Patent Publication Number: US-2021184646-A1

Title: Resonator and resonance device

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation of PCT/JP2019/027553 filed Jul. 11, 2019, which claims priority to JP Application No. 2018-190070, filed Oct. 5, 2018, the entire contents of each of which are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present invention relates to a resonator and a resonance device including the resonator. 
     BACKGROUND 
     A resonance device, which is an example of micro-electro-mechanical systems (MEMS), is currently used as a timing device incorporated in electronic apparatuses, such as smartphones. The resonance device includes, for example, a lower cover, an upper cover, and a resonator placed in a cavity defined between the upper cover and the lower cover. The resonator includes, for example, a piezoelectric film, an upper electrode, a lower electrode, and an insulating film. The upper and lower electrodes are laid with the piezoelectric film therebetween. The insulating film is disposed between layers in the resonator or is on a surface of the resonator. 
     Japanese Unexamined Patent Application Publication No. 2012-65293 (hereinafter “Patent Document 1”) discloses a specific configuration of such a resonator. The resonator concerned includes a base section, a vibration arm, a piezoelectric element, and a mass addition portion. The vibration arm extends from the base section in such a manner that the vibration arm can be bent and vibrate. The piezoelectric element is disposed on the vibration arm. The mass addition portion is closer than the piezoelectric element to a distal end of the vibration arm. The mass addition portion includes at least one mass addition film. Moreover, the at least one mass addition film and one of layers constituting the piezoelectric element are made of the same material. In addition, the piezoelectric element and the mass addition film may be formed all at once. 
     Such a conventional resonator typically includes a mass addition portion disposed in such a manner that the amount of displacement of a vibration part responsible for vibration is greater in a region corresponding to the mass addition portion than in any other region. The resonator is held in a vibration space defined within a resonance device. Upon application of, for example, drop impacts on the resonance device, the mass addition portion would come into contact with an inner wall of the resonance device and would, consequently, become damaged. Such a damaged mass addition portion could be a cause of fluctuations in the frequency of the resonator. 
     The mass addition portion has a surface in one shape or another, which is formed by removal of at least part of the surface in a process of adjusting the frequency. The shape of the surface of the mass addition portion can affect how effectively the mass addition portion will resist being damaged by accidental contact with the inner wall of the resonance device. In Patent Document 1, however, no particular mention is made on the shape of the surface of the mass addition portion. 
     SUMMARY OF THE INVENTION 
     The exemplary embodiments of the present invention have been made in view of such circumstances. It is an object of the present invention to provide a resonator conducive to improved reliability and a resonance device including the resonator. 
     A resonator according to an exemplary aspect of the present invention includes a vibration part and a mass addition portion. The vibration part includes a piezoelectric film, an upper electrode, and a lower electrode. The upper and lower electrodes are disposed on opposite sides with the piezoelectric film therebetween. The amount of displacement of the vibration part is greater in a region corresponding to at least part of the mass addition portion than in any other region. The mass addition portion has an inclined surface that slopes in such a manner that the mass addition portion has end regions and a central region thinner than at least one of the end regions when the vibration part is viewed in section. 
     The exemplary embodiments of the present invention provide a resonator conducive to improved reliability and a resonance device including the resonator. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic external perspective view of a resonance device according to a first exemplary embodiment. 
         FIG. 2  is an exploded perspective view of the resonance device according to the first exemplary embodiment, schematically illustrating the structure of the resonance device. 
         FIG. 3  is a plan view of a resonator according to the first exemplary embodiment, schematically illustrating the structure of the resonator. 
         FIG. 4  is a sectional view of the resonance device taken along a line extending in the X-axis direction, schematically illustrating the multilayer structure of the resonance device in  FIG. 1 . 
         FIG. 5  is a sectional view of the resonance device taken along a line extending in the Y-axis direction, schematically illustrating the multilayer structure of the resonance device in  FIG. 1 . 
         FIG. 6  is a sectional view of a mass addition portion according to the first embodiment, the sectional view being taken along a Y-Z plane. 
         FIG. 7  is a sectional view of the mass addition portion according to the first embodiment, the sectional view being taken along a Z-X plane. 
         FIG. 8  is a sectional view of a mass addition portion according to a second embodiment, the sectional view being taken along a Y-Z plane. 
         FIG. 9  is a sectional view of a mass addition portion according to a third embodiment, the sectional view being taken along a Y-Z plane. 
         FIG. 10  is a sectional view of a mass addition portion according to a fourth embodiment, the sectional view being taken along a Y-Z plane. 
         FIG. 11  is a plan view of a resonator according to a fifth embodiment, schematically illustrating the structure of the resonator. 
         FIG. 12  is a sectional view of a mass addition portion according to the fifth embodiment, the sectional view being taken along a Y-Z plane. 
         FIG. 13  is a plan view of a resonator according to a sixth embodiment, schematically illustrating the structure of the resonator. 
         FIG. 14  is a sectional view of a mass addition portion according to the sixth embodiment, the sectional view being taken along a Z-X plane. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Hereinafter, exemplary embodiments of the present invention will be described with reference to the accompanying drawings. In the accompanying drawings, the same or like reference signs denote the same or like constituent components. The accompanying drawings are provided merely as examples. The individual components are schematically illustrated in terms of their dimensions and shapes. The following embodiments should not be construed as limiting the technical scope of the present invention. 
     First Exemplary Embodiment 
     The following describes the configuration of a resonance device  1  according to a first exemplary embodiment with reference to  FIGS. 1 and 2 .  FIG. 1  is a schematic external perspective view of a resonance device according to a first embodiment.  FIG. 2  is an exploded perspective view of the resonance device according to the first embodiment of the present invention, schematically illustrating the structure of the resonance device. 
     Resonance Device  1   
     As shown, the resonance device  1  includes a resonator  10 , a lower cover  20 , and an upper cover  30 . The lower cover  20  and the upper cover  30  face each other with the resonator  10  therebetween. The lower cover  20 , the resonator  10 , and the upper cover  30  are stacked on top of each other in the stated order in the Z-axis direction. The resonator  10  and the lower cover  20  are joined to each other, and the resonator  10  and the upper cover  30  are joined to each other. A vibration space for the resonator  10  is defined between the lower cover  20  and the upper cover  30  joined to each other through the resonator  10 . According to an exemplary aspect, the resonator  10 , the lower cover  20 , and the upper cover  30  are each made of a semiconductor substrate, a glass substrate, an organic substrate, or any other substrate that may be processed with a micromachining technology. 
     The following describes the individual components of the resonance device  1 . The following description will be given assuming that the resonance device  1  is placed with the upper cover  30  on an upper side (i.e., on a top side) and the lower cover  20  on a lower side (i.e., on a back side). 
     In general, micro-electro-mechanical systems (MEMS) are used to produce the resonator  10 , which is thus regarded as a MEMS resonator. The resonator  10  includes a vibration part  110 , a holding part  140 , and a holding arm  150 . The vibration part  110  can simply be referred to as a vibrator and is held in the vibration space. The vibration part  110  may vibrate out of an X-Y plane, that is, in an out-of-plane bending-vibration mode. In some embodiments, the vibration part  110  may vibrate in the X-Y plane, that is, in an in-plane bending-vibration mode. The holding part  140  (which can generally be considered a frame) is in the form of, for example, a rectangular frame, in which the vibration part  110  is enclosed. The holding arm  150  forms a connection between the vibration part  110  and the holding part  140 . 
     The lower cover  20  includes a bottom plate  22  and a side wall  23 . The bottom plate  22  is in the form of a rectangular flat plate lying in an X-Y plane. The side wall  23  extends in the Z-axis direction from a peripheral edge portion of the bottom plate  22 . The side wall  23  is joined to the holding part  140  of the resonator  10 . The lower cover  20  has a recess  21  on its surface facing the vibration part  110  of the resonator  10 . The recess  21  is defined by a top surface of the bottom plate  22  and an inner surface of the side wall  23 . Moreover, the recess  21  is a cavity having a cuboid shape whose top is open. The vibration space for the resonator  10  is partially defined by the recess  21 . The lower cover  20  includes, on its inner surface, a projection  50 , which projects from the top surface of the bottom plate  22  into the vibration space. 
     According to an exemplary aspect, the structure of the upper cover  30  and the structure of the lower cover  20  except for the projection  50  are mirror images of each other with respect to the resonator  10  disposed therebetween. More specifically, the upper cover  30  includes a bottom plate  32  and aside wall  33 . The bottom plate  32  is in the form of a rectangular flat plate lying in an X-Y plane. The side wall  33  extends in the Z-axis direction from a peripheral edge portion of the bottom plate  32 . The side wall  33  is joined to the holding part  140  of the resonator  10 . The upper cover  30  has a recess  31  on its surface facing the vibration part  110  of the resonator  10 . The recess  31  is a cavity having a cuboid shape whose bottom is open. The vibration space for the resonator  10  is partially defined by the recess  31 . 
     Alternatively and in some embodiments, the structure of the lower cover  20  and the structure of the upper cover  30  may not be mirror images of each other. For example, the lower cover  20  or the upper cover  30  may be dome-shaped. The recess  21  of the lower cover  20  and the recess  31  of the upper cover  30  may have different shapes. For example, the recess  21  and the recess  31  may be of different depths. 
     Resonator  10   
     The following describes, in more detail, the vibration part  110 , the holding part  140 , and the holding arm  150  of the resonator  10  according to an embodiment of the present invention with reference to  FIG. 3 .  FIG. 3  is a plan view of a resonator according to the first embodiment of the present invention, schematically illustrating the structure of the resonator. 
     Vibration Part  110   
     The vibration part  110  is enclosed in the holding part  140  (i.e., a frame) when viewed in plan from the side on which the upper cover  30  is disposed. The vibration part  110  and the holding part  140  are arranged with a predetermined amount of clearance left therebetween. The vibration part  110  includes a vibration-generating section  120  and a base section  130  (or simply a base). The vibration-generating section  120  includes four vibration arms, which are denoted by  121 A,  121 B,  121 C, and  121 D, respectively. The base section  130  is connected to the vibration-generating section  120 . It is not required that four vibration arms be included in the vibration-generating section  120 . Instead, the vibration-generating section  120  may include one vibration arm or any other number of vibration arms. The vibration-generating section  120  and the base section  130  in the present embodiment are provided as one member. 
     Vibration Arms  121 A to  121 D 
     The vibration arms  121 A,  121 B,  121 C, and  121 D extend in the Y-axis direction and are arranged side by side in the stated order in the X-axis direction at predetermined spacings. The vibration arm  121 A has a fixed end connected to a front end portion  131 A (or simply front end) of the base section  130  and an open end located away from the front end portion  131 A of the base section  130 . The base section  130  will be described later. The vibration arm  121 A includes a mass addition portion  122 A (or mass additional portion) and an arm portion  123 A, which are in line with each other in the direction in which the vibration arm  121 A extends. The mass addition portion  122 A is provided to the open end. The arm portion  123 A extends from the fixed end and is connected to the mass addition portion  122 A. This means that the amount of displacement of the vibration part  110  is greater in the region corresponding to the mass addition portion  122 A than in any other region. Similarly, the vibration arms  121 B,  121 C, and  121 D include their respective mass addition portions, which are denoted by  122 B,  122 C, and  122 D, and also include their respective arm portions, which are denoted by  123 B,  123 C, and  123 D. The arm portions  123 A to  123 D each have a width of about 50 μm in the X-axis direction and a length of about 450 μm in the Y-axis direction. 
     Two of the four vibration arms, or more specifically, the vibration arms  121 A and  121 D are considered to be outer vibration arms on the outer side in the X-axis direction. The other two, or more specifically, the vibration arms  121 B and  121 C are considered to be inner vibration arms on the inner side in the X-axis direction. The width of a clearance between the arm portion  123 B of the inner vibration arm  121 B and the arm portion  123 C of the inner vibration arm  121 C is referred to as a release width W 1 . The width of a clearance between the arm portion  123 A of the outer vibration arm  121 A and the arm portion  123 B of the inner vibration arm  121 B is referred to as a release width W 2 , with the outer vibration arm  121 A and the inner vibration arm  121 B being adjacent to each other in the X-axis direction. The width of a clearance between the arm portion  123 D of the outer vibration arm  121 D and the arm portion  123 C of the inner vibration arm  121 C is also referred to as the release width W 2 , with the outer vibration arm  121 D and the inner vibration arm  121 C being adjacent to each other in the X-axis direction. The release width W 1  is greater than the release width W 2 . In one exemplary aspect, the device is configured such that the release width W 1  is greater than the release width W 2  and offers improved vibration characteristics and improved durability. The release widths W 1  and W 2  are not limited to particular values. For example, the release width W 1  may be about m, and the release width W 2  may be about 10 μm in exemplary aspects.  FIG. 3  is a nonrestrictive example. That is, the release width W 1  between the arm portions of the inner vibration arms may be smaller than or equal to the release width W 2  between each of the inner vibration arms and the corresponding outer vibration arm. 
     The mass addition portions  122 A to  122 D include, on their surfaces, their respective mass addition films, which are denoted by  125 A to  125 D. Specifically, each of the mass addition films  125 A to  125 D geometrically conforms to the corresponding one of the mass addition portions  122 A to  122 D when viewed in plan from the side on which the upper cover  30  is disposed. With the addition of the mass addition films  125 A to  125 D, the weight per unit length (hereinafter also simply referred to as weight) of each of the mass addition portions  122 A to  122 D is greater than the weight of the corresponding one of the arm portions  123 A to  123 D. The vibration part  110  may thus be small in size and have improved vibration characteristics. In addition to providing the additional weight to tip portions (or simply tips) of the vibration arms  121 A to  121 D, the mass addition films  125 A to  125 D enable adjustment of the resonant frequencies of the vibration arms  121 A to  121 D, or more specifically, the mass addition films  125 A to  125 D may each be partially removed for use as frequency adjustment films. 
     In the present embodiment, the width of each of the mass addition portions  122 A to  122 D in the X-axis direction is greater than the width of the corresponding one of the arm portions  123 A to  123 D in the X-axis direction. The mass addition portions  122 A to  122 D having greater width have correspondingly greater weight. Although it is required that the weight per unit length of each of the mass addition portions  122 A to  122 D be greater than the weight per unit length of the corresponding one of the arm portions  123 A to  123 D, the width of each of the mass addition portions  122 A to  122 D in the X-axis direction is not necessarily as described above. The width of each of the mass addition portions  122 A to  122 D in the X-axis direction may be equal to or smaller than the width of the corresponding one of the arm portions  123 A to  123 D in the X-axis direction. 
     When viewed in plan from the side on which the upper cover  30  is disposed, the mass addition portions  122 A to  122 D each have a substantially rectangular shape with four rounded corners (e.g., radius corners). The arm portions  123 A to  123 D are substantially rectangular, with radius corners being formed at the fixed ends connected to the base section  130  and at junctions connected to the mass addition portions  122 A to  122 D. The shape of each of the mass addition portions  122 A to  122 D and the shape of the arm portions  123 A to  123 D are not necessarily as described above. For example, the mass addition portions  122 A to  122 D may each be trapezoidal or L-shaped in alternative aspects. Moreover, the arm portions  123 A to  123 D may each be trapezoidal or may each have, for example, a slit. 
     When viewed in plan from the side on which the upper cover  30  is disposed, the arm portion  123 B of the inner vibration arm  121 B and the arm portion  123 C of the inner vibration arm  121 C are arranged side by side with the projection  50  therebetween, with the projection  50  projecting from the lower cover  20 . The projection  50  extends along the arm portions  123 B and  123 C in the Y-axis direction. According to an exemplary aspect, the projection  50  is about 240 μm long in the Y-axis direction and is about 15 μm long in the X-axis direction. The projection  50  makes the lower cover  20  less prone to warpage. 
     Base Section  130   
     Referring to  FIG. 3 , the base section  130  viewed in plan from the side on which the upper cover  30  is disposed includes the front end portion  131 A (i.e., a front end), a rear end portion  131 B (i.e., a rear end), a left end portion  131 C (i.e., a left end or left side), and a right end portion  131 D (i.e., right end or right side). The front end portion  131 A, the rear end portion  131 B, the left end portion  131 C, and the right end portion  131 D are each part of a peripheral region of the base section  130 . Specifically, the front end portion  131 A adjoins the vibrations arms  121 A to  121 D and extends in the X-axis direction. The rear end portion  131 B is on the side opposite the vibration arms  121 A to  121 D and extends in the X-axis direction. The left end portion  131 C is in line with the vibration arm  121 A in a distance from the vibration arm  121 D and extends in the Y-axis direction. The right end portion  131 D is in line with the vibration arm  121 D in a distance from the vibration arm  121 A and extends in the Y-axial direction. 
     The left end portion  131 C has an end linked to one end of the front end portion  131 A and another end linked to one end of the rear end portion  131 B. The right end portion  131 D has an end linked to the other end of the front end portion  131 A and another end linked to the rear end portion  131 B. The front end portion  131 A and the rear end portion  131 B are on opposite sides in the Y-axis direction. The left end portion  131 C and the right end portion  131 D are on opposite sides in the X-axis direction. The front end portion  131 A is connected with the vibration arms  121 A to  121 D. 
     When viewed in plan from the side on which the upper cover  30  is disposed, the base section  130  has a substantially rectangular shape whose long sides, respectively, are the front end portion  131 A and the rear end portion  131 B and whose short sides, respectively, are the left end portion  131 C and the right end portion  131 D. As shown, the base section  130  is substantially symmetric with respect to an imaginary plane P, which lies along perpendicular bisectors that respectively bisect the front end portion  131 A and the rear end portion  131 B. It is noted that the base section  130  is not necessarily rectangular as illustrated in  FIG. 3  and may have any other shape that is substantially symmetric with respect to the imaginary plane P. For example, the base section  130  may have a trapezoidal shape two sides of which, respectively, are the front end portion  131 A and the rear end portion  131 B, with either of these portions being longer than the other. At least one of the front end portion  131 A, the rear end portion  131 B, the left end portion  131 C, and the right end portion  131 D may be bent or curved. 
     The imaginary plane P is a plane of symmetry of the entirety of the vibration part  110 . The imaginary plane P may thus be regarded as a plane passing through the center of the vibration arms  121 A to  121 D in the X-axis direction and is located between the inner vibration arms  121 B and  121 C. Specifically, each of the outer vibration arm  121 A and the inner vibration arm  121 B, which are adjacent to each other, and the corresponding one of the outer vibration arm  121 D and the inner vibration arm  121 C, which are adjacent to each other, are arranged symmetrically about the imaginary plane P. 
     According to an exemplary aspect, the maximum distance between the front end portion  131 A and the rear end portion  131 B of the base section  130  in the Y-axis direction is herein referred to as a base section length and is, for example, about 40 μm. Moreover, the maximum distance between the left end portion  131 C and the right end portion  131 D of the base section  130  in the X-axis direction is herein referred to as a base section width and is, for example, about 300 μm. Referring to  FIG. 3 , which illustrates a configuration example, the base section length is the length of the left end portion  131 C or the right end portion  131 D, and the base section width is the length of the front end portion  131 A or the rear end portion  131 B. 
     Holding Part  140   
     The holding part  140  (or frame) is provided such that the vibration part  110  is held in the vibration space defined by the lower cover  20  and the upper cover  30 . The vibration part  110  may, for example, be enclosed in the holding part  140 . Referring to  FIG. 3 , the holding part  140  viewed in plan from the side on which the upper cover  30  is disposed includes a front frame  141 A, a rear frame  141 B, a left frame  141 C, and a right frame  141 D. The front frame  141 A, the rear frame  141 B, the left frame  141 C, and the right frame  141 D are each part of a substantially rectangular frame body in which the vibration part  110  is enclosed. Specifically, the front frame  141 A is located beyond the vibration-generating section  120  when viewed from the base section  130  and extends in the X-axis direction. The rear frame  141 B is located beyond the base section  130  when viewed from the vibration-generating section  120  and extends in the X-axis direction. The left frame  141 C is located beyond the vibration arm  121 A when viewed from the vibration arm  121 D and extends in the Y-axis direction. The right frame  141 D is located beyond the vibration arm  121 D when viewed from the vibration arm  121 A and extends in the Y-axis direction. Moreover, the holding part  140  is also symmetrically disposed about the imaginary plane P. 
     The left frame  141 C has an end connected to one end of the front frame  141 A and has another end connected to one end of the rear frame  141 B. The right frame  141 D has an end connected to the other end of the front frame  141 A and another end connected to the other end of the rear frame  141 B. The front frame  141 A and the rear frame  141 B are on opposite sides in the Y-axis direction with the vibration part  110  therebetween. The left frame  141 C and the right frame  141 D are on opposite sides in the X-axis direction with the vibration part  110  therebetween. The holding part  140  is not necessarily in the form of a frame extending continuously in the circumferential direction. It is required that the holding part  140  extend along at least part of the periphery of the vibration part  110 . 
     Holding Arm  150   
     The holding arm  150  is disposed on the inner side with respect to the holding part  140  and forms a connection between the base section  130  and the holding part  140 . Referring to  FIG. 3 , the holding arm  150  viewed in plan from the side on which the upper cover  30  is disposed includes a left holding arm  151 A and a right holding arm  151 B. The left holding arm  151 A forms a connection between the rear end portion  131 B of the base section  130  and the left frame  141 C of the holding part  140 . The right holding arm  151 B forms a connection between the rear end portion  131 B of the base section  130  and the right frame  141 D of the holding part  140 . The left holding arm  151 A includes a holding rear arm  152 A and a holding side arm  153 A, and the right holding arm  151 B includes a holding rear arm  152 B and a holding sidearm  153 B. The holding arm  150  is symmetric with respect to the imaginary plane P. 
     The holding rear arms  152 A and  152 B extend from the rear end portion  131 B of the base section  130  (opposite the vibration arms) and lie between and the rear end portion  131 B of the base section  130  and the holding part  140 . Specifically, the holding rear arm  152 A extends toward the rear frame  141 B from the rear end portion  131 B of the base section  130  and is bent to extend toward the left frame  141 C. The holding rear arm  152 B extends toward the rear frame  141 B from the rear end portion  131 B of the base section  130  and is bent to extend toward the right frame  141 D. 
     The holding side arm  153 A extends along the outer vibration arm  121 A and lies between the outer vibration arm  121 A and the holding part  140 . The holding side arm  153 B extends along the outer vibration arm  121 D and lies between the outer vibration arm  121 D and the holding part  140 . Specifically, the holding sidearm  153 A extends toward the front frame  141 A from an end portion of the holding rear arm  152 A adjacent to the left frame  141 C and is bent to be connected to the left frame  141 C. The holding side arm  153 B extends toward the front frame  141 A from an end portion of the holding rear arm  152 B adjacent to the right frame  141 D and is bent to be connected to the right frame  141 D. 
     According to alternative aspects, the holding arm  150  is not necessarily configured as described above. For example, the holding arm  150  may be connected to the left end portion  131 C and the right end portion  131 D of the base section  130 . The holding arm  150  may be connected to the front frame  141 A of the holding part  140 . 
     Multilayer Structure 
     The following describes the multilayer structure and actions of the resonance device  1  according to the first embodiment with reference to  FIGS. 4 and 5 .  FIG. 4  is a sectional view of the resonance device taken along a line extending in the X-axis direction, schematically illustrating the multilayer structure of the resonance device in  FIG. 1 .  FIG. 5  is a sectional view of the resonance device taken along a line extending in the Y-axis direction, schematically illustrating the multilayer structure of the resonance device in  FIG. 1 . For purposes of the exemplary multilayer structure of the resonance device  1 ,  FIG. 4  schematically illustrates, for example, the arm portions  123 A to  123 D, an extended line C 2 , an extended line C 3 , a through-via electrode V 2 , and a through-via electrode V 3  that are viewed in section; however, this does not necessarily mean that their cross sections are on the same plane. For example, the through-via electrodes V 2  and V 3  may be parallel to a Z-X plane defined by the Z-axis and the X-axis and may be located away, in the Y-axis direction, from the cross sections of the arm portions  123 A to  123 D. The same holds for  FIG. 5 . That is, to describe the exemplary multilayer structure of the resonance device  1 ,  FIG. 5  schematically illustrates the mass addition portion  122 A, the arm portion  123 A, an extended line C 1 , the extended line C 2 , a through-via electrode V 1 , and the through-via electrode V 2  that are viewed in section; however, this does not necessarily mean that their cross sections are on the same plane. 
     The holding part  140  of the resonator  10  of the resonance device  1  is disposed on and joined to the side wall  23  of the lower cover  20 . The holding part  140  of the resonator  10  is also joined to the side wall  33  of the upper cover  30 . The resonator  10  is held between the lower cover  20  and the upper cover  30 . The lower cover  20 , the upper cover  30 , and the holding part  140  of the resonator  10  define the vibration space in which the vibration part  110  vibrates. The resonator  10 , the lower cover  20 , and the upper cover  30  are each formed by using, for example, a silicon substrate (hereinafter referred to as an Si substrate). In some embodiments, the resonator  10 , the lower cover  20 , and the upper cover  30  may each be formed by using a silicon-on-insulator (SOI) substrate, which is a silicon layer with a silicon oxide film laid thereon. 
     Resonator  10   
     The vibration part  110 , the holding part  140 , and the holding arm  150  of the resonator  10  are integrally formed in the same process. The resonator  10  includes an Si substrate F 2  and a metal film E 1 . The Si substrate F 2  is an example of the substrate, and the metal film E 1  is stacked on top of the Si substrate F 2 . The metal film E 1  is overlaid with a piezoelectric film F 3 , and a metal film E 2  is stacked on top of the piezoelectric film F 3 . The metal film E 2  is overlaid with a protective film F 5 . Each of the mass addition portions  122 A to  122 D includes the corresponding one of the mass addition films  125 A to  125 D on the protective film F 5 . The vibration part  110 , the holding part  140 , and the holding arm  150  each have a geometry obtained by patterning the multilayer body including mainly the Si substrate F 2 , the metal film E 1 , the piezoelectric film F 3 , the metal film E 2 , and the protective film F 5 . The multilayer body may be patterned by dry etching in which the multilayer body is exposed to argon (Ar) ion beams for removal processing. 
     The Si substrate F 2  is, for example, a degenerate n-type silicon (Si) semiconductor having a thickness of about 6 μm and doped with n-type dopants such as phosphorus (P), arsenic (As), and antimony (Sb). The resistance value of degenerate silicon (Si) for use as the Si substrate F 2  may, for example, be less than 16 mΩ·cm and is more preferably not more than 1.2 mΩ·cm. On a lower surface of the Si substrate F 2  is a temperature characteristics correction layer F 21 , which is formed from silicon oxide such as SiO 2 . 
     The temperature characteristics correction layer F 21  enables, at least at or near room temperatures, a reduction in the temperature coefficient of the resonant frequency of the resonator  10 , that is, a reduction in the rate of change in resonant frequency per unit temperature. The temperature characteristics correction layer F 21  included in the vibration part  110  enables the resonator  10  to exhibit improved temperature characteristics. The vibration part  110  may include a temperature characteristics correction layer provided on an upper surface of the Si substrate F 2  or may include temperature characteristics correction layers respectively provided on the upper and lower surfaces of the Si substrate F 2 . 
     The temperature characteristics correction layer F 21  on the mass addition portions  122 A to  122 D desirably has a uniform thickness. For purposes of this disclosure, the uniform thickness means that variations within a range of ±20% from the thickness mean value of the temperature characteristics correction layer F 21  are tolerated. 
     The metal films E 1  and E 2  each include a vibration-generating electrode and an extended electrode. The vibration-generating electrode causes the vibration arms  121 A to  121 D to vibrate. The extended electrode electrically connects the vibration-generating electrode to an external power source. In the arm portions  123 A to  123 D of the vibration arms  121 A to  121 D, regions being part of the metal film E 1  and functioning as the vibration-generating electrode are opposite to regions being part of the metal film E 2  and functioning as the vibration-generating electrode, with the piezoelectric film F 3  being located between the metal films E 1  and E 2 . Regions functioning as the extended electrodes of the metal films E 1  and E 2  may, for example, extend out from the base section  130  to the holding part  140  through the holding arm  150 . The metal film E 1  is electrically continuous throughout the resonator  10 . The regions of the metal film E 2  that are included in the outer vibration arms  121 A and  121 D are electrically isolated from the regions of the metal film E 2  that are included in the inner vibration arms  121 B and  121 C. The metal film E 1  is a lower electrode, and the metal film E 2  is an upper electrode. 
     The thickness of each of the metal films E 1  and E 2  is, for example, not less than about 0.1 μm and not more than about 0.2 μm. After being formed, the metal films E 1  and E 2  undergo removal processing (e.g., etching) and are pattered into mainly the vibration-generating electrodes and the extended electrodes. The metal films E 1  and E 2  are formed from, for example, metallic materials whose crystal structure is a body-centered cubic structure. Specifically, the metal films E 1  and E 2  are each formed from, for example, molybdenum (Mo) or tungsten (W). When the Si substrate F 2  is a regenerate semiconductor substrate having a high electrical conductivity, the metal film E 1  may be eliminated, and the Si substrate F 2  may double as a lower electrode. 
     The piezoelectric film F 3  is a thin film formed from a piezoelectric material for converting between electrical energy and mechanical energy. The piezoelectric film F 3  expands and contracts in the Y-axis direction in an X-Y plane in accordance with the electric field generated in the piezoelectric film F 3  by the metal films E 1  and E 2 . Through the expansion and contraction of the piezoelectric film F 3 , the open ends of the vibration arms  121 A to  121 D undergo displacement toward the bottom plate  22  of the lower cover  20  and displacement toward the bottom plate  32  of the upper cover  30 . This means that the resonator  10  vibrates in the out-of-plane bending-vibration mode. 
     The piezoelectric film F 3  is formed from a material having a wurtzite hexagonal crystal structure. For example, the piezoelectric film F 3  includes, as a principal component, a nitride or an oxide, and more specifically, aluminum nitride (AN), scandium aluminum nitride (ScAlN), zinc oxide (ZnO), gallium nitride (GaN), or indium nitride (InN). Scandium aluminum nitride is obtained by substituting part of aluminum in aluminum nitride with scandium. Instead of being substituted with scandium, part of aluminum in aluminum nitride may be substituted with magnesium (Mg) and niobium (Nb), with magnesium (Mg) and zirconium (Zr), or with any other two elements. The piezoelectric film F 3  has a thickness of about 1 μm. In some embodiments, the thickness of the piezoelectric film F 3  may be in the range of about 0.2 μm to about 2 μm. 
     The protective film F 5  is provided to protect the metal film E 2  from oxidation. Although it is preferred that the protective film F 5  be on the side on which the upper cover  30  is disposed, the protective film F 5  does not necessarily lie open to the bottom plate  32  of the upper cover  30 . The protective film F 5  may be overlaid with, for example, a parasitic capacitance reduction film that reduces the capacitance of wiring of the resonator  10 . The protective film F 5  is a nitride film formed from aluminum nitride (AlN) or silicon nitride (SiN X ) or is an oxide film formed from aluminum oxide (Al 2 O 3 ), tantalum pentoxide (Ta 2 O 5 ), or silicon nitride (SiO X ). 
     Each of the mass addition films  125 A to  125 D is a surface of the corresponding one of the mass addition portions  122 A to  122 D and faces the upper cover  30 . Each of the mass addition films  125 A to  125 D is a frequency adjustment film for the corresponding one of the vibration arms  121 A to  121 D. The mass addition films  125 A to  125 D are partially removed through trimming processing for adjustment of the frequency of the resonator  10 . With a view to enhancing the efficiency of frequency adjustment, it is desired that the mass addition films  125 A to  125 D be formed from a material whose mass reduction rate at the time of etching is faster than the mass reduction rate of the protective film F 5 . The mass reduction rate is obtained by multiplying the etching rate by the density. The etching rate refers to the thickness removed per unit time. Although it is required that the relationship between the mass reduction rate of the protective film F 5  and the mass reduction rate of the mass addition films  125 A to  125 D be as noted above, the magnitude relationship between the etching rate of the protective film F 5  and the etching rate of the mass addition films  125 A to  125 D may be adjusted as desired. With a view to increasing the weight of the mass addition portions  122 A to  122 D efficiently, it is preferred that the mass addition films  125 A to  125 D be formed from a material of high specific gravity. For these reasons, the mass additions films  125 A to  125 D are formed from a metallic material such as molybdenum (Mo), tungsten (W), gold (Au), platinum (Pt), nickel (Ni), or titanium (Ti). The protective film F 5  may be partially removed through trimming processing. In this case, the protective film F 5  is also regarded as a frequency adjustment film. 
     During manufacture, the process of adjusting the frequency involves trimming processing in which upper surfaces of the mass addition films  125 A to  125 D are partially removed. The shape of the mass addition films  125 A to  125 D will be specifically described later. As the trimming processing, dry etching involving radiation of argon (Ar) ion beams may be applied to the mass addition films  125 A to  125 D. A wide area may be radiated with ion beams, which thus provide a high degree of processing efficiency. Meanwhile, the mass addition films  125 A to  125 D would be electrically charged by ion beams bearing electrical charges. The vibration orbit of the vibration arms  121 A to  121 D would be changed due to the coulomb interaction in the electrically charged mass addition films  125 A to  125 D, and the vibration characteristics of the resonator  10  would degrade accordingly. According to an exemplary aspect, to avoid such a defective condition, the mass addition films  125 A to  125 D are desirably grounded. 
     Referring to  FIG. 5 , which illustrates a configuration example, the mass addition film  125 A is electrically connected to the metal film E 1  through a through-via electrode extending through both the piezoelectric film F 3  and the protective film F 5 . Similarly, the mass addition films  125 B to  125 D (not illustrated) are electrically connected to the metal film E 1  through through-via electrodes. The mass addition films  125 A to  125 D are not necessarily grounded as noted above, and may, for example, electrically connected to the metal film E 1  through side electrodes extending along side surfaces of the mass addition portions  122 A to  122 D. Instead of being electrically connected to the metal film E 1 , the mass addition films  125 A to  125 D may, for example, be electrically connected the metal film E 2  in a manner so as to reduce the possibility of becoming charged. 
     The extended lines C 1 , C 2 , and C 3  are provided on the protective film F 5  on the holding part  140 . The extended line C 1  is electrically connected to the metal film E 1  through a through-hole extending through both the piezoelectric film F 3  and the protective film F 5 . The extended line C 2  is electrically connected, through a through-hole in the protective film F 5 , to portions of the metal film E 2  that are included in the outer vibration arms  121 A and  121 D. The extended line C 3  is electrically connected, through a through-hole in the protective film F 5 , to portions of the metal film E 2  that are included in the inner vibration arms  121 B and  121 C. In an exemplary aspect, the extended lines C 1  to C 3  are each formed from a metallic material such as aluminum (Al), germanium (Ge), gold (Au), or tin (Sn). 
     Lower Cover  20   
     The bottom plate  22  and the side wall  23  of the lower cover  20  are integrally formed of an Si substrate P 10 . The Si substrate P 10  is formed from nondegenerate silicon and has a resistivity of, for example, 10 Ω·cm or more. The Si substrate P 10  lies open to the inside of the recess  21  of the lower cover  20 . The projection  50  has an upper surface covered with the temperature characteristics correction layer F 21 . With a view to inhibiting electrification of the projection  50 , the Si substrate P 10 , whose electrical resistivity is lower than the electrical resistivity of the temperature characteristics correction layer F 21 , may be exposed at the upper surface of the projection  50 , or an electrically conductive layer may be provided on the upper surface of the projection  50 . 
     The thickness of the lower cover  20  in the Z-axis direction is about 150 μm, for example. The depth of the recess  21  in the Z-axis direction is denoted by D 1  and is about 100 μm, for example. It should be appreciated that the amplitude of the vibration arms  121 A to  121 D is limited by the depth D 1 . That is, their maximum amplitude on the inner side of the lower cover  20  is about 100 μm. 
     The lower cover  20  may be regarded as part of the SOI substrate. With the resonator  10  and the lower cover  20  being regarded as a MEMS substrate integrally formed of the SOI substrate, the Si substrate P 10  of the lower cover  20  is a support substrate of the SOI substrate, the temperature characteristics correction layer F 21  of the resonator  10  is a buried oxide (BOX) layer, and the Si substrate F 2  of the resonator  10  is an active layer of the SOI substrate. Part of the continuous MEMS substrate may be used to form various types of semiconductor elements and circuits on the outer portion of the resonance device  1 . 
     Upper Cover  30   
     The bottom plate  32  and the side wall  33  of the upper cover  30  are integrally formed of an Si substrate Q 10 . It is preferred that atop surface and aback surface of the upper cover  30  and inner surfaces of the through-holes be covered with a silicon oxide film Q 11 . The silicon oxide film Q 11  is formed on atop surface of the Si substrate Q 10  by, for example, oxidation of the Si substrate Q 10  or chemical vapor deposition (CVD). The Si substrate Q 10  lies open to the inside of the recess  31  of the upper cover  30 . A getter layer may be provided on a surface of the recess  31  of the upper cover  30  in a manner so as to face the resonator  10 . The getter layer is formed from, for example, titanium (Ti). The getter layer adsorbs gas removed from a joint part H. The decrease in the degree of vacuum in the vibration space may be minimized accordingly. Alternatively, the getter layer may be provided on a surface of the recess  21  of the lower cover  20  in a manner so as to face the resonator  10 . In some embodiments, two getter layers may respectively be formed on the surface of the recess  21  of the lower cover  20  and the surface of the recess  31  of the upper cover  30  in a manner so as to face the resonator  10 . 
     The thickness of the upper cover  30  in the Z-axis direction is about 150 μm, for example. The depth of the recess  31  in the Z-axis direction is denoted by D 2  and is about 100 μm, for example. The amplitude of the vibration arms  121 A to  121 D is limited by the depth D 2 ; that is, their maximum amplitude on the inner side of the upper cover  30  is about 100 μm. 
     As further shown in the exemplary aspect, terminals are provided on the upper surface of the upper cover  30  (i.e., the surface opposite the surface facing the resonator  10 ) and are denoted by T 1 , T 2 , and T 3 , respectively. The terminal T 1  is a mounting terminal that forms a connection between the metal film E 1  and the ground. The terminal T 2  is a mounting terminal that forms an electrical connection between the external power source and the regions of the metal film E 2  that are included in the outer vibration arms  121 A and  121 D. The terminal T 3  is amounting terminal that forms an electrical connection between the external power source and regions of the metal film E 2  that are included in the inner vibration arms  121 B and  121 C. The terminals T 1  to T 3  are formed of a metallized (base) layer of, for example, chromium (Cr), tungsten (W), or nickel (Ni) and are plated with, for example, nickel (Ni), gold (Au), silver (Ag), or copper (Cu). With a view to achieving balanced parasitic capacitance and balanced mechanical strength, a dummy terminal electrically isolated from the resonator  10  may be provided on the top surface of the upper cover  30 . 
     The through-via electrodes V 1 , V 2 , and V 3  are provided in the side wall  33  of the upper cover  30 . The through-via electrode V 1  forms an electrical connection between the terminal T 1  and the extended line C 1 . The through-via electrode V 2  forms an electrical connection between the terminal T 2  and the extended line C 2 . The through-via electrode V 3  forms an electrical connection between the terminal T 3  and the extended line C 3 . The through-via electrodes V 1  to V 3  are through-holes extending in the Z-axis direction through the side wall  33  of the upper cover  30  and filled with an electrically conductive material. The electrically conductive material is, for example, polycrystalline silicon (Poly-Si), copper (Cu), or gold (Au). 
     The joint part H is provided between the side wall  33  of the upper cover  30  and the holding part  140  such that the side wall  33  of the upper cover  30  is joined to the holding part  140  of the resonator  10 . The joint part H is in the form of a closed loop surrounding the vibration part  110  in the X-Y plane such that the vibration space for the resonator  10  is sealed airtight and maintained under vacuum. The joint part His formed of a metal film obtained by eutectic bonding of, for example, an aluminum (Al) film, a germanium (Ge) film, and an aluminum (Al) film that are stacked on top of each other in the stated order. Alternatively, the joint part H may be formed of a combination of films selected, as appropriate, mainly from a gold (Au) film, a tin (Sn) film, a copper film (Cu), a titanium (Ti) film, and a silicon (Si) film. The joint part H may contain metallic compounds such as titanium nitride (TiN) and tantalum nitride (TaN) to offer enhanced adhesion. 
     Operation 
     In the present embodiment, the terminal T 1  is grounded, and alternating voltages opposite in phase are applied to the terminals T 2  and T 3 , respectively. The electric field generated in the piezoelectric film F 3  in the outer vibration arms  121 A and  121 D and the electric field generated in the piezoelectric film F 3  in inner vibration arms  121 B and  121 C are thus opposite in phase. Consequently, the vibration of the outer vibration arms  121 A and  121 D and the vibration of the inner vibration arms  121 B and  121 C are opposite in phase. When, for example, the mass addition portion  122 A of the outer vibration arm  121 A and the mass addition portion  122 D of the outer vibration arm  121 D undergo displacement toward an inner surface of the upper cover  30 , the mass addition portion  122 B of the inner vibration arm  121 B and the mass addition portion  122 C of the vibration arm  121 C undergo displacement toward the inner surface of the lower cover  20 . That is, the vibration arm  121 A and the vibration arm  121 B, which are adjacent to each other, vibrate vertically in mutually opposite directions about a central axis r 1  extending in the Y-axis direction between the vibration arm  121 A and the vibration arm  121 B. Similarly, the vibration arm  121 C and the vibration arm  121 D, which are adjacent to each other, vibrate vertically in mutually opposite directions about a central axis r 2  extending in the Y-axis direction between the vibration arm  121 C and the vibration arm  121 D. With the direction of twisting moment on the central axis r 1  and the direction of twisting moment on the central axis r 2  being opposite to each other, the base section  130  is bent and vibrates. The vibration arms  121 A to  121 D vibrate in a range of about 100 μm at the maximum and vibrate in a range of about 10 μm under normal driving conditions. 
     Mass Addition Films  125 A to  125 D 
     The following describes the shapes of the mass addition films  125 A to  125 D with reference to  FIGS. 6 and 7  according to an exemplary aspect.  FIG. 6  is a sectional view of a mass addition portion according to the first embodiment, the sectional view being taken along a Y-Z plane.  FIG. 7  is a sectional view of the mass addition portion according to the first embodiment, the sectional view being taken along a Z-X plane. The mass addition films  125 A to  125 D in their respective sectional views taken along Y-Z planes have the same shape. For this reason, the shape of the mass addition film  125 A viewed in section will be described below with reference to  FIG. 6 , and the mass additional films  125 B to  125 D viewed in section will neither be illustrated nor described below. 
     Referring to  FIG. 6 , the mass addition film  125 A includes a film central portion  125 AO, a film front end portion  125 AA (or simply a front end), and a film rear end portion  125 AB (or simply a rear end). The film central portion  125 AO is in a central region of the mass addition portion  122 A. The film front end portion  125 AA and the film rear end portion  125 AB are in an end region of the mass addition portion  122 A. The film front end portion  125 AA is closer than the film central portion  125 AO to the open end, and the film rear end portion  125 AB is closer than the film central portion  125 AO to the fixed end. Moreover, the thickness of the film central portion  125 AO in the Z-axis direction (hereinafter simply referred to as the thickness) is smaller than the thickness of each of the film front end portion  125 AA and the film rear end portion  125 AB. The mass addition film  125 A has, on a top surface side thereof, an inclined surface extending from the film central portion  125 AO to the film front end portion  125 AA and an inclined surface extending from the film central portion  125 AO to the film rear end portion  125 AB. The inclined surfaces of the mass addition film  125 A are formed through trimming processing applied to the mass addition film  125 A. The central region and the end region of the mass addition portion  122 A except for the mass addition film  125 A are substantially equal in thickness to each other. The thickness of the mass addition portion  122 A except for the mass addition film  125 A herein refers to the sum of the thicknesses of the Si substrate F 2 , the temperature characteristics correction layer F 21 , the metal film E 1 , the piezoelectric film F 3 , and the protective film F 5 . When the thickness of the mass addition film  125 A is taken into account, the central region of the mass addition portion  122 A is thinner than the end region of the mass addition portion  122 A. 
     It is noted that the central region of the mass addition portion  122 A herein does not refer to only the exact center of the mass addition portion  122 A and refers to a central region including the center (i.e., a region within a predetermined range from the center) of the mass addition portion  122 A viewed in plan from the side on which the upper cover  30  is disposed. The end region of the mass addition portion  122 A herein does not refer to only an outer edge of the mass addition portion  122 A and refers to an outer region including the outer edge (i.e., a region extending from the outer edge with a predetermined width) of the mass addition portion  122 A viewed in plan from the side on which the upper cover  30  is disposed. As shown, the central region of the mass addition portion  122 A is thinner than the end region of the mass addition portion  122 A. Specifically, the thinnest part of the central region of the mass addition portion  122 A is thinner than the thickest part of the end region of the mass addition portion  122 A. With regard to the example in  FIG. 6 , the thinnest part of the central region of the mass addition portion  122 A is thinner than any other region of the mass addition portion  122 A. The same relationship applies to the film central portion  125 AO, the film front end portion  125 AA, and the film rear end portion  125 AB of the mass addition film  125 A. 
     Each of the inclined surfaces of the mass addition film  125 A is a curved surface whose inclination increases with increasing distance from the central region of the mass addition portion  122 A and with increasing proximity to the end region of the mass addition portion  122 A. The inclination of the curved inclined surfaces changes in a continuous manner. That is, the mass addition portion  122 A has atop surface that is in the form of a bowl. The inclined surfaces may be formed into the given shape by etching through the use of, for example, a shadow mask during the trimming processing. 
     Referring to  FIG. 7 , the mass addition film  125 A also includes a film left end portion  125 AC and a film right end portion  125 AD, which are on the end region of the mass addition portion  122 A. The film left end portion  125 AC is closer than the film central portion  125 AO to the left frame  141 C of the holding part  140  (not illustrated), and the film right end portion  125 AD is closer than the film central portion  125 AO to the right frame  141 D of the holding part  140  (not illustrated). Similarly, the mass addition film  125 B includes a film left end portion  125 BC and a film right end portion  125 BD, the mass addition film  125 C includes a film left end portion  125 CC and a film right end portion  125 CD, and the mass addition film  125 D includes a film left end portion  125 DC and a film right end portion  125 DD. 
     The film central portion  125 AO of the mass addition film  125 A is thinner than the film left end portion  125 AC and is substantially equal in thickness to the film right end portion  125 AD. As in the sectional view taken along the Y-Z plane, the mass addition film  125 A has an inclined surface, which extends from the film central portion  125 AO to the film left end portion  125 AC of the mass addition film  125 A. The mass addition film  125 B includes a film central portion  125 BO, whose thickness is substantially equal to the thickness of the film left end portion  125 BC and is substantially equal to the thickness of the film right end portion  125 BD. The mass addition film  125 C includes a film central portion  125 CO, whose thickness is substantially equal to the thickness of the film left end portion  125 CC and is substantial equal to the thickness of the film right end portion  125 CD. The mass addition film  125 D includes a film central portion  125 DO, whose thickness is substantially equal to the thickness of the film left end portion  125 DC and is smaller than the thickness the film right end portion  125 DD. As with the mass addition film  125 A, the mass addition film  125 D has an inclined surface, which extends from the film central portion  125 DO to the film right end portion  125 DD of the mass addition film  125 D. 
     Specifically, the mass addition film  125 A of the outer vibration arm  121 A and the mass addition film  125 D of the outer vibration arm  121 D each have an inclined surface such that their respective outer end portions are thicker (i.e., have a greater height in the Z-axis direction) than their respective inner end portions, with the inclination of the surface changing continuously from the inner end portion to the outer end portion. The mass addition film  125 B of the inner vibration arm  121 B and the mass addition film  125 C of the inner vibration arm  121 C each have an outer end portion and an inner portion that are substantially equal in thickness to each other and that are substantially equal in thickness to the inner end portion of the mass addition film  125 A of the outer vibration arm  121 A and to the thickness of the inner end portion of the mass addition film  125 D of the outer vibration arm  121 D. The mass addition film  125 A of the outer vibration arm  121 A and the mass addition film  125 D of the outer vibration arm  121 D are each heavier than the mass addition film  125 B of the inner vibration arm  121 B and are each heavier than the mass addition film  125 C of the inner vibration arm  121 C. 
     The shapes of the mass addition films  125 A to  125 D in their respective sectional views taken along Z-X planes are not necessarily as described above. For example, the mass addition films  125 A to  125 D viewed in section may be substantially identical in shape. Specifically, the mass addition films  125 A to  125 D may have their respective film central portions that are thinner than their respective film left end portions and that are thinner than their respective film left end portions, and the mass addition films  125 A to  125 D may each have an inclined surface than is in the form of a bowl. 
     In the present embodiment, the amount of displacement of the vibration part  110  is greater in regions corresponding to the mass addition portions  122 A to  122 D than in any other region (e.g., the base section  130  and the arm portions  123 A to  123 D), and the mass addition portions  122 A to  122 D have inclined surfaces that slope in such a manner that the mass addition portions  122 A to  122 D each have end regions and a central region thinner than the end regions. Specifically, the mass addition portions  122 A to  122 D each have an inclined surface that slopes in such a manner that the mass addition portions  122 A to  122 D each have end regions and a central region thinner than the end regions in a sectional view taken along a line extending in the direction in which the vibration arms  121 A to  121 D extend. When external stress is applied, the amount of deformation in the end regions of each of the mass addition portions  122 A to  122 D is greater than the amount of deformation in the central region of the corresponding one of the mass addition portions  122 A to  122 D. When the vibration part undergoes a large amount of displacement due to, for example, drop impacts, the end regions of the mass addition portions  122 A to  122 D will be the first to come into contact with another member and will be significantly deformed. Consequently, the shock will be lessened. This configuration will eliminate or reduce the possibility that the mass addition portions  122 A to  122 D will become damaged due to, for example, drop impacts. The shock absorbency of the end regions of the mass addition portions  122 A to  122 D is conducive to taking some of the load that would be applied to the fixed ends (i.e., basal portions) of the vibration arms  121 A to  121 D when the mass addition portions  122 A to  122 D come into contact with another member. This will eliminate or reduce the possibility that the basal portions of the vibration arms  121 A to  121 D will become damaged. 
     Each of the inclined surfaces of the mass addition portions  122 A to  122 D is a curved surface whose inclination increases with increasing distance from the central region and with increasing proximity to the end region. This enables a reduction in the impact stress on the surface between the thin central region and the thick end region of each of the mass addition portions  122 A to  122 D. In case of accidental contact with another member, the end regions of the mass addition portions  122 A to  122 D will be subjected to external stress; nevertheless, the external stress will be kept from concentrating in a specific site and will be dispersed throughout the mass addition portions  122 A to  122 D. This makes the mass addition portions  122 A to  122 D more durable. 
     Moreover, the inclined surfaces of the mass addition portions  122 A to  122 D are surfaces of the mass addition films  125 A to  125 D. The forming of the inclined surfaces of the mass addition films  125 A to  125 D may be concurrent with the frequency adjustment during the trimming processing. With the mass addition films  125 A to  125 D being electrically connected to the metal film E 1 , there is little concern for degradation of vibration characteristics that is due to the coulomb interaction, which would otherwise be caused by electrification of the mass addition films  125 A to  125 D during the forming of the inclined surfaces by ion beam etching in the trimming processing. 
     The mass addition films  125 A to  125 D may each have a film central portion and a film rear end portion thicker than the film central portion. In this case, the inclined surfaces may be formed in such a manner that regions located away from the film rear end portions of the mass addition films  125 A to  125 D are radiated with ion beams during ion beam etching. This configuration enables a reduction in the amount of ion beam radiation received by the protective film F 5 , and the electrification of the protective film F 5  is inhibited. The variability of the vibration characteristics that is due to the coulomb interaction may be eliminated or reduced accordingly. 
     The mass addition films  125 A to  125 D may each have a film central portion and a film front end portion thicker than the film central portion. In this case, the region of each of the mass addition films  125 A to  125 D that is most likely to come into contact with the upper cover  30  when the vibration arms undergo a large amount of displacement is thicker than any other region of the corresponding one of the mass addition films  125 A to  125 D. The mass addition films  125 A to  125 D are thus less prone to damage. 
     It is noted that it is not always required that the aforementioned shape of the mass addition portions in sectional views each taken along a line extending in the direction in which the vibration arms extend be applicable to all of the vibration arms. For example, at least one of the vibration arms  121 A to  121 D may include a mass addition portion having an inclined surface that slopes in such a manner that the vibration arm has a central portion and an end portion thicker than the centration portion. In this case, the relevant mass addition portion with the inclined surface formed thereon is less prone to damage. 
     The mass addition films  125 A to  125 D may include a film central portion and a film front end portion and a film rear end portion that are thicker than the central portion. In this case, both the film front end portion and the film rear end portion come into contact with the upper cover  30  when the vibration arms undergo a large amount of displacement. The area of contact between the upper cover  30  and each of the mass addition films  125 A to  125 D is greater than if one of the film front end portion and the film rear end portion of each of the mass addition films  125 A to  125 D is thicker than the film central portion. In case of accidental contact with the upper cover  30 , the mass addition films  125 A to  125 D can thus cause further dispersion of shock. The mass addition films  125 A to  125 D are thus less prone to damage. 
     Upon application of, for example, drop impacts, the base section  130 , the vibration arms  121 A to  121 D, and the holding arm  150  entirely undergo displacement especially when the holding arm  150  includes the holding rear arms  152 A and  152 B and the holding side arms  153 A and  153 B. Both the fixed end and the open end of each of the vibration arms  121 A to  121 D would come close to the upper cover  30 , and consequently, the end regions thicker than the central regions of the mass addition portions  122 A to  122 D would entirely contact the upper cover  30 . As the area of the end region thicker than the central region of each of the mass addition portions  122 A to  122 D is increased, the area of contact between the upper cover  30  and each of the mass addition portions  122 A to  122 D is increased correspondingly, irrespective of the position of the end region relative to the central region. In case of accidental contact with the upper cover  30 , the mass addition portions  122 A to  122 D can thus cause dispersion of shock. 
     At least one of the mass addition films  125 A to  125 D may include a film central portion and a film left end portion thicker than the film central portion and/or a film right end portion thicker than the film central portion. In this case as well, an increase in the area of contact between the upper cover  30  and the relevant mass addition film is achieved. As a result, when there is an accidental contact with the upper cover  30 , the relevant mass addition film can disperses the shock of the impact. 
     A specific configuration examples is as follows. As to the outer vibration arm  121 A on the left side, the film left end portion  125 AC, which is the outer end portion of the mass addition film  125 A, is thicker than each of the film central portion  125 AO and the film right end portion  125 AD the mass addition film  125 A. As to the outer vibration arm  121 D on the right side, the film right end portion  125 DD, which is the outer end portion of the mass addition film  125 D, is thicker than each of the film central portion  125 DO and the film left end portion  125 DC of the mass addition film  125 D. As to the inner vibration arm  121 B, the film left end portion  125 BC and the film right end portion  125 BD of the mass addition film  125 B are each substantially equal in thickness to the film central portion  125 BO of the mass addition film  125 B. As to the inner vibration arm  121 C, the film left end portion  125 CC and the film right end portion  125 CD of the mass addition film  125 C are each substantially equal in thickness to the film central portion  125 CO of the mass addition film  125 C. The mass addition film  125 A to  125 D are formed into the given shape during the trimming processing in such a manner that the mass addition film  125 A to  125 D are etched all at once through a mask having an opening facing all of the mass addition film  125 A to  125 D. In the etching process, the mask having the common opening may be positioned on a target site over the mass addition films  125 A to  125 D more easily than a mask having individual openings facing the mass addition films  125 A to  125 D. The yield of resonators may be improved accordingly. At least specific ones of the vibration arms  121 A to  121 D are formed into the given shape, or more specifically, an increase in the area of contact between the upper cover  30  and each of the mass addition portion  122 A of the outer vibration arm  121 A and the mass addition portion  122 D of the outer vibration arm  121 D is achieved. In case of accidental contact with the upper cover  30 , the mass addition portions  122 A and  122 D can disperse shock caused by the impact. The mass addition portion  122 B of the inner vibration arm  121 B and the mass addition portion  122 C of the inner vibration arm  121 C are each heavier than the mass addition portion  122 A of the outer vibration arm  121 A and are each heavier than the mass addition portion  122 D of the outer vibration arm  121 D, thus yielding an improvement of the drive level dependency (DLD). 
     The vibration arms  121 A to  121 D may each include a film central portion and a film left end portion and a film right end portion that are thicker than the film central portion in a sectional view taken along a line extending in a direction crossing the direction in which the vibration arms  121 A to  121 D extend (i.e., in a sectional view taken along a line extending in the direction in which the vibration arms  121 A to  121 D are arranged side by side). An increase in the area of contact between the upper cover  30  and each of the mass addition portion  122 A of the vibration arm  121 A, the mass addition portion  122 B of the vibration arm  121 B, the mass addition portion  122 C of the vibration arm  121 C, and the mass addition portion  122 D of the vibration arm  121 D is achieved. In case of accidental contact with the upper cover  30 , the mass addition portions  122 A to  122 D can thus cause dispersion of shock. 
     Although according to the exemplary embodiment, the mass addition portions  122 A to  122 D each have, on a top side thereof, an inclined surface that slopes in such a manner that the central region of the mass addition portion is thinner than at least one of the end regions of the mass addition portion, the resonator  10  is not necessarily in the configuration as described above. For example, the protective film F 5  included in the mass addition portions  122 A to  122 D may have inclined surfaces that slope in such a manner that the mass addition portions  122 A to  122 D each have end regions and a central region thinner than at least one of the end regions. In this case, the mass addition films  125 A to  125 D may be omitted or may lie along the inclined surfaces of the protective film F 5 . Similarly, the Si substrate F 2  included in the mass addition portions  122 A to  122 D may have inclined surfaces that slope in such a manner that the mass addition portions  122 A to  122 D each have end regions and a central region thinner than at least one of the end regions. 
     The following describes the configuration of resonators according to additional exemplary embodiments of the present invention. Description of features common to the first embodiment and other embodiments will be omitted, and the following embodiments will be described with regard to only their distinctive features. Specifically, not every embodiment refers to actions and effects caused by similar configurations. 
     Second Exemplary Embodiment 
     The following describes a mass addition portion  222 A of a vibration arm  221 A of a resonator according to a second embodiment with reference to  FIG. 8 .  FIG. 8  is a sectional view of a mass addition portion according to the second embodiment, the sectional view being taken along a Y-Z plane. As with the resonator  10  according to the first embodiment, the resonator according to the second embodiment includes vibration arms each including a mass addition portion. The mass addition portions in sectional views each taken along a line extending in the direction in which the respective vibration arms extend are geometrically identical to the mass addition portion  222 A of the vibration arm  221 A in  FIG. 8 . For this reason, the mass addition portions of the vibration arms other than the vibration arm  221 A will neither be illustrated nor described below. 
     The mass addition portion  222 A of the vibration arm  221 A includes a mass addition film  225 A, which includes a film central portion  225 AO, a film front end portion  225 AA, and a film rear end portion  225 AB. As shown the film rear end portion  225 AB is thicker than the film central portion  225 AO and is thicker than the film front end portion  225 AA. As in the first embodiment, this enables a reduction in the amount of ion beam radiation received by another member (e.g., the protective film) included in the vibration arm  221 A, and as a result, the electrification of the regions adjacent to the mass addition portion  222 A of the vibration arm  221 A is inhibited accordingly. 
     Third Exemplary Embodiment 
     The following describes a mass addition portion  322 A of a vibration arm  321 A of a resonator according to a third embodiment with reference to  FIG. 9 .  FIG. 9  is a sectional view of a mass addition portion according to the third embodiment, the sectional view being taken along a Y-Z plane. As in the second embodiment, the mass addition portions of the vibration arms (not illustrated) other than the vibration arm  321 A will not be described below with respect to their shapes in sectional views. 
     The mass addition portion  322 A of the vibration arm  321 A includes a mass addition film  325 A, which includes a film central portion  325 AO, a film front end portion  325 AA, and a film rear end portion  325 AB. The film front end portion  325 AA is thicker than the film central portion  325 AO and is thicker than the film rear end portion  325 AB. As in the first embodiment, the region of the mass addition portion  322 A that is most likely to come into contact with the upper cover  30  is thicker than any other region of the mass addition portion  322 A, and the mass addition film  325 A is thus less prone to damage. 
     Fourth Exemplary Embodiment 
     The following describes a mass addition portion  422 A of a vibration arm  421 A of a resonator according to a fourth embodiment with reference to  FIG. 10 .  FIG. 10  is a sectional view of a mass addition portion according to the fourth embodiment, the sectional view being taken along a Y-Z plane. As in the second embodiment, the mass addition portions of the vibration arms (not illustrated) other than the vibration arm  421 A will not be described below with respect to their shapes in sectional views. 
     The mass addition portion  422 A of the vibration arm  421 A includes a mass addition film  425 A, which includes a film central portion  425 AO, a film front end portion  425 AA, and a film rear end portion  425 AB. In a sectional view taken along a line extending in the direction in which the vibration arm  421 A extends, the mass addition film  425 A has an inner inclined surface on the film front end portion  425 AA and an inner inclined surface on the film rear end portion  425 AB. The inner inclined surfaces are contiguous to the film central portion  425 AO. The mass addition film  425 A also has an outer inclined surface on the film front end portion  425 AA and an outer inclined surface on the film rear end portion  425 AB. The outer inclined surfaces are curved and located on the respective sides opposite the side on which the film central portion  425 AO is located. The outer inclined surfaces are side surfaces each forming a connection between an upper surface and a lower surface of the mass addition film  425 A. The mass addition film  425 A may be formed into the given shape in the following manner: trimming processing is performed by using a shadow mask such that the upper surface is partially removed to form the inner inclined surfaces, and the upper surface is then entirely subjected to trimming processing in a manner so as to form the outer inclined surfaces. In case of accidental contact with another member, the end regions of the mass addition portions will be subjected to external stress; nevertheless, owing to the inner inclined surfaces and outer inclined surfaces on the film end portions, the external stress will be further kept from concentrating in a specific site and will be further dispersed throughout the mass addition portions. 
     Fifth Exemplary Embodiment 
     The following describes the configuration of a resonator  500  according to a fifth embodiment with reference to  FIGS. 11 and 12 .  FIG. 11  is a plan view of a resonator according to a fifth embodiment, schematically illustrating the structure of the resonator.  FIG. 12  is a sectional view of a mass addition portion according to the fifth embodiment, the sectional view being taken along a Y-Z plane. 
     As with the resonator  10  according to the first embodiment, the resonator  500  according to the fifth embodiment includes a vibration part, a holding member, and a holding arm, which are denoted by  510 ,  540 , and  550 , respectively. As shown, the holding part  540  (i.e., the frame) includes a front frame  541 A, a rear frame  541 B, a left frame  541 C, and a right frame  541 D. The resonator  500  includes an Si  5 F 2 , a temperature characteristics correction layer  5 F 21 , a metal film  5 E 1 , a metal film  5 E 2 , a piezoelectric film  5 F 3 , and a protective film  5 F 5 . 
     The vibration part  510  in an external view is substantially cuboid and is in the form of a flat plate lying in an X-Y plane. When the X-Y plane is viewed in plan as in  FIG. 11 , the vibration part  510  has a rectangular shape with long sides extending in the Y-axis direction. The piezoelectric film  5 F 3  and the metal films  5 E 1  and  5 E 2  are rectangular and extend substantially allover the vibration part  510 . The metal films  5 E 1  and  5 E 2  are laid on opposite sides with the piezoelectric film  5 F 3  therebetween. Upon application of an electric field between the metal film  5 E 1  and the metal film  5 E 2 , which respectively function as a lower electrode and an upper electrode, the piezoelectric film  5 F 3  expands and contracts in the X-axis direction and the Y-axis direction. That is, the vibration part  510  vibrates in the expansion-contraction (contour) vibration mode. It is not required that the vibration part  510  be in the form of a flat plate. For example, the vibration part  510  may have the shape of a quadrangular prism having a certain thickness. Referring to  FIG. 11 , the vibration part  510  has a front side  511 A, a rear side  511 B, a left side  511 C, and a right side  511 D. The front side  511 A and the rear side  511 B, respectively, are adjacent to the front frame  541 A and the rear frame  541 B and constitute a pair of short sides extending in the X-axis direction. The left side  511 C and the right side  511 D, respectively, are adjacent to the left frame  541 C and the right frame  541 D and constitute a pair of long sides extending in the Y-axis direction. Each of the front side  511 A, the left side  511 C, and the right side  511 D is separated from the corresponding one of the front frame  541 A, the left frame  541 C, and the right frame  541 D by a certain release width. 
     Mass addition portions are placed in four corners and are denoted by  522 A to  522 D, respectively. The amount of displacement of the vibration part  510  is greater in the four corners than in any other region. When the X-Y plane is viewed in plan, the mass addition portions  522 A to  522 D are substantially rectangular and each have a pair of long sides and a pair of short sides. The long sides respectively extend along the left side  511 C and the right side  511 D, and the short sides respectively extend along the front side  511 A and the rear side  511 B. The mass addition portions  522 A to  522 D are covered with mass addition films  525 A to  525 D, each which is substantially rectangular and extends substantially all over a top surface of the corresponding one of the mass addition portions  522 A to  522 D. The mass addition film  525 A is adjacent to the corner defined by the front side  511 A and the left side  511 C. The mass addition film  525 B is adjacent to the corner defined the rear side  511 B and the left side  511 C. The mass addition film  525 C is adjacent to the corner defined by the rear side  511 B and the right side  511 D. The mass addition film  525 D is adjacent to the corner defined by the front side  511 A and the right side  511 D. 
     Referring to  FIG. 12 , the mass addition film  525 A has inclined surfaces that slope in such a manner that a film central portion  525 AO is thinner than each of a film front end portion  525 AA and a film rear end portion  525 AB. The mass addition film  525 A may have inclined surfaces that slope in such a manner that the film central portion  525 AO is thinner than a film left end portion (not illustrated) and a film right end portion (not illustrated). For example, the mass addition film  525 A may have inclined surfaces that slope in such a manner that the film front end portion and the film left end portion that are located away from a central portion of the vibration part  510  are thicker than the film central portion, with the film central portion being equal in thickness to the film rear end portion and the film right end portion that are close to the central portion of the vibration part  510 . The mass addition films  525 B to  525 D may each have inclined surfaces similar to the inclined surfaces of the mass addition film  525 A. 
     The holding arm  550  includes a rear holding arm  551 B. The rear holding arm  551 B forms a connection between the rear side  511 B of the vibration part  510  and the rear frame  541 B of the holding part  540 . The rear holding arm  551 B includes connecting arms, which are denoted by  552 B,  553 B, and  554 B, respectively. The connecting arm  552 B forms a connection between the vibration part  510  and the connecting arm  553 B, and the connecting arm  554 B forms a connection between the connecting arm  553 B and the rear frame  541 B. The connecting arm  552 B is connected to a center of the rear side  511 B in the X-axis direction, and the connecting arm  554 B is connected to a center of the rear frame  541 B in the X-axis direction. The connecting arms  552 B and  554 B, respectively, are connected to centers of the connecting arm  553 B in the X-axis direction. The connecting arms  552 B and  554 B are substantially equal in width in the X-axis direction. When viewed in plan, the connecting arm  553 B is in a semicircular shape whose diameter is greater than the width of each of the connecting arms  552 B and  554 B in the X-axis direction. The width of the connecting arm  553 B in the X-axis direction is denoted by WB and decreases with increasing distance from the connecting arm  552 B and with increasing proximity to the connecting arm  554 B. In other words, the connecting arm  553 B has a straight side wall adjacent to the connecting arm  552 B and an arc-shaped side wall adjacent to the connecting arm  554 B. The arc-shaped wall of the connecting arm  553 B reflects vibration generated in the vibration part  510 , thus enhancing the vibration confinement effect. 
     Sixth Exemplary Embodiment 
     The following describes the configuration of a resonator  600  according to a sixth embodiment with reference to  FIGS. 13 and 14 .  FIG. 13  is a plan view of a resonator according to a sixth embodiment, schematically illustrating the structure of the resonator.  FIG. 14  is a sectional view of a mass addition portion according to the sixth embodiment, the sectional view being taken along a Z-X plane. 
     As with the resonator  500  according to the fifth embodiment, the resonator  600  according to the sixth embodiment includes a vibration part, a holding member, and a holding arm, which are denoted by  610 ,  640 , and  650 , respectively. The vibration part  610  has a front side  611 A, a rear side  611 B, a left side  611 C, and a right side  611 D and vibrates in the expansion-contraction vibration mode in the X-axis direction and the Y-axis direction. The holding part  640  includes a front frame  641 A, a rear frame  641 B, a left frame  641 C, and a right frame  641 D. The vibration part  610  includes an Si substrate  6 F 2 , a temperature characteristics correction layer  6 F 21 , a metal layer  6 E 1 , a metal layer  6 E 2 , a piezoelectric film  6 F 3 , and a protective film  6 F 5 , which are stacked on top of each other. 
     When the X-Y plane is viewed in plan as in  FIG. 13 , the vibration part  610  has a rectangular shape with long sides extending in the X-axis direction. The front side  611 A and the rear side  611 B constitute a pair of long sides extending in the X-axis direction, and the left side  611 C and the right side  611 D constitute a pair of short sides extending in the Y-axis direction. When the X-Y plane is viewed in plan, the vibration part  610  is covered with a mass addition portion  622 , which extends substantially all over a surface of the mass addition portion  622 . In other words, the vibration part  610  is covered with a mass addition film  625 , which extends substantially all over a surface of the vibration part  610 . Referring to  FIG. 14 , the mass addition film  625  has inclined surfaces that slope in such a manner that a film central portion  6250  is thinner than each of a film left end portion  625 C and a film right end portion  625 D. The mass addition film  625  may have inclined surfaces that slope in such a manner that the film central portion  6250  is thinner than a film front end portion (not illustrated) and a film rear end portion (not illustrated). 
     The mass addition film  625  may have inclined surfaces that slope in such a manner that the film left end portion  625 C and the film right end portion  625 D are each partially thinned. To give a specific example, the mass addition film  625  may have inclined surfaces that slope in such a manner that regions adjacent to corner portions defined by the sides  611 A to  611 D are each thicker than regions adjacent to midsections of the sides  611 A to  611 D and are each thicker than a central portion enclosed within the sides  611 A to  611 D. 
     The holding arm  650  includes a front holding arm  651 A and a rear holding arm  651 B, which are arranged with the vibration part  610  therebetween in the Y-axis direction. The front holding arm  651 A forms a connection between the front frame  641 A of the holding part  640  and the front side  611 A of the vibration part  610 , and the rear holding arm  651 B forms a connection between the rear frame  641 B of the holding part  640  and the rear side  611 B of the vibration part  610 . The rear holding arm  651 B is structurally similar to the rear holding arm  551 B in the fifth embodiment, and the front holding arm  651 A and the rear holding arm  651 B are mirror images of each other with respect to the vibration part  610  disposed therebetween. 
     Exemplary embodiments of the present invention will be described, in part or in whole, as follows. It is noted that the following should not be construed as limiting the scope of the present invention. 
     An exemplary aspect of the present invention provides a resonator including a vibration part and a mass addition portion. The vibration part includes a piezoelectric film, an upper electrode, and a lower electrode. The upper and lower electrodes are disposed on opposite sides with the piezoelectric film therebetween. The amount of displacement of the vibration part is greater in a region corresponding to at least part of the mass addition portion than in any other region. The mass addition portion has an inclined surface that slopes in such a manner that the mass addition portion has end regions and a central region thinner than at least one of the end regions when the vibration part is viewed in section. 
     When external stress is applied, the amount of deformation in the at least one of the end regions of the mass addition portion is greater than the amount of deformation in the central region the mass addition portion. When the vibration part undergoes a large amount of displacement due to, for example, drop impacts, the at least one of the end regions of the mass addition portion will be the first to come into contact with another member and will be significantly deformed. Consequently, the shock will be lessened from the impact of the drop of the device. This will eliminate or reduce the possibility that the mass addition portion will become damaged due to, for example, drop impacts. 
     According to another exemplary, the resonator also includes a base section. The vibration part includes at least one vibration arm that has a fixed end connected to a front end portion of the base section and an open end located away from the front end portion. The mass addition portion is provided to the open end of the at least one vibration arm. The inclined surface of the mass addition portion slopes in such a manner that the central region is thinner than the at least one of the end regions in a sectional view taken along a line extending in a direction in which the at least one vibration arm extends. 
     The shock absorbency of the at least one of the end regions of the mass addition portion is conducive to taking some of the load that would be applied to the fixed end (i.e., a basal portion) of the at least one vibration arm when the mass addition portion comes into contact with another member. This will eliminate or reduce the possibility that the basal portion of the at least one vibration arm will become damaged. 
     In still another aspect, the inclined surface is a curved surface whose inclination increases with increasing distance from the central region and with increasing proximity to the at least one of the end regions. 
     This configuration eliminates a region of stress concentration, or more specifically, a corner portion on the surface between the thin central region and the thick end region of the mass addition portion. The mass addition portion is thus more durable to resist being damaged by accidental contact with another member. 
     Still another exemplary aspect is provided in which the at least one vibration arm includes a protective film for insulation. The upper electrode is overlaid with the protective film. The mass addition portion includes a mass addition film on the protective film. The inclined surface is a surface of the mass addition film. 
     The forming of the inclined surface of the mass addition film may thus be concurrent with frequency adjustment during trimming processing. 
     In still another aspect, the mass addition film is electrically conductive and is electrically connected to the upper electrode or the lower electrode. 
     There is little concern for degradation of vibration characteristics that is due to the coulomb interaction, which would otherwise be caused by electrification of the mass addition film during the forming of the inclined surface by ion beam etching in the trimming processing. 
     Still another exemplary aspect is provided in which the mass addition film includes a film central portion in the central region and a film rear end portion closer than the film central portion to the fixed end. The film rear end portion of the mass addition film is thicker than the film central portion of the mass addition film. 
     The inclined surface of this configuration may be formed in such a manner that a region located away from the film rear end portion of the mass addition film is radiated with ion beams during ion beam etching. This configuration enables a reduction in the amount of ion beam radiation received by the protective film, and the electrification of the protective film is inhibited. The variability of the vibration characteristics that is due to the coulomb interaction may be eliminated or reduced accordingly. 
     Still another exemplary aspect is provided in which the mass addition film includes a film central portion in the central region and a film front end portion closer than the film central portion to the open end. The film front end portion of the mass addition film is thicker than the film central portion of the mass addition film. 
     The region of the mass addition film that is most likely to come into contact with another member when the at least one vibration arm undergoes a large amount of displacement is thicker than any other region of the mass addition film. The mass addition film is thus less prone to damage. 
     Still another exemplary aspect is provided in which the resonator also includes a holding part and a holding arm. The holding part holds the base section and the at least one vibration arm. The holding arm forms a connection between the base section and the holding part. The holding arm includes a holding rear arm and a holding side arm. The holding rear arm is connected to a rear end portion opposite the front end portion of the base section. The holding side arm is connected to the holding rear arm and extends along the at least one vibration arm in a manner so as to lie between the base section and the holding part. 
     Upon application of, for example, drop impacts, the base section and the at least one vibration arm entirely undergo displacement. Both the fixed end and the open end of the at least one vibration arm would come close to another member, and consequently, the end region thicker than the central region of the mass addition portion would entirely come into contact with the relevant member. As the area of the end region thicker than the central region of the mass addition portion is increased, the area of contact between the mass addition portion and the relevant member is increased correspondingly, irrespective of the position of the end region relative to the central region. In case of accidental contact with the relevant member, the mass addition portion can thus cause dispersion of shock. 
     Still another exemplary aspect provides a resonance device including the resonator, a lower cover, and an upper cover. The lower cover is joined to the resonator. The upper cover is joined to the lower cover with the resonator therebetween. A vibration space in which the at least one vibration arm vibrates is defined between the upper cover and the lower cover. 
     In general, the embodiments above have been described to facilitate the understanding of the present invention and should not be construed as limiting the scope of the present invention. The present invention may be altered and/or improved without departing from the spirit of the present invention and embraces equivalents thereof. That is, the embodiments with design changes made as appropriate by those skilled in the art fall within the scope of the present invention as long as the features of the present invention are involved. For example, constituent components in the embodiments above and the arrangement, materials, conditions, shapes, and sizes of the constituent components are not limited to those mentioned in the description and may be changed as appropriate. Resonators that operate in modes other than the bending-vibration mode and the expansion-contraction vibration mode may include such a mass addition portion. Effects similar to those of the aforementioned resonator may be produced when the amount of displacement of the vibration part is greater in a region corresponding to at least part of the mass addition portion than in any other region and when the mass addition portion has an inclined surface that slopes in such a manner that the mass addition portion has end regions and a central region thinner than at least one of the end regions. Varying combinations of the components of the embodiments may be devised as long as they are technically possible, and these combinations also fall within the scope of the present invention as long as the features of the present invention are involved. 
     REFERENCE SIGNS LIST 
     
         
         
           
               1  resonance device 
               10  resonator 
               20  lower cover 
               30  upper cover 
               21 ,  31  recess 
               22 ,  32  bottom plate 
               23 ,  33  side wall 
               110  vibration part 
               121 A to  121 D vibration arm 
               122 A to  122 D mass addition portion 
               123 A to  123 D arm portion 
               125 A to  125 D mass addition film 
               125 AO film central portion 
               125 AA film front end portion 
               125 AB film rear end portion 
               125 AC film left end portion 
               125 AD film right end portion 
               130  base section 
               131 A front end portion 
               131 B rear end portion 
               131 C left end portion 
               131 D right end portion 
               140  holding part 
               141 A front frame 
               141 B rear frame 
               141 C left frame 
               141 D right frame 
               150  holding arm 
               151 A left holding arm 
               151 B right holding arm 
               152 A,  152 B holding rear arm 
               153 A,  153 B holding side arm 
             F 2  Si substrate 
             F 21  temperature characteristics correction layer 
             F 3  piezoelectric film 
             F 5  protective film 
             E 1  metal film (lower electrode) 
             E 2  metal film (upper electrode)