Materials Letters 62 (2008) 4173–4174

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Materials Letters

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Dielectric response of piezoelectric ceramics at low voltage excitations

Sunil Sudhakaran a, Kok Boon Chong a, David Barrat b, Asim K. Ray a,⁎a School of Engineering and Materials Science, Queen Mary, University of London, London E1 4NS, United Kingdomb Blackburn MicroTech Solutions, LP Displays, Philips Road, Blackburn BB1 5RZ, LP Displays, United Kingdom

⁎ Corresponding author. Tel.: +44 207882 7767.E-mail address: a.k.ray@qmul.ac.uk (A.K. Ray).

0167-577X/$ – see front matter © 2008 Elsevier B.V. Aldoi:10.1016/j.matlet.2008.06.030

A B S T R A C T

A R T I C L E I N F O

Article history:

An improved model is pro Received 25 April 2008Accepted 12 June 2008Available online 15 June 2008

Keywords:Piezoelectric materialsFerroelectricsCeramicsElectrical properties

posed for the interpretation of the dielectric response of a piezoelectric leadzirconate titanate (PZT) ceramic at low voltage excitations appropriate for microdevices by consideringmultiple relaxation processes. The model parameters are optimised in order to achieve a satisfactoryagreement between the predicted values and experimental data obtained from room temperaturemeasurements on a commercially available PZT-805 ceramic sample.

© 2008 Elsevier B.V. All rights reserved.

1. Introduction

Piezoelectricmaterials such as lead zirconate titanate (PbZrxTi1−xO3)ceramics have been extensively used in the fabrication of actuators forpotential applications in aerospace, automotive, civil engineering andconsumer electronics includingmicrophones, telephone receivers andhigh-density hard disk drive [1–4]. The study of the dielectricbehaviour of piezoelectric materials becomes important for optimis-ing the device characteristics. A PZT stack was excited by threedifferent values of 20, 50, and 100 Vrms for the peak-to-peak voltage atfrequencies up to 5 kHz and an RC equivalent circuit model wasproposed to provide the physical interpretation for experimentalbehaviour [5]. PZT-based devices are having interesting features suchas high frequency bandwidth, fast response, and high sensitivity.Miniaturization of PZT-based devices will not only perfect manyexisting products, but also open vast new applications. The polarisa-bility of the PZT material was found to have arisen from dipolarpolarization polarisation which can be described by a normal Debyemodel. For the frequency range investigated, the degree of polariza-tion polarisationwas strongly dependent upon the excitation voltages.Some applications such as microsurgical devices and microrobotsemploying bulk PZTs work under the excitation voltage as low as1 Vrms. PZT-based microactuators can lead to compact ultrasonicsurgical tools for infected cell removal and cardiovascular depositionand it is anticipated that these appliances will require excitation at

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low voltages. The contributions to the electrical displacement fromboth the electric field and polarization polarisation become equallysignificant under this low voltage operation. In this letter, thedielectric behaviour at low voltage excitation was reported basedupon the experiments carried out on commercially available MorganCeramics PZT805 (belongs to the PZT8 class) discs.

2. Experimental methods

The Morgan Ceramics PZT805 samples were 1 mm thick and20 mm in diameter and were known to resonate at 117 kHz. UsingSolartron Impedance Gain analyser S1260, impedance and capaci-tance measurements were performed at the excitation voltage of1 Vrms as a function of frequency around the resonant frequency atroom temperature of 21 °C for a parallel circuit connection. The dc biasvoltage was kept zero in order to keep the intrinsic polarisation thesame throughout the experiment. For the interpretation of the results,an equivalent circuit was proposed and the performance of the circuitwas simulated using Agilent Advanced Design System.

3. Results and discussions

The results of the impedance measurements are given in Fig. 1 as a Cole–Cole plot.Appearance of non-circular patterns due to the merger of two circular regions withdifferent radii were was found to exist indicating that the multiple dipole contributionsto the dielectric behaviour become prevalent for the present PZT sample. Fig. 2 presentsan equivalent circuit for consisting of a series inductance, capacitor and resistor (LCR)resonating circuit in parallel with a capacitor. Lumped elements Rm, Lm and Cm weretaken to be the electrical analogue components describing the mechanical properties ofthe PZT material. The impedances Z1 and ZC represents the imaginary part (dielectricloss) and real part of permittivity, respectively. Values for the sample PZT805 understudy were Rm=1.61 Ω, Lm=2.39 mH and Cm=0.924 nF. Values of Zc and Z1 were

Fig. 3. Comparison of analytical and experimental results for the normalized normalisedcurrent in a PZT actuator. A. Experiment and B. Simulation.

Fig. 1. Cole–Cole plot obtained from the impedance spectroscopic measurement on PZT-8sample.

4174 S. Sudhakaran et al. / Materials Letters 62 (2008) 4173–4174

optimised to give the best fit to experimental data using the Debye dispersion relationof the complex dielectric constant ɛ ωð Þ ¼ ɛ1 ωð Þ þ jɛ2 ωð Þ in the forms:

ɛV¼ ɛ∞ þ ɛs−ɛ∞βτ1 þ 1−βð Þτ2

βτ11þ ωτ1ð Þ2

þ 1−βð Þτ21þ ωτ2ð Þ2

!ð1Þ

ɛW ¼ ɛs−ɛ∞βτ1 þ 1−βð Þτ2

βτ211þ ωτ1ð Þ2

þ 1−βð Þτ221þ ωτ2ð Þ2

!ð2Þ

where ε∝ and εs are the permittivity at the high frequency and the static, low frequencylimits, respectively. The equations include polarisations with two diploes having τ1 andτ2 as their individual relaxation frequencies [6]. The factor β determines the relativecontributions from two polarisations. Values of permittivity were calculated fordifferent combinations of relaxation times τ1, τ2 and β over the frequency range 80 kHzto 230 kHz andwere then used in the circuit model in order to obtain the circuit current.A comparison of the circuit currents normalised with maximum currents obtained fromsimulation and experiment is shown in Fig. 3.

The values of the parameters ε∞ and εs were estimated to be 2000 and 100.Optimum values of 1.2 µs and 1 µs were obtained for the two dipole relaxation times.The optimum value of β=0.99 indicates that the dominating polarisation of 99% isintrinsic with a 1% contribution of extrinsic polarisation arising from defects such asoxygen vacancies and inhomogeneous composition. The variation of β by 0.01 showed alarge deviation from the experimental results. This indicated that a 1% variation inpolarisation distribution, the deviation in relative permittivity is very high. Theresonating frequency obtained from the simulationwas found to be 107 kHz and differsfrom the experimental value of 117 kHz by 6%. This difference lies in the acceptablerange considering the high dielectric constant and the lumped element approximation.

Dielectric properties of two different variants of commercial PZT were studied overa frequency range of 1–1000 kHz and non-Debye dielectric behaviour was observed [7].A simple equivalent circuit consisting of bulk resistance and bulk capacitance in parallelwas proposed to account for relaxation mechanisms. Soft PZT-5 samples exhibitedincrease in impedance due to the microcracks caused by the repeated cycling at 50 Hz

Fig. 2. A schematic diagram of the electrical equivalent circuit of the PZT actuator.

with a peak field of 15 kV/cmwhereas similar stress at 20 kV/cm decreased impedanceof hard samples (PZT-4) due to trapping of oxygen vacancies in the domainwalls. In ourpresent case, more complex circuits become necessary for explaining PZT805 dielectricbehaviour at excitation field as low as 1 V/cm.

4. Conclusions

In this letter, an equivalent LCR resonant equivalent circuit issuccessfully developed using the dielectric properties of the PZTsample. The effect of intrinsic and extrinsic polarisations is employedfor interpretation of experimental data on dielectric behaviour of thePZT-8 sample when excited at low voltages of 1 Vrms. The simulationand experimental results were found to be in good agreement.

Acknowledgments

Authors acknowledge Technology Strategy Board, UK for thefinancial support and Agilent, Europe for providing the ADS license.

References

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