DOI: 10.1007/s00339-004-2770-3

Appl. Phys. A 80, 229–235 (2005)

Materials Science & ProcessingApplied Physics A

a. visinoiu�

r. scholzm. alexed. hesse

Morphology dependence of the dielectricproperties of epitaxial BaTiO3 filmsand epitaxial BaTiO3/SrTiO3 multilayersMax Planck Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany

Received: 14 August 2003/Accepted: 12 March 2004Published online: 30 June 2004 • © Springer-Verlag 2004

ABSTRACT Epitaxial BaTiO3 films and epitaxialBaTiO3/SrTiO3 multilayers were grown by pulsed laserdeposition on vicinal surfaces of (001)-oriented Nb-dopedSrTiO3 (SrTiO3 : Nb) single-crystal substrates. Atomic forcemicroscopy was used to investigate the surface topographyof the deposited films. The morphology of the films, of theBaTiO3/SrTiO3 interfaces, and of the column boundarieswas investigated by cross-sectional high-resolution transmis-sion electron microscopy. Measurements of the dielectricproperties were performed by comparing BaTiO3 films andBaTiO3/SrTiO3 multilayers of different numbers of individuallayers, but equal overall thickness. The dielectric loss saturatesfor a thickness above 300 nm and linearly decreases with de-creasing film thickness below a thickness of 75 nm. At the samethickness of 75 nm, the thickness dependence of the dielec-tric constant also exhibits a change in the linear slope both forBaTiO3 films and BaTiO3/SrTiO3 multilayers. This behaviouris explained by the change observed in the grain morphologyat a thickness of 75 nm. For the thickness dependence of the di-electric constant, two phenomenological models are considered,viz. a ‘series-capacitor’ model and a ‘dead-layer’ model.

PACS 77.22.-d; 77.22.Ch; 77.55.+f; 77.22.Gm; 77.84.Dy;81.15.-z; 81.16.Mk; 81.65.-b; 68.55.-a; 68.37.-d

1 Introduction

BaTiO3 and Ba-rich solid solutions of (Ba, Sr)TiO3

are attractive in applications due to their large dielectric per-mittivity at T > Tc (where Tc is the ferroelectric transitiontemperature), a sufficiently low temperature dependence ofthe remanent polarization at T < Tc, a moderate coercive field,and a large electro-optic coefficient. One of their most promis-ing applications is their use as a high-ε dielectric layer withinstorage capacitors for high-density dynamic random accessmemories (DRAMs).

Generally, dielectric and ferroelectric superlattices offera promising approach to create new ferroelectric materialsand to study the origin of their remarkable properties. For ex-ample, BaTiO3/SrTiO3 superlattices show a large increase of

� Fax: +1-434/9244576, E-mail: visinoiu@virginia.edu

the dielectric constant and a larger optical non-linearity com-pared to BaTiO3 films [1, 2]. The tetragonality and the fer-roelectric distortions of BaTiO3 can be enhanced in strainedsuperlattices by the help of the mismatch between BaTiO3

(tetragonal lattice parameters at room temperature: a = b =0.3994 nm and c = 0.4038 nm) and SrTiO3 (cubic lattice pa-rameter ac = 0.3905 nm) [3, 4]. The properties of such su-perlattices are sensitive to the thickness of each layer andalso to the microstructure and the morphology of the inter-faces. Therefore, a control of the microstructure at an atomicscale and the characterization of the surface and the interfacesare particularly important. A well-defined control of the mi-crostructure of a superlattice, however, also requires insightinto the initial growth stages of the involved thin-film materi-als. Microstructure and morphology also play, however, a rolein determining the dielectric behaviour.

In this paper, the dielectric properties and the morphologyof epitaxial BaTiO3 films and BaTiO3/SrTiO3 multilayersare studied to elucidate structure–property relations in thissystem.

2 Experimental

Epitaxial BaTiO3 and SrTiO3 films were grown on(001)-oriented SrTiO3 : Nb substrates by pulsed laser deposi-tion (PLD). A KrF excimer laser (λ = 248 nm) was focusedonto a ceramic BaTiO3 or SrTiO3 target, respectively, locatedin a vacuum chamber. The optimum deposition conditionsturned out to be identical for the two materials (Table 1).They were obtained by varying the substrate temperaturefrom 550 ◦C to 750 ◦C, the oxygen pressure from 0.1 mbarto 0.4 mbar, and the energy fluence at the target surface from2 to 4 J/cm2 for each of the two materials. The films werecooled after deposition in vacuum at a pressure of 10−6 mbar.During deposition of multilayers, the vacuum was not inter-

Target– Deposition Oxygen Laser Laser Lasersubstrate temperature pressure fluence at energy repetitiondistance target surface rate

6 cm 700 ◦C 0.2 mbar 3 J/cm2 600 mJ 1 Hz

TABLE 1 Deposition conditions for BaTiO3 and SrTiO3 used in thepresent study

230 Applied Physics A – Materials Science & Processing

rupted. The surface topography of the deposited films was in-vestigated by atomic force microscopy (AFM) using a DigitalInstruments 5000 microscope working in tapping mode withultra-sharp silicon tips. Morphology and microstructure ofthe films and interfaces were investigated by cross-sectionalhigh-resolution transmission electron microscopy (TEM) ina JEOL 4010 electron microscope at a primary beam energy of400 keV. In order to perform electrical measurements, Pt topelectrodes with 100 nm thickness and 0.15 mm diameter weredeposited by rf sputtering through a metallic mask. Electricalcharacterization was performed using a TF Analyzer 2000 fer-roelectric tester (AixACCT) and a Hewlett Packard HP 4195Aimpedance analyser. C–V measurements were carried out byapplying an ac signal with an amplitude of 10 mV at 1 MHz,while a dc bias was swept at a rate of 0.2 V/s from 0 to Vmaxand vice versa with a delay time of 0.5 s.

3 Results and discussion

The surface state of the substrate has an importantinfluence on the early stages of film growth. In order to prop-erly study the growth mechanism, a well-defined substratesurface is required. Therefore, (001)-oriented SrTiO3 : Nbsingle-crystal substrates with a miscut angle of 0.1◦ were sub-jected to a specific chemical and thermal treatment in orderto obtain vicinal surfaces with atomically flat terraces. Thedetails of the substrate preparation and the effects of etchingand annealing treatment, respectively, on the final substratesurfaces have been discussed in detail elsewhere [5]. Themorphology of the SrTiO3 substrates before deposition con-sists of single TiO2-terminated surface terraces with regularand sharp edges (Fig. 1).

3.1 Morphology of epitaxial BaTiO3 films

Epitaxial BaTiO3 films with nominal thicknessfrom 1 nm to 1 µm were deposited onto the chemically andthermally treated vicinal SrTiO3 : Nb substrates. The nomi-nal thickness is defined as the typical thickness the film wouldhave if it would grow in the layer-by-layer mode, thus beinga measure of the amount of deposited material. The surfacesof the deposited films were studied by AFM and their struc-ture by cross-sectional high-resolution TEM. The results ofthese investigations were described previously [5] and can besummarized as follows.

In the early growth stage, a very thin, complete layer uni-formly covers the substrate surface at 1 nm nominal thicknessof the BaTiO3 thin film. The film/substrate interface is welldefined and sharp.

FIGURE 1 AFM topography image (2×2 µm2 area) and schematic draw-ing of a vicinal SrTiO3 : Nb substrate surface prepared by chemical andthermal treatment

At 5 nm nominal thickness, small islands nucleate on topof the previous uniform wetting layer (Fig. 2a). The RMSroughness of the terraces’ surface suddenly increases from0.16 nm for the 1-nm-thick film to 0.847 nm for the 5-nm-thick film. The height of the individual islands is about 3 nm,and they have a lateral size in the order of 5 nm. A sharp andwell-defined film/substrate interface was revealed by TEM(Fig. 2b). Obviously, at a thickness of about 5 nm individ-ual islands begin to grow, resulting in a layer-then-island(Stranski–Krastanov) growth mechanism [5].

Further on, the density of these small islands increases.No further drastic changes in the morphology of the films

FIGURE 2 AFM topography image (0.5 × 0.5 µm2 area and 5 nm inheight) (a) and cross-sectional high-resolution TEM image (b) of a nominally5-nm-thick BaTiO3 film

FIGURE 3 AFM topography image (0.5 × 0.5 µm2 area and 30 nm inheight) of a nominally 75-nm-thick BaTiO3 film (a) and cross-sectional TEMimage of a 150-nm-thick BaTiO3 film (b)

VISINOIU et al. Dielectric properties epitaxial BaTiO3 and multilayers 231

were observed on increasing the film thickness up to a nom-inal value of 75 nm, when some of the islands start togrow in size and incorporate the surrounding islands, i.e.small islands coalesce together into larger ones. At thisstage of growth, large round islands form the topogra-phy of the BaTiO3 film (Fig. 3a). Their height varies from10 to 25 nm, while their lateral size increases to about50–100 nm.

With a further increase of the film thickness, the larger is-lands develop into a columnar structure (Fig. 3b), as describedin detail in [5]. A column-like structure is often observedin laser-ablated epitaxial thin films of complex oxides (e.g.Pb(ZrxTi1−x)O3 [6] or YBa2Cu3O7−δ [7]).

3.2 Morphology of epitaxial BaTiO3/SrTiO3multilayers

The AFM and TEM analyses of a sequence ofBaTiO3/SrTiO3 multilayers of different overall thicknessesmostly show similar features as for the epitaxial BaTiO3 films.The results of these analyses were reported elsewhere [8] andcan be summarized as follows.

In the early stages of epitaxial BaTiO3/SrTiO3 multilayergrowth, BaTiO3 forms one or several complete monolay-ers on the substrate surface. Subsequently, three-dimensionalclusters nucleate on the continuous layers, probably dueto the stress induced by the lattice mismatch at 5 nm indi-vidual thickness of the BaTiO3 layers in a BaTiO3/SrTiO3multilayer system (Fig. 4a and b) The cross-sectional high-resolution TEM image shows the beginning of BaTiO3 is-land formation (arrows) on a uniform, continuous BaTiO3

layer of about 3 to 4 nm in thickness on top of a 5-nm-thickSrTiO3 layer. This observation is an indication for a Stranski–Krastanov growth mechanism followed by the BaTiO3 layersgrowing on the deposited SrTiO3 layers.

Further on, at about 75 nm thickness, islands becomelarger due to coalescence, and later a columnar structure ofboth BaTiO3 and SrTiO3 layers is developed (Fig. 5a). In thediffraction pattern of a thick multilayer system with about200 nm thickness of the individual layers taken from a sampleregion around the BaTiO3/SrTiO3 interface, the reflectionsof BaTiO3 and SrTiO3 are well separated, indicating a well-relaxed state of the BaTiO3 lattice (Fig. 5b).

The morphology of the BaTiO3-on-SrTiO3 interfaces isdifferent from that of the SrTiO3-on-BaTiO3 interfaces. Thisphenomenon was also discussed in [8].

FIGURE 4 AFM topography image (0.5 ×0.5 µm2 area and 3 nm in height) (a) andcross-sectional high-resolution TEM image(b) of an epitaxial BaTiO3/SrTiO3/BaTiO3multilayer system of 15-nm overall thickness(5-nm nominal thickness of each layer)

FIGURE 5 Cross-sectional TEM image (a) and diffraction pattern (b) takenfrom an epitaxial BaTiO3/SrTiO3 multilayer grown on a SrTiO3(001) sub-strate. The thickness of the individual BaTiO3 layers is about 260 nm and thatof the individual SrTiO3 layers is about 210 nm

3.3 Dielectric properties

Dielectric measurements were performed on Pt/BaTiO3/SrTiO3 : Nb and Pt/BaTiO3/ . . . /SrTiO3/BaTiO3/

SrTiO3 : Nb heterostructures with different thicknesses of theindividual BaTiO3 and SrTiO3 layers. The dependence of thedielectric constant, ε, and the dielectric loss tangent, tan δ, onthe BaTiO3 film thickness is shown in Fig. 6a. Both ε and tan δ

show an approximately linear dependence on the BaTiO3 film

232 Applied Physics A – Materials Science & Processing

FIGURE 6 Thickness dependence of the dielectric constant and the dielec-tric loss tangent measured on Pt/BaTiO3/SrTiO3 : Nb heterostructures fordifferent thicknesses of the BaTiO3 film. The lines are only to guide the eye(a). Dependence of the effective dielectric constant (b) and of the dielectricloss tangent (c) on the overall thickness of two series of BaTiO3/SrTiO3 mul-tilayers and for BaTiO3 films. Dielectric measurements were carried out atroom temperature by applying an ac signal with an amplitude of 10 mV at1 MHz

thickness, however with two different slopes above and belowa thickness of 75 nm.

It is interesting to note that the dielectric loss almost sat-urates for thicknesses above 200–300 nm (Fig. 6b), while itabruptly decreases below a thickness of 75 nm. This thicknessrepresents the turning point at which the dielectric constantalso changes its thickness dependence. Consequently, this

points to a common origin of both effects. A close lookat the AFM and TEM results shows that at this thicknessthe morphology of the BaTiO3 films changes from a small-grained structure into larger grains or columns by coales-cence, as was shown previously. The same turning point at75 nm is also present in the thickness dependence of thedielectric constant measured on BaTiO3/SrTiO3 multilay-ers. The dielectric loss tangent of the multilayers saturatesfor a thickness above 200–300 nm (Fig. 6c), while belowan overall thickness of 75 nm the dielectric constant lin-early decreases with decreasing overall thickness, and thisbehaviour is independent of the number of multilayers, point-ing to some interface effect. Somewhat larger values ofthe dielectric constant were measured for samples consist-ing of five multilayers in comparison with those consist-ing of three multilayers – a fact which is consistent withthe literature.

The measured values of the dielectric constant of ourBaTiO3 films and BaTiO3/SrTiO3 multilayers on SrTiO3 : Nbsubstrates are in fair agreement with literature values. Forexample, Tabata and co-workers [2, 9] found thickness-dependent dielectric constants between 150 and 900 forBaTiO3/SrTiO3 multilayers of widely varying structure onSrTiO3 : Nb substrates. A dielectric constant of 1000 wasfound by Hayashi et al. for thick BaTiO3 films [10]. In viewof the well-known single-crystal values of dielectric constantsfor bulk BaTiO3, viz. εa = 4400 and εc = 150, in all of thesecases thin films and multilayers have intermediate ε values,which should be a consequence of the particular stress–strainconditions, domain states, and/or defect characteristics of therespective thin films or multilayers. The latter factors certainlyalso determine the observed various thickness dependencesof the dielectric constant. A common point of all publishedwork is the significant influence of the layer structure of theBaTiO3/SrTiO3 multilayers – in terms of periodicity, symme-try, and thickness of the individual layers – on the dielectricconstant [2, 9, 11, 12].

Tsurumi et al. [11], however, reported much highervalues of the dielectric constant than mentioned above,using undoped SrTiO3 substrates and interdigital electrodesdeposited on top of the multilayers. For example, a max-imum of the dielectric constant of 720 000 was found fora [(BaTiO3)10/(SrTiO3)10]4 superlattice which containedfour periods, each of which consisted of 10 unit cells inthickness of BaTiO3 and SrTiO3 each. It can be assumedthat the compressive strain exerted by the SrTiO3 layers onthe BaTiO3 layers, and the thickness- and strain-dependentformation of misfit dislocations at the BaTiO3/SrTiO3 in-terfaces, should play a role in the formation of this max-imum. In view of the facts, however, that Tsurumi et al.’smultilayers were not grown on Nb-doped, but on non-doped, non-conducting SrTiO3 substrates, and that they meas-ured the dielectric constant not in a perpendicular, three-dimensional geometry but in a two-dimensional surfacegeometry, a comparison of Tsurumi et al.’s results with theresults of the other authors (including our work) seems to bedifficult.

In order to discuss the overall thickness dependence ofthe dielectric constant, two alternative approaches are consid-ered. First, a series-capacitor model is applied by consider-

VISINOIU et al. Dielectric properties epitaxial BaTiO3 and multilayers 233

FIGURE 7 Measured ratio d/ε asa function of the BaTiO3 film thicknessshowing different slopes for films withthicknesses below 75 nm (a) and above75 nm (b). Dielectric measurementswere carried out at room temperatureby applying an ac signal with an ampli-tude of 10 mV at 1 MHz

ing the contributions of the bulk of the ferroelectric and theferroelectric–electrode interfaces. In this model, the effectivecapacitance of the dielectric layer is given by

1

Ceff= 1

Cb+ 1

CPt+ 1

CSrTiO3 : Nb, (1)

where the eff subscript represents the effective value exper-imentally measured, b means the bulk value, Pt refers tothe Pt/BaTiO3 top interface, and SrTiO3 : Nb refers to theSrTiO3 : Nb/BaTiO3 bottom interface. To simplify the calcu-lations the two metal–dielectric interfaces are considered asbeing identical. Since we are not able to calculate the con-tribution of the SrTiO3 : Nb/BaTiO3 interface to the effectivevalue of the capacitance, it is assumed to be equal to that of thePt electrode/BaTiO3 ferroelectric interface [13]. Consideringthe total thickness d being given by

d = db +2di �⇒ db = d −2di, (2)

equation (1) becomes

d

εeff= d

εb+2di

(1

εi− 1

εb

), (3)

where d is the nominal thickness of the film, db is the bulkthickness, di is the thickness of the film–electrode interface, εbis the bulk dielectric constant, and εi is the dielectric constantof the ferroelectric–electrode interface.

Assuming that εb � εi, we can write

d

εeff= d

εb+ 2di

εi. (4)

Using the experimental data for the dielectric constant ofFig. 6a and replotting them into d/ε values for the two dif-ferent thickness regions (below and above 75 nm) results inFig. 7a and b, where the lines represent the linear fits to theexperimental values. As a result, in the case of thin films (be-low 75 nm), di/εi was calculated as 0.085 ±0.003 and εb is581.5±82, while in the case of thick films (above 75 nm) di/εiis 0.128 ±0.03 and εb is 1519 ±144. The last value is in goodagreement with the usual bulk dielectric constant of BaTiO3.

Although the series-capacitor model was used success-fully in order to explain the thickness dependence of the di-electric constant, this model does not take into account themorphology of the BaTiO3 films. Therefore, another model

was additionally considered, viz. the dead-layer model de-veloped recently by Sinnamon et al. [14, 15]. This model takesinto account that the film consists of columnar grains and thatcolumn boundaries and the bulk of the columns have differ-ent dielectric properties and act in parallel. Thus, it is possibleto calculate the area fractions of the defective material in theboundaries and of the bulk-like material in a column of circu-lar section.

The effective dielectric constant, εeff, is given by the rela-tive area of each capacitor multiplied with its dielectric con-

FIGURE 8 Measured vertical and lateral sizes of BaTiO3 film grains versusfilm thickness (a). Measured dielectric constant as a function of the lateralsize of the BaTiO3 grains (points) and the polynomial fit (curve) according tothe model of Sinnamon et al. [15] (b). Dielectric measurements were carriedout at room temperature by applying an ac signal with an amplitude of 10 mVat 1 MHz

234 Applied Physics A – Materials Science & Processing

FIGURE 9 Cross-sectional high-resolution TEM images of a thick BaTiO3film showing the presence of structurally modified grain-boundary layers.The BaTiO3 film thickness is 150 nm (a). TEM image taken at large de-focus revealing structurally modified grain-boundary layers (indicated byarrows) between BaTiO3 columns, as well as between SrTiO3 columns inBaTiO3/SrTiO3 multilayers. The thickness of the individual BaTiO3 layersis about 260 nm and that of the individual SrTiO3 layers is about 210 nm (b)

stant as follows [15]:

εeff = εb

[π

( g2 − t

)2

π( g

2

)2

]+ εt

[π

( g2

)2 −π( g

2 − t)2

π( g

2

)2

]

= 4t2

g2(εb − εt)− 4t

g(εb − εt)+ εb, (5)

where εb is the relative dielectric constant of the bulk mate-rial, t is the thickness of the grain-boundary dead layer, g is thediameter of the grain columns, and εt is their relative dielectricconstant.

This model is able to reproduce the measured dielectricconstant as a function of the lateral size of the columns. Con-sidering this model for BaTiO3 films with a thickness above75 nm and fitting the experimental data (shown in Fig. 8b)with a polynomial function of second order in 1/g, the fol-lowing parameters can be calculated: t = 11.95± 1.6 nm,εt = 143.7 ±25.8, and εb = 1254 ±231. In other words, thethickness of the grain-boundary dead layer is about 12 nm.The diameter of the circular column section for differentfilm thicknesses was experimentally measured by atomicforce microscopy (Fig. 8a) and confirmed by cross-sectionalTEM.

A natural limit of applicability of the dead-layer model isgiven by the limiting case when the defective boundary re-gion takes up the entire grain (i.e. when t = g/2). At this point

εeff = εt and it will be constant for any further decrease ingrain size. The applicability of the dead-layer model is re-stricted to the columnar structure, i.e. above 75 nm film thick-ness. Therefore, this model cannot be applied for thin filmswhere no columns occur.

If the grain-boundary dead layers represent structurallymodified layers, it should be possible to prove their existenceby high-resolution TEM. Figure 9a taken from a thick BaTiO3film (150 nm) shows structurally modified grain-boundarylayers of about 8 nm thickness. It is reasonable to assume thatthese layers represent the grain-boundary dead layers. Thevalue of 8 nm is in rather fair correspondence to the above-calculated value of 12 nm, which supports the application ofSinnamon et al.’s model to these films.

So far, the nature of the structurally modified grain-boundary layers has not been determined. From the high-resolution TEM images the presence of amorphous regions isdeduced, but it is uncertain whether the amorphous materialstems from the ion beam thinning process or not. More de-tailed investigations including incoherent dark-field imagingof film regions far from the surface are under way.

Unfortunately, it is very difficult to apply the previouslydiscussed dead-layer model to BaTiO3/SrTiO3 multilayersbecause too many parameters are involved. Nevertheless,TEM analysis shows the presence of structurally modifiedgrain-boundary layers in BaTiO3/SrTiO3 multilayers, too(Fig. 9b).

In the framework of the present work it is not possible toexpress a preference for one or the other of the above twomodels. Given their very different preconditions, but theirequally good correspondence to the experimental results, it islikely that a realistic model has to include features of both ofthem, probably with different weights for different-thicknessregions.

4 Conclusion

The topographical and morphological analysisof epitaxial BaTiO3 films and epitaxial BaTiO3/SrTiO3

multilayers of different thicknesses grown by PLD hasshown that at the beginning of growth, a layer-then-island(Stranski–Krastanov) growth mechanism occurs. The fine-grained structure of thin BaTiO3 films begins to turn intoa columnar structure at a thickness of 75 nm. This changeof the morphology is reflected by the dielectric propertiesof the films and the multilayers: the dielectric loss tan-gent saturates for a thickness above 300 nm, and linearlydecreases with decreasing film thickness below a thick-ness of 75 nm. The dielectric constant also linearly de-creases with decreasing overall thickness below a thickness of75 nm.

For an explanation of the overall thickness dependenceof the dielectric constant, two approaches have been consid-ered: the series-capacitor model and the dead-layer model.The assumption of grain-boundary dead layers proved to bevalid in the case of a columnar film structure (i.e. above75 nm thickness). In the case of the BaTiO3 films, the grain-boundary dead-layer thickness was calculated to be about12 nm. The presence of structurally modified layers that canbe the microscopic origin of the dead layers along the bound-

VISINOIU et al. Dielectric properties epitaxial BaTiO3 and multilayers 235

aries was proven by TEM investigations in both BaTiO3 filmsand BaTiO3/SrTiO3 multilayers.

ACKNOWLEDGEMENTS The authors are grateful to Dr. D.N.Zakharov for one of the TEM images. This work has in part been supportedby the Deutsche Forschungsgemeinschaft through the Group of ResearchersFOR 404 at Martin-Luther-Universitat Halle-Wittenberg.

REFERENCES

1 G. Burns: Phys. Rev. B 10, 1951 (1974)2 T. Shimuta, O. Nakagawara, T. Makino, S. Arai, H. Tabata, T. Kawai:

J. Appl. Phys. 91, 2290 (2002)3 V. Srikant, E.J. Tarsa, D.R. Clarke, J.S. Speck: J. Appl. Phys. 77, 1517

(1995)4 J. Kim, Y. Kim, Y.S. Kim, J. Lee, L. Kim, D. Jung: Appl. Phys. Lett. 80,

3581 (2002)

5 A. Visinoiu, M. Alexe, H.N. Lee, D.N. Zakharov, A. Pignolet, D. Hesse,U. Gösele: J. Appl. Phys. 91, 10 157 (2002)

6 W.C. Goh, S.Y. Xu, S.J. Wang, C.K. Ong: J. Appl. Phys. 89, 4497(2001)

7 S.Y. Xu, C.K. Ong, X. Zhang: Solid State Commun. 107, 273 (1998)8 A. Visinoiu, R. Scholz, S. Chattopadhyay, M. Alexe, D. Hesse: Jpn.

J. Appl. Phys. 41, 6633 (2002)9 H. Tabata, H. Tanaka, T. Kawai: Appl. Phys. Lett. 65, 1970 (1994)

10 T. Hayashi, N. Oji, H. Maiwa: Jpn. J. Appl. Phys. 33, 5277 (1994)11 T. Tsurumi, T. Ichikawa, T. Harigai, H. Kakemoto, S. Wada: J. Appl.

Phys. 91, 2284 (2002)12 T. Tsurumi, S. Mitarai, S.M. Nam, Y. Ishibashi, O. Fukunaga: in Proc.

IEEE 10th Int. Symp. Applications of Ferroelectrics, 1996, Vol. 1, p. 49913 C.S. Hwang: J. Appl. Phys. 92, 432 (2002)14 L.J. Sinnamon, R.M. Bowman, J.M. Gregg: Appl. Phys. Lett. 78, 1724

(2001)15 L.J. Sinnamon, M.M. Saad, R.M. Bowman, J.M. Gregg: Appl. Phys.

Lett. 81, 703 (2002)