Research paper
Residual stress and Young's modulus of pulsed laser deposited PZT thin
films: Effect of thin film composition and crystal direction of
Si cantilevers
H. Nazeer
a, M.D. Nguyen
b,c,d, G. Rijnders
b, L. Abelmann
a,e,⁎
, Ö. Sardan Sukas
baTransducers Science and Technology (TST), MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500, AE, Enschede, The Netherlands b
Inorganic Materials Science (IMS), MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500, AE, Enschede, The Netherlands
c
SolMateS B.V., Drienerlolaan 5, Building 46, 7522, NB, Enschede, The Netherlands
d
International Training Institute for Materials Science (ITIMS), Hanoi University of Science and Technology, No. 1 Dai Co Viet road, Hanoi, 10000, Viet Nam
e
KIST Europe, Campus E7 1, 66123 Saarbrucken, Germany
a b s t r a c t
a r t i c l e i n f o
Article history: Received 9 October 2015
Received in revised form 2 March 2016 Accepted 3 April 2016
Available online 13 April 2016
We investigated the residual stress and Young's modulus of Pb(ZrxTi1−x)O3(PZT) thinfilms with a (110) preferred orientation and a composition x ranging from 0.2 to 0.8. Thefilms are grown by pulsed laser deposition on silicon cantilevers aligned along the〈110〉 and 〈100〉 silicon crystal directions. Changes in resonance frequency and static bending of the cantilevers are used to determine the Young's modulus and residual stress respectively. The Young's modulus was found to be in the range of 100–200 GPa. The residual stress is tensile and shows a sharp increase from about 50 to 250 MPa at a composition of x = 0.2 to 0.4. These mechanical parameters clearly depend on the cantilever orientation with respect to the silicon crystal, which we suspect to be linked to the epitaxial growth of thefilms. The variation in stress with composition can be explained by the difference in thermal expansion between silicon and PZT, if we assume an intrinsic stress of 200–300 MPa to be already present immediately after deposition. Strain calculated from X-ray diffraction data leads to unreasonably high residual stress values, at least one order of magnitude higher than measured by cantilever bending.
© 2016 Elsevier B.V. All rights reserved.
1. Introduction
Lead zirconate titanate Pb(ZrxTi1−x)O3(PZT) is an eminent material
that has been identified for micro-electromechanical system (MEMS)
devices because of its excellent ferroelectric and piezoelectric properties
[1,2]. Recent advancements can be observed by the use of PZT thinfilms in MEMS, for instance micro-pumps[3], probe based data storage[4], micro-machined ultrasonic transducers[5], ferroelectric random access memory[6], accelerometers[7]and energy harvesting devices[8]. The properties of PZT thinfilms can be tuned by changing the Zr/Ti ratio to make them suitable for a particular application[9]. For instance, Ti-rich PZT (x = 0.2) is used in energy harvesting devices[10], whereas the composition Pb(Zr0·52Ti0.48)O3is suitable for a wide variety of
appli-cations requiring a high piezoelectric response[11]. This control of properties by varying the Zr/Ti ratio is accompanied by a variation in
the mechanical characteristics of the PZT thinfilms, of which the
Young's modulus and residual stress are investigated in this paper. Sol–gel[12], sputter-[13]and pulsed laser deposition (PLD)[1]are used for the fabrication of PZT thinfilms. These processes result in the
built up of residual stress, depending on the process parameters and the deposition process itself. Residual stress also depends on the proper-ties of the used substrate because of the very different mechanical and thermal properties of the substrate as compared to the PZT thinfilms. When combined these two effects result in residual stress with values reported in literature from one to several hundred MPa[14].
The functionality and reliability of PZT thinfilm devices depend, among other factors, on the residual stress in the PZT thinfilms. For in-stance, strain induced modification of the dielectric properties of thin films was discussed by Horwitz et al.[15]. Similarly, piezoelectric and electromechanical properties vary with the residual stress[16,17]. Controlling the crystal orientation by utilizing stresses is discussed in
[18,19], whereas Desu et al. discussed the effect of residual stress on the electrical properties such as resistivity[20]. In order to fabricate
reliable MEMS devices utilizing PZT thinfilms as an active device
layer, it is necessary to accurately investigate the compositional depen-dence of residual stress.
Single crystal silicon is an elastically anisotropic material. We also found an anisotropy in the Young's modulus of Pb(Zr0·52Ti0.48)O3thin
film deposited on silicon cantilevers aligned in the 〈110〉 and 〈100〉 crys-tal directions of silicon[21]. Therefore, we investigate the compositional dependence of residual stress in PZT thinfilms deposited on the 〈110〉 and〈100〉silicon cantilevers, taking into account the anisotropic Young's
⁎ Corresponding author.
E-mail address:l.abelmann@utwente.nl(L. Abelmann).
http://dx.doi.org/10.1016/j.mee.2016.04.004
0167-9317/© 2016 Elsevier B.V. All rights reserved.
Contents lists available atScienceDirect
Microelectronic Engineering
j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / m e emodulus of PZT thinfilms and silicon. The design and fabrication of MEMS devices using PZT thinfilms as an active device layer on single crystal silicon substrate require the residual stress values of PZT along different crystal direction of silicon, which we investigate in this paper. The residual stress of pulsed laser deposited PZT thinfilms was de-termined by measuring the changes in static deflection of cantilevers, on which thefilms were deposited. This residual stress was compared to stress calculated from the X-ray diffraction (XRD) measurements and Young's modulus and to stress originating from a mismatch in ther-mal expansion coefficients between PZT and the silicon substrate. The theoretical background of these methods are explained inSection 2. In
Sections 3.1 and 3.2, the fabrication of micron sized measurement devices and the deposition of the PZT thinfilms are explained. Residual stress in the PZT thinfilms depends on their orientation, therefore we performed XRD measurements to analyse the crystal orientation of
different compositions of PZT thinfilms. These measurements are
discussed inSection 3.3. Resonance frequency and static deflection measurements were performed to determine the in-plane Young's modulus and residual stress in PZT thinfilms, seeSections 3.4 and 3.5. Measurement results are reported inSection 4. Finally, a comparison between the different methods to determine the residual stress is discussed inSection 5.
2. Theory
2.1. Stress determined from cantilever bending
PZT thinfilms of various compositions were deposited by PLD on
separate wafers after the release of the cantilevers from the substrate (seeSections 3.1 and 3.2). Tension or compression in the PZT thinfilm leads to a curvature of the cantilever on which it is deposited (see
Fig. 1). The static deflection of the free end of the cantilever was measured both before and after deposition. The residual stress in the thinfilm was determined by using Stoney's equation (Eq.(1)), which is valid when the thickness offilm is very small in comparison to the thickness of the substrate[22,23]:
σf¼ 1 6 Est2s 1−νs ð ÞRtf; with R ¼ L2 2ξ; ð1Þ
the symbols are residual stressσ, Young's modulus E, thickness t, length L, radius of curvature R, Poisson's ratio v and deflection ξ respectively. Subscripts‘s’ and ‘f’ denote the silicon and PZT thin film.
The residual stress is a combination of stress caused by the PZTfilm itself and to some extent due to the bottom electrode SrRuO3(SRO) and
buffer layer yttria-stabilized zirconia (YSZ). However, the PZTfilm is much thicker than the underlying layers, therefore curvature is mainly caused by the PZT thinfilm.
2.2. Stress originating from thermal expansion differences
There are two main mechanisms for stress contribution in the PZT thinfilms: stress developed during growth of the film and stress caused by cooling down from the deposition temperature due to a difference in thermal expansion of thefilm and the substrate. By taking into account only the thermal mismatch effect, the residual stress in the PZT thin films can be calculated using the average coefficient of thermal expansion (CTE) of the PZT thinfilms and silicon in the temperature range between room temperature and deposition temperature (600 °C) from Eq.(2).
σf¼ αð f−αsÞΔT Ef
1−νf ð2Þ
Symbols α, v and ΔT are the average CTE, poisson's ratio and
difference in deposition (600 °C) and room temperature (20 °C), respectively. In this studyαs= 3.6 × 10−6°C−1[24,25,26]and vf=
0.3[27,28]were used.
2.3. Stress determined from lattice strain
From the X-ray diffraction (XRD) data one can estimate the in-plane strain in thefilm deposited on the substrate, taking the values of PZT bulk ceramic as a non-strained reference. In combination with the mea-sured in-plane Young's modulus, residual stress can be calculated as: σf¼ aip;c−aip; f E1−νf
f ð3Þ
In the above equation aip,cand aip,fare the in-plane lattice
parame-ters of the PZT bulk ceramics and PZT thinfilms, respectively. The lattice parameters of the PZT thinfilms for different compositions (x = 0.2– 0.8) were calculated from the XRD patterns whereas, published data were used bulk PZT ceramics[29]. The residual stress was calculated by these two methods and compared with the stress measured from cantilever bending inSection 5.
3. Experimental details
3.1. Fabrication of silicon cantilevers
Fabrication of the cantilevers from double side polished single crys-tal silicon on insulator (SOI) wafers is discussed in detail in[21]. The thickness of the cantilevers is determined by the thickness of the (001) silicon device layer (3.0 ± 0.5). Standard photolithography is used to define the cantilever width of 30 and length varying from 250 to 350 in steps of 10. The photo lithography mask is transferred into
the device layer by deep reactive ion etching (DRIE) [30]. The
cantilevers are freed from the handle wafer by means of a backside DRIE etch, with different process settings. During this etch, the front side of the wafer is protected by a polyimide pyralin coating. An illustra-tion of this important process step is given inFig. 2(a). In thefinal step, the buried oxide etch stop layer of 500 thickness is etched by hydrofluoric acid vapours[31]. Cantilevers are characterised by optical and scanning electron microscopy (seeFig. 2(b)). Cantilevers with different crystal orientation and through holes to release the cantilevers can be clearly seen in the samefigure.
3.2. PZT thinfilm deposition
The pulsed laser deposition technique allows us to epitaxially grow PZT on silicon substrates, as explained in[32]. The deposition starts with 10 thick buffer layers of yttria-stabilized zirconia (YSZ) and strontium ruthenate (SRO), followed by a 100 thick PZT without break-ing the vacuum. Different Zr/Ti compositions of Pb(ZrxTi1−x)O3(x = Fig. 1. Schematical representation of a cantilever fabricated from a silicon on insulator
wafer. The upward static deflection is due to the tensile residual stress in the PZT thin film that was grown on the cantilever.
0.2,0.3,0.4,0.52,0.6 and 0.8) were deposited on individual dies. Each die is containing 66 cantilevers, of which 22 cantilevers in two identical sets of 11 cantilevers of varying lengths. Two sets oriented along the〈110〉 and〈100〉 crystal directions of silicon were measured.
3.3. XRD measurements
A Bruker D8 Discover X-ray diffractometer with a Cu Kα cathode in the Bragg-Brentano geometry was used to investigate the orientation of the obtained PZT thinfilms. X-ray radiation of 0.15 wavelength was
used at 40 and 40. We measuredθ–2θ scans in the range of 20–80°
with 0.01°/s for all compositions of the PZT thinfilms (x = 0.2–0.8). The peaks in the diffraction patterns of the different compositions of
PZT thinfilms were identified using the JCPDS database. Results are
discussed inSection 4.1.
3.4. Resonance frequency measurements
The resonance frequency of cantilevers was measured both before and after deposition of the PZT. From the frequency shift we can deter-mine the Young's modulus of the deposited thinfilm[21], provided that we know the density andfilm thickness. Cantilevers of varying lengths, aligned parallel to the〈110〉 and 〈100〉 crystal directions of silicon, were measured by a MSA-400 micro system analyzer scanning laser-Doppler vibrometer. Measurements were taken at ambient conditions, using only thermal excitation of the resonance. From the amplitude spectrum, the resonance frequency was obtained by curvefitting with a theoreti-cal expression for a second order mass-spring system with damping. 3.5. Static deflection measurements
The residual stress of the deposited PZT thinfilms was determined from the radius of curvature of the cantilevers, which we measured by white light interferometry. In all cases, the profile of the cantilevers measured before the deposition of the PZT thinfilms was straight within the accuracy of measurement, so only the curvature after deposition
needs to be determined. A measurement of a 250 long cantilever after deposition of PZT is shown inFig. 3(a). From this measurement we ob-tained the maximum deflection of the free end of the cantilever, as shown inFig. 3(b). This information was used to calculate the curvature R of the cantilevers, so that we can determine the residual stress using Eq.(1).
As an example, the residual stress in a Pb(Zr0·52Ti0.48)O3film
calcu-lated from the static deflection of cantilevers of varying length aligned parallel to the〈110〉 crystal direction of silicon is shown inFig. 3(c). As expected, the residual stress is independent on cantilever length. The mean value of the residual stress was found to be 263 with a standard error of ±1. A thorough error analysis was performed to calculate the propagation of errors to the calculated value of the residual stress of the PZT. The resulting values are presented as error bars for each single cantilever.
4. Measurement results 4.1. Crystal structure
X-ray diffraction (XRD) patterns show that the PZT thinfilms have a (110)-preferred orientationfor all compositions (x = 0.2–0.8)[33]. There is a clear shift in the (110) peak position with increasing Zr content, which can be related to a variation in lattice parameters. The
out-of-plane lattice parameters were measured fromθ-2θ XRD scans.
Reciprocal space mapping was used to determine the in-plane lattice parameters. With increasing Zr content, the out-of-plane lattice param-eter increases, whereas the in-plane lattice paramparam-eter decreases slightly (seeFig. 4(a)). On the other hand, the ratio of in-plane lattice parameter (c) to out-of-plane lattice parameter (a) or c/a ratio decreases with increasing Zr content. The lattice parameters of PZT bulk ceramics[29]
are shown for comparison. The in-plane lattice parameters of PZT thin films are higher than those of PZT ceramics for x b 0.52 and lower for xN 0.52, whereas at x = 0.52, in-plane lattice parameters are approxi-mately equal.
The volume of a unit cell can be calculated from the lattice parame-ters and is shown as a function of composition inFig. 4(b). Compared to PZT bulk ceramics, the volume of a PZT unit cell is lower for the Zr rich compositions whereas it is higher for the Ti rich compositions. 4.2. Young's modulus
The in-plane Young's modulus of the PZT thinfilms is strongly
dependent on composition (Fig. 5(a)). In this study, the in-plane Young's modulus (E) of bulk PZT ceramics is defined as[34]:
E¼3k 2
33εrε0ð1−νÞÞ
d233 ð4Þ
where, k33, d33,εr,ε0and v are the electromechanical coupling factor,
longitudinal piezoelectric coefficient, material dielectric constant, vacu-um dielectric constant (ε0= 8.854 × 10−12F/m) and Poisson's ratio
(v = 0.3), respectively. The values of k33, d33andεras a function of Zr/
Ti ratio of bulk PZT ceramics are found in[35].
Moreover, there is a significant difference in Young's modulus for films deposited on cantilevers aligned parallel to the 〈100〉 and 〈110〉 silicon directions, which clearly indicates that the in-plane Young's modulus is anisotropic. We believe the origin of this effect lies in the epitaxial growth of the PZT on the silicon crystal[21].
The minimum value for the Young's modulus obtained from the can-tilevers aligned parallel to the〈100〉 silicon direction is found to be 103.5 with a standard error of ±1.9 for x = 0.52. At the same composition for the〈110〉 aligned cantilevers, the Young's modulus value is 113.5 GPa with a standard error of ± 1.5. For this cantilever orientation, the minimum Young's modulus is shifted towards Ti rich composition[33].
Fig. 2. (a) Illustration of the microfabrication process for the Si cantilevers. In subsequent steps, the pyralin and the photoresist layers will be removed. (b) Scanning electron micrograph of the fabricated Si cantilevers, aligned parellel to the〈100〉 or 〈100〉 crystal directions of silicon.
The dip in the Young's modulus value at x = 0.52 (〈100〉 silicon di-rection) is in agreement with the data published for PZT bulk ceramic, but the value is 44% higher[35]. Reasons for the higher Young's modulus of the PZT thinfilms, such as clamping effect, are discussed in detail in
[33].
4.3. Residual stress
The residual stress of PZT thinfilms deposited on the two crystal directions of silicon〈110〉 and 〈100〉 was determined to be tensile and
strongly dependent on thefilm composition (seeFig. 5(b)). For Ti
rich compositions of x = 0.2 and 0.3, the value of residual stress obtained from the〈110〉 aligned silicon cantilevers is small compared to the compositions of x = 0.4 and above. A similar trend was also ob-served from the cantilevers of varying length aligned parallel to the 〈100〉 crystal direction of silicon. For Ti rich compositions from x = 0.2
to x = 0.4, the stress increases sharply and then remains constant with-in error bounds at a higher value of around 270 MPa for the PZTfilms with compositions of x = 0.4 and above. However, on the〈110〉 oriented cantilever the residual stress still varies considerably at higher Zr values with a maximum of 291 at x = 0.52. These variations cannot be attributed to measurement uncertainties.
The effect of residual stress on the pinning of ferroelectric domains
have been proposed in the previous studies[37]. Residual stress
clamping hinders polarization switching and prevents domain wall motion, leading to a decrease in the ferroelectric polarization. Observing the results for the ferroelectric properties in our previous paper[33]
indicated that the remnant polarizations are decreased with increasing Zr content or with increasing residual stress. The relationship between ferroelectric and Zr/Ti ratio can be also explained by the changing c/a ratio. An increase in c/a ratio (or increasing Ti content) implies a larger displacement of the central Ti4 + ion, and hence, there is a larger
Fig. 3. White light interferometry measurement of the static deflection of a 250 long cantilever after deposition of a Pb(Zr0·52Ti0.48)O3thinfilm. Coordinates along the length and width of
the cantilever are represented by l and y. The variable z represents the out-of-plane deflection of the cantilever, which is as high as 4.
Fig. 4. (a) Lattice parameters and (b) volume of unit cells of the PZT thinfilms and PZT bulk ceramics as a function of Zr content. The trend is compared with the data published by Shirane et al.[29]for bulk PZT ceramics. The lines are guides to the eye.
switching polarization or remnant polarization [38]. Since large polarization and simple domain structure is desired, the tetragonal Ti-rich PZTfilms, such as Pb(Zr0·2Ti0.8)O3, with low residual stress are
in-teresting for storage applications[39]. However, the large piezoelectric coefficients of PZT films are very attractive for various microactuator and microsensor applications. While the polarization is more affected by the c/a ratio (or residual stress), the piezoelectric coefficient is influ-enced by the possible easy polarization directions. At the morphotropic phase boundary (Zr/Ti = 52/48) of PZT material, 14 possible polariza-tion direcpolariza-tions exist (six〈100〉 possible directions for the tetrahedral
phase and eight 〈111〉 possible directions for the rhombohedral
phase), where the material exhibits outstanding piezoelectric and dielectric properties[40]. Our previous papers indicated that the highest values of longitudinal piezoelectric coefficient (d33,f) and dielectric
constant are obtained at the Zr/Ti ratio of 52/48, while the transverse piezoelectric coefficient (d31,for e31,f) and mass-sensitivity are observed
to be highest for the tetragonal composition at the Zr/Ti ratio of 40/60, although these compositions have a high residual stress[33,41].
The minimum in the Young's modulus at x = 0.52, corresponds to a maximum in the piezoelectric coefficient d33,f, as reported earlier[33]. A
maximum in the residual stress at x = 0.52 was reported as well in literature for sol–gel derived PZT thin films [24], but at a lower maximum stress (90). Residual stress in sol–gel PZT thin film with a composition of x = 0.52 was also reported as 108 MPa and 180 MPa
by other authors[12,42]. Similar behaviour was also observed for
sputtered PZT thinfilms on platinum electrodes that show compressive stress for x = 0 and 0.1, which changes into tensile stress at x = 0.25 and above[36](seeFig. 5(b)). Compared to sputtered PZT, our measured PZT thinfilms show lower stress values for all compositions except at x = 0.4–0.52[36].
5. Discussion
5.1. Residual stress estimated from difference in thermal expansion The maximum in the residual stress at x = 0.52 coincides with a maximum of the CTE of PZT thinfilms[24]. This suggests that at least a part of the residual stress is caused by the difference in CTE between the PZTfilm and the silicon substrate. Average CTE data has not been
published for PZT thinfilm over the temperature range of interest.
Therefore, we extrapolated published thermal expansion data of PZT bulk ceramics[43,44]to 600 °C (seeFig. 6, curves labelled Noheda and Shirane). These values should be compared with the average CTE of silicon (dotted line).
Using Eq.(2)we can now calculate the residual stress building up during cooling down from deposition temperature (600 °C) to room temperature, (seeFig. 7, labelled RS-CTE). The trend is comparable to the residual stress calculated from cantilever deflection (curves labelled PZTfilms), but there is a large negative offset. We suspect that this offset is caused by a tensile residual stress of 200,300, which is already present at the deposition temperature.
For comparison, we show the average CTE calculated from cantilever bending for our PZTfilms as well inFig. 6. The compositional variation of CTE follows the same trend as published in literature for PZT bulk ceramics, but the values are 75% higher for x around 0.2 and 25% higher for x around 0.8 (seeFig. 6). The average CTE of our PZTfilms is higher compared to sol–gel PZT films (3.7 × 10−6–5.3 × 10−6°C−1)[24], and
comparable to the range of values mentioned for the other PLD-PZT films (6 × 10−6–7 × 10−6°C−1) in literature[45].
5.2. Residual stress estimated from lattice parameters
From the XRD data one can estimate the in-plane strain in different compositions of thefilm, taking the values of PZT bulk ceramics as a non-strained reference. In combination with the measured in-plane
Fig. 5. Composition dependence of (a) the Young's modulus (b) the residual stress of PZT thinfilms deposited on cantilevers aligned parallel to the 〈100〉 and 〈110〉 crystal direction of silicon. The trends are compared with the data published by Jaffe et al.[35]and Bruchhaus et al.[36]for bulk PZT ceramics. The lines are guides to the eye.
Fig. 6. Average coefficient of thermal expansion for cooling down from deposition temperature (600 °C) to room temperature as a function of composition. The average CTE is estimated from the residual stress calculated from the static deflection and the Young's modulus and compared with the data from[43,44]. Note that this average CTE also includes volume changes due to changes in crystal structure.
Young's modulus of the corresponding PZT composition in two crystal directions of silicon (Fig. 5(a)), one can estimate the residual stress by using Eq.(3). The strain in the PZT thinfilm varies from negative to pos-itive value as the Zr content increases, with a transition around x = 0.52. Therefore, the calculated residual stress also changes from compressive to tensile at x around 0.52, where the in-plane lattice parameters of the
PZT thinfilms matches with their PZT bulk ceramics. This approach
however leads to unlikely high values ranging from−3.2 + 4.0, at
least an order of magnitude higher than for the range of values observed from cantilever deflection, seeFig. 7(labelled RS-LP, note that the values are divided by 10!).
Discrepancy between the residual stress from XRD data and the
curvature measurements was already reported in literature [46],
although in their case the difference between XRD and curvature measurements was only a factor of two. We can therefore only assume that the peak shift in the XRD is not caused by strain alone, but also originates from other effects such as grain size variation and columnar growth of our epitaxial PZT thinfilms.
It should be noted that residual stress estimates from thermal ex-pansion differences or strain measured by XRD rely on bulk ceramic data and assumptions we made. For design purposes we suggest to use the actually measured data from cantilever curvature as reported inFig. 5(b).
6. Conclusion
We studied the effect of the Zr/Ti ratio on the Young's modulus and residual stress of Pb(ZrxTi1−x)O3thinfilms with a (110) preferred
ori-entation deposited on silicon cantilevers aligned along the〈110〉 and 〈100〉 silicon crystal direction.
The Young's modulus was found to be in the range of 100–120 GPa. The values and the variation with composition are different for both cantilever orientations. We believe this anisotropy is caused by the ep-itaxial growth of our PZTfilms on silicon.
The residual stress measured from static deflection was found to be tensile for all compositions measured (x = 0.2 to 0.8) and shows a sharp increase from about 50 to over 250 MPa for compositions from x = 0.2 to 0.4. These values are higher than commonly found for sol–gel depos-itedfilms (90 to 180 MPa). Compared to sputter deposited PZT films, the residual stress in our PZTfilms is lower for all compositions except for x = 0.4–0.52.
The residual stress forfilms deposited on 〈100〉 cantilevers remains constant for compositions of x = 0.4 and above, whereas it reaches a maximum value for the〈110〉 oriented cantilevers at x = 0.52, followed by a slight reduction. This effect is larger than the experimental error, and might again be connected to the epitaxial growth of thefilms.
A maximum residual stress of 291.1 MPa with a standard error of 4.9 MPa was measured for the Pb(Zr0·52Ti0.48)O3thinfilm deposited
on the silicon cantilever directed along the 〈110〉 silicon crystal
direction. For identical cantilevers but aligned parallel to the〈100〉 crystal direction of silicon, we found 270.6 MPa with a standard error of 2.9 MPa.
Using thermal expansion coefficients for PZT bulk ceramics and
silicon, we estimated the residual stress caused by cooling down from deposition to room temperature. The variation in stress with composi-tion is predicted qualitatively, but at a large negative offset. We suspect this is due to a 200–300 MPa intrinsic tensile stress which is already present at the deposition temperature.
The in-plane and out-of-plane lattice parameters measured by XRD on PZT thinfilms show a remarkably different behaviour with composi-tion as compared to PZT bulk ceramics. From the difference we estimat-ed the residual stress, which was found to be at least an order of magnitude higher than measured by cantilever bending. We suspect that the peak shifts in the XRD measurement are not only caused by strain variation, and therefore leads to the unreasonably high values.
The values reported here on the mechanical properties of pulsed laser deposited PZTfilms, and especially the presence of anisotropy, is crucial for the design and realisation of MEMS devices based on this exiting material.
Acknowledgements
The authors gratefully acknowledge the support of the SmartMix Program (SmartPie) of the Netherlands Ministry of Economic Affairs and the Netherlands Ministry of Education, Culture and Science. The authors also thank the assistance of M.J. de Boer for etching, R.G.P. Sanders for laser Doppler vibrometer measurements, J.G.M. Sanderink and H.A.G.M. van Wolferen for SEM, and N.R. Tas for helpful discussions. References
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