Residual stress effect on coupling electromechanical factor of epitaxial Barium Strontium Titanate (BST) thin films

Accepted Manuscript Title: Residual stress effect on coupling electromechanical factor of epitaxial Barium Strontium Titanate (BST) thin films Authors: Souhir Mseddi, Wolfgang Donner, Andreas Klein, Anouar Njeh PII: DOI: Reference:

S0093-6413(17)30632-8 https://doi.org/10.1016/j.mechrescom.2017.12.001 MRC 3236

To appear in: Received date: Accepted date:

28-11-2017 2-12-2017

Please cite this article as: Mseddi, Souhir, Donner, Wolfgang, Klein, Andreas, Njeh, Anouar, Residual stress effect on coupling electromechanical factor of epitaxial Barium Strontium Titanate (BST) thin films.Mechanics Research Communications https://doi.org/10.1016/j.mechrescom.2017.12.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Publication Office:

Elsevier UK

Mechanics Research Communications. Year Editor-in-Chief:A. Rosato New Jersey Institute of Technology, Newark, New Jersey, [email protected]

Residual stress effect on coupling electromechanical factor of epitaxial Barium Strontium Titanate (BST) thin films

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Souhir Mseddi1, Wolfgang Donner2, Andreas Klein2 and Anouar Njeh1. 1

Laboratoire de Physique des Matériaux, Faculté des Sciences de Sfax, Université de Sfax, Tunisie. Institute of Materials Science, University of Technology, Petersenstr.23, 64287 Darmstadt, Germany *[email protected] Tel.:+216-53686849;

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Highlights

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The aim of this work is to study the:

Theoretical investigation of piezoelectric layered structures.

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Influence of the measured residual stresses on the propagation behaviour of SAW in BST piezoelectric structure.

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The main novelty of this paper is that the initial stresses were measured and were applied for the study of the acousto-elastic response in the epitaxial

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thin films of Ba0.8Sr0.2TiO3/Pt/MgO. Naturally the electromechanical coupling factor is affected by the existence of the residual stresses.

Abstract

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Acoustoelastic (AE) effect of a mechanically pre-stressed layered piezoelectric structure of BST is investigated. Two samples of BST (Ba0.8Sr0.2TiO3) thin films were grown by rf-magnetron sputtering deposition techniques on a Pt(100)/MgO(100) and Pt(110)/MgO(110) substrates. The crystallographic orientation of BST thin films is analyzed by X-ray diffraction (XRD). A laser acoustic waves (LA-waves) technique is used to generate surface acoustic waves (SAW) propagating in both samples for epitaxial relationship examination. We perform an extended model to determine the residual stress and strain in BST films using the (XRD) X-ray diffraction measurement and the piezoelectric constitutive equations. Theoretical analysis of (SAW) propagation in a pre-stressed layered piezoelectric structure is achieved to discuss the effect of the measured residual stresses of BST films on the propagation behavior of Rayleigh waves and on the coupled electromechanical factor. Keywords: Surface acoustic wave; Residual stress; BST thin films, XRD-analysis.

1. Introduction

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Investigations on the propagation of elastic waves, especially the surface acoustic wave, in layered piezoelectric media have been of great interest since films deposited on supporting substrates are generally a requisite for acoustic devices. Lately, there has been a growing focus in studying the effect of external perturbations like residual stresses and strains on the propagation of surface acoustic waves. The residual stresses in thin film are unavoidable and important because they can result in frequency shift, a change in the SAW’s velocity and controlling the selectivity of a filter and temperature compensation of the devices [1-10]. Many techniques for instance the nano-indentation fracture method, X-ray diffraction, and Raman spectroscopy were utilized to measure these residual stresses in thin films. As

0093-6413© 2015 The Authors. Published by Elsevier Ltd.

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well, the sin 2  techniques have been useful to perform the residual stress evaluations within thin films [11-12]. However, as we know, it is possibly incorrect to evaluate the residual stresses in piezoelectric thin films by conventional XRD measurement, where thin films are assumed as isotropic and the piezoelectric coupling effects are neglected. We propose in the present work an extend model to evaluate residual stresses in epitaxial piezoelectric Barium Strontium Titanate (BST) films with X-ray diffraction. Then, a detailed analysis of the effect of these residual stresses on surface acoustic wave velocity is performed. Authors theoretically analyzed the Acousto-elastic (AE) effect of pre-stressed layered systems using the ordinary differential equation method (ODE) and the stiffness matrix method (SMM) [1315]. The (AE) study involves the application of the ODE method to analyze the effect of residual stress on the dispersion behavior of Rayleigh wave mode propagating in a BST layered piezoelectric thin layers deposited on a relatively thick substrate. Vast technological interest is focusing on Barium Strontium Titanate (BaxSr1-xTiO3) films due to their desirable and extensive properties used for various devices applications such as integrated optical devices [16], phase shifters [17] multichip modules (MCM), high-density interconnect (HDI), ULSI-DRAMs capacitors [18] and acoustic resonator [19]. Most of the BST properties such as piezoelectricity, pyroelectricity, and ferroelectricity are strongly depend on the composition, crystal structure, size, etc [20-23]. Despite that BST thin films with cubic symmetry do not exhibit a piezoelectric effect, however a strong electrostrictive activity with acoustic resonance phenomena, has been observed [24-27]. In this paper, we are focused in two BST thin films deposed by rf-magnetron sputtering deposition techniques on a Pt(110)/MgO(110) and on a Pt(100)/MgO(100) substrate. Two complementary techniques XRD and LA-waves are employed to improve the knowledge about anisotropy and films setting. From XRD diagrams crystallographic results relative to films orientation and measurement of initial stresses are derived, and LA-waves technique through a computational procedure leads to the dependence of phase velocity on frequency namely the dispersion curves. Various results, relative to the crystallography and the mechanical properties of BST/Pt/MgO multilayer, are reported. In Sec. II, we present the model to evaluate initial stresses. Section III is devoted to the experimental studies with a brief description of XRD and LA-waves equipments. In Sec. IV, we describe the theoretical studies of (SAW) propagating in prestressed multilayered BST medium. Theoretical dispersion curves are plotted by application. The effect of the initial stress on the phase velocity and in the coupled electromechanical factor is discussed in detail.

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2. Theoretical analysis 2.1. X-ray diffraction for residual stress evaluation

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For such layered structure, the strain state has a much more complicated pattern due to the non uniform structure; the misfit of interatomic distance, the difference between the film and the substrate thermal expansion coefficients and the phase transition of the film during and after deposition. A non-destructive method for the determination of stresses has been applied basing on the X-ray diffraction technique. Under residual stress the crystal plane spacing d  is different from d 0 of the samples free of residual stress. The strain

L 

, in the arbitrary orientation defined by angles  and  ,

can be shown by the relative changes of the diffraction plane spacing and is associated with the diffraction peak displacement, that is: d   d 0 d  d0 d0

(1)

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 L 

L The evaluation of the strain tensor  S or stress tensor  S from the measured strain component   requires a ij jk

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transformation from the laboratory system (L) to the specimen system (S). Usually, the measured strain is along the  axis L3 which is chosen in such way it coincides with the scattering vector sh' k 'l '  [h' k ' l ' ] * . For the specimen reference frame (S), axis S3 is oriented perpendicular to the specimen surface and axes S1 and S2 are on the surface plane. The strain tensor in the specimen reference frame (S) is given according to:

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L L     33  A3k A3l  klS

(2)

Where A is the matrix which transforms the (S) system to the (L) system is defined as: cos  cos Aik     sin   cos  sin  

sin  cos cos  sin  sin 

 sin    0   cos 

(3)

Eqs. (2) and (3) are combined to give:  L  ( 11S cos 2    22S sin 2    12S sin 2   33S ) sin 2   ( 13S cos    23S sin  ) sin 2   33S (4)

For epitaxial thin film growing along (hkl) plane, the tilt angle  for an (h’k’l’) scattered plane can be calculated by

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the following equation [28]. b 2c 2 hh' a 2c 2 kk' a 2b 2ll '

cos 

b 2 c 2 h 2  a 2 c 2 k 2  a 2 b 2 l 2 b 2 c 2 h' 2  a 2 c 2 k ' 2  a 2 b 2 l ' 2

Where a, b and c are the lattices parameters of the sample. The describing electromechanical equations for a linear piezoelectric material can be written in the sample system as: S S (5)  ijS  Cijkl  klS  eijk EkS S S  ijS  sijkl  klS  d ijk EkS

(6)

S DiS  d ijk  Sjk   ijS E Sj

Where

 ijS

(7)

is the strain tensor,

 klS

is the stress tensor,

DiS and EkS

S are the electric displacement and electric field, sijkl

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is the elastic compliance tensor, d ijkS and eijkS are the piezoelectric tensors and ijS is the dielectric tensor in the sample reference frame (S). Eq. (5) presents the contribution of elastic and piezoelectric phenomena which can be defined by S S  ijS,el  Cijkl  klS and  ijS, p  eijk EkS , respectively.At a stress free surface of the thin film, the mechanical and electrical boundary conditions are given as:  iS3  0 D 0

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(8)

S i

(9)

Eqs. (7) and (9) yield to: S S EmS  mi dijk  Sjk

(10)

From Eqs. (4) and (11), we have L   F ( , , hkl, h' k ' l ' , a, b, c, s L , d L , L )  klS ,

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(12)

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 S is the inverse of S . Where  mi  mi From Eqs. (10) and (6) the strain tensor components, defined in the sample system (S), are given by: S S T S (11)  ijS  sijkl  klS  dijm mp d pkl  klS

wher F ( , , hkl, h' k ' l ' , a, b, c, s L , d L , L ) is the X-ray stress factor for ideal (hkl)-textured ferroelectric thin films. Eq. (8) yields

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L L to three unknown stress components ( 11S ,  22S and  12S ) which can be calculated by measuring  in at least two   33

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different crystal faces. The idea is, for each fixed azimuthal orientation angle = 1, we measure the diffraction angle for all available reflections planes. Then we change for another (hkl) group having an azimuthal orientation angle = L vs.sin2 yields the unknown stress tensor components ( 2. Consequently we have the slope and the intercept of   hkl

S and 11S ,  22  12S ). In this work, we have used the elastic constants Cijkl instead of the X-ray elastic constants (XECs) s1

and s2hkl , defined for a specific lattice (hkl) plane, because several lattice planes are taken into account. More detail is referred to [28].

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2.2 Theoretical SAW analysis

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In the natural state, material medium is free of stress and strain. Then, in the initial state that material medium is deformed through the presence of residual stresses or applied loading. This deformation from the natural to initial state is called static deformation. When a dynamic deformation is superposed on the initial state by the wave motion, the material medium is further deformed to the final state. The coordinate system adopted to study the SAW propagation is shown in Fig. 1. The surface waves propagate in the ‘x1’ direction along a surface whose normal is in the ‘x3’ direction. In a prestressed material medium, the equations of motion and boundary conditions are presented in the absence of body forces as: u   2 ui   (13) ( )  ( S  ) l    x j 

D j x j

0

ij

jk

il

 x k 

t 2

(14)

Where  ij is the stress tensor,  Sjk is the residual stress, ui are the SAW particle displacement components, D j is the electric displacement and  il is Kronecker tensor with (i, l=1,2,3) and (j,k=1, 3). The mechanical displacement ui and the electric potential  are considered to be independent of the ‘x2’ direction (Fig.1). The matrix method approach is

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based on the development of the first-order matrix ordinary differential equation (ODE) [29, 30]. The physical model for studding the effect of residual stress on the SAW behavior is based on the (ODE) modified matrix. Modification of the ODE considers the influence of residual stress. The general displacement vector is presented as U   u1 u2 u3   T (or 

its time derivative U  i  u1 u2 u3  T ), the general stress vector   13  23  33 D3 T and the state vector by     . General   U 

solution for the state vector is written as: (15)

 ( x1 , x3 , t )   ( x3 ) exp i (mx x1  t ) 1

Where ω indicates the angular frequency and m x1 is the slowness vector component along ‘x1’. The governing equation for the state vector ξ is given by a system of differential equations:   i  A   x3

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(16)

The fundamental acoustic tensor A is defined as: 1 mx 13 33 A   1 1  33

 I   (11  13 331 31)mx2  1

1 m x1 33 31

 

(17)  denotes the density of the material medium and I' is the 4×4

1 0 I'  0  0

0 1 0 0

0 0 0  0

0 0 1 0

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identity matrix with zero(4,4) element defined as: (18)

From (Eq.17) it is evident that tensor A makes up an eigenvector equation where the eigenvalues are the set of m x3

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third component of slowness vectors. When the whole partial waves are coupled together, the state vector is eight dimensioned.  jk is the (4  4) matrices formed from the elastic constants C ijkl , piezoelectric constants e jkl and C1 jk 3 C2 jk 3 C3 jk 3  

C3 jk 2 e jk 2

e jk 3

S jk

ek1 j   ek 2 j  ek 3 j     jk 

(19)

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C1 jk 2 C2 jk 2   Sjk

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C1 jk1   Sjk  C2 jk1 jk    C3 jk1   e jk1

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dielectric constants  jk :

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The resolution of the problem requires finding the eigenvalues and eigenvectors of the fundamental acoustic tensor A. The evaluation of SAW velocity is related to the mechanical and electrical boundary conditions. Details of the physical model for residual stress are reported in Ref [13]. The electromechanical coupling coefficient is obtained by using the relation: V f  Vs (20) K2 2 Vf

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Where V f and Vs are the theoretical SAW velocities with the boundary conditions for an electrically free case and electrically shorted case, respectively. 3. Experiments 3. 1. Sample preparation

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At first, MgO substrates were ultrasonically cleaned with isopropanol for 15 min and finally dried with a nitrogen jet. Then two BST thin films of about 600 nm thickness were realized via RF magnetron sputtering on Pt/MgO(100) and Pt/MgO(110) substrates. The substrate to target distance d was of about 10 cm. During deposition process, the substrate temperature was of about 550 °C and the deposition rate was 0.85 nm/min. 3. 2. Phase analysis

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A Bruker D8 X-ray diffractometer with Cu Kα radiation was used to analyze the crystalline phases in BST powder. The 2θ angle range was from 20o to 81o with a step scan of 0.02° and a sampling time of 5 s. We are interested in the determination of Ba and Sr concentration, usually called stochiometry ‘x’ (BaxSr1_xTiO3) and the lattice parameters of BST. XRD patterns reveal that the sample crystallizes in the quadratic structure as shown in Fig. 2. Using the program Fullprof, the Rietveld profile fitting technique was used to refine the crystal structure of the BST compounds. After several Rietveld refinement cycles the residual factors of the resulting difference profile are R wp = 5.12 % and Rp = 3.78 %. The lattice parameters was determined to be a= 3.9748 Å and c= 3.9849 Å. The concentration of Ba was 78.66 % and that of Sr was 21.34 %. For BST thin films, X-ray measurements were carried out in Bragg-Brentano mode (BBG) with PTS-3003 diffractometer. The XRD patterns of the sample were shown in Fig. 3. No additional peaks due

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to BaTiO3 or SrTiO3 were observed, which confirms the existence of only Ba(0.78)Sr(0.22)TiO3 phase. BST thin film deposited on Pt(100)/MgO(100) substrate shows an orientation along (100) lattice plane. The second film, deposited on Pt(110)/MgO(110) substrate reveal a BST orientation along (101) direction. 3.3 Epitaxial relationship determination

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The laser acoustic waves (LA-waves) technique is suitable for a nondestructively characterizing of the mechanical thin films parameters. This method is very suitable since SAWs are dispersive during propagating on a layered structure. Consequently from the experimental and the numerical dispersion curves one can determine the relationship from the film and the substrate. Laser acoustic wave equipment utilized for this study has been developed in the Fraunhofer-Institut for Material and Beam Technology, Dresden, Germany. A nitrogen laser with duration 0.5 ns and adjustable pulse energy 0.4 mJ is used as excitation source and is focused on the sample surface by a cylindrical lens. A PVDF transducer with frequency bandwidth of 250 MHz is used as line receiver. The Rayleigh wave velocity VR depending on frequency is determined by using Fourier transformation techniques. According to the preceding experimental, procedure dispersion curves are plotted for the following layered structures: BST(100)/Pt(100)/MgO(100) and BST(101)/Pt(110)/MgO(110). Their corresponding plots are reported in Fig. 4. All measured Rayleigh velocities correspond to the first mode. The recorded dispersion curves are sensitive to the stratification process. Basing on a theoretical SAW analysis, an optimization method is used to deduce the epitaxial relationship between the set of layers as shown in Fig. 1. 3. 4. Residual stress measurements

 

as a function of sin 2  for BST(100) and BST(101) structure

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present the dependency of residual strain

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After the characterization of orientation of the BST thin films, we selected the diffraction (hkl) planes for residual stress measurements. For BST(100), the selected planes are (100), (201), (302), (101) and (103) for = 180° and ((100), (311), (211) and (111) for = 135°. Those for BST film deposited on MgO(110) are (101), (302), (201) and (100). We note that  represents the azimuthal angle with respect to the BST [01-1] direction for BST/Pt(100)/MgO(100) and BST[10-1] for BST(101)/Pt(110)/MgO(110). To reduce the errors providing from diffractometer misalignment, :2 scan has been measured using powder BST samples and the goniometer error function G(,,) has been determined. All measurements for (hkl) diffraction angles were corrected with use of G(,,) function. Figure 5 and figure 6

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respectively. To determine necessary parameters for XRD measurement of initial stress in BST thin films, we use the elastic, piezoelectric and dielectric constants of BST presented in table 2 and we extract necessary data as the slope and the intercept from fig.5 and fig.6. Applying the initial stress model and using the data obtained from XRD measurements we perform the residual stresses and strain as shown in table1.

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S S The negative sign of  11 and  22 indicates that a compressive in-plane stress is applied in the perpendicular crystallographic directions for BST thin films. The stresses in both crystallographic direction of BST(100) thin film are -420 MPa and -422 MPa, which are in good agreement with the anisotropy of the scattering plane (100). Using Eq. (5) the total value of  ijS, p (100) is of about -30 MPa, which provide that piezoelectric coupling factor play an important

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role in the determination of residual stress. The contribution of coupling factor on residual stress components is of about 3.75 %. Similar results have been obtained for BST(101) thin film. Residual stress components applied in both crystallographic directions [10-1] and [010] are -368 MPa and -294 MPa, respectively. The piezoelectric factor is close to -22.4 MPa, which presents 3.5% of the applied residual stress. 4. Acoustoelastic effect investigation

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Analytical solutions of the Rayleigh phase velocity in homogeneously pre-stressed piezoelectric structure of Ba0.78Sr0.22TiO3 have been achieved. The mechanical and electrical material constants of BST thin films are reported in Table 2. These material parameters are reached from the ratio of SrTiO3 and BaTiO3.

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Computation dispersion curves for the first Rayleigh modes, propagating on Ba 0.8Sr0.2TiO3/Pt(100)/MgO(100) and Ba0.8Sr0.2TiO3/Pt(110)/MgO(110) layered structure are reported in Figs. 7, the phase velocities for the surface electrically free and shorted conditions are plotted for the fundamental mode of Rayleigh waves as a function of h/λ, in the absence of the residual stresses. The SAW velocities decrease from Rayleigh velocity of MgO substrate to the top layers with increasing frequency. It can be seen that these velocities for both BST(100)/Pt(100)/MgO(100) and BST(101)/Pt(110)/MgO(110) structure are slightly similar for h/λ>1. The existence of Pt films between BST film and MgO substrate acts as a perturbing parameter on the wave propagation velocity. As known, high frequency SAWs are more affected by the material properties close to the free surface while the low-frequency wave components contain essentially information on the bulk material properties of the substrate. Though, being interested in the first Rayleigh

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mode for frequencies up to 250 MHz, which represent the experimental frequency range, optimization method is made to check similarities between computed dispersion curves and experimental ones. Consequently computation hypothesis has been done, basing on a slight deviation, to assume the relationships between the set of layers as shown in Fig 1. This is mandatory to express the entire rigidity and electrical tensor in the same frame work. From Fig. 7, we compute the electromechanical coupling coefficient K 2 relative to the propagation of the first Rayleigh wave. Figure 9 shows the variation of the electromechanical coupling coefficient K 2 with respect to h/λ for the BST(100)/Pt(100)/MgO(100) structure and BST(101)/Pt(110)/MgO(110) structure in the case without residual stress. For the BST(100)/Pt(100)/MgO(100) structure the electromechanical coupling coefficient reaches highest values of K 2 =2.34% for h/λ =0.1 and vanished for h/λ=0.3. With increasing h/λ the electromechanical coupling coefficient exhibits a second maximum at h/λ =0.5 with K 2 =0.46% then it will be stabilized at almost K 2 =0.3% value. For the second sample BST(101)/Pt(110)/MgO(110), the electromechanical coupling coefficient reaches a first maximum of almost K 2 =1% for h/λ =0.1 and exhibits a second maximum at h/λ =0.4 with K 2 =0.8%. With increasing h/λ the electromechanical coupling coefficient is stabilized at the K 2 =0.4% value. For Acoustoelastic (AE) investigation we adopt the case that there exist a compressive residual stresses in the BST layers using the data in the table 1. From dispersion curves it is hard to discuss the Acoustoelastic (AE) effect for the reason that this effect is extremely weak. Accordingly, to graphically show the effects of the measured residual stress on the SAW velocity, the variations of phase velocity change V / V with h/λ of Rayleigh wave are plotted in Fig. 9. The relative change V  V  V0 is V

V

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calculated where V and V0 are the phase velocities without and with residual stress, respectively for both electrically free and electrically shorted case. Linear behaviour was observed for low frequency range. Comparing the effects of initial stress for each sample we found that the maximum fractional velocity change is about 0.4%±0.03 for a h/λ=0.5. For higher frequency range we found a stable AE behaviour when the phase velocity change is stabilized. This behaviour is explained by the homogenous character of BST thin films where the acoustic waves are completely localized within the stressed BST films with a homogenous distribution of residual stresses. For each structure, comparing the relative change of phase velocity of the electrically shorted case Vs / Vs and the electrically free case V f / V f we observe a small deviation. Fig.10 illustrate the variations of the electromechanical coupling coefficient

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K 2 with the frequency thickness product for the first Rayleigh wave corresponding to the measured residual stress S S and  12 . K 2  K 02  K 2 where K 02 is the value of K 2 in the case with residual stress. For both BST  11S ,  22

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structure the curve of K 2 present an alternative behaviour with increasing h/λ then these curves tend asymptotically to a horizontal line as h /   2.5 . The results obtained in this paper show that the measured residual stress has in important effect on the phase velocity as well on the coupled electromechanical factor K 2 . It is obvious that a few hundred of (MPa) residual stress brings a variation on the coupled electromechanical factor K 2 up to 0.01%. 5. Conclusion

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Two sample of BST films have been deposited on Pt(110)/MgO(110) and Pt(100)/MgO(100) substrate by r-f magnetron sputtering technique. XRD technique was used to characterize the structural properties of the BST materials. The concentration of Ba and Sr in BST materials has been found to be of about 78 % and 22 %, respectively. XRD results lead to a quadratic lattice for BST thin film with a= 3.9748 Å and c= 3.9849 Å as lattice parameters. Additionally LA-waves technique has been used to characterize (BST/Pt/MgO) multilayer by SAW. The investigation is limited to the first Rayleigh modes. Basing on the investigated frequency range (50-250MHz), the recorded experimental dispersion curves have been found to be sensitive to the stratification process and agree with the theoretical predictions to deduce the epitaxial relationship. Measurement of residual stresses on BST films were based on XRD method. Theoretical SAW analysis is performed on the basis of ODE and SMM methods. Physical model to evaluate the Acoustoelastic (AE) effect in layered piezoelectric structure is basing on the modified ordinary differential equation (ODE). Modification was touching the fundamental acoustic tensor ‘A’ to be adapted for a piezoelectric media under residual stress. The effects of residual stress on the phase velocity of Rayleigh waves and on the electromechanical coupling coefficient were investigated, numerical calculations have been achieved for both Ba0.78Sr0.22TiO3/Pt(100)/MgO(100) and Ba0.78Sr0.22TiO3/Pt(110)/MgO(110) layered structure. Homogenous character of BST thin films was deduced from the behaviour of phase velocity change in high frequency range. The impact of residual stress on the electromechanical coupling coefficient presents an alternative variation K 2 with h/λ. The

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measured residual stress brings a variation on the coupled electromechanical factor K 2 up to 0.01%. These results are momentous and supportive to improve the behaviour of the SAW devices. Acknowledgments Authors are grateful the Alexander von Humboldt foundation for financial support. The authors would like to thank the anonymous reviewers for their valuable comments.

References

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[1] J. Su, Z.B. Kuang_, H. Liu, Love wave in ZnO/SiO2/Si structure with initial stresses, Journal of Sound and Vibration 286 (2005) 981–999. [2] H. Liu, T.J. Wang, Z.K. Wang, Z.B. Kuang, Effect of a biasing electric field on the propagation of symmetric Lamb waves in piezoelectric plates, Int. J. Sol. Str. 39 (2002) 2031–2049 [3] H. Liu, Z.K. Wang, T.J. Wang, Effect of initial stress on the propagation behavior of Love waves in a layered piezoelectric structure, Int. J. Sol.Str. 38 (2001) 37–51. [4] Z. Qian, F. Jin, et al., Love waves propagation in a piezoelectric layered structure with initial stresses, Acta Mec. 171 (2004) 41–57. [5] Z. Qian, F. Jin, K. Kishimoto, Z. Wang, Effect of initial stress on the propagation behavior of SH-waves in multilayered piezoelectric composite structures, Sen. Act. A 112 (2004) 368–375. [6] F. Jin, Z. Qian, Z. Wang, K. Kishimoto, Propagation behavior of Love waves in a piezoelectric layered structure with inhomogeneous initial stress, Smart Materials and Structures 14 (2005) 515–523. [7] Z. Qian, F. Jin, K. Kishimoto, Z.T. Lu, Propagation behavior of Love waves in a functionally graded half-space with initial stress, Int. J. Sol. Str. 46 (2009) 1354–1361. [8] Z. Qian, F. Jin, T. Lu, K. Kishimoto, Transverse surface waves in a 6 mm piezoelectric material carrying a prestressed metal layer of finite thickness, App. Phy. Let. 94 (2009) 093513. [9] Z. Qian, F. Jin, T. Lu, K. Kishimoto, S. Hirose, Effect of initial stress on Love waves in a piezoelectric structure carrying a functionally graded material layer, Ultr. 50 (2010) 84–90. [10] H. Liu, Z.B. Kuang, Z.M. Cai, Propagation of Bleustein–Gulyaev waves in a prestressed layered piezoelectric structure, Ultr. 41 (2003) 397–405. [11] A. Njeh, T. Wieder, and H. Fuess, Powder Diffr. 15, 211 (2000) [12] A. Njeh, D. Schneider, H. Fuess, and M. H. Ben Ghozlen, Z. Naturforsch.64A, 112 (2009). [13] S. Mseddi, F. Tekeli, A. Njeh , W. Donner, M. H. Ben Ghozlen, Effect of initial stress on the propagation behavior of SAW in a layered piezoelectric structure of ZnO/Al2O3, Mec. Res. Com. 76 (2016) 24-31 [14] S. Mseddi, A. Njeh, M. H. Ben Ghozlen, Acoustoelastic Effects in Anisotropic Layered Structure of Cu/Si(001), Mec. Adv. Mat. Str 21 (2014) 710–715. [15] M. Kamel, S. Mseddi, A. Njeh, W. Donner, M. H. Ben Ghozlen, Acoustoelastic effect of textured (Ba,Sr)TiO3 thin films under an initial mechanical stress, J. App. Phy 118 (2015) 225305. [16] D Y Wang and C L Mak, Optical properties of Ba0.5Sr0.5TiO3 thin films grown on MgO substrates by pulsed laser deposition, Ceram. Inter, 30 (2004) 1745 [17] K Kim, Integration of Coplanar (Ba,Sr)TiO3 Microwave Phase Shifters onto Si Wafers Using TiO2 Buffer Layers, IEEE trans. on Ultras. Ferr. and freq. control, 53 (2006) 3 [18]C S Hwang et all, Deposition of extremely thin (Ba,Sr)TiO3 thin films for ultra-large-scale integrated dynamic random access memory application, Appl. Phys. Lett. 67 (1995) 2819 [19]O Vendik and I Vendik, Electromechanical coupling coefficient of isotropic sample with a marked electrostriction, J. Euro. Ceram. Soc. 27 (2007) 2949 [20] C. Fu, C. Yang, H. Chen, L. Hu, and Y.Wang, Mater. Lett. 59, 330 (2005). [21] J. Zhang, J. Zhai, X. Chou, and X. Yao, Mater. Chem. Phys. 111, 409 (2008). [22] T. Zhang, J. Wang, B. Zhang, J. Jiang, R. Pan, and J. Wang, Mater. Res. Bull. 43, 700 (2008). [23] S. Mseddi, A. Njeh, D. Schneider, H. Fuess, and M. H. Ben Ghozlen, J. Appl. Phys. 110, 104506 (2011). [24] O. G. Vendik and A. N. Rogachev, Tech. Phys. Lett. 25, 702 (1999). [25] S. Gevorgian, A. Vorobiev, and T. Lewin, J. Appl. Phys. 99, 124112 (2006). [26] S. Tappe, U. Boettger, and R. Waser, Appl. Phys. Lett. 85, 624 (2004). [27] H. X. Cao and Z. Y. Li, Phys. Lett. A 334, 429 (2005). [28] H. Wu, L. Wu, J.Li,G. Chai and S.Du, Phy.B. 405,1113-1118 (2010). [29] A. H. Fahmy and E. L. Adler, Appl. Phys. Lett. 22, 495 (1973). [30] E. L. Adler, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 41, 876 (1994).

Author name / Mechanics Research Communications00 (2015) 000–000

8

SC R

IP T

(a)

(b)

TE D

M

A

N

U

Figure 1: The coordinate system for SAW propagating on BST(100)(a) and BST(101)(b) multilayer, and the epitaxial relationship for all components

Figure 2: X-ray diffraction patterns of BST powder sample 20000

10000

BST/Pt(110)/MgO(110)

Pt(200)

MgO(200)

8000

BST/Pt(100)/MgO(100)

BST(100) 0 20

30

40

50

Intensity [c/s]

10000

EP

Intensity [c/s]

BST(200)

BST(202)

2000

60

70

Pt(220)

4000

0

80

20

2 [°]

CC

MgO(110)

BST(101)

6000

30

40

50

60

70

80

2 [°]

(a)

(b)

Figure 3: X-ray diffraction patterns of BST thin film deposited on a Pt(100)/MgO(100) substrate (a) and on a Pt(110)/MgO(110) (b) substrate. 5300

BST(100)/Pt(100)/MgO(100)

5500

5200

5400

V [m/s]

V [m/s]

BST(101)/Pt(110)/MgO(110)

5250

A

5600

5150 5100

5300

5050 5200

5000 5100

4950 20

40

60

80

100

120

140

160

180

20

200

40

60

80

100

120

140

160

180

200

f [MHz]

f [MHz]

(a) Figure 4: Experimental dispersion curves of the surface acoustic wave propagating for BST(100)/Pt(100)/MgO(100)(a) and BST(101)/Pt(110)/MgO(110)(b) structure.

(b)

Author name / Mechanics Research Communications00 (2015) 000–000

0,0015

(hkl) (100)

0,0010

Linear fit of  (201)

0,0005



9

(302)

0,0000

(101)

-0,0005 -0,0010

(103) -0,0015 0,0

0,2

0,4

0,6

0,8

1,0

2

sin ()

(a) 0,0015

Linear fit of 

(311)

0,0010

IP T

(hkl)

(100)



0,0005

-0,0005

SC R

(211)

0,0000

(111) -0,0010 -0,1

0,0

0,1

0,2

0,3

0,4

0,5

0,6

2

sin ()

0,7

(b)

U

Figure 5: Dependency of residual strain  as a function of sin 2  for BST(100)/Pt(100)/MgO(100) structure.  0,0014 0,0012

(hkl)

(101)

0,0010

Linear fit of 

N

(201) (302)

0,0008

0,0004

A



0,0006

0,0002

-0,0004 0,0

M

0,0000 -0,0002

0,1

(100)

0,2

0,3

0,4

0,5

2

sin ()

  as a function of sin 2  for BST(101)/Pt(110)/MgO(110)

TE D

Figure 6: Dependency of residual strain 5500

CC

phase velocity (m/s)

EP

5000

Vs BST100 Vf BST100

4500

Vs BST101 Vf BST101

4000

3500

3000 0,0

0,5

1,0

1,5

2,0

2,5

h/

A

Figure 7: The dispersion relations for the first wave modes of Rayleigh wave for the electrically free case and the electrically shorted case without initial stresses.

Author name / Mechanics Research Communications00 (2015) 000–000

10

2.5

2.0

K2 BST100 K2 BST101

K2 %

1.5

1.0

0.5

0.0 0.0

0.5

1.0

1.5

2.0

2.5

h/

IP T

Figure 8: Variations of the electromechanical coupling coefficient with h/λ for the first Rayleigh wave mode in the case without initial stress. 0,5

Vs/Vs BST100

0,3

Vf/Vf BST100 Vs/Vs BST101

0,2

Vf/Vf BST101 0,1

0,5

1,0

1,5

2,0

h/

Figure 9: Variations of phase velocity change

2,5

U

0,0 0,0

SC R

V/V (%)

0,4

V / V with h/λ for the electrically free case and the electrically shorted case of Rayleigh

A

N

wave in BST100 and BST101

0,010

M

0,008 0,006

k2 %

0,004 0,002

k2 BST100 k2 BST101

TE D

0,000 -0,002 -0,004

-0,006 0,0

0,5

1,0

1,5

2,0

2,5

h/

A

CC

EP

Figure 10: Variations of the electromechanical coupling coefficient with h/λ for the first Rayleigh wave mode

Author name / Mechanics Research Communications00 (2015) 000–000

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Table 1: Residual stresses and strain components for both BST structures. S  22 .

 33S

12S .

(M Pa)

 11S .  12S (M Pa) (M Pa) 10  3

10  3

.10 3

10  6

-420 -368

-422 -294

-2.24 -1.306

1.45 1.10

1.15 0

 11S

Structure

BST(100)/Pt/MgO BST(101)/Pt/MgO

S  22

0.103 0

-1.82 -1.6

Table 2: Material constants of Ba0.78Sr0.22TiO3 . Elastic constants (1011N/m2) Material constant

Piezoelectric constants (c/m2)

Dielectric constants (10-11F/m)

Dens ity (Kg/ m3)

e15

e31

e33

11

33

ρ

8.7 2

2.4 8

10. 84

761. 478

617. 223

C 1

C12

C13

C33

C44

C66

1

0.7 44

1.8 36

0.6 08

0.6 08

5902

IP T

0.7 56

A

CC

EP

TE D

M

A

N

U

SC R

Ba0.8Sr0.2 TiO3

1 . 9