Controllable Fabrication of Percolative Metal Nanoparticle Arrays Applied for Quantum Conductance-Based Strain Sensors

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Article Controllable Fabrication of Percolative Metal Nanoparticle Arrays Applied for Quantum Conductance-Based Strain Sensors

Zhengyang Du, Ji’an Chen, Chang Liu, Chen Jin and Min Han * National Laboratory of Solid State Microstructures, College of Engineering and Applied Sciences and Collaborative Innovation Centre of Advanced Microstructures, Nanjing University, Nanjing 210093, China; [email protected] (Z.D.); [email protected] (J.C.); [email protected] (C.L.); [email protected] (C.J.) * Correspondence: [email protected]; Tel.: +86-25-83686248

Received: 13 October 2020; Accepted: 28 October 2020; Published: 29 October 2020

Abstract: We use gas phase deposition of well-defined nanoparticles (NPs) to fabricate closely-spaced Pd NP arrays on flexible membranes prepatterned with interdigital electrodes (IDEs). The evolution of the morphology and electron conductance of the NP arrays during deposition is analyzed. The growth of two-dimensional percolation clusters of interconnected NPs, which correlate with the percolation pathway for electron conduction in the NP deposits, is demonstrated. The percolative nature of the NP arrays permits us to finely control the percolation geometries and conductance of the NP film by controlling the NP deposition time so as to realize a precise and reproducible fabrication of sensing materials. Electron transport measurements reveal that the electrical conductance of the NP films is dominated by electron tunneling or hopping across the NP percolating networks. Based on the percolative and quantum tunneling nature, the closely-spaced Pd NP films on PET membranes are used as flexible strain sensors. The sensor demonstrates an excellent response ability to distinguish tiny deformations down to 5 10 4 strain and a high sensitivity with a large gauge factor of 200 up to × − 4% applied strain.

Keywords: nanoparticle arrays; gas phase deposition; percolation; quantum conductance; strain sensors

1. Introduction Strain and pressure sensors are important micro-electro-mechanical system (MEMS) devices, with applications in various areas such as industrial control, automotive and aerospace systems, consumer electronics, environmental monitoring and wearable devices and electronic skins [1–4]. To achieve strain and pressure gauging, a number of transduction mechanisms including capacitive, piezoelectric, piezoresistive, as well as transistor sensing have been utilized. Among them piezoresistive sensing is the most frequently used transduction mechanism, owing to advantages such as low cost, scalable, DC input and easy signal collection, as well as its simple structure and manufacturing process [5–7]. However, conventional resistive strain sensors, mainly metallic foil or semiconductor strain gauges, show significant limitations, such as the low gauge factor of the former or the fragile and high temperature coefficient of the latter. Recently, conductive polymer composites incorporating conductive fillers such as carbon blacks, nanoparticles (NPs), nanotubes, as well as graphene membranes in/on an insulating polymer matrix have been used as strain/pressure sensing elements [8–16]. Strains applied on these composites may cause a drastic fall in resistivity due to the formation of percolation paths [15]. However, the sensitivities of the devices based on such materials are moderate and susceptible to

Materials 2020, 13, 4838; doi:10.3390/ma13214838 www.mdpi.com/journal/materials Materials 2020, 13, 4838 2 of 12 significant hysteresis. Furthermore, the uncontrollable, sudden drastic resistivity drop at the critical volume fraction and the non-reliability (large variations) on the electric response induce many problems regarding fabrication and assessment. Recently, a new configuration of piezoresistive strain/pressure sensing elements fabricated from percolation-based conductive closely-spaced metal NP arrays was proposed [17–19]. Electron conduction in the highly disordered NP arrays is dominated by a Coulomb blockade and electron tunneling and hopping across the NP percolating networks [20–22]. The conductance of the NP arrays deposited on the electrodes is correlated to the number of percolative paths they contain. Since electron conduction by tunneling or hopping between closely-spaced NPs is extremely sensitive to inter-particle spacing, breaking or regenerating of the percolative paths could be induced by tiny changes in the NP array geometries. Differently from current piezoresistive strain sensors, the devices based on the closely-spaced NP arrays transduce the deformation on the electrodes covered with NPs to the change of the quantum conductance of the NP arrays [17,23]. They are characterized with high sensitivities and resolutions, wide dynamic ranges, reduced thermal disturbances, as well as reduced power consumptions. In this paper, we fabricate closely-spaced metallic NP films via gas phase depositing of preformed NPs with a controlled coverage. The evolution of the electron conductance and the geometry of the NP percolating networks with the deposition process and the deformation of the flexible substrate is analyzed. The closely-spaced metal NP films are employed to fabricate a strain sensor prototype, and its strain sensing characteristic is demonstrated.

2. Materials and Methods Closely-spaced metal NP films were prepared with gas phase NP deposition. Generally, NPs of either metals could be used in the present piezoresistive sensing scheme. Here, we chose Pd NPs since they hardly coalesce after depositing on the surface even at a very high NP density so that prefect percolative NP arrays can be formed. This behavior is important to achieve a high stability in sensor applications. A Pd NP beam was generated in a magnetron plasma gas aggregation cluster source [24,25]. The setup consisted of a DC magnetron discharge head equipped in an aggregation tube ended with an orifice 3 mm in diameter, a differential pumping unit, as well as a high vacuum deposition chamber. Figure1 shows a schematic drawing of this setup. A planar Pd target of 99.999% purity was used for magnetron sputtering. 140 sccm of argon flow (99.99% purity) was introduced into the aggregation tube to maintain a stable pressure of 120 Pa. The magnetron discharge was operated by a 500 W power supply (MDX500, Advanced Energy, Fort Collins, CO, USA). Pd atoms were sputtered from the target and formed clusters through the aggregation process in the argon gas. By extracting the clusters at the high vacuum differential pumping stage through the orifice, a collimated NP beam was formed. The Pd NPs were deposited on the substrate in the high vacuum deposition chamber. A stable deposition rate of 0.4 Å/s, monitored using a quartz crystal microbalance, was maintained by regulating the discharge power. By controlling the deposition time with a shutter, the coverage of NPs on the substrate could be precisely controlled. To fabricate strain sensors and measure the conductance of the closely spaced NP arrays, Pd NPs were deposited on interdigital electrodes (IDEs) prepatterned on the surface of polyethylene terephthalate (PET) membrane. The PET membrane is a 6 20 mm2 slice with a thickness of × 0.1 mm. The silver IDEs, with a 100 nm thickness and 15 µm electrode separation, were deposited on the membrane via shadow mask vacuum evaporation. The electrodes covered an area of several ten square millimeters, with an as-prepared resistance of about 1010 Ω. During NP deposition, the conductance across the electrode gap was monitored in real time. The deposition was cut immediately by operating a shutter when a predetermined conductance was approached. Materials 2020, 13, 4838 3 of 12 Materials 2020, 13, x FOR PEER REVIEW 3 of 12

Figure 1. A schematic diagram depicting the cluster source and nanoparticles (NP) beam Figure 1. A schematic diagram depicting the cluster source and nanoparticles (NP) beam deposition deposition setup. setup. The morphologies of the Pd NP arrays were characterized with a transmission electron microscope (TEM,To FEI fabricate TECNAI strain F20s sensors TWIN, Thermoand measure Fisher the Scientific, conductance Hillsboro, of the OR, closely USA). spaced For TEM NP characterization, arrays, Pd NPs amorphouswere deposited carbon on films interdigital supported electrodes on copper (IDEs) grids wereprepatterned used as substrates.on the surface The TEM of polyethylene images were digitalizedterephthalate by (PET) using membrane. a public domain The PET Java membrane image processing is a 6 × 20 program,mm2 slice ImageJwith a thickness (National of Institutes 0.1 mm. ofThe Health). silver IDEs, The sizes with and a locations100 nm thickness of each nanoparticle and 15 μm were electrode extracted. separation, A Visual were Basic deposited program writtenon the bymembrane ourselves via was shadow used to mask perform vacuum percolation evaporation. analysis The on theelectrodes digitalized covered TEM an images. area of several ten squareThe millimeters, conductance with and an current-voltage as-prepared (I-V)resistance characteristic of about of 10 the10 NPΩ. During arrays wereNP deposition, measured with the aconductance digital source across meter the (Keithley electrode 2400). gap The was data moni acquisitiontored in was real carried time. outThe with deposition a LabView was coded cut programimmediately through by operating a USB interface. a shutter Thewhen temperature a predetermined of the conductance sample was constantlywas approached. controlled in the rangeThe of 10–300morphologies K by thermally of the contactingPd NP arrays the samplewere characterized with the copper with finger a transmission of an optical cryostatelectron systemmicroscope (Janis (TEM, CCS-150, FEI TECNAI Janis Research, F20s TWIN, Wilmington, Thermo MA, Fisher USA). Scientific, Hillsboro, OR, USA). For TEM characterization,The response amorphous characteristics carbon of thefilms fabricated supported strain on copper sensors grids were were evaluated used byas substrates. measuring The the conductanceTEM images changeswere digitalized of the NP arraysby using deposited a public on domain the IDEs Java following image the processing applied strains. program, The ImageJ strains were(National induced Institutes by subjecting of Health). the PETThe membranessizes and locations to a series of each of bending nanoparticle cycles orwere pull-and-release extracted. A Visual cycles drivenBasic program with a micrometer.written by ourselves In the bending was used case, to perform the PET membranepercolation wasanalysis deformed on the bydigitalized adjusting TEM the micrometerimages. getting in touch with the membrane surface near the location of the IDEs. The strain was calculatedThe conductance from the deformation and current-voltage geometry (I-V) of the characte membraneristic surfaceof the NP measured arrays were from measured a microscope. with Ina digital the pull-and-release source meter (Keithley case, one 2400). side ofThe the data PET acquisition slice was fastenedwas carried on theoutfixed with basea LabView of an optical coded benchprogram adjusting through bracket, a USB andinterface. the other The sidetemperature was pulled of withthe sample the micrometer was constant of thely adjustingcontrolled bracket. in the Therange strain of 10–300 was calculated K by thermally directly contacting from the relative the sample change with of the lengthcopperof finger the PET of an slice optical reading cryostat from thesystem micrometer. (Janis CCS-150, The conductance Janis Research, was Wilmington, measured by MA, recording USA). the current in the NP arrays, with a constantThe biasresponse voltage characteristics of 1 V applied of tothe the fabricated IDEs. strain sensors were evaluated by measuring the conductance changes of the NP arrays deposited on the IDEs following the applied strains. The 3.strains Results were and induced Discussion by subjecting the PET membranes to a series of bending cycles or pull-and- releaseFigure cycles2a showsdriven awith TEM a microimagemicrometer. ofIn athe film bending of the depositedcase, the PET Pd NPs.membrane The NPs was are deformed randomly by distributedadjusting the and micrometer well isolated. getting The filmin touch contains with numerous the membrane closely surface spaced NPnear assembling the location areas. of the The IDEs. size distributionThe strain was histogram calculated of thefrom Pd the NPs deformation is counted fromgeometry the TEM of the image membrane and shown surface in Figuremeasured2b. We from can a seemicroscope. the NP assemblies In the pull-and-release are mainly composed case, one of aside group of the of NPs PET with slice diameters was fastened between on the 7.5 fixed nm to base 10 nm. of Theiran optical size distributionbench adjusting can bebracket, well fitted and the with other a log-normal side was pulled function with with the a micrometer mean diameter of the of adjusting 9 nm and abracket. standard The deviation strain was of about calculated 1.4 nm. directly Meanwhile, from athe small relative number change of smaller of the NPs length can alsoof the be observed,PET slice withreading a broad from sizethe distributionmicrometer. fromThe conductance 2.5 nm to 7.5 was nm. measured In addition, by a recording tiny number the ofcurrent larger in NPs the with NP diametersarrays, with around a constant 12.5 nm bias can voltage be distinguished. of 1 V applied They to the may IDEs. coalesce from smaller ones after depositing on surface. From the high resolution TEM image shown in Figure2c, flat facets can be frequently identified from the individual Pd NPs, indicating that the NPs are polyhedron nanocrystals with

Materials 2020, 13, x FOR PEER REVIEW 4 of 12

3. Results and Discussion Figure 2a shows a TEM microimage of a film of the deposited Pd NPs. The NPs are randomly distributed and well isolated. The film contains numerous closely spaced NP assembling areas. The size distribution histogram of the Pd NPs is counted from the TEM image and shown in Figure 2b. We can see the NP assemblies are mainly composed of a group of NPs with diameters between 7.5 nm to 10 nm. Their size distribution can be well fitted with a log-normal function with a mean diameter of 9 nm and a standard deviation of about 1.4 nm. Meanwhile, a small number of smaller NPs can also be observed, with a broad size distribution from 2.5 nm to 7.5 nm. In addition, a tiny number of larger NPs with diameters around 12.5 nm can be distinguished. They may coalesce from Materials 2020, 13, 4838 4 of 12 smaller ones after depositing on surface. From the high resolution TEM image shown in Figure 2c, flat facets can be frequently identified from the individual Pd NPs, indicating that the NPs are randompolyhedron orientations. nanocrystals In the with assembling random orientations. region, although In the theassembling adjacent region, NPs are although in close the proximity adjacent to eachNPs other, are in it canclose be proximity distinguished to each in other, the TEM it can image be distinguished that the NPs in are the separate TEM image from eachthat the other NPs with are an edge-to-edgeseparate from distance each other of about with 1an nm, edge-to-edge sometimes distance 1.5 nm orof more.about The1 nm, gaps sometimes separating 1.5 nm the or NPs more. might The gaps separating the NPs might be thin amorphous shells, most likely PdOx, developed on the NP be thin amorphous shells, most likely PdOx, developed on the NP surfaces due to oxidation [15]. surfaces due to oxidation [15].

FigureFigure 2. 2.(a ()a A) A transmission transmission electron electron microscopemicroscope (TEM) microimage microimage of of the the deposited deposited Pd Pd NP NP arrays arrays showingshowing a closelya closely spaced spaced assembling assembling morphology. morphology. (b) Size (b) distributionSize distribution histogram histogram of Pd NPsof Pd measured NPs frommeasured the TEM from image. the TEM (c) Aimage. high-resolution (c) A high-resolution TEM image TEM demonstrating image demonstrating polyhedron-shaped polyhedron-shaped Pd NPs arrangedPd NPs inarranged close proximity. in close proximity.

TheThe evolution evolution of theof morphologythe morphology and electronand electron conductance conductance of the of NP the films NP during films NPduring deposition NP is examined.deposition is Figure examined.3 shows Figure the conductance 3 shows the evolutionconductance of theevolution Pd NP filmof the measured Pd NP film simultaneously measured withsimultaneously the deposition with process. the deposition At the earlier process. stage At of the the earlier deposition, stage of the th coveragee deposition, of the the NPs coverage on the of surface the is tooNPs low on the to generatesurface is anytoo low electron to generate conduction any electr acrosson conduction the electrodes, across therefore, the electrodes, no conductance therefore, no can beconductance measured. After can be 185 measur s of deposition,ed. After with185 s an of equivalent deposition, 7.4 with nm Pdan beingequivalent deposited, 7.4 nm a conductancePd being whichdeposited, is distinguishable a conductance with which the leakage is distinguishabl conductancee with of thethe substrateleakage conductance starts is observed. of the substrate This means thestarts NP coverageis observed. is su Thisfficiently means high the NP to generatecoverage electronis sufficiently conduction high to paths generate in the electron NP film conduction distributed acrosspaths the in electrodes.the NP film Between distributed 200 across and 350 the s, el theectrodes. conductance Between displays 200 and a dramatic350 s, the increase conductance by two ordersdisplays of magnitude, a dramatic increase growing by approximatelytwo orders of magnitude, exponentially growing with approximately the deposition exponentially time. After with that, thethe rising deposition of the conductancetime. After that, becomes the rising slow of and the finallyconductance tends tobecomes plateaus, slow generating and finally another tends to two ordersplateaus, of magnitude generating increase another within two orders the next of magnit 360 s deposition.ude increase When within a totalthe next deposition 360 s deposition. time of 690 s is reached,When a total the depositiondeposition istime stopped of 690 bys is operating reached, the a shutter. deposition The is conductance stopped by thenoperating remains a shutter. stable at aboutThe 100conductance nS, which then is four remains orders stable of magnitude at about 100 larger nS, which than theis four leakage orders conductance of magnitude of larger the substrate. than the leakage conductance of the substrate. Four specimens for TEM characterization are collected during the NP deposition stage either before or after a measurable electron conductance can be observed. The deposition time of these specimens is 100 s, 175 s, 350 s and 650 s, respectively. TEM microimages of these specimens are shown in Figure4. The surface coverages of the Pd NPs measured from Figure4a–d are 28%, 40%, 62% and 79%, respectively. Considering there is a direct correspondence between the NP coverage and the deposition time, the time-dependent conductivity curve shown in Figure3 is indicative of the percolation character in NP films [26,27]. The NP deposited film can be simply described with a two-dimensional network, where a random fraction of the interconnections is occupied. The number, size and shape of the connected structures can be explained using percolation theory [28]. At a defined coverage the percolation threshold is approached and the NP network becomes conducting over the length scale defined by the separation of the electrodes. On the other hand, it has been shown in previous studies that the electron conduction in metal NP arrays is proceeded by tunneling or hopping between neighboring NPs [29,30]. The tunneling conductance between adjacent nanoparticles depends exponentially on the separation gap between them. We thus set a critical separation gap permitting electron conduction and used the percolation approach to analyze the development of the electron conductance of the NP films during the deposition process. Assuming a critical separation gap of 1.2 nm, we searched Materials 2020, 13, 4838 5 of 12 the percolation clusters from the digitalized TEM images by mapping the NPs onto two-dimensional networks composed of electrically interconnected NPs. The arrangements of the percolation clusters inMaterials the NP 2020 films, 13, x FOR are shownPEER REVIEW in Figure 4e–h. In the figure, each percolation cluster is indicated with5 of 12 different colors.

Figure 3. Electron conductance of the Pd NP ﬁlm monitored during the NP deposition process. MaterialsFigure 2020, 133. ,Electron x FOR PEER conductance REVIEW of the Pd NP film monitored during the NP deposition process.6 of 12

Four specimens for TEM characterization are collected during the NP deposition stage either before or after a measurable electron conductance can be observed. The deposition time of these specimens is 100 s, 175 s, 350 s and 650 s, respectively. TEM microimages of these specimens are shown in Figure 4. The surface coverages of the Pd NPs measured from Figure 4a–d are 28%, 40%, 62% and 79%, respectively. Considering there is a direct correspondence between the NP coverage and the deposition time, the time-dependent conductivity curve shown in Figure 3 is indicative of the percolation character in NP films [26,27]. The NP deposited film can be simply described with a two-dimensional network, where a random fraction of the interconnections is occupied. The number, size and shape of the connected structures can be explained using percolation theory [28]. At a defined coverage the percolation threshold is approached and the NP network becomes conducting over the length scale defined by the separation of the electrodes. On the other hand, it has been shown in previous studies that the electron conduction in metal NP arrays is proceeded by tunneling or hopping between neighboring NPs [29,30]. The tunneling conductance between adjacent nanoparticles depends exponentially on the separation gap between them. We thus set a critical separation gap permitting electron conduction and used the percolation approach to analyze the development of the electron conductance of the NP films during the deposition process. Assuming a critical separation gap of 1.2 nm, we searched the percolation clusters from the digitalized TEM images by mapping the NPs onto FigureFigure 4. 4.TEM TEM images images ofof the Pd Pd NP NP films films with with deposition deposition time time of ( ofa) 100 (a) 100s, (b s,)175 (b )175s, (c) s,350 (c )s 350and s(d and) two-dimensional networks composed of electrically interconnected NPs. The arrangements of the (d)650 650 s sand and the the corresponding corresponding digita digitalizedlized NP NP location location mapping mapping (e– (eh–),h with), with each each percolation percolation cluster cluster percolationbeingbeing marked clustersmarked with with in dithe differentfferent NP films colors. colors. are shown in Figure 4e–h. In the figure, each percolation cluster is indicated with different colors. FromFrom Figure Figure4, 4, we we can can find find that that whenwhen the NP coverage coverage is is low, low, such such as asthat that in inFigure Figure 4a 4witha with a a coveragecoverage of 28%, 28%, the the NP NP arrays arrays are are mainly mainly composed composed of electrically of electrically separated separated particles. particles. Only a Only few a fewpercolation percolation clusters clusters of very of very small small size, size, containing containing less lessthan than 10 NPs, 10 NPs, can be can identified, be identified, as shown as shown in inFigure Figure 4e.4e. Obviously, Obviously, there there is isno no percolation percolation path pathwayway for electron for electron conduction conduction across acrossthe upper the edge upper and the bottom edge of the image. With the increase of the NP coverage, the size and the density of the percolation clusters increases significantly, as shown in Figure 4f. In Figure 4c, the NP coverage becomes sufficiently larger (62%), a few large percolation clusters connecting the upper edge and the bottom edge of the image appear, as shown in Figure 4g. An NP film with sufficient electron conductivity is thus formed. However, there still remains a number of relatively smaller percolation clusters, which can potentially grow into percolation pathways for electron conduction. Therefore, the conductance displays a dramatic increase with further NP deposition. In Figure 4d, the NP coverage becomes so high (79%) that most of the NPs are composed in a huge percolation cluster expanding over the whole image (Figure 4h). Although a few small percolation clusters embedded in the huge percolation cluster can still be identified, they will merge into the existing huge one rather than grow into a separate percolation pathway under further NP deposition and therefore contribute little to the increase of the electron conductance. As a result, the conductance increases slowly and approaches plateaus under further NP deposition. In Figure 5, the size distributions of the percolation clusters are compared for the NP films with different deposition times. In every coverage, the number of the percolation clusters decreases rapidly with the cluster size. With the increase of the coverage, both the total number of percolation clusters and the number of smaller clusters sufficiently decrease, accompanied with the formation of a small number of larger clusters. This indicates that more and more smaller percolation clusters are merged into larger ones with the ongoing cluster deposition. The largest size of the percolation clusters increases significantly with the NP coverage, however, their number always remains low. Therefore, in a network system formed by random deposition of particles, there is no way to generate large size percolation clusters in high density. This means the electron conductance of the NP arrays is contributed to by a limited number of percolation pathways for electron conduction.

Materials 2020, 13, 4838 6 of 12 edge and the bottom edge of the image. With the increase of the NP coverage, the size and the density of the percolation clusters increases significantly, as shown in Figure4f. In Figure4c, the NP coverage becomes sufficiently larger (62%), a few large percolation clusters connecting the upper edge and the bottom edge of the image appear, as shown in Figure4g. An NP film with su fficient electron conductivity is thus formed. However, there still remains a number of relatively smaller percolation clusters, which can potentially grow into percolation pathways for electron conduction. Therefore, the conductance displays a dramatic increase with further NP deposition. In Figure4d, the NP coverage becomes so high (79%) that most of the NPs are composed in a huge percolation cluster expanding over the whole image (Figure4h). Although a few small percolation clusters embedded in the huge percolation cluster can still be identified, they will merge into the existing huge one rather than grow into a separate percolation pathway under further NP deposition and therefore contribute little to the increase of the electron conductance. As a result, the conductance increases slowly and approaches plateaus under further NP deposition. In Figure5, the size distributions of the percolation clusters are compared for the NP films with different deposition times. In every coverage, the number of the percolation clusters decreases rapidly with the cluster size. With the increase of the coverage, both the total number of percolation clusters and the number of smaller clusters sufficiently decrease, accompanied with the formation of a small number of larger clusters. This indicates that more and more smaller percolation clusters are merged into larger ones with the ongoing cluster deposition. The largest size of the percolation clusters increases significantly with the NP coverage, however, their number always remains low. Therefore, in a network system formed by random deposition of particles, there is no way to generate large

Materialssize percolation 2020, 13, x FOR clusters PEER REVIEW in high density. This means the electron conductance of the NP arrays7 of 12 is contributed to by a limited number of percolation pathways for electron conduction.

Figure 5. Size distributions of the percolation clusters analyzed from the TEM images of the Pd NP Figurefilms with 5. Size deposition distributions time of of 100 the s, percolation 175 s, 350 s andclusters 650 s.analyzed The coverage from the of the TEM NP images films is of shown the Pd in NP the filmscorresponding with deposition legend. time of 100 s, 175 s, 350 s and 650 s. The coverage of the NP films is shown in the corresponding legend. In Figure6, the arrangements of the percolation clusters in the NP films with 62% coverage, mappedIn Figure by assigning 6, the arrangements a critical separation of the gappercolation for electron clusters conduction in the NP of 0.8films nm, with 1.0 nm62% and coverage, 1.2 nm, mappedare shown, by togetherassigning with a critical the size separation distributions gap for of theelectron percolation conduction clusters. of 0.8 By nm, using 1.0 anm smaller and 1.2 critical nm, areseparation shown, together gap, the with larger the percolation size distributions clusters of split the percolation into a number clusters. of smaller By using ones, a smaller and the critical size separationdistribution gap, curve the shifts larger to apercolation smaller size clusters region. Meanwhile,split into a thenumber size of of the smaller largest ones, percolation and the cluster size distributiondecreases significantly. curve shifts to This a smaller means size the region. number Meanwhile, of percolation the size pathways of the largest for electron percolation conduction cluster decreases significantly. This means the number of percolation pathways for electron conduction reduces if the critical separation gap for electron conduction becomes smaller. Reducing the critical separation gap in the percolation analysis is equivalent to the effect of expanding the NP arrays, therefore, the number of percolation pathways for electron conduction can be sufficiently changed via a strain applied on the NP arrays.

Materials 2020, 13, 4838 7 of 12

reduces if the critical separation gap for electron conduction becomes smaller. Reducing the critical separation gap in the percolation analysis is equivalent to the eﬀect of expanding the NP arrays, therefore, the number of percolation pathways for electron conduction can be suﬃciently changed via Materialsa strain 2020 applied, 13, x FOR on thePEER NP REVIEW arrays. 8 of 12

FigureFigure 6. 6. DigitalizedDigitalized NP NP location location mappings mappings generated generated fr fromom the the TEM TEM image image of of the the Pd Pd NP NP film film with with depositiondeposition time of 350 s.s. The percolationpercolation clustersclusters are are searched searched by by assuming assuming a criticala critical separation separation gap gap for forelectron electron conduction conduction of (ofa) ( 0.8a) 0.8 nm, nm, (b )(b 1.0) 1.0 nm nm and and (c )(c 1.2) 1.2 nm, nm, respectively. respectively. Each Each percolation percolation cluster cluster is ismarked marked with with di differentfferent colors. colors. (d ()d Size) Size distributions distributions of of the the percolation percolation clusters clusters in in (a –(ac–).c). In the above image analyses, the length scale of the percolation system is about 100, as normalized In the above image analyses, the length scale of the percolation system is about 100, as to the NP size. Although this length is smaller than the separation between the electrodes used normalized to the NP size. Although this length is smaller than the separation between the electrodes for conductance measurement (with a normalized length of 1500), it is sufficiently large enough to used for conductance measurement (with a normalized length of 1500), it is sufficiently large enough ensure that there is not significant difference on the percolation threshold between the two systems, to ensure that there is not significant difference on the percolation threshold between the two systems, since according to the percolation theory of finite system [31], the percolation threshold changes little since according to the percolation theory of finite system [31], the percolation threshold changes little with the system size when the normalized system size is larger than 100. Therefore, it is reasonable with the system size when the normalized system size is larger than 100. Therefore, it is reasonable to assume that the above percolation nature analyzed from the TEM images is applicable to the real to assume that the above percolation nature analyzed from the TEM images is applicable to the real system used in the electron conduction measurements. system used in the electron conduction measurements. In order to understand the electron transport characteristics in the Pd NP films, the current–voltage In order to understand the electron transport characteristics in the Pd NP films, the current‒ (I–V) curves are measured from 20 K to room temperature. The measurement is carried out on a voltage (I–V) curves are measured from 20 K to room temperature. The measurement is carried out pair of IDEs deposited with Pd NPs with a coverage of 62%. As shown in Figure7a, at cryogenic on a pair of IDEs deposited with Pd NPs with a coverage of 62%. As shown in Figure 7a, at cryogenic temperatures the I–V curves display a current plateau with low applied bias voltages, demonstrating temperatures the I–V curves display a current plateau with low applied bias voltages, demonstrating Coulomb blockade behavior. The I–V curve at 20 K can be well fitted by the Nordheim-Fowler Coulomb blockade behavior. The I–V curve at 20 K can be well fitted by the Nordheim-Fowler equation [32], indicating tunnel emission is the dominate transport mechanism at this temperature. With the increase of the temperature, the I–V characteristic becomes more and more linear, displaying a smooth transition from the blocked regime to the unblocked regime. At room temperature, no current plateau is observable, but the I–V curve is still distinctly nonlinear. The I–V curves could be well fitted by a sinh function, suggesting electron hopping becomes the dominate transport mechanism [33]. To get a deeper insight into the charge transport mechanism, we deduced zero bias

Materials 2020, 13, 4838 8 of 12 equation [32], indicating tunnel emission is the dominate transport mechanism at this temperature. With the increase of the temperature, the I–V characteristic becomes more and more linear, displaying a smooth transition from the blocked regime to the unblocked regime. At room temperature, no current plateau is observable, but the I–V curve is still distinctly nonlinear. The I–V curves could be well fitted by a sinh function, suggesting electron hopping becomes the dominate transport mechanism [33]. ToMaterials get a deeper 2020, 13,insight x FOR PEER into REVIEW the charge transport mechanism, we deduced zero bias conductance9 of 12 (G) from the I-V curves measured at different temperatures. Figure7b shows the temperature dependence conductance (G) from the I-V curves measured at different temperatures. Figure 7b shows the of the conductance. A significant conductance increase is observed with the increase of temperature, temperature dependence of the conductance. A significant conductance increase is observed with the indicating that the electron transport in the NP film is strongly different from the normal metallic films. increase of temperature, indicating that the electron transport in the NP film is strongly different from Inthe fact, normal the positive metallic temperature films. In fact, coe thefficient positive of conductance temperature is coefficient indicative of of conductance thermally activated is indicative transport. of In Figure7b, from room temperature to 200 K, ln(G) scales as 1/T, indicating that thermally activated thermally activated transport. In Figure∼ 7b, from room temperature to ∼200 K, ln(G) scales as 1/T, hoppingindicating dominates that thermally the transport activated in hopping this temperature dominates regimethe transport [22]; electronin this temperature transfer occurs regime between [22]; 1/2 spatiallyelectron adjacent transfer NPs. occurs At between lower temperature, spatially adjacent deviation NPs. from At thelower 1/T temperature, scaling occurs, deviation ln(G) scales from asthe T , indicating1/T scaling that occurs, variable ln(G) range scales hoppingas T1/2, indicating becomes that the variable dominant rang electrone hopping transport becomes mechanism the dominant [21 ]; electronelectron transfer transport occurs mechanism between the[21]; energetically electron transf closester occurs NP states. between For the temperatures energetically lower closest than NP 50 K, thestates. conductance For temperatures can be fitted lower neither than 50 with K, the 1/T cond scalinguctance nor withcan be T1 /fitted2 scaling, neither indicating with 1/T that scaling thermally nor activatedwith T1/2 hopping scaling, no indicating longer dominates that thermally the electron activate transport.d hopping In no this longer regime, dominates electrons the are electron tunneling whentransport. the applied In this bias regime, voltage electrons is sufficient are tunneling to overcome when the the charging applied energies bias voltage of the NPs.is sufficient The electron to transportovercome behavior the charging observed energies above of is the analogous NPs. The to previouselectron transport studies onbehavior two-dimensional observed above NP arrays is withanalogous well-defined to previous inter-particle studies separation on two-dimensional gaps [20,22,34 NP], suggesting arrays with that well-defined the electron inter-particle conductance in theseparation fabricated gaps NP films[20,22,34], is proceeded suggesting by that quantum the el transportectron conductance dominated in by the tunneling fabricated and NP/or films hopping is andproceeded is subject by to aquantum Coulomb transport blockade dominated at moderate by voltages. tunneling and/or hopping and is subject to a Coulomb blockade at moderate voltages.

Figure 7. (a) The I-V curves of the 62% coverage Pd NP film measured at different temperatures. Figure 7. (a) The I-V curves of the 62% coverage Pd NP film measured at different temperatures. The The solid curve and dashed curve fit the experimental data with a Nordheim-Fowler equation and solid curve and dashed curve fit the experimental data with a Nordheim-Fowler equation and sinh sinh function, respectively. The inset shows a magnified view to illustrate the blockade characteristics function, respectively. The inset shows a magnified view to illustrate the blockade characteristics at at cryogenic temperatures. (b) Temperature dependences of the zero bias conductance. The solid curve cryogenic temperatures. (b) Temperature dependences of the zero bias conductance. The solid curve and dashed curve fit the experimental data with lnG ~ 1/T scaling and lnG ~ 1/T1/2 scaling, respectively. and dashed curve fit the experimental data with lnG ~ 1/T scaling and lnG ~ 1/T1/2 scaling, respectively. The Pd NP-coated PET membranes are used as strain sensors and their strain sensing responses are The Pd NP-coated PET membranes are used as strain sensors and their strain sensing responses studied at room temperature. In Figure8a, the measured conductance response in the pull-and-release are studied at room temperature. In Figure 8a, the measured conductance response in the pull-and- cycles of the PET membrane is given as the relative resistance variation ∆R/R (where ∆R is the resistance release cycles of the PET membrane is given as the relative resistance variation ΔR/R (where ΔR is changethe resistance induced change by deformation induced by and deformation R is the resistance and R is without the resistance strain). without The specimen strain). The under specimen testing is a 62%under coverage testing is Pd a 62% NP filmcoverage deposited Pd NP on film an depo IDEsited patterned on an IDE PET patterned membrane PET with membrane 0.1 mm with thickness. 0.1 Themm curve thickness. shows The that curve for each shows pull-and-release that for each cyclepull-and the-release resistance cycle increases the resistance quickly, increases which corresponds quickly, towhich the decrease corresponds of the to conductance the decrease ofof the conductance NP film, once of thethe deviceNP film, is once stretched, the device and is returns stretched, to the originaland returns value to instantly the original once value the appliedinstantly stress once isthe released. applied stress The strainis released. sensing The response strain sensing is rapid, reversibleresponse and is rapid, reproducible. reversible The and stretching reproducible. of the Th PETe stretching membrane of the induces PET membrane a strain on induces the surface a strain where on the surface where the NPs deposit. The inter-particle separation gaps in the NP film thus increase, which results in an increase on the resistance of the NP film.

Materials 2020, 13, 4838 9 of 12 the NPs deposit. The inter-particle separation gaps in the NP ﬁlm thus increase, which results in an increaseMaterials on 2020 the, 13 resistance, x FOR PEER of REVIEW the NP ﬁlm. 10 of 12

Figure 8. (a) Electrical resistance response curve of the strain sensor under pull-and-release cycles. Figure 8. (a) Electrical resistance response curve of the strain sensor under pull-and-release cycles. (b) (b) Relative resistance changes as a function of the applied strains. The insert illustrates the response Relative resistance changes as a function of the applied strains. The insert illustrates the response behavior to very small strains generated by subjecting the PET membrane to bending cycles. behavior to very small strains generated by subjecting the PET membrane to bending cycles. Figure8b shows the sensor response plotted as a function of the applied strains. The response Figure 8b shows the sensor response plotted as a function of the applied strains. The response is is taken as the peak resistance variation ∆R/R, after the PET membrane is pulled to a stable state. taken as the peak resistance variation ΔR/R, after the PET membrane is pulled to a stable state. In the In the inset of Figure8b, the sensor response curve is magnified to illustrate the response behavior inset of Figure 8b, the sensor response curve is magnified to illustrate the response behavior to very to verysmall smallapplied applied strains. strains. Such small Such strains small are strains generated are generated by subjecti byng subjecting the PET membrane the PET membrane to bending to bendingcycles, cycles,which whichinduce induce stretching stretching strains strainson the onsurface the surface where wherethe NPs the deposit. NPs deposit. In either In eithercase, the case, theresistance resistance increases increases with with the the applied applied strain strain sensitivel sensitively.y. As As can can be be seen seen from from the the figure, figure, the the sensor sensor can can 4 distinguish tiny strain changes down to 5 10 −4. In the small applied strain region (<0.5%), the strain distinguish tiny strain changes down to 5× × 10− . In the small applied strain region (<0.5%), the strain sensorsensor displays displays a a constant constant sensitivity, which which is ischaracterized characterized with with the gauge the gauge factor factor g = (Δ gR/R)/= (ε∆. RThe/R) /ε. Thegauge gauge factor factor is calculated is calculated to be to ~55 be ~55in this in strain this strain region. region. The constant The constant gauge factor gauge enables factor a enables linear a linearresponse response of the of relative the relative resistance resistance changes changes to the toap theplied applied strains. strains. In the moderate In the moderate strain region, strain from region, from1.0% 1.0% to to4.0%, 4.0%, a high a high gauge gauge factor factor is maintained, is maintained, between between 100 100 to to200, 200, and and increases increases gently gently with with the the appliedapplied strains. strains. The The sensor sensor can can reversibly reversibly respondrespond to applied strains strains up up to to 4.0%. 4.0%. However, However, this this upper upper limitationlimitation comes comes from from the the elastic elastic limit limit of of the the PETPET membrane.membrane. It It is is possibly possibly extended extended significantly significantly if if otherother more more elastic elastic materials, materials, such such as as PDMS PDMS (polydimethylsiloxane),(polydimethylsiloxane), are are used. used. TheThe behavior behavior of theof NPthe film-basedNP film-based strain strain sensor sensor can be can understood be understood by considering by considering the percolative the andpercolative quantum and tunneling quantum nature tunneling of the closely-spacednature of the closely-spaced NP arrays. The NP IDEsarrays. we The used IDEs have we a used huge have aspect ratioa huge of total aspect electrode ratio lengthof total versus electrode electrode length separation.versus electrode With aseparation. moderate NPWith coverage a moderate above NP the percolationcoverage thresholdabove the corresponding percolation threshold to the finite corresponding length of the electrodeto the finite separation length [31of], the a large electrode number separation [31], a large number of percolative paths are contained in the NP arrays. Since the of percolative paths are contained in the NP arrays. Since the tunneling conductance between adjacent tunneling conductance between adjacent NPs depends exponentially on the inter-particle separation NPs depends exponentially on the inter-particle separation gap, the number of percolative paths gap, the number of percolative paths for electron conduction could be changed by a tiny deformation for electron conduction could be changed by a tiny deformation in the geometries of the NP arrays, in the geometries of the NP arrays, which induces breaking or regenerating of the percolation clusters. which induces breaking or regenerating of the percolation clusters. Furthermore, the deformation also Furthermore, the deformation also induces a change on the distribution of inter-particle gaps along inducesthe conductive a change percolation on the distribution pathways, of which inter-particle also influence gaps along the tunneling the conductive conductance percolation sensitively. pathways, As whicha result, also influencethe conductance the tunneling of percolative conductance NP arrays sensitively. is sensitively As a result, related the to conductance the deformation of percolative of the NPsubstrate arrays is on sensitively which the related NPs deposit. to the deformation of the substrate on which the NPs deposit.

4. Conclusions4. Conclusions GasGas phase phase NP NP beam beam deposition, deposition, as aas low-cost a low-cost and an semiconductord semiconductor device-compatible device-compatible process, process, is used is to fabricateused to fabricate closely closely spaced spaced NP arrays NP arrays on flexible on flexible membranes membranes patterned patterned with with IDEs. IDEs. The evolutionThe evolution of the morphologyof the morphology and electron and conductanceelectron conductance of the NP of films the duringNP films deposition during deposition is examined is examined by performing by real-timeperforming conductance real-time measurement,conductance measurement, TEM characterization TEM characterization and image analysis. and image It is analysis. shown that It is the NPshown film is that composed the NP offilm two-dimensional is composed of two-dimens percolationional clusters percolation of interconnected clusters of NPs.interconnected The conductance NPs. The conductance of the NP film is contributed to by a limited number of percolation pathways for electron conduction. Both the percolation geometries and conductance of the NP film are determined

Materials 2020, 13, 4838 10 of 12 of the NP film is contributed to by a limited number of percolation pathways for electron conduction. Both the percolation geometries and conductance of the NP film are determined by the NP coverage, which is finely controlled by the deposition time under a constant deposition rate. This permits us to finely control the NP deposition process to realize a precise and reproducible fabrication of sensing materials for strain and deformation gauging. Electron transport measurement reveals that the electrical conductance of the NP films is dominated by electron tunneling and hopping across the NP percolating networks. Since the tunneling conductance between adjacent NPs depends exponentially on the inter-particle separation gap, the number of percolative paths for electron conduction and the distribution of inter-particle gaps along the conductive percolation pathway could be changed by a tiny deformation in the geometries of the NP arrays, resulting in a sensitive influence on the tunneling conductance. Based on the percolative and quantum tunneling nature, the closely-spaced Pd NP films on PET membranes are used as sensing materials for flexible strain sensors, which demonstrate an excellent ability to distinguish tiny strain changes down to 5 10 4 and a high sensitivity with a × − large gauge factor of 200 up to 4% applied strain.

Author Contributions: Conceptualization, Z.D. and M.H.; methodology, Z.D. and J.C.; investigation, Z.D., J.C., C.L. and C.J.; data curation, Z.D. and J.C.; writing—original draft preparation, Z.D.; writing—review and editing, M.H.; visualization, Z.D.; supervision, M.H.; funding acquisition, M.H. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China (Grant Nos. 11627806, 21875218, 51872261 and U1909214), the National Key R&D Program of China (Grant No. 2016YFA0201002) and the Natural Science Foundation of Zhejiang Province (LR19E020002). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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