Abstract:
A method of manufacturing a ladder filter including first and second resonators includes: forming a piezoelectric film on an entire surface of a substrate that has respective lower electrodes of the first and second resonator formed thereon, an conductive film on the piezoelectric film, and a second film on the conductive film; forming a pattern of the second film in a prescribed region in the second area; forming a first film on an entire surface of the substrate; etching the first film, forming a pattern of the first film, the second film and the conductive film in the second area, and forming a pattern of the first film and the conductive film in the first area, to form respective upper electrodes from the conductor film; and thereafter, etching the piezoelectric film to form respective patterns of the piezoelectric film in the first and second areas, respectively.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This is a divisional application, which claims the benefit of U.S. patent application Ser. No. 11/907,704, filed in Oct. 16, 2007, now abandoned which claims the benefit of Japanese Patent Application No. 2006-282290, filed Oct. 17, 2006. The disclosures of the prior applications are hereby incorporated herein in their entirety by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to ladder type filters, and more particularly, to a ladder type filter using a piezoelectric thin-film resonator. 
     2. Description of the Related Art 
     There has been an increasing demand for compact and lightweight resonators and filters using such resonators due to rapid spreading of wireless equipment such as cellular phones. In the past, dielectric filters and surface acoustic wave (SAW) filters were used. Recently, there has been a considerable activity in the research and development of a piezoelectric thin-film resonator and a filter using such a resonator. 
     The piezoelectric thin-film resonators may be categorized into an FBAR (Film Bulk Acoustic Resonator) type and an SMR (Solidly Mounted Resonator) type. The FBAR has a primary structure composed of an upper electrode, a piezoelectric film and a lower electrode, and a hollow space provided below the lower electrode and located within an overlapping region (resonance portion) in which the upper and lower electrodes overlap with each other across the piezoelectric film. The hollow space may be defined between the lower electrode and a silicon substrate by wet-etching a sacrificed layer on a main surface of the silicon substrate. The hollow space may also be formed by wet- or dry-etching the substrate from the backside thereof. The SMR employs an acoustic reflection film instead of the hollow space, in which a first film having a relatively high acoustic impedance and a second film having a relative low acoustic impedance are alternately laminated with a film thickness of λ/4 where λ is the wavelength of an acoustic wave of the resonator. 
     The upper and lower electrodes may be made of aluminum (Al), copper (Cu), molybdenum (Mo), tungsten (W), tantalum (Ta), platinum (Pt), ruthenium (Ru), rhodium (Rh), iridium (Ir) or the like. The piezoelectric thin film may be made of aluminum nitride (AlN), zinc oxide (ZnO), lead zirconium titanate (PZT), lead titanate (PbTiO 3 ) or the like. The substrate may be made of glass other than silicon. 
     The operation principles of the piezoelectric thin-film resonators will now be described. The following description is exemplarily directed to the FBAR. A voltage of a high frequency is applied between the upper electrode and the lower electrode. An acoustic wave resulting from the inverse piezoelectric effect is excited within the piezoelectric film in the resonance portion. A distortion of the piezoelectric film caused by the acoustic wave is converted into an electric signal developing between the upper electrode and the lower electrode due to the piezoelectric effect. The acoustic wave is reflected by an interface between the air and the upper electrode and another interface between the air and the lower electrode. Thus, the vertical vibration having major displacement is caused in the thickness direction of the piezoelectric film. The resonant phenomenon of the vertical vibration is utilized to form a resonator having a desired frequency response and a filter using such a resonator. 
     The resonance phenomenon is specifically caused at a frequency at which the total thickness H of the lower electrode, the piezoelectric film and the upper electrode (including a film added to the upper electrode) is equal to an integer multiple (n times) of half the wavelength λ (λ/2) of the acoustic wave excited. That is, the resonance phenomenon is caused at the frequency at which H=nλ/2. Assuming that V denotes the propagation velocity of the acoustic wave that depends on the material used to form the piezoelectric film, the resonance frequency F is equal to nV/(2H). This shows that the resonance frequency F can be controlled by the total thickness H of the film laminate. 
     A ladder filter is a typical example of the piezoelectric thin-film resonator. The ladder filter is composed of series resonators arranged between an input terminal and an output terminal and parallel resonators, and functions as a bandpass filter.  FIG. 1A  shows an equivalent circuit of a series resonator S, and  FIG. 1B  shows an equivalent circuit of a parallel resonator P.  FIG. 1C  shows transmission characteristics of the series resonator S and the parallel resonator P. The series resonator S has a maximum value at a resonance frequency frs and a minimum value at an anti-resonance frequency fas. The parallel resonator P has a minimum value at a resonance frequency frp and a maximum value at an anti-resonance frequency fap.  FIG. 2A  shows an equivalent circuit of a ladder filter composed of a single stage formed by one series resonator S and one parallel resonator P.  FIG. 2B  shows a bandpass characteristic of the ladder filter shown in  FIG. 2A . The bandpass filter can be configured by setting the resonance frequency frs of the series resonator S and the anti-resonance frequency fap of the parallel resonator P approximately equal to each other. The anti-resonance frequency fas of the series resonator S corresponds to the frequency of an attenuation pole on the high-frequency side of the pass band, and the resonance frequency frp of the parallel resonator P corresponds to the frequency of an attenuation pole on the low-frequency side. 
     In order to obtain a desired pass band of the ladder filter, it is required that the resonance frequencies of the series resonator S and the parallel resonator P are designed to have a slight difference (normally, a few %). In a case where the series resonator S and the parallel resonator P are formed on an identical substrate, a frequency adjustment step (Δf adjustment step) is needed to make the series resonator S and the parallel resonator P. The center frequency of the pass band can be adjusted by adjusting the resonance frequencies of both the series resonator S and the parallel resonator P (f 0  adjustment step). 
     Japanese Patent Application Publication No. 2005-286945 discloses a technique in which a first adjustment film and a second adjustment film are stacked on an upper electrode as a frequency adjustment film, and the first adjustment films on the series resonator S and the parallel resonator P are made different from each other in thickness. The Δf adjustment step is implemented by setting the first adjustment films on the series resonator S and the parallel resonator P different from each other in thickness, and the f 0  frequency adjustment is implemented by adjusting the thickness of the second adjustment film of each of the series resonator S and the parallel resonator P. Thus, the Δf adjustment step and the f 0  adjustment step can be performed separately. 
     Japanese Patent Application Publication No. 2006-128993 discloses that an edge of a piezoelectric film is located further in than an edge of a region in which the upper and lower electrodes overlap with each other. With this structure, it is possible to prevent the acoustic wave from leaking outwards from the resonance portion. This is called lateral leakage of acoustic wave. The structure may be formed by wet etching the piezoelectric film. 
     As has been described, the technique disclosed in Japanese Patent Application Publication No. 2005-286945 employs the Δf adjustment step of causing the first adjustment films of the series resonator and the parallel resonator to have different thickness values. For example, the first adjustment film of the series resonator is etched and thinned. However, it is very difficult to reliably stop etching when the first adjustment film has been etched halfway. It is thus very difficult to reliably set the difference between the resonance frequency of the series resonator and that of the parallel resonator. 
     SUMMARY OF THE INVENTION 
     The present invention has been made in view of the above circumstances and provides a ladder filter capable of reliably setting the difference between the resonance frequency of the series resonator and that of the parallel resonator. 
     According to an aspect of the present invention, there is provided a ladder filter including: a series resonator having a first film laminate in which an upper electrode and a lower electrode face each other across a piezoelectric film, and a first film provided on the first film laminate; and a parallel resonator having a second film laminate having a structure similar to that of the first film laminate, a second film provided on the second film laminate, and another first film identical to the first film. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Preferred embodiments of the present invention will now be described with reference to the accompanying figures, in which: 
         FIG. 1A  is an equivalent circuit diagram of a series resonator; 
         FIG. 1B  is an equivalent circuit diagram of a parallel resonator; 
         FIG. 1C  is a graph of frequency characteristics of the series resonator and the parallel resonator; 
         FIG. 2A  is an equivalent circuit diagram of a ladder filter of a single stage; 
         FIG. 2B  is a bandpass characteristic of the ladder filter; 
         FIG. 3  is an equivalent circuit diagram of a ladder filter in accordance with a first embodiment of the present invention; 
         FIG. 4A  is composed of a part (a) that shows a plan view of a series resonator employed in the first embodiment, and a part (b) that shows a cross-sectional view taken along a line A-A in part (a); 
         FIG. 4B  is a cross-sectional view of a parallel resonator taken along line A-A; 
         FIGS. 5A through 5F  are cross-sectional views of a method for manufacturing the series and parallel resonators; 
         FIGS. 6A through 6F  are cross-sectional views of a subsequent process of the method; 
         FIGS. 7A ,  7 B and  7 C are plan view of a region  50  and its vicinity; 
         FIG. 8  is a cross-sectional view of a parallel resonator in accordance with a first comparative example; 
         FIG. 9A  is a Smith chart of characteristics of resonators of the first comparative example; 
         FIG. 9B  is a Smith chart of characteristics of resonators of the first embodiment; 
         FIG. 10A  is a graph of a bandpass characteristic of the first comparative example; 
         FIG. 10B  is a graph of a bandpass characteristic of the first embodiment; 
         FIG. 11  is composed of a part (a) that shows a plan view of a parallel resonator in accordance with a second embodiment, and a part (b) that shows a cross-sectional view taken along a line A-A shown in part (a); and 
         FIG. 12  is a plan view of a parallel resonator in accordance with a third embodiment. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     A description will now be given of preferred embodiments of the present invention. 
     First Embodiment 
       FIG. 3  is a circuit diagram of a ladder filter in accordance with a first embodiment of the present invention. Series resonators S 1 , S 2  and S 3  are connected in series between an input terminal Tin and an output terminal Tout. A parallel resonator P 1  is connected to a node between the series resonators S 1  and S 2  and ground. A parallel resonator P 2  is connected to a node between the series resonators S 2  and S 3  and ground. The series resonators S (S denotes any of S 1  through S 3 ) and the parallel resonators P (P denotes any of P 1  and P 2 ) have different structures, as will be described later. 
     The structure of the series resonators S will be described below. A part (a) of  FIG. 4A  shows a plan view of the series resonator S, and a part (b) shows a cross-sectional view taken along a line A-A shown in part (a). A lower electrode  12  is provided on a silicon substrate  10  so as to form a hollow space  30  that is formed between the silicon substrate  10  and the lower electrode  12  and is oriented upwards. The hollow space  30  is be defined by a raised portion of the lower electrode  12  having a dome shape. Thus, the hollow space  30  may be referred to as a dome-shaped hollow space. The dome-shaped portion of the lower electrode  12  may have a gradually increasing height towards the center of the hollow space  30  from its periphery. The lower electrode  12  may have Ru/Cr (ruthenium/chromium) structure. A piezoelectric film  14  that may be made of, for example, aluminum nitride (AlN) and has the main axis in the (002) direction, is provided on the lower electrode  12 . An upper electrode  16  is provided on the piezoelectric film  14  so that an overlapping region (resonance portion  52 ) can be defined in which the upper electrode  16  overlaps with the lower electrode  12  across the piezoelectric film  14 . The upper electrode  16  may be made, for example, Ru. The lower electrode  12 , the piezoelectric film  14  and the upper electrode  16  form a film laminate  18 . A first film  22  made of Cr is provided on the upper electrode  16 . A third film  24 , which may be made of, for example, silicon oxide (SiO 2 ), is provided on the first film  22 , the substrate  10  and the piezoelectric film  14 . 
     A guide path  32  for etching a sacrificed layer, which will be described later, is provided in the lower electrode  12  so as to run in a direction B-B. An end of the guide path  32  is not covered with the piezoelectric film  14 , and apertures  34  are formed in the lower electrode  12  and are connected to the ends of the guide path  32 . An opening  36  is provided in the piezoelectric film  14  for making an electric connection with the lower electrode  12 . In the opening  36 , at least a part of an outer curved edge  42  of the piezoelectric film  14  is further in, by a distance “d”, than an outer curved edge of a region  50  in which the upper electrode  16  overlaps with the lower electrode  12  across the piezoelectric film  14 . 
     The parallel resonator P will now be described with reference to  FIG. 4B , which shows a cross-sectional view taken along the line A-A of the parallel resonator P. The parallel resonator P differs from the above-mentioned series resonator S in that a second film  20  made of, for example, titanium (Ti), is provided between the upper electrode  16  and the first film  22 . The other structures of the parallel resonator P are the same as those of the series resonator S. 
     The laminate that contributes the resonance frequency of the resonance portion  52  of the series resonator S is, from the top, SiO 2 /Cr/Ru/AlN/Ru/Cr. In contrast, the laminate that contributes the resonance frequency of the resonance portion  52  of the parallel resonator P is, from the top, SiO 2 /Cr/Ti/Ru/AlN/Ru/Cr. The parallel resonator P is provided with the second film made of Ti, and can be designed to have a different resonance frequency from that of the series resonator S. Thus, a response of the bandpass filter a shown in  FIG. 2B  can be obtained. 
     A description will now given of a method for manufacturing the series resonator S and the parallel resonator P. Referring to  FIGS. 5A and 5D , a sacrificed layer  38  made of MgO (magnesium oxide) is deposited on the silicon substrate  10  by sputtering so as to have a thickness of approximately 40 nm. Next, the sacrificed layer  38  is formed into a given shape by lithography and etching. Referring to  FIGS. 5B and 5E , the next step is to deposit a Cr film having a thickness of approximately 100 nm and a Ru film having a thickness of approximately 250 nm by sputtering. Then, the film laminate is shaped into the lower electrode  12  by the lithography and etching. Thereafter, AlN for the piezoelectric film  14  is deposited to a thickness of 1150 nm on the lower electrode  12  and the substrate  10  by sputtering. Then, a Ru film having a thickness of 250 nm for the upper electrode  16  is formed on the piezoelectric film  14  by sputtering. 
     Referring to  FIGS. 5C and 5F , a Ti film having a thickness of 115 nm for the second film  20  is formed by sputtering so as to cover the upper electrode  16 . Then, using lithography and etching, the second film  20  is etched so that it remains on the sacrificed layer  38  of the parallel resonator P and does not remain thereon in the series resonator S. In this etching, the Ti film and the Ru film are etched with a selectivity, so that the second film  20  can be etched without losing the thickness of the upper electrode  16 .  FIG. 7A  shows a positional relationship between the upper electrode  16 , the second film  20  and a region (which will become the region  50  and will be referred to as region  50  for the convenience&#39; sake) in the parallel resonator P. The second film  20  is formed so as to include the region  50 . Referring to  FIGS. 5C and 5F , a Cr film having a thickness of approximately 20 nm for the first film  22  is deposited on the upper electrode  16  and the second film  20  by sputtering. 
     Referring to  FIGS. 6A and 6D , the first film  22  is formed into a given shape by lithography and etching.  FIG. 7B  shows a positional relationship between the upper electrode  16 , the second film  20 , the first film  22  and the region  50  in the parallel resonator P. When the first film  22  is etched, the second film  20  is etched. Thus, the outer curved edges of the upper electrode  16 , the first film  22  and the second film  20  are aligned with each other on the right side of the region  50 . In contrast, the second film  20  is greater than the region  50  on the left side of the region  50 . The outer curved edges of the upper electrode  16  and the first film  22  are aligned with each other. 
     Referring to  FIGS. 6B and 6E , the piezoelectric film  14  is etched by lithography and etching. This etching may be wet etching using a phosphoric acid. The piezoelectric film  14  is over-etched, so that the outer curved edge of the piezoelectric film  14  can be further in than the region  50 . After the piezoelectric film  14  of AlN is etched, the third film  24  made of SiO 2  is formed on the first film  22 , the substrate  10  and the piezoelectric film  14 .  FIG. 7C  shows a positional relationship between the lower electrode  12 , the upper electrode  16 , the second film  20 , the first film  22  and the region  50  in the parallel resonator P. The outer curved edge of the piezoelectric film  14  is further in than the region  50  on the right side of the region  50 . Thus, the outer curved edge of the resonance portion  52  is further in than the outer edge of the region  50  on the right side of the region  50 . In contrast, the outer curved edge of the resonance portion  52  coincides with the outer curved edge of the region  50  on the left side of the region  50 . 
     Referring to  FIGS. 6C and 6F , etchant for etching the sacrificed layer  38  is applied to the guide path  32  (see  FIG. 4A ) through the apertures  34 , and the sacrificed layer  38  is removed. The stress of the film laminate  18  composed of the lower electrode  12 , the piezoelectric film  14  and the upper electrode  16  is set so as to be compressive stress by adjusting the sputtering conditions for the respective films. Thus, when etching of the sacrificed layer  38  is finished, the film laminate is raised so that the dome-shaped hollow space  30  oriented towards the film laminate  18  can be formed between the lower electrode  12  and the substrate  10 . The compressive stress may be set in the range of −150 MPa to −300 MPa. Through the above process, the series resonator S and the parallel resonator P can be completed. 
     The first embodiment and a first comparative example are compared with each other.  FIG. 8  is a cross-sectional view of a ladder filter in accordance with the first comparative example. As compared to  FIG. 4B , a second film  20   a  of the first comparative example is provided between the first film  22  and the third film  24 . The first comparative example may be fabricated by forming the second film  20  and the first film in the reverse sequence in  FIGS. 5C and 5F . That is, in  FIGS. 6B and 6E , when the piezoelectric film  14  is etched, the second film  20  is merely protected by photoresist. 
       FIGS. 9A and 9B  are Smith charts of the first comparative example and the first embodiment, respectively, in which the S 11  characteristics of three parallel resonators in a wafer are shown. The resonators used for measurement have an oval shape of the resonance portion  50  having a major axis of 247 μm and a minor axis of 176 μm. The distance “d” in  FIG. 4B  is selected so that lateral leakage of acoustic wave can be restrained. The three resonators of the first embodiment have almost the same the S 11  characteristics. In contrast, the three resonators of the first comparative example have different S 11  characteristics. 
       FIGS. 10A and 10B  show bandpass characteristics of the first comparative example and the first embodiment, respectively, in each of which the bandpass characteristics of formed in a wafer are shown. The regions  50  of the parallel resonators P of the ladder filters used for measurement have an oval shape that typically has a major axis of 180 μm and a minor axis of 151 μm. The parallel resonators P in each ladder filter have respective oval shapes having slightly different sizes. The regions  50  of the series resonators S of the ladder filters used for measurement have an oval shape that typically has a major axis of 233 μm and a minor axis of 195 μm. The series resonators S in each ladder filter have respective oval shapes having slightly different sizes. The distance “d” in FIGS.  4 A(b) and  4 B is selected so that lateral leakage of acoustic wave can be restrained. There is no difference in the bandpass characteristic between the four filters of the first embodiment. In contrast, there are considerable differences in the bandpass characteristic between the four filters of the first comparative example. Further, a great ripple takes place in the pass band, whereas the first embodiment does not have any considerable ripple. The first embodiment is capable of realizing the ladder filters having little difference in the bandpass characteristic and having suppressed ripples. 
     In the series resonators S of the first embodiment, the first film  22  is provided on the film laminate  18 . In the parallel resonators P of the first embodiment, the second film  20  is provided on the film laminate  18 , and the first film  22  is provided on the second film  20 . Thus, the presence/absence of the second film  20  defines the difference Δf between the resonance frequency of the series resonator S and that of the parallel resonator P. The first films  22  of the series resonator S and the parallel resonator P are made of an identical material. Thus, another film may be formed on the first film  22  of the series resonator S and that of the parallel resonator P with almost the same adhesiveness. 
     For example, referring to  FIGS. 6A and 6B , films that contact resist (not shown) in the series resonator S and the parallel resonator P at the time of etching the piezoelectric film  14  are the first films  22  in the first embodiment. In contrast, in the first comparative example, the first film  22  contacts resist (not shown) in the series resonator S, and the second film  20   a  contacts resist (not shown) in the parallel resonator P at the time of etching the piezoelectric film  14 . It is to be noted that Ti of the second film  20   a  is likely to be etched in wet etching and is weaker in adhesive strength to the resist than Cr of the first film  22 . Thus, in the first comparative example, the second film  20   a  is unwillingly etched. The degree of etching of the second film  20   a  depends on the position on the wafer. This leads to deviations in the resonance characteristic and those in the bandpass characteristic. 
     Preferably, the second film  20  has a good etching selectivity to the upper electrode  16 . Preferably, the first film  22  is made of a material having a strong adhesive strength to another film. This is taken into consideration in the first embodiment. That is, the first film  22  is provided on the film laminate  18  in the series resonators S, and the second film  20  is provided between the film laminate  18  and the first film  22  in the parallel resonators P. It is thus possible to prevent the thickness of the upper electrode  16  from being reduced to due to over etching at the time of forming the second film  20  and to prevent the difference Δf between the series resonator S and the parallel resonator P from deviating from the target values. It is further possible to form films on the first films  22  in the series resonator S and the parallel resonator P with an increased and identical adhesive strength. 
     Preferably, the first film  22  may be made of a material having good adhesiveness to another material, and the second film  20  is made of a material having a good etching selectivity to the upper electrode  16 . Particularly, the first film  22  and the second film  20  are made of an electrically conductive material in order to cause these films to function as the upper electrode  16 . 
     The third films  24  are provided on the first films  22  in the series resonators S and the parallel resonators P. The third films  24  of the series resonators S and the parallel resonators P can be simultaneously etched, so that the resonance frequencies of the series resonators S and the parallel resonators P can be simultaneously adjusted. It is thus possible to adjust the center frequency f 0  of the pass band. Preferably, the third film  24  is made of a material that makes it possible for the first film  22 , the second film  20  and the film laminate  18  to be etched during the f 0  adjustment. The third film  24  also functions as a protection film for the first film  22 , the second film  20  and the film laminate  18 . In this viewpoint, the third film  24  is an insulation film such as a metal oxide film or a metal nitride film. 
     Referring to  FIG. 7C , in the parallel resonator P, it is preferable that the region provided with the second film  20  includes the region  50  in which the upper electrode  16  faces the lower electrode  12  across the piezoelectric film  14 . If there is a part of the region  50  in which the second film  20  is not formed, the resonance characteristic will deviate from the designed characteristic. 
     Preferably, the first films  22  in the series resonators S and the first films  22  in the parallel resonators P have an identical thickness. It is thus possible to adjust the frequency difference Δf by only the thickness of the second films  20  and to suppress the deviations of the characteristics. 
     The hollow space has a dome shape that is oriented upwards, that is, towards the film laminate  18 . It is thus unnecessary to etch the substrate  10 . This improves the productivity and prevents degradation of the mechanical strength of the substrate  10 . Further, only a small region is needed to form the hollow space  30 , and the integration can be facilitated. The miniaturized hollow space  30  prevents the reliability of the film laminate  18  from being degraded due to mechanical vibrations. Further, the miniaturized hollow space  30  makes it possible to thin the sacrificed layer  38  and to secure good orientation of the piezoelectric film  14 . 
     The film laminate  18  composed of the lower electrode  12 , the piezoelectric film  14  and the upper electrode  16  has compressive stress. It is thus possible to reliably form the dome-shaped hollow space  30 . The apertures  34  connected to the hollow space  30  are formed in the lower electrode  12 . The sacrificed layer  38  is etched through the apertures  34 , so that the dome-shaped hollow space  30  can be defined. 
     The region  50  in which the upper electrode  16  faces the lower electrode  12  across the piezoelectric film  14  is included in a region formed by projecting the hollow space  30  onto the substrate  10 . This allows the film laminate  18  to vibrate. 
     The piezoelectric film  14  may be made of aluminum nitride or zinc oxide having an orientation having the main axis in the (002) direction. It is thus possible to provide the piezoelectric thin-film resonators having good resonance characteristics. 
     Second Embodiment 
     A second embodiment has a structure in which a hollow space  30   a  is provided in the substrate  10 . A part (a) of  FIG. 11  is a plan view of a resonator according to the second embodiment, and a part (b) thereof is a cross-sectional view taken along a line A-A. Referring to  FIG. 11 , the hollow space  30   a  is formed in the substrate  10  below the region  50  in which the upper electrode  16  faces the lower electrode  12  across the piezoelectric film  14 . The hollow space  30   a  may be formed so as to have a substantially vertical wall by deep-RIE (reactive ion etching). 
     Third Embodiment 
       FIG. 12  is a plan view of a series resonator S and a parallel resonator P in accordance with a third embodiment. Referring to  FIG. 12 , the region  50  in which the upper electrode  16  faces the lower electrode  12  across the piezoelectric film  14  has a polygonal shape composed of anti-parallel sides. The other structures of the third embodiment are the same as those of the first embodiment. The region  50  may have an oval shape in the first embodiment, or a polygonal shape composed of anti-parallel sides in the second embodiment. There are no parallel sides in the region  50 . It is thus possible to prevent the acoustic wave reflected by the outer edge of the piezoelectric film  14  from being reflected and remaining in the resonance portion  52  as a standing wave in the lateral directions. It is thus possible to prevent ripples from taking place in the pass band. 
     The first through third embodiments are ladder filters using FBARs. The present invention includes ladder filters using SMRs. The substrate  10  may be made of quartz crystal, glass or GaAs. The lower electrode  12  and the upper electrode  16  may be made of not only Ru but also another material as described in the Description of the Related Art. Preferably, the sacrificed layer  38  may be made of a material that is easily removable by etchant. For example, the sacrificed layer  38  may be made of ZnO, Ge or Ti. The films may be formed by evaporation other than sputtering. The first film  22  is not limited to the Cr film but may be made of another material as long as similar effects are obtained. The second film  20  is not limited to the Ti film but may be made of another material as long as similar effects are obtained. The third film  24  is not limited to SiO 2  but may be made of another material with similar effects are obtained. 
     The present invention is not limited to the specifically disclosed embodiments, but other embodiments and variations may be made without departing from the scope of the present invention. 
     The present application is based on Japanese Patent Application No. 2006-282290 filed on Oct. 17, 2006, the entire disclosure of which is hereby incorporated by reference.