreases nonexponentially for FAPbI3 with and without the application of external pressure. Thus, the simulations demonstrate the dynamical coupling between the FA+ cation and the inorganic lattice. Under pressure, the reorientational dynamics of the FA+ are further suppressed, which is evident from the much slower decay of the function. To obtain the reorientational relaxation time of FA+ molecular cations, we fit these functions with a stretched exponential decay function (see section S3 in the Supporting Information for details). For FAPbI3 at 0 and 1.7 GPa, the relaxation times for FA+ are calculated as 8.8 and 88.1 ps, respectively, indicating the strong influence of external pressure on cation rotation. Raman scattering experiments have identified similar pressure-induced suppression of cation rotation in high-quality single crystals of MAPbI3.[68]

Under pressure, the FA+ molecules align their N–N molecular axis preferentially along the a- or b-axis (Figure S1). Such cation ordering in hybrid perovskites has also been found for their low-temperature phases.[69,70] As discussed in previous studies on FAPbI3, FA+ cations interact with the Pb/I frame through N–H···I hydrogen bonds.[22,71] These hydrogen bonds strengthen the H···I bonds and weaken the N–H bonds. In response, the N–H bending and stretching vibrational modes (Figure b) are red-shifted in the frequency ranges 1550–1625 and 3250–3550 cm–1, respectively (see Table S2 for all the peak values). With the compression of FAPbI3, these vibrational modes are further red-shifted in frequency, indicating a strengthening of the hydrogen bonds with applied pressure. At 1.7 GPa, the shifts are 5 and 10 cm–1 for the symmetric and asymmetric N–H stretching modes, respectively, and 9 cm–1 for the N–H bending mode. The simulated changes in the peak values of the vibrational frequencies with pressure match well with experimental infrared spectroscopy studies.[22] The reduced volume inside the Pb/I frame and suppressed FA+ dynamics allow the amino H atoms to stay spatially close to the iodide sites for longer, forming stronger N–H···I hydrogen-bonding interactions.

To summarize, the pressure-induced structural distortions have a major influence on the FA+ cation dynamics in halide perovskites. Stronger hydrogen bonds indicate enhanced dynamical coupling between the FA cation and inorganic Pb/I sublattices in compressed FAPbI3, which modifies the structural, electronic, and optical properties of these halide perovskites.

Tuning the Band Gap and Band Alignment

We now investigate the pressure-induced changes in the electronic properties of FAPbI3 and the mixed-cation FA0.75Cs0.25PbI3. With the application of pressure, the band gap decreases, exhibiting a red-shift in the absorption edge (Figure a, Figure S2, and Table S3). Thus, unlike many other semiconductors, these iodide perovskites exhibit a positive band deformation potential. We note that the underestimation of band gaps with respect to experimental values arise due to the partial consideration of many-body effects with PBE functionals, in good agreement with previous studies.[72] In addition, the calculated relative red-shift in the FAPbI3 band gap using the PBE functional agrees well with experimental reports[21] (see Table S3).

Figure 3

Change in electronic properties of FA0.75Cs0.25PbI3 with applied pressure. (a) Tuning of the band gap calculated with the HSE06 functional, including SOC corrections. (b) Modification in energy of conduction band minima (upper panel) and valence band maxima (lower panel). All band edge energies are scaled to the VBM under 0 GPa.

The alignment of the valence and conduction band edges of these perovskites with respect to the charge transport layers directly affects the extraction of photogenerated carriers from the absorber layer.[73,74] Following a well-developed method for band alignment[39,75,76] (as detailed in section S4 of the Supporting Information), we find that the valence band maximum (VBM) of FA0.75Cs0.25PbI3 shifts to a significantly higher energy by ≈0.20 eV with an applied pressure of 3 GPa. The conduction band minimum (CBM) also moves to high energy with increased pressure, but by only ≈0.08 eV. The band edges of the parent FAPbI3 show similar changes with applied pressure.

To understand the variation in the band gap and band edges with pressure, we examine the partial density of states and charge densities of the VBM and CBM. As shown in Figure (and Figures S3 and S4), the antibonding overlap between Pb 6s and I 5p orbitals form the VBM, whereas nonbonding Pb 6p orbitals with a very small contribution from I 5p generate the CBM in FA0.75Cs0.25PbI3 and FAPbI3. With the application of pressure, the Pb–I bond lengths shorten, and there is an increase in tilting of the PbI6 octahedra. The shorter Pb–I bonds increase the antibonding overlap between the Pb 6s and I 5p orbitals, increasing the energy of the valence band edge. This enhanced interaction between participating orbitals also increases the band dispersion in the VBM. In contrast, the tilting of the PbI6 octahedra lowers the Pb–I–Pb angles, which reduces the antibonding overlap in the VBM. Thus, the VBM energy should decrease due to increased octahedral tilting, as found in previous studies.[39,76,77] However, the shorter Pb–I bonds dominate over the distorted Pb–I–Pb angles, ultimately increasing the antibonding orbital overlap between Pb and I with applied pressure. The valence band edge consequently moves to a higher energy.

Figure 4

Electronic charge density of the VBM of FA0.75Cs0.25PbI3 under pressure of (a) 0 and (b) 2 GPa. Color code: red and blue depict 0 and 0.0001 eÅ–3, respectively. The white dashed lines indicate Pb–I bonds, the average distance of which is given.

With lattice compression, the band edge of the CBM also shifts to higher energy but to a smaller extent than the VBM. As the Pb–I bonds shorten under pressure, the I 5p orbitals overlap with Pb 6p nonbonding orbitals in CBM, increasing the covalency of the conduction band edge. The increase in covalency in the predominantly ionic conduction band results in a small upshift in its energy level. With a more covalent nature, the band dispersion of the CBM enhances under applied pressure. The charge density plots in Figure S5 further illustrate the enhanced covalent character of the conduction band under lattice compression. As the application of pressure largely shifts the VBM to a higher energy, the band gap of FA0.75Cs0.25PbI3 and FAPbI3 decreases. Our findings are in agreement with photoluminescence and ultraviolet photoelectron spectroscopy experiments.[21,22]

The photogenerated carriers in the absorber layer of solar cells are transferred and extracted by the energy level aligned with the charge transporting layer.[73,74,78] Energetic differences between the band edge levels create an energy offset at the interface that leads to a reduction in the built-in potential, which reduces the open circuit voltage (Voc) and fill factor. The interface between commonly used hole transporting layers (i.e., spiro-OMeTAD and PEDOT:PSS) and halide perovskites (i.e., MAPbI3, FAPbI3 and their mixed phases) generally exhibit band offset energies in the range 0.2–1 eV.[78] A reduction in this band offset energy would lead to an increase in the power conversion efficiency. Typically, the modification of the hole transporting layers by chemical doping has been explored to optimize band alignment.[79,80] Interestingly, we find that the shift in the VBM of FA0.75Cs0.25PbI3 to a higher energy on applied pressure could result in an improved alignment. Thus, physical modification of perovskite layers can be an efficient alternative approach for band alignment and for optimization of the photovoltaic performance.

Spin-Splitting at Band Edges

Previous studies have demonstrated that hydrostatic pressure can be used to modify the extent of spin-splitting and the direct–indirect band transition in MAPbI3.[81] Motivated by this recent interest, we also investigate the band edge characteristics of FA0.75Cs0.25PbI3 and FAPbI3 under pressure.

As shown in Figure as well as Figures S5 and S6, the CBM at the Γ point exhibits spin-splitting for FA0.75Cs0.25PbI3 and FAPbI3 with and without external pressure. However, in the valence band, spin-splitting is insignificant and the VBM remains at the Γ point. This different spin-splitting behavior in the band edges of FA0.75Cs0.25PbI3 results in an indirect band gap, which is narrower than the direct gap by 5–7 meV. The spin–orbit coupling strength and consequently the Rashba-type splitting directly depend on the atomic weight of the elements that form the band edges of semiconductors. Thus, spin-splitting is more prominent in the conduction band, which is dominated by heavier Pb atoms, than for the valence band, where relatively lighter iodine atoms largely contribute.

Figure 5

Rashba-type effect in mechanically compressed mixed A-cation perovskites. The band structure including SOC corrections for FA0.75Cs0.25PbI3 at (a) 0 and (b) 2 GPa. The spin-splitting of the CBM at the Γ-point along different high-symmetry directions is evident without and with applied pressure as shown in (c) and (d), respectively. For clarity, the spin-split valence bands are represented in green and blue solid lines, and the conduction bands are shown with black and red solid lines. All bands apart from band edges are drawn by dashed black lines.

To quantify the magnitude of the Rashba-type effect, we calculate the Rashba parameter, α = ER/2Δk, where Δk is the SOC-induced momentum offset and ER is the energy difference between the spin-splitted bands in a particular direction. By applying a hydrostatic pressure of up to 3 GPa in FA0.75Cs0.25PbI3, we find α values of 0.71–0.81 and 0.56–0.62 eV Å in the M → Γ and R → Γ directions, respectively (Figure S7). As shown in Figure , the external hydrostatic pressure distorts the mixed cation lattice anisotropically. The Rashba parameter, which is very sensitive to local structural changes in the lattice, is modified to a different extent along different high-symmetry k-paths. Importantly, in contrast to a previous report[81] on Rashba-type splitting in MAPbI3 decreasing with external pressure, we find this effect is slightly enhanced with lattice compression for FA0.75Cs0.25PbI3 and FAPbI3.

In the static structure, orientation of the weakly polar FA+ cations and distortion in the inorganic Pb/I frame can break the inversion symmetry resulting in Rashba-type effects. As an atomic-scale probe of the structural origin of this effect, we replace all FA+ molecules with the nonpolar Cs+ in FA0.75Cs0.25PbI3 under 2 GPa pressure and then optimize the Cs+ positions only. As Figure S8a shows, the spin-splitting at the band edges of this model of CsPbI3 is very similar to that of mixed A-cation perovskites. In contrast, the high-symmetry cubic phase of CsPbI3 does not exhibit spin-splitting in the band edges (see Figure S8b). Thus, the inversion symmetry-breaking of the inorganic Pb/I frame is the cause of the Rashba-type spin-splitting in these halide perovskites and not the particular conformation of the polar FA cations. These findings demonstrate that the A cations indirectly influence the optoelectronics of hybrid perovskites by maintaining the symmetry-lowering distortions of the inorganic Pb/I frame.

It is evident that lattice distortions in the halide perovskites modify the band gap as well as the nature of band edges and optical transitions. Interestingly, such structural distortions do not significantly enhance the spin-splitting and indirect band gap. However, as pressure can induce permanent structural distortions, it can stabilize these electronic and optical modifications for longer time scales, which can be detected experimentally.

The formation of an indirect band gap can result in the accumulation of photogenerated electrons at the spin-splitted CBM. In such a situation, the band-to-band radiative recombination of carriers can be hindered, resulting in a possible increase in carrier lifetimes. However, spin-splitting and its effect on carrier dynamics have been much debated.[62,82,83]

In addition to the field of photovoltaics, the Rashba-type effect in halide perovskites also opens up new applications related to spintronics and spin–orbitronics.[84,85]

Change in Absorption Properties

To explore the effect of pressure on the optical properties, we calculate the absorption spectra of FA0.75Cs0.25PbI3 (Figure a), for which the absorption edge moves to lower energy, exhibiting a prominent red-shift in the optical spectra. As the optical transition from the VBM to CBM dominates the absorption edge, the narrowing of the electronic band gap under pressure directly causes this red-shifted absorption in these perovskites (Figure S9).[21,22]

Figure 6

Optical absorption properties of FA0.75Cs0.25PbI3. (a) Spatially averaged absorption spectra under external pressure range 0–2 GPa, with inset showing the zoomed band edges. (b) Crystal axes of the anisotropic lattice. The spatially resolved absorption spectra for the crystal under (c) 0 and (d) 2 GPa pressure.

In the absence of any external pressure (Figure c), the absorption edge along the c-axis (shown in Figure b) is red-shifted by 0.16 and 0.14 eV compared to the edge along the a- and b-axes, respectively. This anisotropic character of the optical spectra is enhanced with applied pressure (Figure d).

The band edge optical absorption is dominated by the transition between the VBM and CBM, with their contributions dominated by the Pb/I frame. The Pb–I bonds are found to be almost the same with differences of <0.01 Å in all three crystal axes (Figure b). In contrast, the Pb–I–Pb angles (Figure c) are different in all three directions due to the dominant rotation of PbI6 octahedra along the c-axis. The larger Pb–I–Pb angles along the c-axis result in the red-shifted absorption edge.

With increased pressure, the PbI6 octahedra tilt more along the c-axis, enhancing the anisotropy in the Pb–I–Pb angles. Consequently, the anisotropic nature of the absorption edge also becomes more prominent under pressure, as shown in Figure c,d. Thus, applying hydrostatic pressure affects the absorption properties of hybrid perovskites by changing the PbI6 octahedral tilting.

The strong anisotropic nature of the compressed lattice can account for the photoluminescence profile with additional peaks for FAPbI3 and MAPbI1.2Br1.8.[22] Thus, pressure can be also used to modify the excited state properties of these photovoltaic materials.

Effect on Defect States

The prevalence of intrinsic point defects (vacancies and/or interstitials) is related to their defect formation energy, which is a function of the Fermi level across the band gap (see section S1 in the Supporting Information for details). If a transition level of a defect state lies near the band edge, such that it is likely to be thermally ionized at room temperature, it is a shallow defect. Conversely, deep defects are positioned close to the middle of the band gap and are unlikely to be ionized at room temperature. While shallow trapped states do not significantly affect recombination rates, deep traps act as recombination centers for photogenerated carriers, leading to solar cell efficiency losses.[72,86,87]

By calculating the thermodynamic transition levels for intrinsic vacancy defects of FAPbI3 and FA0.75Cs0.25PbI3 at ambient pressure, we find that all the defects are shallow in nature, which explains the defect tolerance of hybrid perovskites (see Figure S10).[72] However, under an applied pressure, the iodide vacancies (VI) change their transition levels significantly within the band gap (Figure ). We also see a significant shift of the VPb doubly charged transition states at 2 GPa, although this shift moves the transition states to within the valence band and therefore would not affect recombination rates (Figure S10). Moreover, according to Shockley–Read–Hall recombination theory only neutral and singly charged defects act as recombination centers.[88,89] We therefore focused on the defect properties of iodide vacancies (VI) in their positive, neutral, and negatively charged states.

Figure 7

Iodide vacancy formation energies in FA0.75Cs0.25PbI3 at the lowest energy equatorial sites. The most stable charge state is shown at (a) 0 and (b) 2 GPa. The charge densities of the defect state at these pressures have been shown in (c) and (d). The stable charge states at other pressures are shown in the Supporting Information.

As pressure introduces large structural distortions leading to nonequivalent iodide sites, we have calculated transition levels considering all such sites and find very similar defect properties. Consistent with other computational studies on halide perovskites at ambient pressure, iodide vacancies are stabilized mainly in their positively and negatively charged states, with ϵ(+/0) and ϵ(0/−) transitions near or in the CBM (Figure a).[72,90,91] At low pressures (≤0.5 GPa), the transition state levels of vacancy defects remain largely unchanged and would not significantly affect the charge carrier lifetime (Figure a and Figure S11).

At higher pressures (2 GPa) (Figure b and Figure S12), deep-level states appear with the ϵ(+/0) transition at ∼0.25–0.65 eV from the CBM. The calculated optical spectra consequently exhibits prominent absorption peaks below the band gap energy (Figure S13). Formation of such midgap states would lead to higher recombination rates that are detrimental to solar cell performance. A recent study by Jones et al.[24] shows that grain clusters of MAPbI3 under a compressive strain have shorter photoluminescence lifetimes and carrier dynamics compared to unstrained regions. This is in agreement with our work, where we show a shift of shallow to deep states of VI in FAPbI3 and FA0.75Cs0.25PbI3, which would lead to a reduction in charge carrier lifetimes.

To understand the origin of these deep-level states, the structure and electronic nature of the defect sites have been explored. As shown in Figure c,d, the two Pb atoms nearest to the VI are ∼6.1 Å apart at 0 GPa pressure but form Pb–Pb dimers that are ∼4.2 Å apart at 2 GPa. Hence, applied pressure pushes these two Pb atoms together to form bonds across the VI site, which shifts down the corresponding energy level, placing it deep within the band gap. The charge densities of the defect states clearly show localization over these Pb–Pb dimers. Such midgap states with strongly localized charge density give rise to deep-level states.

Conclusions

The effects of external pressure on the structural and optoelectronic properties of iodide perovskites are thoroughly explored at the atomic level. By combining static and dynamic ab initio computations, we have investigated FAPbI3 and mixed-cation FA0.75Cs0.25PbI3, revealing the following key conclusions:

(a) With applied pressure, the inorganic Pb/I framework undergoes structural distortion with a reduction in the Pb–I bond lengths and increased tilting of the corner-sharing PbI6 octahedra. These structural distortions restrict the rotational dynamics of the FA+ molecular cation and enhance its coupling with the Pb/I inorganic framework with stronger N–H···I hydrogen bonding.

(b) The electronic structure responds strongly to the lattice compression with significant narrowing of the band gap. The valence band maximum shifts to higher energy with applied pressure, indicating improved energy level alignment between the perovskite absorber and hole collecting organic layers, which may enhance solar cell performance.

(c) Symmetry breaking in the compressed lattice leads to Rashba-type spin-splitting of the conduction band. The absorption coefficients exhibit strong anisotropy along a, b, and c lattice directions due to the pressure-induced distorted structure.

(d) The intrinsic vacancy defects of FAPbI3 and FA0.75Cs0.25PbI3 at ambient pressure are all shallow in nature, which explains the defect tolerance of hybrid perovskites. Under pressure, the iodide vacancy is modified to a deep-level state that would strongly affect the optoelectronic properties of compressed lattices.

Our study provides an atomistic understanding of pressure-induced effects as a materials design strategy to tune the structure–property relationships of lead iodide perovskites.