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Influence of Material Parameters on Acoustic Wave Propagation Modes in ZnO/Si Bi-Layered Structures Hui-dong Gao, Shu-yi Zhang, Senior Member, IEEE, Xue Qi, Kiyotaka Wasa, Life Fellow, IEEE, and Hao-dong Wu Abstract—The influences of material properties on acoustic wave propagation modes in ZnO/Si bi-layered structures are studied. The transfer matrix method is used to calculate dispersion relations, wave field distributions, and electromechanical coupling coefficients of acoustic wave propagation modes in ZnO/Si bi-layered systems, in which the thickness of the substrate is of the same order of magnitude as the wavelength of the propagating wave modes. The influences of the thin film parameters on the acoustic wave propagation modes and their electromechanical coupling coefficients of the wave modes also are obtained. In addition, some experimental results for characterizing the wave propagation modes and their frequencies have also been obtained, which agree well with the theoretical predictions.
I. Introduction iezoelectric ZnO thin films with c axis (hexagonsymmetrical axis) orientation have been widely used in electro-acoustic and microelectronic devices due to their high electromechanical coupling coefficients [1]–[4]. However, silicon wafers are the most widely used material for microelectronic, micromechanical, and microelectromechanical system (MEMS) devices [5], [6]. Combining the merits of the excellent piezoelectricity of ZnO and the versatility of Si, ZnO/Si systems are expected to be very promising structures in the development of electroacoustic, MEMS, and other integrated devices. Furthermore, several theoretical modeling works of the acoustic wave propagation in film/substrate bilayered structures were presented. Rayleigh surface acoustic wave (SAW) modes were considered when the thin films were thick enough compared with the wavelengths of SAW, in which the influence of the substrates was neglected [2], [7]. In some other works, Love wave modes were considered, dealing with the wave propagation in a structure of a thin film deposited on top of a half space [8], [9]. With more usual theoretical models the multilayered structures were considered as thin plates, for which different plate modes—
P
Manuscript received February 16, 2005; accepted May 9, 2005. This work is supported by National Natural Science Foundation of China under No. 10374051. The authors are with the Lab of Modern Acoustics, Institute of Acoustics, Nanjing University, Nanjing, 210093, China (e-mail:
[email protected]). K. Wasa is also with the Faculty of Science, Yokohama City University, Yokohama, Kanagawa, 236-0027, Japan.
Fig. 1. Multilayered structure configuration.
such as Lamb modes, flexural plate modes, SH-acoustic plate modes, and/or stiffened-shear modes and stiffened Lamb modes, etc.—have been calculated [10]–[13]. In ZnO/Si structures, the thicknesses of commercial silicon wafers are usually in the range of 100 to 500 µ, which are in the same order of ultrasonic wavelengths at the frequencies of several tens of megahertz. In this case, the influences of both the substrates and the thin films are all very significant for the wave propagation. In this paper, bi-layered structures with ZnO films deposited on Si substrates are considered. An exact modeling of the dispersion relation for multimodes propagation is carried out with the transfer matrix method, which is a very robust method for the numerical calculation of wave propagation in multilayered structures if the acoustic wavelengths are in the same order as the thicknesses of the structures [10], [11], [14], [15]. The influences of material parameters on the acoustic wave propagation also are studied in detail, which could be helpful for designing electro-acoustic devices, sensors, and actuators. The numerical calculations of the acoustic wave modes are compared with the experimental results for different thin film thicknesses. Reasonable match of the experimental measurements and the theoretical predictions is obtained.
II. Theory of Acoustic Wave Propagation in Multilayered Structures In order to solve the wave propagation problem in a multilayered structure (see Fig. 1), the governing equation of elastic waves should be satisfied in each layer. In a piezoelectric layer, under the quasistatic approximation,
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the coupled piezoelectric field equations are given by the equations of motion and electrostatic charge [16]: ⎧ ∂ 2 uk ∂2φ ⎪ ⎪ + ekij − ρ¨ uj = 0, cijkl ⎪ ⎪ ∂xl ∂xi ∂xi ∂xk ⎨
P[N ]+ = ΨP[1]− , .
⎪ ⎪ ∂2φ ∂ 2 uk ⎪ ⎪ ⎩εij − eijk = 0, ∂xi ∂xj ∂xi ∂xj
(1)
The constitutive relations are as: ⎧ ∂φ ⎪ , σij = cijkl Skl + ekij ⎪ ⎪ ⎨ ∂xk (2)
⎪ ⎪ ⎪ ⎩Dk = ekij Sij − εkl ∂φ , ∂xl where: ⎧ 1 ∂ui ∂uj ⎪ ⎪ S = + , ⎪ ij ⎪ ⎨ 2 ∂xj ∂xi
(3)
⎪ ⎪ ⎪ ∂φ ⎪ ⎩Ei = − , ∂xi
where ui and φ are the particle displacements and the electric potential, respectively; cijkl , ekij , and εij are the elastic constants, the piezoelectric constants and the dielectric constants, respectively; σij , sij , Dk , and Ek are the stress, the strain, the electric displacement, and the electric field, respectively. For an acoustic plane wave propagating in the x1 direction, using the partial wave method, the solution for the displacements, the stresses, the electric potentials, and the electric displacements for a piezoelectric layer is expressed by: (u1 , u2 , u3 , φ) = 8
(X1q , X2q , X3q , X4q ) Bq expiξ(x1 +αq x3 −ct) ,
(4)
q=1
(X5q , X6q , X7q , X8q ) Bq expiξ(x1 +αq x3 −ct) ,
(5)
q=1
where ξ and c are the wave number and phase velocity of the wave along x1 direction, respectively; αq (q = 1, 2, . . . 8) are the eight solutions of the Christoffel equation; (X1q , X2q , X3q , X4q ) is the null space of the singular matrix, which denotes the relative amplitude of (u1 , u2 , u3 , φ) of the q th partial wave; Bq is the weight coefficient for the q th partial wave. Combining all the eight field quantities into a vector form, we denote: T
P = [u1 , u2 , u3 , φ, σ31 σ32 , σ33 D3 ] .
(6)
where P[N ]+ and P[1]− are the values of P at the top and bottom surfaces of the system, respectively; Ψ is called the transfer matrix of the system [15]. Now, different boundary conditions can be applied to obtain the dispersion relation of the wave propagation. In the case of stress-free and open-circuit boundary conditions, the field quantities at the free surface can be expressed as:
+ + + P[N ]+ = u+ 1 , u2 , u3 , φ , 0, 0, 0, 0 ,
(7) − − − P[1]− = u− 1 , u2 , u3 , φ , 0, 0, 0, 0 . Substituting the boundary conditions into (6), a characteristic equation is expressed as: ⎡ ⎤ ⎡ ⎤ ⎡ −⎤ u1 0 Ψ51 Ψ52 Ψ53 Ψ54 ⎢0⎥ ⎢Ψ61 Ψ62 Ψ63 Ψ64 ⎥ ⎢u− ⎥ ⎢ ⎥=⎢ ⎥⎢ 2 ⎥. (8) ⎣0⎦ ⎣Ψ71 Ψ72 Ψ73 Ψ74 ⎦ ⎣u− ⎦ 3 0 Ψ81 Ψ82 Ψ83 Ψ84 φ− From (8), the parameters ξ and c of the possible wave propagation modes can be obtained. Then, the whole wave field distribution along the thickness can be obtained by (4) and (5), which also generally is called wave structure. If the free-surface boundary conditions are stress free and short circuit, then:
+ + + P[N ]+ = u+ 1 , u2 , u3 , 0, 0, 0, 0, D3 ,
(9) − − − P[1]− = u− 1 , u2 , u3 , 0, 0, 0, 0, D3 . In this case, the wave mode and the corresponding wave structure also can be derived with a similar procedure. Different electric boundary conditions will lead to a shift of the phase velocity for a given wave mode. The difference in wave phase velocity is related to the electromechanical coupling coefficient (ECC) [17]: k 2 = 2 (Co − Cs ) /Co ,
(σ31 , σ32 , σ33 , D3 ) = 8
A transfer matrix relating both surface boundary conditions can be formulated by applying all the interface continuity conditions, then:
(10)
where Co and Cs are the phase velocities of the acoustic waves under open-circuit and short-circuit boundary conditions, respectively. As a result, by calculating the phase velocity shift of the wave mode under these two boundary conditions, we can estimate the ECC of the wave modes, which is a very important parameter for optimizing the structure designs.
III. Numerical Calculation for ZnO/Si Bi-Layered Structures For ZnO/Si bi-layered structures, ZnO thin films with c axis orientation are deposited on (100) Si wafers as
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Fig. 2. ZnO/Si bi-layered model.
shown in Fig. 2. The acoustic waves are excited along with the 110 direction of the Si wafer by a pair of interdigital transducer (IDT) deposited on the ZnO surface, also shown in Fig. 2. Because the coordinate selected in Fig. 2 is not the crystallographic axis direction of Si wafers, the coordinate transformation is necessary. Based on the partial wave method, the Christoffel equation for Si is: ⎡ ⎤⎡ ⎤ ⎡ ⎤ K11 0 K13 0 X1 0 ⎢ 0 K22 0 0 ⎥ ⎢X2 ⎥ ⎢0⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ (11a) ⎣K13 0 K33 0 ⎦ ⎣X3 ⎦ = ⎣0⎦ , 0 0 0 K44 X4 0 and for ZnO is: ⎡ K11 ⎢ 0 ⎢ ⎣K13 K14
0 K22 0 0
K13 0 K33 K34
⎤⎡ ⎤ ⎡ ⎤ K14 X1 0 ⎢X2 ⎥ ⎢0⎥ 0 ⎥ ⎥⎢ ⎥ = ⎢ ⎥. K34 ⎦ ⎣X3 ⎦ ⎣0⎦ K44 X4 0
(11b)
From both Christoffel (11a) and (11b), one can see that the displacements in the x2 direction do not couple with the other components of the field quantities; therefore, shear horizontal acoustic plate modes (SH-APM) cannot be excited by the IDT. As a result, the following investigation is focused on the propagation characters of RayleighLamb type, i.e., shear perpendicular acoustic plate modes (SP-APM), in which the displacements in the x1 and the x3 directions couple with the electric field of the IDT, and there is no polarization in the x2 direction [11]. A. Calculation Results of Wave Parameters According to the materials used in our experiment, the thickness of silicon substrate is 100 µm. When the thickness of the ZnO thin film is 10 µm, several lower order wave dispersion curves under the stress-free and open-circuit boundaries are shown in Fig. 3, in which the parameters used in the calculation are from the corresponding crystals. From Fig. 3, the wavelengths of different wave modes are considered as 100 µm (indicated by circles), and the corresponding phase velocity and frequency of each mode can be obtained. Fig. 4 shows the wave structures of six waves with lower order modes, whose wavelengths are all 100 µm. Fig. 4(a) shows the displacement fields and Fig. 4(b) shows the stress fields in the perpendicular x3 direction. From Fig. 4,
Fig. 3. Dispersion relation of SP-APM modes.
one can see that the Rayleigh-Lamb type modes are not conventional Lamb waves with symmetric (S) and asymmetric (A) modes due to the asymmetry of the bi-layered structures induced by the ZnO layer. Meanwhile, because the silicon substrate is in moderate thickness, the wave modes are much more complicated than the case of very thin substrates [11]. The first two modes are the combination of the quasi-A0 and quasi-S0 modes, which mainly propagate in the two surfaces of the system. The first mode is the SAW in the top surface of ZnO thin film, which also penetrates into the Si wafer. Because the phase velocity of acoustic waves in ZnO is less than that in Si, the phase velocity of the first mode is less than the second one, which propagates mainly in the rear surface of the silicon wafer (see Fig. 3). The displacement distributions of the other acoustic guided wave modes, such as modes 3, 4, 5, and 6, are even more complicated as the mode number goes up. The distributions of displacements and stress amplitudes of the higher order of Rayleigh-Lamb type modes display several oscillations along the x3 direction. B. Electromechanical Coupling Coefficient Based on (10), the ECC of each mode can be obtained from the different phase velocities under the boundary conditions of open circuit and short circuit. Shown in Fig. 5 is the relation between ECC (k 2 ) and the wave number ξ. When ξ is small (i.e, the wavelength λ is larger than the thickness h of the structure), there exist only two modes 1 and 2. When λ is less than h, the ECC of mode 1 decreases very quickly from a large value, then approaches a constant. For mode 2, the ECC decreases from a small value to almost zero as ξ increases. For modes 3 and 4, both ECC increase very quickly with ξ to 105 /m, and the mode 4 has a peak value when ξ is about 8.5 × 104 1/m. In addition, the ECC of modes 5 and 6 are quite low.
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Fig. 6. Frequency and ECC of the SP-APM modes vary with film thickness: (a) frequency, (b) ECC.
C. Effect of Thin Film Parameters on Frequency and ECC Fig. 4. Relative amplitude distribution of the field quantities along x3 direction. (a) Displacements u1 and u3 . (b) Stresses σ13 and σ33 .
Fig. 5. Variation of ECC as a function of wave number.
It is well-known that the density, the elastic constants, the piezoelectric constants, the dielectric constants, and the thickness of the thin ZnO films are strongly dependent on the preparation methods and conditions. The effects of the material properties and parameters on the acoustic wave propagation in the bi-layered structures are calculated and discussed. 1. Effect of the Thickness of Thin ZnO Films: As the thickness of the Si substrate is constant, the thickness influence of the thin ZnO films on the frequency (f ) and the ECC (k 2 ) of the acoustic modes are shown in Fig. 6(a) and (b), respectively. When the film thickness increases, the frequencies of all the modes decrease. When the thickness of the film approaches zero, the wave modes are similar to the modes in a monolayer silicon substrate. The first two modes become A0 and S0 modes in a single plate structure. When the thickness of the film increases, the first mode approaches to the wave propagating in the ZnO sur-
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Fig. 7. Frequency and ECC vary with relative density ρf ilm /ρbulk : (a) frequency, (b) ECC.
Fig. 8. Frequency and ECC vary with relative elastic constant C11 : (a) frequency, (b) ECC.
face, and the second is not changed. The frequencies of the other modes also are affected by the thin film thickness, but to different extents. For the ECC, Fig. 6(b) shows that modes 1, 3, and 4 have large ECC, especially mode 3 increases quickly with the film thickness. Furthermore, the ECC for modes 2, 5, and 6 are almost zero when the film thickness is less than 20 µ.
tivity of the ECC of modes 2 and 6 are always extremely small.
2. Effect of Density of Thin ZnO Films: Fig. 7 shows the influence of the density of the films on the acoustic wave propagation. Usually, the density of thin films deposited on substrates is smaller than that of the same material in crystals because of defects and voids. It is assumed that the ZnO film density changes from 0.6 to 1.0 times the one of ZnO crystals. The frequencies of modes 1, 4, and 5 are more sensitive to the film density than the ones of the other modes, as shown in Fig. 7(a). The ECC of mode 1 almost does not change with the density. However, the ECC of mode 3 increases dramatically with the increase of the film density. For mode 4, a maximum value of the ECC is reached when the density ratio is about 0.7. The sensi-
3. Effect of Elastic Constants of Thin ZnO Films: As the C11 changes in a range of 0.8 to 1.2 times the corresponding value of the crystals, the variation of C11 has some influences on the frequencies of modes 3 and 4, as shown in Fig. 8(a). But for the other modes, the influence is very small, generally less than 1%, and thus can be neglected. According to the Christoffel (11a) and (11b), the Rayleigh-Lamb type waves (with X2 = 0) are not related to C66 based on the relation between C66 and K22 , which has no influence on the characters of the acoustic wave modes. The ECC of modes 1 and 3 decreases with the increase of C11 , and mode 4 has a positive response apparently to the increase of C11 [see Fig. 8(b)]. The ECC of the other modes almost equals to zero. On the effect of other components of the elastic constants of the films, the theoretical calculations show that the results are almost in the same order as that of C11 . However, different elastic constants tend to have different influences on the wave modes.
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Fig. 10. Variation of ECC as functions of relative dielectric constants: (a) ε11 , (b) ε33 .
4. Effect of Piezoelectric Constants of Thin ZnO Films: The effects of the piezoelectric constants of the films on the frequencies of the different acoustic wave modes are all very small and can be neglected. Nevertheless, the effects of different components of piezoelectric constants on the ECC of different modes are shown in the Fig. 9. 5. Effect of Dielectric Constants of Thin ZnO Films: The effects of the dielectric constants of the films on the frequency of the different modes are also very small, and almost negligible. Fig. 10 shows the numerical result of ECC versus dielectric constants.
IV. Experiment
Fig. 9. Variation of ECC as functions of relative piezoelectric constants: (a) e15 , (b) e31 , (c) e33 .
In the experiment, the ZnO/Si bi-layered samples are prepared by depositing c-axis oriented ZnO thin films on the Si (100) substrate wafers using radio frequency (RF) magnetron sputtering. High purity ZnO (99.99%) powders used as a sputtering target is packed into a cathode copper tray of 60 mm in diameter and 5 mm in depth. The typical optimizing sputtering condition is the growth temperature at 300◦C and the growth rate at 0.2 to 0.5 µm/hour. The thickness of the Si substrate is 100 µm, and the thick-
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Fig. 11. Experimental frequency response for different film thicknesses: (a) 7 µm, (b) 13.5 µm.
TABLE I Comparison of Theoretical and Experimental Results. Thin film thickness
Mode
1
3
4
5
6
7.0 µm
Theoretical frequency (MHz)
45.73
66.79
78.17
88.83
94.30
13.5 µm
Experimental frequency (MHz)
45.75
67.80
78.42
89.13
95.71
Theoretical phase velocity (m/s)
4573
6679
7817
8883
9430
Experimental phase velocity (m/s)
4632
6650
7850
8850
9450
Theoretical frequency (MHz)
41.45
62.75
70.61
83.81
92.44
Experimental frequency (MHz)
42.25
63.25
70.37
83.48
91.25
Theoretical phase velocity (m/s)
4145
6275
7061
8381
9244
Experimental phase velocity (m/s)
4188
6250
7000
8125
9125
nesses of the ZnO thin films are 2 to 15 µm, which can be measured by a surface profiler. For the experimental acoustic devices, a pair of Al IDT is prepared on the top of the ZnO film by the conventional SAW microfabrication technology, which excite acoustic waves propagating in the 110 direction of the silicon substrate shown in Fig. 2. The period, wavelength, aperture, and number of fingers of the IDT are 50 µm, 100 µm, 4 mm, and 60 pairs, respectively, and the central distance between both IDT is 12 mm. The frequency responses of the acoustic wave devices are measured with a network analyzer. The measured results of two acoustic devices with the thicknesses of the ZnO films of 7.0 µm and 13.5 µm on the Si substrates with the same thickness of 100 µm, as examples, are shown in Fig. 11. From Fig. 11, it can be seen in both devices, that mode 2 cannot be observed, and the signal of mode 3 increases greatly with the film thickness, but the signals of modes 1 and 4 are not changed much with the thickness, and the signals of modes 5 and
6 are very small. In addition, the frequencies of the modes described above decrease as the film thickness increases. All of these results are in agreement with the theoretical prediction shown in Fig. 6(b). Due to the fact that the preparation conditions cannot be controlled exactly, the film thickness and quality may not be repeated exactly. Therefore, the amplitude dependency on the film thickness for the observed 5 modes is always changed in different devices, still they are mainly consistent with the theoretical predictions. The central frequencies and phase velocities of the acoustic devices are listed in the Table I. If the differences of the material constants between sputtered films and the corresponding crystal materials are considered, the theoretically simulated frequencies and phase velocities of both devices also are listed in Table I. In general, there are good agreements between the numerical calculations and the experimental data; the error is less than 3%.
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V. Conclusions The transfer matrix method is applied to investigate the acoustic wave modes in bi-layered electro-acoustic structures consisting of piezoelectric ZnO thin films on top of silicon substrates. The dispersion relations, wave structures, and electromechanical coupling coefficients of the acoustic wave modes are obtained for the case in which the thickness of the substrates is of the same order as the wavelength. The effects of the material parameters of the sputtered ZnO thin films on the acoustic propagation modes are studied numerically. At the same time, several experimental results also are presented, which agree well with the theoretical calculation. Several conclusions are obtained as follows: 1. The acoustic waves propagating in the 110 direction of silicon wafers are pure mode waves. The transverse isotropic nature of ZnO leads to the symmetry of the wave excitation and propagation in the x1 x2 plane. These facts lead to the decoupling of the acoustic wave displacement in the x2 direction with the electric field. Then the Rayleigh-Lamb type waves can be excited by IDT, but SH-APM cannot be exited. 2. The analyses of the ECC of the acoustic wave modes show that, as the ZnO films are rather thin, modes 1, 3, and 4 have comparably large electromechanical coupling coefficients, but that of modes 5 and 6 is smaller. Meanwhile, the ECC of the different modes are affected by the film parameters in different extents, but the coupling of mode 2 is so small that it can be neglected. 3. The frequencies of the wave modes are mainly affected by the thickness and density of the ZnO films. The effects of the elastic constants on the frequency are smaller, but the effects of the piezoelectric and dielectric properties of the films almost can be neglected. 4. The experimental results of the frequency of the acoustic wave propagation in the ZnO/Si bi-layered structures agree well with the theoretical predictions.
[7] M. B. Assouar, O. Elmazria, R. J. Rioboo, F. Sarry, and P. Alnot, “Modelling of SAW filter based on ZnO/diamond/Si layered structure including velocity dispersion,” Appl. Surface Sci., vol. 164, pp. 200–204, 2000. [8] J. Du and G. L. Harding, “A multilayer structure for Love-mode acoustic sensors,” Sens. Actuators, vol. A65, pp. 152–159, 1998. [9] K. K. Zadeh, A. Trinchi, W. Wodarski, and A. Holland, “A novel Love-mode device based on a ZnO/ST-cut quartz crystal structure for sensing applications,” Sens. Actuators, vol. A100, pp. 135–143, 2002. [10] A. H. Fahmy and E. A. Adler, “Propagation of acoustic surface waves in multilayers: A matrix description,” Appl. Phys. Lett., vol. 22, pp. 495–497, 1973. [11] A. A. Nassar and E. L. Adler, “Propagation and electromechanical coupling to plate modes in piezoelectric composite membranes,” in Proc. IEEE Ultrason. Symp., 1983, pp. 369–372. [12] R. M. White, P. Wiche, Jr., S. W. Wenzel, and E. T. Zellers, “Plate-mode ultrasonic oscillator sensors,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 34, pp. 162–171, 1987. [13] N. T. Nguyen and R. M. White, “Design and optimization of an ultrasonic flexural plate wave micropump using numerical simulation,” Sens. Actuators, vol. 77, pp. 229–236, 1999. [14] J. T. Stewart and Y. K. Yong, “Exact analysis of the propagation of acoustic waves in multilayered anisotropic piezoelectric plates,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 41, pp. 375–390, 1994. [15] M. J. S. Lowe, “Matrix techniques for modeling ultrasonic waves in multilayered media,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 42, pp. 525–542, 1995. [16] A. H. Nayfeh, Wave Propagation in Layered Anisotropic Media. New York: Elsevier, 1995. [17] K. Yamanouchi, N. Sakurai, and T. Satoh, “SAW propagation characteristics and fabrication technology of piezoelectric thin film/diamond structure,” in Proc. IEEE Ultrason. Symp., 1989, pp. 351–354.
References
Hui-dong Gao was born in Anhui, China, in 1977. He received a B.S. degree in physics from the Department for Intensive Instruction, Nanjing University (NJU), China, in 2000. He received a M.S. degree in acoustics from the Department of Electronic Science and Engineering, NJU, in 2003. He is currently a Ph.D. candidate in the Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA. His current research is focused on piezoelectric ultrasonic sensor designs and ultrasonic guided wave technologies for structural health monitoring of aircraft and aerospace structures. Mr. Gao is a student member of American Society for Nondestructive Testing (ASNT) and American Institute of Aeronautics and Astronautics (AIAA).
[1] T. Mitsuyu, O. Yamazaki, K. Ohji, and K. Wasa, “Piezoelectric thin films of ZnO for SAW devices,” Ferroelectrics, vol. 42, pp. 233–240, 1982. [2] H. Nakahata, K. Higaki, A. Hachigo, S. Shikata, N. Fujimori, Y. Takahashi, T. Kajihara, and Y. Yamamoto, “High frequency surface acoustic wave filter using ZnO/diamond/Si structure,” Jpn. J. Appl. Phys., vol. 33, pp. 324–328, 1994. [3] Y. Kim, W. D. Hunt, F. S. Hickernell, R. J. Higgins, and C. K. Jen, “ZnO films on {001}-cut 110-propagating GaAs substrates for surface acoustic wave device applications,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 42, pp. 351–361, 1995. [4] S. H. Seo, W. C. Shin, and J. S. Park, “A novel method of fabricating ZnO/diamond/Si multilayers for surface acoustic wave (SAW) device applications,” Thin Solid Films, vol. 416, pp. 190– 196, 2002. [5] W. S. Trimmer, Micromechanics and MEMS (Classic and Seminal Papers to 1990). New York: IEEE Press, 1997. [6] J. W. Garner, V. K. Varadan, and O. O. Awadelkarim, Microsensors, MEMS, and Smart Devices. New York: Wiley, 2001.
Shu-yi Zhang (M’86–SM’88) graduated from the Department of Physics, Nanjing University (NJU), China, and then from the postgraduate school of the same University with a speciality in acoustics. Since then, she was working in the Institute of Acoustics, NJU, and has been a Professor and the Director of the Institute of Acoustics (1992–2001). Now she is a Professor of the Department of Electronic Science and Engineering of NJU and the Chairperson of the Academic Committee of the State Key Laboratory of Modern Acoustics, China, and also a Member of Chinese Academy of Sciences. Her research interests include ultrasonic physics, ultrasonic NDE and micro-ultrasonic devices, as well as photoacoustic and thermal wave imaging and characterizations of materials. She has published more than 300 papers.
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gao et al.: acoustic wave modes in bi-layered electro-acoustic structures Xue Qi received his B.S. degree in physics from the Department for Intensive Instruction of Nanjing University, China, in 2002. He is now a postgraduate student in the Department of Electronic Science and Engineering of Nanjing University. His research work includes ultrasonic and photoacoustic nondestructive evaluations of materials.
2369 Hao-dong Wu was born in Yixing, Jiangsu, China, in 1964. He received his B.S. degree from the Department of Physics, Suzhou University, China, in 1985 and received M.S. degree and Ph.D. degree from the Department of Electronic Science and Engineering, Nanjing University, China, in 1998 and 2001, respectively. Now he is an Associate Professor of the Department of Electronic Science and Engineering, Nanjing University, China. His current research interests include ultrasonic transducer designs and ultrasonic measurements.
Kiyotaka Wasa (F’90–LF’03) graduated from Osaka University (E.E) of Japan in 1960 and received Ph.D. degree on Plasma Physics from Osaka University in 1968. He joined Panasonics in 1960 and studied on plasma in a magnetron discharge (1960–1990). He was a deputy director of RITE (Research Institute of Innovative Technology for the Earth) of Japan (1990–1998), and then a Professor of Yokohama City University of Japan (1998– 2003). He is now an Adjunct Professor of Yokohama City University of Japan and an Honorary Professor of UEST (University of Electronic Science and Technology) of China and Nanjing University of China. He has done seminal works on the magnetron sputtering and has developed numerous thin film materials and electronic devices, including ZnO, diamonds, and high Tc superconductors.
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