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1 In the format provided by the authors and unedited. DOI: /NNANO Position dependent and millimetre-range photodetection in phototransistors with micrometre-scale graphene on SiC Biddut K. Sarker, Edward Cazalas, Ting-Fung Chung, Isaac Childres, Igor Jovanovic, and Yong P. Chen NATURE NANOTECHNOLOGY 1

2 1. Simulation of electric fields near graphene under light excitation We modeled the graphene field-effect transistors (GFETs) and conducted finite element method (FEM) simulations of the electric field and potential distribution within the SiC substrate using COMSOL Multiphysics. The thickness of SiC substrate ( 416 µm) used in the modeled device matches that of our experimental devices. To qualitatively capture the effect of the native oxide between SiC and graphene and the part of SiC substrate that remains insulating under illumination, we assumed the conductivity of the top 10 nm portion (representing native oxide and/or some portion of SiC that did not become conducting) of our SiC substrate to be unaffected by illumination in our simulation. The laser illumination modifies the electric field within the SiC via the change in conductivity within SiC. The conductivity of the SiC substrate increases by absorption of incident light, whereby electrons and holes are produced in the SiC. The change in SiC conductivity due to light illumination can be calculated by Δσ = qμ= q τμ (1) where q(=q τ) is the number of steady state carriers produced per unit volume and q is the number of carriers produced per unit volume per unit time through light absorption, μ is the sum of electron and hole mobility (490 cm 2 /V/s, provided by manufacturer, PAM-Xiamen) of the carriers within SiC and τ is the carrier lifetime (recombination time). Here, we assume that τ = 1 μs. 1,2 We consider the influence of penetration depth of the light in the SiC substrate. For simplicity, we divided the total thickness of SiC substrate into three parts and used the profile of light absorption throughout the depth of the SiC substrate to calculate the charge density produced per unit time for each part separately. For example, the photo-generated charge carriers per unit volume for the top 1/3 of SiC substrate is calculated to be q = C/m 3 /s for P = 1 μw. The final SiC conductivity of the top 1/3 SiC substrate due to laser illumination is given as σ = σ t + Δσ = P( ) S/m (2) where P is in μw and σ t S/m is the typical value of unirradiated SiC conductivity given by the manufacturer (PAM-Xiamen). Similarly, the final SiC conductivity of the middle third and lower third of the SiC substrate are P( ) S/m and P( ) S/m, respectively. The calculated SiC conductivities are used as inputs in the model to simulate the electric field for a given laser power. Finally, the electric field at the location under the graphene NATURE NANOTECHNOLOGY 2

3 (near to SiC/graphene interface) is extracted and plotted as a function of laser power (Fig. 1e in the main text). 2. Control experiments To confirm that photoresponse of our GFETs is not due to SiC/metal Schottky contact and also photoresponse is truly due to the graphene field-effect, we fabricated two different control devices: SiC devices (without graphene) and dummy devices (no graphene, gold used in the channel). The optical images of a fabricated SiC device and dummy device are shown in the inset of Fig. S1a and S2a, respectively. The I ds - V g and I ds - t characteristics of the SiC device and dummy device with and without illumination are shown in Fig. S1a and b, and Fig. S2a and b, respectively. We find that the current in the SiC device is very low (of the order of na), consistent with the insulating SiC substrate. In addition, currents of the both control devices do not change under light illumination. These measurements confirm that the photoresponse of our GFETs does not result from the SiC/metal Schottky contact or collecting charge carriers from the SiC; rather it results from the photo-modulated charge carriers in the SiC underneath the graphene via field-effect. Supplementary Figure S1. SiC device (without graphene). (a) Dependence of the drain-source current on the backgate voltage (I ds - V g ) of a SiC device (without graphene) without and with laser illumination. Inset: Optical image of the SiC device (without graphene). (b) Drain-source current as a function of time (t) while the laser switches on and off. Shaded area indicates the time interval during which the laser is on. Both the I ds vs V g and I ds vs t were measured with V ds = 75 mv, and V g = 30 V and at laser powers (P) of 5, 60 and 720 µw. NATURE NANOTECHNOLOGY 3

4 Supplementary Figure S2. Dummy device (gold channel instead of graphene). (a) I ds - V g characteristics of a dummy device without and with illumination. Inset: Optical image of the dummy device. (b) I ds - t characteristics when the laser switches on and off. Shaded area indicates the time interval during which the laser is on. Both the I ds - V g and I ds - t were measured with V ds = 10 mv, and V g = 30 V at P = 5, 60, and 720 µw. 3. Leakage current of GFETs Supplementary Figure S3: (a) The dependence of gate leakage current (I g ) on the gate voltage (V g ) for a few illumination positions. (b) Time dependent leakage current as the laser switches between on and off. Shaded area indicates the time interval while laser is on. To confirm photoresponse of GFETs is not due to collection of charges from the SiC substrate by the contacts, we recorded gate leakage current (I g ) during the photocurrent measurements. Both the I g vs V g (Fig. S3a) and I g vs t (Fig. S3b) plots show that gate leakage currents both in the dark and under illumination at various distances are small (<1 na). NATURE NANOTECHNOLOGY 4

5 Furthermore, the leakage current is much lower than the measured photocurrent (in the range of µa) and does not increase much with illumination, indicating that gate leakage current does not contribute to the measured photocurrent in our devices. 4. Nonlocal photoresponse measured at different wavelengths We have performed a study of the nonlocal photoresponse at several different wavelengths in additional devices fabricated using the method presented in the main text. We used three different laser sources generating light at 532 nm (visible), 397 nm (ultraviolet), and 1550 nm (near-infrared), and performed the measurements on the same device. Our devices show a position dependent photoresponse for different wavelengths and that nonlocal photoresponse data can be fitted by our model. These measurements further confirm that nonlocal photoresponse is reproducible, and our model can explain the nonlocal photoresponse mechanism. We describe the experiments and analysis in more detail, as follows. For the measurements with the 532 nm laser source, the device was attached to the scanning stage of the Raman system, similar to the method described in the main text. For the 397 nm and 1550 nm sources, the photoelectrical measurements were performed in a different experimental setup. A 397 nm or 1550 nm laser beam was focused onto the device using a 25 mm diameter lens with a focal length of 75 mm. The electrical socket holding the device was mounted onto a micro translation stage (position accuracy ~10 μm for each axis). The laser spot diameters for the 397 nm and 1550 nm sources were ~ μm (1/e 2 intensity diameter), covering the entire device area (channel area ~50 m 2 ). The central position (X ~0 μm) for the 397 nm and 1550 nm measurements is defined at the location where the strongest photocurrent is measured. NATURE NANOTECHNOLOGY 5

6 Supplementary Figure S4: Position dependent photoresponse of field-effect for a device under illumination with different light wavelengths. Source-drain (I ds ) as a function of back gate-voltage (V g ) measured at several representative positions (X) under illumination with excitation wavelength of (a) 532 nm with P = 8.5 µw, (b) 397 nm with P = 9.6 µw. (c) I ds as a function of V g measured at a fixed position under illumination with excitation wavelength of 1550 nm with P = 3 mw. The dark current (I dark ) is represented by black dashed lines, indicating p- type (since I dark decreases with increasing V g ) doping in graphene before illumination. A strong field-effect is observed for the 532 nm and 397 nm laser sources, and a much weaker field-effect is observed for the 1550 nm laser source. Gate leakage current (I g ) versus V g both in dark and under illumination with the (d) 532 nm, (e) 397 nm and (f) 1550 nm laser sources. For all three sources, the leakage current is below 1 na, while the photocurrent is on the order of µa. We have observed reproducible nonlocal photoresponse in our devices at different wavelengths. In Figure S4, we present the results from one of the devices measured with the 532 nm, 397 nm, and 1550 nm laser sources. The device exhibits strong and qualitatively similar field-effect (change in the source-drain current I ds vs. gate voltage V g curve) for the illumination position at X = 0 µm for both the 532 nm and 397 nm sources, as shown in Fig. S4 (a, b). The minimum position and shape of field-effect curves change with increasing the illumination distance, and the current become nearly independent of V g at larger distances. These results are NATURE NANOTECHNOLOGY 6

7 in good qualitative agreement with our results presented in the main text (measured at 532 nm in a different device). The device shows a much weaker field-effect for the 1550 nm laser source, even up to a relatively high power (P ~3 mw) (Fig. S4c). This is expected since the excitation energy (0.8 ev) of the 1550 nm laser is much smaller than the SiC bandgap (~3.1 ev). A small number of in-gap and impurity states in SiC may contribute to the small response observed. We have measured the gate leakage current, which is found to be small (<1 na) for all three light sources (Fig. S4 (d-f)). Because of the weak field-effect photoresponse for 1550 nm laser, we focus below only on the nonlocal photoresponse analysis for 397 nm and 532 nm laser, at two representative gate voltages (V g = -20V and +20V), presented in Fig. S5. The model in the main text assumed an intrinsic graphene, which is at charge neutrality point (CNP, with no net doping) before the illumination. This is a good approximation for the device presented in the main text as its dark current (I dark ) is close to the current (I 0 ) at CNP (the minimum in the ambipolar I light in Fig. 1d). In this case, the graphene current (I ds ) upon illumination increases by an amount (I photo = I light I dark = I light I 0 ) given by Eq. (5) in the main text, due to the photo-doped carriers induced in graphene by the photo-excited charges in the substrate transported (by the E-field) under graphene. However, the graphene device presented in Fig. S4 is already (p-) doped (mostly from extrinsic, environmental doping) away from CNP without illumination (as seen by the significantly larger I dark than the CNP current I 0 measured under light for example in Fig. S4a, the CNP minimum in the ambipolar I light gives I 0 ~11 A whereas I dark at V g = +20V is about 17 A, with an extra current that we refer to as I dope = I dark I 0 ~6 A due to the doping that already existed in graphene before illumination in this experiment). To apply our model in this case we make the following simple extension to take care of the offset from the pre-illumination doping: I light = I 0 + I dope I' photo, where I' photo = [T(x)P/P 0 ] is still the photo-induced current given by our model (main text Eq. (5)), and the + (or ) sign is taken if the photo-doped carriers are the same (or opposite) type as the preillumination doping (which gives I dope ), and the absolute value reflects the ambipolar conduction in graphene and the fact current is interpreted as positive regardless of the carrier type. Therefore the measured photocurrent for doped graphene would be I photo = I light I dark = (I 0 + I dope I' photo ) NATURE NANOTECHNOLOGY 7

8 (I 0 + I dope ) = I dope I' photo I dope. If the photo-doped carriers are of the same type as the preillumination doping in graphene ( + sign above), we have I photo = I' photo and no correction to our original model is needed. This is the case, for example, for V g = -20 V (with p-type photoinduced doping), and the measured photocurrent (I photo ) and photoresponsivity (R) versus position (X) can be fitted with the same procedure as used in the main text. The results for the 532 nm and 397 nm laser sources for V g = -20 V are shown in Fig. S5a and S5c, respectively. On the other hand, if the photo-doped carriers are of the opposite type as the pre-illumination doping in graphene, I photo = I dope I' photo I dope = either I' photo (if I' photo < I dope, in which case I photo is negative and decreases with increasing I' photo ) or I' photo 2I dope (if I' photo > I dope, and I photo will become positive again for sufficiently large I' photo ). This explains the non-monotonic behavior in the measured I photo vs X (as the intrinsic I' photo monotonically increases with decreasing X), for example, for V g = +20V (with n-type photo-induced doping opposite to the p-type preillumination doping in graphene) seen in Fig. S4 (a, b). To fit the data in this case, we first convert the measured apparent photocurrent I photo to the intrinsic photo-induced current I' photo as follows: I' photo = I photo for large X (for example X > 100 μm in Fig. S4a), where the measured I photo is seen to decrease with decreasing X (expected to increase I' photo ), and I' photo = I photo +2I dope for smaller X (e.g., X = 0 to 100 μm in Fig. S4a), where I photo increases with decreasing X. Then we can apply our model in the main text to fit the corrected I' photo and R' = I' photo /P (representing the intrinsic photoresponse that would have been expected if the graphene had started as chargeneutral). Figure S5b & d demonstrates the fits with extracted data for V g = +20V exposed to 532 nm and 397 nm laser sources, respectively. The fits (Fig. S5) suggest that our model can explain the observed position dependent photoresponse quite well. The model fit parameters (defined in the main text, Eq. (6)), include β, γ, and ε, as displayed in Fig. S5. The fit parameter of primary interest is the recombination length of carrier charge, ε. Here, the ε fitted for the 532 nm measurements is consistent between different devices (see Fig. 4e and Fig. S5). The ε fitted for the 397 nm measurements is larger than that for the 532 nm data, possibly due to a larger excitation spot size ( 330 m for the 397 nm laser, or 0.6 m for the 532 nm laser). NATURE NANOTECHNOLOGY 8

9 Supplementary Figure S5: Log-log plots of photocurrent (I photo ) (or corrected photocurrent I' photo ) and photoresponsivity (R) (or corrected photoresponsivity R') versus illumination distance (X) measured with 532 nm at V g = -20V (a) and at V g = +20V (b) and with 397 nm at V g = -20V (c) and at V g = +20V (d) for the device presented in Fig. S4. The filled (outline) symbols correspond to the photoresponsivity (photocurrent) data (note the two sets of symbols overlap each other as the photoresponsivity is simply scaled from the photocurrent by a constant power within each plot), while the dashed lines represent the fit to our model. The model fit parameters are included within each plot, including β, the scaling factor for the photocurrent, γ, the nonlinearity of graphene response, and ε, the carrier charge recombination length. See main text Eq. (5) for the detailed definitions. NATURE NANOTECHNOLOGY 9

10 5. Shift of Dirac point voltage with illumination distance Supplementary Figure S6. Dirac point voltage (V Dirac ) as a function of illumination distance (X). The V Dirac is the gate voltage at which I photo -V g curve shows a minimum photocurrent. We extracted the V Dirac for different positions from the I photo -V g plots shown in Fig. 2a in the main text. 6. Position dependent transconductance Supplementary Figure S7. (a) Transconductance (g m ) as a function of a gate voltage (V g ) for a few representative illumination positions X = 0, 50, and 100 μm. (b) The plots of magnitude of maximal electron transconductance (left y-axis) and hole transconductance (right y-axis) versus distance exhibit a reduction in transconductance with increasing illumination distance from graphene. To investigate the effect of illumination position on the gate voltage modulation of photocurrent, we plotted transconductance (g m ) as a function V g for a few representative NATURE NANOTECHNOLOGY 10

11 illumination positions in Fig. S7a. The transconductance is calculated by taking the derivative of photocurrent data with respective to the V g, ie. g m = di photo /dv g. Hole transconductance (g m _hole) and electron transconductance (g m _electron) are extracted at the minimum and maximum of the g m vs V g plot (Fig. S7a), respectively and magnitudes are plotted as a function of distance (Fig. S7b). The transconductance for both electrons and holes decreases with increasing distance, indicating the reduction of effect of gate voltage on the photocurrent with increasing illumination distance from the graphene. 7. Time dependent photocurrent at high laser power Supplementary Figure S8. (a, b) Photocurrent as a function of time while the laser switches between on and off with laser power of (a) P = 60 µw, and (b) P = 720 µw. In both the measurements, V ds = 75 mv; and V g = 30 V. Shaded regions in a-b label are time intervals during which the laser is on. We also measured time-dependent photocurrent (I photo vs t) by illuminating the device with relatively high laser powers of 60 and 720 µw, as shown in Figs. S8a and S8b, respectively. Both the figures show photocurrent decreases as the illumination position moves away from the graphene, similar to what was observed for the lower laser power of 5 µw. However, a photocurrent overshoot (photocurrent exhibits a maximum which exceeds the steady-state photocurrent) is observed when the laser power of 720 µw is illuminated directly on the graphene or nearby graphene (0 < X <10 µm). Similar photocurrent overshoot has been observed in quantum well infrared photodetectors. 3,4 This photocurrent overshoot may be attributed to the NATURE NANOTECHNOLOGY 11

12 time-dependent nonlinearity of photoresponsivity due to the redistribution of the electric field in the device substrate. 8. Position dependent photocurrent Photocurrent rise time (τ rise ) and fall time (τ fall ) are calculated by fitting the photocurrent rise and decay versus time data to an exponential function, as shown in Fig. S9a and S9b, respectively. The red circles represent the measured data points, whereas the solid lines represent the exponential fits to the measured data. In Fig. S9c, we plotted the fall time as a function of illumination distance for the three incident laser powers. We found dramatic increase in the fall time at short distances and a saturation trend at larger distances. Although the fall time is slightly higher than the rise time for a given distance and a laser power, the behaviors of the fall time versus distance (Fig. S9c) and rise time versus distance (Fig. 3c in the main text) are similar. Supplementary Figure S9. (a, b) Photocurrent (I photo ) as a function of time for laser illumination with P = 5 µw on the graphene (X = 0 µm) of a GFET. Shaded region is the time interval during when the laser is on. The red circles represent measured data points, whereas the solid line represents the exponential fit to the measured data to extract (a) rise time, and (b) fall time. (c) Photocurrent fall time (τ fall ) as a function of illumination position (X) for various incident laser powers. 9. Position dependent electric field near the graphene Figure S10 shows a plot of electric field (E) (calculated with COMSOL Multiphysics) directly under the graphene of a GFET as a function of laser illumination position (X) at V g = 30 V and two different laser powers (P), without considering the transport and recombination of the photo excited carriers, showing that electric field decreases sharply with increasing distance but NATURE NANOTECHNOLOGY 12

13 does not depend significantly on the laser powers. The behavior of this position dependent electric field curve is markedly different from the behavior of position dependent photoresponsivity curve (does not change much with distance up to ~100 µm and then decreases sharply as shown in Fig. 4e in the main text). This suggests that only the change of electric field (modulated by photo generated carriers, but not considering transport of such carriers) at graphene with illumination distance cannot fully explain quantitatively the observed photoresponse when the illumination occurs away from the graphene. To better explain the position dependent photoresponse, the transport of photo-generated carriers should be included in our model. Supplementary Figure S10. Electric field (E) (calculated with COMSOL Multiphysics) directly under the graphene of a GFET as function of laser illumination position (X) at V g = 30 V and different laser powers P. In these simulations, the transport and recombination of the photo-excited carriers are not considered. 10. Disentangling the effects of position and intensity of the incident light As shown in Fig. S10, the electric field of a GFET is more strongly dependent on the illumination distance than on the incident P within typical operation range. Therefore, the distance dependence of the E-field for a single device can be already used as a first measurement of position (although it is insufficient to measure the power P) of illumination. However, a multichannel approach (measuring the E-field response from two or more devices) can be used to measure the power of the illumination (and disentangle its effect from the position). As a proof of principle demonstration, we modeled two devices using the COMSOL Multiphysics NATURE NANOTECHNOLOGY 13

14 simulation. In the model, we consider two devices (separated by a fixed distance of 20 m) and the light (for a representative P = 0.1 µw) that are illuminated at various positions (X) between those two devices (Fig. S11a). For each illumination position, a pair of electric fields (E 1 and E 2 for device 1, 2 respectively) is calculated using the similar to what explained above section (see Table 1). The illumination position is plotted as function of E 1 (Fig. S11b) and it is found that this dependence can be fitted to the following function (for this specific P): X = f (E) = 27.04*(e -0.07*E ) (3) Supplementary Figure S11: (a) Schematic of the two GFETs which are separated by a fixed distance. A laser is illuminated at different positions (X) between the GFETs. (b) Plot of position (X, distance from GFET1) of illumination versus electric field under GFET1. The dependence of distance (X = 20 m) from GFET2 on E-field (E 2 ) underneath is similar. The data points were calculated for illumination power P = 0.1 W and separation between two GFET devices to be 20 m. Using Eq. (3), f(e 1 )+f(e 2 ) is calculated for each pair of E 1 and E 2 for each position. We also calculated the f(e 1 )+f(e 2 ) for other powers P = 1 µw and 0.01 µw using similar procedures. Finally, f(e 1 )+f(e 2 ) versus X is plotted for different laser powers in Fig. S12a, and f(e 1 )+f(e 2 ) versus P is plotted for a few distances in Fig. S12b. These plots show that f(e 1 )+f(e 2 ) is mostly independent of illumination distance (X); however, f(e 1 )+f(e 2 ) strongly depends on the laser power. Here, the distance is the measurable quantity as it is converted from E-field. This simple example demonstrates that an appropriately processed sum signal from two devices can be NATURE NANOTECHNOLOGY 14

15 dependent on (therefore used to measure) illumination power but not significantly dependent on position. Therefore, the effect of illumination position and light intensity can, in principle, be distinguished when two or more spatially separated graphene devices are utilized to form a multi-channel detector. Supplementary Table 1: The table shows the simulated electric fields E 1 and E 2 for device 1and 2 respectively with P=0.1 µw and calculated f(e 1 ), f(e 2 ) and f(e 1 ) + f(e 2 ) for different illumination positions (X). Supplementary Figure S12: (a) Plots of f(e 1 ) + f(e 2 ) as function of illumination position (X) for different laser powers (P). (b) Plots of f(e 1 ) + f(e 2 ) as function of P for different X s. The function f(e 1 ) + f(e 2 ) does not change with the positions of illumination but changes with the laser power. NATURE NANOTECHNOLOGY 15

16 11. Effect of the device density in an array of photodetectors In order to understand the impact of device density in a photodetectors array, we also conducted another simulation using COMSOL Multiphysics. In this simulation, we consider two GFETs which are separated by a set distance and the light is incident between the two GFETs, at equal distance from each device (Fig. S13a). We varied the distance between the GFETs and recorded the simulated electric field (E) at the GFETs for different laser powers (P). Since the position of laser illumination is at equal distance from two GFETs, the electric fields at both GFETs are the same. We plotted the electric field as a function of separation of GFETs, as shown in Fig. S11b. We found that the electric field decreases with increasing separation and the electric field becomes less dependent on the separation when larger than 300 µm (Fig. S13b). This suggests that in an array of photodetectors, (a) the separation between photodetectors should not be more than 300 µm to ensure good position sensitivity and (b) photoresponsivity can be increased by placing the photodetectors closer (limited by the fabrication process). Supplementary Figure S13: (a) Schematic of the two GFETs separated by a set distance. The separation is varied and a laser beam illuminates the point at an equal distance from these two GFETs. (b) Electric field as a function of the separation between two GFETs for different laser powers (P). 12. Potential for detection a broad light spectrum using GFETs In addition to large-area detection and position sensitivity, one of the advantages of our photodetector fabrication method is that it can take advantage of a wide range of undoped semiconductors (differing in bandgaps and other electro-optical properties) as substrates for NATURE NANOTECHNOLOGY 16

17 fabricating photodetectors. This allows detection of a broad light spectrum (based on the bandgaps of substrates) and gives more design flexibility while potentially lowers cost. For example, one could detect infrared light by fabricating devices on the narrow band-gap undoped semiconductors such as InAs (bandgap ~0.42 ev), 5 PbSe (bandgap ~ 0.28 ev), 6 InSb (bandgap ~ 0.24 ev), 5 etc. 13. Supplemental discussion of the responsivity and nonlocal photoresponse of the GFETs The photoresponsivity of our device (fabricated on undoped silicon carbide substrate) reaches ~18 A/W at room temperature for local light incidence (on graphene) as shown in this paper. This photoresponsivity is much higher than photoresponsivity (on the order of ma/w) of previous graphene photodetectors typically fabricated on doped Si substrates based on direct light interaction with graphene itself Techniques such as integrating graphene with photonic nanostructures (e.g. microcavities, waveguides, plasmonic arrays, etc.) have been developed to moderately increase the photoresponsivity up to a few tens of ma/w A very high photoresponsivity (10 7 A/W) has been demonstrated in graphene-quantum dot (QD) hybrid phototransistors. 17 However, all the previous graphene photodetectors (including graphene/qd hybrid detectors) are based on local detection and require light incidence on or very close to graphene, and the responsivity would vanish if light is incident away from the channel. The GFET phototransistor on undoped substrates described in this work, in contrast, allows nonlocal detection and light incidence, and can still maintain substantial photoresponsivity even when the light is incident as far as >100 m away from graphene channel. We also note that the responsivity of our device is higher than the required responsivity (1 A/W) in most practical applications, 18,19 and also higher than photoresponsivity (~0.5 A/W) of a commercial photodiode (Hamamatsu silicon photodiode). We also anticipate that the responsivity of devices based on the demonstrated approach can be further improved by optimizing the fabrication processes and measurement conditions (e.g. increasing the sourcedrain bias voltage). Our simple approach can also be generalized to other type of graphene (such as CVD graphene, and epitaxial graphene directly grown on SiC) and other beyond-graphene 2D-semiconductors or to the detection of higher-energy radiation NATURE NANOTECHNOLOGY 17

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