Lateral Perovskite Single‐Crystal Capacitors for Self‐Powered Photodetection

High‐quality perovskite single crystals (SCs) are emerging as promising optoelectronic materials and extensive photodetectors have been reported based on their SC frameworks, however, they are all disabled without applied external bias, and this is an evident obstacle for practical applications. Here, self‐powered photodetection (SPD) of perovskite SCs based on capacitance effects is reported when the capacitor releases its previously stored electric power by discharging operations. The capacitive results are highly in accord with numerical simulations of dielectrics, rather than the common ion migration. The lateral structures show good selectivity for local illuminations and consequently the induced self‐driven photovoltaic effects, but such influences on the SPD can be ignored when the capacitors are charged with sufficient electric power. This work first shows an attempt at achieving SPD in the form of lateral capacitors and may provide another new strategy for self‐powered perovskite devices.


Introduction
Lead halide perovskites are attracting tremendous attention due to their high performance in photovoltaics, [1][2][3][4] photodetectors, [5][6][7][8][9][10][11][12][13][14] light-emitting diodes, [15][16][17] and lasers. [18][19][20][21] Performances aside, stability issue is of great concern before these devices can be commercialized in harsh environments. Although great efforts, such as Lewis passivations, [22,23] improved annealing strategies, [24,25] hydrophobic organic chain intercalations [26][27][28] and alloy procedures [29] have been done to enhance their resistance to moisture, oxygen, and light, the solution-processed single crystals (SCs) of perfect lattice phase and ultralow specific surface bring great breakthrough for the stability issue. In recent years, centimeter-scale SCs, methylammonium-lead bromide (MAPbBr 3 ), and iodide counterparts capacitors. The capacitances are sensitively dependent on crystal volume and the best value of ≈200 µF cm -3 is measured from a bulk SC interdigital electrode capacitor. Perovskite is a kind of excellent optoelectronic material, thus the MSC capacitors here are still used to serve for their photoelectric performances. As a power-storing device, SPD is achieved when the capacitor releases its previously stored electric power by discharging operations. Lateral structures also show good selectivity for local illuminations and consequently the induced photovoltaic effects, but their influences on the SPD of the capacitor can be ignored when capacitors are charged with sufficient electric power.

Fabrications and Characterizations of MSC and MSC Capacitor
The large-sized MSCs used in this work are slowly crystallized from a supersaturated MAPbBr 3 solution in a non-sealed bottle under room temperature (23-25 °C, relative humidity at 55%) without gradient heat-treating, vapor-assistance, antisolventassistance or vibration, schematically illustrated in Figure 1a.
The semi-finished products in the precursor solutions, photographed under room light in Figure 1bi, are gradually enlarged during crystallizing processes without any interruptions. Then the mass-produced centimeter-scale MSCs are harvested after 1 week (Figure 1bii). Their atomic force microscopy (AFM) surface morphology image in Figure S1a, Supporting Information informs readers of the quite smooth surface with a considerably low roughness of 15.9 nm. Figure 1c shows MSC a clear band-edge cutoff extending to nearly 560 nm compared with the film counterparts. Under one-photon (405 nm) and twophoton (800 nm) illumination, the MSC can emit different fluorescence from the surface (535 nm, carriers) and internal bulk (575 nm, exciton) due to the spatial distributions of photoinduced species. We reason the unsymmetrical luminescence spectrum at 575 nm resulting from the strong self-absorption [41] or photon recycling effect. [42] Only diffraction peaks of maximal facets drawn in the powder X-ray diffraction (XRD) spectrum ( Figure 1d) indicate their good single-crystalline. The excellent stability of our MSCs is displayed by the XRD spectrum recorded again after 18-month exposure to 55% humidity ( Figure S1d, Supporting Information) with only some slight small facet diffraction peaks emerging.
The long-term ultrastability is a fundamental basis for real device applications. Our stand-free lateral MSC capacitors are photographed in Figure 1ei with a smooth surface (iii). Details are shown in the sketch in Figure S1c, Supporting Information and the devices are operated by using two metal probes ( Figure 1eii) to contact an external source. As schematically illustrated in Figure 1f, the power-storing capacitors can be charged or discharged with a high operation. The dynamic 3D spatial electric flux lines between lateral electrodes drive the photoinduced electrons and holes forming time-resolved photocurrents. The electric fields almost keep maintained when the capacitor is cut off, and the capacitor will provide a driven force for photocurrent when the circuit is turned on again without bias. Noticed that, self-driven directive photovoltaic currents are triggered under local illuminations, resulting in the lateral capacitor photocurrents are also position-related.

MSC Capacitor Characterizations
Each of two adjacent wafer electrodes with partially sandwiched dielectric perovskite materials can be considered as a unit lateral capacitor, possessing much more controllability and operability than the conventional sandwiched one. Its real-time chargingdischarging cycles (CDC) sustaining 300 s versus increasing bias are displayed in Figure 2a. Nearly stable charging current at ≈140 s and discharged charge quantity within 150 s (in timeaxis from 150 to 300 s) are extracted in Figure 2b and Figure 2c, respectively. A knee point, the division between normal and analogous electric breakdown regions, is clearly turned up at ≈0.7 V. The impedance and capacitance values are respectively calculated as 2 × 10 8 Ω and 680 nF in normal working regions. The capacitance value is confirmed by the formula of C = Q/U, where C is capacitance, Q is stored charge quantity (SCQ) and U is open circuit voltage. The SCQ sampled within 150 s is 80.5% of that within 4500 s, case of 0.8 V is as an example shown in the inset of Figure 2c, thus the real capacitance value should be confirmed as 850 nF (650 nF/80.5%). The capacitor of the electric broken state exhibits a much lower impedance of 4 × 10 7 Ω, smaller transient discharging currents (inset of Figure 2b), as well as the unstable capacitance of 3100 nF at 0.7-1.0 V bias and 280 nF when bias exceeds 1.0 V.
To evaluate the SCQ capability, classic cyclic voltammetry (CV) tests are performed. Actually, such tests are heavily dependent on the bias ( Figure S2, Supporting Information) and scan rate ( Figure S3, Supporting Information). Better performances can be gained under lower bias and slower scan rates. The representative 5-cycle results with scan rates at 4 V s -1 and close-lopped bias between -1 and +1 V are recorded in Figure 2d, showing approximate rectangular CV shapes with a hysteresis voltage at 1.4 V. Capacitor discharging dynamics are quantitatively analyzed in Figure 2e, the discharging lifetimes fitted from normalized curves in the left inset show nearly linear growth with bias. The relationship between charged time and SCQ in the right inset indicates the charging process is mainly completed in prophase and no more obvious increment emerged after 30 s. Artificial intermittent discharging currents (inset) released from a bias of 0.8 V in Figure 2f linear versus voltages, the slope calculated of 3 × 10 7 Ω is as the resistance of perovskite material dielectric sandwiched by two wafer electrodes, much lower than normal capacitor impedance for direct current but almost close to that of the electrical breakdown state. Uninterrupted time-variant CDC tests are conducted to examine the maximal transient discharging current as the function of charged time (Figure 2g and inset), and the saturation value can be obtained after charging 5 s, read from fitted curves.

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The asymmetry between discharging and charging states when the capacitor is cut off for ≈150 s in an intermittent CDC experiment ( Figure S4, Supporting Information) throws a question about the internal power consumption rates of capacitor SCQ in an open circuit state. In Figure 2h, seven CDCs are continuously sampled with capacitor off-state durations gradient increasing from a few to hundreds of seconds. The charging/ discharging processes are both settled as ≈35 s, bias is designed as 0.5 and 1 V. The maximal transient discharging currents, reasonably representing the remaining SCQ are plotted as functions of off durations in Figure 2i, and the maximal transient charging current is as a control. The power-storage lifetimes are respectively calculated as 1340 (0.5 V) and 4614 s (1 V), the reason for a longer lifetime is most likely due to the enhanced capacitance from 680 to 3100 nF ( Figure 2c).
Benefiting the lateral structure, in Figure 2j, a capacitor named A-B style can be used as a unit power device in a complex circuit. The unit capacitor performance extracted from CDC testing under a bias of 0.8 V (Figure 2j) is displayed in Figure 2k. The linear degradations in performance are reasoned by the weakened capacitance, illustrated by sharpening CV shapes ( Figure S5, Supporting Information). Figure 2l exhibits the high operation of array lateral structures, due to the existence of additional electrode C, the discharging process, no matter whether in capacitor A-B or A-C, aims to balance the redistribution of charge on electrodes, showing electric power transfer capability.
We further explore multi-parameter capacitors in Figures S6-S11, Supporting Information with one of Figure 2 as a control. In Figure S6, Supporting Information, the absent designed thin Ti wafer which is used to contact the Au wafer with the MSC surface tightly results in evidently weakened performances, with an increased impedance of 2 × 10 9 Ω, a reduced capacitance value of 305 nF and a faster discharging lifetime. In Figure S7, Supporting Information, benefiting large-sized electrodes of 4.5 mm 2 , a bulk SC interdigital electrode capacitor shows satisfactory performances with a tested value of 4050 nF (≈200 µF cm -3 ), a high transient current of 150 nA, a low resistance of 5 × 10 6 Ω, as well as the nearly doubled power-storage lifetime of 2520 s. These two contrastive results directly elaborate on the importance of contact and area of the electrodes. In Figure S8, Supporting Information, a capacitor with smallersized electrodes of 0.04 mm 2 area is tested as a disproof with very a poor capacitance value test as only 20 nF and severely sharpened CV curve shapes.
In Figure S9, Supporting Information, pretty poor performances are measured in a surface-coarsened MSC capacitor with an increased impendence of 2 × 10 9 Ω and a small capacitance value of only 52 nF, blamed on the substantial lattice dislocations and high electric resistance. Moreover, charging processes are evidently influenced by defective electron filling under high bias (1.5 V), indicated by gradually increasing current in prophase within 250 s. Thus, the CDC process of capacitors will be normal in case of the defect states are fully filled under sufficient long-term charging (≈1500 s in our experiment). In Figure S10, Supporting Information, we explore the possibility of capacitor effects on a 1.5 µm-thick micro-platelet with a lateral dimension reaching the millimeter scale. However, only very faint capacitor effects, SCQ calculated as 130 pC and nearly linear CV shape can be elaborately discovered despite its extremely smoothed surface. It can be understood as 99.94% (1-1.5 µm/2.5 mm) of perovskite material applied as dielectrics are clear away while electrode construction is unchanged, shown in the diagrammatic sketch. In Figure S11, Supporting Information, a classical sandwiched capacitor is fabricated by laying our MSC onto a 50 nm-thickness Au film, and such mechanical contact also shows us well capacitance of 120 nF due to the smooth surface, providing a straightforward operation of turning devices from lateral to vertical styles.

Surface Photovoltaic Effects of MSC
Lateral structure comes with great convenience for local light manipulation. As schematically illustrated in Figure 3a, the device is operated under a coordinate axe system with the origin (0, 0) calibrated as the midpoint of two electrodes and the unit as a micrometer. Logically, except for the origin (0, 0), the unequal diffusions from local illumination locations to bilateral electrodes will certainly result in self-driven photovoltaic currents. The green arrow indicates the positive direction of the current. The current signals of 405 nm illumination of rectangular on/off switching cycles are sampled in Figure 3b, and the bias is zero. The cycle period is 5 s with duty a ratio of 50%, and the laser (captured in the inset) shifting step is 10 µm per cycle, ranging from (-100, 0) to (100, 0). Data from three switching cycles sampled in each location are aimed to ensure accuracy. The origin symmetry of current-position relationships in Figure 3c demonstrates the directive photovoltaic effects and such symmetry is imperfect when the surface is roughened along the x-axis ( Figure S12, Supporting Information). In Figure S13, Supporting Information, we study their stability affected by the illumination intensities, current deterioration of 960 s-decay occurs in on-state when the device illuminated by a stronger laser, which is generally interpreted by the crystal photolysis. In contrast, the current remains stable under the weaker illuminate case, moreover, the current in off-state shows an increasing trend to a saturation of 50 pA. We reason it to ultralong carriers' lifetime, the carriers generated in the previous switch cycle have not yet fully diffused to electrodes when the next switch cycle has been started, and finally causes the accumulation in off-state currents.
Almost identical current-time detections under a series of given biases are recorded in Figure 3d. It should be noted that the signal collection can be only started when the capacitor approaches equilibrium states. The gradually broken origin symmetry in Figure 3e as bias enhanced from 0.05 to 1 V clearly shows the coordinate-related relationships between external bias and internal photovoltaic effects, being competitive in the negative while cooperative in the positive x-axis. The inset reads photovoltaic effect at (-100, 0) under an illuminating intensity of 0.8 µW is suppressed to zero under ≈0.3-0.4 V bias, such neutralized bias is larger under a stronger illumination in Figure S14, Supporting Information for it is adverse to the axial-symmetry. In Figure S15, Supporting Information, the identical current-time detection conducted on the capacitors with a larger separation of 500 µm requires a larger neutralized bias at ≈0.4-0.8 V. In Figure S16, Supporting Information, www.advelectronicmat.de the identical experiments under the illumination of 1064 nm laser just need a smaller value of ≈0.05-0.1 V due to the weak nonlinear two-photon absorption and deep penetration depth. It is worth noticing that the photovoltaic voltage is much lower than neutralized one for the latter needs to overcome the whole electric field covering the 200 µm distance rather than the local voltage difference. In Figure S17, Supporting Information, we preliminary investigate its possibility to be applied to a lateral solar photovoltaic device, it can output a relatively stable (degradation lifetime of 5 h) current of 6 nA or open circuit voltage of 0.11 V under 0.4 mW illumination of white light at the location of (100, 0).
Self-driven directive photovoltaic current distribution along the y 1 -axis is recorded in Figure 3f under the identical operation in Figure 3b. In Figure 3g, a strict axisymmetric currentposition relationship caused by smooth MSC surface is fitted composed of two exponential decay curves with a decay length of 209 µm. Restricted by perfect spatial symmetry, the photovoltaic current is nonexistent along the y-axis. Two contrastive current-position distributions along the y-and y 1 -axis under the bias of 0.7 V are recorded in Figure 3h and plotted in Figure 3i, with the fitted decay length respectively enhanced to 138 and 243 µm, due to the support of capacitor electric field. In Figure S18, Supporting Information, the decay length is found independent of the bias. Under the blessing of photovoltaic effects and capacitor electric field induction, photoinduced free carriers where far beyond carriers diffusion distance, such as locations of (0, 500) and (100, 500), can be still detected as 20 and 505 pA respectively under 0.8 µW illumination.

Numerical Simulation of Dielectrics for MSC Capacitor
To verify the authenticity of our lateral MSC capacitor and electric field spatial distribution, numerical simulation through the finite element method is applied on a simplified capacitor where only a pair of wafer Au electrodes is designed on the surface center of an MSC with dimensions of 6 × 5 × 2.5 mm. The 1.5 µm-thick one is a control. Spatial electric potential distribution covering MSC surface illustrated by pseudo-color maps and 3D spatial electric flux lines drawn as the brown curve arrows are all displayed in Figure 4a,b. The bias is specified as 1 V and the dielectric constant used in our simulation reach to giant 10 8 of magnitude in electrostatic field state. The simulated Although ion migration in perovskite is very common, in our devices, the capacitance originates from dielectric polarity rather than ion migration, due to the considerable weak electric field strength (<0.01 V µm -1 ), moreover, the capacitance value results are also highly in accordance with the numerical simulations of dielectrics. Also apparently, the certain bias voltages in the discharging capacitors (Figure 2f and Figure S7g, Supporting Information) also show that the ion migration does not exist in our MSC capacitors.
Surface current density is directly proportional to local electric field strength, thus, a clear cognition of photocurrent constituents will be achieved with aid of simulations. Coordinate-resolved electric field intensity along the y-and y 1 -axis in Figure 4c show absolute identical intensity after y/y 1 -axis exceeds ≈200 µm (zoomed in inset), telling that the current intensity difference in Figure 3i after 200 µm is totally caused by photovoltaic effects. Electric field distribution along the x-axis in Figure 4d shows an analogous line type to that of Figure 3e under 1 V bias, in addition, the current and electric field intensity ratios of position (±100, 0) to (0, 0) are both approximately fourfold. The good match between experiments and simulations further demonstrated the photovoltaic effect photocurrents can be majorly suppressed under excessive high bias.

SPD of MSC
Although perovskite SC materials may be inferior in capacitance performance compared with other materials with a larger specific area, such as poly-porous carbon materials and classical metal-organic frame materials, the capacitor framework used here is aimed to achieve the SPD of perovskite SC materials without external sources (applied bias) to enhance their real applications in harsh conditions.
In Figure 5a-c, current-time tests are conducted out in one capacitor CDC sustaining 1000 s, under a series of bias as 0.01 (i), 0.05 (ii), 0.1 (iii), 0.3 (iv), 0.4 (v), 0.6 (vi), 0.8 (vii) and 1 V (viii), meanwhile, illumination of 200 rectangular on/off switching cycles is focused on three representative positions of (-100, 0), (100, 0) and (0, 0) respectively. To highlight the roles of capacitors, the intensity of illuminating laser is settled as a relatively low power at 0.8 µW. As schematically illustrated in Figure 5d, a clear and systematic understanding of these dynamic data can be obtained as a result of the competitive or cooperative relationships between time-resolved bias difference and internal photovoltaic voltage around electrodes. In Figure 5d, sign ΔV 1 and ΔV 2 are the bias difference between electrodes and external source in the capacitor charging state, ΔV 3 is the bias difference between two electrodes in the capacitor discharging state, and ΔV 4 is the internal photovoltaic voltage. ΔV 1 , ΔV 2 , and ΔV 3 are dynamic and gradually decreased to zero as the capacitor reaching to equilibrium states after charging or discharging operations, while ΔV 4 maintains a constant under intensityfixed illuminations. The arrows indicate the positive direction.
In the charging state at location (100, 0), due to the mutually competitive ΔV 1 and ΔV 4 , the negative photovoltaic effect current is gradually suppressed integrally under higher bias and positive bias-driven photocurrent being dominant. Emphatically, due to the weakening of ΔV 1 over time, the current signal will reverse from negative to positive at a certain time node, and the time node is delayed under higher bias, ≈50 s of 0.3 V, ≈150 s of 0.4 V case (inset of iv and v). Such time node is nonsexist under excessive bias (vi, vii, and viii) for the capacitor has approached or exceeded saturation state, causing ΔV 1 is always higher than ΔV 4 . While in the releasing state, the current will always be negative because the ΔV 3 and ΔV 4 have turned to a mutually cooperative relationship, the current intensity is decreasing over time for weakened ΔV 3 and this phenomenon becomes more evident under higher bias. Note www.advelectronicmat.de that the "positive" and "negative" mentioned here are in contrast with the capacitor dark current which is calibrated as the benchmark.
The current signals will show opposite performances when the illumination location moves to (100, 0). In the charging state, the relationship between ΔV 2 and ΔV 4 turned mutually cooperative, current signals maintain positive with gradually decreasing intensity over time, more evident in higher bias. Without a doubt, the reverse of the current signal from negative to positive will certainly occur in power releasing state as the result of mutually competitive ΔV 3 and ΔV 4 . The time node is also delayed under higher bias,  www.advelectronicmat.de the current will be finally gradually converted to photovoltaic current (≈1.0 nA) after the capacitor is fully discharged going through a long timeslot, such as more than 2500 s under 1.5 V bias case ( Figure S19d, Supporting Information).
Intuitively, pure capacitor-related current signals will be observed when the illumination location moves to the origin (0, 0). The annoying slight positive currents in discharging state (insets of i, ii, iii, and iv) under lower bias are as the photovoltaic effect, may be induced by the imperfect MSC surface or imprecise coordinate axis. Such interference can be gradually ignored under higher bias along with conspicuous capacitive currents, and the single is no longer reversed.
The photovoltaic effect current shows a weak current but it still influences the SPD of the capacitor with low powerstorage levels (i, iii, and iv for example). Different from the intensity-fixed photovoltaic effect (≈1 nA), the photocurrents of the capacitor effect are electric-field-positive-related. Thus, the photovoltaic effect can be gradually ignored when the capacitor reaches higher power-storage levels.
Due to the blessing of dynamic capacitor currents and voltages, the parameters of photodetection are also time-resolved. Their dynamic capacitive on/off ratios at location (0, 0) sampled with 50 s interval under a series of charging biases (0.4, 0.6, 0.8, and 1 V for instants) are calculated in Figure S20, Supporting Information. The on/off ratios keep increasing as the capacitor approaches equilibrium states with the dark current gradually approaching zero. Due to the time-resolved voltage on the electrodes, the dynamic photoresponsivities cannot be calculated versus time, in Figures S21 and S22, Supporting Information, we provide the static photoresponse performances measured at location (100, 0). The pure electric-fielddriven photoresponsivity is calculated as 0.4 mA W -1 under a bias of 0.6 V. The intensity of illuminating laser is 0.8 µW. In Figure S23, Supporting Information, we explore the steadystate current signal intensity of location (0, 0) as a function of electrode-separated distances and the ultralong detection distance of millimeter levels reflects the importance of capacitor induction. In Figure S24, Supporting Information, we conduct identical current-time detection under local illumination of 1064 nm at origin (0, 0) and show similar performance. Due to the two-photon absorption, the near-infrared photoinduced carriers are generated inside the MSC rather than on the lateral surface ( Figure S25, Supporting Information), and may be influenced by internal defects or dislocations inside the crystals.

Conclusions
In summary, MAPbBr 3 SCs are obtained by a simple roomtemperature slow crystallization approach, based on these high-quality products, we report on the integration of stable lateral power-storing capacitors on the surface of MSC and then applied them to the SPD applications. As an electricpower-storage device, the SPD is achieved when the capacitors are operated in discharging states. Their capacitances are sensitively dependent on SC volume and electrode patterns, the best value of ≈200 µF cm -3 is measured from a bulk SC interdigital electrode capacitor. Array lateral structures provide high operation of electric power transfer within unit switches on the surface, also the selectivity for the self-driven directive photovoltaic currents triggered by local illuminations. Our work shows a positive and novel self-powered device exploration on the perovskite SCs.

Experimental Section
Crystal Growth and Characterization: All chemical reagents were of analytical grade. N,N-dimethylformamide (DMF, 99.9%), lead bromide (PbBr 2 , 99.999%), and methylammonium bromide (MABr, 99.999%) were purchased from Sigma Aldrich. MAPbBr 3 turbid liquid was prepared by dissolving superfluous mole-equal PbBr 2 and MABr into DMF solvent and then laid on a hot platform of 80 °C for 2 h to precipitate small crystals. The precipitated crystals were re-dissolved for 12 h under room temperature until no more fragile crystal can be re-resolved to fabricate the supersaturated MAPbBr 3 solutions. To be crystallized supernatant was sucked out and filtered by a membrane with an aperture diameter of 0.2 µm, and then big MSCs with the dimension of centimeter scales were gained after ≈7 days at room temperature without any redundant treatment.
The absorption spectra measurements were performed on a Shimadzu UV-2500 spectrometer with a light slit width of 5 mm. The photoluminescence measurements were taken on a Renishaw via Raman spectrograph with 405 and 800 nm solid-state lasers as excitation sources. Powder XRD measurements were performed by a Rigaku D/Max-B X-ray diffractometer with diffracted beam monochromator and conventional cobalt target X-ray tube set to 40 kV and 30 mA respectively. The electrical conductivity measurements were conducted by a homebuilt electric system with source meter bias ranging from 0.1 to 10 V. The surface morphology digitizations were realized by a NT-MDT AFM with the pixel of 256 × 256.
Fabrication and Measurement of Lateral-Structure MSC Capacitor Devices: Easily, customized aluminum shadow masks with different patterns were fixed onto the smooth surface of MSC, then 5 nm Ti and 50 nm Au were thermally deposited successively with a vacuum degree of ≈5 × 10 -5 to 2 × 10 -4 pa. Real-time current signals detection experiments were conducted by a multi-parameter MaiTa optoelectronic system, which combined a high-precision sources meter as a voltmeter and ammeter simultaneously, two probes used to contact MSC device electrodes with an external source meter, continuous fiber lasers (405, 1064 nm) used as light sources, and two sets of 3D displacement platform used to locate the illumination positions. The time resolution of this system was 0.12 s and the laser output mode was modulated by a controller.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.