Jpn. J. Appl. Phys. Vol. 38 (1999) pp. 3288–3292 Part 1, No. 5B, May 1999 c °1999 Publication Board, Japanese Journal of Applied Physics
Properties of Leaky, Leaky Pseudo, and Rayleigh Surface Acoustic Waves on Various Rotated Y-cut Langasite Crystal Substrates Michio K ADOTA ∗ , Jun NAKANISHI, Takeshi K ITAMURA and Makoto K UMATORIYA Murata Mfg. Co., Ltd., Nagaokakyo-shi, Kyoto 617-8555, Japan (Received November 27, 1998; accepted for publication January 29, 1999)
A leaky surface acoustic wave (LSAW) and a leaky pseudo SAW (LPSAW) of various rotated Y-cut langasite substrates grown by the Czochralski method were measured by an ultrasonic microscope. The measured results agreed well with the values calculated using Ilyaeve’s material constants of five kinds of material. Rayleigh SAW transversal filters, having various aluminum (Al) thicknesses of interdigital transducers (IDT), were constituted on (0◦ , 140–150◦ , 24–25◦ ) and (12◦ , 150–153◦ , 36–37◦ ) plates. A temperature coefficient of frequency (TCF) of the Rayleigh SAW filters was measured by measuring their center frequency. It was clarified that (0◦ , 142◦ , 24.5◦ ) and (0◦ , 143◦ , 24◦ ) plates at normalized Al-IDT thickness (H Al /λ) 0.0125, and (12◦ , 153◦ , 37◦ ) plates at H Al /λ = 0.0625 showed turnover temperatures of 25◦ C, 30◦ C and 28◦ C and excellent TCFs (1F/F/◦ C = 1.83, 1.63, and 1.95 ppm/◦ C). Measured results of electromechanical coupling factor on their substrates showed similar values (ks2 = 0.41, 0.42 and 0.46%) to the theoretical ones. The (12◦ , 153◦ , 37◦ ) plate having the largest coupling factor is the most suitable one for SAW devices. Furthermore, the velocity, the coupling factor, and the propagation loss of LSAW on air/various Y-X langasite plates (0◦ , θ , 0◦ ) were also calculated. KEYWORDS: langasite, LSAW, LPSAW, Rayleigh SAW, TCF, coupling factor
1. Introduction Substrates having a suitable electromechanical coupling factor (ks ) and a good temperature coefficient of frequency (TCF) are required for applications of the surface acoustic wave (SAW) resonator-type and ladder-type filters requiring a specific bandwidth, because their bandwidth greatly depends on the coupling factor of the substrate. Most SAW filters are required to have good TCFs. In particular, narrow-band SAW filters strongly require substrates having excellent TCFs.It is known that an ST-cut X propagation quartz and a ZnO film on ST-cut 35◦ X propagation quartz substrates have TCF'0.1) A new piezoelectric single crystal langasite having excellent TCF and an appropriate electromechanical coupling factor has recently attracted attention as a material for bulk wave and SAW devices.2–8) The authors grew large size (diameter: 2–3" φ) langasite single crystals. Various (–80◦ , –60◦ , . . . , 80◦ ) rotated Y-cut plates were cut from them. The authors measured the leaky SAW (LSAW) and the leaky pseudo SAW (LPSAW) on their plates using an ultrasonic microscope. These results were compared with the theoretical values calculated by five kinds of material constants.9–14) Some optimal plates, having, theoretically and experimentally, an excellent TCF in Rayleigh SAW, have been reported.5, 7, 8) However, they have been evaluated without considering the effect of thickness of the Al interdigital transducer (IDT), and some of them do not have zero power flow angles (PFA). In this study, we measured the TCFs of the transversal SAW filters having various thicknesses of AlIDT on (0◦ , 140–150◦ , 24–25◦ ) and (12◦ , 150–153◦ , 36–37◦ ) plates. No measured coupling factors of SAW on langasite substrates have been reported. In this paper, it is reported that their measured coupling factors show similar values to the calculated ones.Optimal plates with better TCFs or larger coupling factors have been obtained compared to the values reported until now. Velocity, coupling factor, and propagation loss of LSAW propagating in the X direction on air/rotated Y-plates are also calculated. ∗ E-mail
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2. LSAW and LPSAW on Langasite Plates Measured by Ultrasonic Microscope Figure 1 shows 2" φ and 3" φ of langasite single crystals grown by the Czochralski method. Rotated Y-cut plates were cut from a single crystal (rotation angle: −80◦ ,−60◦ , . . . , 80◦ ). The velocities of LSAW and LPSAW were measured using the ultrasonic microscope.3, 5, 7) When the surface of the substrate is free (in contact with air), Rayleigh SAW and LSAW propagate on the langasite substrate. On the other hand, using the ultrasonic microscope, the velocities of the LSAW and the LPSAW, which radiate the energy of longitudinal wave components to the water, propagating on the boundary between the substrate and water, are measured.15) These LSAW and LPSAW correspond to a Rayleigh SAW and a LSAW propagating on a free surface of the substrate, respectively.5, 7) In this study, the line focus beam (LFB) ultrasonic microscopic system was used (Model AMS-5000: Honda Electronics Co., Japan). The absolute measurement accuracy of the LSAW velocities propagating on a gadolinium galliun garnet substrate measured using our ultrasonic microscope was less than 0.03%.16) As an example, Fig. 2 shows the measured and theoretical velocities of the LSAW and the LPSAW propagating on a 60◦ rotated Y-cut plate as a function of the propagation direction ψ; (Euler angle: 0◦ ,150◦ , ψ). In the figure,the open circles (◦) and closed circles (•) represent the measured LSAW and LPSAW velocities, respectively. Various lines show the theoretical values of LSAW and LPSAW on the water/substrate, calculated using five kinds of material constants reported.9, 14) The section without measured values in the figure indicates that the longitudinal component of the wave was too small to be measured by the ultrasonic microscope. The measured and calculated LSAW and LPSAW velocities propagating on other various rotated Y plates have been reported in detail in ref. 7. Figure 3 shows the measured and theoretical LSAW and LPSAW velocities propagating in the X direction on the various rotated Y-cut plates as a function of the cut angle; (Euler angle: 0◦ , θ , 0◦ ). From the measured and calculated values in Figs. 2 and 3, it is evident that the theoretical values obtained using Ilyaev’s constants
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Fig. 1.
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Langasite crystals grown by the Czochralski method.
Fig. 3. LSAW and LPSAW velocitiess on various rotated Y-plates (Euler angle: 0◦ , θ=0–180◦ , 0◦ ).
Fig. 4. Frequency shifts on temperature for various cut angles θ (0◦ , θ=140–150◦ , 24–25◦ ) at H Al /λ=0.0125. Fig. 2. LSAW and LPSAW velocities on 60◦ rotated Y-cut plate (Euler angle: 0◦ , 150◦ , ψ = 0–180◦ ).
are close to our measured values. 3. TCF and Coupling Factor of Rayleigh SAW on (0◦ , 140–150◦ , 24–25◦ ) Plates There have been many reports about optimal Euler angles having excellent TCFs in Rayleigh SAW, as determined from experimental and theoretical studies.2–8) The measured values of TCF, which have been reported until now, disregard AlIDT thickness. In this paper, TCFs of Rayleigh SAW on various plates were measured by measuring center frequencies of the transversal SAW filters with various thicknesses of AlIDT; (0◦ , θ =140–150◦ , ψ=24–25◦ ), where ψ is a propagation angle for PFA=0 at the cut angle θ . The SAW filter consisted of input and output electrodes having 15 pairs of normal single IDTs with λ=12µm.(λ is wavelength of SAW). Figure 4 shows the measured results of frequency shift on (0◦ , 140– 150◦ , 24–25◦ ) plates as a function of temperature from −20 to
80◦ C at the normalized thickness of Al (H Al /λ) = 0.0125. The peak temperature in the frequency shift curve in this figure is called the turnover temperature (of frequency shift). Figure 5 shows the measured turnover temperature as a function of the cut angle θ . The turnover temperature shifts towards the high temperature region in proportion to the cut angle. The Euler angles which showed turnover temperatures of 25◦ C and 30◦ C for the Al-IDT thickness=0.0125 are (0◦ , 142◦ , 24.5◦ ) and (0◦ , 143◦ , 24◦ ) plates, respectively. These frequency shifts from –20 to 80◦ C per 1◦ C (1F/F/◦ C) are 1.83 and 1.63 ppm/◦ C, respectively. These are better TCFs than those reported until now. For the analysis, although the TCF calculations using Ilyaev’s constants indicate that the (0◦ , 150◦ , 24◦ ) plate has a turnover temperature of 25◦ C, those using Sakharov’s and Adachi’s constants represent (0◦ , 139◦ , 25◦ ) and (0◦ , 140◦ , 25◦ ) plates. There is a difference of 11◦ at the cut angle θ between them. This difference is due to the difference of their material constants. For angles of (0◦ , 140◦ , 25◦ ) and (0◦ , 150◦ , 24◦ ), the TCFs having a different Al-IDT thick-
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Fig. 5. Turnover temperature on cut angle θ at (0◦ , θ=140–150◦ , 24–25◦ ).
Fig. 7. Coupling factors on various cut angle θ (0◦ , θ=140–150◦ , 24–25◦ ) at H Al /λ=0.0125.
Fig. 6. Frequency shifts of SAW filter having various Al-IDT thicknesses on temperature.
Fig. 8. Frequency shifts on temperature for (12◦ , 150–153◦ , 36–37◦ ) at H Al /λ=0.0125 and 0.0625.
ness were measured. Figure 6 shows these frequency shifts as a function of temperature from −20 to 80◦ C. These turnover temperatures are also denoted as closed circles, triangles and upside-down triangles in Fig. 5. As shown in Figs. 5 and 6, the turnover temperature shifts toward the low-temperature region with increasing Al film thickness. Accordingly, when the normalized Al thickness exceeds 0.0125, the cut angle θ , in which the turnover temperature shows 25–30◦ C, is larger than 143◦ . In general, SAW devices having Al-IDT thicker than 0.0125 are used. So the optimal cut angle θ is larger than 143◦ ; (Euler angle: 0◦ , 143–150◦ , 24◦ ). No measured electromechanical coupling factor of SAW on langasite substrates have been reported. We measured the electromechanical coupling factor in Rayleigh SAW on (0◦ , 140–150◦ , 24–25◦ ) plates by measuring motional conductance circles of normal IDTs consisting of 20 pairs of single electrodes with λ = 26 µm.6) Figure 7 shows the measured results as a function of the cut angle θ . In this figure, open triangles (1) indicate measured results and the solid line indicates values calculated using Ilyaev’s constants. The measured results are similar to the calculated values. The (0◦ , 142◦ , 24.5◦ ) and (0◦ , 143◦ , 24◦ ) plates showing excellent TCFs have large coupling factors of their square (ks2 ) = 0.41% and 0.43 %, respectively. When the cut angle θ is large, the coupling factor becomes large as shown in Fig. 7.
As mentioned above, in general, the Al-IDT thickness for SAW devices is thicker than 0.0125. It is convenient to use substrates with θ >143◦ for TCF and coupling factor. Compared with other reported cut angle plates of langasite, the (0◦ , 142◦ , 24.5◦ ) and (0◦ ,143◦ , 24◦ ) plates show PFA=0, excellent TCFs, and large electromechanical coupling factors. So, for SAW devices requiring an appropriate narrow-band width, these cut angle plates are suitable. 4. TCFs and Coupling Factors on (12◦ , 150–153◦ , 36– 37◦ ) Plates We also measured TCFs and coupling factors on (12◦ , 150– 153◦ , 36–37◦ ) plates at H Al /λ=0.0125 and 0.0625. The measured frequency shifts on temperature are shown in Fig. 8. The (12◦ , 153◦ , 37◦ ) plates showed a turnover temperature of 35◦ C and 28◦ C and a good TCF (1F/F/◦ C= 2.24 and 1.95 ppm/◦ C). It is considered that a plate between (12◦ , 152◦ , 37◦ ) and (12◦ , 153◦ , 37◦ ) plates at H Al /λ≤0.0125 shows a better TCF because the (12◦ , 151◦ , 36◦ ) plate at H Al /λ=0.0125 showed a turnover temperature of 5◦ C. The (12◦ , 153◦ , 37◦ ) plate, having a similar TCF value to (0◦ ,142–143◦ , 24.5–25◦ ) plates has a large coupling factor (ks2 =0.46%), which is larger than the above mentioned ones on (0◦ , 142–143◦ , 24.5–25◦ ) plates. In the case of (12◦ , 150–153◦ , 36–37◦ ) plates, measured frequency shifs on temperature are not coincident with
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Table I. Cut angles having good TCF. Euler Angle langasite (90◦ ,90◦ ,21◦ )2) (0◦ ,140◦ ,30◦ )4) (0◦ ,140◦ ,24◦ )8) (0◦ ,142◦ ,24.5◦ ) (0◦ ,143◦ ,24◦ ) (12◦ ,153◦ ,37◦ ) (12◦ ,153◦ ,37◦ ) ST-X quartz ZnO/ST35Xquartz
PFA (◦ ) cal.
1F/F/◦ C (ppm/◦ C) meas.
11 4 2 0 0 0 0 0 0
2.0 — 1.94 1.83 1.63 2.24 1.95 0.9 1.1
ks2 (%) cal.
meas.
0.21 0.31 0.37 0.40 0.44 0.45 0.45 0.14
— — — 0.41 0.42 0.46 0.46 0.14 1.0–1.2
Velocity (m/s)
H Al /λ
2620 2740 2738 2754 2756 2934 2834 3158 2900
— — — 0.0125 0.0125 0.0125 0.0625 — —
the calculated ones using any constants. Table I shows the properties of optimum cut angle substrates having a good TCF (1F/F/◦ C) reported experimentally until now and those measured in this study. As references, the value for ST-X quartz and the ZnO/ST-35◦ X quartz having TCF'0 are also shown in this table.1) As shown in Table I, (0◦ , 142◦ , 24.5◦ ), (0◦ , 143◦ , 24◦ ) and (12◦ , 152–153◦ , 37◦ ) plates show PFA=0, excellent TCFs and large coupling factors. In particular, the (12◦ , 152–153◦ , 37◦ ) plate has a large coupling factor, and is suitable for SAW devices. 5.
LSAW on Air/Substrates
Though the above mentioned LSAW was the one propagating on water/substrate measured by the ultrasonic microscope, in this section we report an LSAW propagating with decay on a free substrate in contact with air (air/substrate). The velocity, electromechanical coupling factor, and propagation loss (decay) of LSAW on (0◦ , θ =0–180◦ , 0◦ ) langasite plates in contact with air were calculated. Figure 9 shows the velocity and propagation loss of LSAW on various rotated YX propagation plates as a function of cut angle θ . Figure 10 shows their electromechanical coupling factors. An optimal cut angle having a zero loss and a large coupling factor could not be obtained.
Fig. 9.
LSAW velocities and losses on air/(0◦ , 0–180◦ , 0◦ ) plates.
6. Conclusions Various rotated Y plates were obtained from large size langasite single crystals grown by the Czochralski method. The velocities of the LSAW and LPSAW were measured using an ultrasonic microscope, and compared with theoretical values, calculated using five kinds of material constants. Out of them, the theoretical values calculated using Ilyaev’s material constants were closest to the measured ones. The TCFs of Rayleigh SAW filters with various Al-IDT thicknesses for various plates (0◦ , θ =140–150◦ , 24–25◦ ) and (12◦ , 150–153◦ , 36–37◦ ) having PFA=0 were measured. As a result, it was clarified that the (0◦ , 142◦ , 24.5◦ ) and (0◦ , 143◦ , 24◦ ) plates at H Al /λ=0.0125, and (12◦ , 153◦ , 37◦ ) plates at H Al /λ=0.0625 showed the turnover temperatures of 25◦ C, 30◦ C, and 28◦ C and excellent TCFs: 1F/F/◦ C=1.83, 1.63, and 1.95 ppm/◦ C, respectively. We measured and obtained large electromechanical coupling factors (their square ks2 = 0.41%, 0.42%, and 0.46%, respectively) of Rayleigh SAWs on langasite for the first time, which were almost equal to the calculated ones. These (0◦ , 142◦ , 24.5◦ ), (0◦ , 143◦ , 24◦ ), and (12◦ , 153◦ , 37◦ )
Fig. 10. LSAW coupling factors on air/(0◦ , 0–180◦ , 0◦ ) plates.
plates showing PFA=0, excellent TCFs, and large coupling factors are suitable substrates for SAW devices. In particular, the (12◦ , 153◦ , 37◦ ) plate with the largest coupling factor was the most suitable one. In the calculation of LSAW on the free rotated Y plates (Euler angle: 0◦ , 0–180◦ , 0◦ ), LSAW having both, a zero loss and a large coupling factor, could not be obtained. Acknowledgement We thank Professor Tsuguo Fukuda of Tohoku University for his useful guidance on the crystal growth.
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