Strain relaxation and critical temperature in epitaxial ferroelectric Pb(Zr_0.20Ti_0.80)O₃ thin films

Article

Reference

Strain relaxation and critical temperature in epitaxial ferroelectric Pb(Zr

_0.20

Ti

_0.80

)O

₃

thin films

GARIGLIO, Stefano, et al.

Abstract

Strain relaxation and the ferroelectric critical temperature were investigated in a series of epitaxial Pb(Zr0.20Ti0.80)O-3 thin films of different thicknesses grown on metallic 0.5%

Nb-doped SrTiO3 substrates. Detailed x-ray diffraction studies reveal that strain relaxation progressively occurs via misfit dislocations as the film thickness is increased from fully coherent films (for films below 150 A) to essentially relaxed films (for thicknesses above typically 800 A). It is found that this change in the strain state does not modify the ferroelectric critical temperature which is found for all the samples to be around 680 degrees C, a value much higher than the bulk.

GARIGLIO, Stefano, et al . Strain relaxation and critical temperature in epitaxial ferroelectric Pb(Zr

_0.20

Ti

_0.80

)O

₃

thin films. Applied Physics Letters , 2007, vol. 90, no. 20, p. 202905

DOI : 10.1063/1.2740171

Available at:

http://archive-ouverte.unige.ch/unige:114271

Disclaimer: layout of this document may differ from the published version.

1 / 1

Strain relaxation and critical temperature in epitaxial ferroelectric Pb „ Zr

_0.20

Ti

_0.80

… O

₃

thin films

S. Gariglio,^a兲 N. Stucki, and J.-M. Triscone

DPMC, University of Geneva, 24 Quai E.-Ansermet, 1211 Geneva 4, Switzerland G. Triscone

Ecole d’Ingénieurs de Genève (EIG/HES-SO), 4 rue de la Prairie, 1202 Geneva, Switzerland

共

Received 13 February 2007; accepted 21 April 2007; published online 16 May 2007

兲

Strain relaxation and the ferroelectric critical temperature were investigated in a series of epitaxial Pb

共

Zr_0.20Ti_0.80

兲

O₃ thin films of different thicknesses grown on metallic 0.5% Nb-doped SrTiO₃ substrates. Detailed x-ray diffraction studies reveal that strain relaxation progressively occurs via misfit dislocations as the film thickness is increased from fully coherent films

共

for films below 150 Å

兲

to essentially relaxed films

共

for thicknesses above typically 800 Å

兲

. It is found that this change in the strain state does not modify the ferroelectric critical temperature which is found for all the samples to be around 680 ° C, a value much higher than the bulk. ©2007 American Institute of Physics.

关DOI:

10.1063/1.2740171兴

The availability of high quality epitaxial ferroelectric oxide thin films and heterostructures allows some model sys- tems to be designed and fundamental questions related to ferroelectricity to be revisited.^1–9These high quality materi- als may also find their way into advanced specific applications.¹⁰ The epitaxial growth not only provides samples and structures of single crystal quality but also al- lows some properties to be tuned and improved, for instance, by using strain engineering. In perovskite ferroelectrics, the effect of mechanical boundary conditions has been studied both theoretically and experimentally.^5–8 Theoretically, it is shown that the strain induced by the two-dimensional clamp- ing of a film renormalizes the second-order and the fourth- order polarization terms of the Gibbs energy expansion, lead- ing to a modification of the paraelectric-ferroelectric phase transition temperature Tc

共Refs.

5 and 6兲 and ferroelectric polarization, both effects having been experimentally ob- served. Dramatic examples of the role of strain include the induction of room temperature ferroelectricity in strained SiTiO₃ thin films⁹ and a large enhancement of polarization and transition temperature in BaTiO₃films.⁸

In this letter, we have studied the effect of thickness reduction on the structural and physical properties of epitax- ial Pb共Zr0.20Ti_0.80

兲O

3

共PZT 20/ 80兲

thin films in order to bet- ter understand the interplay between strain and ferroelectric- ity. Using x-ray diffraction, the crystallographic structure and the ferroelectric phase transition temperatures were studied in a series of ferroelectric PZT 20/ 80 thin films, grown onto metallic

共001兲

0.5% Nb-doped SiTiO₃

共Nb-STO兲

substrates, with thicknesses ranging from 150 to 1230 Å.

The deposition of PZT 20/ 80 films was carried out by off-axis magnetron sputtering in 180 mTorr of an oxygen/

argon mixture at a substrate temperature of 510 ° C. These growth conditions lead to c-axis oriented PZT 20/ 80 films with a low surface rms roughness ranging from 4 Å for very thin films to 12 Å for thicker films, measured over 5⫻5␮^m2. Detailed x-ray measurements were performed with a high-resolution Philips X’Pert diffractometer using a

four-bounce asymmetric Ge共220兲 monochromator and CuK␣1 radiation. The

共001兲

and

共103兲

PZT reflections were used to determine the lattice constants as the sample was heated between 25 and 900 ° C in a domed hot stage in air.

In epitaxial films and heterostructures, the strain induced by the lattice mismatch between the film and the substrate can be accommodated up to a critical thickness hc by an elastic deformation of the film lattice which adjusts perfectly to the substrate lattice parameter. Aboveh_c, the strain will be progressively relaxed by the formation of misfit dislocations at the film-substrate interface.¹¹At room temperature, PZT 20/ 80 is tetragonal

共

P4mm space group

兲

with a= 3.9525 Å andc= 4.1484 Å.¹²Forc-axis oriented PZT 20/ 80 thin films grown on top of Nb-STO

共cubic,

a= 3.905 Å兲substrates, the in-plane lattice mismatch is −1.2%. At the growth tempera- ture, PZT 20/ 80 is cubic and paraelectric with a lattice pa- rameter of 4.017 Å: the lattice mismatch with Nb-STO sub- strate

共a

= 3.925 Å at 510 ° C兲 is −2.3% and using the Matthews-Blakeslee criteria,¹¹a critical thickness of 20 Å is

a兲Electronic mail: [email protected]

FIG. 1. 共a兲Room temperature thickness dependence ofa共䊏兲andc 共䉱兲 lattice parameters for PZT 20/ 80 thin films. The continuous lines are guides for the eyes, while the dashed lines are the bulk values.共b兲Room tempera- ture in-plane film-substrate separation vs inverse of the thickness. The line is a fit to the data for strain relaxation via misfit dislocations.

APPLIED PHYSICS LETTERS90, 202905

共

2007

兲

0003-6951/2007/90共20兲/202905/3/$23.00 90, 202905-1 © 2007 American Institute of Physics Downloaded 18 May 2007 to 129.194.8.73. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

estimated. By measuring the in-plane a and out-of-plane c lattice parameters for different thicknesses, we quantify the elastic deformation of the strained films and track the relax- ation as a function of the film thickness. We extracta- and c-axis values from

共00l兲

and

共103兲

diffraction peaks and the thickness from the finite size fringes.

Figure1

共

a

兲

shows the evolution of the lattice parameters as a function of film thicknessh. A 150 Å thick film is found to be pseudomorphic with the Nb-STO substrate as shown by the analysis of reciprocal space maps around the

共103兲

peaks, which indicates that the PZT 20/ 80 in-plane lattice param- eter reduces to that of Nb-STO

关

see Fig.2

共

b

兲兴

. As a conse- quence, thec-axis parameter elongates. Increasing the thick- ness induces a progressive relaxation of the strain, as can be seen in Fig.1共a兲, where thea axis is found to increase and the c axis to decrease with increasing film thickness, with lattice parameter values close to those of the bulk ferroelec- tric phase for thick films. In Fig.1共b兲, we plot the in-plane lattice separation between the film and the substrate

共a

PZT

−a_STO

兲

measured from the

共103兲

peaks in reciprocal space maps. Assuming that misfit dislocations accommodate the strain, the density of misfit dislocations is expected to in- crease as

关

1 −

共

h_c/h

兲兴

.¹³The misfit strain follows a thickness

dependence identical to that of the dislocation density and thus the separation value varies as

共

a_PZT

共

h

兲

−a_STO

兲

=

共a

PZT

共⬁兲

−a_STO

兲关1 −共h

c/h兲兴, where

共a

PZT

共⬁兲

−a_STO

兲

is the in-plane lattice mismatch for fully relaxed films. A fit to the data

共line in the graph兲

gives a critical thicknesshcof 173 Å and

共a

PZT

共⬁兲−

a_STO

兲

equals to 0.059 Å. Further evidence of the presence of misfit dislocations is found in omega scans around the

共001兲

peak of the films. Analyses of the rocking curves clearly show that the reflection contains two compo- nents: a sharp peak and a broader diffuse scattering contri- bution which increases as the film thickness increases, as shown in Fig.2

共

a

兲

. Very similar diffraction data have been observed in epitaxial thin films grown onto mismatched sub- strates

共ErAs/ GaAs, Nb/ Al

2O₃, CeO₂/ SrTiO₃

兲

and have been related to the presence of misfit dislocations.^14–16Even if a comprehensive theory that relates the microstructural properties and the x-ray diffraction spectrum is still missing, the coexistence of Bragg and diffuse scattering components can be explained by long-range order and correlation of short-scale disorder, respectively.¹⁴ In this picture, the sharp Bragg component arises from the crystallographic order of the regions of the film that are in registry with the substrate.

In fact, the Bragg peak appears to be similar for the substrate and for all the films: the full widths at half maximum ex- tracted for all the scans are identical with a value of 0.025°.

We note that the intensity of the maxima of this Bragg com- ponent increases with the square of the thickness, as one would expect from the diffraction theory of perfect crystals.

This thickness dependence of the intensity implies that the regions in registry with the substrate keep their structural coherence throughout the whole film thickness. These obser- vations suggest that the misfit dislocations are vertical edge dislocations. The diffuse component is related to the disorder introduced by the dislocations and the intensity of the diffuse component correlates with the density of misfit dislocations.

As can be seen in Fig.2

共

a

兲

, the diffuse component is absent for the 150 Å thick film, appears for the 200 Å film, and becomes progressively more intense for thicker films.

Figure 3共a兲 shows the temperature evolution of the c lattice parameter for a 400 Å thick film. Thecaxis shrinks up to 680 ° C and then starts to expand. The change in be- havior is ascribed to the ferroelectric-paraelectric transition with an estimatedTcof about 680 ° C. In the same figure, the behavior of thea axis is also shown. At room temperature,

FIG. 2. 共Color online兲 共a兲Rocking curves共␻^scans兲around the共001兲re- flection for the Nb-STO substrate and PZT films of different thicknesses.共b兲 Reciprocal space map around the共103兲reflection of a 150 Å PZT thick film and Nb-STO substrate. The alignment of the peaks alongQxdemonstrates the coherent growth of the PZT film on the Nb-STO substrate.

FIG. 3. 共Color online兲 共a兲Evolution of the lattice pa- rameter for the Nb-STO substrate共䊏兲and of thec关䉱 measured from共103兲reflection and쐓measured from 共001兲reflection兴anda关쎲from共103兲reflection兴lattice parameters of a 400 Å thick PZT film with temperature.

The structural phase transition occurs around 680 ° C.

共b兲 Structural transition temperatures vs thickness for the different PZT thin films. The dashed line shows the bulkTc.共c兲Intensity of ␪^-2␪ scans around the共001兲 PZT reflection as a function of temperature for the 400 Å thick film.

202905-2 Gariglioet al. Appl. Phys. Lett.90, 202905共2007兲

Downloaded 18 May 2007 to 129.194.8.73. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

theaaxis is about 3.96 Å. As the temperature increases, the a-axis value increases, following the expansion of the sub- strate as can be seen in Fig.3

共

a

兲

, where the evolution of the substrate lattice parameter is also shown. This result suggests that the dislocation density which is introduced during the growth does not change when cycling the temperature. Note that in contrast to bulk where the transition corresponds to a change from a ferroelectric-tetragonal to a paraelectric-cubic structure, the data suggest that the transition corresponds to a change from a ferroelectric–non-central-symmetric–

tetragonal to a paraelectric–central-symmetric–tetragonal structure, an effect due to the clamping to the substrate.

Such measurements of the evolution of the lattice param- eters with temperature allow us to extract the transition tem- perature of each sample. The results are reported in Fig.3共b兲.

As can be seen, the transition temperature does not vary significantly with thickness: strained and relaxed films dis- play a rather similar transition temperature.¹⁷Because of the large strain-polarization coupling, the modification of the strain state should induce substantial changes in theT_cof the films. Using the prediction of Pertsevet al.⁶for PZT 20/ 80, we could expect aTcof 1000 ° C for the thinnest films

共mis-

fit strainSm= −23⫻10⁻³, following the definition in Ref.5兲.

As the film thickness is increased and the strain progres- sively released, theT_cshould approach the value of 680 ° C for the thickest relaxed films

共S

m= −10⫻10⁻³

兲, a prediction

in good agreement with the data. This value is higher than the bulk

共460 ° C兲

since the film, although relaxed, still pre- sents a misfit strainSmof −9⫻10⁻³ when compared to the cubic paraelectric phase. These results also seem to suggest that at the growth temperature, it is energetically more favor- able for the film to relax in a tetragonal ferroelectric state than in a cubic paraelectric state, which would require more dislocations. This results in a room temperature phase with increasedT_cand possibly explains the large critical thickness for misfit dislocations.¹⁸ This is good news for applications since it implies that thick relaxed films can have a critical temperature substantially higher than the bulk. Finally, as mentioned above, an intriguing result is the observation of a thickness independent critical temperature despite the in- crease in misfit strain as the films are getting thinner. Al- though there is no obvious candidate to explain this result, several effects could play a role. We note that the possible change in Zr content along the film growth direction as re- laxation takes place, reported in Ref. 19, may lead to a change in stoichiometry as the film thickness is increased.

Also, the finite thickness of the thinnest films used in this study may influence the ferroelectric properties.^2,7Finally, an effect due to inhomogeneous strain,²⁰ for instance, due to

oxygen vacancies and other local defects, cannot be ex- cluded. Such effects would certainly complicate the picture and may explain why in PZT thin films, the correlation be- tweenc/a, the polarization, andT_c, used for PbTiO₃in Ref.

2and demonstrated in PbTiO₃/ SrTiO₃superlattices,^3,21does not seem to hold.

The authors thank N. Reyren, C. Lichtensteiger, and M.

Dawber for useful discussions. This work was supported by the Swiss National Science Foundation through the National Center of Competence in Research “Materials with Novel Electronic Properties-MaNEP,” Division II, ESF

共Thiox兲,

and the EU STREP programs Macomufi and Nanoxide.

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202905-3 Gariglioet al. Appl. Phys. Lett.90, 202905共2007兲

Downloaded 18 May 2007 to 129.194.8.73. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp