In situ electrical measurements of polytypic silver nanowires

IOP PUBLISHING NANOTECHNOLOGY

Nanotechnology 19 (2008) 085711 (6pp) doi:10.1088/0957-4484/19/8/085711

In situ electrical measurements ofpolytypic silver nanowiresXiaohua Liu1,2, Jing Zhu1,2, Chuanhong Jin3, Lian-Mao Peng3,Daiming Tang4 and Huiming Cheng4

1 Beijing National Center for Electron Microscopy, Tsinghua University, Beijing 100084,People’s Republic of China2 Laboratory of Advanced Materials, Department of Materials Science and Engineering,Tsinghua University, Beijing 100084, People’s Republic of China3 Key Laboratory for the Physics and Chemistry of Nanodevices and Department ofElectronics, Peking University, Beijing 100871, People’s Republic of China4 Shenyang National Laboratory for Materials Science, Institute of Metal Research,Chinese Academy of Sciences, Shenyang 110016, People’s Republic of China

E-mail: [email protected]

Received 31 October 2007, in final form 3 January 2008Published 4 February 2008Online at stacks.iop.org/Nano/19/085711

AbstractNovel 4H structure silver nanowires (4H-AgNWs) have been reported to coexist with the usualface-centered cubic (FCC) ones. Here we report the electrical properties of these polytypicAgNWs for the first time. AgNWs with either 4H or FCC structures in the diameter range of20–80 nm were measured in situ inside a transmission electron microscope (TEM). Both kindsof AgNW in the diameter range show metallic conductance. The average resistivity of the4H-AgNWs is 19.9 μ� cm, comparable to the 11.9 μ� cm of the FCC-AgNWs. The failurecurrent density can be up to ∼108 A cm−2 for both 4H-and FCC-AgNWs. The maximum stablecurrent density (MSCD) is introduced to estimate the AgNWs’ current-carrying ability, whichshows diameter-dependence with a peak around 34 nm in diameter. It is attributed to fastannihilation of the current-induced vacancies and the enhanced surface scattering. Ourinvestigations also suggest that the magnetic field of the electromagnetic lens may alsointroduce some influence on the measurements inside the TEM.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

The effect of size on the electrical properties of metals hasattracted continuous interest for reasons of both fundamentaland technical significance. The resistivity of thin metallicconductors increases with shrinking dimensions comparable toor less than the mean free path (MFP), due to enhanced diffusescattering of the conducting electrons at the surfaces and thegrain boundaries [1–4]. With the assumption that the bulkMFP holds constant at smaller sizes, rigorous calculations havepredicted a monotonic increment in electrical resistivity [1, 2],implying a weakening ability to carry a large current density inthin conductors. However, as known, metallic crystals becomenearly perfect and defect-free at the nanoscale. The defects,either intrinsic or current-induced, tend to diffuse fast to thesurfaces and disappear. This may have an influence on thetransport behavior of nanoconductors.

In contrast to intense studies on the size-dependentresistivity of thin conductors, less attention has been given toestimating their ability to transport current, except for failuretests [5, 6]. The development of integrated circuits (IC)requires interconnects of low resistivity, high electromigrationresistance and high ability to carry a large current density.Silver is promising for the next generation of interconnects dueto its highest conductivity and high electromigration resistanceat ambient conditions [4, 7]. However, polytypism has recentlybeen reported in silver nanowires (AgNWs), i.e. single-crystalline 4H-and face-centered cubic (FCC)-AgNWs coexistwith diameters ranging 10–100 nm [8–11]. The electricalproperties of these polytypic AgNWs remain unexplored.

Here we report in situ electrical measurements ofindividual single-crystalline 4H- and FCC-AgNWs with20–80 nm diameters by employing a scanning tunnelingmicroscope (STM) inside the transmission electron microscope

0957-4484/08/085711+06$30.00 © 2008 IOP Publishing Ltd Printed in the UK1

Nanotechnology 19 (2008) 085711 X Liu et al

(TEM). Current–voltage (I –V ) curves of an individual NWcan be obtained, while conventional TEM characterizations,such as selected-area electron diffraction (SAED) and imaging,can be realized simultaneously [12, 13]. Consequentlythe nominal resistivities of both 4H- and FCC-AgNWs areexperimentally obtained. Furthermore, a parameter calledmaximum stable current density (MSCD) is introduced toestimate the current-carrying ability of the AgNWs, whichis revealed to be diameter-dependent. A phenomenologicalmodel is proposed to explain the size effect by considering fastannihilation of the current-induced vacancies at the surfacesof the NWs in addition to the enhanced surface scatteringsuggested by the classical size effect. The magnetic field inthe polepiece of the TEM is found to be influential in these insitu conductance measurements, especially for those ultrathinand straight NWs.

2. Experiments

Single-crystalline AgNWs with different diameters are pre-pared by using a template-assisted electrochemical deposi-tion method [8]. The commercial STM–TEM sample hold-ers (Nanofactory® Instruments AB) are used inside the 200 kVTEMs (either Tecnai G20 or JOEL 2010) to carry out the elec-trical measurements with a two-terminal configuration. CleanAgNWs are adhered to a 250 μm-diameter Pt or Au electrode.A tungsten (W) or Pt–Ir alloy tip is piezotube-driven to touchthe free end of a protruding AgNW on the electrode. The tipcan be moved in three dimensions in steps as fine as 0.02 nm.The vacuum level in the TEM column is ∼10−5 Pa. The elec-tron diffraction patterns and the images are also taken to de-termine the crystal structure and the geometry of the measuredAgNWs.

3. Results and discussions

In the two-terminal configuration, the measured resistance, R,can be written as R = Rc + RNW, where Rc is the sum ofthe contact and the systemic resistances. RNW corresponds tothe resistance of the AgNW. Because Ag is highly conductiveand the contact resistance cannot be excluded for a singlemeasurement in the configuration, it is important to reduceRc. Initial I –V curves are usually nonlinear but symmetric,indicating a large contact resistance [13]. Various approachesare used to minimize the influence of Rc, for instance byapplying a large bias between the W-tip and the electrode toremove the oxide layer on the W-tip. We also develop anothermethod to attain good contacts by in situ coating the tip withmelted Ag. Firstly the tip is moved to touch a suspendedAgNW. By applying a large bias, the AgNW will melt andthe debris of the melted AgNW forms a Ag-layer on the tip,usually ball-shaped, resulting in very good contacts. The Ag-coated tip is then used in the next measurements. Figures 1(b)–(d) show the measurements of a FCC-AgNW using this kind oftip. By moving the tip along a straight AgNW, the I –V curvesare acquired for different lengths of the AgNW (multi-sitemeasurements). Rc is also measured by directly connecting thetip and the electrode, which can be regarded as the resistance

Figure 1. Experimental scheme and multi-site measurements.(a) Schematic illustration of in situ electrical measurements of anindividual NW combined with crystal structure characterizationsinside the TEM. (b)–(d) Multi-site I–V measurements of aFCC-AgNW. (b) Good contacts can be obtained by touching the freeend of the AgNW with the Ag-coated W-tip at this site (marked as‘B’). The inset electron diffraction pattern, in which two spotsmarked by yellow triangles are indexed, corresponds to FCC-Ag withthe zone axis of [11̄0]. The AgNW bundle, which supports themeasured AgNW, is attached to a gold electrode (not shown). (c) TheW-tip is moved to another site (marked as ‘C’), thus the I–V curvefor a shorter AgNW is obtained. (d) Plot of the resistance (R) versusthe length (L) for the FCC-AgNW. The inset shows the linear I–Vcurves obtained at the two sites shown in (b) and (c), marked as Band C, respectively. The other dot corresponding to contactresistance, Rc, is obtained by direct contact of the tip and theelectrode. The R–L plot fits well to the formula ofR = Rc + (ρ/S)L with S being the cross-sectional area of the NW.The retrieved nominal resistivity (ρ) for this FCC-AgNW is42.7 μ� cm and the contact resistance (Rc) is 365 �.

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Figure 2. The resistances versus the geometries of the AgNWs.(a) For FCC-AgNWs two classes are plotted according to a high orlow contact resistance (Rc), with the resistivities of ρH and ρL

retrieved from linear fittings, respectively. An average value of11.9 μ� cm can be obtained as the nominal resistivity of theFCC-AgNWs. (b) For 4H-AgNWs, linear fitting of the experimentaldata gives the average nominal resistivity of 19.9 μ� cm.

of the AgNWs with 0 nm length. The resistance–length (R–L)relation is plotted for the FCC-AgNW and fitted by the formulaR = Rc + ρL/S, where ρ is the nominal resistivity of theFCC-AgNW with a cross-sectional area S and length L. Thenwe can obtain Rc = 365 � and ρ = 42.7 μ� cm for thisFCC-AgNW.

However, multi-site measurements are not successfulfor most samples due to limitations of the tip’s movement.Generally we can obtain linear I –V curves by annealing thecontacts with a large bias. Since the contact resistance cannotbe excluded from a single measurement, we plot the measuredresistances of different samples as a function of the geometricalparameter, L/S (figure 2) [14]. For the FCC-AgNWs, someI –V curves are symmetrical and nonlinear, indicating highercontact resistances. The resistances are then retrieved from thehigh-bias part of the curves [13]. For the linear I –V curves,resistances are directly retrieved by linear fitting. The averagenominal resistivities of the FCC-AgNWs are obtained by linearfitting the R–L/S plots, being 17.3 μ� cm and 6.4 μ� cmfor the high-Rc and low-Rc data, respectively. The averagenominal resistivity of the FCC-AgNWs is 11.9 μ� cm, larger

than the 1.6 μ� cm of bulk FCC-Ag. This is reasonabledue to the enhanced surface scattering in the single-crystallinethin wires according to the classical size effect [2]. For 4H-AgNWs, linear fitting of the experimental data gives an averageresistivity of ∼19.9 μ� cm. Our experimental results indicatethat 4H-AgNWs are as good metallic conductors as FCC-AgNWs. The electrical properties of the AgNWs seem to beless sensitive to the crystal structure.

Figure 3 shows the electrical measurements for a 4H-AgNW until its failure. The resistance retrieved from the linearI –V curve is 402 �, corresponding to a nominal resistivityof 32.7 μ� cm. When the bias is increased to 691 mV, anabrupt drop in current occurs, indicating that failure starts at acritical current density of ∼1.17×108 A cm−2 (the ‘pre-break’point). The transport consequently becomes unstable, showingsome fluctuations in contrast to the smooth curve of stabletransport before the ‘pre-break’ point. The breakdown doesnot take place until the bias reaches 844 mV, correspondingto a critical failure current density of 1.32 × 108 A cm−2

(the ‘break’ point). The failure current density is quite largeand comparable to that of Wiley’s report [15]. However,we note that in our experiments the catastrophic failure of aAgNW usually produces two spherical droplets and a large gapbetween them, as shown in figure 3(c). The gap between thedebris can be as large as ∼1000 nm, indicating that a largepart of the AgNW seems to melt almost simultaneously. Butan open circuit does not form immediately at the ‘pre-break’point. This suggests there would be a thinning process duringthe failure. This differs from the manner of failure of theAgNWs on substrates [5, 15], in which tiny gaps (several tensof nanometers in length) appear at one end of the NW close tothe electrode, being a sign of failure by electromigration [5].Because our AgNWs are isolated in the vacuum, the heatdissipation can only be realized by thermal transport alongthe NWs. There should be a highest temperature (high-T )point in the middle of the NWs where the failure caused byJoule heating most probably takes place [16, 17]. Intuitively,once a gap at the high-T point is formed, there will be noJoule heating effect and thus no further burning. In ourexperiments, the large gap after failure suggests a picture of a‘thinning’ process before the ‘break’ point, where the centralpart remains continuous. However, the thinning process ishardly a snapshot for the fast failure. Instead, morphologiesof hillocks and necks are recorded as a result of an incompleteburning, as shown in figure 3(d), indicating mass transport bysurface diffusion prior to the breakdown of the NW. Basedon the above experimental observations, we speculate thatthe failure of the AgNWs in our experiments is initiatedwith the thinning process by high surface atom diffusion,corresponding to the unstable transport stage between the ‘pre-break’ and the ‘break’ points in figure 3(b). During the thinningprocess, conductance of the NWs largely remains unchanged,indicating that the surface layer contributes little to the currenttransport. Furthermore, current saturation is never observedfor the AgNWs even until the breakdown, unlike the well-known positive temperature coefficient of resistivity at hightemperatures for metals. It seems that a large current density inthe NW leads to intense surface diffusion but has little effect on

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Figure 3. Manner of failure of the AgNWs. (a) The measurement of a 4H-AgNW (D = 44 nm; L = 1872 nm). The inset SAED pattern, inwhich the spots marked by two yellow triangles are indexed, corresponds to 4H-Ag with a zone axis of [5̄72̄3]. (b) I–V curve of the4H-AgNW. It can be divided into three parts with increasing bias by the ‘pre-break’ and the ‘break’ points, i.e. stable transport, unstabletransport and open circuit, respectively. The stable transport ceases at the bias of 691 mV (the ‘pre-break’ point) with a critical current densityof 1.17 × 108 A cm−2. However, the final breakdown of the NW does not take place until the bias reaches 844 mV (the ‘break’ point) with acurrent density of 1.32 × 108 A cm−2. Between these two points the transport is unstable as the current fluctuates, implying that surfacediffusion occurs but the NW remains continuous. The slope of the I–V curve is almost the same as that in the stable transport stage,indicating that the conducting path largely remains and the surface contributes little to the current. (c) The debris of the burnt AgNW. Twoballs formed after the failure at two ends of the gap. The tip had been moved closer to the electrode than the original distance for clarity. Thelarge gap (over 1000 nm) between the two balls suggests that a thinning process may take place before the open circuit forms. (d) Incompletefailure of another AgNW. The thinning process can be seen as a snapshot when an open circuit forms earlier than in a complete burning. Thehillock and necks clearly indicate intense diffusion of the surface atoms under large current stress before the breakdown.

the central part. This is consistent with the dominant surfacescattering mechanism in thin metallic conductors first proposedby Lovell [18]. Nearly all free paths start and end at thesurfaces and most diffuse scatterings occur in the thin layernear the surfaces, resulting in a highly conducting central partand a much less conducting surface layer [2, 18]. Furthermore,due to the finite lateral sizes, the surfaces can also serve as asink for the current-induced defects (mainly vacancies in puremetal). It has been reported that the current density gradientcan drive the excess vacancies to diffuse to the region withlower current density [19], i.e. from the central part to thesurfaces in our AgNWs. The current-induced vacancies candiffuse fast to the surfaces even at large current densities, andscatterings seldom take place in the central part. As known,according to Matthiessen’s rule, scattering by the surfaces isless dependent on temperature than scattering by the latticephonons [20]. Thus surface scattering mechanism is alwaysdominant in our experiments and the temperature-dependentscattering part is considered to be constant and less important.Fast diffusion of vacancies to the surfaces effectively maintainsthe perfect central part at the cost of aggravated surfacescattering and surface stress. The failure is directly caused bythe enhanced surface scattering, with the momentum transfer

from the conducting electrons to the surface atoms, resultingin high mobility of the latter. At ultra large current densitiesexceeding the critical value (∼108 A cm−2 in our experiments),the mobility of the surface atoms becomes large enough todiffuse and/or escape rapidly, while the central part remainscontinuous to hold the current.

We have found the large critical failure current densitiesfor both 4H- and FCC-AgNWs up to ∼108 A cm−2. However,another important issue for conductors is the ability to carrya stable current. Thus we introduce a parameter called themaximum stable current density (MSCD), J , to estimate thisability. Electrical transport in a conductor with a currentdensity below the MSCD should be reproducible and causeno failure. Experimentally, we can obtain this parameter byapplying a bias sweep in a symmetric range with respect tothe zero bias, getting reproducible I –V curves and graduallywidening the range until failure occurs. In our experiments,the sampling rate of bias sweep is 1 kHz, corresponding to1 ms per step, which is much longer than the reported mean-time-to-failure (MTTF) of Ag interconnects under large currentstress [6]. The sampling time at each bias step is long enoughto establish stable current in the NWs. So we actually testthe stable transport properties of these AgNWs subjected to

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Figure 4. Diameter dependence of the maximum stable currentdensity (MSCD, J ). The experimental MSCD reaches its maximumat diameters around 34 nm. The fitting curve in a solid line is basedon the assumption that the bulk mean free path (MFP) holds in thethin AgNWs, λ = 52 nm, while the fitting curve in a dashed linecorresponds to a reduced MFP, λ′ = 25 nm. They both predict a peakof MSCD with similar positions close to the experimental one.However, an evident discrepancy can be seen at small diameters(about 20–34 nm) for the solid line with the large MFP of λ. This isattributed to the influence of the magnetic field in the polepiece of theTEM. The transverse magnetic field deflects the conducting electronsin the straight thin AgNWs and enhances the surface scattering. Theelectromagnetic force results in a shortened MFP and the rapid dropof the measured MSCD at small diameters.

a pulsed bias of low frequency, as an analog to the actualwork conditions in IC devices [21]. In our experiments,the transport is reproducible for 20 circles of the bias sweepwithout visible changes in morphology of the NWs, unlike theone-off failure test. The value of MSCD for each AgNW canbe calculated from the largest stable current and its geometry.In contrast to the determination of the NW’s resistivity in thetwo-terminal configuration, MSCD is much less sensitive tothe contact condition because the failure always occurs at theNW and the largest stable current represents the property ofthe measured NW, rather than that of any other parts in thecircuit. Figure 4 shows the plot of experimental MSCD versusthe effective diameter (J–D curve) for the AgNWs. There isan evident peak around a diameter of 34 nm, at which MSCDattains its maximum of ∼55 MA cm−2. It decreases slowly to∼10 MA cm−2 at ∼80 nm but rapidly below ∼29 nm.

This size effect of MSCD in AgNWs can be explainedby combination of the classical size effect arising fromsurface scattering and the fast diffusion of the current-inducedvacancies to the surfaces for nanoconductors with finite lateralsize. As mentioned above, the current density should beuneven in the AgNWs. In the perfect central part, the current-induced vacancies can diffuse rapidly to the surfaces, resultingin a highly conducting path that has the main contribution tothe current even at large current densities. This is consistentwith the classical size effect on electrical transport in thinmetallic wires suggested by Dingle’s pioneering work [2].With the assumption that the MFP remains the bulk value andthe surface scatterings are totally or partially diffuse, Dingle’srigorous calculations give a monotonically decaying radial

distribution of the current density in a wire [2]. However, afast drainage of the current-induced vacancies must be realizedbecause the AgNWs can carry a large and stable current density(>10 MA cm−2) without failure. In a cylinder-shaped AgNWwith a radius of R (D = 2R, D being the diameter), the unevenradial distribution of the current density in Dingle’s thin wirescan be approximately treated as a surface layer with uniformbut low current density ( js) and a central part with a muchlarger current density ( jc). The thickness of the surface layer isds. Then the distribution function of the current density alongthe radius (r ) of a AgNW can be expressed as follows:

j (r) ={

jc(r) = f · jc0 · fv, (0 � r � R − ds)

js(r) = (1 − f ) · js0, (R − ds � r � R),(1)

where jc0 is the current density for the central part withoutvacancies; js0 is the current density for the surface layerwithout enhanced surface scattering; f is the distributionfactor defined as the probability of the conducting electronsbeing scattered from the surface layer into the central part;fv is the factor defined to estimate the influence of varyingvacancy concentrations on the current density. Because aconducting electron contributing to the current should be eitherin the central part or in the surface layer, there must bethe probability of 1 − f for a conducting electron to movefrom the central part to the surface layer. The distributionfactor, f , actually estimate the intensity of surface scatteringin thin conductors. It should be a function of the diameterof the AgNW and the MFP. When the diameter is smallerthan the MFP, the surface scattering becomes predominantand the central part contributes most to the current. For thephenomenological model represented by equations (1), thefunction f = 1/{1 + exp[(D − λ)/t]}, is employed, in whichλ is the MFP and t describes how fast the shrinking lateralsizes enhance the surface scatterings. This function gives anessentially identical but much simpler description of Dingle’ssize effect in thin wires [2]. The vacancy concentrationshould vanish exponentially with decreasing distance to thesurfaces of the NWs. In single-crystalline AgNWs with largecurrent densities, intrinsic vacancies can be neglected, thusonly the current-induced vacancies are considered. Accordingto a random hopping mechanism of vacancy diffusion inpure metals [22], the effect of the vacancies is treated byan exponential function fv(r) = exp{[r − (R − ds)]/ l} bycomparing the distance to the surface layer (the sink) with theeffect diffusion length, l. Thus experimental MSCD is theaverage current density by calculating the integral of j (r) overthe cross-sectional area S:

J = 1

S

∫S

j (r) dS. (2)

As shown in figure 4, there are two fittings to the experimentalresults. The solid line corresponds to the fitting using thebulk MFP of FCC-Ag, λ = 52 nm [7], and the rest fittingparameters as are extracted as jc0 = 75 MA cm−2, js0 =0.01 MA cm−2, ds = 2 nm, t = 8 nm, and l = 50 nm. Thedashed line corresponds to another fitting using a reduced MFP,λ′ = 25 nm, and the other fitting parameters as are extracted asjc0 = 600 MA cm−2, js0 = 0.01 MA cm−2, ds = 8.5 nm,

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t = 12 nm, and l = 50 nm. Roughly, the two fittingsindicate the same tendency, agreeing with the measured J–Dcurve. The peak positions for the two fittings are close to eachother, at critical diameters of 30 nm for λ and 34 nm for λ′.The main discrepancy for the two fittings is that MSCD dropsfaster at small diameters with a smaller MFP for λ′ than withλ. The MFP of λ′ (25 nm) is close to the reported values inAgNWs and in Ag thin films [3, 15, 23]. It seems that theshorter MFP is more consistent with the experimental results.However, as discussed above, the central part is nearly defect-free. Intuitively, the MFP, referred to the ‘bulk’ properties ofthe AgNW, should be at least as large as that in bulk FCC-Ag (52 nm). Actually, the rapid drop in MSCD at smallerdiameters may arise from the influence of the magnetic fieldin the polepiece of the TEMs. It has been reported that thetransverse magnetic field causes a positive magnetoresistancein a straight thin conductor [3, 24]. When the magnetic fieldis perpendicular to the current in a very thin and straight wire,nearly all conducting electrons are driven to the surface by theLorentz force. This largely enhances the surface scattering andshortens the MFP, resulting in a smaller current density as wellas a faster failure than without a magnetic field. Other fittingparameters are reasonable for our experimental conditions.The current density in the central defect-free part is ultra highdue to little scattering. The effective diffusion length forthe current-induced vacancies, l = 50 nm, which representsa critical distance of fast diffusion for the vacancies to thesurface, is also acceptable for the short-cut diffusion of thevacancies along finite distances to the sink [22]. The thicknessof the surface layer, ds, which also represents the influence ofsurface scattering on the total current, is larger for a shortenedMFP when the effect of the magnetic field is considered.

4. Conclusions

In summary, the electrical properties of single-crystallineAgNWs with either a 4H or FCC structure were measuredin situ inside the TEMs. Both 4H- and FCC-AgNWs behaveas metallic conductors with comparable average resistivitiesof 19.9 μ� cm and 11.9 μ� cm, respectively, both oneorder larger than that of bulk FCC-Ag (1.6 μ� cm). Thefailure current density for the AgNWs is of magnitude upto ∼108 A cm−2. The maximum stable current density(MSCD) of the AgNWs is introduced to estimate the abilityof the AgNWs to transport current, which shows a diameter-dependence, with the maximum of ∼55 MA cm−2 arounda diameter of 34 nm. This size effect is attributed to anabnormal distribution of the current density in the NWs, as aresult of a compromise between two factors, i.e. the enhancedsurface scattering and the fast diffusion of the current-inducedvacancies to the surface. This is consistent with the observedmanner of failure of the AgNWs. The magnetic field inthe electromagnetic lens may also introduce some influence

on the in situ conductance measurements in the TEM. Ourinvestigations reveal an abnormal size effect on the electricalcurrent transport of nanoconductors made of a good metal(Ag), suggesting that metallic NWs with proper diametersmay serve as good interconnects and that defect dynamicsand surface scattering both play important roles in electricaltransport at the nanoscale.

Acknowledgments

We acknowledge the financial support from the ChineseNational Natural Science Foundation, National 973 Projectof China, and the National Center for Nano-Science andTechnology of China.

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