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Piezoelectric coefficient measurement of piezoelectric thin films: an overview
Materials Chemistry and Physics 75 (2002) 12–18
Piezoelectric coefficient measurement of piezoelectric thin films: an overview J.-M. Liu a,b,c,∗ , B. Pan a , H.L.W. Chan a,b , S.N. Zhu a , Y.Y. Zhu a , Z.G. Liu a a
Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China Department of Applied Physics, Hong Kong Polytechnic University, Kowloon, Hong Kong International Centre for Materials Sciences, Chinese Academy of Sciences, Shenyang 110016, China b
c
Abstract An overview on the state-of-art piezoelectric measurements of thin films is given. The principles and advantages/disadvantages of the conventional techniques are discussed for piezoelectric applications. Concerning a direct measurement of piezoelectric coefficient and taking into account of 1.0–100.0 m in film thickness, a displacement of 0.1 nm cannot be reliably detected by utilizing the reverse piezoelectric effect, unless the probe’s resolution reaches up to 10−3 nm. The sensitivity of charge-integrator cannot be worse than ∼0.1 nC, typically. Such a high resolution in terms of displacement and charge may not be always reachable if the measurement is not carefully calibrated and manipulated. New demands on the techniques have been placed and a more careful selection of the techniques to be used is required. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Piezoelectric coefficient; Piezoelectric thin films
1. Introduction The rapid progress of micro-electro-mechanical systems (MEMS) has created a need of a number of new functional materials to be integrated in thin film form on silicon wafers for the fabrication of micro-machined devices in microelectronic, optoelectronic, biological and chemical fields among many others. It has been accepted that piezoelectric thin films as integrated into silicon technologies promise a tremendous number of applications. However, up-to-date, there might have been just the microwave acoustic delay lines and the surface-acoustic-wave (SAW) operating transducers representing the hugely manufactured devices where piezoelectric thin films are used as transducers. The long-term hanging-up of those promised applications is related to several important issues. (1) Most of the piezoelectric materials are inorganic oxides and organic polymers, an integration of which with the IC’s remains challenging. (2) Thin film piezoelectrics show a big variety of microstructures depending on the processing parameters. The applicable properties (direct and reverse piezoelectric effect, frequency resonance, electro-mechanical coupling, ∗ Corresponding author. Present address: Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China. Tel.: +86-25-3595979; fax: +86-25-3595535. E-mail address: [email protected] (J.-M. Liu).
etc.) are microstructure-sensitive. For examples, the piezoelectric coefficient (dij , i.e. d33 or d31 ) for Pb(Ti1−x Zr x )O3 (PZT) samples of the same composition but fabricated using different techniques may exhibit a difference over 10 times or more from one to another. (3) Stability and reliability of the property performance against circumstance fluctuations or irradiation remain to be confirmed in a sense of industrial manufacture. Therefore, development of an easily accessible and handling technique for dij evaluation without losing the reliability cannot be emphasized more [1–24]. This paper presents a comprehensive review of the state-of-art measuring techniques for dij of piezoelectric thin films.
2. Classification and the state-of-art 2.1. Principle Conventionally, the techniques for piezoelectric measurement of thin films fall into two categories: direct measurement and indirect measurement. With the former one relies on a direct probe of either the displacement induced by applied electric field or charge amount produced by imposing a load, from which d33 or e31 can be extracted out. The indirect measurement looks into the intrinsic linkage
0254-0584/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 2 ) 0 0 0 2 3 - 8
J.-M. Liu et al. / Materials Chemistry and Physics 75 (2002) 12–18
13
Fig. 1. A classification of currently employed techniques for piezoelectric coefficient measurement and their principles.
between the mechanical properties (stress and strain) and the electrical ones (voltage or charge), utilizing piezoelectric effects such as bulk or surface acoustic wave. An updated but incomplete list of those techniques in terms of the underlying mechanisms is given in Fig. 1. 2.2. Direct measurement 2.2.1. Normal load method This technique relies on the piezoelectric response of the film sample sandwiched between top and bottom electrodes to a mechanical load. It is basically a quasi-static method and the response rate is several orders of magnitude higher than the sampling rate so the data are reliable. For a force F applied to the sample, the electric charge Q is generated. A standard capacitor C0 (100 nF) much larger than the sample capacitance in order to meet the zero-field condition is connected in series with the sample. An electrometer parallel to C0 is employed to measure the voltage V0 over C0 . d33 (eff) = ∂D3 /∂T3 = Q/F = C0 V0 /F , where D3 and T3 are the longitudinal electrical displacement and stress normal to the sample surface, respectively. The sensitivity of Q is ∼1.0 pC. The advantage of this technique is simple and direct. The disadvantages include: (1) the stress distribution over the sample surface area covered with the tip is non-uniform due to the round shape of the tip; and (2) the compressed area of the sample surface is seriously clamped with its unloaded neighboring parts, so that the transverse effect takes part in the response. In practice, it is nearly impossible to
produce a tip with the contact surface as flat and smooth as the thin film surface, needless to mention its stiffness matter. 2.2.2. Periodic compressional force An improvement to the normal load yields using the ultrasonic piezoelectric transducer. A schematic of this is given in Fig. 2 [7]. A piezoelectric transducer connected with a metallic rod is submitted close to the sample surface and in contact with substrate. The step-like electric pulses from pulse generator are applied to the transducer that radiates longitudinal acoustic pulses into the metallic rod (probe) and then the coupling liquid (e.g. water). The acoustic pulses produce mechanical load onto the film. In turn, due to the piezoelectric effect, the mechanical displacement of the film produces output electrical signal at the electrodes, supposing the collected charge is Qm . Now replace the film sample with a reference piezoelectric layer of known d33,R such as LiNbO3 or quartz thin plate and perform the same measurement, collecting the charge QR .
Fig. 2. Experimental setup for d33 measurement based on acoustic wave propagation [7].
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Fig. 3. Experimental setup for cantilever technique [5].
Consequently, the film’s d33 is: d33 (eff) =
Qm d33,R QR
(1)
Here the load onto the coupling area of the film surface is uniformly applied once the area covered with coupling liquid is much larger than the top electrode. The reported sensitivity of this technique is d33 ∼0.03 pC. Nevertheless, the disadvantage of this method is the requirement of the exactly same performance to the film sample and the reference plate. This seems to be very difficult in terms of the probe–sample distance and the shape and size of the coupling liquid, especially for the latter if the film and reference plate have different wetting properties with the liquid. Furthermore, the pulsed frequency must be much higher than that of the conductive electrons in the film sample in order to avoid the circuit-shorting of the piezoelectric field, and much lower than that for the lattice fundamental mode in order to avoid the resonance. Of course, we do not mention the bending effect of the substrate, which is really hard to estimate. 2.2.3. Cantilever method The cantilever method is one of the most popular techniques for evaluating the piezoelectric property of thin films deposited on silicon wafers [2,5,18], because of its simplicity and easy handling. A schematic of this technique is shown in Fig. 3. The piezoelectric film is deposited onto an electrodecoated silicon cantilever beam with one end fixed and the other end being free. The beam has a length of l and thickness of h. A top electrode of area A is sputtered onto the film, covering from position x1 to x2 . A load at the free end of the beam produces a shift of ∆ along z-axis, generating the uniaxial strain S1 . The electrical displacement along z-axis is D3 = ε33 E3 + e31 S1 , where ε33 is the dielectric constant along z-axis, E3 the induced electric field and e31 the piezoelectric coefficient. Assuming no strain along z-axis or y-axis, which is not true, strictly speaking, the strain S1 , supposed to be uniform along x-axis over the whole beam is: x1 + x2 3∆h 1 − (2) S1 = 2 2l 3
Fig. 4. Schematic drawing of the experimental setup of PPR for d33 measurement [1].
The recorded voltage signal amplitude in the oscilloscope is: t AS1 e31 R 2 C 2 ω2 Vmax = − 1 + exp − (3) C 1 + R 2 C 2 ω2 RC where R and C are the input resistance and capacitance of the oscilloscope and ω the natural frequency of the beam. E + s E ), The measured e31 is related to d31 via d31 = e31 (s11 12 E E where s11 and s12 are the elastic compliance coefficients under steady electric field. Although only the transverse piezoelectric coefficient can be measured by the cantilever scheme, it has a unique advantage that its sensitivity is very high and the data are reliable. The measurement is performed under a condition close to the service circumstance of real sensors or actuators. The shortcomings reserved for this technique are, first, the zero strain along z-axis (S3 ) is assumed, which is not true. Secondly, one is allowed to wonder how true the assumption of uniform uniaxial strain along the beam is, consequently whether Eq. (2) is applicable or not. Finally, the time needed for releasing the load is a critical parameter determining the first Vmax recorded by the oscilloscope. The more accurate the data are the shorter the time is. With the manipulating mechanism shown in Fig. 3, it seems very hard to achieve short release time. A solution to this problem was proposed by Dubois and Muralt [2]. 2.2.4. Pneumatic pressure rig The methods described above produce the effective piezoelectric coefficient. A new technique for measuring real d33 , i.e. pneumatic pressure rig (PPR), was reported recently [1]. The PPR that utilizes gas pressure to produce charge seems to be simple and reliable. In Fig. 4, we reproduce the scheme of PPR developed by Xu et al. [1]. The silicon wafer deposited with piezoelectric thin film sandwiched with bottom and top electrodes is clamped by two plastic O-rings. The two rings are pressed from two sides
J.-M. Liu et al. / Materials Chemistry and Physics 75 (2002) 12–18
with two metallic components each machined with one cavity, configuring as a PPR, as shown in Fig. 4. The pressure in the two cavities remains the same at any time because they are connected with the same gas passage. The piezoelectric effect is activated by introducing (or releasing) high-pressure nitrogen gas into (or out of) the cavities so that a static pressure P is established onto the thin film surface and back-surface of the substrate too. The charge-integrator connecting with the electrodes at a virtual-ground mode probes the as-induced charge Q. d33 is then derived out through taking the slope of the induced charge against the pressure. A prime advantage of this method is that it produces real d33 that has been never achieved by direct measurement for thin film, to the authors’ best knowledge. The experiment indicated that the sensitivity of this method is ±10 pC N−1 , relatively worse than the cantilever method. 2.2.5. Optical interferometry The single-beam optical interferometry utilizes either Michelson or Mach-Zehnder scheme to detect microdisplacement of the moving sample surface, if the displacement is very small. In Fig. 5, shows the schematic drawing of the Michelson interferometer [6]. The operation mechanism of this technique is as follows. The polarized laser beam is focused by a condenser lens before being separated into two equal beams. The probing beam is directed to the sample surface coated with top electrode and reflected back to the beam-splitter. It recombines with the beam reflected from the reference mirror in the reference arm and produces an interference pattern at the detection plane. The interferometer’s optimized operation should be at the peak sensitivity point, i.e. the λ/4 position, which is achieved with the help of the feedback circuit connected to retain the system exactly at the point. When the sample is vibrating at a relative low frequency driven by an ac-signal of magnitude V0 , the corresponding interferometric intensity change is detected by a photodiode
15
and monitored by a lock-in amplifier. The intensity change is linearly proportional to the sample surface displacement once the latter is small (<10 nm). Because the interferometry has an extra-high resolution in displacement (<10−3 nm), the piezoelectric coefficient of ultra-thin films can be evaluated with good reliability. An alternative to the Michelson interferometry is the Mach-Zehnder method, which seems to produce higher displacement resolution than the Michelson one [4]. The high resolution of the two single-beam interferometers has been demonstrated by various researchers. Therefore, they are very helpful to evaluate the displacement profile over the whole sample surface. However, the single-beam interferometry has two drawbacks, basically vital. The first is that the film is clamped with the substrate, so that the pure thickness mode vibration is seriously clamped unless the two electrodes cover the whole sample, which is in real impossible. The second one is attributed to the possible substrate bending in response to the film vibration. The displacement due to substrate bending may be several orders of magnitude higher than that of the film itself. Kholkin et al. [22] gave an estimation of the substrate bending effect and proposed several ways to diminish it. The second shortcoming mentioned above can be avoided if one uses double-beam interferometry, because the pathlength difference of the two laser beams focusing onto forth and back surface of the sample remains the only signal probed by the interferometry. Therefore, the substrate bending effect can be in principle erased. The modified MachZehnder interferometry and optical Doppler vibrometer represent the most popular techniques for d33 measurement. 2.3. Indirect measurement A number of indirect methods are often employed to evaluate the piezoelectric properties of thin films. These methods rely more or less on the frequency resonance effect observed
Fig. 5. Schematic drawing of single-beam Michelson interferometry [6].
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J.-M. Liu et al. / Materials Chemistry and Physics 75 (2002) 12–18
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for a geometry-specified sample commonly consisting of piezoelectric thin films sandwiched with top and bottom electrodes and coated onto a bulk or thick plate (substrate). They can be in category named as the dynamic methods. The common difficulty of the dynamic methods is that the piezoelectric coefficient cannot be obtainable unless some tough assumptions are made and some properties from the bulk materials are consulted for the approximate calculations, from which d33 or d31 is finally evaluated. The number of the methods falling into this category is big and we just choose two of them for brief illustration.
Fig. 6. Configuration of two-layer resonator [9].
2.3.1. Bulk and surface acoustic wave response The acoustic wave methods look at the piezoelectric film grown on a substrate as a transducer, with an electrode pattern for the generation of bulk acoustic waves (BAW) or surface acoustic waves (SAW), driven by an ac electrical field. The BAW travel from the top electrode, along the longitudinal direction and toward the finite depth of the substrate and then echo back, whiles the SAW travel from one end, along the film surface layer and are received by the pattern electrode on the other end. With such a scheme and using a pulsed frequency measurement, the generated and detected signals were separated in time and could be measured to determine the transducer conversion loss. The subsequent train of echo signals was used to determine the acoustic propagation loss of the substrate. The coupling factor of the film is then determined. For BAW, d33 or e33 can be calculated from the coupling factor kt2 if a pure thickness mode is excited: d33 S s D k2 , (4) e33 = D d33 = ε33 33 t s33
where γF = 2π fLF /VF , γS = 2π fLS /VS , and LF , LS are the thickness of the film and substrate, respectively; S A L the clamped capacitance of the resonator; C0 = ε33 F F S 2 D d 2 the thickness coupling factor of the film; kt = ε33 s33 33 D = 1/(ρ V 2 ) the stiffd33 the piezoelectric coefficient; s33 F F ened elastic compliance coefficient; zS = ZS /ZF , where ZS = ρS VS AS is the acoustic impedance of the substrate and ZF = ρF VF AF is the acoustic impedance of the film; ρ S , VS , AS the density, wave velocity and surface area of the substrate; ρ F , VF , AF the density, wave velocity and surface area of the film; P0 the spontaneous polarization of the film. The impedance spectrum of this composite structure can be measured using the impedance anaylzer. Cheeke et al. [9] gave an example for deposited PZT film from which one can determine a series of frequencies at which |Zin (f)| reaches the maximal (peak) or minimal (valley) values, from which d33 or d31 can be evaluated. This composite resonance method is complicated from the computational reliability point of view. It is applicable to thick film rather than thin film, noting that thick films are preferred for MEMS applications.
where superscripts S and D denote the steady- and dynamic-mode, respectively. A detailed description of BAW scheme for evaluation of kt2 for a piezoelectric thin film transducer can be found in the well-known paper of Meitzler and Sittig [20]. For SAW, e31 or d31 can be evaluated in a similar manner. 2.3.2. Composite resonance The composite resonance is mainly developed for two-layer composite structure, one being the thin film and the other the substrate, without taking into account of the very thin electrodes [9]. It represents a simplified example of BAW. In fact, it is impossible to just excite resonance of the film since the film is rigidly clamped onto the substrate. Any modeling has to take the composite resonance into consideration. The two-layer composite resonator is given schematically in Fig. 6. The input electrical impedance is written from Sittig’s model: kt2 2 tan(γF /2) + zS tan γS 1 V Zin = 1− (5) = i jωC0 γF 1 + zS tan γS /tan γF
3. Summary A summary of the state-of-art of the measurement techniques is given for piezoelectric thin films. Table 1 summarizes a range of techniques, from which one can understand the advantages and disadvantages for each of them. Acknowledgements The authors acknowledge the financial support from the Innovation and Technology Fund of Hong Kong (ITF AF/147/98), the NSF of China through the innovative group project and project 50172020, and the Key Projects for Basic Research of China as well as LSSMS of Nanjing University. References [1] F. Xu, F. Chu, S. Trolier-McKinstry, J. Appl. Phys. 86 (1999) 588. [2] M. Dubois, P. Muralt, Sens. Actuat. A 77 (1999) 106.
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[3] W. Ren, H.J. Zhou, X.Q. Wu, L.Y. Zhang, X. Yao, Mater. Lett. 31 (1997) 185. [4] C.M. Lueng, H.L.W. Chan, C. Surya, W.K. Fong, C.L. Choy, P. Chow, M. Rosamond, J. Non-Cryst. Solids 254 (1999) 123. [5] B. Jaber, D. Remiens, E. Cattan, P. Tronc, B. Thierry, Sens. Actuat. A 63 (1997) 91. [6] S. Muensit, D. Wilson, I.L. Guy, Proceedings of the Optoelectronic and Microelectronic Materials and Devices, IEEE, New Jersey, 1997, p. 329. [7] P. Verardi, F. Cracium, M. Dinescu, Proceedings of the Ultrasonics Symposium, Vol. 1, IEEE, New Jersey, 1997, p. 569. [8] H.D. Chen, K.R. Udayakumar, L.E. Cross, J.J. Bernstein, L.C. Niles, Proceedings of the ISAF’94, IEEE, New Jersey, 1995, p. 495. [9] J.D.N. Cheeke, Y. Zhang, Z. Wang, M. Lukacs, M. Sayer, Proceedings of the Ultrasonics Symposium, Vol. 2, IEEE, New Jersey, 1998, p. 1125. [10] M. Sakata, S. Wakabayashi, H. Goto, H. Totani, M. Takeuchi, T. Yada, Proceedings of the MEMS ’96, IEEE, New Jersey, 1996, p. 263. [11] F.S. Hickernell, Proceedings of the Ultrasonics Symposium, Vol. 2, IEEE, New Jersey, 1998, p. 235. [12] V. Bharti, T. Kaura, R. Nath, IEEE Trans. Dielectrics Electrical Insulation 2 (1995) 1106.
[13] P. Drogui, P. Gonnard, L. Lebrun, M. Troccaz, D. Barbier, Proceedings of the ISAF’96, Vol. 1, IEEE, New Jersey, 1996, p. 153. [14] W. Tjhen, T. Tamagawa, C.P. Ye, C.C. Hsueh, P. Schiller, D.L. Polla, Proceedings of the MEMS’91, IEEE, New Jersey, 1991, p. 114. [15] K.R. Udayakumar, S.F. Bart, A.M. Flynn, J. Chen, L.S. Tavrow, L.E. Cross, R.A. Brooks, D.J. Ehrlich, Proceedings of the MEMS’91, IEEE, New Jersey, 1991, p. 109. [16] K.F. Etzold, R.A. Roy, K.L. Saenger, J.J. Cuomo, Proceedings of the Ultrasonics Symposium, IEEE, New Jersey, 1990, p. 747. [17] E. Markiewicz, J. Kulek, C. Pawlaczyk, IEEE Trans. Dielectrics Electrical Insulation 6 (1999) 304. [18] J.J. Bernstein, S.L. Finberg, K. Houston, L.C. Niles, H.D. Chen, L.E. Cross, K.K. Li, K. Udayakumar, IEEE Trans. Ultrasonics, Ferroelectrics, Frequency Contr. 44 (1997) 960. [19] D.L. Denburg, IEEE Trans. Sonics Ultrasonics SU-18 (1971) 31. [20] A.H. Meitzler, E.K. Sittig, J. Appl. Phys. 40 (1969) 4341. [21] Q.M. Zhang, W.Y. Pan, L.E. Cross, J. Appl. Phys. 63 (1988) 2492. [22] A.L. Kholkin, Ch. Wutchrich, D.V. Taylor, N. Setter, Rev. Sci. Instrum. 67 (1996) 1935. [23] Q.M. Zhang, S.J. Jang, L.E. Cross, J. Appl. Phys. 65 (1989) 2807. [24] J.-M. Liu, S.Y. Xu, W.Z. Zhou, X.H. Jiang, C.K. Ong, L.C. Lim, Mater. Sci. Eng. A 269 (1999) 67.
Piezoelectric coefficient measurement of piezoelectric thin films: an overview J.-M. Liu a,b,c,∗ , B. Pan a , H.L.W. Chan a,b , S.N. Zhu a , Y.Y. Zhu a , Z.G. Liu a a
Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China Department of Applied Physics, Hong Kong Polytechnic University, Kowloon, Hong Kong International Centre for Materials Sciences, Chinese Academy of Sciences, Shenyang 110016, China b
c
Abstract An overview on the state-of-art piezoelectric measurements of thin films is given. The principles and advantages/disadvantages of the conventional techniques are discussed for piezoelectric applications. Concerning a direct measurement of piezoelectric coefficient and taking into account of 1.0–100.0 m in film thickness, a displacement of 0.1 nm cannot be reliably detected by utilizing the reverse piezoelectric effect, unless the probe’s resolution reaches up to 10−3 nm. The sensitivity of charge-integrator cannot be worse than ∼0.1 nC, typically. Such a high resolution in terms of displacement and charge may not be always reachable if the measurement is not carefully calibrated and manipulated. New demands on the techniques have been placed and a more careful selection of the techniques to be used is required. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Piezoelectric coefficient; Piezoelectric thin films
1. Introduction The rapid progress of micro-electro-mechanical systems (MEMS) has created a need of a number of new functional materials to be integrated in thin film form on silicon wafers for the fabrication of micro-machined devices in microelectronic, optoelectronic, biological and chemical fields among many others. It has been accepted that piezoelectric thin films as integrated into silicon technologies promise a tremendous number of applications. However, up-to-date, there might have been just the microwave acoustic delay lines and the surface-acoustic-wave (SAW) operating transducers representing the hugely manufactured devices where piezoelectric thin films are used as transducers. The long-term hanging-up of those promised applications is related to several important issues. (1) Most of the piezoelectric materials are inorganic oxides and organic polymers, an integration of which with the IC’s remains challenging. (2) Thin film piezoelectrics show a big variety of microstructures depending on the processing parameters. The applicable properties (direct and reverse piezoelectric effect, frequency resonance, electro-mechanical coupling, ∗ Corresponding author. Present address: Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China. Tel.: +86-25-3595979; fax: +86-25-3595535. E-mail address: [email protected] (J.-M. Liu).
etc.) are microstructure-sensitive. For examples, the piezoelectric coefficient (dij , i.e. d33 or d31 ) for Pb(Ti1−x Zr x )O3 (PZT) samples of the same composition but fabricated using different techniques may exhibit a difference over 10 times or more from one to another. (3) Stability and reliability of the property performance against circumstance fluctuations or irradiation remain to be confirmed in a sense of industrial manufacture. Therefore, development of an easily accessible and handling technique for dij evaluation without losing the reliability cannot be emphasized more [1–24]. This paper presents a comprehensive review of the state-of-art measuring techniques for dij of piezoelectric thin films.
2. Classification and the state-of-art 2.1. Principle Conventionally, the techniques for piezoelectric measurement of thin films fall into two categories: direct measurement and indirect measurement. With the former one relies on a direct probe of either the displacement induced by applied electric field or charge amount produced by imposing a load, from which d33 or e31 can be extracted out. The indirect measurement looks into the intrinsic linkage
0254-0584/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 2 ) 0 0 0 2 3 - 8
J.-M. Liu et al. / Materials Chemistry and Physics 75 (2002) 12–18
13
Fig. 1. A classification of currently employed techniques for piezoelectric coefficient measurement and their principles.
between the mechanical properties (stress and strain) and the electrical ones (voltage or charge), utilizing piezoelectric effects such as bulk or surface acoustic wave. An updated but incomplete list of those techniques in terms of the underlying mechanisms is given in Fig. 1. 2.2. Direct measurement 2.2.1. Normal load method This technique relies on the piezoelectric response of the film sample sandwiched between top and bottom electrodes to a mechanical load. It is basically a quasi-static method and the response rate is several orders of magnitude higher than the sampling rate so the data are reliable. For a force F applied to the sample, the electric charge Q is generated. A standard capacitor C0 (100 nF) much larger than the sample capacitance in order to meet the zero-field condition is connected in series with the sample. An electrometer parallel to C0 is employed to measure the voltage V0 over C0 . d33 (eff) = ∂D3 /∂T3 = Q/F = C0 V0 /F , where D3 and T3 are the longitudinal electrical displacement and stress normal to the sample surface, respectively. The sensitivity of Q is ∼1.0 pC. The advantage of this technique is simple and direct. The disadvantages include: (1) the stress distribution over the sample surface area covered with the tip is non-uniform due to the round shape of the tip; and (2) the compressed area of the sample surface is seriously clamped with its unloaded neighboring parts, so that the transverse effect takes part in the response. In practice, it is nearly impossible to
produce a tip with the contact surface as flat and smooth as the thin film surface, needless to mention its stiffness matter. 2.2.2. Periodic compressional force An improvement to the normal load yields using the ultrasonic piezoelectric transducer. A schematic of this is given in Fig. 2 [7]. A piezoelectric transducer connected with a metallic rod is submitted close to the sample surface and in contact with substrate. The step-like electric pulses from pulse generator are applied to the transducer that radiates longitudinal acoustic pulses into the metallic rod (probe) and then the coupling liquid (e.g. water). The acoustic pulses produce mechanical load onto the film. In turn, due to the piezoelectric effect, the mechanical displacement of the film produces output electrical signal at the electrodes, supposing the collected charge is Qm . Now replace the film sample with a reference piezoelectric layer of known d33,R such as LiNbO3 or quartz thin plate and perform the same measurement, collecting the charge QR .
Fig. 2. Experimental setup for d33 measurement based on acoustic wave propagation [7].
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J.-M. Liu et al. / Materials Chemistry and Physics 75 (2002) 12–18
Fig. 3. Experimental setup for cantilever technique [5].
Consequently, the film’s d33 is: d33 (eff) =
Qm d33,R QR
(1)
Here the load onto the coupling area of the film surface is uniformly applied once the area covered with coupling liquid is much larger than the top electrode. The reported sensitivity of this technique is d33 ∼0.03 pC. Nevertheless, the disadvantage of this method is the requirement of the exactly same performance to the film sample and the reference plate. This seems to be very difficult in terms of the probe–sample distance and the shape and size of the coupling liquid, especially for the latter if the film and reference plate have different wetting properties with the liquid. Furthermore, the pulsed frequency must be much higher than that of the conductive electrons in the film sample in order to avoid the circuit-shorting of the piezoelectric field, and much lower than that for the lattice fundamental mode in order to avoid the resonance. Of course, we do not mention the bending effect of the substrate, which is really hard to estimate. 2.2.3. Cantilever method The cantilever method is one of the most popular techniques for evaluating the piezoelectric property of thin films deposited on silicon wafers [2,5,18], because of its simplicity and easy handling. A schematic of this technique is shown in Fig. 3. The piezoelectric film is deposited onto an electrodecoated silicon cantilever beam with one end fixed and the other end being free. The beam has a length of l and thickness of h. A top electrode of area A is sputtered onto the film, covering from position x1 to x2 . A load at the free end of the beam produces a shift of ∆ along z-axis, generating the uniaxial strain S1 . The electrical displacement along z-axis is D3 = ε33 E3 + e31 S1 , where ε33 is the dielectric constant along z-axis, E3 the induced electric field and e31 the piezoelectric coefficient. Assuming no strain along z-axis or y-axis, which is not true, strictly speaking, the strain S1 , supposed to be uniform along x-axis over the whole beam is: x1 + x2 3∆h 1 − (2) S1 = 2 2l 3
Fig. 4. Schematic drawing of the experimental setup of PPR for d33 measurement [1].
The recorded voltage signal amplitude in the oscilloscope is: t AS1 e31 R 2 C 2 ω2 Vmax = − 1 + exp − (3) C 1 + R 2 C 2 ω2 RC where R and C are the input resistance and capacitance of the oscilloscope and ω the natural frequency of the beam. E + s E ), The measured e31 is related to d31 via d31 = e31 (s11 12 E E where s11 and s12 are the elastic compliance coefficients under steady electric field. Although only the transverse piezoelectric coefficient can be measured by the cantilever scheme, it has a unique advantage that its sensitivity is very high and the data are reliable. The measurement is performed under a condition close to the service circumstance of real sensors or actuators. The shortcomings reserved for this technique are, first, the zero strain along z-axis (S3 ) is assumed, which is not true. Secondly, one is allowed to wonder how true the assumption of uniform uniaxial strain along the beam is, consequently whether Eq. (2) is applicable or not. Finally, the time needed for releasing the load is a critical parameter determining the first Vmax recorded by the oscilloscope. The more accurate the data are the shorter the time is. With the manipulating mechanism shown in Fig. 3, it seems very hard to achieve short release time. A solution to this problem was proposed by Dubois and Muralt [2]. 2.2.4. Pneumatic pressure rig The methods described above produce the effective piezoelectric coefficient. A new technique for measuring real d33 , i.e. pneumatic pressure rig (PPR), was reported recently [1]. The PPR that utilizes gas pressure to produce charge seems to be simple and reliable. In Fig. 4, we reproduce the scheme of PPR developed by Xu et al. [1]. The silicon wafer deposited with piezoelectric thin film sandwiched with bottom and top electrodes is clamped by two plastic O-rings. The two rings are pressed from two sides
J.-M. Liu et al. / Materials Chemistry and Physics 75 (2002) 12–18
with two metallic components each machined with one cavity, configuring as a PPR, as shown in Fig. 4. The pressure in the two cavities remains the same at any time because they are connected with the same gas passage. The piezoelectric effect is activated by introducing (or releasing) high-pressure nitrogen gas into (or out of) the cavities so that a static pressure P is established onto the thin film surface and back-surface of the substrate too. The charge-integrator connecting with the electrodes at a virtual-ground mode probes the as-induced charge Q. d33 is then derived out through taking the slope of the induced charge against the pressure. A prime advantage of this method is that it produces real d33 that has been never achieved by direct measurement for thin film, to the authors’ best knowledge. The experiment indicated that the sensitivity of this method is ±10 pC N−1 , relatively worse than the cantilever method. 2.2.5. Optical interferometry The single-beam optical interferometry utilizes either Michelson or Mach-Zehnder scheme to detect microdisplacement of the moving sample surface, if the displacement is very small. In Fig. 5, shows the schematic drawing of the Michelson interferometer [6]. The operation mechanism of this technique is as follows. The polarized laser beam is focused by a condenser lens before being separated into two equal beams. The probing beam is directed to the sample surface coated with top electrode and reflected back to the beam-splitter. It recombines with the beam reflected from the reference mirror in the reference arm and produces an interference pattern at the detection plane. The interferometer’s optimized operation should be at the peak sensitivity point, i.e. the λ/4 position, which is achieved with the help of the feedback circuit connected to retain the system exactly at the point. When the sample is vibrating at a relative low frequency driven by an ac-signal of magnitude V0 , the corresponding interferometric intensity change is detected by a photodiode
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and monitored by a lock-in amplifier. The intensity change is linearly proportional to the sample surface displacement once the latter is small (<10 nm). Because the interferometry has an extra-high resolution in displacement (<10−3 nm), the piezoelectric coefficient of ultra-thin films can be evaluated with good reliability. An alternative to the Michelson interferometry is the Mach-Zehnder method, which seems to produce higher displacement resolution than the Michelson one [4]. The high resolution of the two single-beam interferometers has been demonstrated by various researchers. Therefore, they are very helpful to evaluate the displacement profile over the whole sample surface. However, the single-beam interferometry has two drawbacks, basically vital. The first is that the film is clamped with the substrate, so that the pure thickness mode vibration is seriously clamped unless the two electrodes cover the whole sample, which is in real impossible. The second one is attributed to the possible substrate bending in response to the film vibration. The displacement due to substrate bending may be several orders of magnitude higher than that of the film itself. Kholkin et al. [22] gave an estimation of the substrate bending effect and proposed several ways to diminish it. The second shortcoming mentioned above can be avoided if one uses double-beam interferometry, because the pathlength difference of the two laser beams focusing onto forth and back surface of the sample remains the only signal probed by the interferometry. Therefore, the substrate bending effect can be in principle erased. The modified MachZehnder interferometry and optical Doppler vibrometer represent the most popular techniques for d33 measurement. 2.3. Indirect measurement A number of indirect methods are often employed to evaluate the piezoelectric properties of thin films. These methods rely more or less on the frequency resonance effect observed
Fig. 5. Schematic drawing of single-beam Michelson interferometry [6].
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for a geometry-specified sample commonly consisting of piezoelectric thin films sandwiched with top and bottom electrodes and coated onto a bulk or thick plate (substrate). They can be in category named as the dynamic methods. The common difficulty of the dynamic methods is that the piezoelectric coefficient cannot be obtainable unless some tough assumptions are made and some properties from the bulk materials are consulted for the approximate calculations, from which d33 or d31 is finally evaluated. The number of the methods falling into this category is big and we just choose two of them for brief illustration.
Fig. 6. Configuration of two-layer resonator [9].
2.3.1. Bulk and surface acoustic wave response The acoustic wave methods look at the piezoelectric film grown on a substrate as a transducer, with an electrode pattern for the generation of bulk acoustic waves (BAW) or surface acoustic waves (SAW), driven by an ac electrical field. The BAW travel from the top electrode, along the longitudinal direction and toward the finite depth of the substrate and then echo back, whiles the SAW travel from one end, along the film surface layer and are received by the pattern electrode on the other end. With such a scheme and using a pulsed frequency measurement, the generated and detected signals were separated in time and could be measured to determine the transducer conversion loss. The subsequent train of echo signals was used to determine the acoustic propagation loss of the substrate. The coupling factor of the film is then determined. For BAW, d33 or e33 can be calculated from the coupling factor kt2 if a pure thickness mode is excited: d33 S s D k2 , (4) e33 = D d33 = ε33 33 t s33
where γF = 2π fLF /VF , γS = 2π fLS /VS , and LF , LS are the thickness of the film and substrate, respectively; S A L the clamped capacitance of the resonator; C0 = ε33 F F S 2 D d 2 the thickness coupling factor of the film; kt = ε33 s33 33 D = 1/(ρ V 2 ) the stiffd33 the piezoelectric coefficient; s33 F F ened elastic compliance coefficient; zS = ZS /ZF , where ZS = ρS VS AS is the acoustic impedance of the substrate and ZF = ρF VF AF is the acoustic impedance of the film; ρ S , VS , AS the density, wave velocity and surface area of the substrate; ρ F , VF , AF the density, wave velocity and surface area of the film; P0 the spontaneous polarization of the film. The impedance spectrum of this composite structure can be measured using the impedance anaylzer. Cheeke et al. [9] gave an example for deposited PZT film from which one can determine a series of frequencies at which |Zin (f)| reaches the maximal (peak) or minimal (valley) values, from which d33 or d31 can be evaluated. This composite resonance method is complicated from the computational reliability point of view. It is applicable to thick film rather than thin film, noting that thick films are preferred for MEMS applications.
where superscripts S and D denote the steady- and dynamic-mode, respectively. A detailed description of BAW scheme for evaluation of kt2 for a piezoelectric thin film transducer can be found in the well-known paper of Meitzler and Sittig [20]. For SAW, e31 or d31 can be evaluated in a similar manner. 2.3.2. Composite resonance The composite resonance is mainly developed for two-layer composite structure, one being the thin film and the other the substrate, without taking into account of the very thin electrodes [9]. It represents a simplified example of BAW. In fact, it is impossible to just excite resonance of the film since the film is rigidly clamped onto the substrate. Any modeling has to take the composite resonance into consideration. The two-layer composite resonator is given schematically in Fig. 6. The input electrical impedance is written from Sittig’s model: kt2 2 tan(γF /2) + zS tan γS 1 V Zin = 1− (5) = i jωC0 γF 1 + zS tan γS /tan γF
3. Summary A summary of the state-of-art of the measurement techniques is given for piezoelectric thin films. Table 1 summarizes a range of techniques, from which one can understand the advantages and disadvantages for each of them. Acknowledgements The authors acknowledge the financial support from the Innovation and Technology Fund of Hong Kong (ITF AF/147/98), the NSF of China through the innovative group project and project 50172020, and the Key Projects for Basic Research of China as well as LSSMS of Nanjing University. References [1] F. Xu, F. Chu, S. Trolier-McKinstry, J. Appl. Phys. 86 (1999) 588. [2] M. Dubois, P. Muralt, Sens. Actuat. A 77 (1999) 106.
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[3] W. Ren, H.J. Zhou, X.Q. Wu, L.Y. Zhang, X. Yao, Mater. Lett. 31 (1997) 185. [4] C.M. Lueng, H.L.W. Chan, C. Surya, W.K. Fong, C.L. Choy, P. Chow, M. Rosamond, J. Non-Cryst. Solids 254 (1999) 123. [5] B. Jaber, D. Remiens, E. Cattan, P. Tronc, B. Thierry, Sens. Actuat. A 63 (1997) 91. [6] S. Muensit, D. Wilson, I.L. Guy, Proceedings of the Optoelectronic and Microelectronic Materials and Devices, IEEE, New Jersey, 1997, p. 329. [7] P. Verardi, F. Cracium, M. Dinescu, Proceedings of the Ultrasonics Symposium, Vol. 1, IEEE, New Jersey, 1997, p. 569. [8] H.D. Chen, K.R. Udayakumar, L.E. Cross, J.J. Bernstein, L.C. Niles, Proceedings of the ISAF’94, IEEE, New Jersey, 1995, p. 495. [9] J.D.N. Cheeke, Y. Zhang, Z. Wang, M. Lukacs, M. Sayer, Proceedings of the Ultrasonics Symposium, Vol. 2, IEEE, New Jersey, 1998, p. 1125. [10] M. Sakata, S. Wakabayashi, H. Goto, H. Totani, M. Takeuchi, T. Yada, Proceedings of the MEMS ’96, IEEE, New Jersey, 1996, p. 263. [11] F.S. Hickernell, Proceedings of the Ultrasonics Symposium, Vol. 2, IEEE, New Jersey, 1998, p. 235. [12] V. Bharti, T. Kaura, R. Nath, IEEE Trans. Dielectrics Electrical Insulation 2 (1995) 1106.
[13] P. Drogui, P. Gonnard, L. Lebrun, M. Troccaz, D. Barbier, Proceedings of the ISAF’96, Vol. 1, IEEE, New Jersey, 1996, p. 153. [14] W. Tjhen, T. Tamagawa, C.P. Ye, C.C. Hsueh, P. Schiller, D.L. Polla, Proceedings of the MEMS’91, IEEE, New Jersey, 1991, p. 114. [15] K.R. Udayakumar, S.F. Bart, A.M. Flynn, J. Chen, L.S. Tavrow, L.E. Cross, R.A. Brooks, D.J. Ehrlich, Proceedings of the MEMS’91, IEEE, New Jersey, 1991, p. 109. [16] K.F. Etzold, R.A. Roy, K.L. Saenger, J.J. Cuomo, Proceedings of the Ultrasonics Symposium, IEEE, New Jersey, 1990, p. 747. [17] E. Markiewicz, J. Kulek, C. Pawlaczyk, IEEE Trans. Dielectrics Electrical Insulation 6 (1999) 304. [18] J.J. Bernstein, S.L. Finberg, K. Houston, L.C. Niles, H.D. Chen, L.E. Cross, K.K. Li, K. Udayakumar, IEEE Trans. Ultrasonics, Ferroelectrics, Frequency Contr. 44 (1997) 960. [19] D.L. Denburg, IEEE Trans. Sonics Ultrasonics SU-18 (1971) 31. [20] A.H. Meitzler, E.K. Sittig, J. Appl. Phys. 40 (1969) 4341. [21] Q.M. Zhang, W.Y. Pan, L.E. Cross, J. Appl. Phys. 63 (1988) 2492. [22] A.L. Kholkin, Ch. Wutchrich, D.V. Taylor, N. Setter, Rev. Sci. Instrum. 67 (1996) 1935. [23] Q.M. Zhang, S.J. Jang, L.E. Cross, J. Appl. Phys. 65 (1989) 2807. [24] J.-M. Liu, S.Y. Xu, W.Z. Zhou, X.H. Jiang, C.K. Ong, L.C. Lim, Mater. Sci. Eng. A 269 (1999) 67.