Thermodynamic stabilization of mixed-halide perovskites against phase segregation

Mixing iodide and bromide in halide perovskite semiconductors is an effective strategy to tune their bandgap, therefore mixed-halide perovskites hold great promise for color-tunable LEDs and tandem solar cells. However, the bandgap of mixed-halide perovskites is unstable under (sun-)light, since the halides segregate into domains of different bandgaps. Using pressure-dependent ultrafast transient absorption spectroscopy, we show that high external pressure increases the range of thermodynamically stable halide mixing ratios. Chemical pressure, by inserting a smaller cation, has the same effect, which means that any iodide-to-bromide ratio can be thermodynamically stabilized by tuning the crystal volume and compressibility. We interpret this stabilization by an alteration of the Helmholtz free energy via the previously overlooked PdeltaV term.


Introduction
Metal halide perovskite semiconductors have recently received tremendous attention in materials science, as these have yielded highly efficient solar cells, light-emitting diodes, and radiation detectors. [1][2][3] The unprecedented performance of perovskites is due to their outstanding optoelectronic properties, such as high optical absorption coefficients and relatively low trap densities, resulting in excellent charge transport and efficient radiative recombination. 4,5 Another key characteristic of metal-halide perovskites is that their bandgap is highly dependent on their chemical composition, meaning that any desired absorption onset or emission energy in the visible can be obtained by tuning the composition. For instance, mixing iodide and bromide in MAPb(I 1-x Br x ) 3 (with MA = methylammonium, CH 3 NH 3 + ) results in bandgaps intermediate to full iodide (x = 0, 1.6 eV) and full bromide (x = 1, 2.3 eV). 6,7 The combination of excellent optoelectronic properties and bandgap tunability makes perovskites the most promising candidate for tandem solar cells, 8 in which a mixed-halide perovskite with a bandgap of 1.7 eV (x ~ 0.2) could increase the power conversion efficiency of record silicon cells up to 41%. 9 A major drawback of mixed-halide perovskites is that their bandgap is unstable under illumination, since the halides segregate into iodide-rich and bromide-rich domains. 10,11 The lower-bandgap iodide-rich domains act as charge carrier recombination centers and this halide segregation is thus detrimental for device performance. It is thus essential that the halide segregation is fully suppressed for any application of mixedhalide perovskites where stable bandgaps are required. Although some studies have shown that halide segregation is affected by changes in the chemical composition, external pressure, or mechanical strain, [12][13][14] the underlying mechanism has remained unclear. 15 Here we show that the crystal volume and compressibility are key factors in determining the thermodynamic stability of mixed-halide perovskite thin films against halide segregation. We use transient absorption spectroscopy (TAS) to track the formation of both the iodide-and bromide-rich domains during segregation.
The measurements are performed at hydrostatic pressures ranging from ambient to 0.3 GPa and for several initial mixing ratios x, which enables us to study the mixing ratio of the segregated phases, x s , for different unit cell volumes. We find that at high pressure, the composition at which the segregation discontinues depends on both the external pressure and the initial composition.
Our findings can be understood from a change in the thermodynamics (Helmholtz free energy) of the mixtures. Tuning the free energy minimum by a change of the unit cell volume and compressibility is an effective approach to obtain mixed-halide perovskites that are stable against photo-induced halide segregation. Consistently, we find that chemical compression of the perovskite, via replacing MA ions with the smaller Cs ions, effectively suppresses halide segregation at ambient pressure. Altogether, our results show that stable mixed-halide perovskites of any desired halide composition can be designed by modifying the crystal mechanics so that the desired halide ratio falls in a miscible regime of the phase diagram, enabling a rational route toward thermodynamically stable mixed-halide perovskites.

Results and discussion
The MAPb(I1-xBrx)3 perovskite is an example of a pseudo-binary mixture (or solid solution). The accessible solubility range is determined by the free energy of mixing ∆F(x): the free energy of the mixed phase with respect to the phase-separated iodide (x = 0) and bromide (x = 1) compounds: First-principles calculations of Equation 1 confirm a positive enthalpic term ∆H(x = 0.5) ~ 2 kJ/mol due to chemical strain in the mixed MAPb(I 1-x Br x ) 3 perovskite, 16 which originates from the ionic size mismatch of I -(2.22 Å) and Br -(1.96 Å). This enthalpic cost of straining the bonding environment is offset by the gain in configurational entropy (T∆S). 16 For a binary mixture, the entropy reaches a maximum at x = 0.5 with a value of also ~ 2 kJ/mol (0.7 k B T at T = 300 K). Analysis of ∆F(x) shows two minima (at x ~ 0.2 and at 0.75) under ambient conditions. The region in between these minima represents the miscibility gap (i.e. the range of compositions that are thermodynamically unstable). What has been overlooked thus far is that the enthalpy contains a P∆V term where pressure (P) can be used as an additional lever to control the stability range, which we explore in the following.
Thin films of mixed-halide MAPb(I 1-x Br x ) 3 with 0 < x < 1 were spin-coated from solution, see Experimental Methods for procedures and Supplementary Figure 1 for UV-VIS and XRD, and their initial stoichiometries x were determined from SEM-EDX. The initial bandgaps vary from 1.6 eV (x = 0) to 2.3 eV (x = 1).
However, the bandgaps of 0.2 < x < 1 are unstable under illumination with a continuous wave (cw) laser, showing photoluminescence (PL) emission energies of 1.68 -1.75 eV, independent of x (see Supplementary   Figure 2). This bandgap instability has been widely observed in mixed-halide perovskites, 10,13,17,18 and is attributed to segregation of the halides into iodide-and bromide-rich domains. After segregation, all light emission originates from the iodide-rich domains, which have a lower bandgap. Therefore, this halide segregation is a limiting factor for perovskite-based LEDs if the desired emission energy falls in between 1.7 and 2.3 eV. In perovskite-based solar cells, recombination of charges in these low-bandgap domains significantly lowers the voltage, 17 and thus segregation severely limits their overall power conversion efficiency. The shared emission energy of ~ 1.7 eV corresponds to a segregated composition x s ~ 0.2, and the MAPb(I 1-x Br x ) 3 perovskite is unstable if x > x s (= 0.2 at ambient conditions). 10,19 Since this threshold coincides with a cubic-to-tetragonal phase transition around room temperature, 7 it was previously proposed that this phase transition impedes full halide segregation. 18,19 As we show below, however, this assignment is inconsistent with the behavior of mixed-halide perovskites under hydrostatic pressure.
We used pressure-dependent TAS measurements, as shown in Figure 1a, to follow the segregation in time for different initial mixing ratios and pressures. Importantly, while PL measurements only probe the emissive iodide-rich phase, 10,20 TAS measures the bleach from each excited state population and hence allows us to trace both the formation of iodide-rich and bromide-rich phases. 21   To investigate the effect of light soaking on the energetic landscape of the perovskite, we illuminated the sample with a continuous-wave (cw, intensity equivalent to 24 sun) laser for 20 minutes. A fixed delay time of ~15 ps was used, which is prior to recombination and energy transfer events but after cooling of the charges into the iodide-and bromide-rich domains. 22,23 As shown in Figure 1c, This observation shows that halide segregation is substantially suppressed at high pressure.   As an alternative explanation, we consider mechanical effects associated with the less compressible and smaller unit cell volume for samples with higher bromide content as the origin of the reduced segregation.
Since MAPbBr 3 has a larger bulk modulus than MAPbI 3 , 11,24 the volume change upon applying pressure to the mixed-halide MAPb(I 1-x Br x ) 3 perovskite is smaller for higher bromide contents (see Supplementary  drives photo-induced segregation at x > 0.2. 16,26 For high pressure or Cs content, with smaller unit cell volumes, the mixing enthalpy is reduced so that the entropy dominates for a larger range of mixing ratios. We rationalize these observations from an alteration of x s due to the P∆V term in the free energy of mixing (Equation 1). Whereas ∆S is unchanged under the mild pressure we apply, due to a regular perovskite structure being maintained, the previously neglected P∆V term does change ∆H(x). As the bulk modulus of the iodide (9 GPa for MAPbI 3 ) is much smaller than the bromide (18 GPa for MAPbBr 3 ), the iodide-rich regions undergo a larger volume change and pay a larger enthalpic penalty. From continuum mechanics, the combination of P = 0.3 GPa and x = 0.5 results in ΔV = 5Å 3 , and PΔV = 1 kJ/mol. Given that the magnitude of TΔS is limited to 2 kJ/mol, this represents a substantial contribution. In addition, the higher compressibility of iodide means that the ionic size mismatch decreases with pressure, which will lower the microscopic strain of the mixed system and allow T∆S to dominate and stabilize the mixture for larger values of x (see Figure 3d).
The observation that segregation only occurs under light requires a modification of the equilibrium thermodynamics (Equation 1) 16 in the presence of electronic excitations. 26 Local inhomogeneities in halide distribution may result in low-bandgap regions (already present in the dark), 27 which act as traps to photoexcited holes. The bandgap difference ∆E g between the high-and low-bandgap domains then provides the driving force for the light-induced phase segregation process. 26 This electronic term in the phase diagram is expected not to change significantly with pressure, as the bandgaps of both the iodide-and bromide compounds, and their mixtures, show a similar pressure dependence (see also Supplementary Figure 11).
However, the pressure-induced shift in minimum ∆F (dark) significantly extends the miscible regime of x in compressed perovskites and thus, the range of compositions that is entropically stabilized.
Previous approaches to suppress halide segregation are mainly based on the reduction of iodide vacancies, for instance by adding potassium iodide or using an excess of halides during the synthesis. 12,22 The reduction of vacancies lowers the density of mobile ions, which considerably slows ion migration and consequently the halide segregation. Slowing down the rate of halide segregation is an effective approach to kinetically stabilize mixed-halide perovskites. 26 However, as long as these systems are thermodynamically unstable, they are still prone to segregate slowly and hence, thermodynamic stabilization achieved through manipulating the unit cell is the only route to applications of mixed-halide perovskites that require longterm (i.e. many decades) stability.

Conclusions
To conclude, we have shown that compressing mixed-halide MAPb(I 1-x Br x ) 3 perovskite thin films, either via applying external pressure or via reducing the cation size, greatly impacts their stability against photo-induced halide segregation. Using pressure-dependent transient absorption spectroscopy, we followed the compositional changes in both the iodide-and the bromide-rich phases associated with segregation. At ambient pressure the segregation discontinues if the iodide-rich phase reaches x s ~ 0.2, this threshold is substantially shifted with pressure, reaching x s ~ 0.6 at 0.3 GPa for an initial mixing ratio of x = 0.7. We interpret these findings from an alteration of the Helmholtz free energy via the previously overlooked P∆V term. This term, which is larger than traditional inorganic semiconductors allows owing to the mechanical softness of halide perovskites, provides a lever to extend the range of thermodynamically stable mixedhalide compositions by increasing the pressure or decreasing the volume. Importantly, these results suggest that any iodide-to-bromide ratio could in principle be thermodynamically stabilized against halide segregation by tuning the crystal volume and compressibility, enabling full bandgap tunability of stable mixed-halide perovskites. the beam in the pump path (using 500 Hz as frequency), 400 nm pulse pump was generated by doubling 800 nm pulse with a beta barium borate (BBO) crystal. A short-pass filter was placed after the BBO crystal in the pump path, to remove 800 nm residue from the fundamental beam.

Author contributions
The white-light continuum probe pulses were produced by focusing the 800 nm fs pulses through a 2 mm-sapphire plate. The probe spot size was chosen to be smaller than the pump spot size to obtain homogenous excitation over the probed area. The two beams were then spatially overlapped inside the pressure cell. To follow the evolution in time of the system, the pump-probe delay time was changed from 0 to 1000 ps using a mechanical delay stage. Unless states otherwise, the pump excitation density was ~10 18 cm -3 (see Supplementary Figure S12 for different excitation densities).
The samples were light-soaked using a 405 nm continuous wave (cw) single-mode fiber-coupled laser source (Thorlabs). The cw laser was focussed on the same spot as the pump and probe and its spot size (diameter of 243 micrometer) was large enough to fully cover the probed area (< 50 micrometer). The intensity of the light-soaking source was 2.37 × 10 3 mW/cm 2 (~24 sun), and no segregation was observed in absence of the cw source (see Supplementary Figure S13).