Measurement of thin film piezoelectric constants using x-ray diffraction technique

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Phys. Scr.T129 (2007) 353–357 doi:10.1088/0031-8949/2007/T129/078

Measurement of thin film piezoelectricconstants using x-ray diffractiontechniqueY H Yu, M O Lai and L Lu

Department of Mechanical Engineering, National University of Singapore, Singapore 117576

E-mail: yh1.yu@hotmail.com

Received 27 February 2007Accepted for publication 21 July 2007Published 30 November 2007Online atstacks.iop.org/PhysScr/T129/353

AbstractA new method to measure the piezoelectric constants ofd f

33 andd f31 of thin films using x-ray

diffraction (XRD) is proposed. Piezoelectric constantd f33 is calculated from the measurement

of change in out-of-plane lattice spacing of the piezoelectric films while piezoelectric constantd f

31 is obtained from the change in the slope ofdφψ versus sin2ψ curves before and afterapplying an electric field over the film. This method improves the accuracy by directlymeasuring the strains in the films induced by the externally applied electric field instead of thesurface displacement that could easily be interfered with by environment/vibration andsurface morphology of the thin films.

PACS numbers: 79.20.Ds, 77.84.Dy, 77.84.−s, 78.70.Ck

(Some figures in this article are in colour only in the electronic version.)

1. Introduction

Piezoelectric ceramics have been widely used in sensors,actuators and other devices [1, 2]. Due to the developmentof miniatures in MEMS and NEMS technologies, the highperformance of piezoelectric thin films has recently beenintensively studied [1–5].

Since all piezoelectric thin films are grown on muchthicker substrates, deformations on piezoelectric thin filmsare several orders of magnitude smaller than those oftheir counterpart bulk materials. Therefore, measurementtechniques for physical characters of bulk piezoelectricceramics may not be adequate for thin films. For bulkpiezoelectric ceramics, the most commonly used methodsare based on the principle of dynamic characteristics suchas resonance and anti-resonance, and static methods. Thesetechniques are difficult to implement in thin films owing tosubstrate constraint and extremely small deformation in filmswhich may not be detected using the conventional techniques.Therefore, it is necessary to develop new techniques tomeasure these physical properties of thin films.

After the first report on the measurement of piezoelectricconstants of thin films in 1990 [6], a great deal of research has

been carried out in the field of characterization of piezoelectricfilms. Generally, the measurement techniques can be dividedinto two categories. One is to use the direct piezoelectric effectwhere the electric charge is collected as an external force isapplied. Another approach adopts the converse piezoelectriceffect where mechanical response is measured as an externalelectric field is applied. The former includes normal loadingmethod [7], pneumatic loading method (PLM) [8, 9], waferflexure [10], embedded beam method [11] and acoustoelectricprobe [12]. The latter includes atomic force microscopy(AFM)/scanning tunnelling microscopy (STM) [13] andinterferometer method [14, 15]. The normal loading methodcan only measured33. However, roughness of its contacttip affects the homogeneity of the applied stress; and it canproduce a significant bending effect which would generate agreat amount of charge through the transverse piezoelectriceffect [16]. Although the PLM overcomes the difficulties inloading non-uniformity, bending effect and loading direction,the friction between the O-ring and the sample surface couldintroduce remnant in-plane stress to the film and thus result inmeasurement error [8].

The wafer flexure method can only measured31. It makesuse of the charge generated when a uniform pressure acts

0031-8949/07/129353+05$30.00 © 2007 The Royal Swedish Academy of Sciences Printed in the UK 353

Y H Yu et al

X3

g(hkl)

Bottom electrode

Functiongenerator

PZT

Gold

Substrate

ψ

φ

X1

X2

Gold

Figure 1. Schematic set-up for piezoelectric constant measurement.

on a wafer surface [10]. The drawback is reliance on themathematical models which require explicit knowledge ofdimensions of the substrate, supporting house, locations ofthe test capacitors, Young’s modulus and Poisson’s ratioof the substrate and piezoelectric film.

In general, the AFM/STM technique detects localvibration induced by an ac signal applied between theconductive tip of the scanning force microscope and thebottom electrode of the sample. Since the radius of the tipapex is in the range of tens of nanometres, the measuredpiezoelectric response is grain dependent. For some grains,the contribution fromd15 may be significant and the measuredresponse from out-of-plane of a piezoelectric thin film couldbe substantially different from the effective value along thepoling direction [15].

The laser interferometer [14, 15] has been used tomeasure the dynamic displacement at the surface of thin films.A single beam laser interferometer has difficulty in separatingthe bending and the movement of the substrate from thethickness change of a piezoelectric film induced by anelectrical field [14]. Therefore, double-beam interferometershave been employed to suppress the bending and themovement of the substrate. Since the thickness change isas small as sub-ångstrom, the measurement is very sensitiveto noise such as thermal drift of the sample, fluctuationin refractivity of air in the optical path, and electricaland mechanical instabilities. Thus such a technique usuallyrequires a very stable environment [15].

In this study, a new method using an x-ray diffraction(XRD) technique is proposed to measure bothd33 andd31 ofa piezoelectric film. Because it directly measures the strainsinduced by an electric field, environmental instability onsurface displacement can be avoided.

2. Principle of measurement technique

Strains in a piezoelectric film induced by electric field can bemeasured by XRD. The experimental set-up is schematicallyshown in figure1. A function generator is connected to the topand bottom electrodes of the piezoelectric thin film capacitor.An x-ray diffractometer is used to measure the 15 changeswithin the piezoelectric thin film induced by the appliedelectric field.

2.1. Strain measurement using XRD

For randomly oriented polycrystalline or isotropic materials,a general equation for measuring strain field using the XRDtechnique can be described by equation (1) [17].

(S′

33)φψ = S33 + (S11 cos2 φ + S12 sin 2φ

+ S22 sin2 φ− S33) sin2ψ

+ (S23 sinφ + S13 cosφ) sin 2ψ, (1)

whereψ is the angle between the diffraction vectorg(hkl)and the specimen surface normal,φ is the angle between themeasurement direction and the coordination axisX1, (S′

33)φψis the strain in the direction defined by Euler anglesφ andψ , S11, S12, S22, S33, S23 and S13 are the components ofstrain tensor,dφ,ψ is the measured lattice plane spacing of thediffraction plane (hkl), andd0 is the unstrained lattice planespacing of the diffraction plane (hkl).

For thin films with equi-biaxial stress state whereS12 =

S13 = S23 = 0, andS11 = S22, equation (1) can be simplifiedto be:

(S′

33)φψ = (dφψ − d0)/d0 = S33 + (S11 − S33) sin2ψ. (2)

2.2. Measurement of strain induced by electricity

There generally exists an equi-biaxial residual stress/strainfield in piezoelectric films [18]. XRD measures the total strainin the films and that includes the residual strains and theelectricity induced strains. Therefore, equation (2) should berewritten to include electric field induced strains:

dEiφψ = (SEi

11 − SEi33)d0 sin2ψ + SEi

33d0 + d0, (2a)

where the superscript ‘Ei ’ denotes the electric field along thei-axis in the film (i = 1,2 and 3).SEi

11 andSEi33are in-plane and

out-of-plane strains of the piezoelectric films.Whenψ = 0, equation (2a) becomes

dEiφ,0 = SEi

33d0 + d0 = I Ei (3)

orSEi

33 = I Ei /d0 − 1. (3a)

Taking the differential of equation (2a) with respect to sin2ψ ,it follows that

∂

∂(sin2ψ)dEiφ,ψ = (SEi

11 − SEi33)d0 = GEi . (4)

Combining equations (3a) and (4), it can be shown that

SEi11 = (GEi + I Ei )/d0 − 1, (4a)

whereI Ei andGEi are respectively intercept and slope of thedEiφ,ψ–sin2ψ curve.

Assume that the total strain in the film after applyingelectric field is smaller than the elastic limit of the film,so that the residual strain in the film does not change. Thestrains induced by the electric field are the differences in thestrain fields before and after applying the electric field (Ei = 0andEi = E3 respectively). From equations (3a) and (4a), thestrains induced by electric field can be obtained as

1S11 = (SE311 − S0

11)= (GE3 − G0 + I E3 − I 0)/d0, (5)

1S33 = (SE333 − S0

33)= (I E3 − I 0)/d0, (6)

354

Measurement of thin film piezoelectric constants using x-ray diffraction technique

where1S11 and1S33 are the in-plane and out-of-plane strainsof the piezoelectric film induced by the external electric field.I 0and G0 are respectively the intercept and the slope of thed0φ,ψ–sin2ψ curve without external electric field. Similarly,

I E3 and GE3 are respectively the intercept and the slope ofthedE3

φ,ψ–sin2ψ curve after applying the external electric field.

2.3. Piezoelectric constants

In general, when an external electric field is applied to apiezoelectric material, a strain field will be produced, whichcan be expressed in tensor form as follows [2]:

1Skl =6dikl Ei , (7)

where1Skl is the strain tensor induced by the electric field,Ei

is the electric field anddikl is the piezoelectric constant tensor.When an electric fieldE3 is applied, as shown in figure1, itwill cause

1SE311 =1SE3

22 = d f31E3, (7a)

1SE333 = d f

33E3. (7b)

Therefore, from equations (5) to (7) the piezoelectricconstantsd f

31 andd f33 can be expressed as follows:

d f31=1SE3

11/E3=1SE311 t/V= (GE

− G0 + I E− I 0)t/(V d0),

(8)and

d f33 =1SE3

33/E3 = (I E− I 0)t/(V d0), (9)

wheret is the thickness of the piezoelectric thin film andV isthe electrical potential difference applied to the top electrodeand the bottom electrode. Since the unstrained lattice spacingd0 of the films is often unknown,d0

φ,0 can be used to replaced0without producing significant error (generally less than 0.1%).

3. Experimental

PZT(52/48)/TiN heterostructural thin films were depositedon a nickel alloy substrate by pulsed laser deposition (PLD). ALambda Physik KrF excimer laser beam (wavelength 248 nm,pulse width 25 ns, repetition rate 10 Hz) with an incidenceangle of about 45◦ was employed. The laser ablation wascarried out at a laser fluence of 1–2 J cm−2. The films weredeposited at the optimized substrate temperature of 600◦C.The oxygen partial pressure was 300 m Torr when depositingPZT while the chamber was kept in vacuum when depositingTiN. The substrate was held parallel to the rotating target at adistance of 40 mm. Top gold electrodes of 3 mm in diameterwere deposited on to the piezoelectric thin film surface bysputtering with a shallow mask for piezoelectric constantmeasurement.

A Philips X’Pert MPD x-ray diffractometer with achromium (Cr) anode was used to measure the piezoelectricconstants. The x-ray incident spot size of 1.5 mm diameterwas adopted. A mini probe was built to supply electric field tothe ferroelectric/piezoelectric specimens on Eulerier samplestage. A microscope was used to locate the x-ray spot at thecentre of the top electrodes on the specimens. An arbitraryfunction generator (Tektronix, AFG310) was used to apply

Figure 2. XRD diffractogram of PZT on Ni substrate.

Figure 3. SEM image of cross section of the PZT/TiN/Nimultilayer structures.

the electric field over the top and bottom electrodes of thepiezoelectric film capacitor. Cross-sectional microstructuresof the films were examined using field-emission scanningelectron microscopy (FE-SEM, Hitachi S4100).

4. Results and discussion

At typical θ–2θ diffractograph of the PZT/TiN/Ni multilayerstructures is shown in figure2. A number of diffractionpeaks from multiple planes of PZT was observed while the(100) plane showed some extent of preferred orientation.To minimize the error during strain measurement, the (310)plane of the PZT was selected for strain measurement afterconsidering both x-ray intensity and diffraction angle.

A cross-sectional image of the PZT/TiN/Ni multilayerstructures is shown in figure3. Columnar grain structure of thePZT film grown on Ni substrate with very thin barrier layer ofTiN is observed. The thickness of the PZT film was measuredto be about 2.1µm.

The peak positions of the (310) plane of the PZT film atdifferent tilt anglesψ were evaluated in step sizes of 0.02◦.The measurement time at each step was 10 s.dφψ versussin2ψ curves of the film before and after applying an externalelectric field are shown in figure4. Lineardφψ–sin2ψ curvescan be observed for the capacitor both with and withoutapplication of the electric field.

355

Y H Yu et al

R2 = 0.9749

R2 = 0.9949

1.2920

1.2925

1.2930

1.2935

1.2940

1.2945

1.2950

1.2955

0 0.1 0.2 0.3 0.4 0.5 0.6sin2ψ

d (A

)

0V

5V

Figure 4. dφψ versus sin2ψ curves of PZT film before and afterapplying electric field.

From equations (8) and (9), the piezoelectric constantscould be calculated to bed f

33 = 78× 10–12 m V−1 (pC N−1)and d f

33 = −278× 10−12 m V−1. Compared to the reportedvalue ofd f

33 of about 60–130 pm V−1 for (100) textured PZTfilms using an interferometer [19] and 35 pm V−1 of theunpoled OMCVD PZT at MPB measured using the normalloading method [7], this range of values agree fairly wellwith the measurement result obtained in the present studyfor weakly-oriented and unpoled PZT film using the XRDtechnique. Since the XRD technique is a converse method inwhich the electric field is applied to the piezoelectric film, thefilm is poled to some extent.

It is known that the piezoelectric film is a part of thecomposite film–substrate structure. Mechanical clamping bythe substrate, electrode as well as the surrounding inactivefilm can strongly influence the piezoelectric properties ofthe film [15]. Thus the measuredd f

33 and d f31 values are

the effective piezoelectric constants of the films at certainmeasurement conditions. As a result of such clamping effect,it turns out thatd f

33is always smaller thand33 and the absolutevalue of the films’e f

31 may be larger than that ofe31 for theircounterpart bulk materials [1, 20, 21].

e f31 of PZT films with a thickness of 1–3µm has

been reported to be−8 to −12 C m−2 [19], which may beconverted tod f

31 of about−80 to −120 pC m−1 if a Young’smodulus of 100 GPa is used. This value seems to be lowerthan that measured in this experiment. In fact, a strongerclamping effect is imposed by not only the substrate butalso the surrounding inactive PZT film in the present study.The published Young’s modulus values range from 37 to400 GPa [10]. Thus, the difference in clamping conditionsand possible lower Young’s modulus of the films could havecontributed to the higherd f

31 value measured in this study.All available methods for determination of transverse

piezoelectric constant require explicit knowledge of the elasticmodulus of the piezoelectric films. Such modulii are notknown in most cases [22] and they could be very differentfrom those of the counterpart bulk materials. Thereforee f

31

was measured instead ofd f31 in most cases. The newly

developed method using the XRD technique has the advantageof directly measuring the effective transverse piezoelectricconstantd f

31 without the requirement of the elastic modulusof the piezoelectric films. However, it should be noted thatd f

31

could be affected by the difference in clamping conditions onthe tested capacitors.

Most of the static or quasi-static techniques usingthe converse effect determine the effective piezoelectricconstants of the films through the measurement of the surfacedisplacement of the film or the change in thickness ofthe sample (from top surface of the film to the bottomsurface of the substrate) instead of the strains in the films.The total displacement of the top surface of the film consistsof contributions from the thickness change of not only thefilm but also the substrate and the electrodes as well asfrom deflection due to bending [20]. The displacement dueto bending of the substrate may be several times higher thanthat of the film itself. Since the change in thickness is as smallas sub-ångstrom, the measurement for surface displacementbecomes extremely sensitive to noises such as thermal drift ofthe sample, fluctuation in refractivity of air in the optical path,and electrical and mechanical instabilities. Therefore, such atechnique usually requires a very stable environment [15]. Inaddition, surface morphology and reflection could also affectthe measurement.

Some studies [22] on the effect of top electrode size onthe measured piezoelectric constantd f

33 of thin films havebeen reported. Generally, it is expected that the larger the topelectrode size, the lower the measured piezoelectric constantvalues of the films. Different sizes of top electrode dimensionsare used in thin film piezoelectric constant measurement. Asreported, 1.5 to 2.5 mm in diameter in PLM [8, 9], 1.5 mm indiameter in the normal loading method [7] and 0.5 to 2 mm indiameter for the laser interferometer [15]. In this experiment,top electrode size of 3 mm in diameter is used. The size ofthe top electrode can be significantly reduced if stronger x-raysources such as rotating anode and synchrotron source [23]are adopted.

XRD is a well established method for measuring thestrain and stress within materials. Its repeatability is betterthan 5% [24]. Assuming that the measurements on appliedexternal electric field and film thickness are not the majorcontributor to measuring piezoelectric constants by XRD, therepeatability of this technique is expected to be 5% or better.

5. Conclusions

1. Both d f33 andd f

31 in piezoelectric films can be measuredusing the XRD technique.d f

33 is calculated fromthe change in the out-of-plane lattice spacing of thepiezoelectric films whiled f

31 is obtained from the changein the slope of thedφψ versus sin2ψ curves before andafter applying an electric field over the films.

2. The present newly developed method using the XRDtechnique which directly measures the strains instead ofdisplacement induced by an externally applied electricfield eliminates errors as a result of influence due toenvironment and/or vibration.

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