Patent Publication Number: US-2023143242-A1

Title: Filter

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of priority to Japanese Patent Application No. 2020-121453 filed on Jul. 15, 2020 and is a Continuation application of PCT Application No. PCT/JP2021/025978 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 a filter that utilizes an acoustic wave. 
     2. Description of the Related Art 
     An acoustic wave device of the related art that utilizes a plate wave propagating through a piezoelectric film formed of LiNbO 3  or LiTaO 3  is known. Such an acoustic wave device is used for, for example, a ladder filter. 
     For example, Japanese Unexamined Patent Application Publication No. 2012-257019 discloses an acoustic wave device that utilizes a Lamb wave as the plate wave. Here, a piezoelectric substrate is provided on a support body. The support body, that is, a support substrate has a cavity portion. The piezoelectric substrate is superposed on the cavity portion. The piezoelectric substrate is formed of LiNbO 3  or LiTaO 3 . An interdigital transducer (IDT) electrode is provided on an upper surface of the piezoelectric substrate. A voltage is applied across a plurality of electrode fingers connected to one potential of the IDT electrode and a plurality of electrode fingers connected to the other potential of the IDT electrode. This excites a Lamb wave. Reflectors are provided on both sides of the IDT electrode. Thus, an acoustic wave resonator that utilizes the plate wave is configured. 
     In an acoustic wave device as described in Japanese Unexamined Patent Application Publication No. 2012-257019, the frequency is adjusted by, for example, adjusting the thickness of the piezoelectric substrate. However, when the above-described acoustic wave device is used for the ladder filter, it is difficult to separately adjust the frequency of individual resonators. 
     SUMMARY OF THE INVENTION 
     Preferred embodiments of the present invention provide filters that each enable the frequency of individual resonators to be easily adjusted. 
     A filter according to a preferred embodiment of the present invention includes a piezoelectric film, an acoustic wave resonator that includes a functional electrode on the piezoelectric film, a capacitor on the piezoelectric film and connected in parallel to the acoustic wave resonator, and a resonator electrically connected to the acoustic wave resonator. The functional electrode includes a first busbar and a second busbar that face each other and at least one pair of a first electrode and a second electrode. The at least one pair of the first electrode and the second electrode face each other in a direction intersecting a thickness direction of the piezoelectric film, the first electrode is connected to the first busbar, and the second electrode is connected to the second busbar. The filter further includes a connection electrode on the piezoelectric film and electrically connecting the capacitor and the second busbar to each other. The capacitor includes the first busbar, an insulation film on the first busbar, and a capacitance electrode on the insulation film and electrically insulated from the first busbar. 
     Filters according to preferred embodiments of the present invention each enable the frequency of the individual resonators to be easily adjusted. 
     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 circuit diagram of a ladder filter according to a first preferred embodiment of the present invention. 
         FIG.  2    is a plan view of an acoustic wave resonator and a capacitor according to the first preferred embodiment of the present invention. 
         FIG.  3    is a sectional view taken along line I-I of  FIG.  2   . 
         FIG.  4    is a diagram illustrating an impedance characteristic when the capacitance of the capacitor is varied in a circuit configuration in which the acoustic wave resonator and the capacitor are connected in parallel to each other according to the first preferred embodiment of the present invention. 
         FIG.  5    is a sectional view taken along line II-II of  FIG.  2   . 
         FIG.  6 A  is a schematic elevational cross-sectional view for explaining the Lamb wave propagating through a piezoelectric film of an acoustic wave resonator of the related art, and  FIG.  6 B  is a schematic elevational cross-sectional view for explaining a bulk wave in a thickness slip mode propagating through a piezoelectric film of the acoustic wave resonator according to the first preferred embodiment of the present invention. 
         FIG.  7    is a diagram illustrating an amplitude width direction of the bulk wave in the thickness slip mode. 
         FIG.  8    is a diagram illustrating the relationship between a fractional bandwidth of the acoustic wave resonator and d/p when a center-to-center distance or an average center-to-center distance between a first electrode and a second electrode adjacent to each other is p and the thickness of the piezoelectric film is d. 
         FIG.  9    is a plan view of an acoustic wave resonator and a capacitor according to a second preferred embodiment of the present invention. 
         FIG.  10    is a plan view of an acoustic wave resonator and a capacitor according to a third preferred embodiment of the present invention. 
         FIG.  11    is a plan view of an acoustic wave resonator and a capacitor according to a reference example. 
         FIG.  12    is a plan view of an acoustic wave resonator and capacitors according to a first modification of the third preferred embodiment of the present invention. 
         FIG.  13    is a plan view of an acoustic wave resonator and capacitor according to a second modification of the third preferred embodiment of the present invention. 
         FIG.  14    is a plan view of an acoustic wave resonator and a capacitor according to a fourth preferred embodiment of the present invention. 
         FIG.  15    is a sectional view illustrating a section of an acoustic wave resonator and a capacitor according to a fifth preferred embodiment of the present invention corresponding to the section taken along line I-I of  FIG.  2   . 
         FIG.  16    is a diagram illustrating a map of the fractional bandwidth when d/p is caused to approach limitlessly to 0 in LiNbO 3  of Euler angles (0°, θ, ψ). 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, the present invention is clarified by describing preferred embodiments of the present invention with reference to the drawings. 
     Each preferred embodiment described herein are exemplary and configurations can be partially replaced or combined between different preferred embodiments. 
       FIG.  1    is a circuit diagram of a ladder filter according to a first preferred embodiment of the present invention. 
     As illustrated in  FIG.  1   , a ladder filter  10  includes a plurality of series arm resonators, a plurality of parallel arm resonators, and a capacitor  16 . The plurality of series arm resonators include an acoustic wave resonator  1 . The capacitor  16  is connected in parallel to the acoustic wave resonator  1 . 
       FIG.  2    is a plan view of the acoustic wave resonator and the capacitor according to the first preferred embodiment.  FIG.  3    is a sectional view taken along line I-I of  FIG.  2   . In  FIGS.  2  and  3   , wiring to connect to the other resonators or terminals is omitted. This also similarly applies to other plan views and sectional views. 
     As illustrated in  FIG.  2   , the acoustic wave resonator  1  includes a piezoelectric film  3 . As illustrated in  FIG.  3   , the piezoelectric film  3  includes a first main surface  3   a  and a second main surface  3   b . The first main surface  3   a  and the second main surface  3   b  are on opposite sides of the piezoelectric film  3  from each other. The piezoelectric film  3  is, for example, a lithium niobate film according to the present preferred embodiment. More specifically, the piezoelectric film  3  is, for example, an LiNbO 3  film. Alternatively, the piezoelectric film  3  may be, for example, a lithium tantalate film. More specifically, for example, an LiTaO 3  film may be used as the piezoelectric film  3 . The thickness of the piezoelectric film  3  is preferably, for example, greater than or equal to about 40 nm and smaller than or equal to about 1000 nm. 
     In  FIG.  2   , a functional electrode  4  is provided on the first main surface  3   a  of the piezoelectric film  3 . The functional electrode  4  includes a plurality of electrodes. The plurality of electrodes are arranged in a direction intersecting the thickness direction of the piezoelectric film  3 . Each of the electrodes has a rectangular or substantially rectangular shape. The plurality of electrodes include a plurality of pairs of a first electrode  6  and a second electrode  7 . According to the present preferred embodiment, the first electrode  6  and the second electrode  7  extend in parallel or substantially in parallel. The first electrode  6  and the second electrode  7  adjacent to each other face each other in a direction orthogonal or substantially orthogonal to a direction in which the first electrode  6  extends. In the following, the direction in which the first electrode  6  extends is defined as the y direction and a direction orthogonal or substantially orthogonal to the y direction is defined as the x direction. Both the x direction and the y direction are directions that intersect the thickness direction of the piezoelectric film  3 . Accordingly, the first electrode  6  and the second electrode  7  adjacent to each other face each other in the direction intersecting the thickness direction of the piezoelectric film  3 . 
     The functional electrode  4  includes a first busbar  8  and a second busbar  9 . The first busbar  8  and the second busbar  9  face each other. One end portion of each of a plurality of the first electrodes  6  is connected to the first busbar  8 . One end portion of each of a plurality of the second electrodes  7  is connected to the second busbar  9 . The plurality of first electrodes  6  and the plurality of second electrodes  7  are interdigitated with each other. The first electrode  6  and the second electrode  7  are connected to respective potentials different from each other. According to the present preferred embodiment, the functional electrode  4  is, for example, an interdigital transducer (IDT) electrode. However, the functional electrode  4  is not limited to the IDT electrode. It is sufficient that the functional electrode  4  include at least one pair of the first electrode  6  and the second electrode  7 . 
     The functional electrode  4  is made of appropriate metal or an appropriate alloy such as, for example, Al or an AlCu alloy. A Cu content in an AlCu alloy is preferably greater than or equal to about 1 weight % and smaller than or equal to about 20 weight %, for example. The functional electrode  4  may include a multilayered metal film. In this case, for example, an adhesion layer may be included. Examples of the adhesion layer include a Ti layer, a Cr layer, and so forth. 
     As illustrated in  FIG.  2   , the functional electrode  4  includes an intersecting region A. In the intersecting region A, the electrodes adjacent to each other are superposed on each other when seen in the x direction. The intersecting region A extends, in the x direction, from one of outermost electrodes of the functional electrode  4  to the other outermost electrode of the functional electrode  4 . The intersecting region A includes outer end portions of the outermost electrodes in the x direction. 
     As illustrated in  FIG.  3   , an insulation film  17  is provided on the first busbar  8  of the functional electrode  4 . A capacitance electrode  18  is provided on the insulation film  17 . The first busbar  8  and the capacitance electrode  18  are electrically insulated from each other by the insulation film  17 . The first busbar  8  and the capacitance electrode  18  face each other with the insulation film  17  interposed therebetween. The capacitor  16  is configured with the first busbar  8 , the insulation film  17 , and the capacitance electrode  18 . 
     In  FIG.  2   , a connection electrode  19  is provided on the first main surface  3   a  of the piezoelectric film  3 . The connection electrode  19  electrically connects the capacitance electrode  18  and the second busbar  9  to each other. Thus, the capacitor  16  is connected in parallel to the acoustic wave resonator  1 . Also referring to  FIG.  2   , the plurality of first electrodes  6  and the plurality of second electrodes  7  are surrounded by the connection electrode  19 , the first busbar  8 , and the second busbar  9 . Herein, the “surrounded” case includes not only a case where an outer periphery of the first electrodes  6  and the second electrodes  7  are entirely surrounded but also a case where, as illustrated in  FIG.  2   , the outer periphery of the first electrodes  6  and the second electrodes  7  are surrounded only in any three directions. The outer periphery refers to a portion where portions of the plurality of first electrodes  6  connected to the first busbar  8 , portions of the plurality of second electrodes  7  connected to the second busbar  9 , and outer edges of two outermost electrodes out of the plurality of first electrodes  6  and second electrodes  7  interdigitated with each other are connected to each other. 
     As illustrated in  FIG.  3   , the acoustic wave resonator  1  includes a support substrate  2 . The piezoelectric film  3  is provided on the support substrate  2 . Of the first main surface  3   a  and the second main surface  3   b  of the piezoelectric film  3 , the second main surface  3   b  is a main surface at the support substrate  2  side. According to the present preferred embodiment, the resonators of the ladder filter  10  share the support substrate  2  and the piezoelectric film  3 . Thus, productivity can be improved. 
     The support substrate  2  includes a cavity portion  13  and a support portion  12 . The support portion  12  has a frame shape. The cavity portion  13  is, for example, a through hole provided in the support substrate  2 . Alternatively, the cavity portion  13  may be, for example, a recessed portion provided in the support substrate  2 . 
     The support substrate  2  is, for example, a silicon substrate. The plane orientation in a surface of the support substrate  2  on the piezoelectric film  3  side is preferably, for example, (100), (110), or (111). The resistivity of the support substrate  2  is preferably greater than or equal to about 4 kΩ, for example. However, the material of the support substrate  2  is not limited to the above description, and examples of the material of the support substrate  2  can include piezoelectric materials such as aluminum oxide, lithium tantalate, lithium niobate, and crystal, various types of ceramics such as alumina, sapphire, silicon nitride, aluminum nitride, silicon carbide, zirconia, cordierite, mullite, steatite, and forsterite, dielectrics such as diamond and glass, semiconductors such as gallium nitride, and so forth. 
     The piezoelectric film  3  is provided on the support portion  12  of the support substrate  2  so as to cover the cavity portion  13 F. In plan view, the entirety or substantially the entirety of the intersecting region A is superposed on the cavity portion  13 . Herein, “plan view” refers to a direction viewed from above in  FIG.  3   . 
     One of the unique features of the present preferred embodiment are that the capacitor  16  includes the first busbar  8 , the insulation film  17 , and the capacitance electrode  18  and connected in parallel to the acoustic wave resonator  1 . Thus, the frequency of the individual resonators can be easily adjusted. These and the details of the circuit configuration of the ladder filter  10  will be described below. 
     As illustrated in  FIG.  1   , the ladder filter  10  includes a first signal terminal  14  and a second signal terminal  15 . According to the present preferred embodiment, the first signal terminal  14  is to be connected to an antenna. The first signal terminal  14  and the second signal terminal  15  may be, for example, wires or electrode pads. The acoustic wave resonator  1 , a series arm resonator S 2 , a series arm resonator S 3 , and a series arm resonator S 4  are connected in this order in series to each other between the first signal terminal  14  and the second signal terminal  15 . The capacitor  16  is connected in parallel to the acoustic wave resonator  1 . 
     A parallel arm resonator P 1  is connected between a ground potential and a junction between the acoustic wave resonator  1  and the series arm resonator S 2 . A parallel arm resonator P 2  is connected between a ground potential and a junction between the series arm resonator S 2  and the series arm resonator S 3 . A parallel arm resonator P 3  is connected between a ground potential and a junction between the series arm resonator S 3  and the series arm resonator S 4 . According to the present preferred embodiment, other than the acoustic wave resonator  1 , all of the plurality of series arm resonators and the plurality of parallel arm resonators are, for example, acoustic wave resonators. However, this is not limiting. 
     The acoustic wave resonator  1  is positioned closest to the first signal terminal  14  in the circuit configuration of the ladder filter  10 . The circuit configuration of the ladder filter  10  is not limited to the configuration illustrated in  FIG.  1   . It is sufficient that the ladder filter  10  include the acoustic wave resonator  1 , at least one resonator other than the acoustic wave resonator  1 , and the capacitor  16 . It is sufficient that the resonators other than the acoustic wave resonator  1  and the acoustic wave resonator  1  are electrically connected, and the capacitor  16  are connected in parallel to the acoustic wave resonator  1 . The acoustic wave resonator  1  may be a parallel arm resonator. 
     As illustrated in  FIG.  2   , layered wiring  9 A is laminated on the second busbar  9  of the acoustic wave resonator  1 . This layered wiring  9 A is connected to the first signal terminal  14  illustrated in  FIG.  1   . The layered wiring  9 A may be connected to the series arm resonator S 2  and the parallel arm resonator P 1 . Since the layered wiring  9 A is provided, electrical resistance of the functional electrode  4  can be reduced. The connection electrode  19  is electrically connected to the layered wiring  9 A and the second busbar  9 . According to the present preferred embodiment, the capacitance electrode  18 , the connection electrode  19 , and the layered wiring  9 A are integrally provided. The layered wiring  9 A is not necessarily provided. Alternatively, the capacitance electrode  18 , the connection electrode  19 , and the layered wiring  9 A may be separately provided and connected to each other. However, when the above-described electrodes are integrally provided as in the present preferred embodiment, the productivity can be improved. In addition, since no contact resistance is generated, resistance of wiring can be reduced. 
     The details of the advantageous effects of the present preferred embodiment will be described below. 
       FIG.  4    is a diagram illustrating an impedance characteristic when the capacitance of the capacitor is varied in the circuit configuration in which the acoustic wave resonator and the capacitor are connected in parallel to each other according to the first preferred embodiment. Referring to  FIG.  4   , the capacitance of the capacitor  16  is different between a result represented by a solid line and a result represented by a broken line. 
     As illustrated in  FIG.  4   , it can be understood that, when the capacitance of the capacitor  16  is varied, the anti-resonant frequency of the acoustic wave resonator  1  varies. As described above, the frequency of the acoustic wave resonator  1  can be separately easily adjusted. To adjust the capacitance of the capacitor  16 , for example, the thickness of the insulation film  17  can be adjusted. Alternatively, for example, the area in which the first busbar  8  and the capacitance electrode  18  face each other can be adjusted. 
     Furthermore, the capacitor  16  includes the first busbar  8  and is configured so as to be integrated with the acoustic wave resonator  1 . The capacitor  16  is superposed on the acoustic wave resonator  1  in plan view. Accordingly, size reduction of the acoustic wave resonator  1  can be facilitated. 
       FIG.  5    is a sectional view taken along line II-II of  FIG.  2   . 
     The insulation film  17  of the capacitor  16  extends from a portion on the first busbar  8  to a portion on the first main surface  3   a  of the piezoelectric film  3 . The insulation film  17  includes an inclined portion  17   a  in a portion thereof that extends from a portion on the first busbar  8  to a portion on the first main surface  3   a . The inclined portion  17   a  is inclined relative to a normal line to the first main surface  3   a . An electrode with which the capacitance electrode  18  and the connection electrode  19  are defined extends from a portion above the first busbar  8  to a portion on the first main surface  3   a  through a portion on the inclined portion  17   a . Thus, stress applied to the electrode can be reduced. Accordingly, wires are unlikely to break. However, the insulation film  17  does not necessarily include the inclined portion  17   a.    
     According to the present preferred embodiment, the insulation film  17  covers one end portion of the first busbar  8  in a direction in which the first busbar  8  extends. In contrast, the insulation film  17  does not cover the other end portion of the first busbar  8 . However, the insulation film  17  may cover both of the end portions of the first busbar  8 . 
     The connection electrode  19  is preferably superposed on the support portion  12  of the support substrate  2  in plan view. More preferably, the connection electrode  19  is not superposed on the cavity portion  13  in plan view. Thus, stress applied to a portion in which the piezoelectric film  3  faces the cavity portion  13  can be reduced. Accordingly, cracks in the piezoelectric film  3  can be further reduced or prevented. 
     Meanwhile, according to the present preferred embodiment, no reflector is provided on the piezoelectric film  3 . The acoustic wave resonator  1  does not include the reflector. The reason why propagation loss is reduced or prevented even in this case is that the acoustic wave resonator  1  utilizes a bulk wave in a thickness slip mode. More specifically, the acoustic wave resonator  1  utilizes the bulk wave in a primary thickness slip mode. The details of the thickness slip mode that the acoustic wave resonator  1  utilizes will be described below. 
     As illustrated in  FIG.  2   , a plurality of pairs of the first electrode  6  and the second electrode  7  adjacent to each are provided in the x direction. This number of pairs is not necessarily an integer and may be, for example, 1.5 pairs, 2.5 pairs, or the like. The case where the electrodes in the functional electrode  4  are adjacent to each other refers not to a case where the electrodes are arranged so as to be in direct contact with each other, but to a case where the electrodes are arranged with a gap interposed therebetween. When the first electrode  6  and the second electrode  7  are adjacent to each other, another hot electrode or ground electrode is not disposed between the first electrode  6  and the second electrode  7 . 
     To drive the acoustic wave resonator  1 , an alternating-current voltage is applied across the plurality of first electrode  6  and the plurality of second electrode  7 . More specifically, the alternating-current voltage is applied across the first busbar  8  and the second busbar  9 . Thus, a resonance characteristic utilizing the bulk wave in the thickness slip mode excited in the piezoelectric film  3  can be obtained. As described above, a region between the first electrode  6  and the second electrode  7  is an exciting region B. Although a single exciting region B is shown as an example in  FIG.  2   , all regions between the plurality of first electrodes  6  and the plurality of second electrodes  7  are exciting regions B. The exciting regions B are included in the intersecting region A. 
     In the acoustic wave resonator  1 , when the thickness of the piezoelectric film  3  is d and the center-to-center distance between the first electrode  6  and the second electrode  7  adjacent to each other in any one pair out of the plurality of pairs of the first electrode  6  and the second electrode  7  is p, d/p is, for example, smaller than or equal to about 0.5. Thus, the bulk wave in the thickness slip mode can be effectively excited, and a good resonance characteristic can be obtained. Here, the center-to-center distance between the first electrode  6  and the second electrode  7  is a distance between the center of the first electrode  6  in the x direction and the center of the second electrode  7  in the x direction. 
     The acoustic wave resonator  1  includes the above-described configuration and utilizes the thickness slip mode. Thus, the quality factor is unlikely to reduce even when the number of pairs of the first electrode  6  and the second electrode  7  is reduced. 
     According to the present preferred embodiment, the piezoelectric film  3  is a Z-cut piezoelectric film. Accordingly, the x direction is a direction orthogonal or substantially orthogonal to the polarization direction of the piezoelectric film  3 . This is not limiting when the piezoelectric film  3  is a piezoelectric film of another cut angle. 
     The difference between the bulk wave in the thickness slip mode and a Lamb wave utilized in the related-art will be described with reference to  FIGS.  6 A and  6 B . 
       FIG.  6 A  is a schematic elevational cross-sectional view for explaining the Lamb wave propagating through a piezoelectric film of an acoustic wave resonator as described in Japanese Unexamined Patent Application Publication No. 2012-257019. Here, the wave propagates through a piezoelectric film  201  as indicated by arrows. Here, in the piezoelectric film  201 , a first main surface  201   a  and a second main surface  201   b  are on opposite sides of the piezoelectric film  201  from each other. The thickness direction connecting the first main surface  201   a  and the second main surface  201   b  is the z direction. The x direction is a direction in which electrode fingers of an IDT electrode are arranged. As illustrated in  FIG.  6 A , the Lamb wave propagates in the x direction. Since the Lamb wave is a plate wave, although the piezoelectric film  201  entirely vibrates, the wave propagates in the x direction. Accordingly, reflectors are disposed on both sides of the IDT electrode in the x direction so as to obtain the resonance characteristic. 
     In contrast, as illustrated in  FIG.  6 B , in the acoustic wave resonator according to the present preferred embodiment, the vibration displacement occurs in the thickness slip direction. Thus, the wave substantially propagates in the z direction and resonates. Accordingly, an x direction component of the wave is significantly smaller than a z direction component of the wave. Since the resonance characteristic is obtained due to propagation of the wave in the z direction, propagation loss is unlikely to occur even when the number of electrode fingers of the reflectors is reduced. Furthermore, the quality factor is unlikely to reduce even when, to facilitate the size reduction, the number of electrode pairs of the first electrode  6  and the second electrode  7  is reduced. 
     As illustrated in  FIG.  7   , amplitude width directions of the bulk wave in the thickness slip mode in a first region  451  included in the exciting region of the piezoelectric film  3  and in a second region  452  included in the exciting region are opposite to each other.  FIG.  7    schematically illustrates the bulk wave when a voltage with which the potential is higher at the second electrode  7  than at the first electrode  6  is applied across the first electrode  6  and the second electrode  7 . The first region  451  is, of the exciting region, a region between the first main surface  3   a  and a virtual plane VP 1  that is orthogonal or substantially orthogonal to the thickness direction of the piezoelectric film  3  and that bifurcates the piezoelectric film  3 . The second region  452  is, of the exciting region, a region between the second main surface  3   b  and the virtual plane VP 1 . 
     As described above, the plurality of pairs of the first electrode  6  and the second electrode  7  are disposed in the acoustic wave resonator  1 . Since the wave does not propagate in the x direction in the thickness slip mode, it is not required that the plurality of electrode pairs of the first electrode  6  and the second electrode  7  be provided. In other words, it is sufficient that at least a single pair of the first electrode  6  and the second electrode  7  is provided. 
     Meanwhile, d/p is, for example, smaller than or equal to about 0.5 according to the present preferred embodiment. Preferably, d/p is, for example, smaller than or equal to about 0.24. In this case, a better resonance characteristic can be obtained. This will be described with reference to  FIG.  8   . 
     A plurality of acoustic wave resonators are obtained with d/p varied.  FIG.  8    is a diagram illustrating the relationship between d/p and a fractional bandwidth of the acoustic wave resonator. 
     As clearly understood from  FIG.  8   , when d/p&gt;about 0.5, the fractional bandwidth is smaller than about 5% even when d/p is adjusted. In contrast, when d/p≤about 0.5, by varying d/p within the range, the fractional bandwidth of greater than or equal to about 5% can be obtained. Thus, a resonator having a high coupling coefficient can be configured. Furthermore, when d/p is smaller than or equal to about 0.24, the fractional bandwidth can be increased to a percentage greater than or equal to about 7%. In addition, when d/p is adjusted within this range, a resonator having a wider fractional bandwidth can be obtained, and accordingly, a resonator having a higher coupling coefficient can be obtained. For example, when there is a variation in the thickness of the piezoelectric film  3 , a value obtained by averaging the thicknesses, that is, an average thickness can be used. 
     The center-to-center distance p between the first electrode  6  and the second electrode  7  adjacent to each is preferably, for example, greater than or equal to about 1 μm and smaller than or equal to about 10 μm. When the dimensions of the plurality of electrodes of the functional electrode  4  in the x direction are defined as a width, the width of each of the first electrode  6  and the second electrode  7  is preferably, for example, greater than or equal to about 50 nm and smaller than or equal to about 1000 nm. 
     According to the present preferred embodiment, the acoustic wave resonator  1  and the capacitor  16  are connected in parallel to each other. However, the other resonators in the ladder filter  10  may be respectively connected in parallel to other capacitors than the capacitor  16 . In this case, the frequency can be separately easily adjusted also in the other resonators. 
     The example of the ladder filter has been described according to the first preferred embodiment, the filter according to the present invention is not limited to the ladder filter. 
       FIG.  9    is a plan view of the acoustic wave resonator and a capacitor according to a second preferred embodiment of the present invention. 
     According to the present preferred embodiment, the configuration of the electrode that connects a capacitor  26  and the second busbar  9  of the acoustic wave resonator  1  to each other and disposition of an insulation film  27  are different from those of the first preferred embodiment. Other than the above-described points, a ladder filter according to the present preferred embodiment has the same or similar configuration to that of the ladder filter  10  according to the first preferred embodiment. 
     The insulation film  27  covers both of the end portions of the first busbar  8  in the direction in which the first busbar  8  extends. The insulation film  27  includes inclined portions  17   a  in portions that cover the respective end portions of the first busbar  8 . A first connection electrode  29 A and a second connection electrode  29 B are connected to the capacitance electrode  18  of the capacitor  26 . According to the present preferred embodiment, the connection electrode includes the first connection electrode  29 A and the second connection electrode  29 B. 
     The first connection electrode  29 A electrically connects one end portion of the second busbar  9  and the capacitance electrode  18  to each other. The second connection electrode  29 B electrically connects the other end portion of the second busbar  9  and the capacitance electrode  18  to each other. The first connection electrode  29 A and the second connection electrode  29 B face each other in the x direction. According to the present preferred embodiment, the capacitance electrode  18 , the first connection electrode  29 A, the second connection electrode  29 B, and the layered wiring  9 A are integrally provided. 
     As illustrated in  FIG.  9   , the first electrodes  6  and the second electrodes  7  are surrounded by the first connection electrode  29 A, the second connection electrode  29 B, the first busbar  8 , and the second busbar  9 . Thus, heat releasing paths can be increased, and accordingly, a heat releasing property can be improved. Furthermore, since an imbalance between portions to which heat stress or the like is applied can be reduced, cracks in the piezoelectric film  3  can be reduced or prevented. 
     The first connection electrode  29 A and the second connection electrode  29 B are preferably superposed on the support portion  12  of the support substrate  2  in plan view. More preferably, neither the first connection electrode  29 A nor the second connection electrode  29 B is superposed on the cavity portion  13  in plan view. These can reduce the stress applied to the portion in which the piezoelectric film  3  faces the cavity portion  13 . Accordingly, cracks in the piezoelectric film  3  can be further reduced or prevented. 
     In addition, the frequency of the acoustic wave resonator  1  can be separately easily adjusted by adjusting the capacitance of the capacitor  26 . Thus, similarly to the first preferred embodiment, the frequency of the individual resonators can be easily adjusted. 
       FIG.  10    is a plan view of the acoustic wave resonator and a capacitor according to a third preferred embodiment of the present invention. 
     The difference between the first preferred embodiment and the present preferred embodiment is that a second capacitor  37  is provided according to the present preferred embodiment. Other than the above-described point, a ladder filter according to the present preferred embodiment has the same or similar configuration to that of the ladder filter  10  according to the first preferred embodiment. 
     A first capacitor  36  is similarly configured to the capacitor  16  according to the first preferred embodiment. The capacitance electrode  18  of the first capacitor  36  and the second busbar  9  of the acoustic wave resonator  1  are connected to each other through the second capacitor  37 . The acoustic wave resonator  1  is connected in parallel to the first capacitor  36  and the second capacitor  37 . The first capacitor  36  and the second capacitor  37  are connected in series to each other. 
     The second capacitor  37  includes a first comb-shaped electrode  34  and a second comb-shaped electrode  35 . Each of the first comb-shaped electrode  34  and the second comb-shaped electrode  35  includes a plurality of electrode fingers. The first comb-shaped electrode  34  and the second comb-shaped electrode  35  are provided on the first main surface  3   a  of the piezoelectric film  3 . The first comb-shaped electrode  34  is electrically connected to the capacitance electrode  18  by a first wiring electrode  39 A. Meanwhile, the second comb-shaped electrode  35  is electrically connected to the second busbar  9  by a second wiring electrode  39 B. The first comb-shaped electrode  34  and the second comb-shaped electrode  35  are interdigitated with each other. The first comb-shaped electrode  34  and the second comb-shaped electrode  35  are superposed on the support portion  12  of the support substrate  2  in plan view. Neither the first comb-shaped electrode  34  nor the second comb-shaped electrode  35  is superposed on the cavity portion  13  in plan view. 
     The second capacitor  37  includes, similarly to the functional electrode  4 , an intersecting region. The intersecting region is a region where the electrode fingers adjacent to each other are superposed on each other when seen in a direction orthogonal or substantially orthogonal to a direction in which each electrode finger of the second capacitor  37  extends. The dimension of the intersecting region of the second capacitor  37  in the direction in which each electrode finger extends is defined as an intersecting width of the second capacitor  37 . 
     The frequency of the acoustic wave resonator  1  can be separately easily adjusted by adjusting the capacitance of the first capacitor  36  and the second capacitor  37 . Thus, similarly to the first preferred embodiment, the frequency of the individual resonators can be easily adjusted. To adjust the capacitance by using the second capacitor  37 , for example, the intersecting width can be adjusted. Alternatively, for example, the number of pairs of the electrode fingers of the second capacitor  37  can be adjusted. 
     According to the above-described preferred embodiments, the capacitor includes the first busbar, the insulation film, and the capacitance electrode. This capacitor corresponds to the first capacitor  36  according to the third preferred embodiment. Here, also when the first capacitor  36  is not provided but the second capacitor  37  is provided, the frequency of the individual resonators can be adjusted. The example of this will be represented by a reference example illustrated in  FIG.  11   . 
     The only differences between the reference example illustrated in  FIG.  11    and the third preferred embodiment are that layered wiring  38 A is provided instead of the capacitance electrode  18  and disposition of the insulation film  17  is different. In plan view, disposition of the layered wiring  38 A is the same or substantially the same as disposition of the capacitance electrode  18  according to the third preferred embodiment. However, the insulation film  17  does not cover the end portion of the first busbar  8  in the direction in which the first busbar  8  extends. Thus, a portion of the layered wiring  38 A is laminated on the insulation film  17  and the other portion of the layered wiring  38 A is laminated on the first busbar  8 . The potential of the layered wiring  38 A is the same as the potential of the first busbar  8 . Accordingly, the first capacitor  36  is not provided. The layered wiring  38 A is connected to the first comb-shaped electrode  34  by the first wiring electrode  39 A. Similarly to the third preferred embodiment, the second capacitor  37  includes the first comb-shaped electrode  34  and the second comb-shaped electrode  35 . 
     Also when the second capacitor  37  is provided, similarly to the second preferred embodiment, the first electrodes  6  and the second electrodes  7  may be surrounded by the electrodes. Also in this case, the frequency of the individual resonators can be easily adjusted. 
     For example, according to a first modification of the third preferred embodiment illustrated in  FIG.  12   , a first capacitor  36 A is configured. Similarly to the second preferred embodiment, the first capacitor  36 A is defined the first busbar  8 , the insulation film  17 , and the capacitance electrode  18 . Furthermore, the second busbar  9  and the capacitance electrode  18  are electrically connected to each other by the second connection electrode  29 B. The insulation film  17  covers only one end portion of the first busbar  8  in the direction in which the first busbar  8  extends. More specifically, the insulation film  17  covers the end portion of the first busbar  8  on the second connection electrode  29 B side. When seen in the y direction, the capacitance electrode  18  is superposed on one end portion of the intersecting region but is not superposed on the other end portion of the intersecting region. However, when seen in the y direction, the capacitance electrode  18  may be superposed on the entirety or substantially the entirety of the intersecting region. When seen in the x direction and the y direction, the first electrodes  6  and the second electrodes  7  are surrounded by the first wiring electrode  39 A, the second capacitor  37 , the second wiring electrode  39 B, the second connection electrode  29 B, the first busbar  8 , and the second busbar  9 . Thus, similarly to the second preferred embodiment, the heat releasing property can be improved and cracks in the piezoelectric film  3  can be reduced or prevented. 
     A second modification of the third preferred embodiment illustrated in  FIG.  13    is similarly configured to the first modification except that the layered wiring  38 A is provided according to the second modification. Also according to the present modification, similarly to the first modification, the first capacitor  36 A is provided. However, according to the present modification, similarly to the reference example illustrated in  FIG.  11   , the layered wiring  38 A is laminated so as to extend over the insulation film  17  and the first busbar  8 . The layered wiring  38 A is connected to the first comb-shaped electrode  34  by using the first wiring electrode  39 A. On the insulation film  17 , the layered wiring  38 A is disposed so as to be separate from the capacitance electrode  18 . The potential of the capacitance electrode  18  is the same as the potential of the second busbar  9 . The potential of the layered wiring  38 A is the same as the potential of the first busbar  8 . Also according to the present modification, the first electrodes  6  and the second electrodes  7  are surrounded by the first wiring electrode  39 A, the second capacitor  37 , the second wiring electrode  39 B, the second connection electrode  29 B, the first busbar  8 , and the second busbar  9 . Thus, similarly to the second preferred embodiment, the heat releasing property can be improved and cracks in the piezoelectric film  3  can be reduced or prevented. 
       FIG.  14    is a plan view of an acoustic wave resonator and the capacitor according to a fourth preferred embodiment of the present invention. 
     The difference between the first preferred embodiment and the present preferred embodiment is that a pair of reflectors  46  and  47  are provided and a plate wave is utilized according to the present preferred embodiment. Other than the above-described points, a ladder filter according to the present preferred embodiment has the same or similar configuration to that of the ladder filter  10  according to the first preferred embodiment. 
     A functional electrode of an acoustic wave resonator  41  is an IDT electrode  44 . The IDT electrode  44  has the same or similar configuration to that of the functional electrode  4  according to the first preferred embodiment. More specifically, the IDT electrode  44  includes the first busbar  8 , the second busbar  9 , a plurality of pairs of the first electrode  6  and the second electrode  7 . However, the design parameters are suited for excitation of the plate wave. The pair of reflectors  46  and  47  are provided on both sides of the IDT electrode  44  in the x direction on the first main surface  3   a  of the piezoelectric film  3 . 
     When the plate wave is utilized, examples of the material of the piezoelectric film  3  include not only lithium tantalate and lithium niobate but also, zinc oxide, aluminum nitride, crystal, lead zirconate titanate (PZT), and so forth. 
     Also according to the present preferred embodiment, the frequency of the acoustic wave resonator  41  can be separately easily adjusted by adjusting the capacitance of the capacitor  16 . Thus, similarly to the first preferred embodiment, the frequency of the individual resonators can be easily adjusted. 
     When the plate wave is utilized, the pair of the reflectors are provided. Thus, the size of the acoustic wave resonator is likely to increase. However, according to the present preferred embodiment, the capacitor  16  includes the first busbar  8  and is configured such that the capacitor  16  is integrated with the acoustic wave resonator  41 . The capacitor  16  is superposed on the acoustic wave resonator  41  in plan view. Accordingly, the frequency can be easily adjusted as described above while the increase in size is reduced or prevented. 
       FIG.  15    is a sectional view illustrating a section of an acoustic wave resonator and the capacitor according to a fifth preferred embodiment of the present invention corresponding to the section taken along line I-I of  FIG.  2   . 
     The differences between the present preferred embodiment and the first preferred embodiment are that an acoustic reflective film  53  is provided and a support substrate  52  does not include a cavity portion according to the present preferred embodiment. More specifically, the acoustic reflective film  53  is provided on the support substrate  52 . The piezoelectric film  3  is provided on the acoustic reflective film  53 . Other than the above-described points, a ladder filter according to the present preferred embodiment has the same or similar configuration to that of the ladder filter  10  according to the first preferred embodiment. According to the present preferred embodiment, the resonators share the acoustic reflective film  53 . 
     The acoustic reflective film  53  is a multilayer body including a plurality of acoustic impedance layers. More specifically, the acoustic reflective film  53  includes a plurality of low acoustic impedance layers and a plurality of high acoustic impedance layers. The low acoustic impedance layers are layers having a relatively low acoustic impedance. The plurality of low acoustic impedance layers of the acoustic reflective film  53  include a low acoustic impedance layer  54   a  and a low acoustic impedance layer  54   b . In contrast, the high acoustic impedance layers are layers having a relatively high acoustic impedance. The plurality of high acoustic impedance layers of the acoustic reflective film  53  include a high acoustic impedance layer  55   a  and a high acoustic impedance layer  55   b . The low acoustic impedance layers and the high acoustic impedance layers are laminated in an alternating sequence. In the acoustic reflective film  53 , the low acoustic impedance layer  54   a  is a layer positioned closest to the piezoelectric film  3 . 
     The acoustic reflective film  53  includes two low acoustic impedance layers and two high acoustic impedance layers. However, it is sufficient that the acoustic reflective film  53  includes at least one low acoustic impedance layer and at least one high acoustic impedance layer. 
     Examples of the material of the low acoustic impedance layers can include silicon oxide, aluminum, and so forth. Examples of the material of the high acoustic impedance layers can include metal materials such as platinum and tungsten and dielectrics such as aluminum nitride and silicon nitride. 
     Also according to the present preferred embodiment, the frequency of the acoustic wave resonator  51  can be separately easily adjusted by adjusting the capacitance of the capacitor  16 . Thus, similarly to the first preferred embodiment, the frequency of the individual resonators can be easily adjusted. 
     Also when the plate wave is utilized similarly to the fourth preferred embodiment, instead of the support substrate  2 , the acoustic reflective film  53  and the support substrate  52  may be provided. 
     Hereinafter, examples of preferred Euler angles (φ, θ, ψ) of a lithium niobate film as the piezoelectric film  3  are described. In the following, the examples in which the piezoelectric film  3  is a lithium niobate film are described. However, the description can be applied also when the piezoelectric film  3  is a lithium tantalate film. 
       FIG.  16    is a diagram illustrating a map of the fractional bandwidth with respect to Euler angles (0°, θ, ψ) of LiNbO 3  when d/p is caused to approach limitlessly to 0. Hatched portions of  FIG.  16    are regions in which a fractional bandwidth of at least 5% can be obtained. When ranges of these regions are approximated, ranges represented by expression (1), expression (2), and expression (3) below are obtained. 
       (0°±10°,0 to 20°, any ψ)  expression (1)
 
       (0°±10°,20 to 80°,0 to 60° (1−(θ−50) 2 /900) 1/2 ) or (0°±10° 20 to 80°,[180°−60° (1−(θ−50) 2 /900) 1/2 ] to 180°)   expression (2)
 
       (0°±10°,[180°−30° (1−(ψ−90) 2 /8100) 1/2 ] to 180°, any ψ)  expression (3)
 
     Accordingly, in the case of the Euler angle range of expression (1), (2), or (3) described above, it is preferable since the fractional bandwidth can be sufficiently increased. 
     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.