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. 2017 Nov 16;2(11):8020–8026. doi: 10.1021/acsomega.7b01471

Spatial Inhomogeneity of Methylammonium Lead-Mixed Halide Perovskite Examined by Space- and Time-Resolved Microwave Conductivity

Frank Caraballo †, Masataka Kumano †, Akinori Saeki †,‡,*
PMCID: PMC6645387  PMID: 31457352

Abstract

graphic file with name ao-2017-01471h_0005.jpg

Reducing the spatial inhomogeneity of solution-processed, multicrystalline methylammonium lead iodide (MAPbI3) perovskite is of great importance for improving its power conversion efficiency, suppressing point-to-point deviations, and delaying degradation during operation. Various techniques, such as conducting-mode atomic force microscopy and photoluminescence mapping, have been applied for this intriguing class of materials, revealing nonuniform electronic properties on the nanometer-to-micrometer scale. Here, we designed a new space- and time-resolved microwave conductivity system that enables mapping of the transient photoconductivity with resolution greater than ∼45 μm. We examined the effects of the precursor concentration of MAPbI3 and the mixing of halides (I– and Br–) on the charge carrier dynamics, crystal size, and inhomogeneity of the films. The optoelectronic inhomogeneity of MAPbI3 and MAPb(I1–xBrx)3 on the sub-millimeter and millimeter scales shows a general correlation with their crystallite sizes, whereas the precursor concentration and halide mixing affect the inhomogeneity in a different way, providing a basis for uniform processing of a multicrystalline perovskite film.

Introduction

Methylammonium lead halide perovskite, MAPbI3 (MA = CH3NH3+),1−3 has emerged as a viable candidate for the construction of efficient, cost-effective solar cells.4−9 The rapid boost of the power conversion efficiency (PCE) of the solar cell, which reaches 22.1% within a short period of time,10 is owing to the excellent intrinsic photophysical properties of MAPbI3, which include direct transition with optimal band gaps,11 small exciton binding energy,12,13 large diffusion length14,15 large charge carrier mobility,16−18 and small loss in open-circuit voltage (Voc).19,20 The improvement in the PCE and the stability of the solar cell have been achieved by the development of new solution-processing methods that have evolved from one-step and two-step techniques21,22 to modified one-step approaches with antisolvent treatment.23−26 A high-quality perovskite film is composed of densely packed multicrystallites with size of hundreds of nanometers. Although the film looks uniform, its optical and electronic properties are inhomogeneous because of nonuniform solvent evaporation during spin coating,27 phase separation, particularly for mixed-halide perovskites,28−30 and fluctuation of crystal growth under thermal annealing.31,32 The distorted stoichiometry of Pb and the halide produces vacancies and carrier traps33−35 that cannot be discriminated using only conventional microscopes, e.g., scanning electron microscope, atomic force microscope, and optical microscope.

Therefore, photo(electro)luminescence mapping,36−39 spatially resolved transient photoabsorption spectroscopy (TAS),40−42 and conducting-mode atomic force microscopy (cAFM) including a Kelvin probe microscope43−45 are powerful tools to visualize the spatial inhomogeneity of trapping sites and the charge-transport efficiency. For example, Wen et al. reported a large spatial variation in photoluminescence (PL) lifetime imaging by using one-photon (surface) and two-photon (bulk) excitation.36 Yamashita et al. found a negative correlation between spatially resolved photocurrent and PL intensity, showing the crucial role of the carrier injection rate on carrier recombination and transport.39 Other reports on PL mapping have shown the existence of a nonuniform carrier-transport efficiency on tens to hundreds of micrometers, which is associated with a trap density.37,38 A cAFM study revealed substantial variations in the photoresponse that are correlated with thin-film microstructural features of nanometer size, such as intragrain and planar defects and grain boundaries.44 Overall, these studies highlight the need for in-depth understanding of the spatial inhomogeneity of perovskite to develop efficient solar cells with small batch-to-batch and point-to-point variations.

In this study, we developed a space- and time-resolved microwave conductivity (STRMC) system, which was applied for photoconductivity mapping of MAPbI3 and MAPb(I1–xBrx)3 (x = 0–1). A conventional time-resolved microwave conductivity (TRMC) system uses a gigahertz electromagnetic wave as the probe and a relatively large spot of a light pulse (ca. 0.2–2 cm2) as the excitation,46−48 which benefits the signal-to-noise ratio of transient photoconductivity (Δσ); however, the obtained Δσ is an averaged value over the spot area. Similarly to the approach used in PL lifetime and TAS mapping, our STRMC system is implemented by reducing the spot size to approximately 20 μm (∼3 × 10–6 cm2) via microscope optics and scanning an XY stage with automatic frequency tuning. In contrast to PL and TAS imaging, which have sensitivities that can be largely improved by efficient amplification of the probing photons, STRMC has been challenging owing to its limited amplification electronics and low spatial convergence with a large wavelength (approximately a few centimeters). However, the evaluation of organic–inorganic perovskites is possible because of their excellent photophysical properties. We demonstrate the inhomogeneity in optoelectronics made of mixed-halide lead perovskite films and examine its correlation with the crystallite size and the lifetime of charge carriers.

Results and Discussion

Optical microscopic images of MAPbI3, MAPb(I0.7Br0.3)3, and MAPbBr3 are shown in Figure 1a–c; the stripe patterns observed in MAPbI3 and MAPbBr3 are caused by the inhomogeneity of the spin-coated mpTiO2 (root-mean-square height ∼33 nm and period ∼80 μm in the lateral direction, analyzed by fast Fourier transform, Figure S1). STRMC evaluations were performed in a 1000 × 1000 μm2 area by scanning a position of the laser spot using a 200 μm step; thus, 6 × 6 = 36 points of transient photoconductivity (Δσ) were obtained for each sample. The map of Δσ maxima (Δσmax) of MAPbI3 displays a distinct inhomogeneity, which is not similar to the appearance of the film in the optical image (Figure 1d). Although the spatial homogeneity of mixed-halide MAPb(I0.7Br0.3)3 is worse than that of MAPbI3 (Figure 1e), it is probably improved in monobromide MAPbBr3 (Figure 1f). We note that the sample damage and resultant change in Δσmax were confirmed to be negligible using repeated measurements of MAPbI3 at the same position (19 times, Figure S2). Although Δσmax varied in the map, the decay lifetimes were mostly unchanged. Histograms of Δσmax statistics are shown in Figure 1g–i. The average of Δσmax, Ave(Δσmax), depends on the halide composition: 5.9 × 10–8 S cm–1 for MAPbI3, 1.2 × 10–8 S cm–1 for MAPb(I0.7Br0.3)3, and 6.7 × 10–8 S cm–1 for MAPbBr3. The diffusion length of charge carriers has been reported to be 1 μm in Cl-doped MAPbI3 (ref (14)) and 50–175 μm in single-crystal MAPbI3 (refs (15, 49)), whereas the grain size of solution-processed multicrystalline MAPbI3 is typically a few hundreds of nanometers to several micrometers.50 Therefore, one point in the map (∼20 μm spot and 200 μm step) includes multiple grains that are different from a neighboring point. An intergrain charge transport is critical to a long-range mobility;51 however, the present STRMC is unable to resolve the electronic properties of the grain interface.

Figure 1.

Figure 1

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Optical microscopy images of (a) MAPbI3, (b) MAPb(I0.7Br0.3)3, and (c) MAPbBr3 on a mpTiO2/quartz plate. Mapping of Δσmax (upper panel) and transients (lower panel) of (d) MAPbI3, (e) MAPb(I0.7Br0.3)3, and (f) MAPbBr3, evaluated by STRMC. (g–i) Statistics of Δσmax. The black solid line is a Gaussian function based on the average and standard deviation of the statistics.

Figure 2a displays a detailed plot of Ave(Δσmax) against the bromide content, the x (0–1) value of MAPb(I1–xBrx)3, and the PbI2 precursor concentration of MAPbI3, [PbI2]. The Ave(Δσmax) value of MAPbI3 is superlinearly increased with [PbI2] (0.1–1 M), which is consistent with the increase in the crystallite size and consequent improvement of electronic quality (vide infra). In contrast, the mixed-halide perovskites exhibit a downward convex trend with a minimum at x ≈ 0.6 (the concentration of the mixed-halide precursor was fixed at 1 M). The standard deviations of Δσmax, Std(Δσmax), of MAPbI3 and MAPb(I1–xBrx)3 indicate mostly an identical dependence on the corresponding Ave(Δσmax) values (Figure 2b).

Figure 2.

Figure 2

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(a) Average and (b) standard deviation of Δσmax evaluated by STRMC. The blue triangles and red circles correspond to MAPbI3 (the lower horizontal axis is the precursor concentration, [PbI2]) and MAPb(I1–xBrx)3 (the upper horizontal axis is the content of Br, x), respectively. The solid lines are eye guides.

To quantify the spatial inhomogeneity of the electronic properties of perovskite films, we plotted the inhomogeneity factor (IF), defined as Std(Δσmax)/Ave(Δσmax), in Figure 3a. The IF represents a dimensionless variation of Δσmax; thus, a small IF means a uniform film. The IF of MAPbI3 is as large as 1.1 at [PbI2] = 0.2 M; then, it decreases dramatically to 0.5–0.3 at [PbI2] > 0.3 M. Accordingly, both the IF and Ave(Δσmax) are improved by increasing [PbI2]. On the other hand, the IFs of MAPb(I1–xBrx)3 remain almost constant at ∼0.4, in contrast to those of MAPbI3. It should be noted that these IFs are larger than the experimental errors observed in MAPbI3 at the same position (IF = 0.023, Figure S2) and at different positions measured on a piece of a homogeneous silicon wafer (IF = 0.06, Figure S3). Accordingly, the IF is an indicator of film inhomogeneity that cannot be evaluated by conventional, nonspatial TRMC.

Figure 3.

Figure 3

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(a) Inhomogeneity factors (IFs) of MAPbI3 (blue triangles: the lower horizontal axis is the precursor concentration, [PbI2]) and MAPb(I1–xBrx)3 (red circles: the upper horizontal axis is the content of Br, x), evaluated by STRMC. (b) Crystallite size of perovskite (L110), determined from the (110) diffraction peak of powder XRD and the Scherrer relation. (c) Position of the (110) peak of the powder XRD of perovskite. (d) IF vs L110 for MAPbI3 (blue triangles) and MAPb(I1–xBrx)3 (red circles). The solid lines are eye guides.

The crystallite sizes (L) of the perovskites were evaluated by XRD and the Scherrer relation52 (L ≈ 0.9λ(Δ2θ cos θ)−1, where λ is the wavelength of an X-ray, Δ2θ is the full width at half-maximum of the peak, and θ is the diffraction angle). The most intense peak ascribed to (110) diffraction53 at 2θ = 14–15° was analyzed and provided the L110 of MAPbI3 ([PbI2] = 0.1–1 M) and MAPb(I1–xBrx)3 (x = 0–1), as shown in Figure 3b (XRD profiles are provided in Figures S4 and S5). The L110 of MAPbI3 increases in a sublinear manner from 17 nm at [PbI2] = 0.1 M to 80 nm at [PbI2] = 1 M, whereas that of MAPb(I1–xBrx)3 exhibits a minimum of 70 nm at x = 0.4 and a maximum of 109 nm at x = 1. The (110) peak position of MAPb(I1–xBrx)3 is proportional to the bromide content (x), which indicates a crystallographically homogeneous mixing of iodide and bromide (Figure 3c). We note that a previous SEM characterization with a helium ion microscope and a secondary ion mass spectrometer (HIM-SIMS) visualized a nanometer-scale phase separation of I– and Br–, which would have an impact on the device performance and phase stability.54 In contrast, the peak shift of MAPbI3 is marginal, as small as +0.05°, over the entire [PbI2]. Interestingly, the L110 curves of MAPbI3 and MAPb(I1–xBrx)3 appear to be similar to those of Ave(Δσmax) and Std(Δσmax) (Figure 2), suggesting a correlation between the crystallite size and Δσmax. Previous studies have shown that large crystallites are advantageous to the charge carrier mobility55 and device efficiency.56 However, the plots of Ave(Δσmax) and Std(Δσmax) vs L110 are rather scattered, particularly in the large-L110 region, although a rough, superlinear trend is observed (Figure S6). Notably, an improved general trend is found when the IF is plotted as a function of L110 (Figure 3d). This indicates that spatial inhomogeneity in a few hundreds of micrometers is associated with a nanometer-scale crystallite size.

Additionally, we examined the dependence of the millimeter-scale Δσmax on the distance from the center of rotation (y) during spin coating (Figure 4a). The Δσmax of MAPbI3 ([PbI2] = 1 M) exhibits a winding curve with a period of ∼5 mm (Figure 4b), whereas the film thickness fluctuates in a different manner (Figure 4c). The AFM height images shown in Figure 4d demonstrate a position-dependent variation in the size and shape of grains. Particle size analysis obtained grain sizes of ∼0.12 μm at y = 0 and 5 mm, which decrease to ∼0.06 μm at y = 10 mm and then increase to ∼0.24 μm at y = 15 mm (Figure 4e). The cross-sectional profiles along the diagonal line of the image indicate a position-dependent variation in height (Figure 4d), accompanied by a monotonic increase in surface roughness (Ra = 10.3, 21.9, 29.1, and 25.4 nm at y = 0, 5, 10, and 15 mm, respectively). The inhomogeneity observed in the AFM images was possibly generated during the toluene (poor-solvent) treatment during spin coating. Toluene was dropped at the center of rotation and immediately spread; consequently, the inhomogeneity of the perovskite precursor was created according to the distance from the center. Moreover, the width of the quartz substrate used in our study was 9 mm; therefore, some changes in the poor-solvent treatment could occur at this distance. The abrupt drop observed in Δσmax (Figure 4b) and the grain size (Figure 4e) at y = 10 mm could be associated with the nonsymmetric shape of the substrate, which caused insufficient interaction between the toluene and perovskite precursor. Overall, Δσmax appears to increase with the distance from the center, which is qualitatively linked to the grain size, not the film thickness. Although a high Δσmax at long distances could favor high charge carrier mobility, the roughness and large deviation of the grain size causes an electric short of the layered solar cell, which would be detrimental to the device performance. Our STRMC evaluations demonstrate that a spatial inhomogeneity of Δσmax on sub-millimeter and millimeter scales is associated mainly with the grain size and that wet-processed organic–inorganic perovskites have a continuous deviation in their spatiotemporal optoelectronic behaviors.

Figure 4.

Figure 4

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(a) Schematic of spin coating on a rectangular quartz plate. (b) Δσmax dependence of MAPbI3 ([PbI2] = 1 M) on the distance from the center of rotation, y (mm). (c) Thickness dependence of an MAPbI3 film on y. (d) AFM height images (2 × 2 μm2) of an MAPbI3 film at y = 0, 5, 10, and 15 mm. (e) Grain sizes evaluated from the AFM images. (f) Cross-sectional height profiles along the diagonal direction from the top left to the bottom right of the AFM image. The color represents y.

Conclusions

A newly developed STRMC system was employed to investigate the spatial inhomogeneity of multicrystalline MAPbI3 and MAPb(I1–xBrx)3 perovskite films. The statistics of Δσmax exhibited a variation in the IF, which depends on the precursor concentration and the ratio of the mixed halide (I/Br). We observed a general decreasing trend of the IF with the crystallite sizes of MAPbI3 and MAPb(I1–xBrx)3, based on evaluations with XRD and the Scherrer relation. This indicates that the crystallite size, not the halide-mixing ratio, is key to the optoelectronic properties and, therefore, the performance of the device.

Experimental Section

Sample Preparation and Characterization

Perovskite chemicals (MAI, MABr, PbBr2, and PbI2) were purchased from Tokyo Chemical Industry (TCI) Co., Ltd. and used as received. A quartz substrate (40 × 9 × 1 mm3) was cleaned with detergent, acetone, isopropyl alcohol, and deionized water. A 200 nm thick mesoporous titanium dioxide (mpTiO2) layer was deposited onto quartz by spin-coating a diluted mpTiO2 paste (PST-18NR, JGC Catalysts and Chemicals Ltd.) in ethanol (paste/ethanol = 1:7 w/w), followed by sintering at 500 °C for 20 min. A 0.1–1 M (0.1 M step) dimethyl sulfoxide (DMSO, purchased from Kanto Chemical Co., Inc.) solution of PbI2 and MAI at 1:1 stoichiometry and a 1 M DMSO solution of PbX2 and MAX (X = I or Br) at a designated stoichiometry (I/Br = 0.9:0.1, 0.8:0.2, 0.7:0.3, 0.6:0.4, 0.5:0.5, 0.4:0.6, 0.3:0.7, 0.2:0.8, 0.1:0.9, 0:1) were prepared in a N2-filled glovebox. Subsequently, an MAPb(I1–xBrx)3 (x = 0–1) precursor layer was formed by spin-coating the DMSO solution with poor-solvent treatment using toluene onto the rotating substrate. The resultant semitransparent film was annealed at 100 °C for 10 min. For the STRMC evaluation, the quartz/mpTiO2/perovskite sample was cut into a ∼3 × 3 mm2 piece (the film at the center of rotation was used). For millimeter-scale STRMC, the sample was separated into 5 × 3 mm2 pieces and evaluated sequentially. Powder X-ray diffraction (XRD) data were collected on a Rigaku MiniFlex-600 X-ray spectrometer using Cu Kα radiation (λ = 1.54187 Å) at room temperature in air. A surface profile of mpTiO2 on a quartz plate was measured using a Bruker Dektak XT surface profiler. The AFM observations were performed using a Bruker Innova system (a cantilever with a spring constant of 2 N m–1) in air.

Space- and Time-Resolved Microwave Conductivity

Figure 5 illustrates a newly designed STRMC system that consists of an in-house X-band microwave circuit (a Rohde & Schwarz SMB100A signal generator, isolators, waveguides, a circulator, a TE102 mode resonant cavity, an iris coupling controller, an amplifier, a detector, and a Tektronix DPO4000 oscilloscope), an Olympus BXFM optical microscope equipped with a charge-coupled device camera and a near-UV-compatible objective lens (model M Plan Apo NUV, Mitsutoyo Co., Ltd.), an XY stage (model KY0830C, Suruga Seiki Co., Ltd.), and a Nd:YAG laser (model GCR-100, Spectra-Physics Inc.; 5–8 ns pulse duration, 10 Hz) with a mechanical shutter. The iris controller, which was driven by a stepping motor, was fabricated using a three-dimensional (3D) printer. A 3 × 3 mm2 specimen was placed on a Teflon rod that was fixed to the microwave cavity and the XY stage. The iris controller, the XY stage, a shutter controller, and the oscilloscope were connected to a computer and controlled by in-house software to perform automatic scanning of the sample (a one-point measurement required approximately 3 min, including movement of the stage, tuning the iris coupling and resonance frequency, opening the shutter, data averaging, and data acquisition). The spatial resolution of our STRMC system was limited by the spot size of the excitation laser pulse (∼20 μm), not the accuracy of the XY stage (∼1 μm). The spot size had a trade-off relationship with the signal intensity and the threshold of significant sample damage. The sample size and the laser spot size were evaluated by the optical microscope with a calibrated micrometer (OB-MM 1/100 mm, Olympus). The effective spatial resolution was ∼45 μm, which was estimated by scanning the laser spot across an edge of a silicon wafer (Figure S7). It should be mentioned that a commercially available scanning microwave microscope with an AFM cantilever has nanometer-scale resolution, whereas it does not allow time-resolved measurements.57,58 Although microwave photoconductance decay technique, which scans the sample under an arm of a microwave guide and light-pulse irradiation, allows both lifetime and conductance measurements, its scanning area is a few tens of centimeters.59 In our STRMC system, continuous microwaves of approximately 9.1 GHz and third-harmonic generation (355 nm) of a Nd:YAG laser (incident photon density I0 ∼ 1017 photons cm–2 pulse–1 after the objective lens) were used as the probe and excitation, respectively. The experiments were performed at 25 °C in air.

Figure 5.

Figure 5

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Schematic of the STRMC system. A part of the resonant cavity has been cut to show the interior.

Acknowledgments

This work was supported by the Japan Society for the Promotion of Science (JSPS) with the KAKENHI Grant-in-Aid for Scientific Research (A) (Grant No. JP16H02285), Grant-in-Aid for Challenging Exploratory Research (Grant No. JP15K13816), and Grant-in-Aid for Scientific Research on Innovative Area (π-figuration, Grant No. JP26620104a) and the PRESTO program (Grant No. JPMJPR15N6) from Japan Science and Technology Agency (JST) of Japan. F. C. acknowledges a scholarship from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan. The authors thank Yoji Miyake at Osaka University Creative Design Studio on Technology for his support in operating the 3D printer.

Supporting Information Available

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.7b01471.

  • Surface profile of mpTiO2 and its FFT (Figure S1); STRMC transients of MAPbI3 and their statistics at the same position (Figure S2); STRMC transients of a piece of silicon wafer and their statistics after scanning (Figure S3); XRD profiles of MAPbI3 (Figure S4); XRD profiles of MAPb(I1–xBrx)3 (Figure S5); Ave(Δσmax) and Std(Δσmax) vs L110 (Figure S6); evaluation of effective spatial resolution (Figure S7) (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao7b01471_si_001.pdf (1.4MB, pdf)

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