Residual Stress Development in Pb(Zr,Ti)O3ZrO2SiO2 Stacks[7]

8/8/2019 Residual Stress Development in Pb(Zr,Ti)O3ZrO2SiO2 Stacks[7]

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Residual stress development in Pb(Zr,Ti)O 3/ZrO 2/SiO 2 stacksfor piezoelectric microactuators

E. Hong a,*, R. Smith b, S.V. Krishnaswamy b , C.B. Freidhoff b , S. Trolier-McKinstry a

a Materials Research Institute, The Pennsylvania State University, University Park, PA 16802, USA b Northrop Grumman Electronics, Sensors System Sector, Baltimore, MD 21203, USA

Received 9 August 2005; received in revised form 9 December 2005; accepted 16 December 2005Available online 31 January 2006

Abstract

The residual stress of multilayers in piezoelectric microelectromechanical systems structures influences their electromechanical propertiesand performance. This paper describes the development of residual stress in 1.6 Am Pb(Zr 0.52 ,Ti0.48 )O3 (PZT)/0.3 Am ZrO 2/0.5 Am SiO 2 stacksfor microactuator applications. The residual stresses were characterized by wafer curvature or load-deflection measurements. PZT and zirconiafilms were deposited on 4-in. (100) silicon wafers with 0.5 Am thick thermally grown SiO 2 by sol– gel processes. After the final filmdeposition, the obtained residual stress of PZT, ZrO 2, and SiO 2 were 100–150, 230–270, and À 147 MPa, respectively. The average stress inthe stack was ¨ 80 MPa. These residual stresses are explained in terms of the thermal expansion mismatch between the layers and the substrate.Load-deflection measurements were conducted to evaluate localized residual stresses using released circular diaphragms. The load-deflectionresults were consistent with the average stress value from the wafer curvature measurements. It was found that more reasonable estimates of thestack stresses could be obtained when mid-point vertical deflection data below 6 Am were used, for diaphragms 0.8–1.375 mm in diameter.D 2005 Elsevier B.V. All rights reserved.

Keywords: Stress measurement; Zirconia; Lead zirconate titanate; Microelectromechanical systems (MEMS); Piezoelectric actuator

1. Introduction

Ferroelectric thin films have been widely incorporated intomicroelectromechanical systems for microactuators andmicrosensors [1,2] . Especially, lead zirconate titanate[Pb(Zr xTi1À x )O3] (PZT) films near the morphotropic phase boundary ( x ¨ 0.5) are often used due to their excellent piezoelectric properties. PZT films have been deposited by pulsed laser deposition, metalorganic chemical vapor deposi-

tion, sputtering, and chemical solution deposition routesamong others [3,4] . In this work, chemical solution depositionwas utilized.

For microactuator applications, unimorph structures withone piezoelectric and one passive layer are commonly adaptedto amplify displacements. To date, micromachined cantilever-type actuators using the d 31 or d33 piezoelectric constant have been fabricated. Kueppers et al. [5] fabricated PZT micro-

actuators consisting of a PZT layer sandwiched between topand bottom electrodes and polysilicon. For 390 Am longcantilevers, maximum tip deflections of 20 Am were obtainedat an applied voltage of 10 V. In contrast, Zhang et al . [6] usedthe d33 piezoelectric constant of PZT to drive their cantilevers.They deposited PZT on silicon nitride and the structures weredriven using interdigitated (IDT) electrodes. The 280 Am longcantilevers generated tip deflections of 30 Am at 100 V.Micromachined switches using the d 33 coefficient allow the

transmission lines to be formed directly beneath the cantilevers[7]. In clamped structures such as diaphragms and bridges, piezoelectric unimorphs using IDT electrodes are preferablesince the piezoelectric layer expands between the IDT fingers,resulting in deflections exceeding the structure thicknesses [8].

Several researchers have investigated residual stress in PZTfilms, focusing on changes in ferroelectric properties due to thestress. Tuttle et al. [9] reported that PZT films deposited onsapphire developed compressive stresses and exhibited higher remanent polarization than those deposited on silicon wafers,which were in tension. It is believed that the stress conditions at the Curie temperature determine the domain configuration of

0040-6090/$ - see front matter D

2005 Elsevier B.V. All rights reserved.doi:10.1016/j.tsf.2005.12.300

* Corresponding author. Tel.: +1 814 865 9931. E-mail address: [email protected] (E. Hong).

Thin Solid Films 510 (2006) 213 – 221www.elsevier.com/locate/tsf



the ferroelectric and consequently influences the ferroelectric properties. In addition, reduction in the residual stresses bymechanical or annealing processes yielded measurable changesin the dielectric, ferroelectric and piezoelectric properties of PZT films [10–12] .

In piezoelectric microelectromechanical systems applica-tions, the stresses of the PZTand other structural layers influencethe mechanical and structural properties as well as electric properties of PZT films. In particular, the stresses in cantileversshould be balanced to obtain flat structures. If not, the structuresare severely bent upward or downward [6], making it impossibleto fabricate functional microdevices. In clamped structures suchas diaphragm and bridges, the residual stress influences theresonance frequencies and response to external stimuli such asdifferential pressures [8]. Thus, to design microactuators andmicrosensors using PZT films, knowledge of the residual stressof the PZT and structural layers is essential.

The present work investigates stress development in PZT/

ZrO2/SiO2 stacks for fabricating diaphragm-type microactua-tors driven by IDT electrodes for micropumps and opticalswitches [13]. A thermally grown SiO 2 layer, which hascompressive stress, was used both as a passive layer and toreduce the average stress of the structures. The silicon oxidewas grown in steam (by wet oxidation). The zirconia layer prevented chemical reaction between PZT and the underlyingSiO2 or silicon. The thickness and process condition wasoptimized to enable subsequent deposit of crack free PZTfilms. PZT and zirconia films were deposited by sol– gel processes on 4-in. silicon (100) wafers with a thermally grownoxide. Changes in the residual stress of each layer in the stackswere characterized by wafer curvature measurements. Theaverage stress of the stacks was confirmed by load-deflectionmeasurements after circular diaphragms of the stacks werefabricated by micromachining techniques.

2. Experimental procedure

2.1. Zirconia film preparation

Zirconia is a chemically stable material, which has a highmelting point (>2370 - C) [14]. ZrO2 buffer layers have previously been shown to prevent reaction between PZT andSiO 2 [15] . The zirconia solution was prepared using 2-

methoxyethanol (2-MOE) as the solvent. The precursor waszirconium n-propoxide (Aldrich Chemical Co., Milwaukee,WI). Initially, zirconium n -propoxide was added to 2-MOE in aflask inside a glove box. The mixture was then reacted at 110 - Cfor 2 h in a dry argon ambient in a rotary evaporator. After reaction, the solution was distilled at 115 - C under vacuum toremove by-products. The solution was modified with 23 vol.%acetic acid and 7 vol.% acetylacetonate at room temperature. It was found that this improves the quality of the film and makes it possible to deposit particle-free, smooth and uniform films on 4-in. wafers. Acetic acid and acetylacetonate are chelating agents;they reduce the tendency of the alkoxide compounds tohydrolyze during deposition [16]. However, solutions with thismodification do not have a shelf life of more than one day. It

seems that an esterification reaction between acetic acid and2-MOE, liberating water, causes precursor precipitation [17].For this reason, the solution was modified just before beingused. The final concentration of the zirconia solution was0.4 M. Either thermally oxidized silicon (0.5 Am SiO2/Si) or silicon wafers were used for zirconia film deposition. Thesilicon oxide was grown on (100) Si wafers in steam at 1000 - C. Zirconia solution was then dispensed onto the wafersusing a syringe with a 0.1- Am filter. The wafers were spun at 3000 rpm for 30 s using a photoresist spinner (HeadWayResearch, Inc., Garland, TX). The spin-coated layer was pyrolyzed by a two-step process (300 - C, 60 s, then 450 - Cfor 60 s) to remove organic compounds. The layer was thencrystallized at 700 - C for 60 s in a Heat-pulse 610 rapid thermal processing unit (AG Associates, Sunnyvale, CA). Each layer was ¨ 70 nm thick. To get the desired thickness, the process wasrepeated. Finally, the zirconia layers were annealed in air in aconventional box furnace at 700 - C for 2 h.

2.2. Lead zirconate titanate film preparation

PZT (with a Zr/Ti ratio of 52:48) solution was preparedusing 2-MOE as the solvent. Details of the processing can befound elsewhere [18]. Lead acetate trihydrate, zirconium n - propoxide, and titanium iso -propoxide (Aldrich Chemical Co.,Milwaukee, WI) were used as precursors. Initially, lead acetatetrihydrate was dissolved in 2-MOE in a rotary evaporator flask in a dry argon ambient at 115 - C. After it was completelydissolved, the solution was distilled under vacuum to a white powder. At the same time, a mixture of zirconium n-propoxideand titanium iso -propoxide was prepared in the glove box. Themixture was stirred for 10 min at room temperature and addedto the flask containing the dehydrated Pb-precursor. The mixturewas reacted for 3 h at 115 - C under a dry argon ambient, thendistilled under vacuum to remove by-products until half of thesolution remained. 22 vol.% acetylacetone, 5 vol.% acetic acid,and additional 2-MOE were added to modify the solution. Theconcentration of the solution was 0.75 M with 20 mol% excesslead content. PZT films were deposited on zirconia passivatedsilicon wafers. For PZT deposition, a lower spin-coating speedof 1500 rpm was used to obtain thicker layers per coating. Thesame heat treatments as the zirconia processing (excepting thefinal 2 h annealing) were conducted. Each layer was ¨ 0.2 Am

thick. To get the desired thickness, the spin coating and thermal processes were repeated.

2.3. Film characterization

The microstructure and orientation of the zirconia and PZTfilms were determined using a scanning electron microscope(S-3500N, Hitachi Ltd., Tokyo, Japan) and a Scintag X-raydiffractometer (Scintag, Inc., Sunnyvale, CA). Ni-filtered CuK a radiation was used and X-ray diffraction data werecollected between 20 - and 60 - 2h at a rate of 2- /min. Thezirconia layer and PZT film thickness were determined fromSEM cross-sectional images or by a surface profiler (AlphaStep 500, Tencor, Inc., San Jose, CA).

E. Hong et al. / Thin Solid Films 510 (2006) 213– 221214



2.4. Fabrication of circular diaphragms

For load-deflection measurements, circular diaphragmswhich had a PZT/ZrO 2 /SiO 2 stack were fabricated usingdeep reactive ion etching (DRIE). The stack was prepared bydepositing the thin film stack on silicon wafers with a 0.5- Amthick SiO 2 layer. Cr/Au (150 A :1500 A ) was formed on top

of the stacks by evaporation to provide good reflective planesfor interferometric measurements. The thicknesses of PZT/ ZrO2 were ¨ 1.6 Am and 0.3 Am, respectively. The diaphragmdiameters were in the range of 0.8– 1.375 mm. Thediaphragms were then released by removing the silicon under the stacks from the back of the wafers using DRIE. Thewafers were clamped electrostatically and the backside wascooled by helium gas.

2.5. Wafer curvature measurement

At the wafer level, the residual stress of a film on a substratewas evaluated by Stoney’s equation [19] . By monitoring thechange in curvature of a wafer before and after deposition of athin film, the film stress was obtained.

The substrates used were 4-in. silicon (100) wafers (biaxialmodulus=181 GPa [20] ). The thicknesses of the wafers were inthe range of 510–570 Am. The curvatures of the wafers weremeasured using a thin film stress measurement system (FLX-2320, Tencor, Inc., San Jose, CA). Zirconia and PZT filmswere sequentially deposited on either 4-in. silicon or siliconwith 0.5 Am thermal SiO 2 on both sides. The curvature wassubsequently measured. To obtain the initial stress of thethermal oxide, the silicon oxide on the backside of the waferswas stripped using buffered oxide etchant, with the front side

of the wafer covered with photoresist. The time delay betweenthe deposition and the measurement was usually about 30 min.

2.6. Load-deflection measurement

The diaphragm load-deflection measurement involves thesimultaneous application of a uniformly distributed pressure

load to either surface of a thin film diaphragm and measure-ment of the out-of-plane deflection [21,22 ]. Fig. 1 shows themeasurement set-up. A vacuum chuck with a suitable windowand vacuum channel was machined from a solid aluminum block. A lever valve was used to subject the device to thevacuum created by a rotary vacuum pump. A needle valve wasthen used to regulate the applied vacuum level by controlledflow of air back into the system. A MKS Baratron Type 127 pressure transducer was connected to a MKS PDR-1-1C power supply and digital readout to monitor the pressure inside thechuck. The midpoint displacement measurement was con-ducted using a Wyko interferometer (Veeco, Tuscon, AZ).

While the wafer curvature measurement evaluates theresidual stress of a film at the wafer-level, this method canevaluate the residual stress in each diaphragm across the wafer.The load-deflection relationship of an edge clamped circular diaphragm, assuming that the deflection is small compared toits radius, is expressed by Eq. (1 ) [23,21 ].

P ¼8t

3r 4 E

1 À md 3 þ

4t r 0

r 2d ð1Þ

where P is the differential pressure, t is the diaphragmthickness, r is the radius of the diaphragm, d is the out-of- plane displacement, E is the Young’s modulus, m is thePoisson’s ratio, and r 0 is the residual stress.

Vacuum Chuck

Specimen

Needle Valve

Vacuum Pump

Lever Valve

Pressure Transducer

Fig. 1. Load-deflection experimental set-up.

diaphragm

reflective plane 500 μ m

Fig. 2. Top surface of diaphragms released by DRIE.

E. Hong et al. / Thin Solid Films 510 (2006) 213 –221 215



By measuring deflections of diaphragms at the mid-point asa function of differential pressure and fitting the data to Eq. (1),the Young’s modulus and residual stress were estimated usingknown geometric parameters ( Fig. 2).

3. Results and discussions

3.1. Structural characterization

It is difficult to deposit crack-free PZT films directly onsilicon or silicon with thermally grown oxide due to Pb-diffusion and formation of a lead silicate glass. In this study,PZT films were deposited on silicon wafers with thermaloxide (or bare silicon wafers) and zirconia layers of thicknessranging from 70 nm to 0.3 Am. As a barrier layer, zirconiashould be kept as thin as possible to minimize its influence onthe micromachined structures. It was found that the minimumthickness of zirconia films needed was greater than 0.2 Am

and the film had to be annealed at 700 - C in air for more than2 h to enable growth of crack free PZT films up to a thickness of 3.0 Am. It was found that PZT films cracked whenever they weredeposited on ZrO 2 less than 0.2 Am thick, independent of whether or not the ZrO 2 was pre-annealed at 700 - C for 2 h. TheX-ray diffraction patterns from the cracked films showed a broad peak (2h = 30 - ) at the position for the pyrochlore phase.

Fig. 3 shows X-ray patterns for zirconia and PZT films. Thezirconia films were deposited on a silicon wafer with 0.5 Amthick SiO 2. The X-ray pattern showed a weak tetragonal ZrO 2

peak, indicating poor crystallinity. After annealing at 700 - Cfor 2 h, a monoclinic phase was developed. The PZT films onthe zirconia were pure perovskite phase without any pyrochloreas observed by the X-ray patterns. A SEM micrograph of thecross-section of the wafer shows a sharp interface between thezirconia and PZT layers. There was no visible sign of reaction between SiO 2, ZrO2 or PZT, indicating that zirconia acted as aneffective buffer layer. Both films exhibited columnar structures.The PZT films showed good uniformity (less than 3% variationacross a 4-in. wafer).

0

100

200

300

400

500

600

700

800

900

1000

20 30 40 50 60

I n t e n s i t y ( a r b . u n i t s )

2 θ (o )

(a)

700 o C, 2 hrs anneal

700 o C RTA T e t r a g o n a l

T e t r a g o n a l

M o n o c l i n i c

S i

0

100

200

300

400

500

600

700

800

20 30 40 50 60

I n t e n s i t y ( a r b . u n i t s )

(b)

P Z T ( 1 0 0 )

P Z T ( 1 1 0 )

P Z T ( 1 1 1 )

P Z T ( 2 0 0 )

P Z T ( 2 1 0 )

P Z T ( 2 1 1 )

2 θ (o )

Fig. 3. X-ray diffraction patterns of (a) zirconia film and (b) PZT film on ZrO 2.

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

0 1 2 3 4 5 6 7 8 9

R e s i d u a l S

t r e s s ( M P a )

Layers (#)

0.5 μ m SiO 2

0.3 μ m ZrO 2Annealed at 700 o C for 2 hrs

0.2 μ m PZT0.4 μ m PZT0.8 μ m PZT1.2 μ m PZT1.6 μ m PZT

HorizontalVertical

Fig. 4. Residual stress of multilayer films on 4-in. SiO 2/Si wafers. Horizontal and vertical refer to a scan line parallel to the primary flat of the wafer and that perpendicular to the flat, respectively.




3.2. Wafer curvature measurement

Fig. 4 shows the stress development in 1.6 Am PZT/0.3 AmZrO2 /0.5 Am SiO 2 stacks. The stress of the initial thermal oxidelayer varies from À 300 to À 310 MPa (compressive).Deposition of a 0.3 Am zirconia film increases the total stressto À 180 MPa. Annealing the wafer at 700 - C for 2 h results ina total stress of À 200 MPa. The first layer of PZT increases thetotal stress to 0 MPa. The total stress of the stack was 80 MPa.To determine the effect of annealing on the thermal oxide, theexperiment was repeated with an additional annealing step at 700 - C for 2 h; it resulted in reduction ofthe stress of the thermaloxide by 13%. The final stress of the stack was ¨ 90 MPa. Thus, by using an additional annealing step for the thermal oxide, thefinal stress of the stack could be controlled. However, thiscomplicates interpretation of the stress in the PZT and ZrO 2

layers because there may be simultaneous stress changes in theSiO2 during the heat treatment steps.

To eliminate the effect of stress changes due to the thermaloxide, the same film stacks were produced directly on Si wafers.Fig. 5 shows the evolution of residual stress with film thickness.The stress of the as-deposited zirconia film was ¨ 80 MPa andthe annealing process drops the stress to À 40 MPa. Thedeposition of the first PZT layer increased the total stress to210 MPa. With the subsequent deposition of PZT layers, thetotal stress approached 100 MPa.

From the total stress, the stress of each layer can becalculated by Eq. (2).

r t t t ¼ Xn

i¼1

r it i ð2Þ

where r t and t t are the total stress and thickness of the stack and r i and t i are the stress and thickness of each layer. n is thenumber of the layers.

Fig. 6 shows the calculated stress of each individual layer using Eq. (2). It is known that the residual stress in a sol–gel

-100

-50

0

50

100

150

200

250

300

0 1 2 3 4 5 6 7 8

Layers (#)

HorizontalVertical

R e s i d u a l S

t r e s s

( M P a )

0.3 μ m ZrO 2

Annealed at 700 o C for 2 hrs

0.2 μ m PZT0.4 μ m PZT0.8 μ m PZT1.2 μ m PZT

1.6 μ m PZT

Fig. 5. Residual stress of multilayer films on 4-in. Si wafers. Horizontal and vertical refer to a scan line parallel to the primary flat of the wafer and that perpendicular to the flat, respectively.

-100

0

100

200

300

400

500

600

700

800

0 1 2 3 4 5 6 7 8

HorizontalVertical

R e s i d u a l S

t r e s s ( M P a )

Layers (#)

0.3 μ m ZrO 2

Annealed at 700 o C for 2 hrs

0.2 μ m PZT

0.4 μ m PZT0.8 μ m PZT1.2 μ m PZT1.6 μ m PZT

Fig. 6. Apparent residual stress of multilayer films on 4-in. silicon wafers with an additional annealing step. Horizontal and vertical refer to a scan line parallel to the primary flat of the wafer and that perpendicular to the flat, respectively.






was in the range of 12.5–24 Am. A typical plot of differential pressure versus the mid point deflection for a 1.375 mmdiaphragm is shown in Fig. 8(a). To estimate the biaxialmodulus a nd the residual stress of the diaphragm actuator, thecurve in Fig. 8(a) was fitted to Eq. (1). The R2 value is0.99972, indicating a very good fit between the model and thedata. For diaphragm actuators, the Young’s modulus wascalculated using a Poisson’s ratio of 0.269 in Eq. (1). ThePoisson’s ratio was calculated using a mixing rule for multilayer structures (Eq. (4)) [28] and the Poisson’s ratios of the layers in the diaphragm actuators in Table 1 .

meff ¼1t

m1 t 1 þ m2t 2 þ m3t 3ð Þ ð4Þ

where mi and t i are the Poisson’s ratio and thickness of the ithlayer.

The estimated Young’s mo duli and residual stress of thediaphragms are summarized in Table 3. The average Young’smodulus was 65.9 GPa with a standard deviation of 3.3 GPa. Inaddition, the average residual stress was 79.1 MPa with astandard deviation of 3.6 MPa.

Small deflection test results:

0510152025Pressur edifference, p(kPa)MidpointDeflectionh(µm)(b)deflectionresponseDiameter (mm)

41 1412 11 11A r



Comparison of large versus small deflection results: Onaverage, the residual stress determined using the full range of load-deflection data was about 8.5% lower than the valueobtained using only small deflection data. In addition, it isimportant to note that the difference between the two methodsdecreased monotonically with diameter, as illustrated by Fig. 9. Note that a steady increase in residual stress with diameter was predicted by fitting the large deflection data, whereas no effect of diameter was predicted by fitting the small deflection data. Sinceall devices tested were obtained from the same wafer andfabricated under identical condition, there was no reason toexpect that the residual stress was a function of device diameter.Rather, two factors were considered to have contributed to thedifference in the estimates of residual stress obtained from largeversus small deflection data. The first factor was the relativemagnitude of the midpoint deflection in comparison to thethickness. For a 0.8-mm diameter diaphragm, the maximummidpoint deflection was 5 times larger than the diaphragmthickness. In comparison, the maximum midpoint deflection for a 1.375 mm diaphragm was 10 times larger than the diaphragmthickness. To quantify the possible effect of the displacement tothickness ratio, the load-deflection data sequence for the largest diameter (1.375 mm) was terminated at various points and the

truncated data set was used to obtain estimates of the residualstress as a function of deflection to thickness ratio, as shown inFig. 10 (a). Referring to the Fig. 10 (a), the truncated data sets for the 1.375-mm device yielded nearly identical estimates of r 0 at all levels of deflection to thickness ratio. This observation lendscredence to the idea that the deflection to thickness ratio does not influence the estimate of residual stress obtained using largeload-deflection data and the non-linear fit.

However, the second factor was the difference in theestimates of the residual stress for large versus small deflectiondata for small diameter devices. In this case, the assumption that the bending stress could be neglected is problematic anddegraded the accuracy of the large deflection estimate. More-over, the difference between the large and small deflection

estimates may provide a first order measure of the relativecontribution of the neglected bending stiffness. In Fig. 10 (b), weshow the difference between the larger deflection estimate for each of 5 devices, and the average small deflection estimate for 6devices. Hence, the difference between the large and smalldeflection estimates of residual stress was negligibly small for the largest devices (1.375 mm), but was nearly 15% for thesmallest device (0.8 mm). Thus, we conclude that the differences between the two estimates of residual stress almost certainly can be attributed to neglecting the effect of strain energy due to bending in the model. In contrast, the small deflection estimatesof residual stress were less variable and showed no dependenceon diameter to thickness ratio. In effect, the assumption that thestrain energy due to bending is small in comparison to that due toin-plane stretching and residual stress starts to break down for large deflections of small devices. However, a good estimate of

Diameter d ( μ m)

R e s i d u a l S

t r e s s 0

( M P a )

75

80

85

90

800 900 1000 1100 1200 1300 1400

Small DeflectionLarge Deflection

Fig. 9. Residual stress determined from large and small load-deflections. (a)

75

80

85

90

0 2 4 6 8 10

Deflection/Thickness Ratio(b)

0

5

10

15

300 400 500 600

Diameter/Thickness Ratio

D i f f e r e n c e

( % )

R e s i d u a l S

t r e s s 0

( M P a )

Fig. 10. (a) Estimate of residual stress as a function of maximum deflection/

thickness ratio and (b) difference in two estimates of residual stress as afunction of diameter/thickness ratio.




the residual stress can still be estimated using the smalldeflection data. Residual stress values estimated from the load-deflection measurement are higher by 7.5% than those from thewafer curvature measurement. This deviation may be explained by (1) stress contribution of Cr/Au electrode for the load-deflection measurement and (2) the thickness reduction of thecompressive thermal oxide during the RIE process. Consideringthese factors, these two measurement methods providedreasonably consistent residual stress values.

4. Conclusions

1.6–2.0 Am PZT and zirconia films were prepared on 4-in. oxidized silicon wafers by sol– gel processes. Bothsolutions used 2-MOE as the solvent. The zirconia actedas a buffer layer to prevent the reaction between the PZT andSiO2. It was found that the zirconia films should be thicker than 0.2 Am and need to be annealed at 700 - C for more

than 2 h to deposit crack-free PZT films. The cross-sectionof the wafer shows sharp interfaces between the layers,indicating no significant reaction. The zirconia film showedstress relaxation, which was apparently related to absorptionof water molecules into the pores. After the final filmdeposition, the residual stress values of PZT, ZrO 2, and SiO 2

by wafer curvature measurements were 100–150, 230–270,and À 147 MPa, respectively. The average stress in 1.6 AmPZT/0.3 Am ZrO2 /0.5 Am SiO2 stacks was ¨ 80 MPa. In theload-deflection measurement, more reasonable residual stres-ses could be estimated using small deflection data. In thelarge deflection case, the deviation of the calculated residualstress might come from an increasing contribution of the bending stress to the deflection. An effective Young’s modulus(65.9 GPa) and a tensile residual stress (85.8 MPa) wereobtained. These two stress measurements for the piezoelectricstacks provided reasonably consistent results.

Acknowlegement

Authors are grateful to Dr. Mark Horn and Dr. LawrencePilione for their advice in stress measurements. The researchreported in this paper was performed in connection withCooperative Agreement number DAAD17-00-21001 with theU.S. Army Research Laboratory.

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