Critical behaviour of the piezoresistive response in RuO<sub>2</sub>–glass composites

Grimaldi, Claudio; Maeder, Thomas; Ryser, Peter; Strässler, S.

doi:10.1088/0022-3727/36/11/315

Cited by 16 publications

(13 citation statements)

References 34 publications

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“…In fact an effective medium calculation with the tunneling-percolation distribution function h͑r͒ ϰ r −1− /2a leads to ⌫ 0 Ͼ 0 when t = t 0 and ⌫ 0 Ͻ 0 when t Ͼ t 0 , 18 in agreement with the experimental results (see Table I). …”

supporting

confidence: 87%

Strain modulation of transport criticality in RuO2-based thick-film resistors

Vionnet-Menot

Grimaldi

Ryser

et al. 2004

Applied Physics Letters

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We show that in RuO 2 -glass composites the nonuniversal resistivity exponent can be modulated by an applied mechanical strain, signaled by a logarithmic divergence of the piezoresistive response at the percolation threshold. We interpret this phenomenon as being due to a tunneling-distance dependence of the transport exponent, supporting therefore a theory of transport nonuniversality proposed some years ago. The study of transport properties of thick-film resistors (TFRs) is of crucial interest for the improvement of sensor devices based on thick-film technology. 1 In particular, the understanding of the interplay between microscopic properties, dc transport, and the piezoresistive response have important implications in the fabrication of robust force and pressure sensor devices.The most common thick-film piezoresistors are composed by submicron conducting RuO 2 grains (or also Pb 2 Ru 2 O 6 and Bi 2 Ru 2 O 7 ) dispersed in an insulating host usually given by a lead-borosilicate glass. 2 The transport properties of TFRs are governed by two main ingredients. On the microscopic level, electron transport is via quantum tunneling through nanometer-thick films of glass separating two neighboring conducting particles, 3-5 while on macroscopic scale transport displays percolation-like behavior, 6,7 with resistivity following a power-law of the form:where 0 is a material-dependent prefactor, x c is the percolation critical volume fraction below which goes to infinity, and t is the dc transport critical exponent. According to the standard theory of transport percolation, 8,9 the microscopic properties, such as the intergrain tunneling in TFRs, do affect the values of 0 and x c , but should leave the critical exponent t unaltered and equal to the universal value t 0 Ӎ 2.0 valid for three-dimensional disordered composites. 10 In contrast to this view, the critical exponent of TFRs has been often found to be larger than t 0 , 7,11 up to about t Ӎ 7.0. 6 Despite the fact that such universality breakdown has been repeatedly reported for decades, and that it has been observed also for systems different from TFRs, 9 a common view regarding its origin is still lacking. 12 We show in this letter that breakdown of universality ͑t Ͼ t 0 ͒ in RuO 2 -based TFRs is accompanied by a logarithmic divergence of the piezoresistive response at the percolation threshold x c , providing evidence that the transport critical exponent t depends upon the mean intergrain tunneling distance, as proposed a few years ago in Ref. 13.Our samples were prepared starting with a leadborosilicate glass powder ͓PbO͑75 wt % ͒-B 2 O 3 ͑10 wt % ͒-SiO 2 ͑15 wt % wt͔͒ +2% of Al 2 O 3 of 1-5 µm grain sizes. Differential scanning calorimetry measurements indicated a glass softening temperature of about 430°C and absence of crystallization. TFRs were then fabricated by mixing two series of RuO 2 powders with 40 and 400 nm grain sizes with the glass particles together with a vehicle of terpineol and ethyl cellulose. The pastes were screen printed on Al 2 O 3 subst...

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supporting

confidence: 87%

Strain modulation of transport criticality in RuO2-based thick-film resistors

Vionnet-Menot

Grimaldi

Ryser

et al. 2004

Applied Physics Letters

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“…Calculations of the piezoresistive response based on the Balberg model confirm this feature. 17 It is worth to point out that in addition to the importance of our results concerning the origin of transport non-universality in tunnelling-percolation materials, the reported logarithmic divergence of Γ has also consequences for applications of Ru-based TFRs in force and pressure sensors. In fact, the efficiency of piezoresistive sensors is measured by the magnitude of Γ.…”

Section: Resultsmentioning

confidence: 70%

“…Similar conclusions can be drawn when we analyse previously published data 18 by using Eq.(4). 17 We can conclude therefore that when the transport exponents are non-universal, they can be modified by an applied strain. Our findings support a tunnelling-percolation theory of universality breakdown proposed some time ago by Balberg.…”

Section: Resultsmentioning

confidence: 82%

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Study of electrical properties of piezoresistive pastes and determination of the electrical transport

Vionnet-Menot

Grimaldi

Maeder

et al. 2005

Journal of the European Ceramic Society

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Abstract. Thick-film resistors (TFRs) consist of a percolating network of conducting oxide nanoparticles dispersed in an insulating glassy matrix, whose resistive properties are dominated by quantum tunneling across insulating layers separating adjacent conducting grains. Tunneling processes are at the origin of the high sensitivity of the TFRs resistances to applied strains. In this work, we aim to define the electrical transport law between metallic nanoparticles in piezoresistive pastes. We have measured transport and piezoresistive response for different RuO 2 -based TFRs as a function of metallic concentration x and RuO 2 grain sizes. The study reveals that the conductivity is shown to vanish as x approaches a critical concentration x c by following a power law with nonuniversal critical exponents, while the piezoresistivity diverges at the same critical concentration. We argue that nonuniversality and diverging piezoresistivity have the same origin and arise from the highly fluctuation inter-grain tunneling distances determined by the segregated microstructure of TFRs.

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“…In a previous publication, 70 we have reanalyzed the piezoresitive data reported in Ref. 37 by assuming a logarithmic divergence of ⌫ rather than the 1 / ͑x − x c ͒ behavior of Eq.…”

Section: Methodsmentioning

confidence: 99%

Tunneling-percolation origin of nonuniversality: Theory and experiments

et al. 2005

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A vast class of disordered conducting-insulating compounds close to the percolation threshold is characterized by nonuniversal values of transport critical exponent t, in disagreement with the standard theory of percolation which predicts t Ӎ 2.0 for all three-dimensional systems. Various models have been proposed in order to explain the origin of such universality breakdown. Among them, the tunneling-percolation model calls into play tunneling processes between conducting particles which, under some general circumstances, could lead to transport exponents dependent of the mean tunneling distance a. The validity of such theory could be tested by changing the parameter a by means of an applied mechanical strain. We have applied this idea to universal and nonuniversal RuO 2 -glass composites. We show that when t Ͼ 2 the measured piezoresistive response ⌫, i.e., the relative change of resistivity under applied strain, diverges logarithmically at the percolation threshold, while for t Ӎ 2, ⌫ does not show an appreciable dependence upon the RuO 2 volume fraction. These results are consistent with a mean tunneling dependence of the nonuniversal transport exponent as predicted by the tunneling-percolation model. The experimental results are compared with analytical and numerical calculations on a random-resistor network model of tunneling percolation.

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Critical behaviour of the piezoresistive response in RuO₂–glass composites

Cited by 16 publications

References 34 publications

Strain modulation of transport criticality in RuO2-based thick-film resistors

Strain modulation of transport criticality in RuO2-based thick-film resistors

Study of electrical properties of piezoresistive pastes and determination of the electrical transport

Tunneling-percolation origin of nonuniversality: Theory and experiments

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Critical behaviour of the piezoresistive response in RuO2–glass composites

Cited by 16 publications

References 34 publications

Strain modulation of transport criticality in RuO2-based thick-film resistors

Strain modulation of transport criticality in RuO2-based thick-film resistors

Study of electrical properties of piezoresistive pastes and determination of the electrical transport

Tunneling-percolation origin of nonuniversality: Theory and experiments

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Critical behaviour of the piezoresistive response in RuO₂–glass composites