Patent Publication Number: US-2022231663-A1

Title: Resonance device and method for manufacturing same

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation of PCT/JP2020/024369 filed Jun. 22, 2020, which claims priority to Japanese Patent Application No. 2019-221957, filed Dec. 9, 2019, the entire contents of each of which are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present invention relates to a resonance device and a method for manufacturing the same. 
     BACKGROUND 
     Currently, resonance devices are used for applications such as timing devices, sensors, oscillators, and the like in various electronic devices such as mobile communication terminals, communication base stations, and home appliances. Such resonance devices include, for example, a lower cover, an upper cover forming the interior space with the lower cover, and a resonator having vibration arms that are held and configured to vibrate in the interior space. Such a resonance device is a type of micro electro mechanical system (MEMS), for example. 
     International Publication No. 2017/212677 (hereinafter “Patent Document 1”) discloses adjusting the frequency of a resonator by causing the distal end portions of excited vibration arms to collide with a lower cover and an upper cover. 
     However, with the frequency adjustment method of Patent Document 1, for example, in a case where a metal film is formed on the upper cover side of the distal end portions of the vibration arms, even when the distal end portions of the vibration arms are caused to collie with the upper cover, the metal film may cause ductile deformation without being shaved, with the result that the weights of the vibration arms may be hardly changed. Further, since the amplitude of the vibration arms is restricted by a collision between the distal end portions of the vibration arms and the upper cover, the weights of the vibration arms may be changed only a little even when the distal end portions of the vibration arms collide with the lower cover. Thus, it cannot always be said that the related-art method is excellent in efficiency of the frequency adjustment process. 
     SUMMARY OF THE INVENTION 
     The exemplary embodiments of the present invention have been made in view of such circumstances. Thus, it is an object of the present invention to provide a resonance device with improved productivity and a method for manufacturing the same. 
     Accordingly, a resonance device is provided according to an exemplary aspect that includes a lower cover, an upper cover joined with the lower cover, and a resonator that has a vibration arm that generates bending vibration in an interior space provided between the lower cover and the upper cover. The vibration arm has a distal end provided with a metal film on a side that faces the upper cover. Moreover, a gap between the distal end of the vibration arm and the upper cover is larger than a gap between the distal end of the vibration arm and the lower cover. 
     In addition, a method for manufacturing a resonance device according to an exemplary aspect is provided that includes preparing a resonance device that includes a lower cover, an upper cover joined with the lower cover, and a resonator that has a vibration arm that generate bending vibration in an interior space provided between the lower cover and the upper cover. Moreover, the resonance device is provided with a gap between a distal end of the vibration arm and the upper cover that is larger than a gap between the distal end portion of the vibration arm and the lower cover. The method further includes a process of adjusting a frequency of the resonator by exciting the resonator to bring the distal end portion of the vibration arm into contact with at least the lower cover. 
     According to the exemplary embodiments of the present invention, a resonance device is provided with improved productivity and a method is provided for manufacturing the same. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a perspective view schematically illustrating the appearance of a resonance device according to a first exemplary embodiment. 
         FIG. 2  is an exploded perspective view schematically illustrating the structure of the resonance device according to the first exemplary embodiment. 
         FIG. 3  is a plan view schematically illustrating the structure of a resonator according to the first exemplary embodiment. 
         FIG. 4  is a sectional view along the X axis conceptually illustrating the stack structure of the resonance device illustrated in  FIG. 1 . 
         FIG. 5  is a sectional view along the Y axis conceptually illustrating the stack structure of the resonance device illustrated in  FIG. 1 . 
         FIG. 6  is a flowchart schematically illustrating a method for manufacturing the resonance device according to the first exemplary embodiment. 
         FIG. 7  is a photograph of the lower cover-side surface of the distal end portion of a vibration arm. 
         FIG. 8  is a photograph of the upper cover-side surface of the distal end portion of the vibration arm. 
         FIG. 9  is a graph illustrating a frequency fluctuation ratio. 
         FIG. 10  is a sectional view schematically illustrating the configuration of a resonance device according to a second exemplary embodiment. 
         FIG. 11  is a sectional view schematically illustrating the configuration of a resonance device according to a third exemplary embodiment. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Now, exemplary embodiments of the present invention are described with reference to the drawings. The drawings of the respective embodiments are exemplary, the dimensions and shapes of the respective parts are schematic, and the technical scope of the present invention should not be interpreted as being limited to the embodiments. 
     First Exemplary Embodiment 
     First, with reference to  FIG. 1  and  FIG. 2 , the configuration of a resonance device  1  according to a first exemplary embodiment is described.  FIG. 1  is a perspective view schematically illustrating the appearance of the resonance device according to the first embodiment.  FIG. 2  is an exploded perspective view schematically illustrating the structure of the resonance device according to the first embodiment. 
     Each component of the resonance device  1  is now described. Each drawing may include an orthogonal coordinate system having an X axis, a Y axis, and a Z axis for convenience to clarify the relationship between the respective drawings and thus to facilitate the understanding of the positional relationship between the respective members. For purposes of this disclosure, the direction parallel to the X axis, the direction parallel to the Y axis, and the direction parallel to the Z axis are referred to as X-axis direction, Y-axis direction, and Z-axis direction, respectively. The plane defined by the X axis and the Y axis is referred to as XY plane, and the same holds true for the YZ plane and the ZX plane. It is noted that, in the present embodiment, as a matter of convenience, the direction of the arrow in the Z-axis direction (+Z-axis direction) is sometimes referred to as up, the direction opposite to the arrow in the Z-axis direction (−Z-axis direction) is sometimes referred to as down, the direction of the arrow in the Y-axis direction (+Y-axis direction) is sometimes referred to as front, the direction opposite to the arrow in the Y-axis direction (−Y-axis direction) is sometimes referred to as back, the direction of the arrow in the X-axis direction (+X-axis direction) is sometimes referred to as right, and the direction opposite to the arrow in the X-axis direction (−X-axis direction) is sometimes referred to as left. However, this is not intended to limit the orientation of the resonance device  1 . 
     As shown, the resonance device  1  includes a resonator  10  and a lower cover  20  and an upper cover  30  facing each other with the resonator  10  interposed therebetween. The lower cover  20 , the resonator  10 , and the upper cover  30  are stacked in this order in the Z-axis direction. The resonator  10  and the lower cover  20  are joined with each other, and the resonator  10  and the upper cover  30  are joined with each other. The interior space is formed between the lower cover  20  and the upper cover  30  joined with each other with the resonator  10  interposed therebetween. The lower cover  20  and the upper cover  30  form a package structure for accommodating the resonator  10 . 
     In an exemplary aspect, the resonator  10  is a MEMS vibration element manufactured using the MEMS technology. The resonator  10  has a vibration portion  110 , a holding portion  140  (i.e., a frame), and a holding arm  150 . The vibration portion  110  is vibratably held in the interior space of the package structure, i.e., it is held so that it is configured to vibrate in the interior space. The vibration mode of the vibration portion  110  extending along the XY plane is an out-of-plane bending vibration mode in which the vibration portion  110  vibrates in a direction crossing the XY plane, for example. The holding portion  140  is formed into a rectangular frame shape to surround the vibration portion  110 , for example. The holding portion  140  forms the interior space of the package structure together with the lower cover  20  and the upper cover  30 . Moreover, the holding arm  150  (which can be a pair of arms) connects the vibration portion  110  and the holding portion  140  to each other. 
     The frequency band of the resonator  10  is, for example, 1 kHz or more and 1 MHz or less. The resonator  10  having such a frequency band largely fluctuates in frequency due to a change in weight of the vibration portion  110 . Thus, during or after the process of joining the resonator  10 , the lower cover  20 , and the upper cover  30  with each other to seal the interior space, the frequency of the resonance device  1  fluctuates in some cases. Even the frequency deviation of the resonance device  1  that tends to fluctuate in frequency as described above can be reduced by adjusting the frequency after sealing as in the present embodiment. 
     As further shown, the lower cover  20  has a rectangular plate-shaped bottom plate  22  provided along the XY plane and a side wall  23  extending from the peripheral portion of the bottom plate  22  toward the upper cover  30 . The side wall  23  is joined with the holding portion  140  of the resonator  10 . The lower cover  20  has, in the surface facing the vibration portion  110  of the resonator  10 , a cavity  21  surrounded by the bottom plate  22  and the side wall  23 . The cavity  21  is a rectangular parallelepiped cavity opening upward. 
     Moreover, the lower cover  20  has a protruding portion  50  protruding from the bottom plate  22  toward the resonator  10 . As illustrated in  FIG. 3 , in a plan view from the upper cover  30  side, the protruding portion  50  is positioned between an arm portion  123 B of an inner vibration arm  121 B and an arm portion  123 C of an inner vibration arm  121 C, which are described later. Thus, the protruding portion  50  extends along the arm portion  123 B and the arm portion  123 C. The length in the Y-axis direction of the protruding portion  50  is approximately 240 μm and the length in the X-axis direction thereof is approximately 15 μm, for example. Advantageously, such a protruding portion  50  improves the mechanical strength of the lower cover  20  to prevent a warp. 
     The upper cover  30  has a rectangular plate-shaped bottom plate  32  provided along the XY plane and a side wall  33  extending from the peripheral portion of the bottom plate  32  toward the lower cover  20 . The side wall  33  is joined with the holding portion  140  of the resonator  10 . The upper cover  30  has, in the surface facing the vibration portion  110  of the resonator  10 , a cavity  31  surrounded by the bottom plate  32  and the side wall  33 . The cavity  31  is a rectangular parallelepiped cavity opening downward. The cavity  21  and the cavity  31  face each other with the resonator  10  interposed therebetween to form the interior space of the package structure. 
     Next, with reference to  FIG. 3 , the components of the resonator  10  (vibration portion  110 , holding portion  140 , and holding arm  150 ) are described in more detail. Specifically,  FIG. 3  is a plan view schematically illustrating the structure of the resonator according to the first embodiment. 
     The vibration portion  110  is provided inside the holding portion  140  in a plan view from the upper cover  30  side. A gap of a predetermined interval is formed between the vibration portion  110  and the holding portion  140 . The vibration portion  110  has an excitation portion  120  having four vibration arms  121 A,  121 B,  121 C, and  121 D and a base portion  130  (also referred to as a “base”) connected to the excitation portion  120 . It is noted that the number of vibration arms is not limited to four and any number of vibration arms, namely, one or more vibration arms can be used in alternative exemplary aspects. In the present embodiment, the excitation portion  120  and the base portion  130  are integrally formed. 
     The vibration arms  121 A,  121 B,  121 C, and  121 D each extend along the Y-axis direction and are arranged in this order in the X-axis direction at predetermined intervals. The vibration arms  121 A to  121 D each have a fixed end connected to the base portion  130  and an open end farthest from the base portion  130 . The respective vibration arms  121 A to  121 D have distal end portions  122 A to  122 D (also referred to as “distal ends”) provided on the open end side, base portions corresponding to the fixed ends, and arm portions  123 A to  123 D connecting the base portions and the distal end portions  122 A to  122 D to each other. In other words, the distal end portions  122 A to  122 D are provided at positions at which a relatively large displacement occurs in the vibration portion  110  during operation. The vibration arms  121 A to  121 D each have, for example, a width in the X-axis direction of approximately 50 μm and a length in the Y-axis direction of approximately 450 μm. 
     Of the four vibration arms, the vibration arms  121 A and  121 D are outer vibration arms located in the outer side portions in the X-axis direction while the vibration arms  121 B and  121 C are inner vibration arms located in the inner side portions in the X-axis direction. A gap having a width W 1  is formed 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. A gap having a width W 2  is formed 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. In a similar manner, the gap having the width W 2  is formed between the arm portion  123 C and the arm portion  123 D. In an exemplary aspect, the width W 1  is larger than the width W 2  to improve the vibration characteristics and the durability. For example, the width W 1  is approximately 25 μm and the width W 2  is approximately 10 μm. However, the size relationship between the width W 1  and the width W 2  is not limited to the one described above. For example, unlike the example illustrated in  FIG. 3 , the width W 1  may be almost the same as the width W 2  or the width W 1  may be smaller than the width W 2  in alternative aspects. 
     Furthermore, the respective distal end portions  122 A to  122 D have metal films  125 A to  125 D on the surfaces on the upper cover  30  side. In other words, in a plan view from the upper cover  30  side, the portions in which the respective metal films  125 A to  125 D are positioned are the distal end portions  122 A to  122 D. The weight per unit length (hereinafter also simply referred to as “weight”) of each of the distal end portions  122 A to  122 D is larger than the weight of each of the arm portions  123 A to  123 D since the distal end portions  122 A to  122 D have the metal films  125 A to  125 D. With this configuration, the vibration characteristics can be improved while the vibration portion  110  can be reduced in size. Further, in addition to functioning to weight the open end-side portions of the vibration arms  121 A to  121 D, the metal films  125 A to  125 D can each be used as a so-called frequency adjustment film for adjusting the resonant frequency of the vibration arm  121 A,  121 B,  121 C, or  121 D by being partially shaved. 
     In the present embodiment, the width along the X-axis direction of each of the distal end portions  122 A to  122 D is larger than the width along the X-axis direction of each of the arm portions  123 A to  123 D. With this configuration, the weight of each of the distal end portions  122 A to  122 D can be further increased. However, as long as the weight of each of the distal end portions  122 A to  122 D is larger than the weight of each of the arm portions  123 A to  123 D, the width along the X-axis direction of each of the distal end portions  122 A to  122 D is not limited to the one described above. The width along the X-axis direction of each of the distal end portions  122 A to  122 D may be equal to or smaller than the width along the X-axis direction of each of the arm portions  123 A to  123 D. 
     In a plan view from the upper cover  30  side, the shape of each of the distal end portions  122 A to  122 D is a substantially rectangular shape having curved surface shapes (for example, so-called round shapes) at the four corners. The shape of each of the arm portions  123 A to  123 D is a substantially rectangular shape having round shapes near the base portion connected to the base portion  130  and near the connection portion connected to the distal end portion  122 A,  122 B,  122 C, or  122 D. However, it is noted that the shape of the distal end portions  122 A to  122 D and the shape of the arm portions  123 A to  123 D are not limited to the ones described above. For example, the shape of each of the distal end portions  122 A to  122 D can be a trapezoidal shape or an L shape in alternative aspects. Further, the shape of each of the arm portions  123 A to  123 D can be a trapezoidal shape or may have slits or the like in alternative aspects. 
     As illustrated in  FIG. 3 , the base portion  130  has, in a plan view from the upper cover  30  side, a front end portion  131 A, a back end portion  131 B, a left end portion  131 C, and a right end portion  131 D. The front end portion  131 A, the back end portion  131 B, the left end portion  131 C, and the right end portion  131 D are each part of the outer edge portion of the base portion  130 . Specifically, the front end portion  131 A is the end portion extending in the X-axis direction on the vibration arms  121 A to  121 D side. The back end portion  131 B is the end portion extending in the X-axis direction on the opposite side of the vibration arms  121 A to  121 D. The left end portion  131 C is the end portion extending in the Y-axis direction on the vibration arm  121 A side when viewed from the vibration arm  121 D. The right end portion  131 D is the end portion extending in the Y-axis direction on the vibration arm  121 D side when viewed from the vibration arm  121 A. The front end portion  131 A and the back end portion  131 B face each other in the Y-axis direction. The left end portion  131 C and the right end portion  131 D face each other in the X-axis direction. The vibration arms  121 A to  121 D are connected to the front end portion  131 A. 
     In the plan view from the upper cover  30  side, the shape of the base portion  130  is a substantially rectangular shape having the front end portion  131 A and the back end portion  131 B as the long sides and the left end portion  131 C and the right end portion  131 D as the short sides. Moreover, the base portion  130  is formed substantially plane symmetrically with respect to a virtual plane P defined along the perpendicular bisector of each of the front end portion  131 A and the back end portion  131 B. Note that, the shape of the base portion  130  is not limited to the rectangular shape as illustrated in  FIG. 3  and may be another shape substantially plane symmetric with respect to the virtual plane P. For example, the shape of the base portion  130  can be a trapezoidal shape in which one of the front end portion  131 A and the back end portion  131 B is longer than the other in an alternative aspect. Further, at least one of the front end portion  131 A, the back end portion  131 B, the left end portion  131 C, and the right end portion  131 D can be bent or curved. 
     It is noted that the virtual plane P corresponds to the symmetric surface of the entire vibration portion  110 . Thus, the virtual plane P is also a plane passing through the center in the X-axis direction of the vibration arms  121 A to  121 D and is positioned between the inner vibration arm  121 B and the inner vibration arm  121 C. Specifically, with respect to the virtual plane P, the outer vibration arm  121 A and the outer vibration arm  121 D are symmetric with each other and the inner vibration arm  121 B and the inner vibration arm  121 C are symmetric with each other. 
     In an exemplary aspect, the base portion length of the base portion  130  that is the longest distance in the Y-axis direction between the front end portion  131 A and the back end portion  131 B is approximately 40 μm, for example. Further, the base portion width of the base portion  130  that is the longest distance in the X-axis direction between the left end portion  131 C and the right end portion  131 D is approximately 300 μm, for example. It is also noted that in the configuration example illustrated in  FIG. 3 , the base portion length corresponds to the length of the left end portion  131 C or the right end portion  131 D and the base portion width corresponds to the length of the front end portion  131 A or the back end portion  131 B. 
     The holding portion  140  (or “frame”) is provided for holding the vibration portion  110  in the interior space formed by the lower cover  20  and the upper cover  30  and surrounds the vibration portion  110 , for example. As illustrated in  FIG. 3 , the holding portion  140  has, in the plan view from the upper cover  30  side, a front frame  141 A, a back frame  141 B, a left frame  141 C, and a right frame  141 D. The front frame  141 A, the back frame  141 B, the left frame  141 C, and the right frame  141 D are each part of the substantially rectangular frame body surrounding the vibration portion  110 . Specifically, the front frame  141 A is the portion extending in the X-axis direction on the excitation portion  120  side when viewed from the base portion  130 . The back frame  141 B is the portion extending in the X-axis direction on the base portion  130  side when viewed from the excitation portion  120 . The left frame  141 C is the portion extending in the Y-axis direction on the vibration arm  121 A side when viewed from the vibration arm  121 D. The right frame  141 D is the portion extending in the Y-axis direction on the vibration arm  121 D side when viewed from the vibration arm  121 A. As also shown, the holding portion  140  is formed plane symmetrically with respect to the virtual plane P. 
     One of the ends of the left frame  141 C is connected to one end of the front frame  141 A and the other end thereof is connected to one end of the back frame  141 B. Similarly, one of the ends of the right frame  141 D is connected to the other end of the front frame  141 A and the other end thereof is connected to the other end of the back frame  141 B. The front frame  141 A and the back frame  141 B face each other in the Y-axis direction with the vibration portion  110  interposed therebetween. The left frame  141 C and the right frame  141 D face each other in the X-axis direction with the vibration portion  110  interposed therebetween. It is noted that the holding portion  140  is only required to be provided in at least part of the periphery of the vibration portion  110  and is not limited to having the circumferentially continuous frame shape. 
     The holding arm  150  is provided inside the holding portion  140  to connect the base portion  130  and the holding portion  140  to each other. As illustrated in  FIG. 3 , the holding arm  150  has, in the plan view from the upper cover  30  side, a left holding arm  151 A and a right holding arm  151 B. The left holding arm  151 A connects the back end portion  131 B of the base portion  130  and the left frame  141 C of the holding portion  140  to each other. The right holding arm  151 B connects the back end portion  131 B of the base portion  130  and the right frame  141 D of the holding portion  140  to each other. The left holding arm  151 A has a holding back arm  152 A and a holding side arm  153 A, and the right holding arm  151 B has a holding back arm  152 B and a holding side arm  153 B. The holding arm  150  is formed plane symmetrically with respect to the virtual plane P. 
     As further shown, the holding back arms  152 A and  152 B extend from the back end portion  131 B of the base portion  130  between the back end portion  131 B of the base portion  130  and the holding portion  140 . Specifically, the holding back arm  152 A extends from the back end portion  131 B of the base portion  130  toward the back frame  141 B and is bent to extend toward the left frame  141 C. The holding back arm  152 B extends from the back end portion  131 B of the base portion  130  toward the back frame  141 B and is bent to extend toward the right frame  141 D. 
     Furthermore, the holding side arm  153 A extends along the outer vibration arm  121 A between the outer vibration arm  121 A and the holding portion  140 . Similarly, the holding side arm  153 B extends along the outer vibration arm  121 D between the outer vibration arm  121 D and the holding portion  140 . Specifically, the holding side arm  153 A extends from the end portion on the left frame  141 C side of the holding back arm  152 A toward the front frame  141 A and is bent to be connected to the left frame  141 C. The holding side arm  153 B extends from the end portion on the right frame  141 D side of the holding back arm  152 B toward the front frame  141 A and is bent to be connected to the right frame  141 D. 
     It is also noted that the holding arm  150  is not limited to the configuration described above. For example, the holding arm  150  can be connected to the left end portion  131 C and the right end portion  131 D of the base portion  130  in an exemplary aspect. Further, the holding arm  150  can be connected to the front frame  141 A or the back frame  141 B of the holding portion  140  in another exemplary aspect. Further, the number of the holding arms  150  can be one or three or more in various exemplary aspects. 
     Next, with reference to  FIG. 4  and  FIG. 5 , the stack structure of the resonance device  1  according to the first embodiment is described.  FIG. 4  is a sectional view along the X axis conceptually illustrating the stack structure of the resonance device illustrated in  FIG. 1 .  FIG. 5  is a sectional view along the Y axis conceptually illustrating the stack structure of the resonance device illustrated in  FIG. 1 . It is noted that  FIG. 4  and  FIG. 5  are not necessarily sectional views on the same plane. For example, in  FIG. 4  in which the arm portions  123 A to  123 D, extended wires C 2  and, C 3 , and through electrodes V 2  and V 3  are illustrated for the description of the stack structure, the through electrodes V 2  and V 3  may be formed at positions away in the Y-axis direction from the cross section of the arm portions  123 A to  123 D that is parallel to the ZX plane. 
     As described above, the resonator  10  is held between the lower cover  20  and the upper cover  30 . Specifically, the holding portion  140  of the resonator  10  is joined with each of the side wall  23  of the lower cover  20  and the side wall  33  of the upper cover  30 . In this way, the lower cover  20 , the upper cover  30 , and the holding portion  140  of the resonator  10  form the interior space in which the vibration portion  110  can vibrate. The resonator  10 , the lower cover  20 , and the upper cover  30  are each formed using a silicon (Si) substrate, for example, in an exemplary aspect. It is also noted that the resonator  10 , the lower cover  20 , and the upper cover  30  can each be formed using a silicon on insulator (SOI) substrate in which a silicon layer and a silicon oxide film are stacked. Further, the resonator  10 , the lower cover  20 , and the upper cover  30  can each be formed using a substrate other than a silicon substrate that can be processed by fine processing technology, for example, a compound semiconductor substrate, a glass substrate, a ceramic substrate, or a resin substrate. 
     Next, the configuration of the resonator  10  is described in more detail. 
     The vibration portion  110 , the holding portion  140 , and the holding arm  150  are integrally formed by the same process. In the resonator  10 , a metal film E 1  is stacked on a silicon substrate F 2  that is an exemplary substrate. Then, on the metal film E 1 , a piezoelectric film F 3  is stacked to cover the metal film E 1 , and a metal film E 2  is stacked on the piezoelectric film F 3 . On the metal film E 2 , a protective film F 5  is stacked to cover the metal film E 2 . In the distal end portions  122 A to  122 D, the respective above-mentioned metal films  125 A to  125 D are stacked on the protective film F 5 . In an exemplary aspect, the external shape of each of the vibration portion  110 , the holding portion  140 , and the holding arm  150  is formed by patterning the multilayer body including the silicon substrate F 2 , the metal film E 1 , the piezoelectric film F 3 , the metal film E 2 , the protective film F 5 , and the like described above by removal machining including dry etching with argon (Ar) ion beam irradiation, for example. 
     The silicon substrate F 2  is formed of a degenerated n-type silicon (Si) semiconductor having a thickness of approximately 6 μm, for example, and can contain phosphorus (P), arsenic (As), antimony (Sb), or the like as the n-type dopant. Moreover, the resistance value of the degenerated silicon (Si) that is used for the silicon substrate F 2  is, for example, less than 16 mΩ·cm and more preferably less than or equal to 1.2 mΩ·cm. Moreover, a silicon oxide film F 21  made of, for example, SiO 2  is formed on the lowest surface of the silicon substrate F 2 . In other words, in the resonator  10 , the silicon oxide film F 21  is exposed to the bottom plate  22  of the lower cover  20 . 
     The silicon oxide film F 21  is provided to function as a temperature characteristics correction layer for reducing the temperature coefficient of the resonant frequency of the resonator  10 , that is, the change rate of resonant frequency per unit temperature at least near a room temperature. With the vibration portion  110  having the silicon oxide film F 21 , the temperature characteristics of the resonator  10  are improved. It is also noted that the temperature characteristics correction layer can be formed on the upper surface of the silicon substrate F 2  or can be formed on each of the upper surface and lower surface of the silicon substrate F 2  in various exemplary aspects. 
     The silicon oxide film F 21  is formed of a material lower in hardness than the bottom plate  22  of the lower cover  20 . For purposes of this disclosure, the term “hardness” used herein is defined by the Vickers hardness. The Vickers hardness of the silicon oxide film F 21  is preferably 10 GPa or less, and the Vickers hardness of the bottom plate  22  of the lower cover  20  is preferably 10 GPa or more. This is to make it easier for the silicon oxide film F 21  of the distal end portions  122 A to  122 D to be shaved by a collision with the bottom plate  22  of the lower cover  20  in a frequency adjustment process. Additionally, since the silicon substrate F 2  may possibly be partially shaved in the frequency adjustment process, the Vickers hardness of the silicon substrate F 2  is preferably 10 GPa or less like the silicon oxide film F 21 . 
     The silicon oxide film F 21  of the vibration portion  110  is desirably formed at a uniform thickness. For purposes of this disclosure, the term “uniform thickness” means that a variation in thickness of the silicon oxide film F 21  is within ±20% from the value of the average thickness. 
     However, as illustrated in  FIG. 5 , the thickness of the silicon oxide film F 21  is reduced toward the open end in the edge portion on the lower cover  20  side of each of the distal end portions  122 A to  122 D of the vibration arms  121 A to  121 D. In other words, the edge portions on the lower cover  20  side of the distal end portions  122 A to  122 D are formed into an oblique or arc shape. This is because the edge portions on the lower cover  20  side of the distal end portions  122 A to  122 D are brought into contact with the bottom plate  22  of the lower cover  20  to be shaved in the frequency adjustment process. It is also noted that in the edge portions on the lower cover  20  side of the distal end portions  122 A to  122 D, the silicon oxide film F 21  can be entirely shaved to expose the silicon substrate F 2  on the lower cover  20  side. 
     The metal films E 1  and E 2  each have an excitation electrode for exciting the vibration arms  121 A to  121 D and an extended electrode for electrically connecting the excitation electrode to an external power source. The portions that function as the excitation electrodes in the respective metal films E 1  and E 2  face each other with the piezoelectric film F 3  interposed therebetween in the arm portions  123 A to  123 D of the vibration arms  121 A to  121 D. The portions that function as the extended electrodes of the metal films E 1  and E 2  are led from the base portion  130  to the holding portion  140  through the holding arm  150 , for example. The metal film E 1  is electrically continuous over the entire resonator  10 . Moreover, the metal film E 2  is electrically separated into the portion formed in the outer vibration arms  121 A and  121 D and the portion formed in the inner vibration arms  121 B and  121 C. The metal film E 1  corresponds to the lower electrode and the metal film E 2  corresponds to the upper electrode. 
     In an exemplary aspect, the thickness of each of the metal films E 1  and E 2  is approximately 0.1 μm or more and 0.2 μm or less, for example. The metal films E 1  and E 2  are, after having been formed, patterned to the excitation electrodes, the extended electrodes, and the like by removal machining such as etching. The metal films E 1  and E 2  are formed of a metal material having a body-centered cubic crystal structure, for example. Specifically, the metal films E 1  and E 2  are formed of molybdenum (Mo), tungsten (W), or the like. Note that, when the silicon substrate F 2  is a highly conductive degenerated semiconductor substrate, the metal film E 1  can be omitted and the silicon substrate F 2  may also serve as the lower electrode. 
     The piezoelectric film F 3  is a thin film formed of a type of piezoelectric material that exchanges electrical energy and mechanical energy with each other. The piezoelectric film F 3  stretches in the Y-axis direction of the in-plane direction of the XY plane depending on the electric field formed on the piezoelectric film F 3  by the metal films E 1  and E 2 . With the piezoelectric film F 3  stretching, the open ends of the respective vibration arms  121 A to  121 D are displaced toward the bottom plate  22  of the lower cover  20  and the bottom plate  32  of the upper cover  30 . Thus, the resonator  10  vibrates in the out-of-plane bending vibration mode. 
     Moreover, in an exemplary aspect, the piezoelectric film F 3  is formed of a material having a wurtzite hexagonal crystal structure and can contain, as its main component, nitride or oxide, for example, aluminum nitride (AlN), scandium aluminum nitride (ScAlN), zinc oxide (ZnO), gallium nitride (GaN), or indium nitride (InN). Note that, scandium aluminum nitride that is aluminum nitride in which the aluminum is partially substituted by scandium, and the aluminum may be substituted by two elements including magnesium (Mg) and niobium (Nb), magnesium (Mg) and zirconium (Zr), or the like instead of the scandium. The thickness of the piezoelectric film F 3  is approximately 1 μm, for example, and may be approximately 0.2 μm to 2 μm. 
     The protective film F 5  protects the metal film E 2  from oxidation, for example. The protective film F 5  is provided on the upper cover  30  side of the metal film E 2  and exposed to the bottom plate  32  of the upper cover  30  in the portion of the vibration portion  110  other than the distal end portions  122 A to  122 D. In other words, in the arm portions  123 A to  123 D of the vibration arms  121 A to  121 D and the base portion  130 , the protective film F 5  is positioned on the uppermost surface. Note that, the protective film F 5  is only required to be provided on the upper cover  30  side of the metal film E 2  and not necessarily exposed to the bottom plate  32  of the upper cover  30 . For example, a parasitic capacitance reduction film for reducing the capacitance of the wires formed on the resonator  10  may cover the protective film F 5 . The protective film F 5  is formed of oxide, nitride, or oxynitride containing aluminum (Al), silicon (Si), or tantalum (Ta), for example. 
     The metal films  125 A to  125 D are provided on the upper cover  30  side of the protective film F 5  in the distal end portions  122 A to  122 D and exposed to the bottom plate  32  of the upper cover  30 . In other words, in the distal end portions  122 A to  122 D, the metal films  125 A to  125 D are positioned on the uppermost surface. In order to adjust the frequency of the resonator  10  by trimming processing of partially removing each of the metal films  125 A to  125 D, the metal films  125 A to  125 D are desirably formed of a material higher in mass reduction rate in etching than the protective film F 5 . The mass reduction rate is represented by the product of an etching rate and density. For purposes of this disclosure, the term “etching rate” indicates a thickness that is removed per unit time. As long as the above-mentioned mass reduction rate relationship is established, the etching rate relationship between the protective film F 5  and the metal films  125 A to  125 D is not limited. Further, in terms of efficiently increasing the weights of the distal end portions  122 A to  122 D, the metal films  125 A to  125 D are preferably formed of a high specific gravity material. From those reasons, the metal films  125 A to  125 D are formed of a metal material, for example, molybdenum (Mo), tungsten (W), gold (Au), platinum (Pt), nickel (Ni), or titanium (Ti). Note that, in trimming processing, the protective film F 5  may also be partially removed. In such a case, the protective film F 5  also corresponds to the frequency adjustment film. 
     The upper surface of each of the metal films  125 A to  125 D is partially removed in trimming processing in a frequency adjustment process before sealing. The processing of trimming the metal films  125 A to  125 D is dry etching with argon (Ar) ion beam irradiation, for example. Wide range irradiation with an ion beam achieves an excellent processing efficiency but has a risk that the metal films  125 A to  125 D are charged with the ion beam having charges. In order to prevent a deterioration in vibration characteristics of the resonator  10  due to the vibration trajectories of the vibration arms  121 A to  121 D changed by the Coulomb interaction with the charged metal films  125 A to  125 D, the metal films  125 A to  125 D are desirably grounded. 
     In the configuration example illustrated in  FIG. 5 , the metal film  125 A is electrically connected to the metal film E 1  by a through electrode passing through the piezoelectric film F 3  and the protective film F 5 . The metal films  125 B to  125 D, which are not illustrated, are also electrically connected to the metal film E 1  by through electrodes. It is also noted that the method for grounding the respective metal films  125 A to  125 D is not limited to the one described above. For example, the metal films  125 A to  125 D may be electrically connected to the metal film E 1  by side electrodes provided on the side surfaces of the distal end portions  122 A to  122 D. Further, as long as the effects of the charging of the metal films  125 A to  125 D can be reduced, the metal films  125 A to  125 D are not necessarily electrically connected to the metal film E 1  and may be electrically connected to the metal film E 2 , for example. 
     As further shown, extended wires C 1 , C 2 , and C 3  are formed on the protective film F 5  of the holding portion  140 . The extended wire C 1  is electrically connected to the metal film E 1  through a through hole formed through the piezoelectric film F 3  and the protective film F 5 . The extended wire C 2  is electrically connected, through a through hole formed in the protective film F 5 , to the portion of the metal film E 2  that is formed in the outer vibration arms  121 A and  121 D. The extended wire C 3  is electrically connected, through a through hole formed in the protective film F 5 , to the portion of the metal film E 2  that is formed in the inner vibration arms  121 B and  121 C. The extended wires C 1  to C 3  are formed of a metal material such as aluminum (Al), germanium (Ge), gold (Au), or tin (Sn). 
     Next, the configuration of the lower cover  20  is described in more detail. 
     In particular, the bottom plate  22  and the side wall  23  of the lower cover  20  are integrally formed of a silicon substrate P 10 . The silicon substrate P 10  is formed of undegenerated silicon and has a resistivity of 10 Ω·cm or more, for example. The silicon substrate P 10  has a lower surface  20 B on the side opposite to the side facing the resonator  10 . The lower surface  20 B of the silicon substrate P 10  extends over the bottom plate  22  and the side wall  23  and corresponds to the lower surface of the lower cover  20 . Further, the silicon substrate P 10  has upper surfaces  22 A and  23 A on the side facing the resonator  10 . The upper surface  22 A of the silicon substrate P 10  is positioned on the bottom plate  22  and corresponds to the upper surface of the bottom plate  22  of the lower cover  20 . The upper surface  23 A of the silicon substrate P 10  is positioned on the side wall  23  and corresponds to the upper surface of the side wall  23  of the lower cover  20 . 
     The silicon oxide film F 21  of the resonator  10  is joined with the upper surface  23 A. The silicon oxide film F 21  is also joined with the upper surface of the protruding portion  50 . However, in terms of preventing the protruding portion  50  from being charged, on the upper surface of the protruding portion  50 , the silicon substrate P 10  lower in electrical resistivity than the silicon oxide film F 21  can be exposed or a conductive layer can be formed in various exemplary aspects. 
     Moreover, the thickness of the lower cover  20  corresponds to the distance between the lower surface  20 B and the upper surface  23 A in the Z-axis direction and is approximately 150 μm, for example. A depth D 1  of the cavity  21  corresponds to the distance between the upper surface  22 A and the upper surface  23 A in the Z-axis direction and is approximately 50 μm, for example. A gap G 1  between the distal end portions  122 A to  122 D of the vibration arms  121 A to  121 D and the lower cover  20  corresponds to the distance between the edge portions on the lower cover  20  side of the open ends of the vibration arms  121 A to  121 D and the upper surface  22 A in the Z-axis direction. 
     As illustrated in  FIG. 5 , when the resonator  10  extends substantially in parallel to the XY plane without voltage application, the gap G 1  on the lower cover  20  side has almost the same size as the depth D 1  of the cavity  21  of the lower cover  20  (i.e., G 1 =D 1 ). The maximum amplitude of each of the vibration arms  121 A to  121 D is restricted by contact between the vibration arms  121 A to  121 D and the lower cover  20 . Thus, the maximum amplitude of the vibration arms  121 A to  121 D is approximately 50 μm that is the same size as the gap G 1  on the lower cover  20  side. 
     Moreover, the resonator  10  may warp upward or downward without voltage application. For purposes of this disclosure, “warping upward” means the resonator  10  is configured so that the distance between the resonator  10  and the upper cover  30  is reduced from the base portion  130  toward the distal end portions  122 A to  122 D. For purposes of this disclosure, “warping downward” means the resonator  10  configured so that the distance between the resonator  10  and the lower cover  20  is reduced from the base portion  130  toward the distal end portions  122 A to  122 D. When the resonator  10  warps upward, the gap G 1  on the lower cover  20  side is larger than the depth D 1  of the cavity  21  of the lower cover  20  (i.e., G 1 &gt;D 1 ). When the resonator  10  warps downward, the gap G 1  on the lower cover  20  side is smaller than the depth D 1  of the cavity  21  of the lower cover  20  (i.e., G 1 &lt;D 1 ). 
     It is noted that the lower cover  20  can be regarded as part of the SOI substrate. When the MEMS substrate is regarded as being formed of the SOI substrate integrally including the resonator  10  and the lower cover  20 , the silicon substrate P 10  of the lower cover  20  corresponds to the support substrate of the SOI substrate, the silicon oxide film F 21  of the resonator  10  corresponds to the BOX layer of the SOI substrate, and the silicon substrate F 2  of the resonator  10  corresponds to the active layer of the SOI substrate. At this time, various semiconductor elements or circuits can be formed using part of the continuous MEMS substrate in the outer side portions of the resonance device  1 . 
     Next, the configuration of the upper cover  30  is described in more detail. 
     Specifically, the bottom plate  32  and the side wall  33  of the upper cover  30  are integrally formed of a silicon substrate Q 10  in an exemplary aspect. The silicon substrate Q 10  has a silicon oxide film Q 11 . The silicon oxide film Q 11  is provided on the portion of the surface of the silicon substrate Q 10  other than the inner wall of the cavity  31 . The silicon oxide film Q 11  is formed by performing thermal oxidation or chemical vapor deposition (CVD) on the silicon substrate Q 10 , for example. The silicon substrate Q 10  has an upper surface  30 A on the side opposite to the side facing the resonator  10 . The upper surface  30 A of the silicon substrate Q 10  extends over the bottom plate  32  and the side wall  33  and formed of the silicon oxide film Q 11 . Further, the silicon substrate Q 10  has lower surfaces  32 B and  33 B on the side facing the resonator  10 . The lower surface  32 B of the silicon substrate Q 10  is positioned on the bottom plate  32  and formed of the silicon substrate Q 10 . The lower surface  33 B of the silicon substrate Q 10  is positioned on the side wall  33  and formed of the silicon oxide film Q 11 . 
     The bottom plate  32  of the upper cover  30  has a metal film  70  that is provided at least in the region of the lower surface  32 B of the silicon substrate Q 10  that faces the distal end portions  122 A to  122 D of the vibration arms  121 A to  121 D. The metal film  70  may be a getter for occluding the gas in the interior space formed by the cavities  21  and  31  to improve the degree of vacuum and occludes a hydrogen gas, for example. The metal film  70  contains, for example, titanium (Ti), zirconium (Zr), vanadium (V), niobium (Nb), or tantalum (Ta) or an alloy containing at least one of those. The metal film  70  may contain the oxide of an alkali metal or the oxide of an alkali earth metal. Between the silicon substrate Q 10  and the metal film  70 , for example, a layer for preventing the diffusion of hydrogen from the silicon substrate Q 10  to the metal film  70 , a layer for improving the adhesion between the silicon substrate Q 10  and the metal film  70 , or another layer, which is not illustrated, may be provided. As also shown, the metal film  70  has a lower surface  70 B on the side facing the resonator  10 . The lower surface  70 B of the metal film  70  corresponds to the lower surface of the bottom plate  32  of the upper cover  30 . 
     The thickness of the upper cover  30  is approximately 150 μm, for example. A depth D 2  of the cavity  31  corresponds to the distance between the lower surface  32 B and the lower surface  33 B in the Z-axis direction and is approximately 60 μm, for example. A gap G 2  between the distal end portions  122 A to  122 D of the vibration arms  121 A to  121 D and the upper cover  30  corresponds to the distance between the edge portions on the upper cover  30  side at the open ends of the vibration arms  121 A to  121 D and the lower surface  70 B of the metal film  70  in the Z-axis direction. In other words, the gap G 2  on the upper cover  30  side corresponds to the distance between the metal films  125 A to  125 D of the vibration arms  121 A to  121 D and the metal film  70  of the upper cover  30 . The gap G 2  (e.g., a first gap) on the upper cover  30  side is larger than the gap G 1  (e.g., a second gap) on the lower cover  20  side (i.e., G 2 &gt;G 1 ). In other words, the space above the vibration arms  121 A to  121 D is wider than the space under the vibration arms  121 A to  121 D. 
     When the resonator  10  extends substantially in parallel to the XY plane without voltage application as illustrated in  FIG. 5 , (gap G 1  on lower cover  20  side)=(depth D 1  of cavity  21  of lower cover  20 ) and (gap G 2  on upper cover  30  side)={(depth D 2  of cavity  31  of upper cover  30 )+(thickness of joining portion H)}-{(thickness of metal films  125 A to  125 D)+(thickness of metal film  70 )} can be established. Thus, the size relationship between the gap G 2  on the upper cover  30  side and the gap G 1  on the lower cover  20  side can be determined using, as variables, the depth D 1  of the cavity  21  of the lower cover  20 , the depth D 2  of the cavity  31  of the upper cover  30 , the thickness of the joining portion H, the thickness of the metal films  125 A to  125 D, and the thickness of the metal film  70 . For example, in the present embodiment, since the depth D 2  of the cavity  31  of the upper cover  30  is larger than the depth D 1  of the cavity  21  of the lower cover  20  (i.e., D 2 &gt;D 1 ), the gap G 2  on the upper cover  30  side is larger than the gap G 1  on the lower cover  20  side (i.e., G 2 &gt;G 1 ). It is also noted that as long as the gap G 2  on the upper cover  30  side is larger than the gap G 1  on the lower cover  20  side, the depth D 2  of the cavity  31  of the upper cover  30  may be smaller than the depth D 1  of the cavity  21  of the lower cover  20 . For example, the thickness of the joining portion H may be increased to make the gap G 2  on the upper cover  30  side larger than the gap G 1  on the lower cover  20  side. Further, the thickness of the metal films  125 A to  125 D or the thickness of the metal film  70  may be reduced to make the gap G 2  on the upper cover  30  side larger than the gap G 1  on the lower cover  20  side. 
     The upper cover  30  has terminals T 1 , T 2 , and T 3 . The terminals T 1  to T 3  are provided on the upper surface  30 A of the silicon substrate Q 10 . Since the terminals T 1  to T 3  are provided on the silicon oxide film Q 11 , the terminals T 1  to T 3  are insulated from each other. The terminal T 1  is a mounting terminal for grounding the metal film E 1 . The terminal T 2  is a mounting terminal for electrically connecting the metal film E 2  of the outer vibration arms  121 A and  121 D to the external power source. The terminal T 3  is a mounting terminal for electrically connecting the metal film E 2  of the inner vibration arms  121 B and  121 C to the external power source. The terminals T 1  to T 3  are formed of a metallized layer (e.g., a foundation layer), for example, chromium (Cr), tungsten (W), or nickel (Ni) plated with nickel (Ni), gold (Au), silver (Ag), copper (Cu), or the like. It is noted that the upper surface  30 A of the silicon substrate Q 10  can have a dummy terminal electrically insulated from the resonator  10  for the purpose of adjusting the parasitic capacitance and mechanical strength balance. 
     As further shown, the upper cover  30  has through electrodes V 1 , V 2 , and V 3 . The through electrodes V 1  to V 3  are provided inside through holes opening in the lower surface  33 B of the side wall  33  and the upper surface  30 A. Since the through electrodes V 1  to V 3  are provided in the silicon oxide film Q 11 , the through electrodes V 1  to V 3  are insulated from each other. The through electrode V 1  electrically connects the terminal T 1  and the extended wire C 1  to each other, the through electrode V 2  electrically connects the terminal T 2  and the extended wire C 2  to each other, and the through electrode V 3  electrically connects the terminal T 3  and the extended wire C 3  to each other. The through electrodes V 1  to V 3  are formed by filling the through holes with polycrystalline silicon (Poly-Si), copper (Cu), or gold (Au), for example. 
     The joining portion H is formed between the side wall  33  of the upper cover  30  and the holding portion  140  of the resonator  10 . The joining portion H is formed into a circumferentially continuous frame shape to surround the vibration portion  110  in a plan view and hermetically seals the interior space formed by the cavities  21  and  31  in the vacuum state. The joining portion H is formed of a metal film including an aluminum (Al) film, a germanium (Ge) film, and an aluminum (Al) film that are laminated in this order with eutectic bonding, for example. Note that, the joining portion H may contain gold (Au), tin (Sn), copper (Cu), titanium (Ti), aluminum (Al), germanium (Ge), titanium (Ti), or silicon (Si) or an alloy containing at least one of those. Further, in order to improve the adhesion between the resonator  10  and the upper cover  30 , the joining portion H may include an insulator containing a metal compound such as titanium nitride (TiN) or tantalum nitride (TaN). 
     Next, with reference to  FIG. 4  and  FIG. 5 , the operation of the resonance device  1  is described. 
     In the present embodiment, the terminal T 1  is grounded, and the terminal T 2  and the terminal T 3  are supplied with alternating voltages in the phases opposite to each other. Thus, the phase of the electric field formed on the piezoelectric film F 3  of the outer vibration arms  121 A and  121 D and the phase of the electric field formed on the piezoelectric film F 3  of the inner vibration arms  121 B and  121 C are opposite to each other. With this, the outer vibration arms  121 A and  121 D and the inner vibration arms  121 B and  121 C vibrate in the phases opposite to each other. For example, when the distal end portions  122 A and  122 D of the respective outer vibration arms  121 A and  121 D are displaced toward the bottom plate  32  of the upper cover  30 , the distal end portions  122 B and  122 C of the respective inner vibration arms  121 B and  121 C are displaced toward the bottom plate  22  of the lower cover  20 . As described above, the vibration arm  121 A and the vibration arm  121 B, which are adjacent to each other, vertically vibrate in the 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. Further, the vibration arm  121 C and the vibration arm  121 D, which are adjacent to each other, vertically vibrate in the 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 this, warp moments in the directions opposite to each other are generated in the central axes r 1  and r 2 , with the result that the bending vibration of the base portion  130  occurs. The maximum amplitude of the vibration arms  121 A to  121 D is approximately 50 μm, for example, and the normal drive amplitude thereof is approximately 10 μm, for example. 
     Next, with reference to  FIG. 6  to  FIG. 8 , a method for manufacturing the resonance device  1  according to the first embodiment is described.  FIG. 6  is a flowchart schematically illustrating the method for manufacturing the resonance device according to the first embodiment.  FIG. 7  is a photograph of the lower cover-side surface of the distal end portion of the vibration arm.  FIG. 8  is a photograph of the upper cover-side surface of the distal end portion of the vibration arm.  FIG. 9  is a graph illustrating a frequency fluctuation ratio. 
     The horizontal axis of the graph of  FIG. 9  indicates the ratio of the gap G 2  on the upper cover  30  side to the gap G 1  on the lower cover  20  side (G 2 /G 1 ). The vertical axis of  FIG. 9  indicates the ratio of a frequency fluctuation amount based on a frequency fluctuation amount per unit time when G 2 /G 1 =1 in Step S 80  for frequency adjustment after sealing, which is described later. 
     As shown in  FIG. 6 , first, a silicon substrate pair is prepared (S 10 ). The silicon substrate pair corresponds to the silicon substrates P 10  and Q 10 . 
     Next, the silicon substrate pair is oxidized (S 20 ). With this, the silicon oxide film Q 11  is formed on the surface of the silicon substrate Q 10  and the silicon oxide film F 21  is formed on the surface of the silicon substrate P 10 . Note that, only the silicon oxide film Q 11  may be formed in this step and the silicon oxide film F 21  may be formed in another step. 
     Next, a cavity pair is provided (S 30 ). The silicon substrates P 10  and Q 10  are each subjected to removal machining including an etching process to form the cavities  21  and  31 . However, the method for forming the cavities  21  and  31  is not limited to the etching process. Further, the cavity  21  may be formed after the resonator  10  has been joined with the lower cover  20 . 
     Next, the resonator is joined with the lower cover (S 40 ). The lower cover  20  and the resonator  10  are heated at a temperature less than or equal to the melting points to join the side wall  23  and the holding portion  140  with each other by pressurization. It is noted that the method for joining the lower cover  20  and the resonator  10  with each other is not limited to thermocompression bonding described above and can be bonded using an adhesive, a brazing filler metal, or a solder, for example. 
     Next, a metal film is provided in the cavity of the upper cover (S 50 ). For example, titanium vapor is deposited on the lower surface  32 B of the silicon substrate Q 10  to form the metal film  70 . The metal film  70  is formed by patterning using a metal mask. Note that, the method for patterning the metal film  70  is not limited to film formation including patterning using a metal mask and may be an etching process or lift-off process using a photoresist. 
     Next, the metal films of the distal end portions are trimmed (S 60 ). The distal end portions  122 A to  122 D of the vibration arms  121 A to  121 D are irradiated with an argon (Ar) ion beam to remove part of the metal films  125 A to  125 D by dry etching. With this, the weights of the distal end portions  122 A to  122 D are changed to adjust the frequency. That is, Step S 60  corresponds to the frequency adjustment process before sealing (e.g., a first frequency adjustment process). Since an ion beam achieves wide range irradiation, Step S 60  for frequency adjustment before sealing is excellent in processing efficiency. It is noted that in the embodiment of the present invention, since the frequency is adjustable after sealing, Step S 60  for frequency adjustment before sealing may be omitted. 
     Next, a joining portion is provided (S 70 ). The respective metallized layers of the resonator  10  and the upper cover  30  are joined with each other under decompression environment. The formed joining portion H hermetically seals the interior space in the vacuum state. That is, Step S 70  corresponds to the sealing process. The joining portion H is provided by a heat treatment. Such a heat treatment is performed at a heating temperature of 400° C. or more and 500° C. or less for a heating time of 1 minute or more and 30 minutes or less, for example. This is because enough joint strength and sealing properties cannot be obtained with heating at a temperature less than 400° C. for a time less than 1 minute, and the energy efficiency for joining and the manufacturing lead time are deteriorated with heating at a temperature higher than 500° C. for a time more than 30 minutes. 
     It is noted that before joining the resonator  10  and the upper cover  30  with each other, the process of activating the metal film  70  as a getter may be carried out. In the process of activating the metal film  70  as a getter, for example, hydrogen having adhered to the surface of the metal film  70  is desorbed by a heat treatment to restore the hydrogen adsorption effect. Such a heat treatment is performed at a heating temperature of 350° C. or more and 500° C. or less for a heating time of 5 minutes or more and 30 minutes or less, for example. This is because the metal film  70  cannot be activated enough with heating at a temperature less than 350° C. for a time less than 5 minutes, and the energy efficiency for activation and the manufacturing lead time are deteriorated with heating at a temperature more than 500° C. for a time more than 30 minutes. 
     Next, the distal end portions are brought into contact with the lower cover (S 80 ). The resonator  10  is excited by being supplied with a voltage larger than a normal drive voltage to cause the edge portions of the distal end portions  122 A to  122 D to collide with the bottom plate  22  of the lower cover  20 . With this, as illustrated in  FIG. 7 , the edge portions of the distal end portions  122 A to  122 D are shaved into an oblique or arc shape. At this time, the silicon oxide film F 21  exposed on the lower cover  20  side is shaved off from the distal end portions  122 A to  122 D, and the silicon substrate F 2  may further be shaved off. The weights of the distal end portions  122 A to  122 D are changed to adjust the frequency. That is, Step S 80  corresponds to the frequency adjustment process after sealing (e.g., a second frequency adjustment process). Since a change in weight of the distal end portions  122 A to  122 D due to a collision is finely adjustable with the intensity of an application voltage or the like, Step S 80  for frequency adjustment after sealing is excellent in processing accuracy. Further, in Step S 80  for frequency adjustment after sealing, the frequency fluctuated in Step S 70  for sealing can be adjusted. The frequency is adjusted twice by the different methods before and after sealing so that highly efficient and highly accurate frequency adjustment is achieved. The frequency adjustment process of causing the edge portions of the distal end portions  122 A to  122 D to collide with the bottom plate  22  of the lower cover  20  may be carried out before Step S 70  for sealing. 
     It is also noted that the particles of the silicon oxide film F 21  or the silicon substrate F 2  shaved off from the distal end portions  122 A to  122 D due to the contact with the lower cover  20  are adsorbed to the resonator  10 , the lower cover  20 , or the upper cover  30 . The particles are small enough to be affected by the van der Waals force and thus not desorbed from the vibrating vibration arms  121 A to  121 D. Thus, the frequency hardly fluctuates due to the adsorption or desorption of the particles. Further, when the silicon substrate F 2  is exposed on the lower cover  20  side in the distal end portions  122 A to  122 D, only the silicon substrate F 2  may be shaved off. 
     In Step S 80  for frequency adjustment after sealing, the distal end portions  122 A to  122 D are hardly brought into contact with the upper cover  30 . Even when the distal end portions  122 A to  122 D are brought into contact with the upper cover  30 , the metal films  125 A to  125 D cause ductile deformation as illustrated in  FIG. 8  so that the weights of the distal end portions  122 A to  122 D are hardly changed. Thus, when the distal end portions  122 A to  122 D are caused to collide with the lower cover  20  and the upper cover  30  equally or when the distal end portions  122 A to  122 D are caused to collide with the upper cover  30  more strongly than with the lower cover  20 , the frequency fluctuation ratio drops. This is illustrated in the graph of  FIG. 9 . As illustrated in  FIG. 9 , when the gap G 1  on the lower cover  20  side and the gap G 2  on the upper cover  30  side have a relationship of 1&lt;G 2 /G 1 , that is, when the distal end portions  122 A to  122 D are caused to collide with the lower cover  20  more strongly than with the upper cover  30 , the time required for Step S 80  for frequency adjustment after sealing can be shortened to improve the manufacturing lead time. 
     As illustrated in  FIG. 9 , the gap G 1  on the lower cover  20  side and the gap G 2  on the upper cover  30  side desirably have a relationship of 1.1≤G 2 /G 1  that achieves a frequency fluctuation ratio of approximately 1.5 times or more. Further, the gap G 1  and the gap G 2  more desirably have a relationship of 1.15≤G 2 /G 1  that achieves a frequency fluctuation ratio of approximately twice or more, and further desirably have a relationship of 1.2≤G 2 /G 1  that achieves a frequency fluctuation ratio of approximately three times or more. However, the thickness of the bottom plate  32  of the upper cover  30  needs to be reduced to increase G 2 /G 1 . Thus, in order to prevent a drop in mechanical strength of the upper cover  30 , the gap G 1  on the lower cover  20  side and the gap G 2  on the upper cover  30  side desirably have a relationship of G 2 /G 1 ≤1.5. Further, the gap G 1  and the gap G 2  more desirably have a relationship of G 2 /G 1 ≤1.4, and further desirably have a relationship of G 2 /G 1 ≤1.3. 
     It is further noted that, in the present embodiment, since the metal film  70  is provided also on the upper cover  30 , even when the distal end portions  122 A to  122 D are brought into contact with the upper cover  30 , the impact due to the collision between the metals is absorbed so that the ductile fracture of the metal films  125 A to  125 D is difficult to occur. The size of metal pieces generated by a ductile fracture tends to be larger than the size of particles generated by a collision with the silicon oxide film F 21  or the silicon substrate F 2 . Thus, when a ductile fracture occurs, the frequency adjustment accuracy drops. Further, the van der Waals force does not act on large metal pieces enough so that the frequency fluctuates due to the desorption of metal pieces from the vibrating vibration arms  121 A to  121 D. With the metal film provided on the portion of the upper cover  30  with which the distal end portions  122 A to  122 D are caused to collide, metal pieces are hardly generated so that a drop in frequency adjustment accuracy and a fluctuation in frequency can be prevented. 
     As described above, in the first embodiment, the depth D 2  of the cavity  31  of the upper cover  30  is larger than the depth D 1  of the cavity  21  of the lower cover  20 . With this, the gap G 2  on the upper cover  30  side is larger than the gap G 1  on the lower cover  20  side. 
     With this, the distal end portions  122 A to  122 D of the vibration arms  121 A to  121 D can be caused to collide with the lower cover  20  instead of the upper cover  30  to efficiently change the weights of the vibration arms  121 A to  121 D. Thus, the time required for the frequency adjustment process can be shortened. 
     The edge portions on the lower cover  20  side of the distal end portions  122 A to  122 D of the vibration arms  121 A to  121 D are formed into an oblique or arc shape. 
     This is because the edge portions on the lower cover  20  side of the distal end portions  122 A to  122 D are shaved due to a collision with the lower cover  20 . In the edge portions on the lower cover  20  side of the distal end portions  122 A to  122 D, rough shaving marks such as asperities are not formed and relatively smooth shaving marks are formed. This means that the amount of the distal end portions  122 A to  122 D shaved by a single collision is small. Thus, the weight change amounts of the distal end portions  122 A to  122 D are finely adjustable and the frequency adjustment accuracy is thus high. 
     The gap G 1  on the lower cover  20  side and the gap G 2  on the upper cover  30  side have a relationship of 1&lt;G 2 /G 1 ≤1.5. 
     With this, while the time required for the frequency adjustment process can be shortened, a drop in mechanical strength of the upper cover  30  can be prevented. 
     The upper cover  30  has the metal film  70  in the portion with which the distal end portions  122 A to  122 D of the vibration arms  121 A to  121 D are caused to collide. 
     With this configuration, an impact that is applied to the metal films  125 A to  125 D of the distal end portions  122 A to  122 D can be mitigated to prevent the ductile fracture of the metal films  125 A to  125 D. Since relatively large metal pieces are not generated from the metal films  125 A to  125 D, the frequency adjustment accuracy is improved. Further, a frequency fluctuation due to the adsorption or desorption of metal pieces can be prevented. 
     Now, the configurations of the resonance device according to additional exemplary embodiments of the present invention are described. It is noted that in the following embodiments, the descriptions on matters common to the first embodiment described above are omitted and only different points are described. In particular, similar actions and effects provided by similar components are not described one by one. 
     Second Exemplary Embodiment 
     Next, with reference to  FIG. 10 , the configuration of a resonance device  2  according to a second exemplary embodiment is described.  FIG. 10  is a sectional view schematically illustrating the configuration of the resonance device according to the second embodiment. 
     In the resonance device  2  according to the second embodiment, the resonator  10  warps downward without voltage application. In other words, the vibration arms  121 A to  121 D are configured so that the distance between the vibration arms  121 A to  121 D and the lower cover  20  is reduced toward the distal end portions  122 A to  122 D. 
     With this configuration, even when the depth D 2  of the cavity  31  of the upper cover  30  is equal to or smaller than the depth D 1  of the cavity  21  of the lower cover  20 , the gap G 2  on the upper cover  30  side can still be larger than the gap G 1  on the lower cover  20  side. 
     Third Exemplary Embodiment 
     Next, with reference to  FIG. 11 , the configuration of a resonance device  3  according to a third exemplary embodiment is described.  FIG. 11  is a sectional view schematically illustrating the configuration of the resonance device according to the third embodiment. 
     In the resonance device  3  according to the third embodiment, the cavity  31  of the upper cover  30  is formed so that the portion facing the distal end portions  122 A to  122 D of the vibration arms  121 A to  121 D is deeper than the portion facing the base portions of the vibration arms  121 A to  121 D. For example, the bottom plate  32  of the upper cover  30  has formed therein a recessed portion facing the distal end portions  122 A to  122 D of the vibration arms  121 A to  121 D. The recessed portion of the bottom plate  32  also faces part of the arm portions  123 A to  123 D of the vibration arms  121 A to  121 D. The gap G 2  between the distal end portions  122 A to  122 D of the vibration arms  121 A to  121 D and the upper cover  30  is larger than a gap G 3  between the base portion  130  and the upper cover  30 . The gap G 3  between the base portion  130  and the upper cover  30  is larger than the gap G 1  between the distal end portions  122 A to  122 D of the vibration arms  121 A to  121 D and the lower cover  20 , for example, and may be equal to or smaller than the gap G 1 . 
     With this configuration, while a drop in mechanical strength of the upper cover  30  can be prevented, the gap G 2  between the distal end portions  122 A to  122 D of the vibration arms  121 A to  121 D and the upper cover  30  can be increased. 
     Now, the exemplary embodiments of the present invention are partially or entirely described as supplementary notes to describe the effects thereof. However, it is noted that the present invention is not limited to the following supplementary notes. 
     According to one exemplary aspect, there is provided a resonance device that has a lower cover, an upper cover joined with the lower cover, and a resonator that has a vibration arm that generate bending vibration in an interior space provided between the lower cover and the upper cover. The vibration arm has a distal end provided with a metal film on a side that faces the upper cover. Moreover, a gap between the distal end portion of the vibration arm and the upper cover is larger than a gap between the distal end portion of the vibration arm and the lower cover. 
     With this configuration, the distal end of the vibration arm can be caused to collide with the lower cover instead of the upper cover to efficiently change the weight of the vibration arm. Thus, the time required for the frequency adjustment process can be shortened. 
     In one aspect, an edge portion on a side of the lower cover of the distal end portion of the vibration arm is formed into an oblique or arc shape. 
     With this configuration, the weight change amount of the distal end portion is finely adjustable and the frequency adjustment accuracy is thus high. 
     In one aspect, the vibration arm is configured so that a distance between the vibration arm and the lower cover is reduced toward the distal end portion. 
     With this configuration, even when the depth of the cavity of the upper cover is equal to or smaller than the depth of the cavity of the lower cover, the gap between the distal end portion of the vibration arm and the upper cover can be larger than the gap between the distal end portion of the vibration arm and the lower cover. 
     In one aspect, the upper cover and the lower cover each have a cavity for forming the interior space, and a depth of the cavity of the upper cover is larger than a depth of the cavity of the lower cover. 
     In one aspect, the gap G 1  between the distal end portion of the vibration arm and the lower cover and the gap G 2  between the distal end portion of the vibration arm and the upper cover have a relationship of 1&lt;G 2 /G 1 ≤1.5. 
     With this configuration, while the time required for the frequency adjustment process can be shortened, a drop in mechanical strength of the upper cover can be prevented. 
     In one aspect, the upper cover has a cavity for forming the interior space, and the cavity of the upper cover is formed so that a portion that faces the distal end portion of the vibration arm is deeper than a portion that faces a base portion of the vibration arm. 
     With this configuration, while a drop in mechanical strength of the upper cover can be prevented, the gap between the distal end portion of the vibration arm and the upper cover can be increased. 
     In one aspect, the upper cover has a metal film that faces at least the distal end portion of the vibration arm. 
     With this configuration, an impact that is applied to the metal film of the distal end portion can be mitigated to prevent the ductile fracture of the metal film. Since relatively large metal pieces are not generated from the metal film, the frequency adjustment accuracy is improved. Further, a frequency fluctuation due to the adsorption or desorption of metal pieces can be prevented. 
     According to another aspect of the present invention, a method for manufacturing a resonance device is provided. The method includes a process of preparing a resonance device that includes a lower cover, an upper cover joined with the lower cover, and a resonator that has a vibration arm that generates bending vibration in an interior space provided between the lower cover and the upper cover, the resonance device in which a gap between a distal end of the vibration arm and the upper cover is larger than a gap between the distal end of the vibration arm and the lower cover. The exemplary method also includes a process of adjusting a frequency of the resonator by exciting the resonator to bring the distal end portion of the vibration arm into contact with at least the lower cover. 
     With this process, the distal end of the vibration arm can be caused to collide with the lower cover instead of the upper cover to efficiently change the weight of the vibration arm. Thus, the time required for the frequency adjustment process can be shortened. 
     In general, it is noted that the exemplary embodiments according to the present invention are appropriately applicable to any device configured to perform electromechanical energy conversion by the piezoelectric effect, such as timing devices, sound generators, oscillators, and load sensors, without any particular limitation. 
     As described above, according to the aspect of the present invention, the resonance device with improved productivity and the method for manufacturing the same can be provided. 
     It is also noted that the exemplary embodiments described above are intended to facilitate the understanding of the present invention and are not intended to limit the present invention. The present invention may be modified and/or improved without departing from the gist thereof, and the present invention also includes equivalents thereof. That is, matters achieved by those skilled in the art appropriately changing the designs in the respective embodiments are also included in the scope of the present invention as long as having the features of the present invention. For example, the elements included in the respective embodiments and the arrangement, materials, conditions, shapes, sizes, and the like thereof are not limited to the examples described above and can be appropriately changed. Further, the elements included in the respective embodiments can be combined as technically possible, and the combinations thereof are also included in the scope of the present invention as long as having the features of the present invention. 
     REFERENCE SIGNS LIST 
     
         
         
           
               1 ,  2 ,  3  resonance device 
               10  resonator 
               20  lower cover 
               30  upper cover 
               70  metal film 
               110  vibration portion 
               140  holding portion 
               150  holding arm 
               121 A to  121 D vibration arm 
               122 A to  122 D distal end portion 
               123 A to  123 D arm portion 
               125 A to  125 D metal film 
             G 1 , G 2  gap 
             D 1 , D 2  cavity depth