Patent Publication Number: US-11650054-B2

Title: Vibrator device, electronic apparatus, and vehicle

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation of application Ser. No. 16/827,809, filed Mar. 24, 2020, which is based on, and claims priority from JP Application Serial Number 2019-057447, filed Mar. 25, 2019, the disclosures of which are hereby incorporated by reference herein in their entireties. 
    
    
     BACKGROUND 
     1. Technical Field 
     The present disclosure relates to a vibrator device, an electronic apparatus, and a vehicle. 
     2. Related Art 
     A vibrator element disclosed in JP-A-2017-194485 (Patent Literature 1) includes a vibrator body, a first support portion and a second support portion that support the vibrator body and that are fixed to a package or the like, a pair of beam portions that couple the vibrator body and the first support portion, and a pair of beam portions that couple the vibrator body and the second support portion. 
     However, since the beam portions have to be formed to fill in a gap of the vibrator body, a shape of the beam portions is limited. Therefore, a frequency design of an unnecessary vibration is limited and it is difficult to implement a vibrator element in which the unnecessary vibration is sufficiently prevented. 
     SUMMARY 
     A vibrator device according to an application example of the present disclosure includes a vibrator structure body. When three axes orthogonal to each other are defined as an A axis, a B axis, and a C axis, the vibrator structure body includes a vibrator element and a support substrate that is aligned with the vibrator element along the C axis. The vibrator element includes vibrating arms configured to flexurally vibrate along a plane parallel to the A axis and the B axis and along the A axis. The support substrate includes a base that supports the vibrator element, a support that supports the base, and a beam that couples the base and the support. A relationship f0&lt;f1 is satisfied in which f0 is a resonance frequency of a vibration of the vibrator structure body along the B axis and f1 is a drive frequency of the vibrator element. 
     In the vibrator device according to the application example of the present disclosure, a relationship Ka&gt;Kb may be satisfied in which Ka is a spring constant of an elastic deformation of the beam along the A axis and Kb is a spring constant of an elastic deformation of the beam along the B axis. In a plan view from a direction along the C axis, the support may include a first support positioned at one side of the A axis with respect to the vibrator element and a second support positioned at another side of the A axis with respect to the vibrator element. 
     In the vibrator device according to the application example of the present disclosure, in a plan view from a direction along the C axis, the support may include a first support positioned at one side of the B axis with respect to the vibrator element and a second support positioned at another side of the B axis with respect to the vibrator element. 
     In the vibrator device according to the application example of the present disclosure, the vibrator element may include: an element base; detection arms extending from the element base towards both sides of the B axis; a first coupling arm extending from the element base along the A-axis; a second coupling arm extending from the element base along the A-axis towards an opposite side to a direction in which the first coupling arm extends; and the vibrating arms including: first vibrating arms extending from a tip end of the first coupling arm towards both sides of the B axis, and second vibrating arms extending from a tip end of the second coupling arm towards both sides of the B axis. The element base may be fixed to the base via a joining member. 
     In the vibrator device according to the application example of the present disclosure, a displacement amplitude magnification of a vibration of the vibrator element along the B axis at the drive frequency f1 may be less than 0.8. 
     In the vibrator device according to the application example of the present disclosure, the vibrator element may include a vibrator substrate and an electrode that is provided on the vibrator substrate. The vibrator substrate and the support substrate may be formed of quartz crystal substrates having the same cut angle. 
     In the vibrator device according to the application example of the present disclosure, in a plan view from a direction along the C axis, the support substrate may overlap the vibrating arm. 
     In the vibrator device according to the application example of the present disclosure, the vibrator element may be a physical quantity sensor element configured to detect a physical quantity. 
     An electronic apparatus according to an application example of the present disclosure includes: the vibrator device; and a signal processing circuit configured to perform signal processing based on an output signal from the vibrator device. 
     A vehicle according to an application example of the present disclosure includes: the vibrator device; and a signal processing circuit configured to perform signal processing based on an output signal from the vibrator device. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a cross-sectional view showing a vibrator device according to a first embodiment. 
         FIG.  2    is a plan view showing the vibrator device shown in  FIG.  1   . 
         FIG.  3    is a plan view showing a vibrator element that is provided in the vibrator device shown in  FIG.  1   . 
         FIG.  4    is a schematic diagram showing driving of the vibrator element shown in  FIG.  3   . 
         FIG.  5    is a schematic diagram showing driving of the vibrator element shown in  FIG.  3   . 
         FIG.  6    is a plan view showing a support substrate that is provided in the vibrator device shown in  FIG.  1   . 
         FIG.  7    is a graph showing a relationship between a frequency ratio f1/fd and a displacement amplitude magnification (gain) of an unnecessary vibration at a drive frequency f1. 
         FIG.  8    is a graph showing a relationship between f0/f1 and the displacement amplitude magnification (gain) of the unnecessary vibration at the drive frequency f1 when the frequency ratio f1/fd=1. 
         FIG.  9    is a plan view showing a vibrator device according to a second embodiment. 
         FIG.  10    is a plan view showing a support substrate that is provided in a vibrator device according to a third embodiment. 
         FIG.  11    is a perspective view showing a personal computer according to a fourth embodiment. 
         FIG.  12    is a perspective view showing a mobile phone according to a fifth embodiment. 
         FIG.  13    is a perspective view showing a digital still camera according to a sixth embodiment. 
         FIG.  14    is a perspective view showing an automobile according to a seventh embodiment. 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Hereinafter, a vibrator device, an electronic apparatus, and a vehicle according to the present disclosure will be described in detail based on embodiments shown in the accompanying drawings. 
     First Embodiment 
       FIG.  1    is a cross-sectional view showing a vibrator device according to the first embodiment.  FIG.  2    is a plan view showing the vibrator device shown in  FIG.  1   .  FIG.  3    is a plan view showing a vibrator element that is provided in the vibrator device shown in  FIG.  1   .  FIGS.  4  and  5    are schematic views showing driving of the vibrator element shown in  FIG.  3   .  FIG.  6    is a plan view showing a support substrate that is provided in the vibrator device shown in  FIG.  1   .  FIG.  7    is a graph showing a relationship between a frequency ratio f1/fd and a displacement amplitude magnification (gain) of an unnecessary vibration at a drive frequency f1.  FIG.  8    is a graph showing a relationship between f0/f1 and the displacement amplitude magnification (gain) of the unnecessary vibration at the drive frequency f1 when the frequency ratio f1/fd=1.  FIGS.  1  to  6    show an A axis, a B axis, and a C axis which are three axes orthogonal to each other for the convenience of description. Hereinafter, an arrow tip end side of each axis is referred to as a “positive side” and an opposite side is referred to as a “negative side”. A positive side of the C axis is referred to as “upper” and a negative side of the C axis is referred to as “lower”. A plan view from a direction along the C axis is simply referred to as a “plan view”. 
     A vibrator device  1  shown in  FIG.  1    is a physical quantity sensor that detects an angular velocity ωc with the C axis serving as a detection axis. Since the vibrator device  1  serves as a physical quantity sensor, the vibrator device  1  can be mounted in various types of electronic apparatus, and the vibrator device  1  has high convenience. Such a vibrator device  1  includes a package  2 , and a circuit element  3 , a support substrate  4 , and a vibrator element  6  that are accommodated in the package  2 . 
     The package  2  includes a base  21  having a recess  211  with an opening formed on an upper surface of the base  21 , and a lid  22  joined, via a joining member  23 , to the upper surface of the base  21  so as to close the opening of the recess  211 . The recess  211  forms an internal space S inside the package  2 . The circuit element  3 , the support substrate  4 , and the vibrator element  6  are accommodated in the internal space S. For example, the base  21  can be formed of ceramics such as alumina and the lid  22  can be formed of a metal material such as Kovar. However, a constituent material of the base  21  and the lid  22  is not particularly limited. 
     The internal space S is airtight, and is in a decompressed state, preferably in a state close to a vacuum state. Accordingly, a vibration characteristic of the vibrator element  6  is improved. However, an atmosphere of the internal space S is not particularly limited and may be in an atmospheric pressure state, a pressurized state, or the like. 
     The recess  211  is configured with a plurality of recesses including a recess  211   a  that is opened on the upper surface of the base  21 , a recess  211   b  that is opened on a bottom surface of the recess  211   a  and has an opening width smaller than an opening width of the recess  211   a , and a recess  211   c  that is opened on a bottom surface of the recess  211   b  and has an opening width smaller than the opening width of the recess  211   b . The support substrate  4  is fixed on the bottom surface of the recess  211   a  in a state in which the support substrate  4  supports the vibrator element  6 . The circuit element  3  is fixed on the bottom surface of the recess  211   c.    
     As shown in  FIG.  2   , the vibrator element  6 , the support substrate  4 , and the circuit element  3  overlap with each other in the internal space S in a plan view. In other words, the vibrator element  6 , the support substrate  4 , and the circuit element  3  are aligned along the C axis. Accordingly, a planar area of the package  2  can be prevented from spreading in directions along the A axis and the B axis, and miniaturization of the vibrator device  1  can be achieved. The support substrate  4  is positioned between the vibrator element  6  and the circuit element  3  and supports the vibrator element  6  from a lower side, that is, from the negative side of the C axis. 
     As shown in  FIGS.  1  and  2   , a plurality of internal terminals  241  are provided on the bottom surface of the recess  211   a , a plurality of internal terminals  242  are provided on the bottom surface of the recess  211   b , and a plurality of external terminals  243  are provided on a lower surface of the base  21 . The internal terminals  241 ,  242  and the external terminals  243  are electrically coupled to each other via wires (not shown) provided in the base  21 . The internal terminals  241  are electrically coupled to the vibrator element  6  via conductive joining members B 1  and B 2  and the support substrate  4 , and the internal terminals  242  are electrically coupled to the circuit element  3  via bonding wires BW. 
     The vibrator element  6  is an angular velocity sensor element that serves as a physical quantity sensor and can detect an angular velocity ωc with the C axis serving as a detection axis. As shown in  FIG.  3   , the vibrator element  6  includes a vibrator substrate  7  and an electrode  8  that is provided on a surface of the vibrator substrate  7 . The vibrator substrate  7  is formed of a Z-cut quartz crystal substrate and includes an element base  70  positioned at a center of the element, detection arms  71  and  72  extending from the element base  70  towards both sides of the B axis, a first coupling arm  73  extending from the element base  70  along the A axis, a second coupling arm  74  extending from the element base  70  along the A axis towards an opposite side to a direction in which the first coupling arm  73  extends, drive arms  75  and  76  that serve as vibrating arms extending from a tip end of the first coupling arm  73  towards both sides of the B axis, and drive arms  77  and  78  that serve as vibrating arms extending from a tip end of the second coupling arm  74  towards both sides of the B axis. The Z-cut quartz crystal substrate spreads in an X-Y plane defined by an X axis serving as an electrical axis and a Y axis serving as a mechanical axis, which are crystallographic axes of the quartz crystal, and has a thickness in a direction along a Z axis serving as an optical axis. 
     Wide portions  711  and  721  wider than portions at base end sides are respectively provided at tip ends of the detection arms  71  and  72 . Wide portions  751 ,  761 ,  771 , and  781  wider than portions at base end sides are respectively provided at tip ends of the drive arms  75 ,  76 ,  77 , and  78 . 
     The electrode  8  includes drive signal electrodes  81 , drive ground electrodes  82 , first detection signal electrodes  83 , first detection ground electrodes  84 , second detection signal electrodes  85 , and second detection ground electrodes  86 . The drive signal electrodes  81  are provided on upper surfaces and lower surfaces of the drive arms  75  and  76 , and on both side surfaces of the drive arms  77  and  78 . On the other hand, the drive ground electrodes  82  are provided on both side surfaces of the drive arms  75  and  76  and on upper surfaces and lower surfaces of the drive arms  77  and  78 . The first detection signal electrodes  83  are provided on an upper surface and a lower surface of the detection arm  71 , and the first detection ground electrodes  84  are provided on both side surfaces of the detection arm  71 . On the other hand, the second detection signal electrodes  85  are provided on an upper surface and a lower surface of the detection arm  72 , and the second detection ground electrodes  86  are provided on both side surfaces of the detection arm  72 . 
     The electrodes  81  to  86  are respectively routed to a lower surface of the element base  70 . Therefore, a terminal  701  electrically coupled to the drive signal electrodes  81 , a terminal  702  electrically coupled to the drive ground electrodes  82 , a terminal  703  electrically coupled to the first detection signal electrodes  83 , a terminal  704  electrically coupled to the first detection ground electrodes  84 , a terminal  705  electrically coupled to the second detection signal electrodes  85 , and a terminal  706  electrically coupled to the second detection ground electrodes  86  are provided on the lower surface of the element base  70 . 
     As shown in  FIG.  3   , the electrode  8  is also provided at the wide portions  751  to  781  of the drive arms  75  to  78  in the vibrator element  6 . In the vibrator device  1 , the electrode  8  at the wide portions  751  to  781  is irradiated with laser light from the positive side of the C axis so that at least a part of the electrode  8  is removed before the lid  22  is joined to the base  21 , thereby reducing a mass of the drive arms  75  to  78  and adjusting a vibration balance or a drive frequency of the vibrator element  6 . Hereinafter, this step is also referred to as a “drive frequency adjustment step”. 
     The above-described vibrator element  6  detects the angular velocity ωc as follows. First, when a drive signal is applied between the drive signal electrode  81  and the drive ground electrode  82 , the drive arms  75  to  78 , as shown in  FIG.  4   , flexurally vibrate along the plane parallel to the A axis and the B axis and along the A axis. Hereinafter, this drive mode is referred to as a drive vibration mode. When the angular velocity ωc is applied to the vibrator element  6  in a state in which the drive arms  75  to  78  are driven in the drive vibration mode, a detection vibration mode shown in  FIG.  5    is newly excited. A Coriolis force is applied on the drive arms  75  to  78  to excite a vibration in a direction indicated by arrows D in the detection vibration mode. In response to the vibration, the detection arms  71  and  72  flexurally vibrate in a direction indicated by arrows E. In the detection vibration mode, a charge generated at the detection arm  71  is extracted as a first detection signal between the first detection signal electrodes  83  and the first detection ground electrodes  84 , and a charge generated at the detection arm  72  is extracted as a second detection signal between the second detection signal electrodes  85  and the second detection ground electrodes  86 . The angular velocity ωc can be detected based on the first and second detection signals. 
     As shown in  FIG.  1   , the circuit element  3  is fixed on the bottom surface of the recess  211   c . The circuit element  3  includes a drive circuit that drives the vibrator element  6  and a detection circuit that detects the angular velocity ωc applied to the vibrator element  6 . However, the circuit element  3  is not particularly limited and may include other circuits such as a temperature compensation circuit. 
     As shown in  FIG.  2   , the support substrate  4  includes a base  40 , a support  41  including a first support  411  and a second support  412  that support the base  40  and are separately provided on both sides of the base  40  along the A axis, a pair of beams  42  and  43  that couple the base  40  and the first support  411 , and a pair of beams  44  and  45  that couple the base  40  and the second support  412 . 
     The element base  70  of the vibrator element  6  is fixed on the base  40  via the conductive joining members B 2 , and the first support  411  and the second support  412  are separately fixed on the bottom surface of the recess  211   a  via the joining members B 1 . That is, the vibrator element  6  is fixed on the base  21  via the support substrate  4 . In this manner, the support substrate  4  is interposed between the vibrator element  6  and the base  21  so that the support substrate  4  can absorb and reduce a stress transmitted from the base  21  and the stress is less likely to be transmitted to the vibrator element  6 . Therefore, a vibration characteristic of the vibrator element  6  can be effectively prevented from deteriorating and changing. 
     Particularly, the first and second supports  411  and  412  are separately positioned on outer sides of the vibrator element  6  in a plan view according to the present embodiment. Specifically, the first support  411  is positioned at the positive side of the A axis with respect to the vibrator element  6 , and the second support  412  is positioned at the negative side of the A axis with respect to the vibrator element  6 . Accordingly, since the first and second supports  411  and  412  can be sufficiently separated from each other with the vibrator element  6  interposed therebetween, the support substrate  4  can support the vibrator element  6  in a more stable manner. Therefore, the vibration characteristic of the vibrator element  6  is improved. 
     The joining members B 1  and B 2  are not particularly limited as long as the joining members B 1  and B 2  have conductivity and joinability. Examples of the joining members B 1  and B 2  may include various metal bumps such as a gold bump, a silver bump, a copper bump, and a solder bump, and may include a conductive adhesive obtained by dispersing a conductive filler such as a silver filler in various adhesives such as a polyimide based adhesive, an epoxy based adhesive, a silicone based adhesive, and an acrylic based adhesive. When the former metal bump is used as the joining members B 1  and B 2 , a gas can be prevented from being generated from the joining members B 1  and B 2 , and an environmental change of the internal space S, particularly a pressure raise, can be effectively prevented. On the other hand, when the latter conductive adhesive is used as the joining members B 1  and B 2 , the joining members B 1  and B 2  are relatively soft, and the above-described stress can be absorbed and reduced in the joining members B 1  and B 2  as well. 
     In the present embodiment, a conductive adhesive is used as the joining members B 1  and a metal bump is used as the joining members B 2 . By using the conductive adhesive as the joining members B 1 , which join the support substrate  4  and the base  21  which use different materials, a thermal stress caused by a difference between thermal expansion coefficients between the support substrate  4  and the base  21  can be effectively absorbed and reduced by the joining members B 1 . On the other hand, since the support substrate  4  and the vibrator element  6  are joined by the six joining members B 2  provided in a relatively narrow area, by using the metal bump as the joining members B 2 , it is possible to effectively prevent a wet spreading like the conductive adhesive, and the joining members B 2  can be effectively prevented from contacting with one another. 
     As shown in  FIG.  3   , the beams  42 ,  43 ,  44 , and  45  respectively have bent portions  421 ,  431 ,  441 , and  451  that meander in an S-shape in intermediate portions of the beams  42 ,  43 ,  44 , and  45 , and are likely to be elastically deformed in a direction along the A axis and in a direction along the B axis. Therefore, the stress transmitted from the base  21  can be more effectively absorbed and reduced by the beams  42  to  45 . However, a shape of each of the beams  42  to  45  is not particularly limited, and for example, may be a straight shape in which the bent portions  421  to  451  are omitted. At least one of the beams  42  to  45  may have a different shape from the other ones of the beams  42  to  45 . 
     In addition, the drive arm  75  of the vibrator element  6  overlaps the beam  42 , the drive arm  76  overlaps the beam  43 , the drive arm  77  overlaps the beam  44 , and the drive arm  78  overlaps the beam  45  in a plan view. Therefore, when the drive arms  75  to  78  are bent in the direction along the C axis due to impact or the like, the drive arms  75  to  78  are brought into contact with the beams  42  to  45  and are prevented from being excessively bent beyond the beams  42  to  45 . That is, the beams  42  to  45  function as stoppers for preventing the drive arms  75  to  78  from being excessively deformed in the direction along the C axis. Accordingly, the vibrator element  6  can be prevented from being broken down. Particularly, since the beams  42  to  45  are soft portions in the support substrate  4 , a contacting impact that is caused by contacting the drive arms  75  to  78  with the beams  42  to  45  can be relieved. In the present embodiment, since tip ends of the drive arms  75  to  78 , that is, the wide portions  751  to  781  overlap the beams  42  to  45 , the drive arms  75  to  78  can be effectively prevented from being excessively deformed in the direction along the C axis. 
     However, the present disclosure is not limited thereto. For example, the base  40  and/or the first and second supports  411  and  412  may overlap the drive arms  75  to  78 , and any one of the base  40 , the first and second supports  411  and  412 , and the beams  42  to  45  may not overlap the drive arms  75  to  78 . 
     The support substrate  4  is formed of a quartz crystal substrate. In this manner, by forming the support substrate  4  with a quartz crystal substrate that is the same with the vibrator substrate  7 , so that thermal expansion coefficients of the support substrate  4  and the vibrator substrate  7  can be made equal. Therefore, a thermal stress caused by a difference between the thermal expansion coefficients of the support substrate  4  and the vibrator substrate  7  is substantially not generated, and the vibrator element  6  is less likely to be subjected to the stress. Therefore, a vibration characteristic of the vibrator element  6  can be more effectively prevented from deteriorating and changing. 
     Particularly, the support substrate  4  is formed of a quartz crystal substrate having the same cut angle with the vibrator substrate  7  that is provided in the vibrator element  6 . In the present embodiment, since the vibrator substrate  7  is formed of the Z-cut quartz crystal substrate, the support substrate  4  is also formed of a Z-cut quartz crystal substrate. Directions of crystallographic axes of the support substrate  4  coincide with directions of crystallographic axes of the vibrator substrate  7 . That is, the directions along the X axis, the directions along the Y axis, and the directions along the Z axis of the support substrate  4  and the vibrator substrate  7  coincide with each other, respectively. Since a quartz crystal has different thermal expansion coefficients in the direction along the X axis, in the direction along the Y axis, and in the direction along the Z axis, by the support substrate  4  and the vibrator substrate  7  having the same cut angle, and having directions of the crystallographic axes coincide with each other, the above-described thermal stress is less likely to be generated between the support substrate  4  and the vibrator substrate  7 . Therefore, the vibrator element  6  is less likely to be subjected to the stress, and a vibration characteristic of the vibrator element  6  is more effectively prevented from deteriorating or changing. 
     The support substrate  4  is not limited thereto. For example, the support substrate  4  has the same cut angle as the vibrator substrate  7 , but may also have directions of the crystallographic axes different from the directions of the crystallographic axes of the vibrator substrate  7 . The support substrate  4  may be formed of a quartz crystal substrate having a cut angle different from the cut angle of the vibrator substrate  7 . In addition, the support substrate  4  may not be formed of a quartz crystal substrate. In this case, a constituent material of the support substrate  4  may be a material having a thermal expansion coefficient difference from the quartz crystal smaller than a thermal expansion coefficient difference between the quartz crystal and a constituent material of the base  21 . 
     A wiring  5  that electrically couples the vibrator element  6  and the internal terminals  241  is provided on the support substrate  4 . As shown in  FIG.  6   , the wiring  5  includes terminals  511 ,  521 ,  531 ,  541 ,  551 , and  561  that are provided on the base  40 , terminals  512 ,  532 , and  542  that are provided on the first support  411 , and terminals  522 ,  552 , and  562  that are provided on the second support  412 . The wiring  5  includes a lead wire  513  that couples the terminal  511  and the terminal  512  through the beam  42 , a lead wire  523  that couples the terminal  521  and the terminal  522  through the beam  44 , a lead wire  533  that couples the terminal  531  and the terminal  532  through the beam  43 , a lead wire  543  that couples the terminal  541  and the terminal  542  through the beams  42  and  43 , a lead wire  553  that couples the terminal  551  and the terminal  552  through the beam  45 , and a lead wire  563  that couples the terminal  561  and the terminal  562  through the beams  44  and  45 . 
     The terminals  511  to  561  provided on the base  40  are electrically coupled, via the joining members B 2 , to the terminals  701  to  706  provided on the element base  70  of the vibrator element  6 , and the terminals  512  to  562  provided on the first and second supports  411  and  412  are electrically coupled, via the joining members B 1 , to the internal terminals  241 , which are not shown. Accordingly, the vibrator element  6  and the circuit element  3  are electrically coupled. 
     A configuration of the vibrator device  1  is briefly described as above. Here, for example, when a weight balance of the drive arms  75  to  78  is not sufficiently adjusted in the drive frequency adjustment step of the vibrator substrate  7  and a gravity center of the vibrator element  6  deviates from a center of the element in the vibrator element  6  described above, an unnecessary vibration in which the vibrator element  6  vibrates along the B axis in the drive vibration mode (hereinafter, simply referred to as an “unnecessary vibration”) occurs. When the unnecessary vibration occurs, a vibration leakage of the vibrator element  6  increases. Accordingly, a Q value decreases and the vibration characteristic of the vibrator element  6  is deteriorated. 
     Therefore, the vibrator device  1  has a configuration in which the unnecessary vibration of the vibrator element  6  is attenuated by the support substrate  4  that supports the vibrator element  6  and the vibration characteristic of the vibrator element  6  is prevented from deteriorating. Hereinafter, the configuration will be described in detail. Hereinafter, a structure body including the vibrator element  6  and the support substrate  4  is referred to as a “vibrator structure body  10 ”. The vibrator structure body  10  includes a vibrator system  100 . The vibrator system  100  includes a mass portion and a spring portion. The mass portion includes the base  40  and the vibrator element  6 , and the spring portion includes the four beams  42  to  45 . 
     As described above, the support substrate  4  that supports the vibrator element  6  is formed separately from the vibrator element  6 , and the support substrate  4  overlaps the vibrator element  6  along the C axis in the vibrator device  1 . Accordingly, the support substrate  4  can be freely designed without being baffled by the vibrator element  6 . A degree of freedom of the design of the support substrate  4  increases, so that the design of the support substrate  4  is more applicable, and the unnecessary vibration of the vibrator element  6  can be more effectively prevented. 
     The vibrator device  1  according to the present embodiment satisfies a relationship f0&lt;f1 in which a resonance frequency of a vibration of the vibrator structure body  10 , that is, the vibrator system  100  along the B axis, is f0, and a drive frequency of the vibrator element  6  alone in the drive vibration mode is f1. Since the unnecessary vibration of the vibrator element  6  is caused by vibration of the drive arms  75  to  78  in the drive vibration mode, a frequency of the unnecessary vibration is substantially equal to the drive frequency f1. Therefore, the relationship f0&lt;f1 is set so as to generate a difference between the frequency of the unnecessary vibration, which is substantially equal to f1, and the resonance frequency f0. In other words, the frequency of the unnecessary vibration deviates from the resonance frequency f0, and a resonance of the vibrator system  100  in response to the unnecessary vibration can be prevented. Therefore, the unnecessary vibration of the vibrator element  6  can be effectively attenuated by the support substrate  4 . 
     Here, a relationship f0&gt;f1 may be satisfied in order to generate a difference between the resonance frequency f0 and the drive frequency f1. However, when f0&gt;f1, it is required to reduce a weight of the mass portion of the vibrator system  100  or increase a spring constant of the spring portion of the vibrator system  100 . In the former case of reducing the weight of the mass portion of the vibrator system  100 , for example, a measure may be taken to reduce a size of the vibrator element  6 . If the size of the vibrator element  6  is reduced, the vibration characteristic of the vibrator element  6  is deteriorated accordingly. On the other hand, in the latter case of increasing the spring constant of the spring portion of the vibrator system  100 , a measure may be taken to harden the beams  42  to  45 . If the beams  42  to  45  are hardened, a stress from the package  2  is likely to be transmitted to the vibrator element  6  along the support substrate  4 . As described above, the vibration characteristic of the vibrator element  6  is deteriorated due to other factors in the case of f0&gt;f1. In contrast, in the case of f0&lt;f1 according to the present embodiment, such a problem does not occur and the vibration characteristic of the vibrator element  6  can be more effectively prevented from being deteriorated. 
     Particularly, the beams  42  to  45  are formed to have lengths along the A axis longer than lengths along the B axis in the present embodiment. Accordingly, the beams  42  to  45  are more likely to be elastically deformed along the B axis than along the A axis. That is, a relationship Ka&gt;Kb is satisfied in which a spring constant of an elastic deformation along the A axis is Ka and a spring constant of an elastic deformation along the B axis is Kb in the spring portion of the vibrator system  100 . Accordingly, the resonance frequency f0 can be effectively reduced and a difference f1−f0 between the resonance frequency f0 and the drive frequency f1 can be made larger. Therefore, an effect of attenuating the unnecessary vibration by the support substrate  4  is improved. The spring constants Ka and Kb preferably satisfy 0.2≤Kb/Ka≤0.8, more preferably satisfy 0.3≤Kb/Ka≤0.7, and still more preferably satisfy 0.4≤Kb/Ka≤0.6. Accordingly, the spring constant Kb can be made sufficiently small while ensuring a mechanical strength of the beams  42  to  45 . Therefore, the effect of attenuating the unnecessary vibration by the support substrate  4  is further improved. However, the present disclosure is not limited thereto. Alternatively, a relationship Ka≤Kb may be satisfied. 
     Next,  FIG.  7    is a graph showing a relationship between f1/fd and a displacement amplitude magnification (gain) of a vibration of the vibrator element  6  along the B axis at the drive frequency f1, in which the frequency of the unnecessary vibration which is a vibration of the vibrator element  6  along the B axis is fd. A “displacement amplitude” is a maximum amplitude of a dimensional displacement during a vibration, and the “displacement amplitude magnification” is a magnification of displacement amplitude to a displacement amplitude when f1/fd is 0.01. A curve Q 1  in the graph represents the vibrator structure body  10  according to the present embodiment, a curve Q 2  represents the vibrator structure body  10  according to a second embodiment to be described later, and a curve Q 3  represents a vibrator element according to a comparative example that is disclosed in Patent Literature 1. 
     As described above, since the frequency fd of the unnecessary vibration is substantially equal to the drive frequency f1, a relationship f1/fd=1 is satisfied. If a comparison is made relative to f1/fd=1 in  FIG.  7   , it can be known that a displacement amplitude magnification (gain) of the vibrator structure body  10  according to the present embodiment is smallest, a displacement amplitude magnification (gain) of the vibrating structure  10  according to the second embodiment to be described later is smaller, and a displacement amplitude magnification (gain) of a vibrator element according to the comparative example is largest. Since a smaller displacement amplitude magnification (gain) indicates a smaller amplitude of the mass portion in the vibrator system  100 , that is, the vibrator element  6  in the direction along the B axis, the unnecessary vibration of the vibrator element  6  can be more effectively attenuated in the vibrator structure body  10  according to the present embodiment. 
       FIG.  8    is a graph showing, when the frequency ratio f1/fd=1, a relationship between f0/f1 and a displacement amplitude magnification (gain) of a vibration of the vibrator element  6  along the B axis at the drive frequency f1. The f0/f1 is a ratio of the resonance frequency f0 of a vibration of the vibrator system  100  along the B axis and the drive frequency f1. It can be known from  FIG.  8    that a smaller f0/f1, that is, a larger difference between the resonance frequency f0 and the drive frequency f1: f1−f0, indicates a smaller displacement amplitude magnification (gain). The displacement amplitude magnification (gain) is less than 0.8 in the present embodiment. The displacement amplitude magnification (gain) of the vibrator element according to the comparative example is 0.8. Therefore, a better effect of attenuating the unnecessary vibration compared to the comparative example can be obtained if the displacement amplitude magnification (gain) is at least less than 0.8. The displacement amplitude ratio (gain) is preferably less than 0.6, more preferably less than 0.4, and still more preferably less than 0.2. Accordingly, a more significant effect of attenuating the unnecessary vibration can be obtained. 
     It can be known from  FIG.  8    that the displacement amplitude magnification is less than 0.8 as long as f0/f1 is less than 0.7, the displacement amplitude magnification is less than 0.6 as long as f0/f1 is less than 0.65, the displacement amplitude magnification is less than 0.4 as long as f0/f1 is less than 0.55, and the displacement amplitude magnification is less than 0.2 as long as f0/f1 is less than 0.4. That is, f0/f1 is preferably less than 0.7, more preferably less than 0.65, still more preferably less than 0.55, and yet still more preferably less than 0.4. 
     The vibrator device  1  is described above. As described above, the vibrator device  1  includes the vibrator structure body  10 . When the A axis, the B axis and the C axis are three axes orthogonal to each other, the vibrator structure body  10  includes the vibrator element  6  and the support substrate  4  that is aligned with the vibrator element  6  along the C axis, and the vibrator element  6  includes the drive arms  75 ,  76 ,  77 , and  78  that flexurally vibrate along the plane parallel to the A axis and the B axis and along the A axis. The support substrate  4  includes the base  40  that supports the vibrator element  6 , the support  41  that supports the base  40 , and the beams  42 ,  43 ,  44 , and  45  that couple the base  40  and the support  41 . The relationship f0&lt;f1 is satisfied in which the resonance frequency of the vibration of the vibrator structure body  10  along the B axis is f0 and the drive frequency of the vibrator element  6  is f1. In this manner, by satisfying the relationship f0&lt;f1, it is possible to generate a difference between the frequency of the unnecessary vibration, which is substantially equal to f1, and the resonance frequency f0, and a resonance of the vibrator system  100  in response to the unnecessary vibration can be prevented. Therefore, the unnecessary vibration of the vibrator element  6  can be effectively attenuated by the support substrate  4 . 
     As described above, the relationship Ka&gt;Kb is satisfied in which the spring constant of the elastic deformation of the beams  42 ,  43 ,  44  and  45  along the A axis is Ka and the spring constant of the elastic deformation of the beams  42 ,  43 ,  44  and  45  along the B axis is Kb. In the plan view from the direction along the C axis, the support  41  includes the first support  411  positioned at one side of the A axis with respect to the vibrator element  6 , that is, the positive side of the A axis in the present embodiment, and the second support  412  positioned at the other side of the A axis, that is, the negative side of the A axis in the present embodiment. As described above, the first and second supports  411  and  412  are provided on both sides of the vibrator element  6  so that the vibrator element  6  can be supported in a more stable manner. Therefore, the vibration characteristic of the vibrator element  6  is stabilized. In addition, the first and second supports  411  and  412  are aligned along the A axis so that the beams  42 ,  43 ,  44 , and  45  which couple the base  40  and the first and second supports  411  and  412  are easily formed to have lengths along the A axis longer than lengths along the B axis, and the relationship Ka&gt;Kb is likely to be satisfied. Therefore, the degree of freedom of the design of the support substrate  4  increases. 
     As described above, the vibrator substrate  6  includes the element base  70 , the detection arms  71  and  72  extending from the element base  70  towards both sides of the B axis, the first coupling arm  73  extending from the element base  70  along the A axis, the second coupling arm  74  extending from the element base  70  along the A axis towards an opposite side to a direction in which the first coupling arm  73  extends, the drive arms  75  and  76  that serve as vibrating arms extending from the tip end of the first coupling arm  73  towards both sides of the B axis, and the drive arms  77  and  78  that serve as vibrating arms extending from the tip end of the second coupling arm  74  towards both sides of the B axis. The element base  70  is fixed on the base  40  via the joining members B 2 . Accordingly, the unnecessary vibration of the vibrator element  6  which is a physical quantity sensor element that detects a physical quantity can be more effectively attenuated, and the vibrator device  1  with high accuracy can be implemented. 
     As described above, the displacement amplitude magnification (gain) of the vibration of the vibrator element  6  along the B axis at the drive frequency f1 is less than 0.8. Accordingly, the unnecessary vibration of the vibrator element  6  can be more effectively attenuated by the support substrate  4 . 
     As described above, the vibrator element  6  includes the vibrator substrate  7  and the electrode  8  that is provided on the vibrator substrate  7 . The vibrator substrate  7  and the support substrate  4  are formed of quartz crystal substrates having the same cut angle. Accordingly, the thermal expansion coefficients of the support substrate  4  and the vibrator substrate  7  can be set to be equal to each other. Therefore, a thermal stress caused by a difference between the thermal expansion coefficients of the support substrate  4  and the vibrator substrate  7  is substantially not generated, and the vibrator element  6  is less likely to be subject to the stress. Therefore, the vibration characteristic of the vibrator element  6  can be more effectively prevented from deteriorating and changing. 
     As described above, the support substrate  4  overlaps the drive arms  75 ,  76 ,  77 , and  78  in the plan view from the direction along the C axis. Therefore, the support substrate  4  functions as a stopper for preventing the drive arms  75  to  78  from being excessively deformed in the direction along the C axis, and the vibrator element  6  can be effectively prevented from being broken down. 
     As described above, the vibrator element  6  is a physical quantity sensor element that detects a physical quantity. Particularly, the vibrator element  6  is an angular velocity sensor element that detects the angular velocity ωc according to the present embodiment. Accordingly, the vibrator device  1  can be mounted in various types of electronic apparatus, and the vibrator device  1  has high convenience. 
     In the first embodiment as described above, the support substrate  4  is positioned between the vibrator element  6  and the circuit element  3  and supports the vibrator element  6  from the lower side, that is, from the negative side of the C axis. Alternatively, the vibrator element  6  may be positioned between the support substrate  4  and the circuit element  3  and the support substrate  4  support the vibrator element  6  from the upper side, that is, from the positive side of the C axis. In the first embodiment, the support substrate  4  is fixed on the bottom surface of the recess  211   a  of the base  21  via the joining members B 1 . Alternatively, the support substrate  4  may be fixed on the circuit element  3  via a joining member. 
     Second Embodiment 
       FIG.  9    is a plan view showing a vibrator device according to the second embodiment. 
     The second embodiment is similar to the first embodiment except for a difference in a direction of the vibrator element  6 . In the following description, the present embodiment will be described with a focus on the difference from the above-described embodiment, and a description of similar matters will be omitted. In  FIG.  9   , the same reference numerals are given to configurations similar to configurations according to the above-described embodiment, and descriptions thereof are omitted. 
     As shown in  FIG.  9   , components other than the vibrator element  6  on the support substrate  4  according to the present embodiment, that is, the package  2 , the support substrate  4 , and the circuit element  3  are rotated around the C axis by 90° with respect to the components according to the first embodiment. That is, the support substrate  4  includes the base  40 , the support  41  including a first support  411  and a second support  412  that support the base  40  and are separately provided on both sides of the base  40  along the B axis, the pair of beams  42  and  43  that couple the base  40  and the first support  411 , and the pair of beams  44  and  45  that couple the base  40  and the second support  412 . The element base  70  of the vibrator element  6  is fixed on the base  40  via the conductive joining members B 2 , and the first support  411  and the second support  412  are separately fixed on the bottom surface of the recess  211   a  via the joining members B 1 . According to such a configuration as well, the unnecessary vibration of the vibrator element  6  can be effectively attenuated by the support substrate  4  as indicated by the curve Q 2  in  FIG.  7   . The direction of the crystallographic axis of the support substrate  4  does not rotate around the C axis, and remains the same as in the above-described first embodiment. 
     As described above, according to the vibrator device  1  in the present embodiment, the unnecessary vibration of the vibrator element  6  can be effectively attenuated by the support substrate  4 , and the vibrator element  6  can be supported in a stable manner by providing the first and second supports  411  and  412  on both sides of the vibrator element  6 . Therefore, the vibration characteristic of the vibrator element  6  is stabilized. 
     Third Embodiment 
       FIG.  10    is a plan view showing a support substrate that is provided in a vibrator device according to the third embodiment. 
     The third embodiment is similar to the first embodiment except for a difference in a configuration of the support substrate  4 . In the following description, the present embodiment will be described with a focus on the difference from the above-described embodiments, and a description of similar matters will be omitted. In  FIG.  10   , the same reference numerals are given to configurations similar to configurations according to the above-described embodiments. 
     As shown in  FIG.  10   , the support substrate  4  according to the present embodiment has a gimbal shape. That is, the support substrate  4  includes a base  46  that is positioned at a central portion of the support substrate  4  and on which the vibrator element  6  is fixed via the joining members B 2 , a support  47  that surrounds the base  46 , supports the base  46 , and is fixed on the bottom surface of the recess  211   a  via the joining members B 1 , and a beam  48  that is positioned between the base  46  and the support  47  and couples the base  46  and the support  47 . 
     The beam  48  is positioned between the base  46  and the support  47  and includes a frame-shaped frame portion  481  that surrounds the base  46 , first beams  482  that couple the base  46  and the frame portion  481 , and second beams  483  that couple the support  47  and the frame portion  481 . The first beams  482  couple the base  46  and the frame portion  481  at a central portion of the first beams  482  in a direction along the B axis. A central axis J 2  of the first beams  482  is along the A axis. On the other hand, the second beams  483  couple the support  47  and the frame portion  481  at a central portion of the second beam  483  in a direction along the A axis. A central axis J 1  of the second beams  483  is along the B axis. That is, the central axis J 1  and the central axis J 2  are orthogonal to each other, and an intersection point of the central axis J 1  and the center axis J 2  substantially coincides with a center O 4  of the support substrate  4 . Alternatively, the central axis J 1  and the central axis J 2  may intersect with each other by an angle greater than 0° and smaller than 90°, and the intersection point of the central axis J 1  and the center axis J 2  may deviate from the center O 4 . 
     The support  47  has a rectangular frame shape, and includes a first support  471  positioned at a positive side of the A axis with respect to the vibrator element  6  and a second support  472  positioned at the negative side of the A axis in a plan view. The first support  471  and the second support  472  are separately fixed on the bottom surface of the recess  211   a  via the joining members B 1 . 
     According to such a configuration as well, the same effect as in the above-described first embodiment can be obtained. Although the support  47  has a frame shape in the present embodiment, the present disclosure is not limited thereto. Alternatively, the support  47 , for example, may have a C shape in which a part of the support  47  in a circumferential direction is deficient. The same applies to the frame portion  481 . 
     Fourth Embodiment 
       FIG.  11    is a perspective view showing a personal computer according to the fourth embodiment. 
     A personal computer  1100  serving as an electronic apparatus shown in  FIG.  11    includes a main body  1104  that includes a keyboard  1102 , and a display unit  1106  that includes a display portion  1108 . The display unit  1106  is rotatably supported with respect to the main body  1104  via a hinge structure. The personal computer  1100  is provided with the vibrator device  1  serving as a physical quantity sensor and a signal processing circuit  1110  that performs signal processing, that is, control of each component based on an output signal from the vibrator device  1 . 
     As described above, the personal computer  1100  serving as an electronic apparatus includes the vibrator device  1  and the signal processing circuit  1110  that performs the signal processing based on the output signal from the vibrator device  1 . Therefore, the personal computer  1100  can obtain the above-described effect of the vibrator device  1  and have high reliability. 
     Fifth Embodiment 
       FIG.  12    is a perspective view showing a mobile phone according to the fifth embodiment. 
     A mobile phone  1200  serving as an electronic apparatus shown in  FIG.  12    includes an antenna (not shown), a plurality of operation buttons  1202 , an earpiece  1204 , a mouthpiece  1206 , and a display portion  1208  provided between the operation buttons  1202  and the earpiece  1204 . The mobile phone  1200  is provided with the vibrator device  1  serving as a physical quantity sensor and a signal processing circuit  1210  that performs signal processing, that is, control of each component based on an output signal from the vibrator device  1 . 
     As described above, the mobile phone  1200  serving as an electronic apparatus includes the vibrator device  1  and the signal processing circuit  1210  that performs the signal processing based on the output signal from the vibrator device  1 . Therefore, the mobile phone  1200  can obtain the above-described effect of the vibrator device  1  and have high reliability. 
     Sixth Embodiment 
       FIG.  13    is a perspective view showing a digital still camera according to the sixth embodiment. 
     A digital still camera  1300  serving as an electronic apparatus shown in  FIG.  13    includes a case  1302 , and a display unit  1310  provided on a rear surface of the case  1302 . The display unit  1310  is configured to perform displaying based on an imaging signal from a CCD, and functions as a finder that displays an object as an electronic image. A light receiving unit  1304  including an optical lens, a CCD, and the like is provided on a front side of the case  1302 . When a photographer confirms an object image displayed on the display unit  1310  and presses a shutter button  1306 , an imaging signal of the CCD at this time point is transferred to and stored in a memory  1308 . In addition, the digital still camera  1300  is provided with the vibrator device  1  serving as a physical quantity sensor and a signal processing circuit  1312  that performs signal processing, that is, control of each component based on an output signal from the vibrator device  1 . 
     As described above, the digital still camera  1300  serving as an electronic apparatus includes the vibrator device  1  and the signal processing circuit  1312  that performs the signal processing based on the output signal from the vibrator device  1 . Therefore, the digital still camera  1300  can obtain the above-described effect of the vibrator device  1  and have high reliability. 
     In addition to the above-described personal computer  1100 , the mobile phone  1200  and the digital still camera  1300 , examples of an electronic apparatus that is provided with the vibrator device  1  may include a smartphone, a tablet terminal, a watch such as a smart watch, an inkjet discharge device such as an inkjet printer, a wearable terminal such as a head mounted displays (HMD), a television, a video camera, a video tape recorder, a car navigation device, a pager, an electronic notebook, an electronic dictionary, a calculator, an electronic game device, a word processor, a work station, a video phone, a surveillance television monitor, electronic binoculars, a POS terminal, an electronic thermometer, a sphygmomanometer, a blood glucose meter, an electrocardiogram measuring device, an ultrasonic diagnosis device, a medical device such as an electronic endoscope, a fish finder, various measuring devices, instruments such as a vehicle, an aircraft, and a ship, a base station for a portable terminal, a flight simulator, and the like. 
     Seventh Embodiment 
       FIG.  14    is a perspective view showing an automobile according to the seventh embodiment. 
     An automobile  1500  serving as a vehicle shown in  FIG.  14    includes a system  1502  such as an engine system, a brake system, and a keyless entry system. The automobile  1500  is provided with the vibrator device  1  serving as a physical quantity sensor and a signal processing circuit  1510  that performs signal processing, that is, control of the system  1502  based on an output signal from the vibrator device  1 . 
     As described above, the automobile  1500  serving as a vehicle includes the vibrator device  1  and the signal processing circuit  1510  that performs the signal processing based on an oscillation signal serving as an output signal from the vibrator device  1 . Therefore, the automobile  1500  can obtain the above-described effect of the vibrator device  1  and have high reliability. 
     In addition to the automobile  1500 , examples of a vehicle that is provided with the vibrator device  1  may include a robot, a drone, a motorcycle, an aircraft, a ship, an electric car, a rocket, a spacecraft, and the like. 
     Although the vibrator device, the electronic apparatus, and the vehicle according to the present disclosure have been described above based on the embodiments shown in the drawings, the present disclosure is not limited thereto. A configuration of each unit may be replaced with any configuration having the same function. Any other components may be added to the present disclosure. The embodiments may be combined as appropriate.