Formation of Optical Gradient in Chemical Solution-Derived PbZr[sub 0.52]Ti[sub 0.48]O[sub 3] Thin Films: Spectroscopic Ellipsometry Investigation

Journal of The Electrochemical Society, 156 �12� G217-G225 �2009� G217

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Formation of Optical Gradient in Chemical Solution-DerivedPbZr0.52Ti0.48O3 Thin Films: Spectroscopic EllipsometryInvestigationI. Aulika,a,z S. Corkovic,b A. Bencan,c S. D’Astorg,b A. Dejneka,d Q. Zhang,b

M. Kosec,c and V. Zaulsa

aInstitute of Solid State Physics, University of Latvia, LV-1063 Riga, LatviabSchool of Applied Sciences, Cranfield University, Cranfield, Bedford MK43 0AL, United Kingdomc“Jozef Stefan” Institute, Si-1000 Ljubljana, SloveniadInstitute of Physics, Academy of Science, 182 21 Prague 8, Czech Republic

Investigation using a variable angle spectroscopic ellipsometer revealed the influence of sample preparation conditions on sol–gelPbZr0.52Ti0.48O3 �PZT 52/48� thin-film homogeneity that allows identification and further optimization of thin-film performance.Separate crystallization of the layers determined the optical gradient appearance, irrespective of the chemical solvents used in thiswork. A more refined analysis showed that a refractive index gradient was apparent in the samples in which lattice parametersstrongly changed with thickness. For these films, energy-dispersive X-ray spectroscopy analysis showed significant variation in Pband Zr. Additionally, complex dielectric functions for each PZT 52/48 thin film in the wide phonon energy �1.03–5.39 eV� rangewere evaluated.© 2009 The Electrochemical Society. �DOI: 10.1149/1.3240580� All rights reserved.

Manuscript submitted June 11, 2009; revised manuscript received August 10, 2009. Published October 22, 2009.

0013-4651/2009/156�12�/G217/9/$25.00 © The Electrochemical Society

Pb�ZrxTi1−x�O3 �PZT� �x = 0–1� thin films have attracted theattention of researchers greatly for the past 30 years due to theirexcellent ferroelectric and electromechanical properties, which haveled to the commercialization of thin PZT films for ferroelectric ran-dom access memory, forming a market of several million USD an-nually. They have also drawn interest for use in pyroelectricdevices1-3 due to their large pyroelectric coefficient. PZT thin filmshave advantages over bulk materials, as they can be directly depos-ited on platinized silicon to allow direct integration with electronics.Due to the superior electromechanical properties of PZT comparedto other ferroelectric ceramics, PZT films have formed an integralpart of the microelectromechanical systems �MEMSs� in variousapplications such as sensors, actuated micromirrors for fine-trackinghigh density optical data storage mechanisms,4 and tunable capaci-tors for high frequency microwave applications or electro-opticmodulators, to name a few. Every application of MEMS requires adifferent thickness of the functional film, leading to the challenge ofmanufacturing film of the required thickness. Among many methodsfor the fabrication of PZT thin films, chemical solution deposition�CSD�, metallorganic chemical vapor deposition, and physical vapordeposition such as radio-frequency �rf� sputtering have been widelyemployed. Among these techniques, CSD methods such as sol–gelprocessing offer low capital costs and easy control of chemical com-position and homogeneity.3 However, the minimum thickness limi-tation of around 100 nm per layer for a crack-free and dense filmdeposited via CSD requires multiple coatings to reach the finalthickness.

The broad applications of PZT films, and inter alia the growinginterest in graded refractive index films for applications in opticaldevices,5,6 make it imperative to study the depth profile of opticalproperties of thin films throughout a single layer and an entire coat-ing. Furthermore, information on the homogeneity of the films andthe physical properties resulting from different processing methodsrepresents crucial knowledge, especially because gradients in opticalproperties have been reported for sputtered PZT films,7,8 and chemi-cal composition gradients were reported for some CSD-fabricatedPZT films.9-12 Variation in chemical composition throughout the filmthickness due to the inhomogeneity results in variation in physicalproperties of the films and lowers the performance of electrome-chanical systems.3,9,10 Thus, knowledge of the compositional gradi-ents within a film allows identification and further optimization ofthin-film performance and applications in piezo- and ferro-devices.

z E-mail: [email protected]

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A challenging aspect of homogeneity studies lies in the develop-ment of an appropriate characterization method because the compo-sitional variation must be determined on a small scale, within100 nm. The detection of concentration gradients of the chemicalelements of PZT thin films can be studied by Z contrast transmissionelectron microscopy �TEM� with energy-dispersive X-ray spectros-copy �EDXS�.9 Fascinating work has been done by Parish et al.,13

where the use of multivariate statistical analysis of energy dispersivespectroscopy �EDS� spectrum images �SIs� in scanning transmissionelectron microscopy �STEM� was extended to allow the two-dimensional �2D� quantitative analysis of cation segregation anddepletion in P�L�ZT thin films. The STEM-EDS SI method allowshigh resolution �� 10 nm� quantification of cation distributions.Zr/Ti and La segregations are found to develop in a decidedly non-planar fashion during crystallization, highlighting the need for 2Danalysis.13 However, sample preparation for TEM and STEM-EDSSI investigations is tedious and time-consuming. Investigation usingother methods such as Rutherford backscattering �RBS� results insample modification or even destruction after analysis. As a nonde-structive technique, spectroscopic ellipsometry �SE� has long beenrecognized as a powerful method for the characterization of thinfilms and their inhomogeneity. SE has already been applied to re-fractive index depth profile studies of oxynitride SiO2Nx films14-17

�additionally confirmed by chemical etching17�, lead silicate glass,18

oxidized copper layers,19 polymers,20 semiconductor indium tin ox-ide films,21,22 and rf-sputtered self-polarized PZT thin films,23 andhas been confirmed by glow discharge optical emission spectros-copy �GD-OES� and pyroelectric profile measurements by the laserintensity-modulation method �LIMM�.24,25 SE has also been appliedto the study of ion implantation depth profiles in silicon wafers andconfirmed by RBS.26,27 The sensitivity of SE was demonstrated ongraded oxygen compositions in YBa2Cu3O7−� �YBCO� thin films, inwhich it was able to detect changes in the oxygen concentration towithin one unit cell.28 SE cannot quantitatively examine cation dis-tribution at a length scale comparable with the feature sizes like inSTEM-EDS SI method13 because the measured area depends on thediameter of the incident light spot of SE �typically �3 mm; byusing focusing nozzles it can be reduced to �0.1 mm�. As a result itis easy to perform relatively large area scans of the sample using SEand evaluate information �for example, depth profile� on an averageacross many features simultaneously. Thus, SE studies give an op-portunity in a nondestructive, rather fast and easy way to analyze theinhomogeneity of material and help to understand how processingaffects structure and thus properties in this system.

In this study, we present results on optical depth profile analyses

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G218 Journal of The Electrochemical Society, 156 �12� G217-G225 �2009�G218

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by SE of sol–gel PbZr0.52Ti0.48O3 �PZT 52/48� thin films made withtwo of the most widely used sol–gel routes, whereby the precursormaterials are the same but the solvents and the preparing procedurediffer. The goal of this work is to investigate whether sol–gel PZT52/48 thin films exhibit a depth profile in their refractive index,which in turn would allow conclusions about chemical compositiongradients. Furthermore, although the chemical composition gradienthas been reported previously, its origin has not been elucidated, andit is not clear if the chemical route or the crystallization process isresponsible for the chemical concentration gradients. The resultsgiven by SE have been validated by X-ray, TEM, and energy-dispersive X-ray �EDX� analysis.

Experimental

Lead zirconate titanate �PZT 52/48� thin films were made by thesol–gel technique using two different solvent systems: a mixture ofacetic acid and methanol �AcOH/MeOH� or 2-methoxyethanol �2-MEO�. The AcOH/MeOH preparation route, developed by Yi,29 wasreported in our earlier work in Ref. 30. To prepare the 2-MEO-basedsol, the route reported in Ref. 9 was applied. The concentrations ofboth sols were adjusted to 0.4 M. The PZT 52/48 films using eithersol were spin-coated onto platinized silicon substrates at 4000 rpmfor 30 s. To crystallize the films, two different thermal profiles wereapplied: all layers crystallized together �LCT� at the same time andeach layer crystallized individually �LCI�. The first profile employedthe deposition of one layer followed by drying at 300°C for 1 min.When the final layer was deposited, the sample was placed on a hotplate at 550°C for 35 min to crystallize. The second thermal profileinvolved individual crystallization of each layer by holding thesample at 300°C for 1 min followed by 550°C for 5 min before thenext layer was coated. The annealing time was sufficient for all filmsto crystallize. For each possible combination of thermal profile andsol, a series of five films was made, with each film having betweenone and five layers. In total, 25 samples were analyzed by ellipsom-etry. The list of samples is summarized in Table I. Samples made atthe same conditions, but with different numbers of layers, aregrouped under the same number. One group of samples was madewith thicker single layers, but the same LCT method was used fordeposition �group 3 in Table I�.

The crystallographic structure and out-of-plane orientation ofeach film was determined by the standard �-2� X-ray diffraction�XRD� method using a Siemens D5005 diffractometer with Cu K�radiation and a Goebel mirror.

Variable angle spectroscopic ellipsometry �VASE� on PZT 52/48films was performed using a J. A. Woollam Co. VASE spectroscopicellipsometer working in rotating analyzer mode. Ellipsometry mea-sures the change in the polarization state of light upon reflection.The ellipsometry results are expressed in terms of � and �, whichreflect amplitude ratio tan � = �rp�/�rs� and phase � = �p − �s of po-larized electromagnetic wave, respectively, and which are related tothe Fresnel reflection coefficients by r /r = tan �ei�, where r , r

Table I. Sample composition, sol–gel solvent, the way of crystalliztemperature of PZT 52Õ48 films.

No. Composition Solvent

15 samplesPZT 52/48

AcOH/MeOH

25 samplesPZT 52/48

AcOH/MeOH

34 samplesPZT 52/48Thick films

AcOH/MeOH

45 samplesPZT 52/48

2-MEO

55 samplesPZT 52/48

2-MEO

p s p s


and �p, �s are the complex Fresnel reflection coefficients and phasesfor p- and s-polarized light, respectively. Primary ellipsometricangles � and � were measured at the spectral range of 230–1200 nm�1.03–5.39 eV� and at incident angles of 55–75° in 5° increments.Additionally, the film substrates were analyzed by ellipsometry toevaluate optical properties of the platinum thin film.

One of the experimental requirements for SE analysis is to fit theexperimental results with an appropriate model. The starting pointfor the fit is a very simple model substrate/thin film that can beextended by assuming the film surface, interface, thickness nonuni-formity, grain effect, and depth profile of optical properties if nec-essary. Various gradient profile models, such as continuous and dis-continuous exponentials, were applied to find the best fit to theexperimental data.31

The model assumed that PZT 52/48 samples consisted of threelayers on the Pt substrate: �i� Interface layer, �ii� PZT film, and �iii�top layer with superficial roughness �a mixture of the void �air� andthe underlying material�. The interface �or intermix between the bot-tom electrode and the film� and surface roughness were described interms of an effective medium approximation �EMA� by the Lorentz–Lorenz equation.32

As the films may have a small lateral thickness gradient, we tookinto account the depolarization of the light, which occurs due to thenonuniformity of the film thickness.33

The Cody–Lorentz �CLO�32,33 and Lorentz oscillators32 were ap-plied to characterize the complex dielectric functions of the PZTthin films and Pt thin film. The explanation of motivation of choos-ing these oscillators to describe the complex dielectric functions ofour materials can be found in Ref. 34 �the Tauc–Lorentz oscillator ispresented in Ref. 34, in which the mathematical and physical con-ceptions are similar to CLO�. Depth profiles of the optical propertieswere modeled by dividing the single layer into slices. The shape ofthe grading profile was characterized using exponential variation�Fig. 1� of the refractive index vs film thickness.31,32 For films with

of the films (LCT or LCI), amount of the layers, and annealing

allization Total layers Annealing

CT1–5

100 nm/layer550°C: 35 min

CI1–5


CT1–4

205 nm/layer300°C: 1 min550°C: 5 min

CT1–5


CI1–5


Final 550°C for 30 min

Figure 1. The optical depth models applied to fit experimental SE data.Continuous lines, exponential variation in n through the film, consideringfilm as a one complete layer. Discontinuous lines, exponential variation in nat each layer of the film. The different shapes of exponent were accom-plished by changing the value of exponent and variation in the refractiveindex.

ation

Cryst

L

L

L

L

L


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no gradient of the refractive index n, or for linearly changing n, theexponent was equal to 1. Variation in the refractive index from thesubstrate to the film surface was adjusted by an exponent greater orsmaller than 1. In this graded model, the fitting parameters are thevalues of the exponent and the variation in n. The optical gradientwas calculated in the wavelength region of 500–900 nm. This is thetransparent region of the samples where the correlation betweenfitting parameters were minimal. In our calculations, the host mate-rials of the PZT 52/48 thin film were considered to be isotropic. Theoptimal values for n, extinction coefficient k, thickness d,d nonuni-formity, roughness, and optical gradient were found by mean squareerror �MSE� procedure for all model minimizations, using softwarepackage WVASE32.

TEM cross-section samples were prepared by mechanical thin-ning, dimpling, and ion milling using 3.8 keV argon ions. Thin-filmstructures were characterized by an analytical electron microscopeJEM 2010F FEG-AEM �TEM� operated at 200 kV acceleratingvoltage. The chemical composition was investigated using a LINKISIS 300 energy dispersive X-ray spectrometer and a Si–Li detector.Bulk ceramic PZT 30/70 samples prepared by the mixed-oxide routeand sintered at 1250°C for 2 h were used as a standard to improvethe accuracy of the quantitative EDXS/TEM measurements.

Results and Discussion

The starting point for the fit of experimental SE data was asimple model substrate/thin film. This model did not agree with theexperiment and thus the model was extended by assuming the filmsurface and thickness nonuniformity. We also took into account theinterface layer between the Pt bottom electrode and the PZT filmbecause Pb excess of 10% was used while preparing sol–gel films tocompensate for the Pb loss during heat-treatment30 that can result inPb interactions with underlying Pt electrodes.11,35 The thickness, thethickness of the interface and top layer, as well as the thicknessnonuniformity of all films evaluated from model fit are summarizedin Table II.

Optical properties of each film �Fig. 2 and 3� were evaluated byfitting experimental ellipsometric data. Experimental data and modelfit are presented in Fig. 4a and b, where films are considered to behomogeneous as a first approach and approximation. This modelgives relatively good agreement between the fit and experimentaldata in the wide spectral range except for in the UV region. This canbe explained by the combination of slight PZT 52/48 anisotropy andinhomogeneous film structure. To estimate this inhomogeneity, morecomplex gradient models were used for further calculations. Unfor-tunately, use of such models together with anisotropic calculations istoo complicated because of too many fitting parameters. Therefore,only the transparent spectral region of PZT 52/48 was taken for ourcalculations, which enabled us to neglect this anisotropy.

Next, the film is considered to be inhomogeneous and so the filmis divided into layers, and the layers into slices. The number oflayers coincides with the number of layers during the sol–gel pro-cessing of the thin films. Each layer is divided into 25 slices. Aremarkable improvement in the fit, following from the considerationof the film with a depth profile, is found for the films of groups 2and 5 �MSE decreased 1.5- to 2.5-fold, Fig. 4�. The improvement ofthe fit due to the simple graded model is shown in Fig. 4c and d. Forother films, the graded model does not yield any improvement, ex-cept for the one layer PZT 52/48 thin film from group 1; this can beexplained by the residual stress in the single layer film. Incorporat-ing the model of porosity, grain boundaries, and EMA �film as anoninteracting mixture of compounds with different optical proper-ties� does not yield any improvement to the fit in any of the films,proving the graded model to be an appropriate solution to experi-mental data fitting. The refractive index depth profiles are presentedat the wavelength of 700 nm �or 1.77 eV�. The characteristics of theoptical gradient at other wavelengths �500–900 nm� are similar; thedifference is only in the value of the refractive index due to thedispersion law. Because the optical properties of the Pt bottom elec-trode are evaluated and also the interface layer between Pt and PZT


thin films is taken into account, the influence of inaccurate substrateoptical properties on SE data fitting of PZT 52/48 thin films isminimized.

Among all analyzed samples, the refractive index gradient wasfound only for two groups of films, which were made by crystalliz-ing each layer before another layer was deposited �LCI�. One groupof films was made using the AcOH/MeOH sol �group 2 from two tofive layers, Fig. 3a� and the other group was made with the 2-MEOsol �group 5 from two to five layers, Fig. 3b�. For the former samplegroup, the simple model, where the film is considered to be a singlecontinuous layer and the refractive index exponentially either in-creases or decreases with the thickness, does not yield any improve-ment to the fit. The model is complicated for films with a gradientprofile assumed to change from layer to layer �Fig. 3a�. The gradientis different for all films, from two layers to three layers up to fivelayer films. This is most likely due to the recurrent annealing ofalready crystallized layers. If we look at the optical properties ofthese samples �Fig. 2a�, they vary from film to film as well. For allfilms, the first layer has no gradient, and only at the interface to thenext layer there is a sharp jump of n�d�. n�d� decreases throughoutthe second layer for two layer films. The third layer shows a slightincrease in n�d�, but after adding the fourth layer �in this layer n�d�slightly increases�, the second and third layers converge and n�d�has the same shape as in the second layer of films that only have twoor three layers. Adding a fifth layer does not change the n�d� shapesin layers one to four.

The confidence of the fit is satisfactory, allowing consideration ofthe direction of n�d� gradient variation, for example, its increase ordecrease throughout each layer. However, the fit does not allowaccurate conclusions about the magnitude of the increase or de-crease in n�d� within films having more than two layers.

The refractive index depth profile was also found for PZT 52/48films made with 2-MEO sol and with individually crystallized layers

Table II. Thickness of the interface between bottom electrode andfilm (nm), thickness of the film d (nm), thickness of the top layer(roughness, nm), and thickness nonuniformity (%).

No.Interface

�nm�d

�nm�Top�nm�

Uniformity�%�

1 0 108 5.5 3.61.2 208 8.5 11.5 314 10.1 1.52.7 408 12.7 2.74.1 532 13.5 1.5

2 0 107 6.7 1.50 212 2.5 1.5

9.9 326 2.1 1.65.9 410 3.5 1.56.9 536 2.7 1.5

3 1.9 207 6.9 1.50.5 408 4.8 1.51.4 625 3.2 1.50.8 819 4.9 1.5

4 2.2 67 1.9 00 137 2.6 1

0.7 205 3.3 1.50.9 272 1.7 1.52.8 342 1.2 1.5

5 3.2 68 1.8 00.1 127 4.9 10 193 4.9 1.5

0.6 263 3.8 1.50.8 327 4.5 1.5


Nr 2 and 5.


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�group 5 from two to five layers�. The trend of refractive index withdepth generally has a square root behavior �Fig. 3b�. There can beseveral reasons for this, such as residual stress in the film, concen-tration gradients of Ti or Zr with the layer, or an increase in excessPb.9 The experimental data fitting is satisfactory when a single con-tinuous layer is considered irrespective of the number of layers dur-ing film deposition. As a result, the confidence �Table II� regardingthe direction of n�d� and the amount of n�d� increase is very high.However, it is not possible to say whether there are some “breaks”in n�d� at the interfaces between PZT 52/48 thin-film layers. Such amodel was also used for fitting and agreed well with experimentaldata, but due to the increase in fitting parameters and consequentdecrease in confidence, the simple model is more advantageous. Oneexception is the case of PZT 52/48 films of group 2, where thesimple model does not yield any improvement to the fit, which isopposite to the findings from PZT 52/48 of group 5. The complexityof the graded model for group 2 is because these samples do nothave an additional final annealing step, while the group 5 samplesdo.

A depth profile that shows increasing refractive index with in-creasing thickness �Fig. 3b� can be explained by a polarization pro-file that is strongly dependent on film thickness: Polarization is ho-mogeneous in the greater part of the thick film except in smallregions at the film boundaries, while it is completely inhomoge-neous in thin films. The degree of polarization inhomogeneity in-creases with decreasing thickness.36 The theory of polarizationthickness dependence36 and the optical depth profile evaluated byellipsometry agree well for rf-sputtered self-polarized PZT thinfilms, which later was verified by GD-OES and pyroelectric profilemeasurements by the LIMM.24,25

The n�d� in the films of group 5 slightly decreases with increas-

Figure 3. Depth profile at 700 nm for the samples with different numbers oflayers made using �a� AcOH/MeOH and �b� 2-MEO sol.

Figure 2. �Color online� Refractive index n and extinction coefficient k as afunction of the photon energy for samples with different numbers of layersfrom one to five �thicknesses can be found in Table II� of the group with �a�Nr 1,2. and 3, �b� Nr 4 and 5, and for comparison of �c� Nr 1 and 4 and �d�



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ing number of layers �Fig. 3b�. This agrees with the evaluated opti-cal properties of the host material of PZT 52/48 of group 5 �Fig. 2b�,where the refractive index also slightly decreases �starting from twolayers� with increasing number of layers. The refractive index ofgroup 5 is higher than that of group 4 samples �Fig. 2b�. The sametrend is detected for films of groups 1 and 2 �Fig. 2a�. If each layeris individually crystallized, we may expect an increase in crystallin-ity of the film due to the repeated annealing, which can result in ahigher refractive index. However, if we compare samples made withdifferent sols but crystallized in the same way �compare group of


samples 1, 4, and 2, 5�, the refractive index is higher for films madewith AcOH/MeOH sol than for films made by 2-MEO sol �Fig. 2cand d�.

In the next step, we look at the XRD data of all samples toinvestigate whether the gradient in refractive index could be ex-plained by orientation differences between films. The XRD resultsfor the AcOH/MeOH LCI samples �Fig. 5a� show a dominant�001�/�100� orientation. �111� peaks were observed in samples withthree or more layers; however, the intensity of these peaks is rather

Figure 4. �Color online� Experimental�collared discontinuous line� and modeled�collared and gray continuous line� ellip-sometric angles � ��b� and �d�� and � ��a�and �c�� at the whole spectral region of230–1000 nm and at five incident anglesof 55–75° to estimate the optical proper-ties of the host material of the PZT 52/48�five layers, made by 2-MEO sol, LCI�,thickness of the film, roughness, interface,and thickness nonuniformity ��a� and �b��;the spectral region of 500–900 nm is fittedby applying exponential-graded model��c� and �d��.

Figure 5. �Color online� The XRD of theLCI samples �groups 2 and 6 from TableI�: �a� X-ray diffractograms of AcOH/MeOH films, �b� magnification of the�002�/�200� peak from �a�, �c� X-ray dif-fractograms of 2-MEO films, and �d� mag-nification of �002�/�200� from �c�.



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small compared to �100� peaks. Also, some pyrochlore was detectedfor this group of samples, indicating that the samples were not com-pletely crystallized even after the additional annealing for 30 min at550°C. A shift in the �001�/�100� peak doublet toward smaller 2�angles was observed, indicating a change in stress with increasingnumber of layers �Fig. 5b�. In the first layer, the lattice parameterequaled 0.4052 and 0.4037 Å for �002� and �200�, respectively. Thislattice spacing increased with increasing number of layers up to0.408 and 0.4047 Å, respectively. This is equivalent to an elongationof 0.7%.

The films made with 2-MEO sol but with the same routineshowed more mixed orientation, with the �111� peaks appearing onlyin samples with three or more layers, Fig. 6b. The first two samples�with one and two layers� were strongly �001�/�100�-oriented. Tak-ing into account that the crystallization process is identical for onelayer films made using either the LCI or LCT routines, thesesamples are excluded from the following discussion and are men-tioned at a later stage. For all other films, it can be concluded thatthe nucleation and PZT crystallization are strongly dictated by thesubstrate due to the lattice match between PZT�111� and Pt�111�.Because the films were crystallized only when the last layer wasdeposited, the samples do not represent a sequential change in ori-entation with increasing number of layers, but rather, each samplestands on its own, showing the influence of the total film thicknesson film crystallization.

However, it seems that crystallization using the LCI routine,where each layer is completely crystallized before the deposition ofthe next layer, causes pronounced changes in the optical properties

Figure 6. �Color online� X-ray diffractograms for samples crystallized usingthe LCT method for �a� ACOH/MeOH films and �b� 2-MEO films.


of group 2 films �Fig. 3a�. In the next step, we take a closer look atthe crystallization of these films. These films exhibit a strong�001�/�100� orientation, but with increasing number of layers, otherpeaks such as �111� appear. The growth of PZT 52/48 films with a�100� orientation when pyrolyzed at 300°C was reported earlier byMarshall et al.37 using an AcOH/MeOH sol and the LCI method.The �100� nucleation on the Pt�111� substrate is likely to take placein the presence of high lead excess and in the pyrolysis temperaturerange between 300 and 350°C. The competing nucleation ofPZT�111� is hindered due to high PbO content and is only enabled athigher temperatures where PbO volatility is increased. Thus, oncethe PbO is removed from the film, the formation of the intermetallicphase Pb3Pt that facilitates the �111� nucleation is enabled, as ob-served on PZT 30/70 films.35

Based on the XRD results from films crystallized using the LCImethod, we obtain a picture of how the orientation of the filmchanges when more layers are added, assuming a reproducible ori-entation. Thus, when processing the films using the LCI method,only the first layer crystallizes directly on the Pt substrate and allsubsequently deposited layers crystallize on top of PZT 52/48. Be-cause the thermal profile used assures a �100� orientation of the film,we would expect the first layer to be �100�-oriented, as well as allsubsequently deposited layers, because the last layer also crystal-lizes on �100� PZT. Nevertheless, both groups of PZT 52/48 filmsprocessed with the LCI method in fact exhibit some �111� orienta-tion for films with more than three layers. The appearance of the�111� orientation can only be explained if some excess of PbO aftercrystallization is assumed, located close to the surface, as recentlyreported by Brennecka et al.38 Indeed, some pyrochlore was foundfor all LCI films made with AcOH/MeOH sol. It is thus possible thatafter the deposition of the next layer, the residual pyrochlore in-duced nucleation and growth in the �111� direction, consuming theuncrystallized matrix and accounting for the appearance of the �111�orientation at later stages within the first layer. Considering the workof Brennecka et al., the uncrystallized pyrochlore phase was mostlikely the lead-deficient fluorite phase, which was also accompaniedby a compositional gradient of Pb/Zr through the layer thickness intheir work. This point is further discussed at a later stage.

The stress is different for each sample from the same LCI group,taking the Stoney relationship for stress dependence of filmthickness.39 Initial high tensile stress in thin films, which decreasesupon further layer deposition, was observed previously for PZT52/48 films.40,41 The reduction in initially high tensile stress withincreasing thickness correlates to the observed peak shift towardsmaller 2� in the XRD. The peak shift indicates the increase inlattice spacing in the out-of-plane direction, which is likely to beaccompanied by a decrease in lattice spacing in plane. However, ourdata are rather limited and do not allow conclusions as to whetherinitially high tensile stress �in plane� decreased or whether it furtherincreased upon deposition of more layers. It was observed earlierthat the presence of pyrochlore is accompanied by large tensilestress. The presence of stress and the variation in stress with filmthickness are reflected in the variation in lattice parameters for eachfilm.

Although both groups of PZT 52/48 films made with LCI pro-cessing showed a pronounced �001�/�100� orientation, there weredifferences between the two groups based on the shift of�002�/�200� peaks. The peak shift of 2-MEO films is due to themore pronounced tetragonal split with increasing numbers of layers,suggesting that with increasing numbers of layers, and thus heat-treatments, stress relaxation, defect healing, and improvement ofcrystallographic structure can occur in each underlying and alreadycrystallized layer. The c/a ratio for these films is 1.008, which is thehighest between all groups of films. The 2-MEO films were also allcompletely crystallized.

As in LCI AcOH/MeOH thin films, the XRD patterns of 2-MEOfilms also show a predominant �001�/�100� orientation �Fig. 5c�.However, the peak position shift is different, Fig. 5d. For 2-MEO



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films, the �002� peak shifts to smaller 2� angles, whereas the �200�peak shifts to higher 2� angles; in other words, the peaks drift apartfrom each other, Fig. 5b and d. This indicates that the tetragonalsplit �002�/�200� increases with increasing film thickness and ishence more pronounced. The crystallinity of the films improves withincreasing thickness.

No optical gradient is found for films with different numbers oflayers when all layers are crystallized at the same time, regardless ofthe sol used. This was also confirmed for films from group 3 madewith thicker layers. The groups of films made with AcOH/MeOH soland by the LCT routine �groups 1, 3, and 4� show a strong �111�orientation with some low intensity peaks of other orientations, suchas �110�, �112�, or even �001�/�100�, except for the one layer filmfrom group 1, Fig. 6a. The latter film was highly�001�/�100�-oriented.

Thus, in pinpointing the cause of the detected optical gradient,any change in orientation with the number of layers can be elimi-nated based on the consideration that the films made with the LCTmethod showed more mixed orientation among the samples, and yetno optical gradient was found for these films. Moreover, the opticalgradient was found in films made with the LCI route, where a strongvariation in lattice parameter with increasing thickness was found,even though the type of gradient was dependent on the sol used.

However, it was reported that the refractive index decreases withdecreasing Ti/Zr concentration.42,43 Likely, the appearance of thedepth profile for the LCI films is connected with the fact thatPbTiO3 �PT� crystallizes before PbZrO3 �PZ�, as can be seen in Ref.44, while crystallizing layers together may avoid preferential PT andPZ crystallizations. Better quality PZT 52/48 composition thin filmscan be made by annealing the films at higher temperatures usingrapid thermal annealing �RTA� or oven, or to have a different Zr/Ticoncentration ratio in each layer with the goal to anticipate the se-lection and diffusion processes.12 RTA usually needs full crystalli-zation at �650°C, but in this study we chose an annealing tempera-ture at 550°C on a hot plate so that the crystallization of the filmsstarted at the interface of Pt/PZT and grew up to the top rather thancrystallizing the films in an oven/RTA, which would lead to crystal-lization from everywhere and smear the possible formation of gra-dient in composition. This use of low annealing temperature leads tothe formation of pyrochlore, particularly in the films of LCI �Fig. 5aand 6a�.

Thus, there are two possible origins of the refractive index gra-dient n�d�. The first is the above-mentioned polarization inhomoge-neity close to the film surface, and the second is the varying Zr/Tiratio and Pb throughout the layer. The latter two can be attributed tothe separate crystallization of each layer, causing the diffusion of Pb,Ti, and Zr ions in the film. The work of Ledermann et al.9 showedthat sol–gel PZT thin films are Ti-rich closer to the substrate andZr-rich closer to the surface, as well as that the concentration of Pbdirectionally increases from the substrate to the surface. If we ex-trapolate this to the optical properties according to the fact that nincreases with decreasing Zr/Ti ratio,3 then we can say from Fig. 3bthat the Zr/Ti ratio decreases directionally from the substrate to thesurface, which is opposite to the observations of Ledermann et al. byTEM. However, sol–gel thin films may have higher concentrationsof Pb at the surface.9,11,45 The experiments of Watts et al.45 andImpey et al.11 suggest that the diffusion of lead to the surface in PZTfilms results from the oxidation of the Pb or from kinetic demixing,both of which would be favored by an incomplete oxidation of thefilm during deposition. Pb2+ diffusion may also lead to self-polarization, which causes the polarization inhomogeneity.36 Due tothe proportionality of the refractive index to the square of the spon-taneous polarization,46 the inhomogeneity of the film can be de-tected as a refractive index depth profile.24,25 Notic that any changein the sample structure affects the polarization and optical propertiesof the material, irrespective of whether it is a result of the stoichi-ometry, compositional gradient, internal stresses, etc. Optical meth-ods such as ellipsometry allow estimation of the film homogeneity


in a nondestructive way without specific requirements of samplepreparation, which is an advantage of ellipsometry over such meth-ods as scanning tunneling microscopy or TEM.

Nevertheless, EDXS/TEM analysis was performed on twosamples from groups 1 and 2, made with AcOH/MeOH sol and byLCI �Fig. 7a and b� and LCT �Fig. 8a and b�, respectively. Bothsamples had three layers deposited. The film �made by LCI� crosssection, presented in Fig. 7a, shows fine grains of a pyrochlore phasebetween perovskite crystallites throughout the film thickness. A py-rochlore layer about 50 nm thick was found at the surface of thefilm. This film had a strong optical gradient. These results are inaccordance with the XRD analysis �Fig. 5�. The EDXS resultsshowed a strong variation in Pb and Zr concentrations throughoutthe thickness of the film �Fig. 7b�. Close to the surface where thepyrochlore layer was observed, a strong reduction in lead concen-tration and an increase in zirconium concentration were detected.The titanium concentration was not much affected by the phaseseparation. Due to the similarities in the sol composition and pro-cessing between our work and the work of Brennecka et al., it canbe concluded that this sample shows the same two-phase structurereported by Brennecka et al. within each layer, whereby the lead-deficient upper layer causes a compositional gradient.

In Fig. 8a, the cross section of the PZT 52/48 �LCT� film withcolumnar grains and additional �10 nm thin pyrochlore layer on thesurface is shown. This film had no optical gradient. No Py wasdetected by XRD analysis due to its low amount �see Fig. 6�. Asshown in Fig. 8b, a more uniform EDXS concentration profile wasobtained in comparison to Fig. 7b.

The results obtained by EDXS agree well with the optical dataevaluated by SE �Fig. 8b�. There are almost no changes in variationin Pb, Zr, and Ti near the substrate of the film, which is reflected inoptical analyses in the linear dependence of n�d�. A significant de-crease in Pb and increase in Zr can be seen in the optical data as adecrease in n�d�. Near the surface, n�d� starts to increase, which

Figure 7. �a� TEM micrograph �dark field� of a cross section of the LCI film,showing pyrochlore phase �Py� between and on the surface of the PZTgrains. �b� EDXS profile performed on the PZT grain from the substrate tothe film surface in comparison with the optical depth profile n�d� establishedby SE.



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agrees with results obtained by Deineka et al.24 from perovskite/pyrochlore PZT thin-film stacks. A slight difference of �50 nm be-tween shift of the EDXS and SE results is due to the inhomogeneityof the film; there is a Py distribution even within the grains of thefilm, and EDXS measurements could not be performed at the samelocation in the sample where SE experiments were evaluated. Toimprove our SE calculation for these films with complex opticalgradients, the films should be considered as media of two materials�EMA model�, PZT 52/48 and Py, where the PbTiO3 and PbZrO3concentrations change within a PZT film. Such complex calculationscan be obtained from SE experimental data if additional SE mea-surements are made on samples of pure Py, PbTiO3, and PbZrO3films �prepared by the same method as PZT films� to extract theiroptical properties. Nevertheless, by applying a simple exponentialgradient model to experimental SE data analysis, reasonable quali-tative data can be obtained, which gives an idea of the quality of thesample, its optical properties, optical gradient, and homogeneity.Moreover, these qualitative SE analyses are in accordance with re-sults obtained with other methods, in this case, EDX and ERD.Thus, the SE method offers the opportunity to accomplish opticalanalyses of thin films in a simple, fast, precise, and nondestructiveway, as well as acquire reasonable results and obtain justified infor-mation about the quality of thin films.

The refractive index gradient of the PZT 52/48 thin films madefrom AcOH/MeOH by LCI is different from those reported. Therefractive index gradient does not smoothly increase with the thick-ness �Fig. 3a�, as it does, for example, in Ref. 24 and 25, which wasexplained by the presence of pyrochlore.

Other depth profiles of sol–gel PZT that have been reported. In

Figure 8. �a� TEM micrograph �bright field� of a cross section of the LCTfilm, showing pyrochlore phase �Py� on the surface of the PZT grains con-sidered as the top layer of the roughness �10 nm in SE calculations. �b�EDXS profile from the substrate to the film surface.


the work of Etin et al.10 the origin and effects of compositionalgradients in PZT films prepared by two sol–gel precursor formula-tions were investigated. The difference between the two formula-tions is the stabilization of the zirconium precursor: �i� Zr precursoris chemically stabilized with AcOH or �ii� Zr is stabilized withacetylacetonate �AcAc�. Formulation �i� led to opposite concentra-tion gradients of Zr �increasing� and Ti �decreasing�, while formu-lation �ii� gave rise to constant Zr and Ti concentrations throughoutthe films. This paper also proves that variation in Zr/Ti ratio in PZTfilms originates early in the crystallization process. These variationsare caused by a mismatch in the thermal decomposition of the indi-vidual Zr/Ti components in the PZT precursor. Once created, thecompositional gradients cannot be eradicated by prolonged heat-treatments. Despite the difficulty of comparing our work with thework of Etin et al. due to the use of different initial solutions, thesegradient studies show that selection of precursors �chemical sol-vents� and processing parameters �drying temperatures and time,crystallization temperature and time, etc.� for the deposition of sol–gel films is influential in controlling the homogeneity of the films.

Conclusion

In summary, investigation using SE reveals the influence ofsample preparation conditions on film homogeneity. The film inho-mogeneity is analyzed by spectral ellipsometry with various appro-priate models including EMA �considering the film as a mixture oftwo materials with different optical properties� and optical gradient�refractive index changes within the film�, while taking the top layerof the films into account. The best fit is found by considering thefilm to have continuous or discontinuous exponential growth of re-fractive index within the film.

The depth profile of the refractive index is established for PZT52/48 thin films made with LCI, irrespective of the chemical solventtype. The analysis of the XRD results of PZT 52/48 films made withLCI shows that these films have a preferred orientation of�001�/�100� in contrast to the films made with LCT, which shows apredominant �111� orientation and no gradient in optical properties.A more refined analysis has shown that a refractive index gradientwas apparent in the samples in which lattice parameters stronglychange with thickness. For these films, EDX analysis showed sig-nificant variation in Pb and Zr.

It can be said that separate crystallization of the layers deter-mines the gradient appearance, irrespective of the chemical solventsused in this work. The smooth increase in refractive index withthickness for the films of group 5 is more likely due to differentcompositions, such as a decrease in Zr/Ti ratio and/or directionalincrease in Pb from the substrate to the film surface accompanied byhigh stress. The complex depth profile of samples of group 2 isexplained by the existence of the lead-deficient fluorite phase be-tween the perovskite crystallites in the layer at the top of the filmand by the variation in Pb and Zr within the film.

Higher values of refractive indexes and lower values of extinc-tion coefficients are established for the PZT films made with AcOH/MeOH solvent, suggesting that these films have better quality interms of density, which may lead to better electrical properties, suchas higher dielectric and piezoelectrical properties. The SE investiga-tions determine that the AcOH/MeOH and 2-MeO chemical synthe-sis routes are not responsible for the gradient appearance and thatthe gradient is mostly formed during the crystallization process.

These qualitative SE analyses are in accordance with results ob-tained with other methods, in this case, EDX and XRD. Thus, theSE method offers the opportunity to accomplish quality analysis ofthin films in a relatively simple, fast, and nondestructive way.

Acknowledgments

This research was done within the 6th Framework Program ofthe Multifunctional and Integrated Piezoelectric Devices �MIND�.This work is supported by the European Social Fund and UNESCOLÓREAL Latvian National Fellowship for Woman in Science, andgrant no. 202/09/J017 and no. AV0Z10100522. We express our



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gratitude to Sebastjan Glinsek for TEM sample preparation. Thefinancial support of EPSRC �U.K.� �EP/EO35043/1� is also grate-fully acknowledged.

Academy of Science assisted in meeting the publication costs of thisarticle.

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Documents

Formation of Optical Gradient in Chemical Solution-Derived PbZr[sub 0.52]Ti[sub 0.48]O[sub 3] Thin Films: Spectroscopic Ellipsometry Investigation