Supporting Information for Visualizing Carrier Diffusion in Individual Single-Crystal Organolead Halide Perovskite Nanowires and Nanoplates Wenming Tian, Chunyi Zhao,, Jing Leng, Rongrong Cui, and Shengye Jin*, Sational Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, 457 Zhong Shan Rd., Dalian, China, 116023. School of Physics and Optoelectronic Engineering, Dalian University of Technology, 2 Ling Gong Rd., Dalian, China, 116024. Synthesis of single-crystal CH 3 NH 3 PbI 3 and CH 3 NH 3 PbBr 3 NWs and NPs Synthesis of CH 3 NH 3 I. The CH 3 NH 3 I was synthesized by mixing 61 ml of methylamine (33 wt% in absolute ethanol) and 65 ml of HI (57 wt% in water by weight) in a flask in an ice bath at 0 C for 2 h with stirring. The methylammonium iodide (CH 3 NH 3 I) was achieved as the solvent was carefully removed using a rotate evaporator (Dragon Laboratory Instruments Limited RE100-PRO, China) at 50 C. The white CH 3 NH 3 I powder was washed with diethyl ether three times. The final product was collected by filtration and dried at 80 C in a vacuum oven for 24 h. Synthesis of CH 3 NH 3 Br. The CH 3 NH 3 Br was synthesized by mixing 30.5 ml of methylamine (33 wt% in absolute ethanol) and 28 ml of HBr (48 wt% in water by weight) in a flask in an ice bath at 0 C for 2 h with stirring. The methylammonium bromine (CH 3 NH 3 Br) was achieved as the solvent was carefully removed using a rotate evaporator (Dragon Laboratory Instruments Limited RE100-PRO, China) at 50 C. The white CH 3 NH 3 Br powder was washed with diethyl ether three times. The final product was collected by filtration and dried at 80 C in a vacuum oven for 24 h. Growth of single-crystal CH 3 NH 3 PbI 3 and CH 3 NH 3 PbBr 3 NWs and NPs. To synthesis single-crystal CH 3 NH 3 PbI 3 and CH 3 NH 3 PbBr 3 NWs and NPs, we smeared appropriate amount of 100 mg/ml PbAc 2 3H 2 O dimethylsulfoxide (DMSO) solution on a glass slide to form a thin film and dried the glass slide for 30 min at 65 C to evaporate off the solvent. We then immersed the PbAc 2 glass slide in 30 mg/ml CH 3 NH 3 I or 5 mg/ml CH 3 NH 3 Br isopropanol solution for ~24 h at room temperature to grow the single-crystal NWs and NPs. It is worth noticing that the glass slides S1
coated with PbAc 2 faced up for CH 3 NH 3 PbI 3 and faced down for CH 3 NH 3 PbBr 3 during reactions. After reaction, the sample was rinsed with isopropanol to remove the residual salt on the film, and then dried under a stream of nitrogen flow. Time-resolved and photoluminescence-scanned confocal microscopy: We use a home-built photoluminescence (PL)-scanned imaging microscopy coupled with a time-correlated single photon counting (TCSPC) to map the PL dynamics within the single-crystal perovskite NWs and NPs. Excitation of the sample is achieved with a supercontinuum white-light laser (SC400-PP, Fianium, UK) of 680 nm or 450 nm wavelength, 1 MHz repetition rate and ~6 ps pulse width. The excitation laser beam focuses on the sample through a 100 air objective lens (NA=0.95, Olympus PLFLN 100X) with the spot radius of 0.624 µm (1/e 2 of the maximum intensity measured with a EMCCD camera, DU-897U-CS0-#BV, Andor, UK) at 680 nm wavelength. The laser intensity at samples is adjusted by a neutral density filter and measured with a power meter (PM100D S130VC, Thorlabs, USA). By parking the excitation laser spot in a specific position of the NWs and NPs, fast scanning of the galvanometer mirror ensures to collect photons emission from the whole particle. Each scanning image contains 256 256 pixels with the dwell time of ~1 ms at each pixel. The PL decay kinetics at any positions in a NW or NP is obtained. The fluorescence signal is collected using a high speed detector (HPM-100-50, Hamamatsu, Japan) with a 710 nm long pass filter and 800 ±40 nm band pass filter. Besides, the 0.25 mm pinhole size is chose during the experiments. With the optical element used in the scan head the magnification, M, from the sample plane into the pinhole is: M=20.8 M lens =2080 (M lens is the magnification of the objective lens); The theoretical optical spot diameter is calculated by dividing the pinhole size with the magnification M: d spot = d pinhole /M=120 nm; The radius of the Airy disc is: S2
r Airy disc = 0.61λ/N.A. = 0.61 780 nm/0.95 = 500 nm (for CH 3 NH 3 PbI 3 with emission spectrum centered at 780 nm); r Airy disc = 0.61λ/N.A. = 0.61 543 nm/0.95 = 349 nm (for CH 3 NH 3 PbBr 3 with emission spectrum centered at 543 nm); Therefore, the resolution of the system is determined by the diffraction limit. Measurements of the diffusion distances in the PL intensity images: The PL-scanned imaging microcopy defines the scanning area by 256 256 pixels. The actual dimension of a scanning area can be measured at different zoom values of the galvanometer mirror scanner. For example, if zoom=1 and 100 objective lens is used, the scanning area is measured as 184 µm 184 µm, and each pixel is 184 µm/(256 zoom) = 718 nm. Based on the size of sample, we choose appropriate zoom, and the actual dimension of each pixel is determined, which is about 20~80 nanometers in our experiments. The location of the excitation spot is picked up at the center of the excitation spot. Distances from a selected pixel to the excitation spot can be calculated by counting pixels between them. Due to the diffraction limit, PL kinetic selected from a single pixel is actually constructed by photons collected from area of the diffraction-limited spot. We therefore define the error of the measured diffusion distance as the diffraction-limited diameter. Calculation of carrier density: Base on the SEM images, we estimate the average thickness (d) of the perovskite NWs and NPs as ~500 nm. The photo-excited charge carrier density ϕ 0 is determined using the following equation: 0 = α Eλ hcv (1 e εd )(1 R pump ) where E is the energy of a single excitation pulse at wavelength λ, ε is the absorption coefficient; d is the optical depth (sample thickness); h is the Planck's constant, c is the speed of light; v is the excitation volume; is the ratio of charge created per photon absorbed, which is assumed to be 1; R pump is the reflectivity of the sample at normal incidence of the excitation beam. The values of ε is 3.9 10 4 cm -1 at S3
680 nm for CH 3 NH 3 PbI 3 1 and 6.5 10 4 cm -1 at 450 nm for CH 3 NH 3 PbBr 3. 2 The carrier density ϕ 0 is estimated for the NWs and NPs ranging from (1.0~4.7) 10 17 cm -3. At these carrier intensity levels, three-body Auger recombination process can be ignored. 3 Absorption of waveguided excitation photons inside the perovskite crystals: the observed PL signals from other than the excitation site may originate from three possible processes: 1) radiative recombination of electrons and holes diffusing from the excitation site; 2) radiative recombination of electrons and holes generated by the excitation of waveguided laser photons; 3) radiative recombination of electrons or holes diffusing from the excitation site with the traps generated by the excitation of waveguided laser photons. However, we exclude the latter two possibilities by calculating the penetration depth (distance) of the waveguided laser photons along the lateral dimension inside the crystal by: I/I 0 =exp(-εd), where I 0 is the initial laser intensity, and I is the laser intensity after passing through of distance of d; ε is the absorption coefficient of CH 3 NH 3 PbI 3 and is 3.9 10 4 cm -1 at the excitation wavelength of 680 nm. We then calculate that for d =1 μm, I/I 0 = 2%; d = 1.5 μm, I/I 0 = 0.3%; d = 2 μm, I/I 0 = 0.04%. So within 2 μm from the excitation spot, almost 100% waveguided excitation photons are absorbed by the perovskite. Therefore, we conclude that the PL signals from diffusion-distances > 2 μm should not be due to the excitation by the waveguided laser. Further details about the simulation of carrier diffusion in the perovskite NWs and NPs. The boundary condition for the diffusion is defined as + (L x,y,t) x = (0,y,t) x = + (x,l y,t) y = (x,0,t) y = 0 (S1) The + and indicate the forward and backward first-order differential. Moreover, we use the Gaussian function to describe the initial (t=0) distribution of charge carriers at the excitation site: (x, y, 0) exc. = (x 0, y 0, 0) exp ( 2 (x x 0) 2 +(y y 0 ) 2 ) (S2) r 2 (x, y, 0) exc. dxdy = 0 (S3) S4
where (x 0, y 0, 0) is the carrier density at the center of the distribution; r is the radius of the distribution which is measured to be ~0.64 μm; ϕ 0 is total initial carrier density. Because Eq. (1) in the main text does not have an analytical solution, we perform the simulation of the carrier diffusion process in perovskite NWs and NPs using a home-built program. The side length of the NWs and NPs (Lx and L Y ) and excitation site (x 0, y 0 ) were determined from the optical and PL intensity images. From this simulation, the change of carrier density as a function of delay time at any position (within a circle area of ~0.5 μm in radius) in the NP is determined, and is used to fit the experimental PL kinetics. Figure S1. (a) SEM image of as-grown CH 3 NH 3 PbBr 3 nanostructures. The emission spectra of CH 3 NH 3 PbI 3 (b) and CH 3 NH 3 PbBr 3 (c) nanostructures. (d) The powder X-ray diffraction (PXRD) pattern and the transmission electron microscope (insets) diffraction pattern of the as-grown CH 3 NH 3 PbI 3 and CH 3 NH 3 PbBr 3 nanostructures. These results confirm the high quality and pure tetragonal (CH 3 NH 3 PbI 3 ) and cubic (CH 3 NH 3 PbBr 3 ) crystal structure of the perovskites without any impurities. S5
Figure S2. Comparison of the carrier diffusion measurements with the excitation at the end (a) and the center (b) of a CH 3 NH 3 PbI 3 NP. The measured diffusion coefficient is 1.67 ± 0.02 cm 2 s -1 for a and 1.60 ± 0.01 cm 2 s -1 for b. The PL images show that the WG effect persists no matter where the sample is excited. Figure S3. The diffusion coefficients of a CH 3 NH 3 PbI 3 NP at 0, 2, 3, 5 and 22 h measured under ambient condition. The imaging collection time is 10 minutes for each data point. The diffusion coefficients are very similar in the first 5 hours and slightly drop after 22 hours, indicating that the perovskite crystal does not undergo significant photoinduced degradation. S6
Figure S4. Time evolution of the PL intensity image of the NP shown in Figure 2. Figure S5. PL kinetics collected at the indicated positions and diffusion distances in the NP shown in Figure 2. Black solid lines are total decay curves collected from the whole NP and normalized to the PL kinetics at different positions. The WG component reduces as the diffusion distance increases, but they all can be well described by the total PL decay from the whole NP. S7
Figure S6. Additional examples of the measurements of CH 3 NH 3 PbI 3 and CH 3 NH 3 PbBr 3 NWs and NPs. S8
Figure S7. (a) Comparison of diffusion coefficient distributions between NWs and NPs. Plots of side length and surface area (normalized by volume) vs diffusion coefficient of CH 3 NH 3 PbI 3 (b) and CH 3 NH 3 PbBr 3 (c) NWs and NPs. S9
Table S1. Fitting parameters of all the examined CH 3 NH 3 PbI 3 and CH 3 NH 3 PbBr 3 NWs and NPs. The charge mobility is calculated from diffusion coefficient. D µ k 1 k 2 CH 3 NH 3 PbI 3 (cm 2 s -1 ) (cm 2 V -1 s -1 ) ( 10 6 s -1 ) ( 10-11 cm 3 s -1 ) 1 1.75±0.03 68.2±1.1 1.59±0.03 9.85±1.20 2 1.65±0.03 64.1±1.0 0.77±0.03 8.24±0.69 3 2.28±0.04 88.8±1.4 0.44±0.02 10.05±0.81 4 2.41±0.04 93.9±1.6 0.56±0.02 6.17±1.01 5 2.23±0.03 87.0±1.0 1.00±0.02 6.16±1.00 6 1.45±0.02 56.5±0.8 0.49±0.03 8.55±0.50 7 1.59±0.01 62.0±0.4 2.02±0.03 6.25±0.51 8 1.60±0.01 62.4±0.6 3.22±0.04 3.08±0.34 9 1.89±0.02 73.7±0.7 0.83±0.02 2.01±0.65 10 2.03±0.02 79.0±0.8 3.05±0.04 1.82±0.68 11 1.94±0.02 75.5±0.9 2.41±0.04 0.28±0.96 12 2.10±0.02 81.7±0.7 2.51±0.02 0.89±0.10 14 2.05±0.02 79.7±0.7 0.82±0.02 3.76±0.26 15 2.15±0.02 83.7±0.7 1.13±0.02 3.66±0.10 16 1.90±0.06 74.0±2.5 4.90±0.2 29.41±6.57 17 1.73±0.02 67.3±0.9 0.81±0.04 7.81±0.24 18 1.82±0.02 70.9±0.7 2.56±0.03 9.9±0.39 19 1.45±0.01 56.4±0.5 0.67±0.02 7.66±0.17 20 2.09±0.02 81.5±0.9 0.92±0.06 14.27±0.8 21 2.23±0.02 86.9±0.9 0.32±0.02 5.10±0.11 22 2.15±0.03 83.6±1.2 0.82±0.08 19.48±1.11 23 1.73±0.01 67.5±0.3 0.75±0.01 7.77±0.10 D µ CH 3 NH 3 PbBr 3 (cm 2 s -1 ) (cm 2 V -1 s -1 ) k 1 k 2 ( 10 6 s -1 ) ( 10-11 cm 3 s -1 ) 1 1.25±0.09 48.7±3.5 3.96±0.44 1.85±1.31 2 0.85±0.02 33.0±1.0 3.51±0.16 1.51±0.53 3 1.03±0.08 40.3±3.1 3.15±0.41 12.86±3.59 4 1.44±0.07 56.1±2.9 1.71±0.48 27.37±3.93 5 0.88±0.04 34.2±1.7 4.12±0.50 18.56±2.73 6 1.26±0.04 49.2±1.6 3.93±0.38 13.41±1.35 7 1.25±0.02 48.5±1.0 7.70±0.11 2.39±0.19 8 1.36±0.04 52.9±1.5 4.27±0.31 6.39±0.85 9 0.88±0.02 34.2±0.7 2.53±0.10 1.95±0.06 10 1.29±0.12 50.2±4.5 1.91±0.60 7.48±1.76 11 1.03±0.06 40.1±2.2 4.72±0.51 1.41±0.47 12 1.22±0.12 47.3±4.5 4.76±0.60 1.02±1.61 13 1.02±0.05 39.7±2.0 2.56±0.32 5.46±0.99 14 1.20±0.07 46.7±2.7 5.88±0.53 2.68±0.72 15 1.18±0.03 45.9±1.3 2.69±0.13 1.61±0.10 16 1.36±0.04 52.9±1.5 4.27±0.31 6.39±0.84 17 0.49±0.04 19.4±1.6 0.55±0.35 71.52±20.11 S10
Figure S8. Excitation intensity-dependent measurement of carrier diffusion in a single-crystal CH 3 NH 3 PbI 3 NP. (a) The optical and (b) PL intensity images of the NP. (c) The total PL decay curves of the NP under different excitation intensities. The inset shows the decays before normalization. As the intensity increases, the amplitude of the fast component becomes larger, implying the presence of the second order recombination process. (d) (e) and (f) PL kinetics at a set of diffusion distances under three different excitation intensities. The solid lines are the fits of the kinetics. The fitting parameters are summarized in Table S2. These results indicate that the measured parameters are consistent under different excitation intensities. Table S2. The fitting parameters of the PL kinetics in Figure S8 under different excitation intensities Excitation Intensity (µj cm -2 pulse -1 ) D ( cm 2 s -1 ) k 1 k 2 * (s -1 ) 10 6 (cm 3 s -1 ) 10-11 0.964 2.11±0.03 4.48±0.07-1.61 1.96±0.02 4.09±0.04 2.41±0.68 3.1 1.93±0.01 3.99±0.09 6.18±1.36 *Under the lowest examined excitation intensity, the fitting of the PL kinetics yields k 2 value of ~ 0. We believe that at the lowest intensity the carrier density at a diffusion distance 4 μm is very low, and the recombination is dominated by the first-order (trapping) process. S11
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