Strain Heterogeneity and Extended Defects in Halide Perovskite Devices

Strain is an important property in halide perovskite semiconductors used for optoelectronic applications because of its ability to influence device efficiency and stability. However, descriptions of strain in these materials are generally limited to bulk averages of bare films, which miss important property-determining heterogeneities that occur on the nanoscale and at interfaces in multilayer device stacks. Here, we present three-dimensional nanoscale strain mapping using Bragg coherent diffraction imaging of individual grains in Cs0.1FA0.9Pb(I0.95Br0.05)3 and Cs0.15FA0.85SnI3 (FA = formamidinium) halide perovskite absorbers buried in full solar cell devices. We discover large local strains and striking intragrain and grain-to-grain strain heterogeneity, identifying distinct islands of tensile and compressive strain inside grains. Additionally, we directly image dislocations with surprising regularity in Cs0.15FA0.85SnI3 grains and find evidence for dislocation-induced antiphase boundary formation. Our results shine a rare light on the nanoscale strains in these materials in their technologically relevant device setting.


Confirmation of sample quality:
Presented below are standard characterisations (powder X-ray diffraction, photoluminescence spectroscopy, scanning electron microscopy, and device current/voltage measurements) to confirm the quality of the samples used in this study.Refinements were performed using Pm3 ̅ m symmetry using Topas Academic software (v7). 1 Fig.S2: Photoluminescence emission spectra (405nm excitation) of Cs0.1FA0.9Pb(I0.95Br0.05)3(purple) and Cs0.15FA0.85SnI3(orange) films.Spectra are concordant with those given in other literature. 2,3Spectra have been normalised after subtraction of a flat background.Fig. S3: Scanning electron micrographs of representative a Cs0.1FA0.9Pb(I0.95Br0.05)3and b Cs0.15FA0.85SnI3films.In both cases, morphological grain sizes are on the order of 0.5-2.0μm.This is slightly larger than average for halide perovskite devices but chosen to better suit the BCDI technique as mentioned in the main text.A cropped region of panel a is used in Fig. 1c of the main text.Discussion of beam damage: It is well known that halide perovskites are X-ray-sensitive materials.As such, here we explicitly consider the effect of X-ray-induced changes on the grains studied.The beam energy used of 11.8keV has been empirically determined to minimise beam damage during previous beamline visits.
For all the grains where we took multiple BCDI measurements, we have calculated the local strain distribution descriptors and plotted them as a function of scan number in Fig. S7.Following this, we have calculated the mean magnitude of the changes from successive measurements to get an estimate of the likely size of the effects of beam damage for each of the values plotted in Fig. 2c and Fig. 2f of the main text.These means are tabulated in Table S1 along with the standard error of the mean magnitudes of beam-induced changes.We consider the mean absolute change as an "error bar due to beaminduced changes", and it is plotted as a grey bar in the bottom right corner of the plots in Fig. 2c & 2f of the main text.We have considered the Cs0.1FA0.9Pb(I0.95Br0.05)3and Cs0.15FA0.85SnI3grains separately, as it appears that the Cs0.1FA0.9Pb(I0.95Br0.05)3grains undergo smaller beam-induced changes.

Determination of Burgers vector magnitudes:
When fitting the displacement vs. arc angle data, the raw data should be collected at a radius, , from the dislocation core small enough such that the strain field due to the dislocation dominates over any other longer-range strain fields present in the crystal, but also large enough to sample enough points around the dislocation core.Practically, in this work a radius of 50nm was chosen as standard, though 35nm was used for the predominantly screw portion of the dislocation in Fig. 3d owing to a lack of space between the dislocation and the crystal edge.
Updating the analysis previously presented in ref. 4 , we can quantitatively characterize the dislocation by considering the form of their local displacement fields.For a pure edge dislocation, atomic displacements are expected only in the plane perpendicular to the dislocation line.Mathematically, the displacement field in the directions perpendicular and parallel to the extra inserted atomic plane,  ⊥ and  ∥ respectively, are given by: 5-8 and Here,  is the Burgers vector that describes the dislocation and which is marked on the diagrams in Fig. 3e, and  is the Poisson ratio of the material (taken to be 0.29; see Table S3 and associated discussion).For a pure edge dislocation, we have extracted the displacement vs. arc angle data from a plane containing the scattering vector, , however, we do not a priori know the angle between  and the normal of the inserted plane, which we label .Hence, we must use a linear combination of Equations S1 & S2 to model the atomic displacement field observed, with their contributions weighted by the cosine and sine of .I.e.we fit the data according to where  is a refinable parameter giving the angle between  and the direction normal to the extra inserted plane.Because we have used an obvious phase discontinuity to identify dislocations in the first place, in general  is small for our data.By contrast, all the atomic displacements for a pure screw dislocation are along the direction of the dislocation line.Labelling this direction z, and this time choosing a slice through the reconstruction perpendicular to our scattering vector, the atomic displacements depend on arc angle, , according to 5,6,9  z = || 2  (S4) Fits of Equation S4 are shown with dotted lines in Fig. 3d.
A pure screw dislocation will give a straight-line local displacement vs. arc angle plot, with that of an edge dislocation having an additional sinusoidal modulation.These facts, in combination with the phase ramps of 2π corresponding to a displacement equal to the lattice spacing of the 100 Bragg peak probed in our BCDI experiment, allows us to identify ⟨100⟩ edge and ⟨100⟩ screw dislocations by inspection.Nevertheless, the refined values of || are given in Table S2.While the agreement of || with  100 is not perfect, it is better than for any of the other (and smaller) -spacings.Errors in these values may originate from compositional inhomogeneity causing local lattice parameter variation, background strain fields in addition to the dislocations', and other edge/screw character which we cannot rigorously characterise without multi-peak BCDI.
Where does the grain appear?Table S2: Burgers vector magnitudes refined for the dislocations shown in Fig. 3 of the main text.Percent errors relative to the  100 lattice spacing of 6.2934Å refined from powder X-ray diffraction data presented in Fig. S1 are also given.
Finally, we require a value of Poisson's ratio, , for Cs0.15FA0.85SnI3 in order to fit the data to the Equation S3.An estimate of  is obtained for this mixed-component system using a compositionally weighted average of values for pure compositions according to a rule of mixtures as below. for pure compositions are tabulated in Table S3.

Fig. S4 :
Fig. S4: JV characteristics for champion a Cs0.1FA0.9Pb(I0.95Br0.05)3-basedand b Cs0.15FA0.85SnI3-based solar cells from batches representative of the devices considered in this work.Box and whisker plots of these c Cs0.1FA0.9Pb(I0.95Br0.05)3-basedand d Cs0.15FA0.85SnI3-based solar cell batches with individual efficiencies for each cell plotted separately on the right.Cs0.1FA0.9Pb(I0.95Br0.05)3devices for JV characterisation have 100nm-thick Au contacts (as opposed to the 60nm-thick contacts used for the BCDI measurements) to reflect what is more commonly used in the field.Similarly, Cs0.15FA0.85SnI3devices for JV characterisation have 120nm-thick Cu contacts (as opposed to the 25nm-thick contacts used for the BCDI measurements).Thinner contacts were used on the beamline to as not to attenuate the X-ray beam any more than necessary.

Fig
Fig. S5: a, c, e, g Reconstructions of individual Cs0.1FA0.9Pb(I0.95Br0.05)3grains and corresponding slices showing their internal strain distributions not shown in the main text.b, d, f, h Histograms of local strain for the grains shown in the same row.  ̅̅̅̅,  ,rms , and  strain distribution descriptors are quoted.

Fig. S5
Fig. S5 continued: i Reconstruction of an individual Cs0.1FA0.9Pb(I0.95Br0.05)3grain and corresponding slices showing its internal strain distributions not shown in the main text.j Histogram of local strain for the grain shown in the same row.  ̅̅̅̅,  ,rms , and  strain distribution descriptors are quoted.

Fig. S6:
Fig. S6: a, c, Reconstructions of individual Cs0.15FA0.85SnI3grains and corresponding slices showing their internal strain distributions not shown in the main text.b, d, Histograms of local strain for the grains shown in the same row.  ̅̅̅̅,  ,rms , and  strain distribution descriptors are quoted.

Fig. S6
Fig. S6 continued: e, g, i, k Reconstructions of individual Cs0.15FA0.85SnI3grains and corresponding slices showing their internal strain distributions not shown in the main text.f, h, j, l, Histograms of local strain for the grains shown in the same row.  ̅̅̅̅,  ,rms , and  strain distribution descriptors are quoted.
Fig. S8 outlines the coordinate system used for edge dislocation analysis.Fits of Equation S3 are shown with dashed lines in Fig. 3d.

Table S1 :
Mean change magnitudes and standard error in the mean change magnitudes for local strain distribution descriptors upon successive exposure to X-rays.

Table S3 :
Poisson ratios for pure composition Sn-based halide perovskites from the literature and their means.