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| (2020) 10:19613 | www.nature.com/scientificreports .?eelectrical 3-9 .Systemsinweak- ?lms 10 -13 .?esesystems 14 -17,19-21 switching 22
,23 .?eir boundaries 22
,23 non-metallicelectricalconductionandnegativeTemperatureCoe?cientofResistance(TCR)within24-300 K taineddowntocryogenictemperatures. NABLA

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| (2020) 10:19613 | www.nature.com/scientificreports/

PulsedMicroplasmaClusterSource(PMCS)

24
,asdescribedindetailin reference 23
.Figure 1ashowsaschematic peakedaround5 nmareformedinanArgonatmospherea?ertheplasmaablationofagold target 23
,25 ,thecluster- athermallygrownoxide layer 22
,23 thermalevaporation(Fig. 1a).Supersonicclusterbeamsarecharacterizedbyhighcollimation:thisguarantees in 23
,26 .?eamountof ofthe?lmsismonitoredin situandexsituinatwo-probecon?guration. Insituelectricalcharacterizationinarangefromroomtemperature(RT,300 K)downto24 Khasbeen performedinvacuum (10 -5 nm 27
Wecharacterizedcontinuous?lmswithanaveragethicknessrangingfrom15to30 nm,andresistance,before switchingactivation 21
-23 ?lms

3,11,28

.?evalueofthedimensionless tunnelconductance g=h/2e 2 R t (T→∞),whereR t (T→∞) is the average tunnel resistance of the granular system at high temperature, discriminates the weak-coupling regime ( g<1 ) from the strong-coupling one ( g>1 3,6 . In Fig.R1b (let panel) we show the evolution of g, obtained by approximating R t to the resistance at room

Figure 1.

rectangularshape7 mm ×3 mm,spacedby1 mmandbridgedbya1 mm×7 mmcluster?lm.?egoldpads are100 nmthick.( voltageintherange-

1 Vto1 V.

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| (2020) 10:19613 | www.nature.com/scientificreports/ thickness 23
.?e opennewconductivepaths.Figure 1bshowsthetransitiontothestrong-couplingregimeatathicknessvalue ofroughly7 nm. Figure 1b(centralpanel)showstheroomtemperatureI-Vcharacteristicsofthecluster-assembled?lm ramp 22
,23 reportedanddiscussed in 22
.Figure 1b(rightpanel)showstheroomtemperatureI-Vcurveinlinearscalefor smallappliedvoltages(valuesintherange- 1 Vto1 V).Alsointhiscase,thetrenddeviatesformthatexpected foranohmicconduction. HRTEManalysishighlightsthetypicalfeaturesofthe?lmfromastructuralpointofview(Fig. 2),namelyits

5 nmwide.

Figure 2.

otherthanmetallicgold.

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| (2020) 10:19613 | www.nature.com/scientificreports/ ?lms 6,29 highdensityofrandomlyorientedcrystallinenanodomainsandgrainboundariesofthe?lms(Fig. 2). eter dln(I2 dln(V) ,whereln(I) and ln(V) are the logarithms of the current and of the applied voltage, respectively 30
,31

2e analysis is carried out by plotting against

V 1 2 , since this curve has a well-degned trend for diherent mecha-

nisms such as ohmic, space charge limited conduction (SCLC), Schottky, Poole-Frenkel, tunnelling, etc.

3,30

2e trend of the gamma parameter for our glms is reported in Fig.R3 showing a transient (blue curve) before

stabilizing around roughly 2, which is typical of SCLC 30
,32,33 . In this regime, the free carrier density is low and the electrical conduction is usually determined by the charges injected from ohmic electrodes 30

In order to exclude the contribution of contact resistance, we tested atom-assembled thin glms with similar

thickness and geometry at RT. We found the standard ohmic behavior 23
. We can also exclude a contribution of

the contact resistance at low temperatures since we did not observe a Schottky conduction contribution in the

gamma curves, as one expects from contact resistance 34

In systems characterized by SCLC, ohmic conduction is usually observed at low bias voltages, due to the pres

ence of a small fraction of thermally generated carriers 32
. Cluster-assembled gold glms show a non-linear I-V

curve even at very low voltages (Fig.R1b let panel) suggesting that diherent concurrent mechanisms contribute

to determine a SCLC regime and to lower the free electron density. Coulomb blockade 9,35 and defect localiza- tion ehects

3,13,36

could be possible causes for the low concentration of free carriers in our systems, due to their

overall disordered crystal structure, which manifests as a very high density of grain boundaries as observed by

HRTEM (Fig.R2).

To gain a deeper insight about the phenomena involved in the conduction process of cluster-assembled Au

glms and to discern among diherent mechanisms, we investigated the evolution of electrical conduction with

temperature

9,37,38

FigureR4 shows the temperature dependence of the current at diherent applied voltages normalized to the

value measured at RT. We observe a steep decrease of the current in the range between RT and 250RK; from

250 to 24RK the decrease continues with a lower slope. 2e trend of the current for diherent applied voltages is

qualitatively similar.

In metallic systems, gnite electrical resistivity arises due to scattering processes from impurities or various

thermal excitations

2,39-41

. 2e scattering events can be considered as statistically independent and thus addi

tive, leading to the Matthiessen"s rule, where any thermally induced scattering simply increases the resistivity

(T) 42
,43 . 2is corresponds to a positive Temperature Coeecient of Resistivity (TCR), i.e. d/dT > 0. FigureR4

Figure 3.

ofa15 nmthickcluster-assembled?lm.

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| (2020) 10:19613 | www.nature.com/scientificreports/ ofnon-metallicsystems. Figure 5ashowsthatcluster-assembledgold?lmshaveanegativeTCR,inparticularnearRT,theoscillation theresistancetemperature variations 22
,23 temperature

5,6,12,28

,althoughnotinsuchalarge blocks 10 .Intheinsulatingregime, temperatures 36
.?e

Figure 4.

voltagesofa25 nmthicksample.?esawtooth-likeshapeofcurvesathighvoltagesisduetoswitchingevents.

Figure 5.

Dataofa25 nmthickcluster-assembled?lm.(a)thetemperaturecoe?cientofresistivity(TCR)for thecurvemeasuredupontheapplicationof20 V.( Arrhenius-liketrendisrecognizableonlyfortemperaturesbelow40 K.

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| (2020) 10:19613 | www.nature.com/scientificreports/ 6,11 ?uctuationsando?set charges 44
voltage 9 .?e?owingofcurrent junctions 6 9 .Increasingthe observed

6,9,28

9,42 .Inourcase,cluster-assembled?lms byHRTEM analysis 22
(seeFig. 2).?iskindofspatiallyextendeddisorderissubstantiallydi?erentfromwhat muchlowercomparedtothatwe?ndinour systems 45
Figure 5bdisplaystheresistancevstheinverseofthetemperatureinlogarithmicscale,showingthatan

R(T)?exp

h t h ,isnotdetectedexceptfortemperatures below40 K.?eobservedbehaviordeviatesfromapurehoppingconductionlikethatintheEfros-Shklovskii model

3,9,46

voltage 6,9 ,evenifdi?erentmechanisms,suchasAnder- observed 36
,47 .Wealsonotethatthetrendis properties. teristic(seeFig. 1b).Figure 6ashowstheI-Vcharacteristicsinthetemperaturerange295 Kto268 K.?etrend ancemeasuredatlowertemperatures.Ontheotherhand,inFig. 6bthecurvesshowsteepslopevariationfor temperatureslowerthan144 K.Althoughthetrendslightlydeviatesfromapurepowerlaw,thisagreeswiththe temperatures 9,35 Atlowtemperatureswealsonoticethattheγparameterexploresvaluesslightlylargerthan2.Figure 7shows theevolutionoftheγparameterfrom298to24 K.?isagreeswiththeobservationofhigherresistancestates motion 9 ofa metal 48
anditselectricalconduction properties 42

Figure 6.

Dataofa25 nmthickcluster-assembled?lm.(a)I-Vcurvesfordi?erenttemperaturesintherange

295 Kto268 K.(

b)I-Vcurvesintherange202 Kto24 K.

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| (2020) 10:19613 | www.nature.com/scientificreports/ ?lms 48
thuscausingsubstantialelectroniclocaliza phenomena 21
-23 ,theevolutionoftheRS InFig. 8aweshowatypicalresistance-timegraphoftheevolutionoftheresistanceunder5 Vbias.Weaddthe histogram(Fig. 8b)oftheresistance,measuredatbothRTand24 Kupontheapplicationofaconstantvoltage, foradurationof300 s.?edi?erentpeaksinthehistogramareduetothedi?erentresistancelevelsexplored duringtheresistiveswitchingphenomena.RemarkablyweobserveasubstantialRSactivityat24 Kspanning

Figure 7.

γparameterasafunctionofthesquarerootofthevoltageofa15 nmthicksample.?egraphshows theevolutionofγforthepositivebranchintheI-Vcurvefrom295to24 K.Atlowvoltages(lowerthan2 V) thecurrentissuppressed;thecurveshowstheparametervaluesforvoltagevaluesgreaterthan2 V.

Figure 8.

(a)?eresistance-timegraph,ofa15 nmthicksample,a300 K(bluecurve)andat24 k(redone).(b) voltage(5 V)atRT(reddata)andat24 K(bluedata).

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| (2020) 10:19613 | www.nature.com/scientificreports/ resistanceoccurthroughtherearrangementof defects 16 ,20 atomsandatomic planes 49
resultinginanassemblyofinteracting nanojunctions 44
,48,50 glemetallicnanojunctionsatcryogenic temperatures 51
,52 resistance 51
,53 phenomena

20,22,54

.?is nanowireswhereionictransportis involved

14,15,17,18,55

nanowires 56
processing 22
,57,58

Received: 3 June 2020; Accepted: 16 October 2020

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