ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 50, no. 2, february 2003 113

Letters

Measurement of Longitudinal PiezoelectricCoefficient of Thin Films by aLaser-Scanning Vibrometer

Kui Yao and Francis Eng Hock Tay

Abstract—A laser scanning vibrometer (LSV) was usedfor the first time to measure the piezoelectric coefficient offerroelectric thin films based on the converse piezoelectriceffect. The significant advantages of the use of the LSV forthis purpose were demonstrated. Several key points werediscussed in order to achieve reliable and accurate results.

I. Introduction

The piezoelectric effects in thin films are being inten-sively explored for their promising applications as sen-

sors and actuators in a variety of micro and nano systems.An efficient characterization technology for the piezoelec-tric properties of the thin films, particularly the piezoelec-tric coefficients, is becoming more and more essential forboth fundamental research and applications [1]. However,the variation among the reported data in the literaturefor piezoelectric films is significantly large [1]–[10]. Thereason is that no widely accepted standard measurementtechnique has been popularly used for thin films. Some ofthe measurement methods are not accurate.

The piezoelectric properties of thin films were mainlyevaluated by either measuring the induced charge underexternal mechanical stress through the direct piezoelectriceffect, or measuring the displacement in response to theapplied electric field due to the converse piezoelectric ef-fect. For the methods using the direct piezoelectric effect[6], [7], it is very difficult to produce a homogeneous uni-axial stress on the thin film without simultaneously gener-ating any bending effect, which results in a large amountof charge through the transverse piezoelectric effect. Thismeasurement has been improved by applying pneumaticpressure as the mechanical stimulus [8]. However, excesscharge induced by the clamping of the sample in the exper-imental set-up still causes additional errors. For the meth-ods using the converse piezoelectric effect, the challengeis to precisely measure the dilatation of the thin films,which can be as small as sub-Angstrom. Sensitive laser in-terferometric method is the most important way becauseof its high resolution and nondestructive advantages [9]–[12]. It is noted that conventional single-beam laser inter-ferometer has difficulty in separating the bending and/ormovement of the substrate from the dilatation of the thin

Manuscript received July 7, 2002; accepted October 24, 2002.The authors are with the Institute of Materials Research and

Engineering, 3 Research Link, Singapore 117602 (e-mail: k-yao@imre.a-star.edu.sg).

films. Therefore, the double-beam, interferometer systemhas been used to simultaneously detect the displacementin both the front and back sides of the thin film samples inorder to eliminate the influence of the substrate movement[10]. However, it is believed that the measurement resultsof the double-beam systems are influenced by the opticalalignment, particularly for the miniaturized samples. Thismethod also may not be applicable in characterizing piezo-electric film when the backside of the film is not accessible,such as the suspended piezoelectric micro electromechani-cal systems (MEMS) structures produced by surface micromachining.

All the above-stated methods using the laser interfer-ometer are based on the displacement measurement onlyat one single point, either along one or two directions. Wethink that the displacement detection at only one point isnot adequate to efficiently evaluate the piezoelectric prop-erties of thin films. To improve the measurement reliabil-ity and accuracy, we monitored the vibration of the wholesurface of the piezoelectric thin films with a laser scanningvibrometer (LSV). The significant advantages of this newcharacterization method with LSV for piezoelectric thinfilms are discussed in this letter.

II. Experimental Procedure

The Pb(Zr0.52Ti0.48)O3 (PZT) thin films under inves-tigation were fabricated through a sol-gel processing onPt/Ti/SiO2/Si substrates by annealing at 700◦C. Thethickness of the films was 1.5 µm. Circular gold top elec-trodes of 200 µm in diameter were deposited on the PZTfilms by sputtering. The PZT films, sandwiched betweenthe Au and Pt electrodes, were poled at 150 kV/cm atroom temperature. The samples were clamped with a fix-ture, which was attached to a transition stage on an opticaltable. The samples could be precisely positioned in threedirections by adjusting three micrometers in the transi-tion stage. The alternating current (AC) driving electricalfield was applied to the piezoelectric films to stimulate thevibration.

The major parts of our LSV system included a laserscanning head (OFV-056), a scanning vibrometer con-troller (OFV-3001-SF6), a communication junction box,which were manufactured by PolyTech GmbH, Berlin, Ger-many, and a host computer. The system was a modifiedMach-Zehnder interferometer, and the vibration velocityand displacement were measured based on the Dopplershift. The out-of-plane vibration signals of the piezoelec-tric films were detected with a photo detector in the laser-scanning head for each point in a specifically defined scan-ning grid. The collected signals then were transmitted tothe computer through the vibrometer controller. In our

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114 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 50, no. 2, february 2003

Fig. 1. The three-dimensional drawing of the instantaneous vibrationdata when the displacement of the PZT film reaches the maximummagnitude.

experiment, the defined grid area for the scanning coveredboth the top electrodes and the surrounding PZT filmsso that the movement of the substrates could be observedsimultaneously. The recorded vibration signals in time do-main were processed in the computer through fast Fouriertransformation (FFT) to generate the corresponding fre-quency spectra. The collected vibration information in-cluded both vibration magnitude and phase for each pointwithin the scanning area; and, therefore, the vibration an-imation could be acquired in the computer.

III. Results

The three-dimensional vibration animation of the piezo-electric films could be displayed on the computer screen.Fig. 1 presents a three-dimensional drawing of the instan-taneous vibration data when the displacement magnitudeof the PZT film reaches the maximum. Fig. 1 does not re-flect the surface roughness of the sample because it is nota drawing of surface morphology. The central area mov-ing upward in Fig. 1 is the Au-electrode covered area; thesurrounding area moving downward below the zero pointis the PZT film without the top-electrode cover (the sub-strate). It was found that the vibration of the PZT filmsand the substrates were always antiphased for our sam-ples. Therefore, the dilatation magnitude of the films wasequivalent to the numerical addition of the displacementof the PZT films and the substrates.

The measured displacement data as presented in Fig. 1and the corresponding calculated longitudinal piezoelectric

coefficients are summarized in Table I. The data of the de-tected displacement at the surface of the film δfilm andthe substrate δsub are the average values. The dilatationmagnitude of the film δ is the numerical sum of δfilm andδsub. The different d33 values in Table I are calculated withthree methods. d33F is calculated based on the assumptionof no in-plane constraint in the electrode-covered film; d33C

is calculated based on the assumption of the opposite ex-treme condition, i.e., in-plane strain is zero due to the ex-tremely strong lateral constraint [6]; d33S is the result froma numerical simulation by finite element method (FEM)with a commercial finite element program ABAQUS (Hi-bbitt, Karlsson, Sorensen, Inc., Pawtucket, RI), in whichthe elasticity of the PZT, electrode, and substrate is takeninto account. The assumption of no in-plane constraint orzero in-plane strain is useful to determine the minimum ormaximum value of d33 as possible. The numerical simula-tion, based on the elasticity of the multilayer structure, isclosest to reality. Therefore, the d33 value calculated fromthe numerical simulation is most realistic.

IV. Discussion

Unlike the single-point displacement detection method,the vibration modal shape of piezoelectric thin films canbe acquired with the LSV. By examining the vibrationmodal shape, those samples with distorted or unexpectedmodality can be excluded from the measurement becausethe data for such samples are unreliable for determiningthe piezoelectric coefficient. Different distorted vibrationmodalities were observed with some thin film samples inour experiments. These distortions may be caused by somehidden defects, such as delamination or uneven stress. Notethat the single-point measurement does not have the capa-bility of identifying the distortion of the vibration modal-ity. Even if the single-point measurement can be repeatedat different points in spite of intensive time and labor con-sumption, the modality cannot yet be acquired becauseof the lack of the phase relationship among the differentpoints. Therefore, by monitoring the vibration modality,the use of LSV greatly improves the reliability and consis-tency of the measurement for piezoelectric thin films.

Our experiments revealed that the displacement valueswere not completely uniform over the whole area, even forthe piezoelectric thin-film samples that exhibited a goodmodality, as shown in Fig. 1. We believe that the unevendistribution of the displacement can be attributed to theresidual stress and boundary effect. It is feasible to estab-lish the relationship between the measured displacementdistribution and the residual stress in order to improvethe characterization accuracy further. However, it is toodifficult to characterize and investigate such phenomenawithout the use of the LSV.

It has been explained in the literature that the measure-ment of the piezoelectric thin films may be highly unreli-able and may even result in incorrect data without moni-toring the movement of the substrate simultaneously [10].

yao and tay: measurement of longitudinal piezoelectric coefficient of thin films 115

TABLE IMeasured Vibration Magnitude Data and the Longitudinal Piezoelectric Constant of the PZT Thin Film Calculated with

Different Methods (V = 5V, and f = 1.5 kHz).

δfilm δsub δ = δfilm − δsub d33F =δ

Vd33C =

δ

V+

2d31SE13

SE11 + SE

12d33S

(by FEM)(pm) (pm) (pm) (pC/N) (pC/N) (pC/N)

588 −96 684 137 297 189

Because the LSV detects both vibration magnitude andphase for the films and the substrates simultaneously, theerror caused by the bending or moving of the substratecan be corrected. As presented in this paper, the electricfield induced dilatation in the films was determined withthe vibration data of both the piezoelectric films δfilm andthe substrates δsub.

It should be pointed out that we have assumed the de-formation of the substrate outside the electrode region tobe the same with that below the top electrode. Such as-sumption does not cause large error in our present mea-surement. The movement of the substrate may be at-tributed to the deformation in the back face of the sampleand the substrate bending. The localized deformation thatoccurs in the back face of the region below the top elec-trode could be substantially different from that outside theelectroded region. According to our quantitative analysis,such deformation, which is proportional to the mass of thethin film and the frequency squared, is several magnitudeorders smaller than the dilatation in the thin film when thevibration is below 1 MHz, due to the small mass of the thinfilm. This is consistent with the previously reported result[10]. Therefore, the movement of the substrate originatesmainly from the substrate bending caused by the piezo-electric film. The substrate bending is continuous over alarge area of the substrate, as described in [10], and thereis no substantial sharp transition at the region below thetop electrode. The very small variation of the detected dis-placement over the area outside the top electrode for thepresent measurement, as shown in Fig. 1, indicates thatthe bending curvature is minor. Thus, the difference be-tween the movement of the substrate below the electrodedregion and outside the electroded region also is very small.The estimated error in the dilatation calculation due tothe difference of the substrate movement in the electrodedregion is smaller than 2% based on the very minor bend-ing curvature according to the data in Fig. 1. However, if alarge bending is detected with the LSV, the magnitude ofthe movement of the substrate below the electrode regionmay need to be calculated based on the detected bendingcurvature to rectify the error.

V. Conclusions

For the first time, LSV was used to determine the lon-gitudinal piezoelectric coefficient of thin films based onthe converse piezoelectric effect. The results demonstrated

several significant advantages of the use of LSV for piezo-electric coefficient measurement, including high reliability,high efficiency, and comprehensive information. To achievereliable and accurate results, the following three guidelinesshould be followed: the scanning range should include thearea without the cover of the top electrode; only data froma good vibration modality are reliable for calculating thepiezoelectric coefficient; and the movement of the substratemust be taken into account in order to precisely determinethe dilatation magnitude of the films. Our measured lon-gitudinal piezoelectric coefficient of the PZT(52/48) thinfilms is 137 pC/N without considering the in-plane con-straint, and 189 pC/N when the elasticity of the multilayerstructure is considered.

Acknowledgments

The authors acknowledge Ms. Yu Shuhui for her exper-imental preparation of the PZT samples, and Mr. Loh WeiMin for his efforts in numerical simulation.

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