Abstract:
A surface acoustic wave resonator includes a piezoelectric substrate including a langasite single crystal material and at least one interdigital transducer having at least one pair of comb-shaped electrodes arranged so as to contact the piezoelectric substrate. The surface acoustic wave resonator operates using a surface acoustic wave including an SH wave as the main component.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a surface acoustic wave resonator, a surface acoustic wave filter, a duplexer, and a communications apparatus including the same. More particularly, the present invention relates to a surface acoustic wave resonator using a surface acoustic wave including an SH wave as the main component. 
     2. Description of the Related Art 
     Conventionally, surface acoustic wave resonators have been used widely in band pass filters and other electronic components included in mobile communications equipment. As an example of such a surface acoustic wave resonator, a surface acoustic wave resonator or a surface acoustic wave filter having a configuration wherein an interdigital transducer (hereinafter referred to as IDT) including a comb-shaped electrode is formed on a piezoelectric substrate is well known. Since a surface acoustic wave including an SH wave as the main component, such as a Love wave, a leaky wave, a BGS wave, or the like can utilize edge reflection in such a surface acoustic wave resonator or surface acoustic wave filter, it is used practically in a small size resonator or surface acoustic wave filter, which does not require a reflector. Further, a piezoelectric single crystal, such as lithium niobate, lithium tantalate, or the like, is used as the material for the piezoelectric substrate of a surface acoustic wave resonator or a surface acoustic wave filter. In order to generate a surface acoustic wave including an SH wave as the main component, a 41° Y cut X propagation substrate or a 64° Y cut X propagation substrate needs to be used in the case of a lithium niobate, and a 36° Y cut X propagation substrate needs to be used in the case of a lithium tantalate. The 41° Y cut X propagation corresponds with the Euler angle indication of (0°, 131°, 0°), the 64° Y cut X propagation corresponds with the Euler angle indication of (0°, 154°, 0°), and the 36° Y cut X propagation corresponds with the Euler angle indication of (0°, 126°, 0°). 
     However, the temperature coefficient of group delay time temperature characteristic (hereinafter referred to as TCD) of these piezoelectric single crystals is not good. More specifically, the TCD of a 41° Y cut X propagation lithium niobate substrate is 80 ppm/° C., the TCD of a 64° Y cut X propagation lithium niobate substrate is 81 ppm/° C., and the TCD of a 36° Y cut X propagation lithium tantalate substrate is 32 ppm/° C. 
     In general, in order to reliably obtain good characteristics in a surface acoustic wave resonator, a material with a good TCD is needed. That is, a material with a small frequency characteristic change according to the temperature change is needed. Therefore, if a surface acoustic wave resonator for generating a surface acoustic wave including an SH wave as the main component is provided with the lithium niobate or the lithium tantalate used as the substrate material as mentioned above, a problem arises in that the frequency characteristic shifts drastically. Moreover, even though lithium tantalate has a TCD which is better than that of lithium niobate, it also experiences the same problem with the frequency characteristic shift. 
     For example, in a surface acoustic wave resonator having a 100 MHz center frequency, a 50° C. temperature change causes a 400 KHz frequency characteristic shift in the case of a 41° Y cut X propagation lithium niobate substrate, a 405 KHz frequency characteristic shift is generated in the case of a 64° Y cut X propagation lithium niobate substrate, and a 160 KHz frequency characteristic shift is generated in the case of a 36° Y cut X propagation lithium tantalate substrate. 
     In order to prevent such a frequency characteristic shift, a temperature compensation circuit has been connected to a surface acoustic wave resonator. However, a problem arises in that the device as a whole including the surface acoustic wave resonator becomes bulky because of the added temperature compensation circuit so that it is difficult to achieve a small size component. 
     SUMMARY OF THE INVENTION 
     In view of the problems described above, preferred embodiments of the present invention provide a surface acoustic wave resonator which operates using an SH wave as the main component and has an excellent TCD. 
     According to one preferred embodiment of the present invention, a surface acoustic wave resonator includes a piezoelectric substrate, and at least one interdigital transducer having at least one pair of comb-shaped electrodes arranged to contact the piezoelectric substrate, the resonator arranged to use a surface acoustic wave including an SH wave as the main component, wherein a langasite single crystal is used as the piezoelectric substrate. 
     Since the langasite single crystal is used as the piezoelectric substance and the SH wave is used as mentioned above, a surface acoustic wave resonator with a large degree of coupling is achieved. 
     The langasite single crystal preferably has the Euler angle (ø, θ, φ) of approximately 0°≦ø≦30°, 0°≦θ≦25°, and φ=−1.07ø+90°±5°, and more preferably, has the Euler angle (ø, θ, φ) of approximately 11°≦ø≦24°, and 17°≦θ≦24°. 
     Alternatively, the langasite single crystal preferably has the Euler angle (ø, θ, φ) of approximately 0°≦ø≦30°, 153°≦θ≦180°, and φ=1.05ø+28°±5°, and more preferably has the Euler angle (ø, θ, φ) of approximately 5°≦ø≦30°, and approximately 153°≦θ≦158.5°. 
     According to preferred embodiments of the present invention, a surface acoustic wave resonator has a TCD which is significantly better than that of a resonator having a lithium niobate substrate or a lithium tantalate substrate. With preferred embodiments of the present invention, it is possible to obtain a TCD value of |10| ppm/° C. or less, and even |5| ppm/° C. or less. 
     Moreover, since the sound velocity is low compared with other materials, a small size component can be achieved, and since the edge reflection of an SH wave can be utilized, a reflector is not required so that an even smaller size component can be achieved. 
     For the purpose of illustrating the invention, there is shown in the drawings several preferred embodiments which are presently preferred, it being understood, however, that the invention is not limited to the precise arrangements and instrumentalities shown. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a perspective view of a surface acoustic wave resonator according to a first preferred embodiment of the present invention. 
     FIG. 2 is a perspective view of a longitudinally coupled surface acoustic wave filter according to a second preferred embodiment. 
     FIG. 3 is a perspective view of a laterally (i.e. transversally) coupled surface acoustic wave filter according to a third preferred embodiment. 
     FIG. 4 is a block diagram for explaining a duplexer according to a fourth preferred embodiment and a communications apparatus according to a fifth preferred embodiment. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     Hereinafter, preferred embodiments of the present invention are explained in detail with reference to the drawings. 
     FIG. 1 is a perspective view of a surface acoustic wave resonator according to a first preferred embodiment of the present invention. 
     As shown in FIG. 1, a surface acoustic wave resonator  1  is provided by forming an interdigital transducer  3  on a piezoelectric substrate  2  made of a langasite single crystal (La 3 Ga 5 SiO 14 ). 
     The interdigital transducer  3  is preferably made of an electrode material, such as Al, Au, or the like such that a pair of comb-shaped electrodes  3   a ,  3   b  are arranged so as to be interdigitated with each other. 
     Then, a second preferred embodiment of the present invention will be explained. FIG. 2 is a perspective view of a longitudinally coupled surface acoustic wave filter according to a second preferred embodiment of the present invention. 
     As shown in FIG. 2, the longitudinally coupled surface acoustic wave filter  11  is provided by forming two interdigital transducers  13  on a piezoelectric substrate  12  made of a langasite single crystal (La 3 Ga 5 SiO 14 ). 
     The interdigital transducers  13  are formed with an electrode material, such as Al, Au, or the like such that a pair of comb-shaped electrodes  13   a ,  13   b  are arranged so as to be interdigitated with each other. Moreover, the interdigital transducers  13 ,  13  are arranged substantially parallel in the surface acoustic wave propagation direction with a certain distance. 
     Furthermore, a third preferred embodiment of the present invention will be explained. FIG. 3 is a perspective view of a laterally coupled surface acoustic wave filter according to a third preferred embodiment of the present invention. 
     As shown in FIG. 3, the transversally coupled surface acoustic wave filter  21  is provided by forming an interdigital transducer  23  on a piezoelectric substrate  22  made of a langasite single crystal (La 3 Ga 5 SiO 14 ). 
     The interdigital transducer  23  is preferably made of an electrode material, such as Al, Au, or the like such that pairs of comb-shaped electrodes  23   a and  23   b ,  23   b  and  23   c , are arranged so as to be interdigitated with each other. 
     Then, fourth and fifth preferred embodiments of the present invention will be explained. FIG. 4 is a block diagram of a duplexer according to a fourth preferred embodiment of the present invention and a communications apparatus according to a fifth preferred embodiment of the present invention. 
     As shown in FIG. 4, the communications apparatus  31  is provided by connecting an antenna terminal of a duplexer  34  including a surface acoustic wave filter  32  for a receiver and a surface acoustic wave filter for a transmitter  33  with an antenna  35 , connecting an output terminal with a receiving circuit  36 , and connecting an input terminal with a transmitting circuit  37 . For the receiving surface acoustic wave filter  32  and the transmitting surface acoustic wave filter  33  of the duplexer  34 , the surface acoustic wave filters  11 ,  21  according to the second and third preferred embodiments are used. 
     Characteristics derived from a cutting angle of the material used for the substrate of the surface acoustic wave resonator used for the application mentioned above are shown in Table 1. Those marked with * before the specimen number are outside the range of preferred embodiments of the present invention. 
     P in the displacement distribution refers to a longitudinal wave, SH a transverse wave having a displacement in the horizontal direction, that is, an SH wave, and SV a transverse wave having a displacement in the vertical direction. Further, the displacement distribution is indicated with the largest wave as 1, and the other waves in the ratio with respect to the largest wave. 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Specimen 
                   
                 Euler angle 
                 TCD 
                   
                 Displacement distribution 
               
             
          
           
               
                 Number 
                 Material 
                 φ 
                 θ 
                 ψ 
                 (ppm/° C.) 
                 K (%) 
                 P 
                 SH 
                 SV 
               
               
                   
               
             
          
           
               
                 *1 
                 LiNbO 3   
                 0.0 
                 131.0 
                 0.0 
                 80.000 
                 17.20 
                 0.0300 
                 1.00 
                 0.4000 
               
               
                 *2 
                 LiNbO 3   
                 0.0 
                 154.0 
                 0.0 
                 81.000 
                 11.30 
                 0.1000 
                 1.00 
                 0.3700 
               
               
                 *3 
                 LiTbO 3   
                 0.0 
                 126.0 
                 0.0 
                 32.000 
                 4.70 
                 0.0300 
                 1.00 
                 0.1300 
               
               
                 4 
                 La 3 Ga 5 SiO 14   
                 0.0 
                 0.0 
                 85.0 
                 −16.000 
                 2.30 
                 0.1800 
                 1.00 
                 0.2800 
               
               
                 5 
                 La 3 Ga 5 SiO 14   
                 0.0 
                 23.5 
                 89.5 
                 −0.200 
                 4.23 
                 0.7400 
                 0.21 
                 0.9060 
               
               
                 *6 
                 La 3 Ga 5 SiO 14   
                 0.0 
                 25.0 
                 89.5 
                 25.345 
                 2.15 
                 0.8200 
                 1.00 
                 1.0000 
               
               
                 7 
                 La 3 Ga 5 SiO 14   
                 5.0 
                 22.0 
                 84.0 
                 5.970 
                 3.73 
                 0.2000 
                 1.00 
                 0.2400 
               
               
                 8 
                 La 3 Ga 5 SiO 14   
                 10.0 
                 0.0 
                 80.0 
                 16.700 
                 3.01 
                 0.0059 
                 1.00 
                 0.0100 
               
               
                 9 
                 La 3 Ga 5 SiO 14   
                 10.0 
                 10.0 
                 79.5 
                 5.270 
                 3.77 
                 0.0480 
                 1.00 
                 0.0699 
               
               
                 10 
                 La 3 Ga 5 SiO 14   
                 10.0 
                 20.0 
                 79.0 
                 −8.651 
                 4.80 
                 0.3100 
                 1.00 
                 0.3000 
               
               
                 11 
                 La 3 Ga 5 SiO 14   
                 10.0 
                 22.0 
                 79.0 
                 5.990 
                 4.44 
                 0.3700 
                 1.00 
                 0.4600 
               
               
                 12 
                 La 3 Ga 5 SiO 14   
                 10.0 
                 23.0 
                 79.0 
                 2.740 
                 4.71 
                 0.5700 
                 1.00 
                 0.7100 
               
               
                 13 
                 La 3 Ga 5 SiO 14   
                 10.0 
                 24.0 
                 79.0 
                 −5.490 
                 4.69 
                 0.7200 
                 1.00 
                 0.9800 
               
               
                 *14 
                 La 3 Ga 5 SiO 14   
                 10.0 
                 25.0 
                 79.0 
                 −8.360 
                 4.66 
                 0.8100 
                 0.62 
                 1.0000 
               
               
                 15 
                 La 3 Ga 5 SiO 14   
                 11.0 
                 17.0 
                 78.5 
                 0.064 
                 4.57 
                 0.2100 
                 1.00 
                 0.2800 
               
               
                 16 
                 La 3 Ga 5 SiO 14   
                 12.0 
                 17.0 
                 77.5 
                 −0.110 
                 4.72 
                 0.2400 
                 1.00 
                 0.3150 
               
               
                 17 
                 La 3 Ga 5 SiO 14   
                 14.5 
                 15.0 
                 75.0 
                 1.159 
                 4.72 
                 0.2100 
                 1.00 
                 0.2920 
               
               
                 18 
                 La 3 Ga 5 SiO 14   
                 14.5 
                 16.0 
                 75.0 
                 0.610 
                 4.89 
                 0.2500 
                 1.00 
                 0.3400 
               
               
                 19 
                 La 3 Ga 5 SiO 14   
                 14.5 
                 17.0 
                 74.5 
                 0.067 
                 4.58 
                 0.2100 
                 1.00 
                 0.2750 
               
               
                 20 
                 La 3 Ga 5 SiO 14   
                 14.5 
                 18.0 
                 74.5 
                 −0.300 
                 4.74 
                 0.2500 
                 1.00 
                 0.3320 
               
               
                 21 
                 La 3 Ga 5 SiO 14   
                 14.5 
                 19.0 
                 74.5 
                 −0.830 
                 4.93 
                 0.3100 
                 1.00 
                 0.4080 
               
               
                 22 
                 La 3 Ga 5 SiO 14   
                 14.5 
                 20.0 
                 74.5 
                 −1.520 
                 5.14 
                 0.4000 
                 1.00 
                 0.5110 
               
               
                 23 
                 La 3 Ga 5 SiO 14   
                 14.5 
                 23.0 
                 74.0 
                 −7.450 
                 5.19 
                 0.8000 
                 1.00 
                 0.9900 
               
               
                 *24 
                 La 3 Ga 5 SiO 14   
                 14.5 
                 25.0 
                 73.0 
                 −29.910 
                 2.66 
                 0.8100 
                 0.23 
                 1.0000 
               
               
                 25 
                 La 3 Ga 5 SiO 14   
                 15.0 
                 17.0 
                 74.0 
                 0.068 
                 4.65 
                 0.2200 
                 1.00 
                 0.2920 
               
               
                 26 
                 La 3 Ga 5 SiO 14   
                 20.0 
                 0.0 
                 69.9 
                 8.860 
                 3.01 
                 0.0059 
                 1.00 
                 0.0100 
               
               
                 27 
                 La 3 Ga 5 SiO 14   
                 20.0 
                 10.0 
                 69.5 
                 5.650 
                 4.23 
                 0.1300 
                 1.00 
                 0.1980 
               
               
                 28 
                 La 3 Ga 5 SiO 14   
                 20.0 
                 18.0 
                 68.5 
                 −0.290 
                 5.07 
                 0.3000 
                 1.00 
                 0.4000 
               
               
                 29 
                 La 3 Ga 5 SiO 14   
                 20.0 
                 20.0 
                 68.5 
                 −2.030 
                 5.51 
                 0.4600 
                 1.00 
                 0.5980 
               
               
                 30 
                 La 3 Ga 5 SiO 14   
                 20.0 
                 23.0 
                 68.0 
                 −8.330 
                 5.59 
                 0.7900 
                 1.00 
                 0.9900 
               
               
                 *31 
                 La 3 Ga 5 SiO 14   
                 20.0 
                 30.0 
                 67.0 
                 −23.400 
                 2.75 
                 0.8200 
                 0.24 
                 1.0000 
               
               
                 32 
                 La 3 Ga 5 SiO 14   
                 24.0 
                 17.0 
                 64.5 
                 0.260 
                 5.12 
                 0.2900 
                 1.00 
                 0.4460 
               
               
                 33 
                 La 3 Ga 5 SiO 14   
                 24.0 
                 24.0 
                 63.0 
                 1.080 
                 5.37 
                 0.7700 
                 1.00 
                 0.9620 
               
               
                 *34 
                 La 3 Ga 5 SiO 14   
                 24.0 
                 25.0 
                 63.0 
                 −6.050 
                 5.38 
                 0.8100 
                 0.70 
                 1.0000 
               
               
                 35 
                 La 3 Ga 5 SiO 14   
                 30.0 
                 0.0 
                 59.0 
                 13.240 
                 3.91 
                 0.6100 
                 1.00 
                 0.1030 
               
               
                 36 
                 La 3 Ga 5 SiO 14   
                 30.0 
                 10.0 
                 59.0 
                 −5.800 
                 3.82 
                 0.1600 
                 1.00 
                 0.2390 
               
               
                 37 
                 La 3 Ga 5 SiO 14   
                 30.0 
                 20.0 
                 57.5 
                 −1.850 
                 5.88 
                 0.5000 
                 1.00 
                 0.6540 
               
               
                 38 
                 La 3 Ga 5 SiO 14   
                 30.0 
                 23.0 
                 57.0 
                 −3.800 
                 6.01 
                 0.7200 
                 1.00 
                 0.9200 
               
               
                 39 
                 La 3 Ga 5 SiO 14   
                 30.0 
                 25.0 
                 56.5 
                 2.148 
                 5.87 
                 0.8000 
                 0.81 
                 1.0000 
               
               
                 *40 
                 La 3 Ga 5 SiO 14   
                 31.0 
                 0.0 
                 5.90 
                 14.025 
                 4.02 
                 1.0000 
                 0.90 
                 0.0930 
               
               
                 *41 
                 La 3 Ga 5 SiO 14   
                 31.0 
                 25.0 
                 56.5 
                 2.345 
                 5.96 
                 0.8200 
                 0.79 
                 1.0000 
               
               
                   
               
             
          
         
       
     
     As shown in Table 1, when a langasite single crystal (La 3 Ga 5 SiO 14 ) is used to form the substrate, the TCD is improved dramatically compared with a conventional lithium niobate substrate, and is also greatly improved compared with a lithium tantalate substrate. 
     Moreover, as seen in Table 1, in the surface acoustic wave resonators using a langasite single crystal (La 3 Ga 5 SiO 14 ), a displacement distribution SH 1 can be found, that is, the SH wave can be the largest there. Thus, it was discovered that the SH wave can be utilized very effectively. 
     More specifically, from Table 1, it is seen that the displacement distribution SH can be 1 within the range wherein the Euler angle (ø, θ, φ) is (0°≦ø≦30°, 0°≦θ≦25°, and φ=−1.07ø+90°±5°), that is, within the range of the specimen numbers 4, 5, 7 to 13, 15 to 23, 25 to 30, 32, 33, and 35 to 39. φ=−1.07ø+90°±5° is the formula determined from the experimental values of the specimens shown in Table 1. 
     Furthermore, as shown in Table 1, it is discovered that in a langasite single crystal (La 3 Ga 5 SiO 14 ), since the TCD value is about |10| ppm/° C. or less within the range wherein the Euler angle thereof is about (11°≦ø≦24°, and 17°≦θ≦24°), that is, within the range of the specimen numbers 15 to 23, 25 to 30, 32 and 33, the TCD is particularly good compared with the other parts in Table 1. 
     Therefore, by using a langasite single crystal (La 3 Ga 5 SiO 14 ) with the Euler angle in the piezoelectric substrates  2 ,  12 ,  22  of the surface acoustic wave resonator shown in FIG.  1  and the surface acoustic wave filters shown in FIGS. 2,  3 , since the TCD is |10| ppm/° C. or less, for example, in the case of a surface acoustic wave resonator having a 100 MHz center frequency, only about 50 KHz frequency characteristic shift is generated by a 50° C. temperature change. Thus, this device is constructed to easily withstand use in an environment with a large temperature change. 
     Characteristics derived from a cutting angle different from those of Table 1 of the material used for the substrate of the surface acoustic wave resonator are shown in Table 2. Items marked with * before the specimen number are outside the range of preferred embodiments of the present invention. As in Table 1, P in the displacement distribution refers to a longitudinal wave, SH a transverse wave having a displacement in the horizontal direction, that is, an SH wave, and SV a transverse wave having a displacement in the vertical direction. Further, the displacement distribution is indicated with the largest wave as 1, and the other waves in the ratio with respect to the largest wave. 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Specimen 
                   
                 Euler angle 
                 TCD 
                   
                 Displacement distribution 
               
             
          
           
               
                 Number 
                 Material 
                 φ 
                 θ 
                 ψ 
                 (ppm/° C.) 
                 K (%) 
                 P 
                 SH 
                 SV 
               
               
                   
               
             
          
           
               
                 *42 
                 La 3 Ga 5 SiO 14   
                 0.0 
                 153.0 
                 24.5 
                 −11.851 
                 6.98 
                 0.7300 
                 0.90 
                 1.0000 
               
               
                 43 
                 La 3 Ga 5 SiO 14   
                 0.0 
                 154.0 
                 23.0 
                 −9.673 
                 6.82 
                 0.7000 
                 1.00 
                 0.9200 
               
               
                 44 
                 La 3 Ga 5 SiO 14   
                 0.0 
                 158.5 
                 25.5 
                 2.550 
                 6.66 
                 0.5900 
                 1.00 
                 0.8380 
               
               
                 45 
                 La 3 Ga 5 SiO 14   
                 0.0 
                 165.0 
                 27.0 
                 −22.489 
                 5.88 
                 0.3700 
                 1.00 
                 0.5580 
               
               
                 46 
                 La 3 Ga 5 SiO 14   
                 0.0 
                 170.0 
                 28.5 
                 −25.604 
                 5.09 
                 0.2500 
                 1.00 
                 0.3940 
               
               
                 47 
                 La 3 Ga 5 SiO 14   
                 0.0 
                 180.0 
                 29.5 
                 −30.532 
                 4.89 
                 0.4600 
                 1.00 
                 0.8300 
               
               
                 *48 
                 La 3 Ga 5 SiO 14   
                 0.0 
                 181.0 
                 29.5 
                 −31.210 
                 4.77 
                 0.6300 
                 0.95 
                 1.0000 
               
               
                 49 
                 La 3 Ga 5 SiO 14   
                 5.0 
                 158.0 
                 30.5 
                 0.897 
                 6.67 
                 0.6000 
                 1.00 
                 0.8400 
               
               
                 50 
                 La 3 Ga 5 SiO 14   
                 5.0 
                 158.5 
                 31.0 
                 0.900 
                 6.69 
                 0.6300 
                 1.00 
                 0.8860 
               
               
                 *51 
                 La 3 Ga 5 SiO 14   
                 10.0 
                 140.0 
                 39.5 
                 −6.250 
                 4.68 
                 0.8100 
                 0.32 
                 1.0000 
               
               
                 *52 
                 La 3 Ga 5 SiO 14   
                 10.0 
                 150.0 
                 34.0 
                 1.940 
                 6.77 
                 0.7800 
                 0.72 
                 1.0000 
               
               
                 53 
                 La 3 Ga 5 SiO 14   
                 10.0 
                 153.0 
                 34.5 
                 −1.820 
                 6.89 
                 0.7700 
                 1.00 
                 1.0000 
               
               
                 54 
                 La 3 Ga 5 SiO 14   
                 10.0 
                 155.0 
                 35.0 
                 −1.470 
                 6.80 
                 0.7300 
                 1.00 
                 0.9620 
               
               
                 55 
                 La 3 Ga 5 SiO 14   
                 10.0 
                 158.5 
                 36.0 
                 −0.210 
                 6.61 
                 0.6100 
                 1.00 
                 0.8400 
               
               
                 56 
                 La 3 Ga 5 SiO 14   
                 10.0 
                 160.0 
                 36.5 
                 14.960 
                 6.48 
                 0.5700 
                 1.00 
                 0.7940 
               
               
                 *57 
                 La 3 Ga 5 SiO 14   
                 20.0 
                 145.0 
                 47.0 
                 −12.120 
                 4.46 
                 0.8100 
                 0.37 
                 1.0000 
               
               
                 *58 
                 La 3 Ga 5 SiO 14   
                 20.0 
                 150.0 
                 44.0 
                 −6.970 
                 6.00 
                 0.8100 
                 0.70 
                 1.0000 
               
               
                 59 
                 La 3 Ga 5 SiO 14   
                 20.0 
                 160.0 
                 47.0 
                 12.190 
                 6.28 
                 0.5600 
                 1.00 
                 0.7500 
               
               
                 *60 
                 La 3 Ga 5 SiO 14   
                 25.0 
                 150.0 
                 48.5 
                 −12.070 
                 5.43 
                 0.8100 
                 0.58 
                 1.0000 
               
               
                 61 
                 La 3 Ga 5 SiO 14   
                 25.0 
                 153.0 
                 50.0 
                 1.455 
                 5.91 
                 0.8100 
                 1.00 
                 1.0000 
               
               
                 62 
                 La 3 Ga 5 SiO 14   
                 25.0 
                 154.0 
                 50.5 
                 0.091 
                 6.04 
                 0.8000 
                 1.00 
                 1.0000 
               
               
                 63 
                 La 3 Ga 5 SiO 14   
                 25.0 
                 155.0 
                 51.0 
                 1.480 
                 6.16 
                 0.7900 
                 1.00 
                 1.0000 
               
               
                 64 
                 La 3 Ga 5 SiO 14   
                 30.0 
                 158.5 
                 57.5 
                 −3.070 
                 5.74 
                 0.5600 
                 1.00 
                 0.7160 
               
               
                 65 
                 La 3 Ga 5 SiO 14   
                 30.0 
                 165.0 
                 58.5 
                 −19.524 
                 5.39 
                 0.3100 
                 1.00 
                 0.4320 
               
               
                 66 
                 La 3 Ga 5 SiO 14   
                 30.0 
                 170.0 
                 59.0 
                 −22.425 
                 4.42 
                 0.1600 
                 1.00 
                 0.2420 
               
               
                 67 
                 La 3 Ga 5 SiO 14   
                 30.0 
                 180.0 
                 60.0 
                 −36.780 
                 3.38 
                 0.5900 
                 1.00 
                 0.8500 
               
               
                 *68 
                 La 3 Ga 5 SiO 14   
                 30.0 
                 181.0 
                 61.0 
                 −39.185 
                 3.35 
                 0.6100 
                 0.90 
                 1.0000 
               
               
                   
               
             
          
         
       
     
     As shown in Table 2, when a langasite single crystal (La 3 Ga 5 SiO 14 ) is used to form the substrate, the TCD is improved dramatically compared with a conventional lithium niobate substrate, and is also improved compared with a lithium tantalate substrate. 
     Moreover, as seen in Table 2, in the surface acoustic wave resonators using a langasite single crystal (La 3 Ga 5 SiO 14 ), a displacement distribution SH 1 can be found, that is, the SH wave can be the largest there. Thus, it was discovered that the SH wave can be utilized very effectively. 
     Moreover, from Table 2, it is discovered that the displacement distribution SH can be 1 within the range wherein the Euler angle (ø, θ, φ) is (0°≦ø≦30°, 153°≦θ≦180°, and φ=1.05ø+28°±5°), that is, within the range of the specimen numbers 43 to 47, 49, 50, 53 to 56, 59, and 61 to 67. φ=1.05ø+28°±5° is the formula found out from the experiment values of the specimens shown in Table 2. 
     Furthermore, as shown in Table 2, in a langasite single crystal (La 3 Ga 5 SiO 14 ), since the TCD value is about |5| ppm/° C. or less within the range wherein the Euler angle thereof is about (5°≦ø≦30°, and 153°≦θ≦158.5°), that is, within the range of the specimen numbers 49, 50, 53 to 55, and 61 to 64, it is learned that the TCD is particularly good compared with the other parts in Tables 1 and 2. 
     Therefore, by using a langasite single crystal (La 3 Ga 5 SiO 14 ) with the Euler angle in the piezoelectric substrates  2 ,  12 ,  22  of the surface acoustic wave resonator shown in FIG.  1  and the surface acoustic wave filters shown in FIGS. 2,  3 , since the TCD is |5| ppm/° C. or less, for example, in the case of a surface acoustic wave resonator having a 100 MHz center frequency, only about 25 KHz frequency characteristic shift is generated by a 50° C. temperature change. Thus, such a device can easily withstand use in an environment with a large temperature change. 
     Although examples of a surface acoustic wave resonator, a longitudinally coupled surface acoustic wave filter, and a transversally coupled surface acoustic wave filter have been explained in the first to third preferred embodiments of the present invention, the present invention is not limited thereto. For example, a transversally coupled surface acoustic wave filter having plural sets of interdigital transducers, or a surface acoustic wave resonator to be used in a ladder type filter with surface acoustic wave resonators arranged like a ladder, or the like, can be adopted, and the same effect can be obtained in a surface acoustic wave resonator with any kind of structure. 
     Furthermore, although surface acoustic wave resonators without a reflector have been explained in the first to third preferred embodiments of the present invention, the present invention is not limited thereto, but can be adopted in a surface acoustic wave resonator having a reflector. 
     While preferred embodiments of the invention have been disclosed, various modes of carrying out the principles disclosed herein are contemplated as being within the scope of the following claims. Therefore, it is understood that the scope of the invention is not to be limited except as otherwise set forth in the claims.