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Photocurrent Mapping in Single-Crystal Methylammonium Lead Iodide Perovskite Nanostructures Rui Xiao, Yasen Hou, Yongping Fu, Xingyue Peng, Qi Wang, Eliovardo Gonzalez, Song Jin, and Dong Yu Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b03782 • Publication Date (Web): 16 Nov 2016 Downloaded from http://pubs.acs.org on November 17, 2016

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Figure 1. Optoelectronic characteristics of MAPbI3 nanowire photodetector devices. (a) Scanning electron microscopic (SEM) image of a typical device, where a MAPbI3 nanowire is transferred on top of prepatterned Au electrodes. (b) I-Vsd curves at laser illumination power from 2.6 to 72 nW, corresponding to a peak intensity of 1.3 - 37 W/cm2. Vsd scans at a rate of 0.2 V/s and first to positive voltage. The arrows indicate the scan direction. Inset: an equivalent circuit diagram composed of two back-to-back diodes. (c) Laser power dependent photocurrent under Vsd = 1.5 V. (d) Photocurrent time trace under uniform light illumination of 10 mW/cm2 as Vsd is switched on and off. 81x79mm (286 x 286 DPI)

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Figure 2. AFM and KPFM characterizations of a MAPbI3 nanoplate device. (a) AFM image of a nanoplate across two electrodes, where the preamp is connected to the left electrode and the bias voltage Vsd is applied to the right electrode as labeled. (b) KPFM cross-sections at Vsd = 2 V and -2 V, respectively. The cross sections are taken along the path from point A to B, C, and D, as indicated in (c). (c) KPFM images at Vsd = 2 V and -2 V, respectively. The dashed lines indicate the path where the cross sections are taken in (b). The black lines are caused by an artifact in potential measurements as the AFM tip scans near the edge of the nanoplate. (d) Energy band diagrams at different Vsd. 81x62mm (286 x 286 DPI)


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Figure 3. Photocurrent mapping of a MAPbI3 nanowire device. All data are taken with laser wavelength at 532 nm and a 40× objective lens with a numerical aperture of 0.6. (a) Schematic of SPCM setup. (b) Optical microscopic image of the device. The Au electrodes are slightly out of focus in order to focus on the top surface of the nanowire. The left electrode touching the left tip of the nanowire is floating. The middle electrode is connected to preamp while the right is connected to the bias voltage. An electrically inactive nanoplate is also seen to the right of the device. (c) SPCM images at various Vsd showing the shift and broadening of the photocurrent peak. The pink stripes indicate the positions of the source-drain electrodes. The color scales are different for each image and the width of the image is 40 µm. (d) Photocurrent line scan along the nanowire axis under Vsd from -1.5 to -0.3 V and 0.3 to 1.5 V with a step of 0.2 V. The photocurrent peaks are indicated by black arrows. (e) Semi-log plots of the positively biased data in (d) showing that the photocurrent follows an exponential curve well. (f) LD vs. Vsd extracted from (e), demonstrating that the slope is insensitive of Vsd. The error bars are determined by fitting multiple line scans. The laser peak intensity is 2.6 W/cm2 for (c-f). (g) Semi-log plots of the photocurrent line scans at Vsd = 1.0 V and various laser powers from 1.3 to 2138 nW, corresponding to peak intensity from 0.26 to 440 W/cm2. (h) LD vs. laser power extracted from (g). 160x81mm (286 x 286 DPI)


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Figure 4. Long carrier diffusion lengths in MAPbI3 nanostructures. (a) SEM image of the device with a 44 µm long nanowire. (b) Photocurrent line scans at Vsd = 2.5 V and - 2.5 V, where the diffusion length is extracted by exponential fitting of the segment close to the reversely biased electrode. All data are taken with laser wavelength at 532 nm and a 40× objective lens with a numerical aperture of 0.6. The laser peak intensity is 2.6 W/cm2. 43x41mm (286 x 286 DPI)


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Figure 5. Wavelength dependent SPCM of MAPbI3 nanoplates. All data are taken with a 100× objective lens with a numerical aperture of 0.95. The laser peak intensity is kept at 0.76 W/cm2 at all wavelength. (a) SPCM images collected using different laser wavelength at Vsd = 1.0 V. (b) Photocurrent as a function of wavelength at three representative points (A: edge, B: electrode, C: center). The positions of the three points are shown in (a). (c) Simulated ratio of absorbed power to the incident power (Pabs/P0) as a function of wavelength, as the laser is focused at the center and the edge of the nanoplate, respectively. Red circle is for laser incident on the center of the nanoplate, blue triangle (inverse triangle) is on the edge with polarization parallel with X (Y) axis. The inset indicates the definition of the coordinates and the orange box represents the nanoplate. (d-g) Cross sections of electric field magnitude distribution in the X-Z plane. The nanoplate is in the X-Y plane while the focusing laser beam is incident from the top along the Z axis. The dashed boxes indicate the position of the nanoplate. (d, e) λ = 700 nm (f, g) λ = 800 nm. (d, f) laser is focused at the center; (e, g) at the edge with polarization along the X axis. 166x82mm (286 x 286 DPI)


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Photocurrent Mapping in Single-Crystal Methylammonium Lead Iodide Perovskite Nanostructures Rui Xiao, 1 Yasen Hou,1 Yongping Fu, 2 Xingyue Peng, 1 Qi Wang, 1 Eliovardo Gonzalez,3 Song Jin,2* and Dong Yu1* 1

Department of Physics, University of California, 1 Shields Avenue, Davis, California 95616,

United States 2

Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue,

Madison, Wisconsin 53706, United States 3

Department of Physics, California State University, 5500 University Parkway, San Bernardino,

California 92407, United States *E-mail: [email protected], [email protected]

Keywords: lead halide perovskite, photocurrent, scanning photocurrent microscopy, carrier diffusion length, nanostructures, photonics

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Abstract: We investigate solution-grown single-crystal methylammonium lead iodide (MAPbI3) nanowires and nanoplates with spatially resolved photocurrent mapping. Sensitive perovskite photodetectors with Schottky contacts are fabricated by directly transferring the nanostructures on top of pre-patterned gold electrodes. Scanning photocurrent microscopy (SPCM) measurements on these single-crystal nanostructures reveal a minority charge carrier diffusion length up to 21 µm, which is significantly longer than the values observed in polycrystalline MAPbI3 thin films. When the excitation energy is close to the bandgap, the photocurrent becomes substantially stronger at the edges of nanostructures, which can be understood by the enhancement of light coupling to the nanostructures. These perovskite nanostructures with long carrier diffusion lengths and strong photonic enhancement not only provide an excellent platform for studying their intrinsic properties but may also boost the performance of perovskite-based optoelectronic devices.

Hybrid organic-inorganic metal halide perovskite compounds, as exemplified by methylammonium (CH3NH3+, MA) lead halide MAPbX3 (X = Cl, Br, I), have recently demonstrated great potentials for cost-effective solar energy conversion. The power conversion efficiency (PCE) of the solar cells based on these compounds had increased from 3% to over 20% in just five years.1-7 To date, experimental efforts on lead halide perovskites have often been focused on the thin film preparation procedures and their effects on film quality such as grain sizes, crystallinity, and resulted solar device efficiencies, while the basic charge transport/relaxation mechanisms in these materials are still under debate.8, 9 The insufficient or inconclusive understanding is partly caused by the polycrystalline thin film samples commonly used, where grain boundaries can convolute the understanding of the intrinsic properties of 2 ACS Paragon Plus Environment

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perovskites. For example, the Ginger group has demonstrated that the photoluminescence (PL) at the grain boundaries is significantly weaker and exhibits much faster nonradiative decay.10 Carrier diffusion lengths were found to be ~1 µm in polycrystalline MAPbI3 perovskite thin films,11 but > 175 µm in MAPbI3 single crystals.12 High quality single crystals or single-crystal nanostructures with lower level of defects and well-controlled facets may result in better solar cells,13 lasing,14 photodetectors,15 and light emitting diodes (LEDs)16 and offer a better material platform for studying their fundamental properties and intrinsic characteristics.12, 17 Most previous optoelectronic studies of halide perovskites were performed using largearea illumination where the entire sample is illuminated by nearly uniform light intensity.1-7, 18 Spatially resolved optoelectronic investigation can reveal important information on charge transport and recombination in these materials. Scanning photocurrent microscopy (SPCM) is a unique technique for extracting a number of important physical properties in one-dimensional (1D) and two-dimensional (2D) nanostructures, including electrical field distribution, local band bending, and carrier diffusion lengths.19-26 In a SPCM setup, a tightly focused laser beam is raster-scanned at the surface of a planar electronic device, while the photocurrent is recorded as a function of illumination position (see more details in a review paper27). Though minority carrier diffusion lengths in nanostructured perovskites have recently been measured using PL imaging,28 SPCM is complementary to this technique and provides an independent measurement of this important physical parameter. Furthermore, SPCM offers a more direct measurement of diffusion lengths in devices with contacts and allows studies of charge transport under electric field. In addition to the 2D scan, excitation wavelength can be adjusted to achieve photocurrent mapping in the vertical dimension. High energy photons are absorbed close to the surface, while photons with energy close to the bandgap tend to penetrate deeper. By varying the incident


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wavelength, we can selectively inject carriers at different distances from the surface, therefore enable the investigation of the spatial distribution of photocurrent in the dimension vertical to the device plane. Very recently, SPCM has been used to study polycrystalline MAPbI3 microwires to investigate ion migration instead of electron/hole transport in perovskite.29 Here, applying this three-dimensional

(3D)

photocurrent

mapping

technique

to

single-crystal

perovskite

nanostructures, we aim to achieve understanding in electronic band structures and charge carrier/photon transport in this exciting optoelectronic material. Methylammonium lead triiodide perovskite (MAPbI3) nanowires and nanoplates are synthesized by a reaction of PbAc2 film and MAI solution in isopropanol via a dissolution and recrystallization mechanism.14,

30

By adjusting the growth parameters, we have synthesized

nanowires and nanoplates of 300 nm - 1 µm in thickness and up to 50 µm in length, suitable for studying the spatial distribution of photocurrent (see Figure S1a and S1b for optical and SEM images). Transmission electron microscopy (TEM) shows these nanostructures are single crystalline (Figure S1b and S1c), consistent with what had been shown previously.14, 30 Because of the solvent and heat sensitivity of the hybrid perovskites, it is difficult to fabricate nanowire (or nanoplate) devices using conventional lithographic method, which requires resist baking, UV or e-beam irradiation, and lift-off in polar solvent. To prevent the degradation of these singlecrystal nanostructures during device fabrication process, we directly transfer the MAPbI3 nanostructures to pre-patterned Au electrodes with a separation of 8-20 µm, without exposing the nanostructures to the detrimental procedures (see experimental details in Methods). Figure 1a exhibits a typical MAPbI3 nanowire device, where a nanowire lies on top of two Au electrodes. The nanowires display well defined facets and smooth and clean surfaces. These devices are stable in ambient air (our lab humidity is usually about 30%) for days without much change in


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morphology or electronic properties. The lifetime of the devices can be further extended if they are kept in a nitrogen glovebox.

Figure 1. Optoelectronic characteristics of MAPbI3 nanowire photodetector devices. (a) Scanning electron microscopic (SEM) image of a typical device, where a MAPbI3 nanowire is transferred on top of pre-patterned Au electrodes. (b) I-Vsd curves at laser illumination power from 2.6 to 72 nW, corresponding to a peak intensity of 1.3 - 37 W/cm2. Vsd scans at a rate of 0.2 V/s and first to positive voltage. The arrows indicate the scan direction. Inset: an equivalent circuit diagram composed of two back-to-back diodes. (c) Laser power dependent photocurrent under Vsd = 1.5 V. (d) Photocurrent time trace under uniform light illumination of 10 mW/cm2 as Vsd is switched on and off. The devices are insulating in dark and the electric current is beyond the sensitivity of our preamp (~1 pA) under a 2.0 V source-drain bias (Vsd). However, the devices are readily conductive under illumination. Figure 1b shows the current-voltage (I-Vsd) characteristics of a typical device, with a diffraction limited laser spot (beam width Wlaser = 250 nm and wavelength

λ = 532 nm) illuminated in the middle of the nanowire. Under illumination, the current-voltage 5 ACS Paragon Plus Environment

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(I-Vsd) curves are nonlinear and the current saturates at high Vsd. The current saturation can be understood with an equivalent circuit diagram composed of two back-to-back diodes (Figure 1b inset), representing the contact barriers. At high Vsd, one of the two diodes is reversely biased and limits the current. The current at high Vsd in the saturation region increases linearly with the light intensity (Figure 1c). From the slope, we calculate a responsivity R = ∆I / P = 0.11 A/W, where ∆I = I - I0 ≈ I is the photocurrent and P is the incident power. A gain of Γ = (∆I/e) / (P/hν) = R hν /e = 0.25 is estimated, where hν is the photon energy and e is the magnitude of the electron charge. The lower-than-unity gain value indicates power loss, which is partly caused by the reflection and fluorescence. Both the responsivity and gain values are high and comparable to previously published values in perovskite-based photodetectors,31 demonstrating the quality of our devices. By carefully examining the I-Vsd curves at low Vsd before saturation, we note a few interesting observations: (1) the I-Vsd curves show a small hysteresis; (2) the current increases superlinearly with Vsd; (3) the current fluctuates slightly (evidenced by the slightly unsmooth IVsd curves before saturation in Figure 1b). It is well known that perovskite-based solar cells show different current densities upon forward and backward scan of bias voltage,9 which has been attributed to ferroelectricity,32 ion drift,33 or charge traps.34 In order to clarify the mechanism of this hysteresis, we measure photocurrent as Vsd is switched on and off. As Vsd is reset from 2 V to 0 V, the photocurrent becomes negative and returns to zero in a few seconds (Figure 1d). When performing this measurement at 80 K (see Figure S2 in the Supporting Information), the current returns to zero immediately after Vsd is reset to zero. This indicates that the ferroelectricity unlikely accounts for the observed hysteresis, since ferroelectric effects are expected to be stronger at low temperature. In addition, our electric field (~0.1 V / µm) is significantly smaller 6 ACS Paragon Plus Environment

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than those used to for ion drift experiment (> 1 V / µm).33 Therefore, it is most likely that the observed photocurrent hysteresis in our devices is caused by charge traps. This also explains the superlinear I-Vsd curves before saturation and the fact that the current is larger when returning from positive bias to zero (scan direction is indicated by arrows in Figure 1b), since the conductance is limited by the unfilled traps at lower bias and the conductance increases after the traps are filled at higher bias. Finally, the fluctuation in the current before saturation can be attributed to the dynamic trapping and detrapping process, as observed in other semiconductor nanowires.35 The photocurrent hysteresis observed in single crystal MAPbI3 in general is smaller compared to the polycrystalline thin films,33, 34 suggesting lower trap density presumably caused by the smaller surface to volume ratio and/or the low-defect-density surface facets in these nanostructures.14 To further confirm the contact barriers, we apply Kelvin probe force microscopy (KPFM) to measure the surface potential of the nanostructure devices. While the atomic force microscopic image (AFM) shows a smooth surface (R.M.S. < 4 nm, Figure 2a) of a MAPbI3 nanoplate, the surface potential distribution is far from being uniform (Figures 2b, c). The potential changes slowly along the line "BC" at the surface of the nanoplate (< 0.3 V across 10 µm), but abruptly along the line "AB" or "CD" between the nanoplate and the contacts (up to 0.6 V sharply across the edge of the nanoplate). Furthermore, at Vsd = 2 V the potential drop is larger on the left electrode (from point B to A) and smaller on the right electrode (from point C to D), while at Vsd = -2 V the larger potential drop shifts to the right electrode (Figures 2b, c). This is consistent with the back-to-back diode model, since the large potential drop is always at the reversely biased electrode, which shifts to the opposite electrode as the polarity of Vsd switches. The large potential drop at the negative electrode indicates a downward band bending from the 7 ACS Paragon Plus Environment

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perovskite to the Au electrode and the n-type doping of the perovskite (Figure 2d). We note that the contact potential measured in small objects by the amplitude-modulated (AM) KPFM is an average of the long range electrostatic potential and tends to be lower than the actual value for small objects.36 While the measured absolute potential is not quantitatively accurate, the relative potential distribution is robust and clearly supports our back-to-back diode model. Such a Schottky barrier is also expected theoretically: the work function of Au is 5.1 eV and the conduction (valence) band edge of MAPbI3 is 3.9 (5.45) eV,37 which indeed suggests a downward band bending from n-type perovskite to Au. The n-type nature of these MaPbI3 nanowires is also consistent with our previous publication.30 The identification of the Schottky junctions not only sheds light on the electronic band bending at the Au/MAPbI3 interface but also assures extraction of carrier diffusion lengths from such devices by SPCM, as at least one Schottky contact is required to obtain carrier diffusion lengths.38

Figure 2. AFM and KPFM characterizations of a MAPbI3 nanoplate device. (a) AFM image of a nanoplate across two electrodes, where the preamp is connected to the left electrode and the bias 8 ACS Paragon Plus Environment

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voltage Vsd is applied to the right electrode as labeled. (b) KPFM cross-sections at Vsd = 2 V and -2 V, respectively. The cross sections are taken along the path from point A to B, C, and D, as indicated in (c). (c) KPFM images at Vsd = 2 V and -2 V, respectively. The dashed lines indicate the path where the cross sections are taken in (b). The black lines are caused by an artifact in potential measurements as the AFM tip scans near the edge of the nanoplate. (d) Energy band diagrams at different Vsd. We now present our SPCM results (Figure 3) by first discussing the photocurrent distribution between the source-drain electrodes, represented by the pink stripes in the figure. At positive (negative) Vsd, the photocurrent peak is near the left (right) electrode. The peak is not exactly at the electrode but a few µm's away (Figures 3c, d). This is because the photocurrent reaches maximum when the photogenerated electrons and holes have the same probability to reach the contacts. When the injection point is away from this peak position but closer to the hole (electron) collecting electrode, the electron (hole) collection will become the limiting factor and the total current decreases.20, 38, 39 The photocurrent peak is close to the hole collecting electrode (negatively biased), indicating the hole (minority carrier) diffusion length is shorter than the electron diffusion length, as expected in an n-type material. As Vsd increases, the peak becomes broader (Figures 3c, d), likely because the increased electric field along the nanowire assists the carrier movement. In this case, the diffusion length = √, where is D is the carrier diffusion coefficient and τ is the carrier lifetime, is replaced by the longer drift length = , where µ is the carrier mobility and E is the electric field.24 As E increases, the LE becomes comparable with the channel length so the photocurrent distribution becomes more uniform. Such field dependent photocurrent distribution indicates that the charge transport in our devices is mainly caused by charge diffusion/drift and is unlikely dominated by the photo-recycling process,40 since the photon transport should not depend on the applied electric field. Quantitatively, a finite element method (FEM) simulation was conducted by solving the Poisson and charge transport


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equations in 1D concurrently.38, 41 The simulation includes both the drift and diffusion of both electrons and holes, but not the photo-recycling process. The simulation results agree with the experimentally measured Vsd dependent SPCM profiles very well, where the photocurrent peaks are broadened at higher Vsd (Figure S3 in the Supporting Information). The physical parameters used in the simulations are listed in Table S1.

Figure 3. Photocurrent mapping of a MAPbI3 nanowire device. All data are taken with laser wavelength at 532 nm and a 40× objective lens with a numerical aperture of 0.6. (a) Schematic of SPCM setup. (b) Optical microscopic image of the device. The Au electrodes are slightly out of focus in order to focus on the top surface of the nanowire. The left electrode touching the left tip of the nanowire is floating. The middle electrode is connected to preamp while the right is connected to the bias voltage. An electrically inactive nanoplate is also seen to the right of the device. (c) SPCM images at various Vsd showing the shift and broadening of the photocurrent peak. The pink stripes indicate the positions of the source-drain electrodes. The color scales are different for each image and the width of the image is 40 µm. (d) Photocurrent line scan along the nanowire axis under Vsd from -1.5 to -0.3 V and 0.3 to 1.5 V with a step of 0.2 V. The photocurrent peaks are indicated by black arrows. (e) Semi-log plots of the positively biased data in (d) showing that the photocurrent follows an exponential curve well. (f) LD vs. Vsd extracted from (e), demonstrating that the slope is insensitive of Vsd. The error bars are determined by fitting multiple line scans. The laser peak intensity is 2.6 W/cm2 for (c-f). (g) Semi-log plots of the photocurrent line scans at Vsd = 1.0 V


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and various laser powers from 1.3 to 2138 nW, corresponding to peak intensity from 0.26 to 440 W/cm2. (h) LD vs. laser power extracted from (g). After understanding the photocurrent distribution between electrodes, we now turn our attention to the segment outside the electrode gap. To more rigorously extract carrier diffusion length, we intentionally make devices with a long segment of the nanowire extended out of the electrode gap, where the electric field is expected to be zero (Figure 3b). The applied bias leads to a potential drop at the Schottky contact where the charge separation occurs, while the part extended out of the gap remains field free and the charge transport in this part is dominated by the charge carrier diffusion. The abrupt potential drop near contacts observed in KPFM measurements also indicates the depletion width is short so that the drift current does not contribute significantly to our SPCM measurements. The photocurrent distributions as a function of the carrier injection position along the nanowire axis at various biases are shown in Figures 3d-f, where the photocurrent decays exponentially along the nanowire axis to the left of the electrodes. Figure 3e exhibits the semi-log plots of photocurrent profiles for several Vsd values. The photocurrent decay in these semi-log plots can be fit well by a straight line, indicating it follows a single exponential curve well. Importantly, the slope is independent of Vsd (Figure 3f), confirming the diffusion nature of the charge transport in this outer segment. The purpose of Vsd is to create a strong band bending at the hole collecting contact to increase our photocurrent signal, while the charge transport process in the unbiased region has a diffusion nature. The photocurrent decay length is determined by the minority carrier (hole) diffusion length as the high density major carriers (electrons) redistribute to satisfy local charge neutrality (see more detailed discussion in ref. 41). Photons generate both electrons and holes in the unbiased region. When the holes diffuse through the unbiased regions and are collected by the contact, the


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corresponding electrons enter the biased region through the nanowire, either move to the other contacts or recombine with holes in the biased region. To better understand the charge recombination mechanism, we measure LD as a function of laser intensity. As the laser peak intensity is increased from 0.26 to 440 W/cm2 by over 3 orders of magnitude, LD slightly increases from 7.0 to 8.2 µm (Figures 3g, h). As D is not expected to change with the laser intensity, the intensity dependence indicates τ slightly increases at high intensity. Previous work42 has demonstrated a reduced τ in the bimolecular recombination in MAPbI3 at high excitation intensity, which we did not observe in the intensity range of our measurements (laser intensity greater than 1 kW/cm2 causes an irreversible decrease of LD). We have also performed SPCM with the entire nanowire exposed to an additional uniform large-area illumination, and found LD is insensitive to a large-area illumination of 0.1 W/cm2 (Figure S4). The observed insensitive intensity dependence indicates that the dark carrier concentration in our devices is higher or comparable to the injected carrier concentration. Otherwise, if photogenerated carrier concentration is higher than the dark carrier concentration (∆n > n0), τ is expected to decrease at high intensity as it should be inversely proportional to the carrier concentration, i.e.,τ ~ 1/(∆n+ n0). The observed slight increase of τ at high intensity may be caused by the filling of the charge traps by the photogenerated carriers. The measured LD in this specific device is about 8 µm. Among the four devices of sufficiently long nanowires measured, LD varies from 8 to 21 µm (results from all measured devices are summarized in Table S2). Figure 4 shows the SPCM data of a device with LD up to 21 µm. In this device, a 44 µm long nanowire lies on top of the two Au electrodes with a separation of 8 µm, with both left and right segments extended out of the electrode gap. The


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focused laser illuminating at the tip of the nanowire more than 15 µm away from the electrodes can still create a strong photocurrent, suggesting that photogenerated carriers diffuse in a long distance. Figure 4 shows that the photocurrent is stronger when the laser is focused near the negatively biased contact, indicating the nanowire is n-type and the minority carriers are holes. The photocurrent decay can again be fit well by a single exponential curve, yielding a long minority carrier (hole) diffusion length of 21.2 (14.6) µm in the left (right) segment. More SPCM data of this device can be found in the Supporting Information (Figure S5). The different diffusion lengths at different segments in the same nanowire indicate that the carrier mobility and recombination lifetime sensitively depend on the local defects likely at the surface, and can vary even in a single nanostructure. To our knowledge, such a long diffusion length has not been reported previously in nanostructured perovskites and perhaps not reported in any semiconductor nanostructures. The measured diffusion lengths in these solution-grown single-crystal MAPbI3 nanostructures are much longer than the value (~ 1 µm) measured in the pure MAPbI3 polycrystalline thin films,11 though it has been recently shown that the insertion of Sr may further extend the carrier diffusion lengths in the polycrystalline thin films.43 On the other hand, our measured diffusion lengths in the nanostructured MAPbI3 are shorter than the bulk MAPbI3 single crystal (reported to be as high as 175 µm).12 This implies that the absence of grain boundaries significantly increases LD, but the large surface to volume ratio reduces LD. The grain boundaries may reduce LD by reducing carrier mobility via carrier scattering and/or by reducing carrier lifetime by surface defect assisted recombination. From LD = 21 µm, the product of mobility and carrier lifetime is extracted to be µτ = 1.7 × 10-4 cm2/V. If using a reasonable lifetime value τ = 1 µs,44 we obtain µ = 170 cm2/(V s). The greater diffusion length, longer lifetime, and higher carrier mobility in the solution-grown single-crystal perovskite 13 ACS Paragon Plus Environment

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nanostructures are truly exciting and promise highly efficient optoelectronic applications based on these nanomaterials.

Figure 4. Long carrier diffusion lengths in MAPbI3 nanostructures. (a) SEM image of the device with a 44 µm long nanowire. (b) Photocurrent line scans at Vsd = 2.5 V and - 2.5 V, where the diffusion length is extracted by exponential fitting of the segment close to the reversely biased electrode. All data are taken with laser wavelength at 532 nm and a 40× objective lens with a numerical aperture of 0.6. The laser peak intensity is 2.6 W/cm2. Finally, we present the wavelength dependent SPCM results on a 600-nm thick MAPbI3 nanoplate device (Figure 5). At short wavelength (λ < 770 nm), the photocurrent is almost uniform as the laser is raster scanned on the surface of the entire nanoplate, even when the laser spot moves out of the region between the two electrodes. This is consistent with the previously observed long carrier diffusion length in hybrid perovskite nanostructures. We note LD is insensitive to the laser wavelength measured in a nanowire device (Figure S6). As the wavelength is increased to 780-810 nm, interestingly, the photocurrent becomes non-uniform, where the edges of nanoplate show much stronger photocurrent than the central part (Figure 5a). Figure 5b shows the wavelength dependent photocurrent at three representative points (A: edge, B: electrode, C: center), where the photocurrent drops much slower at longer wavelength when 14 ACS Paragon Plus Environment

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the laser is on the edge. In addition to the edges, the photocurrent is also enhanced, to a lesser degree, when the laser is scanned to the electrode position. This photocurrent enhancement on the electrodes can be readily understood by remembering that the absorption depth is greatly increased as the excitation photon energy is close to the bandgap of the perovskite. The penetration depth in MAPbI3 increases from ~100 nm at λ = 500 nm to > 1 µm at λ = 770 nm.45 Consequently, at shorter wavelength the absorption is mainly happening near the top surface of the nanoplate, while the photons can reach much deeper at longer wavelength. Therefore, for longer wavelength, the Au electrode surface can reflect the unabsorbed photons back and hence increases absorption and photocurrent.

Figure 5. Wavelength dependent SPCM of MAPbI3 nanoplates. All data are taken with a 100× objective lens with a numerical aperture of 0.95. The laser peak intensity is kept at 0.76 W/cm2 at all wavelength. (a) SPCM images collected using different laser wavelength at Vsd = 1.0 V. (b) Photocurrent as a function of wavelength at three representative points (A: edge, B: electrode, C: center). The positions of the three points are shown in (a). (c) Simulated ratio of absorbed power to the incident power (Pabs/P0) as a function of wavelength, as the laser is focused at the center and the edge of the nanoplate, respectively. Red circle is for laser incident on the center of the nanoplate, blue triangle (inverse triangle) is on the edge with polarization parallel with X (Y) axis. The inset 15 ACS Paragon Plus Environment

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indicates the definition of the coordinates and the orange box represents the nanoplate. (d-g) Cross sections of electric field magnitude distribution in the X-Z plane. The nanoplate is in the X-Y plane while the focusing laser beam is incident from the top along the Z axis. The dashed boxes indicate the position of the nanoplate. (d, e) λ = 700 nm (f, g) λ = 800 nm. (d, f) laser is focused at the center; (e, g) at the edge with polarization along the X axis. The photocurrent enhancement at the nanoplate edges can be qualitatively understood by considering the refraction of the laser beam at the nanoplate surface. As illustrated in the schematic drawing in Figure S7, the laser beam focused on the center of the nanoplate travels mainly vertically after refraction at the top surface, while the laser beam focused on the edge is refracted at the vertical surface into the nanoplate in a direction much more horizontal. As a consequence, the photons impinged on the edge go through a longer optical path and hence are more completely absorbed by the nanoplate. As the thickness of the nanoplate is comparable to the wavelength, the ray optics above can be used to qualitatively understand the enhancement but is not a proper treatment. To more rigorously understand the observed enhancement, finitedifference time-domain (FDTD) simulations are performed to calculate the absorption as a function of wavelength. As shown in Figure 5c, at λ ≥ 780 nm, the simulated ratio of absorbed power to the incident power (Pabs/P0) is indeed significantly higher when the laser is focused on the edge. The simulated electric field distribution (Figures 5d-g) is also consistent with the ray optical picture discussed above, where the light wave extends into the entire nanoplate when the laser is focused on the edge at longer wavelength (Figure 5g). Additional experimental evidence is obtained from the polarization dependence. The edge photocurrent changes by up to 30% as the laser polarization rotates (Figure S8), while this is not seen when the laser is focused at the center of the nanoplate. This is expected as the reflectance at the vertical edge depends on the light polarization. Simulation indeed further confirms the polarization dependence (Figure 5c). Practically, the observation of enhanced light coupling at the nanostructure edges could be useful 16 ACS Paragon Plus Environment

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to photonic design of optoelectronic devices such as solar cells and photodetectors. One may take advantage of such effects to redirect the light to maximize light absorption in this highindex material and design highly narrowband photonic devices.15 In summary, we have fabricated sensitive photodetectors incorporating individual solution-grown single-crystal MAPbI3 nanowires and nanoplates. These nanostructures make Schottky junctions to Au electrodes as evidenced by nonlinear I-Vsd curves and KPFM measurements. By performing SPCM in the electric-field-free region of the nanowires, we have obtained long minority carrier (hole) diffusion lengths up to 21 µm in MAPbI3 nanostructures. This diffusion length is much longer than the values measured in polycrystalline MAPbI3 thin films, indicating greatly improved carrier lifetime and mobility in these nanostructures. The photocurrent peaks broaden under electric field, which can be understood by field-assisted charge transport. This observation excludes the possibility that photo-recycling significantly contributes to photocurrent in our devices. As the excitation energy is shifted close to the bandgap, the photocurrent becomes stronger at the edge of the nanostructures, attributed to the strong light coupling. The results provide new insights to the carrier transport and dynamics and set a new benchmark for the carrier diffusion length in MAPbI3 perovskite nanostructures and open up new opportunities for optoelectronic and photonic applications based on these exciting materials.

Methods The synthesis of these MAPbI3 nanostructures (nanowires and nanoplates) followed previously reported methods14,

30

with minor modifications. A piece of lead acetate (PbAc2) 17


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coated glass slide (~2 cm2) was immersed in a 1 mL CH3NH3I (MAI) solution in isopropanol (IPA) with a concentration of 40 mg/mL in a reaction vial in an oven at 50 °C, with the PbAc2 coated side facing down. The PbAc2 thin film was prepared by dropcasting 100 mg/mL PbAc2·3H2O aqueous solution on a glass slide and dried at 60 °C. In order to obtain a uniform and flat lead acetate film on the substrate, we kept spreading out the lead acetate solution during the drying process, since the solution tended to shrink on the substrate. After a reaction time of ~3 days, the glass slide was taken out, and subsequently washed in IPA and dried under N2 flow. To fabricate nanostructure devices, 10 nm Cr / 90 nm Au electrodes with a separation of 8-20 µm were first made by e-beam lithography and e-beam evaporation on a 300 nm SiO2 covered Si wafer. Then the MAPbI3 nanostructures were mechanically transferred using a microfiber from the as-grown substrates to the device substrates to bridge the electrodes. The electrodes were designed in an interdigitated fashion to increase the chance of successful bridging. The detailed description of our SPCM setup can be found in ref. 27. Briefly, a laser beam is focused to a diffraction limited spot and is raster scanned on the nano-device substrate, while the photocurrent is recorded as a function of laser position and plotted as a 2D image. The central laser spot can be fit well with a Gaussian, with the intensity distribution following ∙

( ) | |

,

where Wlaser ranges from 250 nm to 450 nm as the wavelength is increased from 500 nm to 850 nm when using a 100× objective lens with a numerical aperture of 0.95.26 A 40× objective lens with a numerical aperture of 0.6 is used for large scan size (> 30 µm) to ensure uniform laser intensity over the entire scan area. The beam width when using 40× lens is Wlaser = 400 nm at 532 nm laser wavelength. The wavelength dependence measurements are performed using a super-


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continuum laser (NKT) with an acousto-optic tunable filter (AOTF). The output wavelength can be continuously tuned in the range of 500-900 nm with a spectral width of 1 nm. The repetition rate of the tunable laser is 80 MHz with a pulse width of 5 ps. The high repetition rate makes the tunable laser pseudo-CW. We also used a CW laser (Coherent Compass 315M-100) at λ = 532 nm. FDTD simulation is performed using a commercial software (Lumerical). The complex refractive index of MAPbI3 was obtained from reference

46

. Thin lens sources are used in the

simulation. The wavelength-dependent absorption is simulated through a wave pulse generated by the source. Convergence tests including pulse width, simulation time/region, source location/dimension, and mesh sizes were performed to ensure the validity of the simulation.

Supporting Information Microscopic characterizations of the nanostructure samples studied, low temperature measurements, SPCM simulations, additional SPCM data, polarization dependence, and tables summarizing the simulation parameters and the diffusion lengths in all measured devices. The Supporting Information is available free of charge on the ACS Publications website at http://pubs.acs.org.

Notes The authors declare no competing financial interest.

Acknowledgements 19 ACS Paragon Plus Environment

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This work was supported by the U.S. National Science Foundation Grant DMR-1310678. Y.F. and S.J. thank the support by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Award DE-FG02-09ER46664. Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. We thank Dr. Yiming Yang for his assistance in initializing this work. E. Gonzalez acknowledges the U.S. National Science Foundation Research Experiences for Undergraduates (REU) program under Grant No. PHY-1263201.


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