Patent Publication Number: US-2023141873-A1

Title: Acoustic wave device

Description:
This application claims the benefit of priority to U.S. Provision Application No. 63/052,144 filed on Jul. 15, 2020 and is a Continuation Application of PCT Application No. PCT/JP2021/025976 filed on Jul. 9, 2021. The entire contents of each application are hereby incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an acoustic wave device. 
     2. Description of the Related Art 
     In the related art, an acoustic wave device that uses plate waves propagating in a piezoelectric film made of LiNbO 3  or LiTaO 3  is known. For example, Japanese Unexamined Patent Application Publication No. 2012-257019 discloses an acoustic wave device that uses a Lamb wave which is a type of plate wave. In this acoustic wave device, a piezoelectric substrate is disposed on a support. The piezoelectric substrate is made of LiNbO 3  or LiTaO 3 . An interdigital transducer (IDT) electrode is disposed on the upper surface of the piezoelectric substrate. A voltage is applied between a plurality of electrode fingers of the IDT electrode that are connected to one potential and a plurality of electrode fingers of the IDT electrode that are connected to another potential. This excites the Lamb wave. Reflectors are arranged on both sides of the IDT electrode. As a result, an acoustic wave resonator that uses plate waves is formed. 
     Japanese Unexamined Patent Application Publication No. 2011-182096 discloses an example of a ladder filter. In this ladder filter, a plurality of acoustic wave devices are connected by a plurality of wiring lines. The plurality of wiring lines include a wiring line connected to a hot potential and a wiring line connected to a ground potential. The wiring line connected to the hot potential and the wiring line connected to the ground potential face each other. 
     In an acoustic wave resonator such as that disclosed in Japanese Unexamined Patent Application Publication No. 2012-257019, an unwanted bulk wave may sometimes be excited. The bulk wave propagates in the thickness direction of a piezoelectric substrate. Thus, the bulk wave may sometimes be reflected by a support. In a configuration, such as that described in Japanese Unexamined Patent Application Publication No. 2011-182096, in which wiring lines that are connected to different potentials from each other face each other, an unwanted bulk-wave signal may sometimes be extracted by one of the wiring lines. Alternatively, an unwanted bulk-wave signal may sometimes be extracted by one of busbars that face each other. In such cases, there is a possibility that a ripple may occur in the frequency characteristics of the acoustic wave device. 
     SUMMARY OF THE INVENTION 
     Preferred embodiments of the present invention provide acoustic wave devices that are each able to reduce or prevent a ripple in frequency characteristics. 
     An acoustic wave device according to a preferred embodiment of the present invention includes a support substrate, a piezoelectric layer on the support substrate, a functional electrode on the piezoelectric layer, and first and second electrode films positioned on the piezoelectric layer to face each other and having different potentials from each other. A thickness of the piezoelectric layer in at least a portion of a region overlapping the first electrode film in plan view is different from a thickness of the piezoelectric layer in at least a portion of a region not overlapping the first electrode film in plan view. 
     According to preferred embodiments of the present invention, acoustic wave devices that are each able to reduce or prevent a ripple in frequency characteristics can be provided. 
     The above and other elements, features, steps, characteristics and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a plan view of an acoustic wave device according to a first preferred embodiment of the present invention. 
         FIG.  2    is a sectional view taken along line I-I of  FIG.  1   . 
         FIG.  3    is a sectional view taken along line II-II of  FIG.  1   . 
         FIG.  4    is a graph illustrating a reflection characteristic in the first preferred embodiment of the present invention and a reflection characteristic in a comparative example. 
         FIG.  5    is a sectional view illustrating a case in which an unwanted bulk wave propagates. 
         FIG.  6    is a sectional view illustrating a portion of an acoustic wave device according to a first modification of the first preferred embodiment of the present invention, the portion corresponding to the sectional view illustrated in  FIG.  3   . 
         FIG.  7    is a sectional view illustrating a portion of an acoustic wave device according to a second modification of the first preferred embodiment of the present invention, the portion corresponding to the sectional view illustrated in  FIG.  3   . 
         FIG.  8    is a sectional view illustrating a portion of an acoustic wave device according to a third modification of the first preferred embodiment of the present invention, the portion corresponding to the sectional view illustrated in  FIG.  3   . 
         FIG.  9    is a sectional view illustrating a portion of an acoustic wave device according to a fourth modification of the first preferred embodiment of the present invention, the portion corresponding to the sectional view illustrated in  FIG.  3   . 
         FIG.  10    is a sectional view illustrating a portion of an acoustic wave device according to a fifth modification of the first preferred embodiment of the present invention, the portion corresponding to the sectional view illustrated in  FIG.  3   . 
         FIG.  11    is a plan view of an acoustic wave device according to a sixth modification of the first preferred embodiment of the present invention. 
         FIG.  12    is a sectional view illustrating a portion of an acoustic wave device according to a second preferred embodiment of the present invention, the portion corresponding to the sectional view illustrated in  FIG.  2   . 
         FIG.  13    is a sectional view illustrating a portion of an acoustic wave device according to a first modification of the second preferred embodiment of the present invention, the portion corresponding to the sectional view illustrated in  FIG.  3   . 
         FIG.  14    is a sectional view illustrating a portion of an acoustic wave device according to a second modification of the second preferred embodiment of the present invention, the portion corresponding to the sectional view illustrated in  FIG.  3   . 
         FIG.  15    is a schematic plan view of an acoustic wave device according to a third preferred embodiment of the present invention. 
         FIG.  16    is a sectional view taken along line of  FIG.  15   . 
         FIG.  17    is a circuit diagram of the acoustic wave device according to the third preferred embodiment of the present invention. 
         FIG.  18    is a plan view of an acoustic wave device according to a fourth preferred embodiment of the present invention. 
         FIG.  19    is a sectional view taken along line IV-IV of  FIG.  18   . 
         FIG.  20 A  is a schematic perspective view illustrating the appearance of an acoustic wave device that uses a thickness-shear mode bulk wave, and  FIG.  20 B  is a plan view illustrating an electrode structure on a piezoelectric layer. 
         FIG.  21    is a sectional view taken along line A-A of  FIG.  20 A . 
         FIG.  22 A  is a schematic elevational cross-sectional view illustrating a Lamb wave that propagates through a piezoelectric film of an acoustic wave device, and  FIG.  22 B  is a schematic elevational cross-sectional view illustrating the thickness-shear mode bulk wave that propagates through the piezoelectric film of the acoustic wave device. 
         FIG.  23    is a diagram illustrating the amplitude direction of the thickness-shear mode bulk wave. 
         FIG.  24    is a graph illustrating a resonance characteristic of the acoustic wave device that uses the thickness-shear mode bulk wave. 
         FIG.  25    is a graph illustrating the relationship between d/2p and the fractional bandwidth of each acoustic wave device as a resonator, where p is the center-to-center distance between adjacent electrodes and d is the thickness of the piezoelectric layer. 
         FIG.  26    is a plan view of an acoustic wave device that uses a thickness-shear mode bulk wave. 
         FIG.  27    is a partially cut-away perspective view illustrating an acoustic wave device that uses a Lamb wave. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Preferred embodiments of the present invention will be described below with reference to the drawings to clarify the present invention. 
     The preferred embodiments described in the present specification are examples, and the configurations according to the different preferred embodiments may be partially replaced or combined with one another. 
       FIG.  1    is a plan view of an acoustic wave device according to the first preferred embodiment of the present invention.  FIG.  2    is a sectional view taken along line I-I of  FIG.  1   .  FIG.  3    is a sectional view taken along line II-II of  FIG.  1   . 
     As illustrated in  FIG.  1   , an acoustic wave device  10  includes a piezoelectric substrate  12  and an interdigital transducer (IDT) electrode  11 . As illustrated in  FIG.  2   , the piezoelectric substrate  12  includes a support member  13  and a piezoelectric layer  14 . In the present preferred embodiment, the support member  13  includes only a support substrate. However, the support member  13  may include, for example, a multilayer body including the support substrate and an insulating layer. 
     The support member  13  includes a through hole  13   a  as a cavity portion. The piezoelectric layer  14  covers the through hole  13   a  of the support member  13 . 
     In the present preferred embodiment, the piezoelectric layer  14  is, for example, a lithium niobate layer. More specifically, the piezoelectric layer  14  is, for example, a LiNbO 3  layer. However, the piezoelectric layer  14  may be, for example, a lithium tantalate layer such as a LiTaO 3  layer. 
     In the present preferred embodiment, the support substrate is, for example, a silicon substrate. However, the material of the support substrate is not limited to the above. 
     Returning to  FIG.  1   , the IDT electrode  11  is disposed on the piezoelectric layer  14 . The IDT electrode  11  includes a first busbar  16 , a second busbar  17 , a plurality of first electrode fingers  18 , and a plurality of second electrode fingers  19 . The first busbar  16  corresponds to a first electrode film. The second busbar  17  corresponds to a second electrode film. As illustrated in  FIG.  3   , the first busbar  16  and the second busbar  17  face each other. 
     In the present preferred embodiment, a portion of the piezoelectric layer  14  on which the first busbar  16  is disposed includes an uneven portion  14   c.  More specifically, a portion of a first main surface  14   a  of the piezoelectric layer  14  on which the first busbar  16  is disposed partially has a rough surface. The thickness of the piezoelectric layer  14  at the depressions of the uneven portion  14   c  is smaller than the thickness of a portion of the piezoelectric layer  14  that does not have the uneven portion  14   c.    
     The first busbar  16  and the second busbar  17  are connected to different potentials from each other. In the present preferred embodiment, the first busbar  16  is connected to a ground potential, and the second busbar  17  is connected to a hot potential. However, the first busbar  16  is not limited to being connected to the ground potential, and the second busbar  17  is not limited to being connected to the hot potential. For example, the first busbar  16  may be connected to the hot potential, and the second busbar  17  may be connected to the ground potential. 
     The plurality of first electrode fingers  18  and the plurality of second electrode fingers  19  illustrated in  FIG.  1    correspond to at least one pair of electrodes. The at least one pair of electrodes face each other. More specifically, the first electrode fingers  18  corresponds to a first electrode. The plurality of first electrode fingers  18  are arranged at regular intervals. An end of each of the plurality of first electrode fingers  18  is connected to the first busbar  16 . The second electrode fingers  19  corresponds to a second electrode. The plurality of second electrode fingers  19  are arranged at regular intervals. An end of each of the plurality of second electrode fingers  19  is connected to the second busbar  17 . The plurality of first electrode fingers  18  and the plurality of second electrode fingers  19  are interdigitated with one another. In the following description, the first electrode fingers  18  and the second electrode fingers  19  will sometimes be simply referred to as electrode fingers. The IDT electrode  11  may include a single metal film or may be a multilayer metal film. 
     In the acoustic wave device  10 , the plurality of electrode fingers corresponding to the at least one pair of electrodes correspond to at least one functional electrode. An acoustic wave is excited by applying an alternating-current (AC) voltage to the at least one functional electrode of the IDT electrode  11 . In the present preferred embodiment, the acoustic wave device  10  uses a thickness-shear mode bulk wave. More specifically, the acoustic wave device  10  uses a bulk wave in a first thickness-shear mode as a main wave. The acoustic wave device  10  may be, for example, an acoustic wave device that uses a plate wave, such as Lamb wave, as a main wave. In the present preferred embodiment, a shear horizontal (SH) wave is excited as an unwanted bulk wave. 
     Here, a direction in which the first electrode fingers  18  and the second electrode fingers  19  face one another in plan view will be referred to as an electrode-finger facing direction. The phrase “in plan view” refers to viewing from above in  FIG.  2   ,  FIG.  3   , or the like. A region in which the adjacent electrode fingers overlap one another when viewed in the electrode-finger facing direction is an intersecting region D. The intersecting region D is a region including all of the electrode fingers of the IDT electrode  11  including the two endmost electrode fingers in the electrode-finger facing direction. More specifically, the intersecting region D includes the outer end edge of one of the endmost electrode fingers and the outer end edge of the other endmost electrode finger in the electrode-finger facing direction. 
     In addition, the acoustic wave device  10  includes a plurality of excitation regions C. The excitation regions C are also regions in which the adjacent electrode fingers face each other when viewed in the electrode-finger facing direction. Each of the excitation regions C is defined between a corresponding two of the electrode fingers. More specifically, each of the excitation regions C is a region extending from the center of one of the corresponding pair of electrode fingers to the center of the other of the corresponding pair of electrode fingers in the electrode-finger facing direction. Accordingly, the plurality of the excitation regions C are included in the intersecting region D. The thickness-shear mode bulk wave is excited in each of the excitation regions C. In contrast, in the case where the acoustic wave device  10  uses a plate wave, the intersecting region D defines and functions as an excitation region. 
     The piezoelectric layer  14  includes a first region E 1 , a second region E 2 , and a third region E 3 . The first region E 1  is a region overlapping the first electrode film in plan view. The second region E 2  is a region overlapping the second electrode film in plan view. The third region E 3  is a region not overlapping either the first electrode film or the second electrode film in plan view. The thickness of the piezoelectric layer  14  in the first region E 1  is denoted by d 1 . The thickness of the piezoelectric layer  14  in the second region E 2  is denoted by d 2 . The thickness of the piezoelectric layer  14  in the third region E 3  is denoted by d 3 . As illustrated in  FIG.  2   , the thickness d 2  and the thickness d 3  are the same or substantially the same as each other. 
     One of the unique features of the present preferred embodiment is that the thickness d 1  in at least a portion of the first region E 1  is different from the thickness of the piezoelectric layer  14  in at least portion of the other regions excluding the first region E 1 . More specifically, in the present preferred embodiment, the thickness d 1  in a portion of the first region E 1  is different from the thickness d 2  in the second region E 2  and different from the thickness d 3  in the third region E 3 . The thickness d 1  in a portion of the first region E 1  is smaller than the thickness d 2  and smaller than the thickness d 3 . As a result, in the acoustic wave device  10 , the influence of an unwanted bulk wave on frequency characteristics can be reduced or prevented, and the ripple in the frequency characteristics can be reduced or prevented. This matter will be described below by comparing the present preferred embodiment and a comparative example. 
     The difference between the first preferred embodiment and the comparative example is that the thickness of a piezoelectric layer in the comparative example is uniform in all of the first to third regions. In the first preferred embodiment, a reflection characteristic, which is one of the frequency characteristics, between the first busbar and the second busbar was measured. Similarly, in the comparative example, a reflection characteristic between a first busbar and a second busbar was measured. 
       FIG.  4    is a graph illustrating a reflection characteristic in the first preferred embodiment and a reflection characteristic in a comparative example. Each of the reflection characteristics illustrated in  FIG.  4    is the relationship between S11 and frequency.  FIG.  5    is a sectional view illustrating a case in which an unwanted bulk wave propagates in the comparative example. In  FIG.  5   , a portion of the unwanted bulk wave is indicated by arrow B. 
     As illustrated in  FIG.  4   , in the reflection characteristic in the comparative example, it is understood that a ripple has occurred in the entire or substantially the entire frequency band illustrated in  FIG.  4   . In the comparative example, for example, as illustrated in  FIG.  5   , the unwanted bulk wave propagated from the first busbar  16  is reflected by the support substrate. The signal of the unwanted bulk wave is extracted by the second busbar  17 . This causes the ripple illustrated in  FIG.  4    to occur. In contrast, it is understood that the ripple in the reflection characteristic in the first preferred embodiment is reduced or prevented. 
     For example, when an unwanted bulk wave propagates from the first busbar  16  defining and functioning as the first electrode film to the second busbar  17  defining and functioning as the second electrode film, a portion of the unwanted bulk wave passes through the first region E 1 . Another portion of the bulk wave passes through the first region E 1  and the third region E 3 . The unwanted bulk wave also passes through the second region E 2 . In the first preferred embodiment, the uneven portion  14   c  is provided in a portion of the first region E 1  of the piezoelectric layer  14 . On the other hand, the uneven portion  14   c  is not provided in either the second region E 2  or the third region E 3 . Thus, the thickness of the piezoelectric layer  14  at the depressions of the uneven portion  14   c  is different from the thickness of the piezoelectric layer  14  in the second region E 2  and different from the thickness of the piezoelectric layer  14  in the third region E 3 . As a result, the propagation mode of the unwanted bulk wave in the first region E 1  can be set to be different from that in each of the second and third regions E 2  and E 3 . Consequently, uniform propagation of the unwanted bulk wave between the first electrode film and the second electrode film can be reduced or prevented. Therefore, the influence of the unwanted bulk wave on the reflection characteristic can be reduced or prevented, and the ripple in the reflection characteristic can be reduced or prevented. 
     It is preferable that the surface roughness of the uneven portion  14   c  of the piezoelectric layer  14  is, for example, about 0.2 nm or greater. In this case, the influence of an unwanted bulk wave on the reflection characteristic, which is one of the frequency characteristics, can be effectively reduced or prevented. In the present specification, the surface roughness is based on arithmetic mean roughness Ra defined in JIS B 0601:2001. 
     As illustrated in  FIG.  3   , it is preferable that the thickness dl of the piezoelectric layer  14  in at least a portion of the first region El is different from at least a portion of the thickness d 3  of the piezoelectric layer  14  in a portion of the third region E 3 , the portion of the third region E 3  being located between the first electrode film and the second electrode film. Similarly, it is preferable that the thickness d 1  of the piezoelectric layer  14  in at least a portion of the first region E 1  is different from at least a portion of the thickness d 2  of the piezoelectric layer  14  in the second region E 2 . In other words, it is preferable that the acoustic wave device according to a preferred embodiment of the present invention has a configuration in which the thickness d 1  of the piezoelectric layer  14  in at least a portion of the first region E 1  is different from the thickness of the piezoelectric layer  14  in at least a portion of a region formed of a region overlapping the space between the first electrode film and the second electrode film in plan view and the second region E 2 . As a result, the influence of an unwanted bulk wave on the frequency characteristics can be reduced or prevented with higher certainty, and the ripple in the frequency characteristics can be reduced or prevented with higher certainty. 
     Returning to  FIG.  1   , in the first preferred embodiment, the support member  13  includes only the support substrate. However, the support member  13  may be a multilayer body including the support substrate and an insulating layer. In this case, the piezoelectric layer  14  is provided on the insulating layer. For example, as the material of the insulating layer, a silicon oxide layer, silicon nitride, tantalum oxide, or the like can be used. 
     The cavity portion is not limited to being a through hole. The cavity portion may be, for example, a hollow portion. The hollow portion includes, for example, a recess in the support member. More specifically, the recess is sealed with, for example, the piezoelectric layer  14 , so that the hollow portion is provided. Alternatively, the piezoelectric layer  14  may include a recess that is open toward the support member  13 . This recess may define the cavity portion. In this case, it is not necessary to provide a recess or a through hole in the support member  13 . 
     As described above, at least one of the thickness d 1  in at least a portion of the first region E 1  and the thickness d 2  in at least a portion of the second region E 2  may be different from the thickness d 3  in at least a portion of the third region E 3 . First and second modifications of the first preferred embodiment will be described below. The only difference between the first preferred embodiment and each of the first and second modifications is a portion in which the uneven portion  14   c  is provided. The ripple in the frequency characteristics can be reduced or prevented in both the first modification and the second modification. 
     In the first modification illustrated in  FIG.  6   , the uneven portion  14   c  is provided in the entire or substantially the entire first region E 1  of a piezoelectric layer  24 A. The first region E 1  may include a plurality of regions. There may be variations in the surface roughness of the uneven portion  14   c  among the plurality of regions. 
     In the second modification illustrated in  FIG.  7   , an uneven portion is provided in the entire or substantially the entire first region E 1  and the entire or substantially the entire second region E 2  of a piezoelectric layer  24 B. The uneven portion in the first region E 1  is a first uneven portion  24   c.  The uneven portion in the second region E 2  is a second uneven portion  24   d . Thus, the thickness d 1  in a portion of the first region E 1  and the thickness d 2  in a portion of the second region E 2  are both different from the thickness d 3  in the third region E 3 . 
     The surface roughness of the first uneven portion  24   c  and the surface roughness of the second uneven portion  24   d  may be different from each other. Alternatively, as in the first modification, the first region E 1  may include a plurality of regions. In this case, the surface roughness of the second uneven portion  24   d  may be different from the surface roughness of the first uneven portion  24   c  in at least one of the above-mentioned plurality of regions included in the first region E 1 . 
     A dielectric film may be provided between the piezoelectric layer and at least one of the first electrode film and the second electrode film. Third to fifth modifications of the first preferred embodiment will be described below. The only differences between the first preferred embodiment and each of the third to fifth modifications are the dielectric film provided in each of the third to fifth modifications and the arrangement of the uneven portion. 
     In the third modification illustrated in  FIG.  8   , as in the first modification, the uneven portion  14   c  is provided in the entire or substantially the entire first region E 1  of the piezoelectric layer  24 A. In addition, a dielectric film  25  is provided between the piezoelectric layer  24 A and the first busbar  16  defining and functioning as the first electrode film. On the other hand, the dielectric film  25  is not provided between the piezoelectric layer  24 A and the second busbar  17  defining and functioning as the second electrode film. The dielectric film  25  is not provided between the piezoelectric layer  24 A and a portion of the IDT electrode  11 , the portion being located between the first busbar  16  and the second busbar  17 . By providing the dielectric film  25 , the electromechanical coupling coefficient changes compared with the case where the dielectric film  25  is not provided. In the present modification, the dielectric film  25  is provided, so that the electromechanical coupling coefficient changes in the first region E 1 . As a result, the propagation mode of an unwanted bulk wave in the first region E 1  and the propagation mode of an unwanted bulk wave in the third region E 3  can be set to be different from each other. Therefore, the ripple in the frequency characteristics can be further reduced or prevented. 
     For example, as the material of the dielectric film  25 , a silicon oxide, silicon nitride, a resin, or the like can be used. 
     In the fourth modification illustrated in  FIG.  9   , as in the second modification, the first uneven portion  24   c  is provided in the entire or substantially the entire first region E 1  of the piezoelectric layer  24 B. In addition, the second uneven portion  24   d  is provided in the entire or substantially the entire second region E 2 . Furthermore, the dielectric film  25  is provided between the piezoelectric layer  24 B and the second busbar  17 . On the other hand, the dielectric film  25  is not provided between the piezoelectric layer  24 B and the first busbar  16 . 
     In the fifth modification illustrated in  FIG.  10   , as in the first modification, the uneven portion  14   c  is provided in the entire or substantially the entire first region E 1  of the piezoelectric layer  24 A. In addition, the dielectric film  25  is provided between the piezoelectric layer  24 A and the first busbar  16  and between the piezoelectric layer  24 A and the second busbar  17 . 
       FIG.  11    illustrates, as a sixth modification of the first preferred embodiment, a case in which an acoustic wave device uses a plate wave. As illustrated in  FIG.  11   , in plan view, a pair of reflectors  22 A and  22 B are provided such that one of them is located on one side of the IDT electrode  11 , which is disposed on the piezoelectric layer  14 , and the other is located on the other side of the IDT electrode  11  in the electrode-finger facing direction. This can suitably improve resonance characteristics in the case of using a plate wave. Also in the present modification, the configurations of the piezoelectric layer  14 , the first busbar  16  defining and functioning as the first electrode film, and the second busbar  17  defining and functioning as the second electrode film are the same as or similar to those of the first preferred embodiment. Thus, the ripple in the frequency characteristics can be reduced or prevented. 
       FIG.  12    is a sectional view illustrating a portion of an acoustic wave device according to a second preferred embodiment of the present invention, the portion corresponding to the sectional view illustrated in  FIG.  2   . 
     The present preferred embodiment is different from the first preferred embodiment is that a piezoelectric layer  34  does not include an uneven portion. Another difference between the present preferred embodiment and the first preferred embodiment is that the thickness d 1  of the piezoelectric layer  34  in the entire or substantially the entire first region E 1  is different from the thickness d 3  of the piezoelectric layer  34  in the third region E 3 . The acoustic wave device of the present preferred embodiment has a configuration the same as or similar to that of the acoustic wave device  10  of the first preferred embodiment except with regard to the above-described differences. 
     More specifically, the thickness d 1  of the piezoelectric layer  34  in the entire or substantially the entire first region E 1  is smaller than the thickness d 3  of the piezoelectric layer  34  in the third region E 3 . In addition, the thickness dl is smaller than the thickness d 2  of the piezoelectric layer  34  in the second region E 2 . The thickness d 2  and the thickness d 3  are the same or substantially the same as each other. Also in the present preferred embodiment, the propagation mode of an unwanted bulk wave in the first region E 1  and the propagation mode of an unwanted bulk wave in the third region E 3  can be set to be different from each other as in the first preferred embodiment. Therefore, the influence of an unwanted bulk wave on the frequency characteristics can be reduced or prevented, and the ripple in the frequency characteristics can be reduced or prevented. 
     As in the present preferred embodiment, it is preferable that the thickness d 1  in the entire or substantially the entire first region E 1  and the thickness d 2  in the entire or substantially the entire second region E 2  are different from each other. As a result, the propagation mode of a bulk wave in the first region E 1  and the propagation mode of a bulk wave in the second region E 2  can be set to be different from each other. Therefore, the influence of an unwanted bulk wave on the frequency characteristics can be further reduced or prevented, and the ripple in the frequency characteristics can be further reduced or prevented. 
     First and second modifications of the second preferred embodiment will be described below. The ripple in the frequency characteristics can be reduced or prevent in both the first modification and the second modification as in the second preferred embodiment. 
     In the first modification illustrated in  FIG.  13   , the thickness d 2  of a piezoelectric layer  44 A in the entire or substantially the entire second region E 2  is smaller than the thickness d 3  of the piezoelectric layer  44 A in the third region E 3 . In contrast, the thickness d 1  of the piezoelectric layer  44 A in the first region E 1  is the same or substantially the same as the thickness d 3  of the piezoelectric layer  44 A. In addition, the dielectric film  25  is provided between the piezoelectric layer  44 A and the second busbar  17 . On the other hand, the dielectric film  25  is not provided between the piezoelectric layer  44 A and the first busbar  16 . The dielectric film  25  may be provided between the piezoelectric layer  44 A and at least one of the first busbar  16  defining and functioning as the first electrode film and the second busbar  17  defining and functioning as the second electrode film. 
     In the second modification illustrated in  FIG.  14   , the thickness d 1  of a piezoelectric layer  44 B in the entire or substantially the entire first region E 1  is larger than the thickness d 3  of the piezoelectric layer  44 B in the third region E 3 . In addition, the uneven portion  14   c  is provided in the entire or substantially the entire first region E 1 . The thickness d 2  of the piezoelectric layer  44 B in the second region E 2  is the same or substantially the same as the thickness d 3  of the piezoelectric layer  44 B. The uneven portion  14   c  may be provided in at least one of the first region E 1  and the second region E 2  of the piezoelectric layer  44 B. In addition, the dielectric film  25  is provided between the piezoelectric layer  44 B and the second busbar  17 . On the other hand, the dielectric film  25  is not provided between the piezoelectric layer  44 B and the first busbar  16 . 
     In the first preferred embodiment, the case has been described in which a signal of an unwanted bulk wave propagated from one of the pair of busbars is extracted by the other of the pair of busbars and in which the influence of this signal can be suppressed. Propagation and extraction of a signal of an unwanted bulk wave may sometimes occur also between wiring electrode films in a filter device. A third preferred embodiment of the present invention will be described below in which an acoustic wave device is a filter device. 
       FIG.  15    is a schematic plan view of the acoustic wave device according to the third preferred embodiment. In  FIG.  15   , acoustic wave resonators are schematically represented by polygons with two diagonal lines. 
     An acoustic wave device  50  includes a plurality of resonators including acoustic wave resonators. The acoustic wave device  50  is a filter device. More specifically, the acoustic wave device  50  is, for example, a band-pass filter. However, the acoustic wave device  50  may be a band elimination filter. In the present preferred embodiment, all of the plurality of resonators are acoustic wave resonators. Each of the acoustic wave resonators of the acoustic wave device  50  includes an IDT electrode. Each of the IDT electrodes includes a pair of busbars and a plurality of electrode fingers defining and functioning as functional electrodes. In the present preferred embodiment, a first electrode film  58  and a second electrode film  59  are wiring electrode films. The first region E 1  is a region overlapping the first electrode film  58  in plan view. The second region E 2  is a region overlapping the second electrode film  59  in plan view. The third region E 3  is a region not overlapping the first electrode film  58  or the second electrode film  59  in plan view. 
     The first electrode film  58  and the second electrode film  59  are disposed on the piezoelectric layer  14 , and the plurality of acoustic wave resonators are arranged on the piezoelectric layer  14 . The acoustic wave resonator from which the wiring electrode film defining and functioning as the first electrode film  58  is extended and the acoustic wave resonator from which the wiring electrode film defining and functioning as the second electrode film  59  is extended are different from each other. In other words, the first electrode film  58  and the second electrode film  59  are connected to the plurality of electrode fingers defining and functioning as functional electrodes by a busbar. The first electrode film  58  is connected to the hot potential, and the second electrode film  59  is connected to the ground potential. 
       FIG.  16    is a sectional view taken along line III-III of  FIG.  15   . 
     The first electrode film  58  and the second electrode film  59  face each other. As in the first preferred embodiment, the uneven portion  14   c  is provided in a portion of the first region E 1 . On the other hand, the uneven portion  14   c  is not provided in either the second region E 2  or the third region E 3 . The thickness d 1  of the piezoelectric layer  14  in a portion of the first region E 1  is different from the thickness d 3  of the piezoelectric layer  14  in the third region E 3 . Thus, as in the first preferred embodiment, the propagation mode of a bulk wave in the first region E 1  and the propagation mode of a bulk wave in the third region E 3  can be set to be different from each other. Thus, the ripple in the frequency characteristics can be reduced or prevented. The circuit configuration in the present preferred embodiment will be described below. 
       FIG.  17    is a circuit diagram of the acoustic wave device according to the third preferred embodiment of the present invention. 
     The acoustic wave device  50  is, for example, a ladder filter. In the present preferred embodiment, the plurality of acoustic wave resonators include a serial arm resonator S 1 , a serial arm resonator S 2 , a serial arm resonator S 3 , a serial arm resonator S 4 , a serial arm resonator S 5 , and a serial arm resonator S 6 , a parallel arm resonator P 1 , a parallel arm resonator P 2 , and a parallel arm resonator P 3 . The acoustic wave device  50  further includes a first signal terminal  55  and a second signal terminal  56 . 
     The serial arm resonator S 1 , the serial arm resonator S 2 , the serial arm resonator S 3 , the serial arm resonator S 4 , the serial arm resonator S 5 , and the serial arm resonator S 6  are connected in series to one another in this order between the first signal terminal  55  and the second signal terminal  56 . The parallel arm resonator P 1  is connected between a connection point between the serial arm resonator S 1  and the serial arm resonator S 2  and the ground potential. The parallel arm resonator P 2  is connected between a connection point between the serial arm resonator S 3  and the serial arm resonator S 4  and the ground potential. The parallel arm resonator P 3  is connected between a connection point between the serial arm resonator S 5  and the serial arm resonator S 6  and the ground potential. As illustrated in  FIG.  15   , the acoustic wave device  50  includes a plurality of ground terminals  57 . Each of the parallel arm resonators is connected to the ground terminal through one of the ground terminals  57 . The above-described circuit configuration is an example, and the circuit configuration of the acoustic wave device  50  is not particularly limited. 
     In the acoustic wave device  50 , the first electrode film  58  is the wiring electrode film connecting the serial arm resonator S 1  and the parallel arm resonator P 1  to each other. The second electrode film  59  is the wiring electrode film connecting the parallel arm resonator P 2  and the corresponding ground terminal  57  to each other. A distance L between the first electrode film  58  and the second electrode film  59  has a length different from aperture lengths M of the acoustic wave resonators excluding the acoustic wave resonators to which the first electrode film  58  and the second electrode film  59  are connected. The aperture length of an acoustic wave resonator refers to the distance between a pair of busbars of the acoustic wave resonator. As illustrated in  FIG.  15   , for example, the aperture length of the serial arm resonator S 3  is denoted by M 3 , and the aperture length of the serial arm resonator S 6  is denoted by M 6 . For example, the distance L may be longer or shorter than the shortest aperture length among the aperture lengths M of the acoustic wave resonators excluding the acoustic wave resonators to which the first electrode film  58  and the second electrode film  59  are connected. In the case where the aperture length M 6  is not constant as in the serial arm resonator S 6 , for example, the distance L may be longer or shorter than the shortest aperture length among the aperture lengths M 6 . 
     The IDT electrode of the serial arm resonator S 1  and the IDT electrode of the parallel arm resonator P 1  are connected to the first electrode film  58 , which is one of the first and second electrode films  58  and  59 . In contrast, the IDT electrode of the parallel arm resonator P 2  is connected to the second electrode film  59 . An IDT electrode that is connected to both the first electrode film  58  and the second electrode film  59  may be provided. 
       FIG.  18    is a plan view of an acoustic wave device according to a fourth preferred embodiment of the present invention.  FIG.  19    is a sectional view taken along line IV-IV of  FIG.  18   . 
     As illustrated in  FIG.  18    and  FIG.  19   , in the present preferred embodiment, a functional electrode includes an upper electrode  61 A and a lower electrode  61 B. The upper electrode  61 A is provided on the first main surface  14   a  of the piezoelectric layer  14 . The lower electrode  61 B is provided on a second main surface  14   b  of the piezoelectric layer  14 . The upper electrode  61 A and the lower electrode  61 B face each other with the piezoelectric layer  14  interposed therebetween. The upper electrode  61 A and the lower electrode  61 B are connected to different potentials. A region in which the upper electrode  61 A and the lower electrode  61 B face each other is an excitation region. 
     As illustrated in  FIG.  18   , the first electrode film  58  and the second electrode film  59  are provided on the first main surface  14   a  of the piezoelectric layer  14 . In the present preferred embodiment, the first electrode film  58  and the second electrode film  59  are wiring electrode films. The first electrode film  58  is connected to the upper electrode  61 A. In contrast, a connection electrode  62  is provided on or in the second main surface  14   b  of the piezoelectric layer  14 . The connection electrode  62  is connected to the lower electrode  61 B. The piezoelectric layer  14  includes a through hole. The connection electrode  62  is connected to the second electrode film  59  by passing through the through hole. Thus, the second electrode film  59  is connected to the lower electrode  61 B by the connection electrode  62 . 
     The first electrode film  58  and the second electrode film  59  face each other. In the present preferred embodiment, as in the configuration of the third preferred embodiment illustrated in  FIG.  16   , the first region E 1 , the second region E 2 , and a third region of the piezoelectric layer  14  are defined. In other words, the uneven portion  14   c  is provided in a portion of the first region E 1 . On the other hand, the uneven portion  14   c  is not provided in either the second region E 2  or the third region E 3 . The thickness d 1  of the piezoelectric layer  14  in a portion of the first region E 1  is different from the thickness d 3  of the piezoelectric layer  14  in the third region E 3 . Thus, the propagation mode of a bulk wave in the first electrode film  58  and the propagation mode of a bulk wave in the second electrode film  59  can be set to be different from each other. Thus, the ripple in the frequency characteristics can be reduced or prevented. 
     A bulk acoustic wave (BAW) device such as the acoustic wave device of the present preferred embodiment may be applied to a filter device such as that illustrated in  FIG.  15   . In this case, as in the third preferred embodiment, the first electrode film and the second electrode film may be wiring electrode films connected to different acoustic wave resonators. 
     The thickness shear mode and a plate wave will be described in detail below. A support member in the following case corresponds to a support substrate. 
       FIG.  20 A  is a schematic perspective view illustrating the appearance of an acoustic wave device that uses a thickness-shear mode bulk wave, and  FIG.  20 B  is a plan view illustrating an electrode structure on a piezoelectric layer.  FIG.  21    is a sectional view taken along line A-A of  FIG.  20 A . 
     An acoustic wave device  1  includes a piezoelectric layer  2  made of, for example, LiNbO 3 . The piezoelectric layer  2  may be made of, for example. LiTaO 3 . Regarding the cut-angles of LiNbO 3  and LiTaO 3 , although Z-cut is used, rotated Y-cut or X cut may be used. Although the thickness of the piezoelectric layer  2  is not particularly limited, the thickness of the piezoelectric layer  2  is preferably, for example, about 40 nm or more and about 1,000 nm or less and more preferably, for example, about 50 nm or more and about 600 nm or less in order to effectively excite the thickness shear mode. The piezoelectric layer  2  includes a first main surface  2   a  and a second main surface  2   b  facing each other. Electrodes  3  and electrodes  4  are arranged on the first main surface  2   a.  Here, each of the electrodes  3  is an example of a “first electrode”, and each of the electrodes  4  is an example of a “second electrode”. In  FIG.  20 A  and  FIG.  20 B , the plurality of electrodes  3  are connected to a first busbar  5 . The plurality of electrodes  4  are connected to a second busbar  6 . The plurality of electrodes  3  and the plurality of electrodes  4  are interdigitated with one another. The electrodes  3  and the electrodes  4  each have a rectangular or substantially rectangular shape and each have a length direction. The electrodes  3  and the electrodes  4  face one another in a direction perpendicular or substantially perpendicular to the length direction. The length direction of the electrodes  3  and  4  and the direction perpendicular or substantially perpendicular to the length direction of the electrodes  3  and  4  cross the thickness direction of the piezoelectric layer  2 . Accordingly, it can also said that the electrodes  3  and the adjacent electrodes  4  face one another in a direction crossing the thickness direction of the piezoelectric layer  2 . In addition, the length direction of the electrodes  3  and  4  and a direction perpendicular or substantially perpendicular to the length direction of the electrodes  3  and  4  illustrated in  FIGS.  20 A and  20 B  are interchangeable. In other words, in  FIGS.  20 A and  20 B , the electrodes  3  and  4  may extend in the direction in which the first busbar  5  and the second busbar  6  extend. In this case, the first busbar  5  and the second busbar  6  extend in the direction in which the electrodes  3  and  4  extend in  FIGS.  20 A and  20 B . The electrodes  3  are connected to one potential, and the electrodes  4  are connected to another potential. Each of the electrodes  3  is paired with one of the electrodes  4  that is adjacent to the electrode  3 , and these pairs of electrodes  3  and  4  are arranged in the direction perpendicular or substantially perpendicular to the length direction of the electrodes  3  and  4 . Here, when one of the electrodes  3  and the corresponding electrode  4  are adjacent to each other, the electrode  3  and the electrode  4  are arranged so as not to be in direct contact with each other but so as to be spaced apart from each other. In addition, when one of the electrodes  3  and the corresponding electrode  4  are adjacent to each other, electrodes including the other electrodes  3  and  4  that are connected to a hot electrode or a ground electrode are not located between the electrode  3  and the electrode  4 . The number of the pairs does not need to be an integer and may be, for example, 1.5, 2.5, or the like. It is preferable that the center-to-center distance between each pair of the electrodes  3  and  4 , that is, the pitch of the electrodes  3  and  4 , is, for example, within a range of about 1 μm or more to about 10 μm or less. The width of each of the electrodes  3  and  4 , that is, a dimension of each of the electrodes  3  and  4  in the direction in which the electrodes  3  and  4  face one another, is preferably, for example, within a range of about 50 nm or more to about 1,000 nm or less and more preferably, for example, within a range of about 150 nm or more to about 1,000 nm or less. The center-to-center distance between each pair of the electrodes  3  and  4  corresponds to the distance from the center of a dimension (width dimension) of the electrode  3  in a direction perpendicular or substantially perpendicular to the length direction of the electrode  3  to the center of a dimension (width dimension) of the electrode  4  in a direction perpendicular or substantially perpendicular to the length direction of the electrode  4 . 
     In the acoustic wave device  1 , a Z-cut piezoelectric layer is used, and thus, the direction perpendicular or substantially perpendicular to the length direction of the electrodes  3  and  4  is a direction perpendicular or substantially perpendicular to the polarization direction of the piezoelectric layer  2  unless a different cut piezoelectric body is used as the piezoelectric layer  2 . Here, the term “perpendicular” is not limited to referring to being exactly perpendicular may refer to being substantially perpendicular (the angle formed by the direction perpendicular to the length direction of the electrodes  3  and  4  and the polarization direction is, for example, within a range of about 90° ±10°). 
     A support member  8  is stacked on the second main surface  2   b  of the piezoelectric layer  2  with an insulating layer  7  interposed therebetween. The insulating layer  7  and the support member  8  each have a frame shape, and as illustrated in  FIG.  21   , through holes  7   a  and  8   a  are respectively provided in the insulating layer  7  and the support member  8 , so that a cavity portion  9  is provided. The cavity portion  9  is provided in order not to hinder vibration of the excitation regions C of the piezoelectric layer  2 . Thus, the support member  8  is stacked on the second main surface  2   b  with the insulating layer  7  interposed therebetween and located at a position at which it does not overlap a portion where at least one of the pairs of electrodes  3  and  4  are provided. The insulating layer  7  does not need to be provided. Accordingly, the support member  8  may be stacked directly or indirectly on the second main surface  2   b  of the piezoelectric layer  2 . 
     The insulating layer  7  is made of, for example, a silicon oxide. However, a suitable insulating material such as, for example, silicon oxynitride or alumina can be used other than a silicon oxide. The support member  8  is made of, for example, Si. The plane orientation of a surface of the Si, the surface facing the piezoelectric layer  2 , may be, for example, (100), (110), or (111). The Si of the support member  8  preferably has a high resistivity, which is, for example, about 2 kΩ or higher, and more preferably has a higher resistivity, which is, for example, about 4 kΩ) or higher. The support member  8  may also be made by using a suitable insulating material or a suitable semiconductor material. 
     The plurality of electrodes  3  and  4  and the first and second busbars  5  and  6  are made of, for example, a suitable metal such as Al or a suitable alloy such as an AlCu alloy. In the present preferred embodiment, the electrodes  3  and  4  and the first and second busbars  5  and  6  each have a structure in which an Al film is laminated on a Ti film. A close-contact layer that is not a Ti film may be used. 
     When the acoustic wave device  1  is driven, an AC voltage is applied between the plurality of electrodes  3  and the plurality of electrodes  4 . More specifically, the AC voltage is applied between the first busbar  5  and the second busbar  6 . As a result, resonance characteristics using a thickness-shear mode bulk wave that is excited in the piezoelectric layer  2  can be obtained. In the acoustic wave device  1 , when the thickness of the piezoelectric layer  2  is denoted by d and the center-to-center distance between each pair of the electrodes  3  and  4 , which are adjacent to each other, is denoted by p, d/p is, for example, about 0.5 or smaller. As a result, the above-mentioned thickness-shear mode bulk wave is effectively excited, and favorable resonance characteristics can be obtained. More preferably, d/p is, for example, about 0.24 or smaller, and in this case, more favorable resonance characteristics can be obtained. 
     Since the acoustic wave device  1  has the above-described configuration, even if the number of the pairs of electrodes  3  and  4  is reduced so as to facilitate a reduction in the size of the acoustic wave device  1 , the Q value is less likely to be reduced. This is because the propagation loss will be small even if the number of electrode fingers of reflectors on both sides is reduced. The number of the electrode fingers can be reduced because a thickness-shear mode bulk wave is used. The difference between a Lamb wave used in an acoustic wave device and the thickness-shear mode bulk wave will now be described with reference to  FIGS.  22 A and  22 B . 
       FIG.  22 A  is a schematic elevational cross-sectional view illustrating a Lamb wave that propagates through a piezoelectric film of an acoustic wave device such as that described in Japanese Unexamined Patent Application Publication No. 2012-257019. In  FIG.  22 A , a wave propagates through a piezoelectric film  201  as indicated by arrows. The piezoelectric film  201  includes a first main surface  201   a  and a second main surface  201   b  facing each other, and a thickness direction connecting the first main surface  201   a  and the second main surface  201   b  to each other is the Z direction. The X direction is a direction in which electrode fingers of an IDT electrode are arranged. The Lamb wave propagates in the X direction as illustrated in  FIG.  22 A . Although the entire piezoelectric film  201  vibrates because the Lamb wave is a type of plate waves, the wave propagates in the X direction, and thus, the reflectors are arranged on both sides so as to obtain resonance characteristics. Consequently, a propagation loss of the wave occurs, and if the size reduction is facilitated, that is, if the number of pairs of electrode fingers is reduced, the Q value is reduced. 
     In contrast, as illustrated in  FIG.  22 B , in the acoustic wave device  1 , the vibration displacement direction is the same or substantially the same as the thickness shear direction, and thus, the wave propagates and resonates substantially in a direction connecting the first main surface  2   a  and the second main surface  2   b  of the piezoelectric layer  2  to each other, that is, the Z direction. In other words, an X-direction component of the wave is considerably smaller than a Z-direction component of the wave. The resonance characteristics are obtained as a result of the wave propagating in the Z direction, and thus, a propagation loss is less likely to occur even if the number of electrode fingers of the reflectors is reduced. In addition, even if the number of pairs of electrode fingers including the electrodes  3  and  4  is reduced so as to facilitate the size reduction, the Q value is less likely to be reduced. 
     As illustrated in  FIG.  23   , the amplitude direction of thickness-shear mode bulk wave in a first region  451  that is included in the excitation regions C of the piezoelectric layer  2  is opposite to the amplitude direction of thickness-shear mode bulk wave in a second region  452  that is included in the excitation regions of the piezoelectric layer  2 .  FIG.  23    schematically illustrates a bulk wave in the case where a voltage is applied between the electrodes  3  and  4 , the voltage causing the potential of the electrode  4  to become higher than that of the electrode  3 . The first region  451  is one of the excitation regions and is a region between a virtual plane VP 1  that is perpendicular or substantially perpendicular to the thickness direction of the piezoelectric layer  2  and that divides the piezoelectric layer  2  into two portions and the first main surface  2   a.  The second region  452  is one of the excitation regions and is a region between the virtual plane VP 1  and the second main surface  2   b.    
     As described above, at least one pair of electrodes including one of the electrodes  3  and a corresponding one of the electrodes  4  are arranged in the acoustic wave device  1 . However, this does not cause a wave to propagate in the X direction, and thus, the number of pairs of the electrodes  3  and  4  does not need to be two or more. In other words, it is only necessary that at least one pair of electrodes are provided. 
     For example, the electrodes  3  are electrodes connected to the hot potential, and the electrodes  4  are electrodes connected to the ground potential. However, the electrodes  3  may be connected to the ground potential, and the electrodes  4  may be connected to the hot potential. In the present preferred embodiment, as described above, at least one pair of electrodes are electrodes connected to the hot potential and electrodes connected to the ground potential, and no floating electrode is provided. 
       FIG.  24    is a graph illustrating a resonance characteristic of the acoustic wave device illustrated in  FIG.  21   . The design parameters of the acoustic wave device  1  that has obtained this resonance characteristic are as follows. 
     The piezoelectric layer  2 : LiNbO 3  with Euler angles of (0°, 0°, 90°), thickness=about 400 nm. 
     The length of a region in which the electrodes  3  and the electrodes  4  overlap one another when viewed in the direction perpendicular or substantially perpendicular to the length direction of the electrodes  3  and  4 , that is, the sum of the lengths of the excitation regions C=about 40 μm, the number of pairs of electrodes formed of the electrodes  3  and 4=21, the center-to-center distance between each pair of electrodes=about 3 μm, the width of each of the electrodes  3  and  4 =about 500 nm, d/p=about 0.133. 
     The insulating layer  7 : a silicon oxide film having a thickness of about 1 μm. 
     The support member  8 : Si 
     The length of each of the excitation regions C is a dimension of the excitation region C along the length direction of the electrodes  3  and  4 . 
     In the present preferred embodiment, the electrode-to-electrode distances in the plurality of pairs of electrodes including the electrodes  3  and  4  were set to be the same as one another. In other words, the electrodes  3  and the electrodes  4  were arranged at the same or substantially the same pitch. 
     As is clear from  FIG.  24   , despite the fact that no reflectors are provided, a favorable resonance characteristic, which is a fractional bandwidth of about 12.5%, is obtained. 
     As described above, in the present preferred embodiment, d/p is, for example, about 0.5 or smaller and more preferably about 0.24 or smaller, where d is the thickness of the piezoelectric layer  2  and p is the center-to-center distance between each of the electrodes  3  and the corresponding electrode  4 . This matter will now be described with reference to  FIG.  25   . 
     A plurality of acoustic wave devices were obtained in a manner similar to the acoustic wave device that has obtained the resonance characteristic illustrated in  FIG.  24    except that d/2p was varied.  FIG.  25    is a graph illustrating the relationship between the d/2p and the fractional bandwidth of each of the acoustic wave devices as a resonator. 
     As is clear from  FIG.  25   , when d/2p exceeds about 0.25, that is, d/p&gt;about 0.5, the fractional bandwidth is less than about 5% even if d/p is changed. In contrast, in the case of d/2p about 0.25, that is, d/p about 0.5, the fractional bandwidth can be improved to about 5% or higher by changing d/p within the range. In other words, a resonator having a high coupling coefficient can be provided. In addition, when d/2p is about 0.12 or smaller, that is, d/p is about 0.24 or smaller, the fractional bandwidth can be improved to about 7% or higher. In this case, by changing d/p within the range, a resonator having an even wider fractional bandwidth can be obtained, and a resonator having an even higher coupling coefficient can be achieved. Thus, it is understood that a resonator that uses the thickness-shear mode bulk wave and that has a high coupling coefficient can be provided by setting d/p to be about 0.5 or smaller. 
     As described above, the at least one pair of electrodes may be a single pair of electrodes. 
     For example, if the piezoelectric layer  2  has a non-uniform thickness, a value obtained by averaging the thicknesses may be used. 
       FIG.  26    is a plan view of an acoustic wave device that uses a thickness-shear mode bulk wave. In an acoustic wave device  80 , a pair of electrodes  3  and  4  are provided on the first main surface  2   a  of the piezoelectric layer  2 . An intersecting width is denoted by K in  FIG.  26   . As described above, in the acoustic wave device according to a preferred embodiment of the present invention, the number of pairs of electrodes may be one. Also in this case, a thickness-shear mode bulk wave can be effectively excited as long as d/p is about 0.5 or smaller. 
       FIG.  27    is a partially cut-away perspective view illustrating an acoustic wave device that uses a Lamb wave. The position of the cavity portion  9  when viewed from a piezoelectric layer  83  is indicated by a dashed line in  FIG.  27   . 
     An acoustic wave device  81  includes a support substrate  82 . The support substrate  82  includes a recess that is open toward the upper surface thereof. The piezoelectric layer  83  is laminated on the support substrate  82 , so that the cavity portion  9  is provided. An IDT electrode  84  is provided on the piezoelectric layer  83  so as to be located above the cavity portion  9 . Reflectors  85  and  86  are provided on both sides of the IDT electrode  84  in an acoustic-wave propagation direction. In  FIG.  27   , the outer peripheral edge of the cavity portion  9  is indicated by the dashed line. Here, the IDT electrode  84  includes first and second busbars  84   a  and  84   b,  a plurality of electrodes  84   c  defining and functioning as first electrode fingers, and a plurality of electrodes  84   d  defining and functioning as second electrode fingers. The plurality of electrodes  84   c  are connected to the first busbar  84   a . The plurality of electrodes  84   d  are connected to the second busbar  84   b.  The plurality of electrodes  84   c  and the plurality of electrodes  84   d  are interdigitated with one another. 
     In the acoustic wave device  81 , a Lamb wave which is a type of plate waves is excited by applying an AC electric field to the IDT electrode  84  located above the cavity portion  9 . In addition, since the reflectors  85  and  86  are provided on both sides, the resonance characteristics using the Lamb wave can be obtained. 
     While preferred embodiments of the present invention have been described above, it is to be understood that variations and modifications will be apparent to those skilled in the art without departing from the scope and spirit of the present invention. The scope of the present invention, therefore, is to be determined solely by the following claims.