Patent Publication Number: US-2021167754-A1

Title: Resonator and resonance device including same

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation of PCT/JP2019/017267 filed Apr. 23, 2019, which claims priority to Japanese Patent Application No. 2018-164286, filed Sep. 3, 2018, the entire contents of each of which are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present invention relates to a resonator and to a resonance device that includes a resonator. 
     BACKGROUND 
     In general, resonance devices, which are types of micro-electromechanical system (MEMS), are currently incorporated into electronic devices such as smartphones as a timing device, for example. This type of resonance device, for example, includes a bottom cover, a top cover that forms a cavity together with the bottom cover, and a resonator that is arranged inside the cavity between the bottom cover and the top cover. The resonator includes, for example, a piezoelectric film, an upper electrode and a lower electrode provided with the piezoelectric film interposed therebetween, and an insulating film provided between the layers or on the surface of the resonator. 
     As an example of a specific configuration of such a resonator, for example, Patent Document 1 (identified below) discloses a resonator that includes a first electrode and a second electrode, a piezoelectric film provided between the first electrode and the second electrode, a protective film composed of an insulator provided on the first electrode, and a conductive film composed of a conductor provided on the protective film. The conductive film is electrically connected to either one of the first electrode and the second electrode. 
     Patent Document 1: International Publication No. 2017/208568. 
     In resonators of the related art, it is known that when an insulator or conductor provided on a surface or between layers becomes charged due to ion beam sputtering or the pyroelectric effect, an attractive or repulsive force may act on the resonator due to the Coulomb force and consequently the resonant frequency of the resonator may vary. In the case of a resonator having a vibrating arm that extends from a base thereof and vibrates in a bending vibration mode, the effect of such a Coulomb force is most pronounced at the tip of the vibrating arm where the vibrating arm is most easily displaced and the range of motion is largest. 
     Regarding this point, the charge with which the conductive film is charged in the resonator disclosed in Patent Document 1 can be released to some extent, but the area where the conductive film is provided may be limited, and the effect of the Coulomb force received by the vibrating arm may not be sufficiently eliminated. 
     Increasing the width of the gap formed around the periphery of the vibrating arm can reduce the effect of the Coulomb force received by the vibrating arm. However, if the gap is increased while maintaining the dimensions of the base and vibrating arm, the dimensions of the resonator will likely increase. If the dimensions of the base or vibrating arm are reduced in order to increase the size of this gap, there is also a risk of the vibration characteristics of the resonator being degraded. In particular, if the dimensions of the base are reduced, degradation of vibration characteristics, such as the driving voltage dependence of the frequency, is a concern. 
     SUMMARY OF THE INVENTION 
     The exemplary embodiments of the present invention are provided in light of the above-described circumstances. Thus, it is an object thereof to provide a resonator that can be reduced in size while suppressing variations in the resonant frequency and to provide a resonance device that includes the resonator. 
     An exemplary aspect provides a resonator that includes a base; at least three vibrating arms that include a piezoelectric film, an upper electrode and a lower electrode provided so as to face each other with the piezoelectric film interposed therebetween, first ends of the vibrating arms being fixed ends connected to a front end of the base and second ends of the vibrating arms being open ends provided so as to be spaced away from the front end. Moreover, a frame is provided for holding the base; and a holding arm connects the base to the frame. Each vibrating arm among the at least three vibrating arms includes an arm portion that extends from the front end of the base and a tip that is connected to the arm portion. The holding arm includes a holding side arm that extends parallel to an outer vibrating arm, which is arranged on the outside among the at least three vibrating arms, between the outer vibrating arm and the frame. A release width between the tip of the outer vibrating arm and the frame is larger than a release width between the holding side arm and the frame or a release width between the arm portion of the outer vibrating arm and the holding side arm. 
     According to the exemplary embodiments of the present invention, a resonator is provided with reduced size while suppressing variations in the resonant frequency. Moreover, a resonance device is provided that includes the resonator. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a perspective view schematically illustrating the exterior 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 taken along an X axis conceptually illustrating the multilayer structure of the resonance device illustrated in  FIG. 1 . 
         FIG. 5  is a sectional view taken along a Y axis conceptually illustrating the multilayer structure of the resonance device illustrated in  FIG. 1  during operation. 
         FIG. 6  is a plan view schematically illustrating the structure of a resonator according to a second exemplary embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Hereafter, exemplary embodiments of the present invention will be described while referring to the drawings. In the following description of the drawings, identical or similar constituent elements are denoted by identical or similar reference symbols. The drawings are representative, the dimensions and shapes of the individual parts are schematically illustrated, and the technical scope of the present invention should not be interpreted as being limited to that of the embodiments. 
     First Exemplary Embodiment 
     First, the configuration of a resonance device  1  according to a first embodiment will be described while referring to  FIGS. 1 and 2 .  FIG. 1  is a perspective view schematically illustrating the exterior 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. 
     (Resonance Device  1 ) 
     The resonance device  1  includes a resonator  10  and a bottom cover  20  and a top cover  30  provided so as to face each other with the resonator  10  interposed therebetween. The bottom cover  20 , the resonator  10 , and the top cover  30  are stacked in this order in a Z-axis direction. The resonator  10  and the bottom cover  20  are bonded to each other and the resonator  10  and the top cover  30  are bonded to each other. A vibration space of the resonator  10  is formed between the bottom cover  20  and the top cover  30 , which are bonded to each other with the resonator  10  interposed therebetween. In exemplary aspects, the resonator  10 , the bottom cover  20 , and the top cover  30  are formed using substrates that can be processed using microfabrication techniques, such as semiconductor substrates, glass substrates, and organic substrates. 
     Hereafter, the configuration of each part of the resonance device  1  will be described. For purposes of this disclosure, it is noted that in the following description, the side of the resonance device  1  where the top cover  30  is provided is referred to as “top” (or “front”) and the side of the resonance device  1  where the bottom cover  20  is provided is referred to as “bottom” (or “rear”). 
     In the exemplary aspect, the resonator  10  is a MEMS resonator manufactured using MEMS techniques. The resonator  10  includes a vibrating portion  110 , a holding portion  140  (i.e., a frame), and a holding arm  150 . The vibrating portion  110  is held in the vibration space. The vibration mode of the vibrating portion  110  is not limited and is, for example, an out-of-plane bending vibration mode with respect to the XY plane, but in alternative aspects may instead be an in-plane bending vibration mode with respect to the XY plane. The holding portion  140  is, for example, provided so as to have a rectangular frame shape so as surround the vibrating portion  110 . The holding arm  150  connects the vibrating portion  110  and the holding portion  140  to each other. 
     As further shown, the bottom cover  20  includes a rectangular flat plate shaped bottom plate  22 , which is provided along the XY plane, and a side wall  23  that extends from the periphery of the bottom plate  22  in the Z-axis direction. The side wall  23  is bonded to the holding portion  140  of the resonator  10 . A recess  21 , which is formed by the front surface of the bottom plate  22  and the inner surface of the side wall  23 , is formed on the surface of the bottom cover  20  that faces the vibrating portion  110  of the resonator  10 . The recess  21  is a rectangular parallelepiped shaped opening that opens upwardly and forms part of the vibration space of the resonator  10 . On the inner surface of the bottom cover  20 , a protrusion  50 , which protrudes into the vibration space, is formed on the front surface of the bottom plate  22 . 
     Apart from the protrusion  50 , the structure of the top cover  30  is symmetrical to the structure of the bottom cover  20  with respect to the resonator  10 . In other words, the top cover  30  includes a rectangular flat plate shaped bottom plate  32  provided along the XY plane and a side wall  33  that extends from the periphery of the bottom plate  32  in the Z-axis direction, and the side wall  33  is bonded to the holding portion  140  of the resonator  10 . Moreover, a recess  31  is formed in the top cover  30  on a surface that faces the vibrating portion  110  of the resonator  10 . The recess  31  is a rectangular parallelepiped shaped opening that opens downward and forms part of the vibration space of the resonator  10 . 
     The structure of the bottom cover  20  and the structure of the top cover  30  is not limited to this example, and the structures may instead be non-symmetrical with each other, for example. For example, one out of the bottom cover  20  and the top cover  30  may have a dome-like shape in exemplary aspects. The shapes of the recess  21  of the bottom cover  20  and the recess  31  of the top cover  30  may be different from each other, and for example, the depths of the recess  21  and the recess  31  may be different from each other. 
     (Resonator  10 ) 
     Next, the configurations of the vibrating portion  110 , the holding portion  140 , and the holding arm  150  of the resonator  10  according to the embodiment will be described in detail while referring to  FIG. 3 .  FIG. 3  is a plan view schematically illustrating the structure of the resonator according to the first embodiment of the present invention. 
     (Vibrating Portion  110 ) 
     The vibrating portion  110  is provided inside the holding portion  140  (i.e., the frame) in a plan view from the top cover  30  side. A space is formed between the vibrating portion  110  and the holding portion  140  with a predetermined spacing. The vibrating portion  110  includes an excitation portion  120  that includes four vibrating arms  121 A,  121 B,  121 C, and  121 D and a base portion  130  (or simply a “base”) that is connected to the excitation portion  120 . Note that the number of vibrating arms is not limited to four and an arbitrary number of vibrating arms of three or more may be provided in alternative aspects. In this embodiment, the excitation portion  120  and the base portion  130  are formed so as to be integrated with each other. 
     (Vibrating Arms  121 A to  121 D) 
     The vibrating arms  121 A,  121 B,  121 C, and  121 D extend in the Y-axis direction and are provided parallel to each other in this order with a prescribed spacing therebetween in the X-axis direction. One end of the vibrating arm  121 A is a fixed end that is connected to a front end portion  131 A (i.e., the front end) of the base portion  130 , which is described later, and the other end of the vibrating arm  121 A is an open end that is provided so as to be spaced away from the front end portion  131 A of the base portion  130 . The vibrating arm  121 A includes a tip portion  122 A (or simply a “tip”) that is formed at the open end side and an arm portion  123 A that extends from the fixed end and is connected to the tip portion  122 A. Similarly, the vibrating arms  121 B,  121 C, and  121 D respectively include tip portions  122 B,  122 C, and  122 D and arm portions  123 B,  123 C, and  123 D. The arm portions  123 A to  123 D each have, for example, a width of around 50 μm in the X-axis direction and a length of around 450 μm in the Y-axis direction. 
     Among the four vibrating arms, the vibrating arms  121 A and  121 D are considered outer vibrating arms that are arranged on the outside in the X-axis direction and the vibrating arms  121 B and  121 C are considered inner vibrating arms that are arranged on the inside in the X-axis direction. As an example, a width (hereafter referred to as a “release width”) W 1  of a gap formed between the arm portions  123 B and  123 C of the inner vibrating arms  121 B and  121 C is set so as to be larger than a release width W 2  between the arm portions  123 A and  123 B of the outer vibrating arm  121 A and the inner vibrating arm  121 B, which are adjacent to each other in the X-axis direction, and so as to be larger than a release width W 2  between the arm portion  123 D and  123 C of the outer vibrating arm  121 D and the inner vibrating arm  121 C, which are adjacent to each other in the X-axis direction. Based on this configuration, the vibration characteristics and durability are improved by setting the release width W 1  to be larger than the release width W 2  in this way. The numerical values of the release widths W 1  and W 2  are not restricted, and for example, the release width W 1  is around 25 μm and the release width W 2  is around 10 μm. Note that the release width W 1  between the arm portions of the inner vibrating arms and the release width W 2  between the arm portions of an inner vibrating arm and an outer vibrating arm are not limited to being configured in the manner illustrated in  FIG. 3 , and alternatively, the release width W 1  may be set so as to be smaller than the release width W 2  or both widths may be set to be equal to each other. 
     Moreover, in the exemplary aspect, the width of each of the tip portions  122 A to  122 D in the X-axis direction is larger than the width of each of the arm portions  123 A to  123 D in the X-axis direction. Therefore, the weight per unit length in the Y-axis direction (hereafter, also simply referred to as “weight”) of each of the tip portions  122 A to  122 D is larger than the weight of each of the arm portions  123 A to  123 D. In other words, the tip portions  122 A to  122 D correspond to mass-loaded portions for increasing the weights of the vibrating arms  121 A to  121 D. Thus, the vibration characteristics can be improved while reducing the size of the vibrating portion  110 . In addition, mass-adding films may be provided on the surfaces of the tip portions  122 A to  122 D from the viewpoint of increasing the weights of the tip portions  122 A to  122 D. In an exemplary aspect, such mass-adding films can be used as frequency-adjusting films for adjusting the resonant frequencies of the vibrating arms  121 A to  121 D by shaving away parts of the mass-adding films. 
     In a plan view from the top cover  30  side, the protrusion  50 , which protrudes from the bottom cover  20 , is formed between the arm portions  123 B and  123 C of the inner vibrating arms  121 B and  121 C. The protrusion  50  extends in the Y-axis direction that is parallel to the arm portions  123 B and  123 C. In an exemplary aspect, the length of the protrusion  50  in the Y-axis direction is around 240 μm and the length of the protrusion  50  in the X-axis direction is around 15 μm. Moreover, bending of the bottom cover  20  is suppressed by formation of the protrusion  50 . 
     (Base Portion  130 ) 
     As illustrated in  FIG. 3 , in a plan view from the top cover  30  side, the base portion  130  (or base) includes the front end portion  131 A, a rear end portion  131 B, a left end portion  131 C, and a right end portion  131 D. 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 parts of the periphery of the base portion  130 . Specifically, the front end portion  131 A is an end portion that extends in the X-axis direction on the side near the vibrating arms  121 A to  121 D. The rear end portion  131 B is an end portion that extends in the X-axis direction on the opposite side from the vibrating arms  121 A to  121 D. The left end portion  131 C is an end portion that extends in the Y-axis direction on the side near the vibrating arm  121 A when looking from the vibrating arm  121 D. The right end portion  131 D is an end portion that extends in the Y-axis direction on the side near the vibrating arm  121 D when looking from the vibrating arm  121 A. 
     The two ends of the left end portion  131 C connect one end of the front end portion  131 A and one end of the rear end portion  131 B to each other. The two ends of the right end portion  131 D connect the other end of the front end portion  131 A and the other end of the rear end portion  131 B to each other. The front end portion  131 A and the rear 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. As further shown, the vibrating arms  121 A to  121 D are connected to and extend from the front end portion  131 A. 
     In a plan view from the top cover  30  side, the shape of the base portion  130  is a substantially rectangular shape with the front end portion  131 A and the rear end portion  131 B forming the long sides and the left end portion  131 C and the right end portion  131 D forming the short sides. The base portion  130  is formed so as to substantially have planar symmetry with respect to a virtual plane P defined along a vertical bisector of the front end portion  131 A and the rear end portion  131 B. Note that the base portion  130  is not limited to having a rectangular shape as illustrated in  FIG. 3  and may instead have another shape that substantially has planar symmetry with respect to the virtual plane P in alternative aspects. For example, the shape of the base portion  130  may be a trapezoid, with one of the front end portion  131 A and the rear end portion  131 B being longer than the other. Furthermore, at least one out 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 virtual plane P corresponds to a plane of symmetry of the entire vibrating portion  110 . Therefore, the virtual plane P is a plane that passes through the middle of the vibrating arms  121 A to  121 D in the X-axis direction and is located between the inner vibrating arms  121 B and  121 C. Specifically, the outer vibrating arm  121 A and the inner vibrating arm  121 B, which are adjacent to each other, are formed so as to be symmetrical with the outer vibrating arm  121 D and the inner vibrating arm  121 C, which are adjacent to each other, with the virtual plane P therebetween. 
     A base portion length of the base portion  130 , which is the maximum distance between the front end portion  131 A and the rear end portion  131 B in the Y-axis direction, is around 40 μm, for example. Furthermore, a base portion width, which is the maximum distance between the left end portion  131 C and the right end portion  131 D in the X-axis direction, is around 300 μm, for example. In the example configuration 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 rear end portion  131 B. 
     (Holding Portion  140 ) 
     The holding portion  140  (or frame) is a part for holding the vibrating portion  110  in the vibration space formed by the bottom cover  20  and the top cover  30  and, for example, surrounds the vibrating portion  110 . As illustrated in  FIG. 3 , the holding portion  140  includes a front frame  141 A, a rear frame  141 B, a left frame  141 C, and a right frame  141 D in a plan view from the top cover  30  side. The front frame  141 A, the rear frame  141 B, the left frame  141 C, and the right frame  141 D each form part of a substantially rectangular frame that surrounds the vibrating portion  110 . Specifically, the front frame  141 A is the part that extends in the X-axis direction on the side near the excitation portion  120  when looking from the base portion  130 . The rear frame  141 B is the part that extends in the X-axis direction on the side near the base portion  130  when looking from excitation portion  120 . The left frame  141 C is the part that extends in the Y-axis direction on the side near the vibrating arm  121 A when looking from the vibrating arm  121 D. The right frame  141 D is the part that extends in the Y-axis direction on the side near the vibrating arm  121 D when looking from the vibrating arm  121 A. The holding portion  140  is formed so as to have planar symmetry with respect to the virtual plane P. 
     The two ends of the left frame  141 C are respectively connected to one end of the front frame  141 A and one end of the rear frame  141 B. The two ends of the right frame  141 D are respectively connected to the other end of the front frame  141 A and the other end of the rear frame  141 B. The front frame  141 A and the rear frame  141 B face each other in the Y-axis direction with the vibrating 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 vibrating portion  110  interposed therebetween. In alternative aspect, it is noted that it is sufficient that the holding portion  140  be provided along at least part of the periphery of the vibrating portion  110  and the holding portion  140  is not limited to having a continuous peripheral frame shape as shown in the exemplary embodiment. 
     (Holding Arm  150 ) 
     As further shown, the holding arm  150  is provided inside the holding portion  140  and connects the base portion  130  and the holding portion  140  to each other. As illustrated in  FIG. 3 , the holding arm  150  includes a left holding arm  151 A and a right holding arm  151 B in a plan view from the top cover  30  side. The left holding arm  151 A connects the rear 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 rear end portion  131 B of the base portion  130  and the right frame  141 D of the holding portion  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 side arm  153 B. The holding arm  150  is formed so as to have planar symmetry with respect to the virtual plane P. 
     The holding rear arms  152 A and  152 B extend from the rear end portion  131 B of the base portion  130  between the rear end portion  131 B of the base portion  130  and the holding portion  140 . Specifically, the holding rear arm  152 A extends from the rear end portion  131 B of the base portion  130  toward the rear frame  141 B, bends, and then extends toward the left frame  141 C. The holding rear arm  152 B extends from the rear end portion  131 B of the base portion  130  toward the rear frame  141 B, bends, and then extends toward the right frame  141 D. 
     The holding side arm  153 A extends parallel to the outer vibrating arm  121 A between the outer vibrating arm  121 A and the holding portion  140 . The holding side arm  153 B extends parallel to the outer vibrating arm  121 D between the outer vibrating arm  121 D and the holding portion  140 . Specifically, the holding side arm  153 A extends from the end portion of the holding rear arm  152 A on the side near the left frame  141 C toward the front frame  141 A, bends, and is connected to the left frame  141 C. The holding side arm  153 B extends from the end portion of the holding rear arm  152 B on the side near the right frame  141 D toward the front frame  141 A, bends and is connected to the right frame  141 D. 
     It is noted that the holding arm  150  is not limited to having the above-described configuration. 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 portion  130 . In addition, the holding arm  150  may be connected to the front frame  141 A of the holding portion  140 . 
     (Multilayer Structure) 
     Next, the multilayer structure and operation of the resonance device  1  according to the first embodiment will be described while referring to  FIGS. 4 and 5 .  FIG. 4  is a sectional view taken along the X axis conceptually illustrating the multilayer structure of the resonance device illustrated in  FIG. 1 .  FIG. 5  is a sectional view taken along the Y axis conceptually illustrating the multilayer structure of the resonance device illustrated in  FIG. 1  during operation.  FIG. 4  simply schematically illustrates a cross section including the arm portions  123 A to  123 D, lead-out lines C 2  and C 3 , through electrodes V 2  and V 3 , and so forth in order to describe the multilayer structure of the resonance device  1  and these elements are not necessarily located in the same planar cross section. For example, the through electrodes V 2  and V 3  may be formed at positions that are spaced away in the Y-axis direction from a cross-section that is parallel to the ZX plane defined by the Z-axis and the X-axis and cuts through the arm portions  123 A to  123 D. Similarly,  FIG. 5  simply schematically illustrates a cross section including the vibrating arm  121 A, lead-out lines C 1  and C 2 , through electrodes V 1  and V 2 , and so forth in order to describe the multilayer structure of the resonance device  1  and these elements are not necessarily located in the same planar cross section. 
     In the resonance device  1 , the holding portion  140  of the resonator  10  is bonded to the top of the side wall  23  of the bottom cover  20  and furthermore, the holding portion  140  of the resonator  10  and the side wall  33  of the top cover  30  are bonded to each other. Thus, the resonator  10  is held between the bottom cover  20  and the top cover  30  and a vibration space in which the vibrating portion  110  vibrates is formed by the bottom cover  20 , the top cover  30 , and the holding portion  140  of the resonator  10 . In an exemplary aspect, the resonator  10 , the bottom cover  20 , and the top cover  30  are each formed using a silicon (Si) substrate (hereafter, “Si substrate”), for example. Moreover, the resonator  10 , the bottom cover  20 , and the top cover  30  may be each formed of a silicon on insulator (SOI) substrate in which a silicon layer and a silicon oxide film are stacked one on top of the other. 
     (Resonator  10 ) 
     The vibrating portion  110 , the holding portion  140 , and the holding arm  150  of the resonator  10  are integrally formed with each other using the same process. A metal film E 1  is stacked on a Si substrate F 2 , which is an example of a substrate, in the resonator  10 . A piezoelectric film F 3  is stacked on the metal film E 1  so as to cover the metal film E 1  and a metal film E 2  is stacked on the piezoelectric film F 3 . A protective film F 5  is stacked on the metal film E 2  so as to cover the metal film E 2 . The above-described mass-adding films may be additionally stacked on the protective film F 5  in the tip portions  122 A to  122 D. The vibrating portion  110 , the holding portion  140 , and the holding arm  150  are formed by subjecting a multilayer body consisting of the above-described Si substrate F 2 , the metal film E 1 , the piezoelectric film F 3 , the metal film E 2 , the protective film F 5 , and so on to removal processing and patterning. In the removal processing, for example, the multilayer body is dry etched by radiating an argon (Ar) ion beam. The front surface and the side surface of the resonator  10  where ion etching has been performed are charged with the same polarity as a result of being exposed to the charged particles. 
     The Si substrate F 2  is formed from a degenerate n-type silicon (Si) semiconductor having a thickness of around 6 μm, for example, and can contain phosphorus (P), arsenic (As), antimony (Sb), and the like as n-type dopants. The resistance of the degenerate silicon (Si) used in the Si substrate F 2  is, for example, less than 16 mΩ·cm and more preferably is less than or equal to 1.2 mΩ·cm. In addition, a temperature characteristic correcting layer F 21  composed of a silicon oxide such as SiO 2  is formed on the bottom surface of the Si substrate F 2 . Changes in the resonant frequency of the resonator  10  that occur with changes in the environmental temperature can be reduced as a result of the vibrating portion  110  having the temperature characteristic correcting layer F 21 . A temperature characteristic correcting layer may be formed on the top surface of the Si substrate F 2  or may be formed on both the top surface and the bottom surface of the Si substrate F 2 . 
     The temperature characteristic correcting layer F 21  of the tip portions  122 A to  122 D is preferably formed with a uniform thickness. A “uniform thickness” means that thickness variations of the temperature characteristic correcting layer F 21  lie within ±20% of the average value of the thickness. 
     The metal films E 1  and E 2  each include an excitation electrode for exciting the vibrating arms  121 A to  121 D and a lead-out electrode for electrically connecting the excitation electrode to an external power source or ground potential. As further shown, the parts of the metal films E 1  and E 2  that function as excitation electrodes face each other with the piezoelectric film F 3  interposed therebetween in the arm portions  123 A to  123 D of the vibrating arms  121 A to  121 D. The parts of the metal films E 1  and E 2  that function as lead-out electrodes are, for example, led out to the holding portion  140  from the base portion  130  via the holding arm  150 . The metal film E 1  is electrically continuous throughout the entire resonator  10 . The parts of the metal film E 2  formed in the outer vibrating arms  121 A and  121 D and the parts of the metal film E 2  formed in the inner vibrating arms  121 B and  121 C are electrically isolated from each other. The metal film E 1  corresponds to a lower electrode and the metal film E 2  corresponds to an upper electrode. 
     In an exemplary aspect, the thicknesses of the metal films E 1  and E 2 , for example, lie in a range of around 0.1 to 0.2 μm. The metal films E 1  and E 2  are patterned into excitation electrodes, lead-out electrodes, and so on by performing a removal process such as etching after film deposition. The metal films E 1  and E 2  are, for example, formed of a metal material having a body-centered cubic crystal structure. Specifically, the metal films E 1  and E 2  are formed using molybdenum (Mo), tungsten (W), or the like. 
     The piezoelectric film F 3  is a thin film formed of a type of piezoelectric material that converts electrical energy into mechanical energy and vice versa. The piezoelectric film F 3  expands and contracts in Y-axis directions among in-plane directions of the XY plane in accordance with an electric field formed in the piezoelectric film F 3  by the metal films E 1  and E 2 . The open ends of the vibrating arms  121 A to  121 D are displaced toward the inner surfaces of the bottom cover  20  and the top cover  30  by the expansion and contraction of the piezoelectric film F 3  and the vibrating arms  121 A to  121 D vibrate in an out-of-plane bending vibration mode. 
     Moreover, the piezoelectric film F 3  is formed of a material having a wurtzite-type hexagonal crystal structure and, for example, can have a nitride or an oxide as a main constituent such as aluminum nitride (AlN), scandium aluminum nitride (ScAlN), zinc oxide (ZnO), gallium nitride (GaN), or indium nitride (InN). Scandium aluminum nitride is a substance obtained by replacing some of the aluminum in aluminum nitride with scandium, and instead of scandium, the aluminum may be replaced with two elements such as magnesium (Mg) and niobium (Nb) or magnesium (Mg) and zirconium (Zr). The thickness of the piezoelectric film F 3  is, for example, around 1 μm, but may be around 0.2 to 2 μm. 
     The protective film F 5  protects the metal film E 2  from oxidation. It is noted that the protective film F 5  does not need to be exposed to the bottom plate  32  of the top cover  30  as long as the protective film F 5  is provided on the top cover  30  side of the metal film E 2 . For example, a film that covers the protective film F 5  may be formed such as a parasitic capacitance reducing film that reduces the capacitance of a wiring line formed in the resonator  10 . The protective film F 5  is, for example, formed of a nitride film such as an aluminum nitride (AlN) or silicon nitride (SiN x ) film or an oxide film such as an alumina oxide (Al2O 3 ), tantalum pentoxide (Ta 2 O 5 ) , or silicon oxide (SiO x ) film. 
     The parts of the protective film F 5  provided on the tip portions  122 A to  122 D may be trimmed using an argon ion beam, for example, in order to adjust the resonant frequency. In this trimming process, the front surface and side surface of the resonator  10  are charged with the same polarity as a result of being exposed to the charged particles. When a mass-adding film is additionally provided on the protective film F 5  on the tip portions  122 A to  122 D, the mass-adding film is preferably formed of a material that is easier to trim than the protective film F 5  from the viewpoint of efficiency when the mass-adding film is used as a frequency-adjusting film and the mass-adding film may be a molybdenum (Mo) film, for example. 
     Lead-out lines C 1 , C 2 , and C 3  are formed on the protective film F 5  of the holding portion  140 . The lead-out line C 1  is electrically connected to the metal film E 1  via a through hole formed in the piezoelectric film F 3  and the protective film F 5 . The lead-out line C 2  is electrically connected to parts of the metal film E 2  formed on the outer vibrating arms  121 A and  121 D via through holes formed in the protective film F 5 . The lead-out line C 3  is electrically connected to parts of the metal film E 2  formed on the inner vibrating arms  121 B and  121 C via through holes formed in the protective film F 5 . The lead-out lines C 1  to C 3  are formed of a metal material such as aluminum (Al), germanium (Ge), gold (Au), or tin (Sn). 
     (Bottom Cover  20 ) 
     In an exemplary aspect, the bottom plate  22  and the side wall  23  of the bottom cover  20  are integrally formed using a Si substrate P 10 . The Si substrate P 10  is formed of non-degenerate silicon and has a resistivity greater than or equal to 10 Ω·cm, for example. Moreover, the Si substrate P 10  is exposed inside the recess  21  of the bottom cover  20 . The temperature characteristic correcting layer F 21  is formed on the top surface of the protrusion  50 . However, from the viewpoint of suppressing charging of the protrusion  50 , the Si substrate P 10 , which has a lower electrical resistivity than the temperature characteristic correcting layer F 21 , may be exposed at the top surface of the protrusion  50  or a conductive layer may be formed. A getter layer may be formed on the surface of the recess  21  of the bottom cover  20  on the side that faces the resonator  10 . 
     The thickness of the bottom cover  20  defined in the Z-axis direction is around 150 μm and a depth D 1  of the recess  21 , which is defined in the same way, is around 100 μm. The amplitude of the vibrating arms  121 A to  121 D is restricted by the depth D 1  and therefore the maximum amplitude on the side near the bottom cover  20  is around 100 μm. 
     It is noted that the bottom cover  20  can also be regarded as part of a SOI substrate. If the resonator  10  and the cover lid  20  are regarded as a MEMS substrate formed by an integrated SOI substrate, the Si substrate P 10  of the bottom cover  20  corresponds to a support substrate of the SOI substrate, the temperature characteristic correcting layer F 21  of the resonator  10  corresponds to a box layer of the SOI substrate, and the Si substrate F 2  of the resonator  10  corresponds to an active layer of the SOI substrate. At this time, various semiconductor elements and circuits may be formed using portions of a MEMS substrate that continue outside the resonance device  1 . 
     (Top Cover  30 ) 
     The bottom plate  32  and the side wall  33  of the top cover  30  are integrally formed using a Si substrate Q 10 . It is preferable that the front surface and the rear surface of the top cover  30  and the inner surfaces of the through holes in the top cover  30  be covered by a silicon oxide film Q 11 . The silicon oxide film Q 11  is formed on the front surface of the Si substrate Q 10  by oxidizing the Si substrate Q 10  or by performing chemical vapor deposition (CVD), for example. The Si substrate Q 10  is exposed inside the recess  31  of the top cover  30 . A getter layer may be formed on the surface of the recess  31 , which is on the side facing the resonator  10 , of the top cover  30 . The getter layer is, for example, formed of a material having a strong affinity for oxygen such as titanium (Ti), and adsorbs outgas released from a bonding part H and suppresses reduction of the vacuum in the vibration space. 
     The thickness of the top cover  30  defined in the Z-axis direction is around 150 μm and a depth D 2  of the recess  31 , which is defined in the same way, is around 100 μm. The amplitude of the vibrating arms  121 A to  121 D is restricted by the depth D 2  and therefore the maximum amplitude on the side near the top cover  30  is around 100 μm. 
     As further shown, terminals T 1 , T 2 , and T 3  are formed on the top surface of the top cover  30  (i.e., the surface on the opposite side from the surface facing resonator  10 ). The terminal T 1  is a mounting terminal for grounding the metal film E 1 . The terminal T 2  is a mounting terminal that electrically connects the metal film E 2  of the outer vibrating arms  121 A and  121 D to an external power supply. The terminal T 3  is a mounting terminal that electrically connects the metal film E 2  of the inner vibrating arms  121 B and  121 C to an external power supply. The terminals T 1  to T 3  are formed by plating nickel (Ni), gold (Au), silver (Ag), copper (Cu), or the like on a metallized layer (underlying layer) of chromium (Cr), tungsten (W), nickel (Ni), or the like. Dummy terminals, which are electrically insulated from the resonator  10 , may be formed on the top surface of the top cover  30  for the purpose of adjusting parasitic capacitances and mechanical strength balance. 
     Through electrodes V 1 , V 2 , and V 3  are formed inside the side wall  33  of the top cover  30 . The through electrode V 1  electrically connects the terminal T 1  and the lead-out line C 1  to each other, the through electrode V 2  electrically connects the terminal T 2  and the lead-out line C 2  to each other, and the through electrode V 3  electrically connects the terminal T 3  and the lead-out line C 3  to each other. The through electrodes V 1  to V 3  are formed by filling through holes, which penetrate through the side wall  33  of the top cover  30  in the Z-axis direction, with an electrically conductive material. The filled electrically conductive material is, for example, polycrystaline silicon (poly-Si), copper (Cu), gold (Au), or the like. 
     In the exemplary aspect, the bonding part H is formed between the side wall  33  of the top cover  30  and the holding portion  140  in order to bond the side wall  33  of the top cover  30  and the holding portion  140  of the resonator  10  to each other. 
     The bonding part H is formed in a closed ring shape that surrounds the vibrating portion  110  in the XY plane so as to hermetically seal the vibration space of the resonator  10  in a vacuum state. The bonding part H is formed of eutectically bonded metal films, for example, an aluminum (Al) film, a germanium (Ge) film, and an aluminum (Al) film, stacked in this order. The bonding part H may be formed of a combination of films appropriately selected from among gold (Au), tin (Sn), copper (Cu), titanium (Ti), silicon (Si), and the like. In addition, a metallic compound such as titanium nitride (TiN) or tantalum nitride (TaN) may be sandwiched in the bonding part H in order to improve adhesion. 
     (Operation) 
     In this embodiment, the terminal T 1  is grounded and alternating current voltages of opposite phases are applied to the terminal T 2  and the terminal T 3 . Therefore, the phase of the electric field formed in the piezoelectric film F 3  in the outer vibrating arms  121 A and  121 D and the phase of the electric field formed in the piezoelectric film F 3  in the inner vibrating arms  121 B and  121 C are in opposite phases during operation. This causes the outer vibrating arms  121 A and  121 D and the inner vibrating arms  121 B and  121 C to vibrate with opposite phases from each other. For example, when the tip portions  122 A and  122 D of the outer vibrating arms  121 A and  121 D are displaced toward the inner surface of the top cover  30 , the tip portions  122 B and  122 C of the inner vibrating arms  121 B and  121 C are displaced toward the inner surface of the bottom cover  20 . As described above, the vibrating arm  121 A and the vibrating arm  121 B, which are adjacent to each other, vibrate in opposite vertical directions around a center axis r 1  that extends in the Y-axis direction between the vibrating arm  121 A and the vibrating arm  121 B. In addition, the vibrating arm  121 C and the vibrating arm  121 D, which are adjacent to each other, vibrate in opposite vertical directions around a center axis r 2  that extends in the Y-axis direction between the vibrating arm  121 C and the vibrating arm  121 D. This creates torsional moments in opposite directions at the center axes r 1  and r 2  and bending vibration is generated in the base portion  130 . In an exemplary aspect, the maximum amplitude of the vibrating arms  121 A to  121 D is around 100 μm and the amplitude during normal driving is around 10 μm. 
     (Release Width) 
     Next, a release width around the peripheries of the excitation portion  120  and the holding arm  150  will be described while referring to  FIG. 3 . Since the resonator  10  is configured to have planar symmetry with respect to the virtual plane P, the release width around the peripheries of the outer vibrating arm  121 A, the inner vibrating arm  121 B, and the left holding arm  151 A will be described and description of the release width around the peripheries of the outer vibrating arm  121 D, the inner vibrating arm  121 C, and the right holding arm  151 B will be omitted. 
     As an example, a release width  12 Wa between the tip portion  122 A of the outer vibrating arm  121 A and the left frame  141 C of the holding portion  140  has substantially the same size as a release width  12 Wb between the tip portion  122 A of the outer vibrating arm  121 A and the front frame  141 A of the holding portion  140 . In addition, the release width  12 Wa is substantially the same size as a release width  12 Wc between the tip portion  122 A of the outer vibrating arm  121 A and the tip portion  122 B of the inner vibrating arm  121 B ( 12 Wa= 12 Wb= 12 Wc). Moreover, although not illustrated, the release width between the tip portion  122 B of the inner vibrating arm  121 B and the front frame  141 A of the holding portion  140  has substantially the same size as the release width  12 Wb. 
     As an example, a release width  15 Wa between the holding side arm  153 A of the left holding arm  151 A and the left frame  141 C of the holding portion  140  has substantially the same size as a release width  15 Wb between the holding side arm  153 A of the left holding arm  151 A and the arm portion  123 A of the outer vibrating arm  121 A. A release width  15 Wc between the holding rear arm  152 A of the left holding arm  151 A and the rear end portion  131 B of the base portion  130  has substantially the same size as a release width  15 Wd between the holding rear arm  152 A of the left holding arm  151 A and the rear frame  141 B of the holding portion  140 . The release widths  15 Wa to  15 Wd have substantially the same size as each other ( 15 Wa= 15 Wb= 15 Wc= 15 Wd). A release width  13 W between the rear end portion  131 B of the base portion  130  and the rear frame  141 B of the holding portion  140  has substantially the same size as the release widths  15 Wa to  15 Wd around the periphery of the left holding arm  151 A. 
     The release width around the periphery of the tip portion  122 A of the outer vibrating arm  121 A is not limited to the example described above and the release width  12 Wb may have a different size from the release width  12 Wa and the release width  12 Wc may have a different size from the release width  12 Wa. The release width around the periphery of the left holding arm  151 A is also not limited to the example described above and the release width  15 Wa may be different from the release width  15 Wb and the release width  15 Wc may be different from the release width  15 Wd. At least two out of the release widths  15 Wa to  15 Wd may have substantially different sizes from each other. 
     The release widths  12 Wa to  12 Wc are larger than the release widths  15 Wa and  15 Wb and larger than the release widths  15 Wc and  15 Wd. However, it is sufficient that the release widths  12 Wa to  12 Wc be larger than the release width  15 Wa or  15 Wb and larger than the release width  15 Wc or  15 Wd. 
     In addition, the release widths  12 Wa to  12 Wc are larger than the release width  13 W. 
     As described above, in this embodiment, the release widths  12 Wa and  12 Wb between the vibrating arms  121 A and  121 B and the holding portion  140  are larger than release widths  14 Wa to  14 Wd around the periphery of the left holding arm  151 A. This configuration spaces the tip portions  122 A and  122 B of the vibrating arms  121 A and  121 B away from the holding portion  140  and increases the size of the base portion  130  and the holding arm  150 . 
     Insulators and conductors on the surfaces or between the layers of the vibrating arms  121 A to  121 D, the base portion  130 , the holding portion  140 , and the holding arm  150  are charged due to ion beam exposure in the etching and trimming processes, a pyroelectric effect due to temperature changes in the manufacturing process and operating environment, and so forth. As a result, the vibrating arms  121 A to  121 D exert the effect of the Coulomb force on each other and may be affected by the Coulomb force from the holding portion  140 . The tip portions  122 A to  122 D of the vibrating arms  121 A to  121 D are the parts of the vibrating arms  121 A to  121 D that are most easily displaced and have the largest range of motion and therefore the tip portions  122 A to  122 D are readily affected by the Coulomb force. Therefore, changes in the vibration paths of the vibrating arms caused by Coulomb repulsion or attraction caused by charging of the resonator  10  can be suppressed and variations in the resonant frequency can be suppressed by setting a large release width around the peripheries of the tip portions  122 A to  122 D of the vibrating arms  121 A to  121 D and spacing the tip portions  122 A to  122 D of the vibrating arms  121 A to  121 D away from the holding portion  140 . 
     When the resonator  10  is reduced in size, if the base portion  130  is large, degradation of the driving voltage dependence (DLD) of the frequency is suppressed. In addition, if the base portion  130  and the holding arm  150  are large, the increase of a parasitic capacitance and degradation of isolation can be suppressed. In other words, it is possible to reduce factors that inhibit size reduction of the resonator  10  by setting the release width around the peripheries of the base portion  130  and the holding arm  150  to be smaller and making the base portion  130  and the holding arm  150  larger. 
     Since the release width  12 Wc is the same size as the release width  12 Wa, the effect of the Coulomb force received from the left frame  141 C of the holding portion  140  and the effect of the Coulomb force received from the tip portion  122 B of the inner vibrating arm  121 B are canceled out at the tip portion  122 A of the outer vibrating arm  121 A. Therefore, variations in the vibration path of the outer vibrating arm  121 A can be suppressed. The same applies to the other vibrating arms  121 B and  121 C. 
     Hereafter, the configuration of a resonator according to another embodiment of the present invention will be described. In the following embodiment, description of matters common to the first embodiment is omitted and only the differences are described. In particular, the same operational effects resulting from the same configurations will not be repeatedly described. 
     Second Exemplary Embodiment 
     Next, a resonator  12  according to a second embodiment will be described while referring to  FIG. 6 .  FIG. 6  is a plan view schematically illustrating the structure of the resonator according to the second embodiment. Similar to the resonator  10  according to the first embodiment, the resonator  12  according to the second embodiment includes a vibrating portion  210 , a holding portion  240  (or frame), and a holding arm  250 . The vibrating portion  210  includes a base portion  230  (or base) and vibrating arms  221 A to  221 D, the holding portion  240  includes a front frame  241 A, a rear frame  241 B, a left frame  241 C, and a right frame  241 D, and the holding arm  250  includes a left holding arm  251 A and a right holding arm  251 B. 
     The second embodiment differs from the first embodiment is that the left holding arm  251 A extends from a left end portion  231 C of the base portion  230  and the right holding arm  251 B extends from a right end portion  231 D of the base portion  230 . Specifically, the left holding arm  251 A and the right holding arm  251 B respectively include holding side arms  253 A and  253 B. The holding side arm  253 A extends from the left end portion  231 C toward the left frame  241 C, bends, extends toward the front frame  241 A, bends again, and is connected to the left frame  241 C. The right holding arm  251 B extends from the right end portion  231 D, bends, extends toward the front frame  241 A, bends again, and is connected to the right frame  241 D. The same effect can be obtained with this embodiment as with the first embodiment. 
     Hereafter, some or all of the exemplary embodiments are described herein. However, it is noted that the present invention is not limited to the following configurations and variations can be provided within the spirit of the invention. 
     As described above, an exemplary aspect of the present invention provides a resonator that includes a base; at least three vibrating arms that include a piezoelectric film, an upper electrode and a lower electrode provided so as to face each other with the piezoelectric film interposed therebetween, first ends of the vibrating arms being fixed ends connected to a front end of the base and second ends of the vibrating arms being open ends provided so as to be spaced away from the front end. Moreover; a frame is provided for holding the base; and a holding arm connect the base portion and the holding portion to each other. Each vibrating arm includes an arm portion that extends from the front end of the base and a tip that is connected to the arm portion. The holding arm includes a holding side arm that extends parallel to an outer vibrating arm, which is arranged on the outside among the at least three vibrating arms, between the outer vibrating arm and the frame. A release width between the tip of the outer vibrating arm and the frame is larger than a release width between the holding side arm and the frame or a release width between the arm portion of the outer vibrating arm and the holding side arm. 
     Thus, the tips of the vibrating arms are spaced away from the frame and the sizes of the base and the holding arm can be increased by setting the release width around the periphery of the tips of the vibrating arms to be large. Changes in the vibration paths of the vibrating arms caused by Coulomb repulsion or attraction caused by charging of the resonator can be suppressed and variations in the resonant frequency are suppressed by spacing the tips of the vibrating arms away from the frame. When the resonator is reduced in size, if the base is large, degradation of the driving voltage dependence (DLD) of the frequency can be suppressed. In addition, if the base portion and the holding arm are large, increasing of a parasitic capacitance and degradation of isolation can be suppressed. It is possible to reduce factors that inhibit size reduction of the resonator by setting the release width around the peripheries of the base and the holding arm to be smaller and making the base and the holding arm larger. 
     As an exemplary aspect, the tips are mass-loaded portions and the mass-loaded portions have a larger width than the arm portions. Thus, since the tips of the vibrating arms are heavier, the vibrating arms can be made shorter and the resonator can be reduced in size. 
     As an exemplary aspect, a release width between the mass-loaded portion of the outer vibrating arm and the mass-loaded portion of an inner vibrating arm positioned adjacent to the outer vibrating arm is the same size as the release width between the mass-loaded portion of the outer vibrating arm and the frame. Thus, the effect of a Coulomb force received from a left frame of the frame and the effect of a Coulomb force received from the tip of the inner vibrating arm are canceled out at the tip of the outer vibrating arm. Therefore, variations in the vibration path of the outer vibrating arm can be suppressed. 
     As an exemplary aspect, the holding arm further includes a holding rear arm that extends from a rear end of the base between the base and the frame, and a release width between the tip of the outer vibrating arm and the frame is larger a release width between the holding rear arm and the base or a release width between the holding rear arm and the frame. This configuration enables vibration leakage from the vibrating portion to the frame to be reduced compared with a resonator having a configuration in which holding arms extend from a left end portion and a right end portion of the base. 
     As an exemplary aspect, a resonance device is provided that includes: any of the above-described resonators; a bottom cover that is bonded to the resonator; and a top cover that is bonded to the bottom cover with the resonator interposed therebetween and that forms, together with the bottom cover, a vibration space in which the at least three vibrating arms vibrate. 
     As described above, exemplary aspects of the present invention provide a resonator that can be reduced in size while suppressing variations in the resonant frequency and also provide a resonance device including the resonator. 
     In general, the exemplary embodiments described above are to facilitate an understanding of the present invention and the embodiments are not to be interpreted as limiting the present invention. It is noted that the present invention can be modified or improved without departing from the gist of the invention and equivalents to the present invention are also included in the present invention. In other words, appropriate design changes made to the embodiments by one skilled in the art are included in the scope of the present invention so long as the changes have the characteristics of the present invention. For example, the elements included in the embodiments and the arrangements, materials, conditions, shapes, sizes and so forth of the elements are not limited to those exemplified in the embodiments and can be changed as appropriate. In addition, the elements included in the embodiments can be combined as much as technically possible and such combined elements are also included in the scope of the present invention so long as the combined elements have the characteristics of the present invention. 
     REFERENCE SIGNS LIST 
       1  . . . resonance device 
       9  . . . particle 
       10  . . . resonator 
       20  . . . bottom cover 
       30  . . . top cover 
       21 ,  31  . . . recess 
       22 ,  32  . . . bottom plate 
       23 ,  33  . . . side wall 
       110  . . . vibrating portion 
       121 A to  121 D . . . vibrating arm 
       122 A to  122 D . . . tip portion 
       123 A to  123 D . . . arm portion 
       130  . . . base portion 
       131 A . . . front end portion 
       131 B . . . rear end portion 
       131 C . . . left end portion 
       131 D . . . right end portion 
       140  . . . holding portion 
       141 A . . . front frame 
       141 B . . . rear frame 
       141 A . . . left frame 
       141 B . . . 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 characteristic correcting layer 
     F 3  . . . piezoelectric film 
     F 5  . . . protective film 
     E 1  . . . metal film (lower electrode) 
     E 2  . . . metal film (upper electrode)