JOURNAL OF APPLIED PHYSICS VOLUME 86, NUMBER 1 1 JULY 1999

Thickness dependence of structural and electrical properties in epitaxiallead zirconate titanate films

V. Nagarajan,a) I. G. Jenkins, S. P. Alpay, H. Li, S. Aggarwal, L. Salamanca-Riba,A. L. Roytburd,b) and R. Rameshc)

Department of Materials and Nuclear Engineering, University of Maryland, College Park, Maryland 20742

~Received 8 December 1998; accepted for publication 23 March 1999!

We have studied the effect of misfit strain on the microstructure and properties of ferroelectric leadzirconate titanate thin films. We have changed the misfit strain by varying the film thickness andstudied the thickness effect on the domain formation of epitaxial PbZr0.2Ti0.8O3 ~PZT! films grownby pulsed laser deposition on~001! LaAlO3 substrates with La0.5Sr0.5CoO3 ~LSCO! electrodes. Thenominal thickness of the PZT films was varied from 60 to 400 nm with the LSCO electrodethickness kept constant at 50 nm. X-ray diffraction experiments show that the films relax via theformation of a domains, the fraction of which increase with the ferroelectric film thickness. Thec-axis lattice constant of PZT films calculated from the 002 reflection decreases with increasing filmthickness and approaches the bulk value of;0.413 nm in the films thicker than 300 nm.Cross-sectional transmission electron microscopy images reveal that thea-domain fraction andperiod increase with increasing film thickness. The relaxation of misfit strain in the film isaccompanied by systematic changes in the polarization properties, as well as the switching fields,quantified by the coercive field and the activation field. ©1999 American Institute of Physics.@S0021-8979~99!02013-7#

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I. INTRODUCTION

The bistable polarization states of ferroelectric materis the fundamental property that enables nonvolatile informtion storage in a ferroelectric random access memory devAmong the many desirable attributes for a memory devthe ferroelectric thin film capacitors should show large vues of switched polarization (DP) for short read and writepulses and low coercive voltages. This is motivated byfact that they will be used in circuits that will typically bintegrated using 100 ns wide pulses. Therefore, it is nesary to understand the complex interplay between filmcrostructure and the switching properties and subsequecontrol it. The earliest studies on the switching behaviorlead zirconate titanate thin films suggested that the intrinswitching speed is faster than 1 ns, and is limited only byintrinsic resistance-capacitor time constant of the deviceby instrumental limitations.1 One measure of switchingspeed, the ‘‘activation field,’’ was identified by Merz in hpioneering work on barium titanate single crystals.2 Morerecently, the activation field for polarization reversal hbeen demonstrated to be independent of circuit parameand directly related to the tetragonality ratio (c/a) of theferroelectric layer.3 Cillesen, Prins, and Wolf4 have investi-gated the thickness dependence of the switching voltagtextured oxide ferroelectric thin films prepared by pulsedser deposition~PLD! where they reported that the coercivfield is independent of thickness in films with oxide ele

a!Electronic mail: etop@glue.umd.edub!Electronic mail: ar28@umail.umd.educ!Also at: Center for Superconductivity Research, Department of PhyUniversity of Maryland, College Park, Maryland 20742.

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trodes for films with thicknesses ranging from 200 to 8nm. On the other hand, the coercive field was shown tocrease with decreasing ferroelectric layer for capacitors wa metallic top electrode.4 In order to understand the effects oheteroepitaxy-induced strain and its relaxation with fithickness, it is important to carry out studies on films thspan the range over which strain relaxation occurs by dication formation. Furthermore, the impact of epitaxial straon the polarization properties, as well as ease of switchunder pulsed fields need to be understood. Our work hasfocused on the impact of strain relaxation, including relaation due to 90° domain formation, on the ferroelectric proerties under pulsed switching conditions.

In order to systematically understand the effect of stron the ferroelectric properties, specifically the switching dnamics, we have chosen lattice-mismatched epitaxial hetstructures as the demonstration vehicle. The observed mstructures of tetragonal lead zirconate titanate films wdifferent thicknesses on a~001! LaAlO3 ~LAO! substrate area result of an interplay of two different mechanisms for strarelaxation: misfit dislocation generation at the deposittemperature (TG) and polydomain formation below thparaelectric to ferroelectric transformation temperature (TC).While it is not the primary intention of the article to addremisfit dislocation formation atTG , it is very possible thatthese dislocations assist in the nucleation of the polydomstructure. Polydomain formation in epitaxial films underging a phase transformation is a mechanism that relaxestotal strain energy which is a result of the lattice misfit duethe structural phase transformation, the difference in the thmal expansion coefficients of the film and the substrate,misfit dislocation formation.5 In Fig. 1, we show all possibleorientational variants of the ferroelectric phase~inner circle!

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© 1999 American Institute of Physics

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596 J. Appl. Phys., Vol. 86, No. 1, 1 July 1999 Nagarajan et al.

and possible polydomain structures~outer circle! due to acubic-tetragonal transformation.6 Previously we have obtained a map showing regions of stability of possible domstructures and relative fractions of domains in polydomstructures for epitaxial ferroelectric or ferroelastic filmwhich undergo a cubic-tetragonal transformation.7–11 Themap is constructed in the coordinates of the misfit strbetween the substrate and the film, and the tetragonalitthe film. These parameters, together with an ‘‘effectivsubstrate lattice parameter to incorporate relaxation by mdislocations,12 conveniently combine the effects of earlimentioned sources of strain energy. For relatively thick filwith h@hcr , where h is the film thickness andhcr is thecritical film thickness for the formation of thec/a1 /c/a1 orthe c/a2 /c/a2 polydomain structure, the domain structurecontrolled only by the elastic energy density.7,10 It was alsoshown that thec/a1 /c/a1 and thec/a2 /c/a2 polydomainstructures are energetically equivalent and will be referreas the c/a/c/a structure hereafter.7,10,12 The existence ofsuch a critical thickness is due to microstresses, which aresult of the periodic deviation of the actual misfit strafrom the average misfit on the interface between the polymain structure and the substrate.9 The effect of film thicknesswas accounted for using a simple approximationmicrostresses.9,10 It was shown that the fraction ofc domainsin a c/a/c/a domain structure depends on the filthickness.10 The task of this article is to establish a corretion between the strain relaxation, polydomain formatioand the ferroelectric properties.

In the lead zirconate titanate family of ferroelectrics, tswitching properties can be systematically varied by onemany microstructural parameters, such as the film tetragoity, strain, grain size, etc. Heteroepitaxy provides us withpowerful approach to control the elastic strain that is intduced into the ferroelectric layer, by systematically changthe thickness of the ferroelectric layer. In this work, we hastudied the influence of the thickness of PbZr0.2Ti0.8O3 ~PZT!films on strain relaxation, domain formation and its effectswitching properties. The switching behavior was studiedpulsed measurements with the pulse amplitude and widtkey variables. The familiar ferroelectric hysteresis loop pvides a quasistatic~i.e., low frequency! measure of the polarization and the switching field, i.e., the coercive fie

FIG. 1. Orientational variants of the ferroelectric phase~inner circle! andpossible polydomain structures~outer circle! due to a cubic-tetragonal transformation.

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However, under pulsed testing conditions, the remnant poization, i.e., the difference between the switched respo(P* ) and the nonswitched response (P`), and the activationfield are better measures of the switchability of the capaciThe activation field is obtained via the Merz approach13 froma plot of ln(imax) vs 1/E, wherei max is the switching currentandE is the applied field.

II. EXPERIMENT

The oxide heterostructures were deposited by PLD650 °C under 100 mTorr of oxygen partial pressure. Priordeposition, the substrates were sequentially cleanedtrichloroethylene, acetone, and methanol. The films wcooled under 760 mTorr of oxygen partial pressure at 5min until 200 °C and then by Newtonian cooling to rootemperature. The thickness of the PZT layer was varied fr60 to 400 nm. La0.5Sr0.5CoO3 ~LSCO! electrodes were useto contact the ferroelectric layer with the thickness of top abottom electrode kept constant at 50 nm. All the films wegrown on~001! LAO substrates.

The heterostructures were investigated by x-ray diffrtion ~XRD! using standardu–2u, v, and,f scans to evaluatecrystalline quality and domain structure. A Siemens D50four-circle diffractometer was used to obtain theu–2u, v,and f spectra. Epitaxial quality of the films was confirmeby the presence of only 00l or h00 type of peaks in theBragg scans. From the 200 reflections, the lattice constwere calculated after normalizing with respect to the 2peak of LAO with a lattice parameter of 0.379 nm. Ththickness of the films was measured by Rutherford bascattering spectroscopy.

Cross-sectional transmission electron microscopy~TEM!samples were prepared by gluing the films face to facemechanically thinning them down to 15mm. In addition tothe standard tripod, a novel tool developed by one ofco-authors, was used in the last stage of mechanical poing. A Bal-Tech Ion Milling RES-010 was used to ion mithe sample. For the first 1 1/2 h the conditions were 7 kV a2.5 mA. Then, 5 kV and 1 mA was used for 30 min to finisthe ion milling. TEM studies were carried out on a JEO4000FX microscope operated at a voltage of 300 kV.

The electrical measurements used square bipolar ptrains with the sequence that transverses the entire hysteloops. We obtained polarization data from the outputsponses observed at the top of the read pulse which imdiately follows the delay time after the read pulse. The higspeed tests were performed using an Analogic polynomwaveform generator and the signal responses were meason a Tektronix oscilloscope. The pulse responses were msured using applied voltages that kept a constant appliedof 250 kV/cm across the ferroelectric capacitor. The siggenerator produced square bipolar pulses that were variewidth from 1ms to 1 s. The delay between each pulse was. For activation field measurements the bipolar pulse widwere kept constant at 1ms. The delay time between writand read pulses was 1 s. The applied voltage was varied f1 to 10 V. The net current response were acquired at evoltage level from which current maximum peak was note

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597J. Appl. Phys., Vol. 86, No. 1, 1 July 1999 Nagarajan et al.

The activation field was then obtained from the slope ofnatural log of the current maximum values versus the inveof the applied fields.

III. RESULTS AND DISCUSSION

A. Crystallographic and structural characterization

Figure 2 showsu–2u XRD patterns in the range of 40°50° for 100-, 200-, and 300-nm-thick films. The peaks arfrom 200-type of reflections from the heterostructures. T200-LSCO peak corresponds to a lattice parameter of 0.nm. The measured lattice parameter of the LSCO electrodthe parameter normal to the substrate–bottom electrodeterface and is greater than its bulk value of 0.383 nm,14 in-dicating a tensile strain along the@001# direction of the sub-strate. The cube-on-cube epitaxy between LAO andbottom LSCO layer~La12xSrxCoO3 compounds for 0,x,0.55 have actually a rhombohedral structure but forLa0.5Sr0.5CoO3 composition, the lattice can safely be a

FIG. 2. u–2u XRD patterns in the 40°–50° range for 100-, 200-, and 30nm-thick PZT films.

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sumed to be cubic!15 requires a biaxial strain state with equorthogonal in-plane components concentrated in the LSfilm ~thickness of substrate is much larger than the thicknof LSCO!. In the absence of misfit dislocations at the LAOLSCO interface, if the substrate and the LSCO layerassumed elastically isotropic and their elastic constantsequal, the out-of-plane component of the misfit strain tensezz, is related to the in-plane components as

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the unconstrained~bulk! lattice parameter of LSCO, andexx

andeyy are the in-plane components of the misfit strain. Tvalue of e is approximately21.01% at room temperatur~compression!. Therefore, Eq.~1! finds ezz as 0.90%~ten-sion!. Then, the out-of-plane lattice parameter of the LSClayer,aLSCO

' , can be calculated using

ezz5aLSCO

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which givesaLSCO' 50.386 nm. Compared to the experime

tally observed value of 0.387, we conclude that the intermdiate LSCO layer is coherently strained. Thus, the first layof PZT are deposited on a highly strained LSCO layer.clear shift in the peak position of the 002 PZT peak towahigher peak positions is observed with increasing thickneThe c lattice parameter drops from 0.416 nm for the 60-nthick film to 0.413 nm for 400-nm-thick film. This indicatethat the epitaxial strain in the film relaxes as the film thicness is increased.

To determine the domain fractions,v-rocking curveshave to be used. Fosteret al.16,17 have demonstrated that depending on thex-angle resolution,h00 type of peaks fromthe PZT layer may disappear. This is due to the tilting of ta domains away from the (00l ) planes of the substrate because of the tetragonality of the PZT film. The (h00) planesof the a domains are tilted from the@00l # direction of thesubstrate theoretically by;2.9° along@h00#, @ h00#, @0k0#,and@0k0# directions resulting in a fourfold symmetry. Thuusing the integrated intensities of the 002 and 200 peakthe PZT layer from the standardu–2u XRD pattern to cal-culate domain fractions of the PZT film may give misleadiresults ~usually an overestimation of thec-domainabundance!.18 To obtain the domain populations in thtwinned PZT layer more accurately, the integrated intensiof either thev–x scans~area maps!16–19 or the v-rockingcurves of the 00l andh00 PZT peaks should be employed.20

If the rocking curves are used, thec-domain fractionac isgiven by20

ac>P002

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598 J. Appl. Phys., Vol. 86, No. 1, 1 July 1999 Nagarajan et al.

FIG. 3. v-rocking curves around the 200 and 002 PZpeaks for the~a! 60-, ~b! 200- and,~c! 400-nm-thickPZT films.

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whereP002R andP200

R are the integrated x-ray rocking curvintensities of 002 and 200 reflections of the PZT layer,spectively.P200

R is the volume underone of the a-domainlobes observed in the 200 rocking curve. Measurement oftotal intensity of x-rays diffracted froma domains requirescomplete mapping of the relrods in reciprocal space lattTherefore, to calculate the volume fraction ofa domains,their integrated intensity must be multiplied by a factorfour.

To accurately locate the positions of the 200 peakPZT, the samples were tilted by62.1° alongx. The intensi-ties of both the 002 LAO and 002 PZT peaks were dracally reduced. This way, the positions of the 200 PZT pewere located and specularv-rocking curves around 002 an200 PZT were obtained. The results are illustrated in FigFrom thev-rocking spectra around 200 PZT for all the filmit can be seen that there is only one peak. Therefore, weconclude that the PZT films grown on~001! LAO consist ofa singlec-axis oriented growth plane. Thev-rocking curvesaround the 200 peaks illustrate the fourfold symmetry ofa domains@see Fig. 3~b! and 3~c!#. The reflections indicatethe presence of@101# and @011# type 90° domain structureon the film ~i.e., thec/a/c/a polydomain structure!, exceptfor the 60-nm-thick film for which thev rocking did notshow any appreciable amount ofa domains. It can be observed that the angular separation between the terminal pof the 200 reflections is;4.1°. Therefore, thea domains aretilted away from the (00l ) planes of the substrate by 2.05°

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a fourfold symmetry which is lower than the theoreticvalue of 2.9°. It should be noted that, from Fig. 3~b!, the 200nm film does not reveal a 200 PZT peak, but when we follthe aforementioned method we were able to map aro20% a domains.

Figure 4 shows thatc-domain abundance measured thway decreases continuously to a value of 67% for the fi400-nm-thick film. Figure 4 also plots thec lattice parameterof the PZT film as a function of film thickness. The latticparameter changes from 0.416 nm for the 60 nm film0.413 nm for the 400 nm film. The lattice parameter for t

FIG. 4. c-axis lattice parameter and volume fraction ofc domainsac as afunction of the PZT film thicknessh.

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599J. Appl. Phys., Vol. 86, No. 1, 1 July 1999 Nagarajan et al.

60 nm film indicates that the film is under high internstresses. A comparison to 0.413 nm, the bulk PZTc-latticeparameter,14 indicates that the film is under very high inplane compressive stresses. The 300- and 400-nm-thick fishow a lattice parameter of 0.413 nm indicating almostrelaxation.

This is further confirmed from electron diffraction. Figure 5 plots thec/a ratio from electron diffraction as a function of ferroelectric film thickness. Thec/a ratio calculatedfrom the electron diffraction decreases from 1.08 for thenm film to 1.051 for the 400 nm film. Figures 6 and 7 are tcross-sectional TEM images for 60- and 400-nm-thick filmThese micrographs clearly show that the relative volufraction of the 90° domains increases with film thickneThe measured fractions match reasonably well with thesults obtained from XRD. The average twin period increawith increasing film thickness. Notice that 90° domains apresent in as low as 60-nm-thick films, which could notobserved by XRD probably because of instrumental limtions. Further studies of thinner PZT films~;30 nm! showthe absence of 90° domains. These results are to be publielsewhere.

FIG. 5. Thec/a ratio or the tetragonality calculated from TEM electrodiffraction patterns for the 60-, 100-, and 400-nm-thick PZT films.

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It is evident that the contraction ofc-lattice parameter iscommensurate with the relaxation behavior of the film.other words, it begins to decrease when the film relaxespolydomain formation. This decrease in thec lattice param-eter causes a decrease in the tetragonality of the ferroelelayer. The decrease in tetragonality, as indicated by the etrical characterization, has a significant influence onswitching behavior.

B. Electrical characterization

For the electrical characterization we investigated primrily films in the 100–400 nm range. The properties do nchange very much for films just below this range andwere limited by the equipment to achieve high fields fthicknesses higher than 400 nm. Figure 8 shows the poization as a function of applied field for 100-, 200-, an300-nm-thick films. It can be seen that at a field of just bel150 kV/cm the thicker films show a pulsed switched polization,DP, of more than 80mC/cm2. However, the 100 nmfilm shows negligible switching. But at higher applied fieldthe value ofDP for the 100 nm film rises sharply to a valunearly equal to the saturation value of 200- and 300-nm-thfilms ~it should be noted thatDP>2PS , where PS is thesaturation polarization, since the hysteresis loops are almsquare shaped!. As we further increase the applied fields, tvalue ofDP for 100 nm films is the highest.

As the thickness of the PZT films increase, volume fration of c domains, absolute value ofDP, and thec-latticeparameter decrease. To isolate the effect of tetragonalitythe domain fraction onDP, we have plotted in Fig. 9 anormalizedDP as a function of film thickness. The normaized polarization is defined as

DPN5DPM /ac , ~5!

whereDPM is the average switched polarization measuover different regions of the film. A comparison of Figs. 4,and 9 shows that when the tetragonality of the latticecomes constant,DPN does not change. This shows that tswitching of 90° domains is not likely under the used eletrical fields. At lower thicknesses,DPN increases indicating

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FIG. 6. Cross-sectional bright field TEM image of th60-nm-thick PZT film.

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600 J. Appl. Phys., Vol. 86, No. 1, 1 July 1999 Nagarajan et al.

FIG. 7. Cross-sectional bright field TEM image of th400-nm-thick PZT film. Thea-domain fraction and pe-riod increase with PZT film thickness~compare withFig. 6!.

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that the increase is not purely an effect of 90° domain fmation but an effect of strain as evidenced from higherc/aratios. The 100 nm film shows aDPN close to 140mC/cm2

and then the polarization remains constant at;125 mC/cm2

after the initial rise.The increase in the polarization of the 100-nm-thick fi

is due to high in-plane stresses which are not relaxed bydomain formation. To calculate the in-plane stress,s, theout-of-plane thec-lattice parameter of the film measurefrom theu – 2u scan can be used. The out-of-plane compnent of the strain in the PZT layer is given by

ezz5cPZT

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cPZT0 , ~6!

where cPZT' 50.416 nm is thec lattice parameter from the

u–2u scan, andcPZT0 50.413 nm is the bulkc-axis lattice pa-

rameter of PZT.14 Equation~6! findsezz as;0.007~tension!.Therefore, for a film containing onlyc domains, the in-planecomponents of the strain can be found by noting thatnormal stress in the@001# direction is zero. Then

e5exx5eyy52C33

2C13ezz, ~7!

whereCi j are the components of the tensor of elastic cstants of the tetragonal film. Therefore, the in-plane strcan be determined by

s5sxx5syy5S C111C1222C13

2

C33D e. ~8!

Equation~8! yieldss53.1853109 N/m2 by using the elasticconstants as cited by Kwaket al.21 for PbTiO3

~C1151.43331011N/m2, C1250.32231011N/m2, C13

50.24131011N/m2, and,C3351.31631011N/m2!. A ther-modynamic analysis similar to the one carried out in Ref.shows that the increase in the polarization is proportionas

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dPS /PS>~2Q12/k!s, ~9!

whereQ12 is the electrostrictive coefficient andk is the di-electric stiffness. SubstitutingQ1252.531022 m4/C2 and k51.33109 m/F23 yields ;10%, consistent with the experimental observation.

We next investigated the activation field,Ea , as func-tion of film thickness. Figure 10 plots ln(imax) as function of1/E wherei max is the switching current andE is the appliedfield. Ea was correlated to switching currenti max by Merz2,24

by the following relationship:

i max}exp~2Ea /E!. ~10!

Therefore, the slope of ln(imax) vs 1/E plot gives the value ofEa . There is a distinct increase in the slope as the thicknis decreased. This clearly indicates a decrease in activafield with increasing thickness.

Figure 11 shows the plot ofEa , obtained from Fig. 10as a function of thickness. It can be seen thatEa drops from1090.9 kV/cm for the 100 nm film to 567 kV/cm for the 20nm film and then remains more or less constant with thiness. This large drop inEa is one of the most importan

FIG. 8. Polarization as a function of applied field,E, for 100-, 200-, and300-nm-thick films.

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601J. Appl. Phys., Vol. 86, No. 1, 1 July 1999 Nagarajan et al.

impacts of strain relaxation and domain formation onelectrical behavior of the film. Merz has correlated the wenergies to the activation field and proposed thatEa is pro-portional to the spontaneous strain to the powern, wheren isa semi-empirical constant varying from 2 to 4.2,24 Hence,with decreasing strain we expectEa to decrease. Merz,2,24

Fattuzo and Merz,25 Chynoweth,26 and Drougard andLandauer27 have investigated the thickness dependencesingle crystal BaTiO3 and attribute a similar behavior to‘‘surface’’ layer at the ferroelectric electrode interface. SinEa is a measure of the impedance to switching, it canconcluded that the relaxed thicker films switch more eathan the thin strained films. This can also be seen in Figwhere the thicker films reach the saturation polarizationmuch lower applied fields compared to the 100 nm filFigure 11 also shows the coercive field,Ec , plotted as afunction of thickness of the film. It shows a behavior vesimilar to Ea where it drops from 225 to 90 kV/cm for aapplied field of 333 kV/cm. In a subsequent article, we wpresent the interrelationship between tetragonality, 180°main wall energy, activation field and the switching dynaics. Finally, the exact role of the 90° domains in the switcing process, i.e., whether they facilitate the nucleation

FIG. 9. Plot showing the normalized switched polarizationDPN as a func-tion of the PZT film thickness,h, at a constant applied field of 333 kV/cm

FIG. 10. ln(imax) vs 1/E plots to calculate the activation field,Ea , for the100- to 400-nm-thick PZT films. The slope of the straight line givesEa .

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180° domain walls is yet to be understood. However, itclear from Fig. 11 that the activation field is relatively indpendent of the volume fraction of 90° domains once theragonality of the lattice remains constant.

It is observed that activation field and coercive fieshow a trend strongly dictated by the change in tetragonaThe switched polarization follows the same dependence.increase in tetragonality implies a larger displacement ofcentral Ti14 ion, and hence, larger switched polarizatioThe increase in tetragonality, a direct effect of the largeplane compressive stress in thinner films, causes highervation fields. But once the film relaxes via domain formatithec-lattice parameter and the tetragonality tend to their bvalues. Consequently, the switched polarization and acttion field tends to saturate towards lower values.

IV. CONCLUSION

We have investigated the effect of film thicknessstructural and electrical properties of epitaxial lead zircontitanate films. We have prepared the films by pulsed laablation and characterized the films using four-circle XRTEM, and pulsed switching measurements. A strong depdence of the domain structure of the film on the thicknessthe ferroelectric layer has been shown. The fraction oadomains increases as the film thickness of the ferroelecfilm is increased. As the film thickness is increased, theragonality of the PZT film drops due to relaxation of internstresses by polydomain formation. We also observe a ladrop in activation field as the film relaxes via domain formtion. We attribute the drop in switched polarization to trelaxation of internal stresses and to polydomain formatiThese results illustrate that the microstructure of the ferelectric thin film plays a significant role in the switchinbehavior.

ACKNOWLEDGEMENTS

This work was supported by the National Science Fodation ~NSF! under Grant No. DMR-9633638 and by thNSF–MRSEC under Grant No. DMR-9632521.

FIG. 11. Activation field,Ea , and coercive field,Ec , as function of filmthickness. The coercive field is calculated for an applied field of 333 kV/c

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602 J. Appl. Phys., Vol. 86, No. 1, 1 July 1999 Nagarajan et al.

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