Patent Publication Number: US-2022216853-A1

Title: Acoustic wave filter

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of priority to Japanese Patent Application No. 2019-176704 filed on Sep. 27, 2019 and is a Continuation application of PCT Application No. PCT/JP2020/035303 filed on Sep. 17, 2020. 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 band-pass acoustic wave filter including a plurality of acoustic wave resonators. 
     2. Description of Related Art 
     Various band-pass acoustic wave filters including a plurality of acoustic wave resonators have been proposed. For example, in a ladder filter described in Japanese Unexamined Patent Application Publication No. 2002-217680, a series arm resonator and a parallel arm resonator are configured with acoustic wave resonators. 
     In addition, Japanese Unexamined Patent Application Publication No. 2014-131351 discloses a structure in which a piston mode is formed in an acoustic wave resonator and transverse mode ripples are suppressed. More specifically, in an IDT electrode, a region where electrode fingers each connected to different potential overlap each other in an acoustic wave propagation direction is referred to as an intersecting region. The intersecting region includes a central region located at a center in a direction orthogonal to the acoustic wave propagation direction and includes first and second edge regions provided on respective sides of the central region in the direction orthogonal to the acoustic wave propagation direction. The piston mode is generated by making an acoustic velocity in the first and second edge regions lower than an acoustic velocity in the central region. 
     As the structure for providing the acoustic velocity difference, 1) a structure having a widened portion in which a width in each of the first and second edge regions is wider than that in the central region or 2) a structure in which an acoustic velocity reducing film is laminated in the first and second edge regions are disclosed. 
     When the structure described in Japanese Unexamined Patent Application Publication No. 2014-131351 in which the piston mode is used is applied to an acoustic wave filter including a plurality of acoustic wave resonators as described in Japanese Unexamined Patent Application Publication No. 2002-217680, it is possible to suppress ripples due to a transverse mode. However, when the structure in which the first and second edge regions are the widened portions is used in each of the acoustic wave resonators of the acoustic wave filter and particularly when a reduction in size of the acoustic wave filter is attempted, ripples due to a transverse mode cannot be sufficiently suppressed in some cases. In addition, when the structure in which the acoustic velocity reducing film is laminated in the first and second edge regions is used in each of the acoustic wave resonator, there has been a case in which steepness of filter characteristics at a pass band end portion of the acoustic wave filter is not sufficiently high. 
     SUMMARY OF THE INVENTION 
     Preferred embodiments of the present invention provide acoustic wave filters that are each able to reduce or prevent ripples in a transverse mode and improve steepness of filter characteristics, even when a reduction in size is achieved. 
     An acoustic wave filter according to a preferred embodiment of the present invention includes a plurality of acoustic wave resonators including a piezoelectric substrate and an IDT electrode on the piezoelectric substrate and including first and second electrode fingers interdigitated with each other. When a region in which the first electrode fingers and the second electrode fingers overlap each other in an acoustic wave propagation direction is defined as an intersecting region, the intersecting region includes a central region at a center or approximate center in a direction in which the first and second electrode fingers extend and first and second edge regions on respective outer side portions of the central region in a direction in which the first and second electrode fingers extend, and an acoustic velocity in the first and second edge regions is lower than an acoustic velocity in the central region. The plurality of acoustic wave resonators include a first acoustic wave resonator in which at least one of a width of the first electrode fingers and a width of the second electrode fingers in the first and second edge regions is larger than at least one of a width of first electrode fingers and a width of second electrode fingers in the central region, and a second acoustic wave resonator including at least one of a configuration in which an acoustic velocity reducing film is laminated in the first and second edge regions and a configuration in which an acoustic velocity increasing film to increase the acoustic velocity is laminated in the central region. 
     An acoustic wave filter according to a preferred embodiment of the present invention includes a plurality of acoustic wave resonators including a piezoelectric substrate and an IDT electrode on the piezoelectric substrate and including first and second electrode fingers interdigitated with each other. When a region in which the first electrode fingers and the second electrode fingers overlap each other in an acoustic wave propagation direction is defined as an intersecting region, the intersecting region includes a central region at a center or approximate center in a direction in which the first and second electrode fingers extend and first and second edge regions on respective outer side portions of the central region in a direction in which the first and second electrode fingers extend, and an acoustic velocity in the first and second edge regions is lower than acoustic velocity in the central region. The plurality of acoustic wave resonators include a first acoustic wave resonator in which at least one of a width of the first electrode fingers and a width of the second electrode fingers in the first and second edge regions is larger than at least one of a width of the first electrode fingers and a width of the second electrode fingers in the central region, and a second acoustic wave resonator including at least one of a configuration in which an insulating film made of tantalum pentoxide, hafnium oxide, niobium pentoxide, tungsten oxide, and silicon oxide, or Al, Cu, Pt, Au, Ag, Ti, Ni, Cr, Mo, W, Ta, Mg, Fe, or Ru or alloy mainly including any of Al, Cu, Pt, Au, Ag, Ti, Ni, Cr, Mo, W, Ta, Mg, Fe, or Ru is laminated in the first and second edge regions and a configuration in which a film made of a material selected from the group consisting of aluminum oxide, aluminum nitride, silicon nitride, and silicon oxide is laminated in the central region. 
     According to preferred embodiments of the present invention, acoustic wave filters can be provided that are each able to reduce or prevent transverse mode ripples and improve steepness of filter characteristics, even when a reduction in size is achieved. 
     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 an acoustic wave filter according to a first preferred embodiment of the present invention. 
         FIG. 2A  is a schematic plan view illustrating electrode structure of an acoustic wave resonator of the acoustic wave filter of the first preferred embodiment of the present invention, and  FIG. 2B  is a front sectional view of the acoustic wave resonator. 
         FIG. 3  is a plan view for explaining an IDT electrode of a first acoustic wave resonator. 
         FIG. 4  is a plan view for explaining electrode structure of an IDT electrode of a second acoustic wave resonator. 
         FIG. 5A  is a diagram showing resonance characteristics of the first and second acoustic wave resonators, and  FIG. 5B  is an enlarged diagram showing a portion indicated by a circle A in  FIG. 5A . 
         FIG. 6  is a diagram showing attenuation-frequency characteristics of respective acoustic wave filters of Example 1 of a preferred embodiment of the present invention and Comparative Example 1. 
         FIG. 7  is an enlarged diagram showing a portion indicated by an arrow B in  FIG. 6  and showing attenuation-frequency characteristics of the respective acoustic wave filters of Example 1 and Comparative Example 1. 
         FIG. 8  is a diagram showing attenuation-frequency characteristics of respective acoustic wave filters of Example 2 of a preferred embodiment of the present invention and Comparative Example 1. 
         FIG. 9  is an enlarged diagram showing a portion indicated by an arrow C in  FIG. 8  and showing attenuation-frequency characteristics of the respective acoustic wave filters of Example 2 and Comparative Example 1. 
         FIG. 10  is a circuit diagram of a duplexer including an acoustic wave filter according to a second preferred embodiment of the present invention. 
         FIG. 11  is a circuit diagram of a duplexer including an acoustic wave filter according to a third preferred embodiment of the present invention. 
         FIG. 12A  to  FIG. 12D  are partial front sectional views for explaining modified examples of electrode structure of the second acoustic wave resonator. 
         FIG. 13  is a plan view illustrating an IDT electrode of a second acoustic wave resonator used in an acoustic wave filter according to a fourth preferred embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, the present invention will be clarified by describing preferred embodiments of the present invention with reference to the accompanying drawings. 
     Each of the preferred embodiments described in the present specification is illustrative, and partial replacement or combination of configurations between different preferred embodiments is possible. 
       FIG. 1  is a circuit diagram of an acoustic wave filter according to a first preferred embodiment of the present invention. An acoustic wave filter  1  is, for example, a ladder filter including a plurality of acoustic wave resonators. In the acoustic wave filter  1 , a plurality of series arm resonators S 1 , S 2 - 1 , S 2 - 2 , S 3 , and S 4  are provided in a series arm connecting an input terminal  2  and an output terminal  3 . Further, a plurality of parallel arms connecting the series arm and ground potential is provided. In the respective parallel arms, parallel arm resonators P 1 , P 2 , and P 3  are provided. 
     Each of the series arm resonators S 1 , S 2 - 1 , S 2 - 2 , S 3 , S 4  and the parallel arm resonators P 1  to P 3  is defined by an acoustic wave resonator. 
     In the acoustic wave filter  1 , the plurality of acoustic wave resonators include a first acoustic wave resonator and a second acoustic wave resonator described below. The plurality of acoustic wave resonators may include an acoustic wave resonator having a structure different from the structure of the first acoustic wave resonator and the structure of the second acoustic wave resonator. 
     The first and second acoustic wave resonators have a structure to produce a piston mode and to reduce or prevent transverse mode ripples. The acoustic wave resonator includes a piezoelectric substrate and an IDT electrode on the piezoelectric substrate. In the present specification, a region where first electrode fingers and second electrode fingers of the IDT electrode overlap each other in an acoustic wave propagation direction is referred to as an intersecting region. The intersecting region includes a central region located at a center or approximate center in a direction in which the first and second electrode fingers extend, and first and second edge regions on respective outer side portions of the central region in the direction in which the first and second electrode fingers extend. In the first and second acoustic wave resonators, an acoustic velocity in the first and second edge regions is lower than an acoustic velocity in the central region. Thus, the piston mode is produced, and the transverse mode ripples are reduced or prevented. 
     In order to achieve an acoustic velocity difference between the acoustic velocity in the central region and the acoustic velocity in the first and second edge regions, the first and second acoustic wave resonators have structures as described below. 
     In the first acoustic wave resonator, a width of each of the first and second electrode fingers in the first and second edge regions is larger than a width of each of the first and second electrode fingers in the central region. That is, the first and second edge regions are widened portions. In a preferred embodiment of the present invention, it is sufficient that at least one of the width of the first electrode fingers and the width of the second electrode fingers in the first and second edge regions is larger than at least one of the width of the first electrode fingers and the width of the second electrode fingers in the central region. 
     On the other hand, the second acoustic wave resonator includes, so that the acoustic velocity in the first and second edge regions is lower than the acoustic velocity in the central region, at least one of a configuration in which an acoustic velocity reducing film is laminated in the first and second edge regions and a configuration in which an acoustic velocity increasing film that increases acoustic velocity is laminated on the central region. 
     As described above, the first acoustic wave resonator and the second acoustic wave resonator are different from each other in the configuration to achieve the acoustic velocity difference between the acoustic velocity in the first and second edge regions and the acoustic velocity in the central region. This will be described in more detail below. 
       FIG. 2A  is a schematic plan view illustrating an electrode structure of the acoustic wave resonator of the acoustic wave filter of the first preferred embodiment, and  FIG. 2B  is a front sectional view thereof. The series arm resonators S 1 , S 2 - 1 , S 2 - 2 , S 3 , and S 4  and the parallel arm resonators P 1 , P 2 , and P 3  described above all have such a structure. 
     As illustrated in  FIG. 2A , an acoustic wave resonator  4  includes an IDT electrode  5  and reflectors  6  and  7 . Thus, a one-port acoustic wave resonator is configured. 
     The IDT electrode  5  includes a plurality of first electrode fingers  5   a  and a plurality of second electrode fingers  5   b . The plurality of first electrode fingers  5   a  and the plurality of second electrode fingers  5   b  are interdigitated with each other. A direction orthogonal or substantially orthogonal to a direction in which the first electrode fingers  5   a  and the second electrode fingers  5   b  extend is the acoustic wave propagation direction. When viewed in the acoustic wave propagation direction, a region where the first electrode fingers  5   a  and the second electrode fingers  5   b  overlap each other is the intersecting region. 
     As illustrated in  FIG. 2B , in the acoustic wave resonator  4 , the IDT electrode  5  and the reflectors  6  and  7  are provided on a piezoelectric substrate  8 . Here, the piezoelectric substrate  8  is not particularly limited, but is, for example, a laminated substrate including a support substrate  8   a , a high acoustic velocity material layer  8   b , a low acoustic velocity film  8   c , and a piezoelectric film  8   d . However, the piezoelectric substrate  8  may be, for example, a single piezoelectric substrate made of LiNbO 3  or the like. 
     In the present preferred embodiment, the piezoelectric film  8   d  is made of, for example, LiTaO 3 . The support substrate  8   a  is made of an appropriate insulating material or semiconductor material such as, for example, Si or alumina. In the present preferred embodiment, the support substrate  8   a  is made of, for example, Si. 
     The high acoustic velocity material layer  8   b  is made of a high acoustic velocity material. Here, the high acoustic velocity material refers to a material in which acoustic velocity of a bulk wave propagating therethrough is higher than acoustic velocity of an acoustic wave propagating through the piezoelectric film  8   d . As the high acoustic velocity material, various materials can be used such as, for example, aluminum oxide, silicon carbide, silicon nitride, silicon oxynitride, silicon, sapphire, lithium tantalate, lithium niobate, quartz, alumina, zirconia, cordierite, mullite, steatite, forsterite, magnesia, a DLC (diamond-like carbon) film, or diamond, a medium including the above material as a main component, or a medium including a mixture of the above materials as a main component. 
     The low acoustic velocity film  8   c  is made of a low acoustic velocity material. Here, the low acoustic velocity material refers to a material in which acoustic velocity of a bulk wave propagating therethrough is lower than acoustic velocity of a bulk wave propagating through the piezoelectric film  8   d . As the low acoustic velocity material, various materials can be used such as, for example, silicon oxide, glass, silicon oxynitride, tantalum oxide, or a compound obtained by adding fluorine, carbon, boron, hydrogen, or a silanol group to silicon oxide, or a medium including the above material as a main component. 
     By using the piezoelectric substrate  8  made of the composite substrate described above, a Q factor can be increased. 
     Although the piezoelectric substrate  8  including the high acoustic velocity material layer  8   b  is used in  FIG. 2B , a support substrate made of a high acoustic velocity material may be used instead of the high acoustic velocity material layer  8   b  and the support substrate  8   a . That is, the support substrate  8   a  and the high acoustic velocity material layer  8   b  may be integrally made of a high acoustic velocity material. 
     Further, the low acoustic velocity film  8   c  need not be provided. That is, the piezoelectric film  8   d  may be directly laminated on the high acoustic velocity material layer  8   b.    
     As described above, the first acoustic wave resonator and the second acoustic wave resonator are used in the present invention. 
     In the acoustic wave filter  1  according to the first preferred embodiment, the series arm resonator S 3  is defined by the first acoustic wave resonator. The rest of the acoustic wave resonators, that is, the series arm resonators S 1 , S 2 - 1 , S 2 - 2 , and S 4  and the parallel arm resonators P 1  to P 3  are defined by the second acoustic wave resonators. 
     An acoustic wave resonator described below was prepared as the first acoustic wave resonator. 
     The piezoelectric substrate  8  has laminated structure including, on a Si substrate, a silicon nitride film as the high acoustic velocity material layer  8   b , a silicon oxide film as the low acoustic velocity film  8   c , and a LiTaO 3  film as the piezoelectric film  8   d , and thicknesses were set such that, for example, the silicon nitride film=about 900 nm, the silicon oxide film=about 673 nm, and the LiTaO 3  film=about 600 nm. The IDT electrode  5  and the reflectors  6  and  7  include a main electrode layer made of, for example Al. A thickness of an Al film was, for example, about 145 nm. 
     The electrode structure  11  of the IDT electrode in the first acoustic wave resonator is illustrated as a plan view in  FIG. 3 . In the IDT electrode  5 , an intersecting region D includes a central region F and first and second edge regions E 1  and E 2 . In the first and second edge regions E 1  and E 2 , the first electrode fingers  5   a  and the second electrode fingers  5   b  include widened portions  5   a   1 ,  5   a   2 ,  5   b   1 , and  5   b   2 . A width of each of the widened portions  5   a   1 ,  5   a   2 ,  5   b   1 , and  5   b   2  is larger than a width in the central region F. Here, the width refers to a dimension along the acoustic wave propagation direction in the first and second electrode fingers  5   a  and  5   b.    
     In the first acoustic wave resonator, a wavelength λ determined by an electrode finger pitch in the central region of the IDT electrode was set to, for example, about 2 μm. Further, a duty in the central region was set to, for example, about 0.45. A duty in the first and second edge regions was set to, for example, about 0.73. 
     In the first acoustic wave resonator, the duty of the central region F is, for example, about 0.45, and in the second acoustic wave resonator, duty of the central region F is, for example, about 0.5. In the first acoustic wave resonator and the second acoustic wave resonator, capacitance is adjusted by reducing an interdigitation width. 
       FIG. 4  is a plan view for explaining the electrode structure  21  of an IDT electrode of the second acoustic wave resonator. The second acoustic wave resonator was configured similarly to the first acoustic wave resonator except that the electrode structure of the IDT electrode was different. As illustrated in  FIG. 4 , in an IDT electrode  5 A, acoustic velocity reducing films  22   b  and  22   a  are laminated in the first and second edge regions E 1  and E 2 , respectively. The acoustic velocity reducing films  22   b  and  22   a  are provided in the first and second edge regions E 1  and E 2 , respectively, so as to extend along the acoustic wave propagation direction. The acoustic velocity reducing films  22   a  and  22   b  here are made of, for example, tantalum pentoxide. The acoustic velocity reducing films  22   a  and  22   b  may be made of other insulating materials as long as the materials add mass and reduce acoustic velocity. Further, when provided so as not to short-circuit the first and second electrode fingers  5   a  and  5   b , the acoustic velocity reducing films  22   a  and  22   b  may be made of, for example, metal or the like. 
     In the second acoustic wave resonator, a wavelength of the IDT electrode was set to, for example, about 2 μm, and duty in the central region and the first and second edge regions was set to, for example, about 0.50. 
     Resonance characteristics of the first acoustic wave resonator and the second acoustic wave resonator will be described with reference to  FIGS. 5A and 5B . 
     In  FIG. 5A , a solid line indicates the resonance characteristics of the first acoustic wave resonator, and a broken line indicates the resonance characteristics of the second acoustic wave resonator.  FIG. 5B  is an enlarged diagram illustrating a portion indicated by a circle A in  FIG. 5A . 
     Compared to the first acoustic wave resonator, in the second acoustic wave resonator, it is not necessary to provide a widened portion in the first or second electrode fingers. Thus, even when the duty in the central region is increased, it is easy to increase an acoustic velocity difference between the first and second edge regions and the central region. When the duty in the central region is increased, capacitance between the first electrode fingers and the second electrode fingers is increased. Thus, a reduction in size of the acoustic wave resonator can be achieved. Compared to this, in the first acoustic wave resonator, when the duty in the central region is increased, it is difficult to increase the acoustic velocity difference between the first and second edge regions and the central region. Thus, the second acoustic wave resonator can be designed so as to make duty in the central region larger while maintaining the acoustic velocity difference between the first and second edge regions and the central region. Thus, the second acoustic wave resonator is more likely to achieve a reduction in size of the acoustic wave resonator and a reduction in size of the acoustic wave filter including the acoustic wave resonator while reducing or preventing transverse mode ripples. 
     However, as shown in  FIGS. 5A and 5B , a fractional bandwidth of the second acoustic wave resonator is larger compared to that of the first acoustic wave resonator. Thus, when an acoustic wave filter configured only with the second acoustic wave resonator, for example, a ladder filter is configured, there was a problem in that steepness of filter characteristics was insufficient. In order to improve the steepness, it is conceivable to weight the IDT electrode. However, in this case, there is a problem in that bandpass characteristics deteriorate. 
     As shown in  FIG. 5A , the fractional bandwidth of the second acoustic wave resonator is about 3.9%, whereas the fractional bandwidth of the first acoustic wave resonator is about 3.8%. That is, the second acoustic wave resonator has the larger fractional bandwidth. 
     When the duty in the central region is decreased, the fractional bandwidth is generally increased. When the duty in the central region is increased, the fractional bandwidth is generally decreased. In the first acoustic wave resonator, although the duty in the central region is smaller compared to the second acoustic wave resonator, the fractional bandwidth is smaller. That is, the first acoustic wave resonator has a disadvantage for reduction or prevention of the transverse mode ripples compared to the second acoustic wave resonator, but the fractional bandwidth is easily made smaller compared to the second acoustic wave resonator. Thus, by using the first acoustic wave resonator, the fractional bandwidth can be narrowed and the steepness of the filter characteristics can be increased. On the other hand, by using the second acoustic wave resonator, the transverse mode ripples can be effectively reduced or prevented even when a reduction in size of the acoustic wave filter is achieved. 
     That is, since the acoustic wave filter of the present preferred embodiment includes the first acoustic wave resonator and the second acoustic wave resonator, it is possible to reduce or prevent the transverse mode ripples and improve in steepness of the filter characteristics, even when a reduction in size is achieved. This will be described based on specific examples. 
     As described above, preferably, the duty in the central region of the IDT electrode in the second acoustic wave resonator is larger than the duty in the central region of the IDT electrode in the first acoustic wave resonator. Thus, a reduction in size can be effectively achieved. 
     Example 1 and Comparative Example 1 
     Acoustic wave filters of Example 1 of the acoustic wave filter  1  illustrated in  FIG. 1  and Comparative Example 1 for comparison were prepared. A configuration of the piezoelectric substrate  8  in Example 1 was the same as or similar to the first and second acoustic wave resonators described above. In Example 1, an acoustic wave filter for Band25Tx was provided. A center frequency is about 1822.5 MHz. Design parameters of the series arm resonators S 1 , S 2 - 1 , S 2 - 2 , S 3 , and S 4  and the parallel arm resonators P 1  to P 3  were set as shown in Table 1 below. 
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 S4 
                 P3 
                 S3 
                 P2 
                 S2-2 
                 S2-1 
                 P1 
                 S1 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 Number of Pairs of 
                 Pairs 
                 144 
                 180.5 
                 163.5 
                 131 
                 120 
                 120 
                 119.5 
                 130 
               
               
                 Electrode Fingers of 
               
               
                 IDT Electrode 
               
               
                 Number of Electrode 
                 Number 
                 21 
                 21 
                 21 
                 21 
                 21 
                 21 
                 21 
                 21 
               
               
                 Fingers of Reflector 
               
               
                 Interdigitation Width 
                 μm 
                 24.3 
                 30.2 
                 36.4 
                 51.4 
                 24.1 
                 24.1 
                 57.3 
                 34.9 
               
               
                 Duty 
                   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                 Wavelength 
                 μm 
                 2.013 
                 2.116 
                 2.030 
                 2.090 
                 2.001 
                 2.001 
                 2.088 
                 2.005 
               
               
                   
               
            
           
         
       
     
     In the acoustic wave filter of Example 1, the series arm resonator S 3  is the first acoustic wave resonator, and the rest of the series arm resonators S 1 , S 2 - 1 , S 2 - 2 , S 4  and the parallel arm resonators P 1  to P 3  are defined by the second acoustic wave resonators. The structure of an IDT electrode of each of first and second acoustic wave resonators is the same as or similar to that of the IDT electrode  5  of each of the first and second acoustic wave resonators described above. 
     The series arm resonator S 3  is an acoustic wave resonator having the lowest anti-resonant frequency of the plurality of series arm resonators S 1 , S 2 - 1 , S 2 - 2 , S 3 , and S 4 . 
     As Comparative Example 1, the acoustic wave filter of Comparative Example 1 was prepared similarly to Example 1, except that the series arm resonator S 3  was also the second acoustic wave resonator. 
     In  FIG. 6 , a solid line indicates attenuation-frequency characteristics of the acoustic wave filter of Example 1, and a broken line indicates attenuation-frequency characteristics of the acoustic wave filter of the Comparative Example 1. Further,  FIG. 7  is an enlarged portion showing a portion indicated with a scale of the attenuation on the left side of a portion indicated by the arrow B in  FIG. 6 . 
     As is clear from  FIG. 6  and  FIG. 7 , according to the acoustic wave filter of Example 1, steepness of filter characteristics on a high-frequency side of a pass band is increased compared to the acoustic wave filter of Comparative Example 1. To be more specific, steepness from about 3 dB to about dB, which is a frequency range in which the attenuation increases from about 3 dB to about 35 dB, was about 9.3 MHz in Comparative Example 1, whereas about 9.1 MHz in Example 1. 
     Thus, in the ladder filter of Example 1, since the series arm resonator S 3  is the first acoustic wave resonator, the steepness of the filter characteristics can be effectively increased as described above. Further, since the first and second acoustic wave resonators are provided, transverse mode ripples can be reduced or prevented by producing a piston mode. Thus, it can be seen in the acoustic wave filter of Example 1 that it is possible to achieve the reduction or prevention of the transverse mode ripples and the steepness of the filter characteristics, even when a reduction in size is achieved. 
     Example 2 and Comparative Example 1 
     As Example 2 of a preferred embodiment of the present invention, a ladder filter of Example 2 was prepared similarly to the ladder filter of Comparative Example 1, except that only the parallel arm resonator P 1  was a first acoustic wave resonator. The parallel arm resonator P 1  of the ladder filter of Example 2 is defined by the first acoustic wave resonator as described above, and the configuration of the first acoustic wave resonator was similar to that of the first acoustic wave resonator illustrated in  FIGS. 5A and 5B  described above. 
       FIG. 8  is a diagram showing attenuation-frequency characteristics of the respective acoustic wave filters of Example 2 and Comparative Example 1.  FIG. 9  is an enlarged diagram showing a portion indicated with a scale of the attenuation on the left side of a portion indicated by the arrow C in  FIG. 8 . A solid line indicates the characteristics of Example 2, and a broken line indicates the characteristics of Comparative Example 1. 
     As is clear from  FIG. 8  and  FIG. 9 , in the acoustic wave filter of Example 2, steepness on a low-frequency side of a pass band is increased compared to Comparative Example 1. To be more specific, steepness from about 3 dB to about 20 dB is about 15.2 MHz in Comparative Example 1, whereas about 15.0 MHz in Example 2. The steepness from about 3 dB to about 20 dB is a frequency difference between a frequency at which the attenuation is about 3 dB and a frequency at which the attenuation is about 20 dB. 
     As shown in Table 1, the parallel arm resonator P 1  is an acoustic wave resonator having the highest resonant frequency, of the plurality of parallel arm resonators P 1  to P 3 . 
     In the acoustic wave filter of Example 2, since the parallel arm resonator P 1  is the first acoustic wave resonator as described above, the steepness of the filter characteristics can be effectively increased. Thus, also in Example 2, even when a reduction in size is achieved, reduction or prevention of transverse mode ripples can be effectively achieved, and the steepness of the filter characteristics can be increased. 
     As in Example 1, a series arm resonator having the lowest anti-resonant frequency of a plurality of series arm resonators having anti-resonant frequencies higher than a center frequency is preferably defined by the first acoustic wave resonator. This is because a series arm resonator having the lowest anti-resonant frequency has the largest influence on steepness on a high-frequency side of a pass band. However, at least one acoustic wave resonator among the other series arm resonators S 1 , S 2 - 1 , S 2 - 2 , and S 4  may be the first acoustic wave resonator. Thus, the steepness on the high-frequency side of the pass band can be further increased. More preferably, when all of the series arm resonators are defined by the first acoustic wave resonators, the steepness on the high-frequency side of the pass band can be further increased. 
     On the other hand, as described in Example 2, the parallel arm resonator P 1  having the highest resonant frequency of the plurality of parallel arm resonators having resonant frequencies lower than the center frequency is preferably defined by the first acoustic wave resonator. This is because the parallel arm resonator having the highest resonant frequency has the largest influence on the steepness on the low-frequency side of the pass band. However, at least one of the other parallel arm resonators P 2  and P 3  may be the first acoustic wave resonator. In this case, the steepness on the low-frequency side of the pass band can be further increased. 
     In an acoustic wave filter including a plurality of series arm resonators and a plurality of parallel arm resonators, the plurality of series arm resonators may include a first acoustic wave resonator and a second acoustic wave resonator, and the plurality of parallel arm resonators may include a first acoustic wave resonator and a second acoustic wave resonator. For example, the configuration of the series arm of Example 1 and the configuration of the parallel arm of Example 2 may be provided. As described above, the arrangement of the first acoustic wave resonator and the second acoustic wave resonator in the plurality of acoustic wave resonators is not particularly limited. 
     Furthermore, the acoustic wave filter of preferred embodiments of the present invention can be applied, not limited to a ladder filter, but widely to a band-pass filter including a plurality of acoustic wave resonators. For example, preferred embodiments of the present invention may be applied to a series arm resonator and a parallel arm resonator in a band-pass filter in which a series arm resonator and/or a parallel arm resonator is electrically connected to a longitudinally coupled resonator acoustic wave filter. 
       FIG. 10  is a circuit diagram of a duplexer including an acoustic wave filter according to a second preferred embodiment of the present invention. 
     In a duplexer  31 , an acoustic wave filter  33  of the second preferred embodiment and a longitudinally coupled resonator acoustic wave filter  34  are connected to an antenna terminal  32 . The acoustic wave filter  33  is a transmission filter and is connected between a transmission terminal  36  and a common terminal  35 . The longitudinally coupled resonator acoustic wave filter  34  is a reception filter. The longitudinally coupled resonator acoustic wave filter  34  is connected between the common terminal  35  and a reception terminal  37 . In such a duplexer, when the acoustic wave filter  33  of the second preferred embodiment is used as the transmission filter, transverse mode ripples can be reduced or prevented and steepness of filter characteristics can be increased, even when a reduction in size of the transmission filter is achieved. 
     In addition, of the plurality of series arm resonators S 1  to S 4  and parallel arm resonators P 1  to P 4 , an acoustic wave resonator farthest from the antenna terminal  32  is preferably defined by the first acoustic wave resonator. The acoustic wave resonator farthest from the antenna terminal  32  is the series arm resonator S 1  of the plurality of series arm resonators S 1  to S 4  and additionally, is the parallel arm resonator P 1  of the parallel arm resonators P 1  to P 4 . At least one of the series arm resonator S 1  and the parallel arm resonator P 1  is preferably defined by the first acoustic wave resonator. Unlike the second acoustic wave resonator, an acoustic velocity reducing film is not included in the first acoustic wave resonator, and thus, polarization reversal of a piezoelectric film due to stress of an acoustic velocity reducing film is less likely to occur and electric power handling capability is high compared with the second acoustic wave resonator. Thus, by using, as the first acoustic wave resonator, the series arm resonator S 1  or the parallel arm resonator P 1  closest to the transmission terminal to which large electric power is likely to be applied and to which a load due to voltage is likely to be applied, polarization reversal of the piezoelectric film of the acoustic wave filter  33  can be made to be less likely to occur and electric power handling capability can be increased. 
     In addition, of the plurality of series arm resonators S 1  to S 4  and the parallel arm resonators P 1  to P 4 , an acoustic wave resonator closest to the antenna terminal  32  is preferably defined by the first acoustic wave resonator. The acoustic wave resonator closest to the antenna terminal  32  is the series arm resonator S 4  of the plurality of series arm resonators S 1  to S 4 . The series arm resonator S 4  preferably is defined by the first acoustic wave resonator. When a reduction in size is achieved by increasing duty of the second acoustic wave resonator, there is a problem in that linearity of the duplexer  31  is deteriorated. However, the deterioration of the linearity of the duplexer  31  can be reduced or prevented by using, as the first acoustic wave resonator, the acoustic wave resonator which is closest to the antenna terminal and the linearity of which is most likely to be deteriorated and by setting the duty to be smaller than that of the second acoustic wave resonator. 
     The acoustic wave filter  33  may be used as a reception filter. In this case, of the plurality of series arm resonators S 1  to S 4  and parallel arm resonators P 1  to P 4 , an acoustic wave resonator farthest from the antenna terminal  32  is preferably the first acoustic wave resonator. That is, at least one of the series arm resonator S 1  and the parallel arm resonator P 1  is preferably defined by the first acoustic wave resonator. Unlike the second acoustic wave resonator, an acoustic velocity reducing film is not included in the first acoustic wave resonator, and thus, polarization reversal of a piezoelectric film due to stress of an acoustic velocity reducing film is less likely to occur compared with the second acoustic wave resonator. Thus, by using, as the first acoustic wave resonator, the series arm resonator S 1  or the parallel arm resonator P 1  closest to the reception terminal to which a load due to voltage is likely to be applied, polarization reversal of the piezoelectric film of the acoustic wave filter  33  can be made to be less likely to occur. 
       FIG. 11  is a circuit diagram of a duplexer including an acoustic wave filter according to a third preferred embodiment of the present invention. 
     In a duplexer  41 , a phase shift circuit  42  is connected between the antenna terminal  32  and the acoustic wave filter  33 . In the remaining circuit configurations, the duplexer  41  is the same as or similar to the duplexer  31 . In the duplexer  41  including such a phase shift circuit  42 , the acoustic wave filter of the present preferred embodiment of the present invention may be used as the acoustic wave filter  33 . 
       FIGS. 12A to 12D  are partial front sectional views for explaining modified examples of electrode structure of the second acoustic wave resonator.  FIG. 12A  illustrates a section along an acoustic wave propagation direction and passing through the second edge region E 2  of the acoustic wave resonator illustrated in  FIG. 4 . As described above, the acoustic velocity reducing film  22   a  is provided so as to extend in the acoustic wave propagation direction in the second edge region. 
     As illustrated in  FIG. 12B , an acoustic velocity reducing film  23   a  may be provided between the first and second electrode fingers  5   a  and  5   b  and the piezoelectric film  8   d  in the first and second edge regions. Alternatively, as illustrated in  FIG. 12C , an acoustic velocity reducing film  24   a  may be laminated on the first electrode fingers  5   a  and the second electrode fingers  5   b . In this case, a metallic material or the like may be used as the acoustic velocity reducing film  24   a.    
     Further, as illustrated in  FIG. 12D , an acoustic velocity reducing film  25   a  may be laminated between the first and second electrode fingers  5   a  and  5   b  and the piezoelectric film  8   d . In this case, a metallic material or the like may be used as the acoustic velocity reducing film  25   a.    
     As illustrated in  FIGS. 12A and 12C , when, for example, silicon oxide is provided on the first and second electrode fingers  5   a  and  5   b , silicon oxide defines and functions as an acoustic velocity reducing film. On the other hand, as illustrated in  FIGS. 12B and 12D , when, for example, silicon oxide is provided under the first and second electrode fingers  5   a  and  5   b , silicon oxide defines and functions as an acoustic velocity increasing film. 
     As described above, the acoustic velocity reducing film in the second acoustic wave resonator can be provided in the first and second edge regions in various configurations, and the configuration is not particularly limited. 
     Further,  FIG. 13  is a plan view illustrating electrode structure  51  of a second acoustic wave resonator used in an acoustic wave filter according to a fourth preferred embodiment of the present invention. Here, an acoustic velocity increasing film is laminated so as to cover the first and second electrode fingers  5   a  and  5   b  in the central region F of the intersecting region D. By providing the acoustic velocity increasing film  52  in the central region F, an acoustic velocity in the central region F can be increased. As described above, an acoustic velocity increasing film may be provided in the central region F. In this case, the acoustic velocity increasing film  52  may be laminated between the first and second electrode fingers  5   a  and  5   b  and the piezoelectric film  8   d.    
     Examples of a material capable of defining and functioning as the acoustic velocity increasing film  52  above include Al 2 O 3 , AlN, SiN, SiO x , and the like. 
     Additionally, the acoustic velocity increasing film  52  described above and an acoustic velocity reducing film may be used in combination. That is, the acoustic velocity reducing film may be provided in the first and second edge regions, and the acoustic velocity increasing film  52  may be provided in the central region. 
     The first acoustic wave resonator and the second acoustic wave resonator described above may be provided on the same piezoelectric substrate. Alternatively, a piezoelectric substrate of the first acoustic wave resonator and a piezoelectric substrate of the second acoustic wave resonator may be different piezoelectric substrates. 
     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.