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Impedance spectroscopy analysis of the tunnelling conduction mechanism in piezoresistive

composites

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2014 J. Phys. D: Appl. Phys. 47 345306

(http://iopscience.iop.org/0022-3727/47/34/345306)

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Journal of Physics D: Applied Physics

J. Phys. D: Appl. Phys. 47 (2014) 345306 (5pp) doi:10.1088/0022-3727/47/34/345306

Impedance spectroscopy analysis of thetunnelling conduction mechanism inpiezoresistive composites

Stefano Stassi1, Adriano Sacco2 and Giancarlo Canavese2

1 Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24,10129 Torino, Italy2 Center for Space Human Robotics@PoliTo, Istituto Italiano di Tecnologia, Corso Trento 21, 10129Torino, Italy

E-mail: stefano.stassi@polito.it

Received 31 March 2014, revised 18 June 2014Accepted for publication 30 June 2014Published 1 August 2014

AbstractThe piezoresistive behaviour based on the quantum tunnelling conduction of acopper–polydimethylsiloxane composite was studied by means of impedance spectroscopyand confirmed by the fitting with the tunnelling piezoresistance mathematical model. Thisinvestigation paves the way to the implementation of the impedance spectroscopy technique inthe characterization of piezoresistive pressure sensors for robotic application.

Keywords: piezoresistive composite, impedance spectroscopy, quantum tunnelling,polydimethylsiloxane, spiky particles

(Some figures may appear in colour only in the online journal)

Tactile sensing has been defined as a form of sensing thatcan measure given properties of an object through physicalcontact between the sensor and the object [1]. There areseveral literature reviews describing touch sensing research[1–3] and different available techniques for the transductionof interface contact pressure or force between objects. Mostof these devices originate from biomedical applications suchas the evaluation of wheelchairs and prevention of pressureulcers in hospital beds [4]. Today, these technologies areadopted in a wide range of fields such as computer peripherals,automotive systems, consumer electronics, biomedical devicesand robotics [5–9]. In particular, tactile sensing technologieshave been dramatically broadened out by the increasingdevelopment of humanoid robotics field [2, 10, 11].

Among different possible working principles, there arefew different promising technologies available for thesesensors. Currently the most commonly used methods are thecapacitive and resistive ones. The former is based on thecapacitance change between two conductive parallel platesassembled on a non-conducting soft sheet, in response toan applied force. The advantage of this technique is thatthe output is generally less sensitive to temperature andhumidity variation, but this architecture suffers from parasitic

capacitances. The latter method is based on the resistancechange in a piezoresistive layer when a deformation (inducedby a force or a pressure) is applied. In composite material,this variation is induced by the creation of percolative networkpaths or by the increase in probability of tunnelling conductionwith increasing applied pressure [12, 13].

The work of Maheshwari et al reviews several functionalmaterials based both on metal and organic fillers, highlightingdifferent potential improvements in sensor performances [2].For example, the introduction of nanostructures such as carbonnanotubes, nano-coils and nanowires into tactile/pressuresensors based on conductive polymeric composites, replacingconventional conductive particles, can significantly increasethe sensitivity and force range. Moreover, the enhancementof sensor performance due to the presence of nanostructuredmetal fillers has been previously demonstrated [14–16].

In preceding experimental works, different piezoresistivecomposites, based on nanostructured metal filler dispersedin a silicone matrix as a functional material for tactiledevices, have been reported [16–18]. In these materialsthe achieved wide variation of resistance was ascribed tothe quantum tunnelling conduction induced by the spikyparticles covered by nanometric tips. In the aforementioned

0022-3727/14/345306+05$33.00 1 © 2014 IOP Publishing Ltd Printed in the UK

J. Phys. D: Appl. Phys. 47 (2014) 345306 S Stassi et al

studies, the variation of electrical resistance as a functionof applied deformation embedding the functional materialsbetween planar electrodes has been evaluated. Since underthe undeformed condition the composite material shows aninsulating behaviour, and considering the simple design of adielectric embedded between two conductive electrodes, inprinciple this structure could be suitable both for capacitiveand resistive transduction principles.

Normally the capacitive transduction technique reacheslower output value with respect to the resistive one, sincecapacitive sensors measure the average pressure over theelectrode sensing area, while resistive sensors measure thepeak pressure over the sensing area. So the possibility tocouple the two different transduction techniques could bothstrengthen the pressure measurement and give complementaryinformation useful for the artificial sense of touch. Forexample, in this way it could be possible to extract informationon the morphology and the shape of the object that interactswith the sensitive surface of the device.

To design complex tactile sensing device able tosimultaneously couple capacitive and resistive transductionmechanisms, as well as to properly design the matching read-out electronic circuit, an exhaustive characterization of thefunctional material is mandatory.

Impedance spectroscopy (IS) is a well-establishedtechnique, widely used for the study of a great variety ofdevices and systems, with applications in different fields ofresearch [19–21]. A periodic voltage of variable frequencysuperimposed to a constant bias voltage is applied to the deviceunder study and its electric response is analysed as a functionof the excitation frequency. Even if the transport and charge-transfer processes occurring in real systems are described bynonlinear equations that connect the driving forces to the flux ofthe particles, in the case of excitation voltages with amplitudecomparable to the thermal voltage (i.e. under small signalcondition), it is possible to depict all the processes by linearequations in which the coefficient between the potential andthe current is the electric impedance [22]. With these premises,the device behaviour can be studied by means of an appropriateequivalent electrical circuit.

To the best of our knowledge, here for the first time, theelectrical conduction mechanism based on tunnelling effectinside the prepared composite samples has been analysed bymeans of IS.

The metal–polymer piezoresistive composite presentedin this work was prepared by carefully mixing coppermicroparticles, presenting spiky tips on the surface (LT10,Pometon), in a bi-component polydimethylsiloxane (PDMS)matrix (Sylgard 184, Dow Corning). The fabrication processof the piezoresistive material consisted in dispersing themetallic filler in the elastomer base, adding the PDMS curingagent, pouring the resulting paste in polymethylmethacrylatemoulds, prepared by the micro-milling technique, and thenoutgassing in vacuum in order to remove all the air bubbles inthe final samples. Later the composites were baked in ovenat 70 ◦C for 3 h to cure the polymer and then removed fromthe moulds. The prepared samples were bonded between twocopper metalized polyimide foils with soldered metallic wires,

Figure 1. FESEM image of the nanostructured copper–PDMScomposite. The scale bar corresponds to 10 µm.

acting as electrodes. The composition of the piezoresistivematerial was varied in order to evaluate the role of the metallicfiller content on the electrical response. The samples wereprepared with a quantity in weight of copper particles of 150,200, 250 and 300 phr (per hundred resin by weight) with anarea of 10 × 10 mm and thicknesses of 0.5 and 1 mm. Insteadthe weight ratio between PDMS base and curing agent was keptconstant at 10 : 1, because it represents the best compromisebetween stiffness and mobility of the particles inside thepolymeric matrix in response to compressive pressure [23].

Field emission scanning electron microscope (FESEM)analysis revealed that the particles result well dispersedin the polymeric matrix, without touching each otherand creating percolation paths (figure 1). Moreover, thegentle mixing process prevents the destruction and thesmoothing of the spiky tips on the copper particle surface,which would result in a reduction in the piezoresistiveresponse [14]. Indeed the conduction mechanism inside thecomposite material is the tunnelling conduction between closerparticles divided by a thin layer of insulating polymer thatconstitutes the barrier. Applying a mechanical pressure to thecomposite, the insulating barrier is reduced, thus increasing thetunnelling probability and exponentially decreasing the sampleresistance. This behaviour is enhanced by the presence of thenanostructured tips on the surface of the metallic particles thatwork as charge accumulator, increasing the local electric field.Variations up to seven orders of magnitude of the electricalresistance were reached in 1 mm thick composite applying acompressive pressure of 2 MPa with respect to the value in theundeformed state [18]. The piezoresistive behaviour of thecomposite can be modelled evaluating the resistance variationof a single barrier constituted by two copper particles dividedby a thin layer of PDMS and then enlarging the computation tothe whole material, considering the effect of all the tunnellingpaths. As evaluated by Zhang et al [13, 16], the electricalresistance Rp of a tunnelling composite sample under the effectof a uniaxial pressure p results in

Rp = R0

(1 − p

G

)exp

(−4π

√2mϕ

h2d0

p

G

)(1)

2

J. Phys. D: Appl. Phys. 47 (2014) 345306 S Stassi et al

Figure 2. Nyquist plot of the impedance spectra for the 300 phr(1 mm thick) sample measured at various applied pressure values.The points are experimental data, while the continuous lines arefitting curves evaluated with CPE. The dashed line represents thefitting of the 0 bar curve computed using an ideal capacitor insteadof CPE.

where R0 is the resistance of the sample in the undeformedstate, G is the composite compressive modulus, m is theelectron mass, h is Plank’s constant, and ϕ and d0 are theheight and the width (i.e. the distance between two adjacentmetal particles) of the potential barrier, respectively.

The impedance spectra were acquired by means of anelectrochemical workstation with an ac signal of 10 mV and abias voltage of 5 V, in the frequency range 10 Hz–100 kHz.Since in this kind of composite material only one charge-transfer process (namely the tunnelling effect) occurs, aunique impedance arc has to be expected in the Nyquist plot.In figure 2 an example of the results of IS measurementsperformed at different applied pressures is shown, in particularthe one related to the 1 mm thick sample fabricated with300 phr copper particles/PDMS weight ratio. A monotonicdecrease in the arc while increasing the external pressure can benoted, meaning a decrease in the tunnelling resistance, similarto what was observed by Loyola et al [24] for fibre-reinforcedpolymer nanocomposites. Based on the knowledge of thecharge-transfer process inside the material and on the resultingshape of the IS curves, the experimental data were fitted usingan equivalent circuit [25], where Rs stands for the series fillerresistance, and the interparticle gap is modelled through theparallel of the tunnelling resistance Rp and the constant phaseelement (CPE) Q. The constant phase element Q was usedin substitution to the capacitance C reported in [25]. Infact, the CPEs are generalization of common capacitancesused to take into account some frequency dispersion observedinto impedance spectra [26] due to the roughness of theparticle/polymer interface [27], whose impedance is given bythe formula

ZCPE = 1

Q(jω)β, (2)

where β is the CPE index. In the case of this piezoresistivecomposite the use of the CPE can be physically attributedmainly to the interface between the metal particles and thepolymer and to the geometry of the system. In fact sincethe metallic particles present spiky tips on their surface, asevidenced in figure 1, the basic unit of the material constituted

Figure 3. Tunnelling resistance and interparticle capacitancedependence on the applied pressure for the 300 phr (1 mm thick)sample. Rp and Q values were extracted from the fitting ofimpedance spectra. The Rp points were fitted using equation (1)(R2 value equal to 0.997). Q values were fitted with a linear trend(Q = A × p + B with A = 2.74 × 10−11 and B = −2.96 × 10−10,R2 value equal to 0.981).

by two particles separated by the insulating polymer is far awayfrom the case of an ideal capacitor. With respect to the caseof infinite flat conductive plates, here the two electrodes of thecapacitor follow the particle surface protrusions generating anon-uniform electric field. In the light of this heterogeneousnetwork of elementary capacitors with rough electrodes, theuse of CPE is preferable to ideal capacitor model. Withthe substitution of the capacitance with a CPE, the equationexploited for the fitting procedure was

Z = Rs +Rp

1 + RpQ(jω)β. (3)

The fitting results (also shown in figure 2 superimposedto the measured curves) were in good agreement with theexperimental data, thus proving that the tunnelling effect isthe main conduction mechanism involved in the compositematerial. In order to validate the use of a CPE instead ofan ideal capacitor for modelling the interparticle gap, theexperimental curves were fitted by fixing the CPE index to1 (in this case equation (2) will represent the impedanceof a common capacitance). As an example, in figure 2the fitting curve related to the spectrum acquired at 0 bar isreported. A large mismatch between the experimental and thecomputed data is clearly observable, evidencing the non-idealbehaviour of the metal/polymer interface. In fact, the use of apure capacitance makes the Nyquist plot a perfect semicircle,instead of the depressed arc that was found under real condition(and fitted through a CPE). In figure 3 the dependence of thetunnelling resistance and of the gap capacitance (evaluatedby the fitting process) on the applied pressure is shown. Ascan be clearly seen, the Rp exhibits an exponential decreasefor increasing pressure values, witnessing an enhancement ofthe tunnelling effect due to the reduction in the interparticlegap caused by the applied pressure. At the same time, thereduction in the gap is responsible for the linear increase inthe Q values, since capacitance is inversely proportional to the

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J. Phys. D: Appl. Phys. 47 (2014) 345306 S Stassi et al

Figure 4. Nyquist plot of the impedance spectra of samples fabricated with different compositions measured at 2 bar of applied pressure.The points are experimental data, while the continuous lines are fitting curves evaluated with CPE. In the inset a zoom of the area defined bythe dashed rectangle is reported.

distance between the metal particles. For all the experimentalcurves fitted, the CPE indexes β lie in the range 0.9–0.95,with no dependence on the applied pressure. In fact, thedeviation from the ideal capacitance behaviour (consequenceof the roughness of the metal/polymer interface) is an intrinsiccharacteristic of the material, thus it is not dependent on theapplied pressure. In order to further validate the proposedmodel, the resistance exponential curve was fitted by meansof equation (1). By inserting the values of G and ϕ obtainedfrom a mechanical characterization and from the literature [28],an average interparticle distance under no applied pressurecondition of around 15 nm was found, in agreement with theresults obtained in similar composite systems [13, 28]. Thedata shown in figure 3 represent an average of ten differentmeasurements. In the 1 bar range, more interesting in tactileapplications, the error on the reproducibility for the resistivemeasure is around 10–15% of the resistance value, while thecapacitive one ranges around 1–2%. These error ranges affectthe pressure evaluation with an uncertainty of around 0.25 barfor the resistive measurement and 0.1 bar for the capacitive one.Thus, even if the resistive measurement has a higher sensitivitywith respect to the capacitive one, because of the exponentialdependence due to the tunnelling conduction, the capacitivemeasurement guarantees a better pressure resolution. Forthese reason, the simultaneous evaluation of the capacitiveand resistive variation of the sample (measured through theimpendence spectroscopy method) and their combinationrepresent an advantage with respect to the classic resistivemeasurement method normally used for this composite family.

Similar results were also obtained by varying the materialcomposition and the device thickness. As an example, infigure 4 the Nyquist plots of the impedance of the devicesfabricated with different compositions measured at the sameapplied pressure are reported. As is clearly evident, amonotonic decrease in the impedance arc while increasing thefiller loading can be observed: as in the case of the variationwith the applied pressure (see figure 2), this fact witnesses adecrease in the tunnelling resistance. In figure 5 a comparisonof Rp and Q values obtained for the different devices at the

Figure 5. Tunnelling resistance and interparticle capacitancedependence on the composition for 2 bar of applied pressure. Rp andQ values were extracted from the fitting of impedance spectra.Rp and Q points were fitted with an exponential(Rp = A × exp(−comp/t) + B with A = 6.12 × 1010, t = 19.55 andB = 1.89 × 105, R2 value equal to 0.999) and a linear trend(Q = C × comp + D with C = 1.77 × 10−12 andD = −1.5 × 10−10, R2 value equal to 0.975), respectively.

same applied pressure (2 bar) is reported. It can be seen thatthe sample containing the lower concentration of particlesis characterized by the higher tunnelling resistance and thelower capacitance. While increasing the filler concentration,the mean distance between two filler particles experiencesa reduction that causes the already observed exponentialdecrease in the tunnelling resistance and the linear increasein the gap capacitance. Also in this case, no dependence of β

on the composition was observed.In summary, piezoresistive composite materials were

prepared by dispersing nanostructured copper particles in apolydimethylsiloxane matrix, thus fabricating active devicesin which the electrical conduction mechanism is driven bythe quantum tunnelling effect. By applying an externalmechanical pressure, the interparticle insulating layer reducesits thickness, thus enhancing the tunnelling probability.This conduction mechanism was studied exploiting the IS

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J. Phys. D: Appl. Phys. 47 (2014) 345306 S Stassi et al

technique, analysing the measured data through an equivalentelectrical circuit. This investigation revealed an exponentialdecrease in the tunnelling resistance and a correspondinglinear increase in the interparticle capacitance for increasingapplied pressure values, thus confirming that the tunnellingeffect is the main conduction mechanism involved in theproposed composite material. The obtained results werefurther confirmed by fitting the extrapolated values with a well-known mathematical model, thus validating the importanceof the impedance spectroscopy technique for the study ofpiezoresistive composites. Moreover, this technique can bedirectly implemented for the pressure monitoring in a tactilesensor fabricated with the composite material. Indeed, thepossibility of employing electrical impedance measurementto image the resistance distribution of a layer of conductivefabric due to applied pressure [29] for robotic application hasrecently been demonstrated. The application of this powerfultransduction tool to a continuous sheet of piezoresistivecomposite would enhance the pressure spatial resolutionwithout increasing the number of electrodes, if compared withthe traditional matrix sensor designs affected by wire topologyproblems, and would also increase the pressure resolution bycombining the measurement of both the induced resistance andcapacitance variations.

Acknowledgments

The authors acknowledge the help of Dr Diego Manfredifor FESEM characterization and Dr Valentina Cauda for thefruitful discussion.

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