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EECE Department, Marquette University, P.O.Box 1881, Milwaukee, WI 53201-1881, U.S.A.. Abstract – The temperature coefficient of delay. (TCD) for lowest ...
TEMPERATURE CHARACTERISTICS OF ACOUSTIC WAVES PROPAGATING IN THIN PIEZOELECTRIC PLATES I.E. Kuznetsova, B.D. Zaitsev, and S.G. Joshi* EECE Department, Marquette University, P.O.Box 1881, Milwaukee, WI 53201-1881, U.S.A. Abstract – The temperature coefficient of delay (TCD) for lowest order plate wave modes, A0, S0, and SH0, in LiNbO3 crystal has been calculated. In almost all cases investigated so far TCD is found to be a weak function of the normalized plate thickness h/λ (h = plate thickness, λ= acoustic wavelength). The only exception occurs for the A0 mode in X-Z and YZ plates. It is found that plate waves can provide higher K2 and lower TCD than is possible with SAWs. For example, for SH0 mode in X-Y+1700 lithium niobate K2=0.29 and TCD=54 ppm/0C. Experimental measurements of TCD for SH0 waves in Y-X lithium niobate are found in good agreement with theory. I. INTRODUCTION Recently, acoustic waves in thin piezoelectric plates have become the subject of close attention because of their unique attractive properties for use in sensors, signal processing devices, and material characterization studies [1-3]. The basic characteristics and properties of these waves such as phase and group velocities, electromechanical coupling coefficient, influence of electrical and mechanical boundary conditions, etc. have been investigated in detail [3-6]. These investigations have confirmed the promising practical applications of these waves. However one practical aspect, namely temperature influence on plate acoustic waves, has not been studied. This parameter is very important in device design and it has been investigated both theoretically and experimentally for surface acoustic waves propagating in various piezoelectric materials [7-9]. This paper presents theoretical investigation of temperature influence on the lowest order plate wave modes, A0, S0, and SH0, propagating in thin plate of lithium niobate. We have investigated the dependencies of temperature coefficients of phase velocity, group velocity, and delay on propagation

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direction in main crystallographic X, Y, and Z cuts for various values of plate thickness. II. THEORETICAL ANALYSIS AND RESULTS The geometry of the problem under consideration is shown in Fig.1. Waves propagate along the x1 direction of a piezoelectric plate bounded by planes x3=0 and x3=h. We consider a two dimensional problem in which all field components are assumed to be constant in the x2 direction. The method used to analyze propagation of acoustic wave in piezoelectric plates at fixed temperature has been described previously [3]. In order to consider the effect of temperature we used the following method. The elastic, piezoelectric, and dielectric constants, and the density of the piezoelectric material at actual temperature T were written as [7] ' E T C ijkl [1 + C ijkl (T − TR )] , (1) = C ijkl ' T eikl (T − TR )] , = eikl [1 + eikl

(2)

ε = ε [1 + ε (T − TR )] ,

(3)

' ij

S ij

T ij

ρ = ρ [1 − (2α 11 + α 33 )(T − TR )] , '

where C

E ijkl

(4)

, eikl , ε , and ρ are the elastic, S ij

piezoelectric, dielectric constants, and density at T T reference temperature TR; C ijkl , eikl , and ε ijT are the temperature coefficients for elastic, piezoelectric, and dielectric constants; and αij is thermal expansion coefficient. We calculated the temperature coefficients of phase velocity (TCPV), group velocity (TCGV), and delay (TCD) as

TCPV = TCGV =

v ph (T ) − v ph (TR ) v ph (TR )(T − TR ) v gr (T ) − v gr (TR ) v gr (TR )(T − TR )

TCD = α 11 − TCPV

,

(5)

,

(6) (7)

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Here vph and vgr are phase and group velocities respectively. The various temperature coefficients for the A0, SH0 and S0 plate wave propagating in lithium niobate thin plates were theoretically analyzed using (1) – (6). For calculations we used lithium niobate material constants reported by Kovach, et al. [10] and temperature coefficients reported by Slobodnik [7]. The calculated TCD of the A0, SH0, and S0 plate waves in X (a), Y (b), and Z (c) cuts of lithium niobate for different values of h/λ are shown in Fig.2 –Fig.4 respectively. The obtained results allow us to make the following conclusions. The values of temperature coefficients for all crystallographic situations differ insignificantly and the maximum difference between TCPV and TCGV does not exceed 15-20%. Besides for almost all cases there is only weak dependence of them on plate thickness. The only exception is the A0 mode propagating along Z axis in X and Y cut plates. In this case change in plate thickness in the range h/λ=0.01 – 0.5 leads to change in TCD by as much as a factor of 2. For most piezoactive crystallographic situations TCD for S0 and SH0 waves in lithium niobate is approximately (30-60)×10-6/0C. This is considerably less than the value of TCD = 72×10–6/0C for SAW in 128 Y-X lithium niobate. Thus by using the SH0 mode, one can obtain not only a much higher electromechanical coupling coefficient (K2 as high as 0.36 compared with a value of 0.056 for SAW) but also a lower temperature coefficient of time delay. Table 1. Comparison between plate and surface acoustic waves for lithium niobate Wave type A0 SH0 S0

Cut and K2 TCD, h/λ propagation ppm/0C direction Y-X 0.10 0.013 49.5 Y-X 0.01 0.270 60.0 X-Y+1700 0.01 0.290 54.0 X-Y+300 0.01 0.210 49.0 X-Y+600 0.05 0.160 30.0 Y-X+600 0.09 0.110 38.0 SAW 128Y-X LiNbO3: K2=0.054, TCD=72ppm/0C

III. EXPERIMENTAL RESULTS Theoretical calculations have been verified for SH0 wave propagating in Y-X LiNbO3 plate, which supports the value of electromechanical coupling coefficient as high as ~0.35 [4]. We measured the influence of change in temperature on output signal phase of a 3.5 MHz delay line with the plate thickness of 135 µm (h/λ = 0.1). The fabrication technology of such devices has been described previously [4]. In order to minimize insertion loss, the input and output interdigital transducers were tuned and matched to an impedance of 50 Ω. The midband insertion loss was found to be 8 dB. All spurious signals were suppressed by more than 20 dB compared to the main acoustic signal. In order to measure the TCD, the delay line was placed inside an oven and its time delay measured at a number of different temperatures. Temperature was varied from 220C to about 400C. Measurements show that for SH0 waves propagating in Y-X LiNbO3 plates (thickness h/λ = 0.1) TCD is equal to (67.4±2.4) × 10-6 ppm/0C. This is in good agreement with theoretically calculated value of 67.0 × 10-6 ppm/0C. IV. SUMMARY Temperature coefficient of delay (TCD) for lowest order plate wave modes (A0, S0, and SH0) in LiNbO3 crystal has been calculated. In almost all cases TCD is nearly independent of h/λ. The only exception occurs for A0 mode in X-Z and Y-Z plates. Plate wave can provide higher K2 and lower TCD than is possible with SAW. For example, for SH0 mode in X-Y+1700 LiNbO3 K2=0.29 and TCD=54 ppm/0C. Experimental results obtained for SH0 wave propagating in Y-X LiNbO3 are in good agreement with theoretical data. Zero (or near zero) TCD values may be possible using doubly rotated cuts and/or higher plate wave modes. V. ACKNOWLEDGEMENT This work was supported by a grant from the National Science Foundation. VI. REFERENCES

2001 IEEE ULTRASONICS SYMPOSIUM-158

ϕII

[1]

0

x1

u i, ϕ

h ϕI x3 Figure 1: Geometry of the problem

TCD, ppm/0C

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h/λ=0.03

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M. J. Vellekoop, “Acoustic wave sensors and their technology,” Ultrasonics, vol. 36, pp.714, 1998. [2] D. S. Ballantine, R. M. White, S. J. Martin, A. J. Ricco, E. T. Zellers, G. C. Frye, and H. Wohltjen, Acoustic Wave Sensors, San Diego: Academic Press, 1997, ch.3. [3] S. G. Joshi and Y. Jin, “Propagation of ultrasonic Lamb waves in piezoelectric plates,”J. Appl. Phys., vol.70, pp.4113-4120, Oct. 1991. [4] B. D. Zaitsev, S. G. Joshi, and I. E. Kuznetsova, “Propagation of QSH (quasi shear horizontal) acoustic waves in piezoelectric plates”, IEEE Trans. Ultrason. Ferroel. and Freq. Control, vol.46, pp. 12981302, Sept. 1999. [5] I. E. Kuznetsova, B. D. Zaitsev, S. G. Joshi, and I. A. Borodina, “Investigation of acoustic waves in thin plates of lithium niobate and lithium tantalate,” IEEE Trans. Ultrason. Ferroel. and Freq. Control, vol. 48, pp. 322 – 328, Jan. 2001. [6] B. D. Zaitsev, S. G. Joshi, I. E. Kuznetsova, and I. A. Borodina, “Acoustic waves in piezoelectric plates,” Ultrasonics, vol. 39, pp. 45 – 50, 2001. [7] A. J. Slobodnik, “The Temperature Coefficients of Acoustic Surface Wave Velocity and Delay on Lithium Niobate, Lithium Tantalate, Quartz, and Tellurium Dioxide,” Phys. Sci. Res. Pap., No.477, 1972. [8] C. S. Kim, K. Yamanouchi, S. Karasawa, and K.Shibayama, “Temperature dependence of the elastic surface wave velocity on LiNbO3 and LiTaO3,” Jap. Journ. of Appl. Phys., vol.13, pp.24-27, 1974. [9] K. Nakamura, M. Kazumi, and H. Shimizu, “SH-type and Rayleigh-type surface waves on rotated Y-cut LiTaO3,” Proc. IEEE Ultrasonics Symp., pp. 819-822, 1977. [10] G. Kovacs, M. Anhorn, H.E. Engan, G. Visintini, and C.C.W. Ruppel, “Improved material constants for LiNbO3 and LiTaO3,” Proc. IEEE Ultrasonics Symp., vol. 1, pp. 435-438, 1990. * Shrinivas Joshi e-mail: [email protected]

30

60 90 120 150 180 c SAW

70 0.5 0.25

60 50

0.03

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90

Figure 2: The temperature coefficient of delay versus propagation direction for A0 wave in X-cut (a), Y-cut (b), and Z-cut (c) LiNbO3 plate for different values of h/λ

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Angle, degree Figure 3: The temperature coefficient of delay versus propagation direction for SH0 wave in X-cut (a), Y-cut (b), and Z-cut (c) LiNbO3 plate for different values of h/λ

0

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Figure 4: The temperature coefficient of delay versus propagation direction for S0 wave in Xcut (a), Y-cut (b), and Z-cut (c) LiNbO3 plate for different values of h/λ

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