Patent Publication Number: US-9425766-B2

Title: Elastic wave element, and electrical apparatus and duplexer using same

Description:
This application is a U.S. national stage application of the PCT international application No. PCT/JP2010/006390, filed Oct. 29, 2010. 
     TECHNICAL FIELD 
     The present invention relates to an acoustic wave device and a duplexer and an electronic apparatus including the acoustic wave device. 
     BACKGROUND ART 
     Conventional acoustic wave devices will be explained with reference to drawings.  FIG. 18  is a schematic cross sectional view of a conventional acoustic wave device. 
     As shown in  FIG. 18 , the conventional acoustic wave device includes a piezoelectric substrate  2 , electrodes  3 , and a protective layer  4 . The piezoelectric substrate  2  is made of a lithium niobate material which has, e.g. the Euler angles (0°, −87.5°, 0°). The electrodes  3  may be made of copper disposed on the piezoelectric substrate  2  for exciting major acoustic waves of a wavelength λ. The protective layer  4  is made of silicon oxide disposed on the piezoelectric substrate  2  to cover the electrodes  3 . 
     The protective layer of in the conventional acoustic wave device  1  may have a thickness of, e.g. 0.35° to improve thermal characteristics of the conventional acoustic wave device  1 . In this case, undesired spurious emissions are generated at a frequency about 1.2 times the resonant frequency, as shown in  FIGS. 19 and 20  (See the region enclosed by a dotted line). 
       FIG. 19  is a characteristic diagram of a sample the conventional acoustic wave device  1  where the piezoelectric substrate  2  is made of a lithium niobate material which has the Euler angles (0°, −87.5°, 0°), the electrodes  3  are made of copper with a thickness of 0.03λ, and the protective layer  4  is made of silicon oxide with a thickness of 0.35λ and has a planar upper surface. 
       FIG. 20  is a characteristic diagram showing another sample of the conventional acoustic wave device  1  where the piezoelectric substrate  2  is made of a lithium niobate material which has the Euler angles (0°, −90°, 0°), the electrodes  3  are made of aluminum with a thickness of 0.08λ, and the protective layer  4  is made of silicon oxide with a thickness of 0.35λ and has a projection on the upper surface above each electrode finger of the electrodes  3 . 
     The vertical axis in each of  FIGS. 19 and 20  represents normalized admittance with respect to a matching value. The horizontal axis in each of  FIGS. 19 and 20  represents normalized frequency with respect to a half the frequency of a slow transverse wave (at a speed of 4024 m/s) which appears in the acoustic wave device  1 . It is noted that the vertical axis and the horizontal axis are equally assigned throughout the other characteristic diagrams in this specification. 
     Undesired spurious emissions shown in  FIGS. 19 and 20  are generated by a fast transverse wave produced in the acoustic wave device  1 . In this specification that the fast transverse wave is the fastest one of the transverse waves produced in the acoustic wave device  1  and the slow transverse wave is the slowest one of the transverse waves. 
       FIGS. 21A to 21C  are characteristic diagrams of the conventional acoustic wave device  1  with the protective layer  4  having various thicknesses while the piezoelectric substrate  2  is made of a lithium niobate material which has the Euler angles (0°, −87.5°, 0°), the electrodes  3  are made of copper with a thickness of 0.03λ, and the protective layer  4  is made of silicon oxide and has a planar upper surface.  FIG. 21A  illustrates the relationship between the thickness of the protective layer  4  and an electromechanical coupling coefficient (k 2 ) for the fast transverse wave.  FIG. 21B  illustrates the relationship between the thickness of the protective layer  4  and the Q value (Qs) of resonance.  FIG. 21C  illustrates the relationship between the thickness of the protective layer  4  and the Q value (Qa) of anti-resonance. 
     As shown in  FIG. 21B , the Q value of resonance of the fast transverse wave increases when the thickness of the protective layer  4  is greater than 0.27λ. As shown in  FIG. 21C , the Q value of anti-resonance of the fast transverse wave increases when the thickness of the protective layer  4  is greater than 0.34λ. 
       FIGS. 22A to 22C  are characteristic diagrams of the conventional acoustic wave device  1  including the protective layer  4  having various thicknesses. It is noted that the piezoelectric substrate  2  is made of a lithium niobate material which has the Euler angles (0°, −90°, 0°), the electrodes  3  are made of aluminum with a thickness of 0.08λ, and the protective layer  4  is made of silicon oxide and has a projection on the upper surface above each electrode finger of the electrodes  3 . 
       FIG. 22A  illustrates the relationship between the thickness of the protective layer  4  and the electromechanical coupling coefficient (k 2 ) for the fast transverse wave.  FIG. 22B  illustrates the relationship between the thickness of the protective layer  4  and the Q value (Qs) of resonance.  FIG. 22C  illustrates the relationship between the thickness of the protective layer  4  and the Q value (Qa) of anti-resonance. 
     As shown in  FIG. 22B , the Q value of resonance of the fast transverse wave increases when the thickness of the protective layer  4  is greater than 0.2λ. As shown in  FIG. 22C , the Q value of anti-resonance of the fast transverse wave increases when the thickness of the protective layer  4  is greater than 0.27λ. 
     The conventional acoustic wave device  1  has a drawback that characteristics of a filter or a duplexer employing the conventional acoustic wave device  1  declines by the undesired spurious emissions generated by the fast transverse wave. 
     For the purpose of attenuating the undesired spurious emissions, φ and ψ out of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  2  are modified. 
       FIGS. 23A to 23G and 24A to 24G  are characteristic diagrams of the conventional acoustic wave device  1  when φ and ψ out of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  2  are modified. More particularly,  FIGS. 23A to 23G  illustrate the characteristic diagrams where φ out of the Euler angles is varied while  FIGS. 24A to 24G  illustrate the characteristic diagrams where ψ out of the Euler angles is varied. It is noted that the piezoelectric substrate  2  is made of a lithium niobate material, the electrodes  3  are made of aluminum with a thickness of 0.08λ, and the protective layer  4  is made of silicon oxide and has a projection on the upper surface above each electrode finger of the electrodes  3 . 
     The upper sections in  FIGS. 23A to 23G and 24A to 24G  illustrate the Euler angles (φ, θ, ψ) of the piezoelectric substrate  2 .  FIGS. 23A to 23G and 24A to 24G  do not show the admittance greater than 1e+02 and smaller than 1e−02 of the acoustic wave device. 
     As shown in  FIGS. 23A to 23G and 24A to 24G , the desired spurious emissions can be attenuated when either φ or ψ out of the Euler angles is varied (See  FIGS. 23A, 23G, 24A and 24G ). Even after the compensation, desired spurious emissions other than the above mentioned undesired spurious emissions are generated. Such undesired spurious emissions may derive from a Rayleigh wave. 
     One known example of the prior art with reference to the invention is disclosed in Patent Document 1. 
     CITATION LIST 
     Patent Literature 
     
         
         
           
             Patent Literature 1: WO2005-034347 
           
         
       
    
     SUMMARY OF THE INVENTION 
     In view of the above described drawback, the present invention provides an acoustic wave device designed for, even when the thickness of a protective layer thereof is greater than a predetermined thickness, suppressing the generation of undesired spurious emissions derived from a Rayleigh wave and simultaneously attenuating the desired spurious emissions generated by a fast transverse wave. 
     One aspect of the acoustic wave device according to the present invention includes a piezoelectric substrate made of a lithium niobate material having the Euler angles (φ, θ, ψ), electrodes disposed on the piezoelectric substrate for exciting a major acoustic wave of a wavelength λ, and a protective layer having a thickness of greater than 0.27λand disposed on the piezoelectric substrate so as to cover the electrodes. The Euler angles satisfy: −100°≦θ≦−60° and 1.193φ−2°≦ψ≦1.193φ+2°; or ψ≦−2φ−3° and −2φ+3°≦ψ. 
     Another aspect of the acoustic wave device according to the present invention includes a piezoelectric substrate made of a lithium niobate material having the Euler angles (φ, θ, ψ), electrodes disposed on the piezoelectric substrate for exciting a major acoustic wave of a wavelength λ, and a protective layer having a thickness of greater than 0.2λ and disposed on the piezoelectric substrate so as to cover the electrodes. The protective layer has a projection thereof arranged above each electrode finger of the electrodes. The width of the top of the projection is smaller than the width of each electrode finger of the electrodes. The Euler angles satisfy: −100°≦θ≦−60°, 1.193φ−2°≦ψ≦1.193φ+2°; and either ψ≦−2φ−3° or −2φ+3°≦ψ. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic cross sectional view of an acoustic wave device in accordance with a first exemplary embodiment of the present invention. 
         FIG. 2A  is a characteristic diagram of an example of the acoustic wave device in accordance with the first embodiment of the present invention where the piezoelectric substrate is made of a lithium niobate material having the Euler angles (7°, −87.5°, 8.4°), the electrodes are made of copper with a thickness of 0.03λ, and the protective layer is made of silicon oxide with a thickness of 0.35λ and has a planar upper surface. 
         FIG. 2B  is a characteristic diagram of another example of the acoustic wave device in accordance with the first embodiment of the present invention where the piezoelectric substrate is made of a lithium niobate material having the Euler angles (9°, −87.5°, 10.7°), the electrodes are made of copper with a thickness of 0.03λ, and the protective layer is made of silicon oxide with a thickness of 0.35λ and has a planar upper surface. 
         FIG. 3  is a graphic diagram of characteristics of the acoustic wave device in accordance with the first embodiment of the present invention for showing a preferable area defined by φ and ψ out of the Euler angles (φ, θ, ψ) of the piezoelectric substrate of the lithium niobate material with hatching. 
         FIG. 4  is a graphic diagram of the acoustic wave device in accordance with the first embodiment of the present invention, illustrating a profile of the Q value of a Rayleigh wave in the acoustic wave device when ψ out of the Euler angles (φ, θ, ψ) of the piezoelectric substrate increases and decreases from ψ=1.193φ. 
         FIG. 5  is a graphic diagram of the acoustic wave device of the first embodiment of the present invention, illustrating profiles of the Q value of a Rayleigh wave of the acoustic wave device when ψ out of the Euler angles (φ, θ, ψ) of the piezoelectric substrate increases and decreases from ψ=−2φ. 
         FIG. 6  is a graphic diagram of the acoustic wave device in accordance with the first embodiment of the present invention, illustrating a profile of an electromechanical coupling coefficient of the Rayleigh wave in the acoustic wave device when θ out of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
         FIG. 7  is a graphic diagram of the acoustic wave device of the first embodiment of the present invention, illustrating a profile of a normalized coupling coefficient of an SH wave in the acoustic wave device when θ out of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
         FIG. 8  is a graphic diagram of the acoustic wave device in accordance with the first embodiment of the present invention, illustrating a variation profile of the electromechanical coupling coefficient of a Rayleigh wave with relation to φ of the acoustic wave device when φ and ψ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes along ψ=1.193φ. 
         FIG. 9  is a graphic diagram of the acoustic wave device in accordance with the first embodiment of the present invention, illustrating a variation profile of the normalized coupling coefficient of the SH wave with relation to φin the acoustic wave device when φ and ψ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes along ψ=1.193φ. 
         FIG. 10  is a schematic cross sectional view of an acoustic wave device in accordance with a second exemplary embodiment of the present invention. 
         FIG. 11A  is a characteristic diagram of the acoustic wave device in accordance with the second embodiment of the present invention. 
         FIG. 11B  is a characteristic diagram of the acoustic wave device of the second embodiment of the present invention. 
         FIG. 12A  is an explanatory view of an acoustic wave device with projections in accordance with the second embodiment of the present invention for illustrating a method of manufacturing the acoustic wave device. 
         FIG. 12B  is an explanatory view of the acoustic wave device with eth projections in accordance with the second embodiment of the present invention for illustrating the method of manufacturing the acoustic wave device. 
         FIG. 12C  is an explanatory view of the acoustic wave device with eth projections in accordance with the second embodiment of the present invention for illustrating the method of manufacturing the acoustic wave device. 
         FIG. 12D  is an explanatory view of the acoustic wave device with eth projections in accordance with the second embodiment of the present invention for illustrating the method of manufacturing the acoustic wave device. 
         FIG. 12E  is an explanatory view of the acoustic wave device with eth projections in accordance with the second embodiment of the present invention for illustrating the method of manufacturing the acoustic wave device. 
         FIG. 12F  is an explanatory view of the acoustic wave device with eth projections in accordance with the second embodiment of the present invention for illustrating the method of manufacturing the acoustic wave device. 
         FIG. 12G  is an explanatory view of the acoustic wave device with eth projections in accordance with the second embodiment of the present invention for illustrating the method of manufacturing the acoustic wave device. 
         FIG. 12H  is an explanatory view of the acoustic wave device with eth projections in accordance with the second embodiment of the present invention for illustrating the method of manufacturing the acoustic wave device. 
         FIG. 13  is a view of an arrangement of a duplexer according to one embodiment of the present invention. 
         FIG. 14  is a schematic view of an electronic apparatus according to the embodiments of the present invention. 
         FIG. 15  is a top view of an acoustic wave device according to a third exemplary embodiment of the present invention. 
         FIG. 16  is a circuit diagram of an acoustic wave device according to a fourth exemplary embodiment of the present invention. 
         FIG. 17  is a circuit diagram of the acoustic wave device in accordance with the fourth embodiment of the present invention. 
         FIG. 18  is a schematic cross sectional view of a conventional acoustic wave device. 
         FIG. 19  is a characteristic diagram of an example of the conventional acoustic wave device where the piezoelectric substrate is made of a lithium niobate material having the Euler angles (0°, −87.5°, 0°), the electrodes are made of copper with a thickness of 0.03λ, and the protective layer is made of silicon oxide with a thickness of 0.35° and has a planar upper surface. 
         FIG. 20  is a characteristic diagram of another example of the conventional acoustic wave device where the piezoelectric substrate is made of a lithium niobate material having the Euler angles (0°, −90°, 0°), the electrodes are made of aluminum with a thickness of 0.08λ, and the protective layer is made of silicon oxide with a thickness of 0.35λ and has a projection on the upper surface above each electrode finger of the electrodes. 
         FIG. 21A  is a characteristic diagram of variation of the conventional acoustic wave device where the piezoelectric substrate is made of a lithium niobate material having the Euler angles (0°, −87.5°, 0°), the electrodes are made of copper with a thickness of 0.03λ, and the protective layer is made of silicon oxide and has a planar upper surface, when the thickness of the protective layer is varied. 
         FIG. 21B  is a characteristic diagram of variation of the conventional acoustic device where the piezoelectric substrate is made of a lithium niobate material having the Euler angles (0°, −87.5°, 0°), the electrodes are made of copper with a thickness of 0.03λ, and the protective layer is made of silicon oxide and has a planar upper surface, when the thickness of the protective layer is varied. 
         FIG. 21C  is a characteristic diagram of variation of the conventional acoustic device where the piezoelectric substrate is made of a lithium niobate material having the Euler angles (0°, −87.5°, 0°), the electrodes are made of copper with a thickness of 0.03λ, and the protective layer is made of silicon oxide and has a planar upper surface, when the thickness of the protective layer is varied. 
         FIG. 22A  is a characteristic diagram of variation of the conventional acoustic wave device when the thickness of a protective layer is varied. 
         FIG. 22B  is a characteristic diagram of variation of the conventional acoustic wave device, when the thickness of the protective layer is varied. 
         FIG. 22C  is a characteristic diagram of variation of the conventional acoustic wave device when the thickness of the protective layer is varied. 
         FIG. 23A  is a characteristic diagram of the conventional acoustic wave device when φ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
         FIG. 23B  is a characteristic diagram of the conventional acoustic wave device when φ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
         FIG. 23C  is a characteristic diagram of the conventional acoustic wave device when φ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
         FIG. 23D  is a characteristic diagram of the conventional acoustic wave device when φ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
         FIG. 23E  is a characteristic diagram of the conventional acoustic wave device when φ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
         FIG. 23F  is a characteristic diagram of the conventional acoustic wave device when φ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
         FIG. 23G  is a characteristic diagram of the conventional acoustic wave device when φ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
         FIG. 24A  is a characteristic diagram of the conventional acoustic wave device when ψ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
         FIG. 24B  is a characteristic diagram of the conventional acoustic wave device when ψ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
         FIG. 24C  is a characteristic diagram of the conventional acoustic wave device when ψ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
         FIG. 24D  is a characteristic diagram of the conventional acoustic wave device when ψ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
         FIG. 24E  is a characteristic diagram of the conventional acoustic wave device when ψ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
         FIG. 24F  is a characteristic diagram of the conventional acoustic wave device when ψ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
         FIG. 24G  is a characteristic diagram of the conventional acoustic wave device when ψ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate changes. 
     
    
    
     DETAIL DESCRIPTION OF THE INVENTION 
     First Exemplary Embodiment 
     An acoustic wave device in accordance with the first exemplary embodiment of the present invention will be described below referring to the relative drawings.  FIG. 1  is a schematic cross sectional view of the acoustic wave device  5  according to the first embodiment of the present invention. 
     As shown in  FIG. 1 , the acoustic wave device  5  includes a piezoelectric substrate  6 , electrodes  7 , and a protective layer  8 . The electrodes  7  are disposed on the piezoelectric substrate  6  and are inter-digital transducer (IDT) electrodes for exciting a major acoustic wave which consists of, for example, a shear horizontal (SH) wave of a wavelength λ. The protective layer  8  is disposed on the piezoelectric substrate  6  to cover the electrodes  7 , and made of, for example, silicon oxide having a thickness of greater than 0.27λ. 
     The piezoelectric substrate  6  is a piezoelectric substrate made of a lithium niobate material (LiNbO 3 ) and has the Euler angles (φ, θ, ψ) satisfying: −100°≦θ≦−60°, 1.193φ−2°≦ψ≦1.193φ+2°; and either ψ≦−2φ−3° or −2φ+3°≦ψ. 
     Since the piezoelectric substrate  6  made of the lithium niobate material is of a crystal of trigonal system, the Euler angles are expressed by: 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       ϕ 
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                       θ 
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                     ) 
                   
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                         60 
                         + 
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                         θ 
                       
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                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     ( 
                     
                       
                         60 
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                         ϕ 
                       
                       , 
                       
                         - 
                         θ 
                       
                       , 
                       
                         180 
                         - 
                         ψ 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     ( 
                     
                       ϕ 
                       , 
                       
                         180 
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                         θ 
                       
                       , 
                       
                         180 
                         - 
                         ψ 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     ( 
                     
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                         180 
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     The electrodes  7  have a comb shape. The electrodes  7  are made of, for example, a single metallic substance, such as aluminum, copper, silver, gold, titanium, tungsten, molybdenum, platinum, or chrome, or their alloy or their layered structure. 
     The protective layer  8  is made of, for example, silicon oxide (SiO 2 ). In this case, the frequency/heat characteristics of the acoustic wave device  5  can be improved when the protective layer  8  has a thickness greater than 0.27λ and has a thermal characteristic opposite to that of the piezoelectric substrate  6 . The protective layer  8  may be made of appropriate material other than silicon oxide and, when its material is properly selected, can significantly protect the electrodes  7  from ambient atmosphere. 
     As described, in the case that the protective layer  8  made of, for example, silicon oxide having a thickness greater than 0.27λ to improve the frequency/heat characteristics of the acoustic wave device  5 , φ and ψ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  6  are greater than predetermined values and change substantially along ψ=1.193φ. This arrangement suppresses the generation of spurious emissions deriving from Rayleigh waves and simultaneously attenuates other spurious emissions generated about a frequency range where a fast transverse wave is produced. 
       FIGS. 2A and 2B  are characteristic diagrams of the acoustic wave device  5  where the piezoelectric substrate  6  of the acoustic wave device  5  is made of lithium niobate with the Euler angles (7°, −87.5°, 8.4°) and (9°, −87.5°, 10.7°), the electrodes  7  are made of copper with a thickness of 0.03λ, and the protective layer  8  is made of silicon oxide with a thickness of 0.35λ with a planar upper surface. 
     As shown in  FIGS. 2A and 2B , the acoustic wave device  5  of this embodiment can attenuate undesired spurious emissions on the Rayleigh wave and undesired spurious emissions in a frequency range where the fast transverse wave is produced, which are commonly generated in the conventional acoustic wave device. It is noted that the fast transverse wave is the fastest wave of transverse waves produced in the acoustic wave device  5 . 
       FIG. 3  is a graphic diagram where preferable areas defined by φ and ψ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  6  which is made of a lithium niobate material. It is also noted that θ is determined by −100°≦θ≦−60°, the thickness of the protective layer  8  is greater than 0.27λ, and the electrodes  7  are made of copper with a normalized thickness of 0.03λ. 
     The straight line denoted by ψ=1.193φ shown in  FIG. 3  represents the relationship between φ and ψ when undesired spurious emissions derived from the Rayleigh wave are significantly attenuated. In the area of ±2° about the straight line, more particularly, in the area determined by 1.193φ−2°≦ψ≦1.193φ+2°, the spurious emissions derived from the Rayleigh wave can be attenuated. 
     A reason for the attenuation will be described.  FIG. 4  is a graphic diagram showing the Q value (Qs) of the Rayleigh wave in the acoustic wave device  5  of the first embodiment of the present invention when ψ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  6  increases and decreases from ψ=1.193φ. In  FIG. 4 , the vertical axis represents the Q value of the Rayleigh wave and the horizontal axis represents a change Δψ from ψ=1.193φ. 
     As shown in  FIG. 4 , the Q value of the Rayleigh wave in the acoustic wave device  5  can be confined to below the predetermined level with ψ of the Euler angles (φ, θ, ψ) remaining in the area of ±2° from ψ=1.193φ. Consequently, the undesired spurious emissions derived from the Rayleigh wave can be attenuated in the area defied by 1.193φ−2°≦ψ≦1.193φ+2°. 
     The straight line denoted by ψ=−2φ shown in  FIG. 3  represents the relationship between ψ and φ when the undesired spurious emissions generated significantly by the fast transverse wave. In the area outside by more than ±3° about the straight line, that is the area determined by either ψ≦−2φ−3° or 2φ+3°≦ψ, the spurious emissions generated by the fast transverse wave can be attenuated. 
     A reason for the attenuation will be described.  FIG. 5  is a graphic diagram showing the Q value of the Rayleigh wave in the acoustic wave device  5  of the first embodiment of the present invention when ψ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  6  increases and decreases ψ=−2φ. In  FIG. 5 , the relationship between ψ and the Q value (Qa) of the fast transverse wave is shown when φ=0°, φ=0.5°, φ=1°, φ=1.5°, φ=2°, and φ=2.5°. 
     As shown in  FIG. 5 , the Q value of the fast transverse wave in the acoustic wave device  5  can be reduced to below the predetermined level with ψ of the Euler angles (φ, θ, ψ) remaining in the area outside ±3° from ψ=−2φ. (for example, in the case that ψ is greater than +3° or smaller than −3° for φ=0°). Consequently, the desired spurious emissions generated by the fast transverse wave can be attenuated in the area determined by either ψ≦−2φ−3° or −2φ+3°≦ψ. 
       FIG. 6  is a graphic diagram showing the electromechanical coupling coefficient (k2) of the Rayleigh wave in the acoustic wave device  5  of the first embodiment of the present invention when θ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  6  is varied. As shown in  FIG. 6 , θ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  6  satisfies −100°≦θ≦−60° so as to reduce the electromechanical coupling coefficient (k2) of the Rayleigh wave to smaller than 0.01. 
       FIG. 7  is a graphic diagram showing the normalized coupling coefficient of an SH wave in the acoustic wave device  5  of the first embodiment of the present invention when θ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  6  is varied. The normalized coupling coefficient shown in  FIG. 7  is a value calculated by normalizing the electromechanical coupling coefficient by an electromechanical coupling coefficient at θ=−90°. As shown in  FIG. 7 , the normalized coupling coefficient of the SH wave is smaller than the predetermined level (about 0.65) when θ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  6  remains in a range of −110°≦θ≦−60°. This range includes the range of −100°≦θ≦−60° illustrated in  FIG. 6  as described above. Consequently, the SH wave serving as a major acoustic wave can be produced efficiently while the Rayleigh wave is suppressed with θ remaining within the range of −100°≦θ≦−60°. 
       FIG. 8  is a graphic diagram showing a variation of the electromechanical coupling coefficient (k2) of the Rayleigh wave in relation to φ of the acoustic wave device  5  of the first embodiment of the present invention when φ and ψ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  6  change along ψ=1.193φ. As shown in  FIG. 8 , the electromechanical coupling coefficient of the Rayleigh wave can be decreased to smaller than 0.002 which is much smaller than 0.01 described above when φ≦20°. This is similarly established when the Euler angles of the piezoelectric substrate  6  change in the negative direction in relation to φ. Consequently, φ out of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  6  in the acoustic wave device  5  preferably satisfies a condition, |φ|≦20°. The electromechanical coupling coefficient of the Rayleigh wave can further be decreased by satisfying this condition. 
       FIG. 9  is a graphic diagram showing a variation in relation to φ of the normalized coupling coefficient of the SH wave in the acoustic wave device  5  of the first embodiment of the present invention when φ and ψ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  6  are shifted along ψ=1.193φ. While  FIG. 9  illustrates the Euler angles of the piezoelectric substrate  6  change in the positive direction, the change in relation to φ in the negative direction of the Euler angles in the piezoelectric substrate  6  provides the same effect. More specifically, as shown in  FIG. 9 , the output of the SH wave as a major acoustic wave increases when φ decreases. From this point of view, the embodiment is practical since the electromechanical coupling coefficient of the SH wave remains smaller than the predetermined level when φ of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  6  satisfies |φ|≦20°. 
     Second Exemplary Embodiment 
     Another acoustic wave device  15  according to the second embodiment of the present invention will be described referring to the relevant drawings. It is noted that the arrangement of the acoustic wave device  15  is identical to that of the acoustic wave device  5  of the first embodiment unless otherwise explained. 
       FIG. 10  is a schematic cross sectional view of the acoustic wave device  15  of the second embodiment of the present invention. The acoustic wave device  15  of this embodiment includes a piezoelectric substrate  16 , electrodes  17 , and a protective layer  18 . The piezoelectric substrate  16  is made of a lithium niobate material having the Euler angles (φ, θ, ψ). The electrodes  17  are disposed on the piezoelectric substrate  16  to excite a major acoustic wave of a wavelength λ. The protective layer  18  is disposed on the piezoelectric substrate  16  so as to cover the electrodes  17  and has a thickness greater than 0.2λ. The protective layer  18  has a projection  9  which is aligned substantially with above each electrode finger of the electrodes  17  in the cross section taken along a direction orthogonal to the direction in which the electrode fingers of the electrodes  17  extend. The top  10  of the projection  9  has a width smaller than the width of each electrode finger of the electrodes  17 . 
     The Euler angles of the piezoelectric substrate  16  satisfy −100°≦θ≦−60° and 1.193φ−2°≦ψ≦1.193φ+2° and in addition either ψ≦−2φ−3° or −2φ+3°≦ψ. 
     In the case that the protective layer  18  has the projections, the generation of undesired spurious emissions by the fast transverse wave may become a problem. In this embodiment, the thickness of the protective layer  18  made of, for example, silicon oxide is smaller than 0.2λ for improving the frequency/heat characteristics of the acoustic wave device  15 . In this case, φ and ψ out of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  16  are greater than the predetermined values and change substantially along ψ=1.193φ. Consequently, undesired spurious emissions generated at a frequency range where the fast transverse wave is produced can be attenuated, and undesired spurious emissions derived from the Rayleigh wave are attenuated. 
       FIGS. 11A and 11B  are characteristic graphs of the acoustic wave device  15  of the second embodiment of the present invention. In the acoustic wave device  15 , the piezoelectric substrate  16  is made of lithium niobate having the Euler angles (7°, −87.5°, 8.4°) and (9°−87.5°, 10.7°the electrodes  17  are made of aluminum having a thickness of 0.08λ, and the protective layer  18  is made of silicon oxide with a thickness of 0.35λ and has projections  9  formed on the upper surface thereof with a height T=0.08?. 
     As shown in  FIGS. 11A and 11B , the acoustic wave device  15  of this embodiment can suppress the generation of undesired spurious emissions in a frequency range where the fast transverse wave is produced while undesired spurious emissions derived from the Rayleigh wave are attenuated. 
     Each projection  9  of the protective layer  18  preferably has a shape having each curved side thereof projecting downwardly while each side extending from the top  10  to the bottom  11 . As shown in  FIG. 10 , the width L of the top  10  is determined between two points where the downwardly-projecting sides or their extending lines intersect the straight line parallel to the upper surface at the top  10  of the piezoelectric substrate  16 . 
     As determined in that manner, the width L of the top  10  is smaller than the width of each electrode finger of the electrodes  17 . This arrangement allows the mass of the protective layer  18  to vary at the projections  9  continuously and moderately. As the result, the electrical characteristics of the acoustic wave device  15  can be improved while the generation of undesired reflection caused by the shape of the protective layer  18  is suppressed. 
     The width L at the top  10  of the projection  9  is preferably smaller than ½ the width of each electrode finger of the electrodes  17 . The center of the top  10  may be preferably positioned directly above the center of the electrode finger. This increases the rate of reflection at the electrode fingers due to the effect of the addition of mass, hence improving the electrical characteristics of the acoustic wave device  15 . 
     Moreover, the height T of the projection  9  and the thickness h of the electrode  17  may preferably satisfy 0.03λ&lt;T≦h. As for the relationship between the electrical characteristics and the height T of the projection  9  of the protective layer  18  extending from the bottom  11  to the top  10 , the rate of reflection increases significantly when the height T is greater than 0.03λ from the upper surface of the protective layer  18  which is a planar surface. If the height T of the projection  9  is greater than the thickness h of the electrode  17 , processes of production, which will be described later, has to be increased by more steps for depositing the protective layer  8  and will be troublesome. It is hence desired that the relation of 0.03λ&lt;T≦h is satisfied. 
     Processes of producing the acoustic wave device  15  of the second embodiment of the present invention will be described below. 
       FIGS. 12A to 12H  are views of the acoustic wave device  15  with the projections  9  of the second embodiment of the present invention for showing processes for producing the acoustic wave device  15 . 
     As shown in  FIG. 12A , an electrode layer  22  which turns to at least either electrodes or reflectors is formed on the upper side of a piezoelectric substrate  21  by vapor deposition or sputtering of a material Al or its alloy. 
     As shown in  FIG. 12B , a resist layer  23  is then developed on the upper side of the electrode pattern  22 . 
     As shown in  FIG. 12C , the resist layer  23  is processed to have a predetermined shape by exposure and development technique. 
     As shown in  FIG. 12D , the electrode layer  22  is processed by dry etching or any other appropriate technique to form a desired pattern of IDT electrodes or reflectors, and then, the resist layer  23  is removed. 
     As shown in  FIG. 12E , the electrode layer  22  is then covered by vapor deposition or sputtering of silicon oxide to form a protective layer  24 . It is desired in this step for having the protective layer  24  provided with the prescribed projections  9  to employ a so-called bias sputtering technique where the sputtering is carried out with the piezoelectric substrate  21  being applied with a bias voltage. 
     By the bias sputtering technique, while the protective layer  24  is deposited on the piezoelectric substrate  21  by sputtering the target material of silicon oxide, a bias voltage is applied to sputter portions of the protective layer  24  on the piezoelectric substrate  21 . More specifically, the protective layer  24  is partially shaved while being deposited to control the development of the protective layer  24  for making a desired shape. 
     Controlling the shape of the protective layer  24  may involve varying the ratio between the sputtering power and the bias voltage to be applied to the piezoelectric substrate  21  during the sputtering, or depositing the layer  24  with no bias voltage applied to the piezoelectric substrate  21  at the beginning of the sputtering and then at the following stage applying a bias voltage to the piezoelectric substrate  21  while depositing the layer. With this means, the temperature of the piezoelectric substrate  21  is controlled properly. 
     As shown in  FIG. 12F , a resist layer  25  is then formed on the protective layer  24 . 
     As shown in  FIG. 12G , the resist layer  25  is processed by exposure and development technique to have a desired shape. 
     As shown in  FIG. 12H , unwanted regions of the protective layer  24  are removed by dry etching or any other appropriate technique for making, for example, pads  26  for outputting electrical signals, and then, the resist layer  25  is completely removed. 
     Finally, the finished structure is separated by dicing to obtain the acoustic wave devices  15 . 
     As described above, the bias sputtering technique can deposit the protective layer  24  under a favorable layer depositing condition thus to provide the projections  9  with a predetermined shape. 
     The characteristics of the acoustic wave device  15  of this embodiment are equal to those of the acoustic wave device  5  of the first embodiment shown in  FIGS. 3 to 9 . More particularly, even if the protective layer  18  made of silicon oxide has a thickness of greater than, for example, 0.2λ for improving the frequency/heat characteristic of the acoustic wave device  15 , undesired spurious emissions generated in a frequency range where the fast transverse waves appear can be attenuated, and simultaneously, the generation of undesired spurious emissions derived from the Rayleigh wave can be suppressed by causing φ and ψ out of the Euler angles (φ, θ, ψ) of the piezoelectric substrate  6  to be greater than predetermined values and to change substantially along ψ=1.193φ. 
     As shown in  FIG. 13 , the acoustic wave devices  5  and  15  according to the first and second embodiments is preferably used as a first filter  20  installed in a duplexer  32  which includes the first filter  20  and a second filter  21  which has a higher passing frequency range than the first filer  20 .  FIG. 13  is a diagram showing an arrangement of the duplexer  32  in accordance with embodiments of the present invention. More particularly, although undesired spurious emissions generated by the fast transverse wave in the first filter  20  tend to deteriorate the passing quality of the second filter  21 , the acoustic wave devices  5  and  15  as the first filer  20  can protect the passing quality of the second filter  31  from being disturbed. 
     The acoustic wave devices  5  and  15  of the first and second embodiments may be employed as resonators (not shown) or other types of filter (not shown) including ladder filters and DMS filters. 
     Moreover, as shown in  FIG. 14 , an electronic apparatus  50  may include a filter  33  to which any of the acoustic wave devices  5 ,  15  is applied, a semiconductor integrated circuit device  30  connected to the filter  33 , and a reproducing device  40  connected to the semiconductor integrated circuit device  30 .  FIG. 14  is a diagram of the electronic apparatus  50  in accordance with an embodiment of the present invention. The resonator, the filter, and the electronic apparatus can be improved in communication quality. 
     Third Exemplary Embodiment 
     An acoustic wave device  45  according to a third exemplary embodiment of the present invention will be described referring to the relevant drawings. It is noted that the arrangement of the acoustic wave device  45  is identical to that of the acoustic wave devices  5  and  15  of the first and second embodiments unless otherwise explained. 
       FIG. 15  is a top view of the acoustic wave device  45  according to the third embodiment of the present invention. The acoustic wave device  45  includes, as shown in  FIG. 15 , a piezoelectric substrate  6  having the Euler angles described in the first embodiment, a first acoustic wave resonator  100  mounted on an upper surface of the piezoelectric substrate  6 , and a second acoustic wave resonator  200  mounted on the upper surface of the piezoelectric substrate  6 . The first acoustic wave resonator  100  and the second acoustic wave resonator  200  are connected to each other in series. 
     The first acoustic wave resonator  100  includes interdigital transducer electrode  110  and grating reflectors  120  and  130 . The grating reflectors  120  and  130  are located sandwiching the interdigital transducer electrode  110  between reflectors  120  and  130  on an acoustic wave propagating path. 
     The interdigital transducer electrode  110  includes a bus bar  111  and plural comb-shaped electrodes  112  connected electrically to the bus bar  111 . The comb-shaped electrodes  112  have equal lengths. The comb-shaped electrodes  112  are arranged at equal periods of P 1  and joined to the bus bar  111 . The interdigital transducer electrode  110  further includes plural comb-shaped electrodes  113  connected electrically to a bus bar  114 . The comb-shaped electrodes  113  have equal lengths. The comb-shaped electrodes  113  are arranged at equal periods of P 1  and joined to the bus bar  114 . The comb-shaped electrodes  112  and the comb-shaped electrodes  113  are arranged alternately and interdigitate with each other with interdigitating width L 1  (throughout which adjacent comb-shaped electrodes interdigitate with each other). The bus bar  111  is electrically connected to an input terminal  302 . 
     The grating reflector  120  includes comb-shaped electrodes  122  connected electrically to a bus bar  121 . The comb-shaped electrodes  122  are arranged at equal periods of P 1 / 2  and joined to the bus bar  121 . The grating reflector  130  includes comb-shaped electrodes  132  connected electrically to a bus bar  131 . The comb-shaped electrodes  132  are arranged at equal periods of P 1 / 2  and joined to the bus bar  131 . 
     The second acoustic wave resonator  200  includes interdigital transducer electrodes  210  and grating reflectors  220  and  230 . The grating reflectors  220  and  230  are located to sandwich the interdigital transducer electrodes  210  between reflectors  220  and  230  on an acoustic wave propagating path. 
     The interdigital transducer electrode  210  includes plural comb-shaped electrodes  212  connected electrically to a bus bar  211 . The comb-shaped electrodes  212  are arranged at equal periods of P 2  and joined to the bus bar  211 . The interdigital transducer electrode  210  further includes plural comb-shaped electrodes  213  connected electrically to a bus bar  214 . The comb-shaped electrodes  213  are arranged at equal periods of P 2  and joined to the bus bar  214 . The comb-shaped electrodes  212  and the comb-shaped electrodes  213  are arranged alternately and interdigitate with each other with an interdigitating width L 2 . The interdigitating width L 2  of the comb-shaped electrodes  212  and the comb-shaped electrodes  213  is smaller than the interdigitating width L 1  of the first acoustic wave resonator  100 . The bus bar  214  is electrically connected to an output terminal  304 . 
     The grating reflector  220  includes comb-shaped electrodes  222  connected electrically to a bus bar  221 . The comb-shaped electrodes  222  are arranged at equal periods of P 2 / 2  and joined to the bus bar  221 . The grating reflector  230  includes comb-shaped electrodes  232  connected electrically to a bus bar  231 . The comb-shaped electrodes  232  are arranged at equal periods P 2 / 2  and joined to the bus bar  231 . 
     The first acoustic wave resonator  100  and the second acoustic wave resonator  200  are electrically connected to each other by a connecting line  133 , hence forming a longitudinal connection. Alternatively, the bus bar  114  and the bus bar  211  may be connected directly to each other without the connecting line  133 . In this case, the acoustic wave device can be downsized with no use of the connecting line  133 . 
     Since the interdigitating width L 1  of the comb-shaped electrodes  112  and  113  of the interdigital transducer electrode  110  of the first acoustic wave resonator  100  is different from the interdigitating width distance L 2  of the comb-shaped electrodes  212  and  213  of the interdigital transducer electrode  210  of the second acoustic wave resonator  200 . This structure provides the following effects. 
     A cause of deteriorating the performance of the acoustic wave resonator which is disposed on the piezoelectric substrate  6  made of lithium niobate is the generation of transverse mode spurious emissions. The transverse mode spurious emissions are spurious emissions which are generated in the passing frequency range due to a standing wave occurring in a direction perpendicular to a propagating direction in which the acoustic wave propagates. In the case that the first acoustic wave resonator  100  and the second acoustic wave resonator  200  has the same interdigitating widths, transverse mode spurious emissions of the resonators  100  and  200  match in the generating frequency. This results in signal loss due to the serious spurious emissions generated in the passing frequency range. 
     Further, when the acoustic coupling between the first acoustic wave resonator  100  and the second acoustic wave resonator  200  is not adequate, the transverse mode spurious emissions perfectly match in the generating frequency, hence increasing the signal loss. 
     However, the generation of transverse mode spurious emissions can be separated into different frequency ranges between the first acoustic wave resonator  100  and the second acoustic wave resonator  200  by differentiating the interdigitating widths L 1  and L 2  from each other. 
     More particularly, if the interdigitating width changes from one acoustic wave resonator to the other, the generation of undesired spurious emissions can effectively be shifted into different ranges of the generating frequency. This provides the acoustic wave device with less effect of the spurious emissions and minimum of the signal loss. Also, as compared to an arrangement with apodization, the wave propagating path of each acoustic wave resonator remains not disturbed by dummy electrodes, thus preventing the declination of a Q value. Consequently the acoustic wave device can be improved in the characteristics having less signal loss in the passing frequency range. 
     Moreover, the number N 1  of pairs of the first acoustic wave resonator  100  and the number N 2  of pairs of the second acoustic wave resonator  200  may preferably satisfy N 1 &lt;N 2 . More specifically, the number N 1  of pairs of the comb-shaped electrodes  112  and  113  of the first acoustic wave resonator  100  is preferably smaller than the number N 2  of pairs of the comb-shaped electrodes  212  and  213  of the second acoustic wave resonator  200 . 
     The capacitance C 1  of the first acoustic wave resonator  100  is proportional to the product of the number N 1  of pairs and the interdigitating width L 1 . Similarly, the capacitance C 2  of the second acoustic wave resonator  200  is proportional to the product of the number N 2  of pairs and the interdigitating width L 2 . Accordingly, in the case that the number N 1  of the first acoustic wave resonator  100  is equal to the number N 2  of the second acoustic wave resonator  200 , the relation of L 1 &gt;L 2  provides the relation of C 1 &gt;C 2 . 
     A voltage applied to the second acoustic wave resonator  200  is inverse proportional to the ratio C 2 /C 1  of the first acoustic wave resonator  100  and the second acoustic wave resonator  200 . Therefore, the voltage to be applied to the second acoustic wave resonator  200  under the condition of C 1 &gt;C 2  becomes higher than the voltage applied to the first acoustic wave resonator  100 , hence decreasing the resistance to electrical power. In the case that the relation of N 1 &lt;N 2  is satisfied, the ratio of the capacitance C 1  to the capacitance C 2  is eased so that voltages applied to the comb-shaped electrodes  213  of the interdigital transducer electrode  210  of the second acoustic wave resonator  200  can be lowered, hence increasing the resistance to electrical power. 
     The relation of C 1 &gt;C 2  is preferably satisfied. Even if the acoustic wave resonators are equal in the capacitance, an acoustic wave resonator having a longer interdigitating width and a smaller number of pairs has less resistance to electrical power due to a resistive loss of the comb-shaped electrodes than another acoustic wave resonator having a shorter interdigitating width and a larger number of pairs. For compensation, the relation of capacitances, C 1 &gt;C 2  is employed for determining the conditional setting of the numbers N 1  and N 2 , thereby allowing the voltage applied to each resonator to be controlled and improving the resistance to electrical power. 
     In addition, if the pitch P 1  of the first acoustic wave resonator  100  and the pitch P 2  of the second acoustic wave resonator  200  are equal to each other so as to match the resonance frequency of the acoustic wave resonators, the signal loss can be minimized. Contrary, the pitches P 1  and P 2  are different from each other to broaden the passing frequency range and the band elimination frequency range, thus enhancing the freedom of designing. 
     The acoustic wave device of this embodiment is explained with the first acoustic wave resonator  100  and the second acoustic wave resonator  200  connected in series in two stages. The acoustic wave resonators maybe connected in series in three stages, hence providing the same effect. 
     Fourth Exemplary Embodiment 
     An acoustic wave device  35  according to a fourth embodiment of the present invention will be described referring to the relevant drawings. The arrangement of the acoustic wave device  35  is identical to that of the acoustic wave devices  5  and  15  of the first and second embodiments unless otherwise explained. 
     The acoustic wave device  35  of this embodiment includes a piezoelectric substrate  6  having the Euler angles described in the first embodiment. 
     As shown in  FIG. 16 , the acoustic wave device  35  of this embodiment includes series resonators  7 A,  7 B, and  7 C connected electrically in series between input and output terminals  6 A and  6 B. The acoustic wave device  35  further includes a parallel resonator  8 A connected at one end between the series resonators  7 A and  7 B and at the other end to a ground, and more specifically, connected in parallel to the input terminal  6 A and the output terminal  6 B. The acoustic wave device  35  further includes a parallel resonator  8 B which is connected at one end between the series resonators  7 B,  7 C and at the other end to the ground, and more specifically, connected in parallel to the input terminal  6 A and the output terminal  6 B. 
     The series resonator  7 A includes, as shown in  FIG. 17 , an interdigital transducer electrode  410  which includes comb-shaped electrodes  10 A and  10 B facing each other and disposed on the piezoelectric substrate  6 . The parallel resonator  8 A includes an interdigital transducer electrode  412  which includes comb-shaped electrodes  12 A and  12 B facing each other and disposed on the piezoelectric substrate  6 . 
     The comb-shaped electrodes  10 A and  10 B and the comb-shaped electrodes  12 A and  12 B are arranged such that the interdigitating width of electrode fingers of the comb-shaped electrodes becomes shorter from the center to both ends. 
     In this arrangement, the interditating width weighing coefficient of the interdigital transducer electrode  410  of the series resonator  7 A is smaller than the interdigitating width weighing coefficient of the interdigital transducer electrode  412  of the parallel resonator  8 A. 
     The interdigitating width weighing coefficient is the ratio of a non-facing electrode area where the electrode fingers do not interdigitate on an excitation area. In the series resonator  7 A, the weighing coefficient is the ratio of the sum of the non-facing electrode areas  14 A,  14 B,  14 C, and  14 D to the excitation area  413 . In the parallel resonator  8 A, the weighing coefficient is the ratio of the sum of the non-facing electrode areas  16 A,  16 B,  16 C, and  16 D to the excitation area  415 . According to this embodiment, the interdigitating width weighing coefficient of the interdigital transducer electrode  410  is approximately 0.3 while the interdigitating width weighing coefficient of the interdigital transducer electrode  412  is approximately 0.5. 
     With the above described arrangement, the Q value at the resonant point of the series resonator  7 A can be high while the Q value at the anti-resonant point of the parallel resonator  8 A remains high. 
     As set forth above, an acoustic wave devices according to the present invention are advantageous for practical use where, when the thickness of a protective layer is greater than a predetermined size, undesired spurious emissions generated by a fast transverse wave can be attenuated while the generation of undesired spurious emissions on the Rayleigh wave is suppressed. The acoustic wave devices according to the present invention are hence applicable to a duplexer and electronic apparatus, such as a mobile telephone. 
     REFERENCE NUMERALS 
     
         
           5 ,  15 ,  35 ,  45  Acoustic Wave Device 
           6 ,  16 ,  21  Piezoelectric Substrate 
           6 A,  6 B Input And Output Terminal 
           7 ,  17  Electrode 
           7 A,  7 B,  7 C Series Resonator 
           8 ,  18 ,  24  Protective Layer 
           8 A,  8 B Parallel Resonator 
           9  Projection 
           10  Top 
           10 A,  10 B,  12 A,  12 B,  112 ,  113 ,  122 ,  132 ,  212 ,  213 ,  222 ,  232  Comb-Shaped Electrode 
           11  Bottom 
           14 A,  14 B,  14 C,  14 D,  16 A,  16 B,  16 C,  16 D Non-Facing Electrode Area 
           20  First Filter 
           22  Electrode Layer 
           23 ,  25  Resist Layer 
           26  Pad 
           30  Semiconductor Integrated Circuit Device 
           31  Second Filter 
           32  Duplexer 
           33  Filter 
           40  Reproducing Device 
           50  Electronic Apparatus 
           100  First Acoustic Wave Resonator 
           110 ,  210 ,  410 ,  412  Interdigital Transducer Electrode 
           111 ,  114 ,  121 ,  131 ,  211 ,  214 ,  221 ,  231  Bus Bar 
           120 ,  130 ,  220 ,  230  Grating Reflector 
           133  Connecting Line 
           200  Second Acoustic Wave Resonator 
           302  Input Terminal 
           304  Output Terminal 
           413 ,  415  Excitation Area