Patent Publication Number: US-11662360-B2

Title: Physical quantity sensor having a movable body formed with through-holes to reduce a difference between the inside-hole damping and the squeeze film damping

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 16/371,168, filed Apr. 1, 2019, which claims priority from Japanese Patent Application No. 2018-071189, filed Apr. 2, 2018, the disclosures of which are hereby expressly incorporated by reference herein in their entireties. 
    
    
     BACKGROUND 
     1. Technical Field 
     The present disclosure relates to a physical quantity sensor, a physical quantity sensor device, a composite sensor device, an inertial measurement unit, a vehicle positioning apparatus, a portable electronic apparatus, an electronic apparatus, and a vehicle. 
     2. Related Art 
     For example, an acceleration sensor disclosed in JP-T-2003-519384 includes a substrate, a fixed portion fixed to the substrate, a movable body coupled to the fixed portion via a beam, and a fixed detection electrode which is disposed on the substrate and detects an electrostatic capacitance generated between the fixed detection electrode and the movable body. In a case where acceleration is applied in a direction in which the movable body overlaps the fixed detection electrode, the movable body swings with the beam as a rotation axis, and thus a gap between the movable body and the fixed detection electrode changes such that the electrostatic capacitance changes. Thus, the acceleration sensor disclosed JP-T-2003-519384 can measure acceleration based on the change in the electrostatic capacitance. 
     However, in the acceleration sensor disclosed in JP-T-2003-519384, there is a problem in that an electrostatic capacitance generated between the movable body and the fixed detection electrode is reduced due to a through-hole formed in the movable body, and thus acceleration measurement sensitivity is reduced due to air resistance occurring during swinging of the movable body. 
     SUMMARY 
     A physical quantity sensor according to an aspect of the present disclosure includes a substrate; a movable body that faces the substrate; a fixed portion fixed to the substrate; and a support beam that couples the movable body to the fixed portion, in which the movable body is displaceable with the support beam as a rotation axis, and includes, in a plan view, a first mass located on one side of a second direction orthogonal to a first direction which is a direction along the rotation axis with respect to the rotation axis, a second mass located on the other side of the second direction with respect to the rotation axis, and a connection portion that connects the first mass to the second mass, each of the first mass and the second mass has a plurality of through-holes which penetrate through the movable body in a third direction orthogonal to the first direction and the second direction and each of which has a square shape as an opening shape, 
                   C   =     2   ⁢           ⁢   aL   ⁢           ⁢       8   ⁢           ⁢   μ   ⁢           ⁢   H         β   2     ⁢     r   0   2         ⁢       (     1   +       3   ⁢           ⁢     r   0   4     ⁢     K   ⁡     (   β   )           16   ⁢           ⁢     Hh   3           )     ⁡     [     1   -       l   a     ⁢     tanh   ⁡     (     a   l     )           ]                 (   1   )               
in which a length of the through-hole in the third direction is indicated by H, a length of ½ of a length of the movable body along the first direction is indicated by a, a length of the movable body along the second direction is indicated by L, a gap between a fixed electrode on the substrate and the movable body is indicated by h, a length of one side of the through-hole is indicated by S 0 , a gap between the adjacent through-holes is indicated by S 1 , a viscous resistance is indicated by μ, and damping occurring in the movable body is indicated by C,
 
here,
 
             l   =         2   ⁢           ⁢     h   3     ⁢     H   eff     ⁢     η   ⁡     (   β   )           3   ⁢           ⁢     β   2     ⁢     r   0   2                         H   eff     =     H   +       3   ⁢           ⁢   π   ⁢           ⁢     r   0       8                     η   ⁡     (   β   )       =     1   +       3   ⁢           ⁢     r   0   4     ⁢     K   ⁡     (   β   )           16   ⁢           ⁢     Hh   3                         K   ⁡     (   β   )       =       4   ⁢           ⁢     β   2       -     β   4     -     4   ⁢           ⁢   ln   ⁢           ⁢   β     -   3                 β   =       r   0       r   c                     r   c     =         S   ⁢           ⁢   0     +     S   ⁢           ⁢   1         π                       r   0     =     0.547   ×   S   ⁢           ⁢   0       ,         
and
 
in the above Equation (1), C≤1.5×Cmin in a case in which C when the following equation is established is indicated by Cmin,
 
     
       
         
           
             
               
                 3 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   r 
                   0 
                   4 
                 
                 ⁢ 
                 
                   K 
                   ⁡ 
                   
                     ( 
                     β 
                     ) 
                   
                 
               
               
                 16 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   Hh 
                   3 
                 
               
             
             = 
             1. 
           
         
       
     
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a plan view illustrating a physical quantity sensor according to a first embodiment of the present disclosure. 
         FIG.  2    is a sectional view taken along the line II-II in  FIG.  1   . 
         FIG.  3    is a diagram illustrating voltages applied to the physical quantity sensor illustrated in  FIG.  1   . 
         FIG.  4    is a schematic diagram for explaining damping. 
         FIG.  5    is a graph illustrating a relationship between S 0  and damping. 
         FIG.  6    is a graph illustrating a relationship among S 1 /S 0 , and a sensitivity ratio and a damping ratio. 
         FIG.  7    is a graph illustrating a relationship between a structural body thickness and a hole size. 
         FIG.  8    is a graph illustrating a relationship between a structural body thickness and a hole size. 
         FIG.  9    is a graph illustrating a relationship between a structural body thickness and a hole size. 
         FIG.  10    is a graph illustrating a relationship between a structural body thickness and a hole size. 
         FIG.  11    is a graph illustrating a relationship between a structural body thickness and a hole size. 
         FIG.  12    is a graph illustrating a relationship between a structural body thickness and a hole size. 
         FIG.  13    is a graph illustrating a relationship between a structural body thickness and a hole size. 
         FIG.  14    is a graph illustrating a relationship between a structural body thickness and a hole size. 
         FIG.  15    is a graph illustrating a relationship between a structural body thickness and a hole size. 
         FIG.  16    is a graph illustrating relationships among S 0 min and S 1 min, and H and h. 
         FIG.  17    is a graph illustrating relationships among S 0 min and S 1 min, and H and h. 
         FIG.  18    is a graph illustrating relationships among S 0 min and S 1 min, and H and h. 
         FIG.  19    is a graph illustrating relationships among S 1 min/S 0 min, and H and h. 
         FIG.  20    is a graph illustrating relationships among S 1 min/S 0 min, and H and h. 
         FIG.  21    is a graph illustrating relationships among S 1 min/S 0 min, and H and h. 
         FIG.  22    is a graph illustrating relationships among S 1 min/S 0 min, and H and h. 
         FIG.  23    is a sectional view illustrating a physical quantity sensor device according to a second embodiment of the present disclosure. 
         FIG.  24    is a sectional view illustrating a physical quantity sensor device according to a third embodiment of the present disclosure. 
         FIG.  25    is a plan view illustrating a composite sensor device according to a fourth embodiment of the present disclosure. 
         FIG.  26    is a sectional view of the composite sensor device illustrated in  FIG.  25   . 
         FIG.  27    is an exploded perspective view illustrating an inertial measurement unit according to a fifth embodiment of the present disclosure. 
         FIG.  28    is a perspective view of a substrate of the inertial measurement unit illustrated in  FIG.  27   . 
         FIG.  29    is a block diagram illustrating the entire system of a vehicle positioning apparatus according to a sixth embodiment of the present disclosure. 
         FIG.  30    is a diagram illustrating an operation of the vehicle positioning apparatus illustrated in  FIG.  29   . 
         FIG.  31    is a perspective view illustrating an electronic apparatus according to a seventh embodiment of the present disclosure. 
         FIG.  32    is a perspective view illustrating an electronic apparatus according to an eighth embodiment of the present disclosure. 
         FIG.  33    is a perspective view illustrating an electronic apparatus according to a ninth embodiment of the present disclosure. 
         FIG.  34    is a plan view illustrating a portable electronic apparatus according to a tenth embodiment of the present disclosure. 
         FIG.  35    is a functional block diagram illustrating a schematic configuration of the portable electronic apparatus illustrated in  FIG.  34   . 
         FIG.  36    is a perspective view illustrating a vehicle according to an eleventh embodiment. 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Hereinafter, a physical quantity sensor, a physical quantity sensor device, a composite sensor device, an inertial measurement unit, a vehicle positioning apparatus, a portable electronic apparatus, an electronic apparatus, and a vehicle will be described in detail based on embodiments illustrated in the accompanying drawings. 
     First Embodiment 
     First, a physical quantity sensor according to a first embodiment of the present disclosure will be described. 
       FIG.  1    is a plan view illustrating a physical quantity sensor according to a first embodiment of the present disclosure.  FIG.  2    is a sectional view taken along the line II-II in  FIG.  1   .  FIG.  3    is a diagram illustrating voltages applied to the physical quantity sensor illustrated in  FIG.  1   .  FIG.  4    is a schematic diagram for explaining damping.  FIG.  5    is a graph illustrating a relationship between S 0  and damping.  FIG.  6    is a graph illustrating a relationship among S 1 /S 0 , and a sensitivity ratio and a damping ratio. Each of  FIGS.  7  to  15    is a graph illustrating a relationship between a structural body thickness and a hole size. Each of  FIGS.  16  to  18    is a graph illustrating relationships among S 0 min and S 1 min, and H and h. Each of  FIGS.  18  to  22    is a graph illustrating relationships among S 0 min and S 1 min, and H and h. 
     Hereinafter, for convenience of description, three axes orthogonal to each other will be referred to as an X axis, a Y axis, and a Z axis, a direction parallel to the X axis will be referred to as an “X axis direction (second direction)”, a direction parallel to the Y axis will be referred to as a “Y axis direction (first direction)”, and a direction parallel to the Z axis will be referred to as a “Z axis direction (third direction)”. A tip side of each axis in an arrow direction will be referred to as a “positive side”, and an opposite side thereto will be referred to as a “negative side”. A Z axis direction positive side will be referred to as an “upper side”, and a Z axis direction negative side will be referred to as a “lower side”. 
     In the present specification, the term “orthogonal” includes not only a case where two elements intersect each other at 90° but also a case where two elements intersect each other at an angle (for example, 90°±10° (80° to 100°) which is slightly inclined from 90°. Specifically, a case where the X axis is inclined by about ±10° (−10° to +10°) with respect to a normal direction to a YZ plane, a case where the Y axis is inclined by about ±10° (−10° to +10°) with respect to a normal direction to an XZ plane, and a case where the Z axis is inclined by about ±10° (−10° to +10°) with respect to a normal direction to an XY plane are also included in the term “orthogonal”. 
     A physical quantity sensor  1  illustrated in  FIG.  1    is an acceleration sensor which can measure an acceleration Az in the Z axis direction. The physical quantity sensor  1  includes a substrate  2 , an element assembly  3  disposed on the substrate  2 , and a lid  5  which is bonded to the substrate  2  so as to cover the element assembly  3 . Hereinafter, each portion will be described in detail in order. 
     Substrate 
     As illustrated in  FIG.  1   , the substrate  2  has a depression  21  which is open to an upper surface side thereof. The depression  21  is formed to be larger than the element assembly  3  so as to include the element assembly  3  inside thereof in a plan view from the Z axis direction. The depression  21  functions as a relief portion for preventing the element assembly  3  from being brought into contact with the substrate  2 . As illustrated in  FIG.  2   , the substrate  2  includes a mount portion  22  having a protrusion shape provided on a bottom surface  211  of the depression  21 . The element assembly  3  is bonded to an upper surface of the mount portion  22 . Consequently, the element assembly  3  can be fixed to the substrate  2  in a state of being separated from the bottom surface  211  of the depression  21 . As illustrated in  FIG.  1   , the substrate  2  has grooves  25 ,  26 , and  27  which are open to the upper surface side thereof. 
     As the substrate  2 , a glass substrate made of a glass material (for example, borosilicate glass such as Pyrex glass (registered trademark) or Tempax glass (registered trademark)) containing alkali metal ions (for example, movable ions such as Na + ) may be used. However, the substrate  2  is not particularly limited, and, for example, a silicon substrate or a ceramic substrate may be used. 
     As illustrated in  FIG.  1   , the substrate  2  is provided with electrodes  8 . The electrodes  8  include a first fixed electrode  81 , a second fixed electrode  82 , and a dummy electrode  83  which are disposed on the bottom surface  211  of the depression  21 . The substrate  2  is provided with wirings  75 ,  76 , and  77  disposed in the grooves  25 ,  26 , and  27 . One end part of each of the wirings  75 ,  76 , and  77  is exposed to the outside of the lid  5 , and functions as an electrode pad P for electrical coupling with an external device. As illustrated in  FIG.  2   , the wiring  75  is led to the mount portion  22 , and is electrically coupled to the element assembly  3  on the mount portion  22 . The wiring  75  is also electrically coupled to the dummy electrode  83 . The wiring  76  is electrically coupled to the first fixed electrode  81 , and the wiring  77  is electrically coupled to the second fixed electrode  82 . 
     Lid 
     As illustrated in  FIG.  2   , the lid  5  has a depression  51  which is open to a lower surface side thereof. The lid  5  stores the element assembly  3  in the depression  51 , and is bonded to the upper surface of the substrate  2 . A storage space S storing the element assembly  3  is formed by the lid  5  and the substrate  2 . 
     The storage space S is an air-tight space. The storage space S is enclosed with an inert gas such as nitrogen, helium, or argon, and is preferably substantially in the atmospheric pressure at a usage temperature (−40° C. to 120° C.). However, an atmosphere of the storage space S is not particularly limited, and may be, for example, in a depressed state, and may be in a pressed state. 
     The lid  5  may employ a silicon substrate. However, the lid  5  is not particularly limited, and, for example, a glass substrate or a ceramic substrate may be used. A method of bonding the substrate  2  and the lid  5  to each other is not particularly limited, and may employ a method which is selected as appropriate depending on a material of the substrate  2  or the lid  5 , and may employ, for example, anodic bonding, activation bonding in which bonding surfaces activated through plasma irradiation are bonded together, bonding using a bonding material such as glass frits, or diffusion bonding in which metal films formed on the upper surface of the substrate  2  and the lower surface of the lid  5  are bonded to each other. In the present embodiment, the substrate  2  and the lid  5  are bonded to each other via glass frits  59  (low melting point glass). 
     The lid  5  is preferably coupled to the ground. Consequently, a potential of the lid  5  can be maintained to be constant, and, thus, for example, a change in an electrostatic capacitance between the lid  5  and the element assembly  3  can be reduced. A separation distance D between a bottom surface of the depression  51  and the element assembly  3  is not particularly limited, but is preferably 15 μm or more, more preferably 20 μm or more, and most preferably 25 μm or more. Consequently, an electrostatic capacitance between the lid  5  and the element assembly  3  can be sufficiently reduced, and thus it is possible to measure the acceleration Az with high accuracy. 
     Element Assembly 
     As illustrated in  FIG.  1   , the element assembly  3  includes a fixed part  31  bonded to the upper surface of the mount portion  22 , a movable body  32  which is displaceable with respect to the fixed part  31 , and a support beam  33  coupling the fixed part  31  to the movable body  32 . When the acceleration Az is applied, the movable body  32  swings while subjecting the support beam  33  to torsional deformation with the support beam  33  as a rotation axis J. 
     The element assembly  3  may be formed, for example, by patterning a conductive silicon substrate doped with an impurity such as phosphorus (P), boron (B), or arsenic (As) through etching (particularly, dry etching). The element assembly  3  is bonded to the upper surface of the substrate through anodic bonding. However, a material of the element assembly  3  or a method of bonding the element assembly  3  to the substrate  2  is not particularly limited. 
     The movable body  32  has a rectangular shape along the X axis direction in a plan view, and is formed in a rectangular shape having a long side in the X axis direction, particularly, in the present embodiment. The movable body  32  has a first mass  321  located on the negative side of the X axis direction with respect to the rotation axis J, a second mass  322  located on the positive side of the X axis direction with respect to the rotation axis J, and a connection portion  323  connecting the first mass  321  to the second mass  322 . The movable body  32  is coupled to the support beam  33  at the connection portion  323 . The second mass  322  is longer than in the first mass  321  in the X axis direction, and is greater than the first mass  321  in rotational moment (torque) when the acceleration Az is applied. Due to a difference in the rotational moment, the movable body  32  swings around the rotation axis J when the acceleration Az is applied. Hereinafter, a part which is a basal end of the second mass  322  and is symmetric to the first mass  321  with respect to the rotation axis J will be referred to as a “base part  322 ′”, and a part which is a distal end of the second mass  322  and is asymmetric to the first mass  321  with respect to the rotation axis J will be referred to as a “torque generation part  322 ″”. 
     The movable body  32  has an opening  324  between the first mass  321  and the second mass  322 , and the fixed part  31  and the support beam  33  are disposed in the opening  324 . Such a shape can miniaturize the element assembly  3 . The support beam  33  extends along the Y axis direction, and forms the rotation axis J. However, disposition of the fixed part  31  or the support beam  33  is not particularly limited, and the fixed part  31  or the support beam  33  may be located outside the movable body  32 , for example. 
     Here, the electrodes  8  are described again. The first fixed electrode  81  is disposed to face the first mass  321  in a plan view from the Z axis direction. The second fixed electrode  82  is disposed to face the base part  322 ′ of the second mass  322 . The dummy electrode  83  is disposed to face the torque generation part  322 ″ of the second mass  322 . During driving of the physical quantity sensor  1 , for example, a voltage V 1  illustrated in  FIG.  3    is applied to the element assembly  3 , and the first fixed electrode  81  and the second fixed electrode  82  are respectively coupled to QV amplifiers (charge-voltage conversion circuits). An electrostatic capacitor Ca is formed between the first fixed electrode  81  and the first mass  321 , and an electrostatic capacitor Cb is formed between the second fixed electrode  82  and the base part  322 ′ of the second mass  322 . 
     When the acceleration Az is applied to the physical quantity sensor  1 , the movable body  32  swings centering on the rotation axis J while subjecting the support beam  33  to torsional deformation due to a difference between rotational moments of the first and second masses  321  and  322 . Due to the swinging of the movable body  32 , a gap between the first mass  321  and the first fixed electrode  81  and a gap between the base part  322 ′ of the second mass  322  and the second fixed electrode  82  are changed, and thus capacitances of the electrostatic capacitors Ca and Cb are changed. Thus, the physical quantity sensor  1  can measure the acceleration Az based on the change amounts of the capacitances of the electrostatic capacitors Ca and Cb. 
     A plurality of through-holes  30  which penetrate through the movable body  32  in a thickness direction along the Z axis are formed in the first mass  321  and the second mass  322 . The plurality of through-holes  30  are uniformly disposed over the entire regions of the first mass  321  and the second mass  322 , and are disposed in a matrix form arranged in the X axis direction and the Y axis direction, particularly, in the present embodiment. The plurality of through-holes  30  have square shapes as cross-sectional shapes, and have the same shapes and sizes as each other. Occupancy proportions of the plurality of through-holes  30  are the same as each other in the first mass  321 , the base part  322 ′, and the torque generation part  322 ″. 
     The term “uniform” includes not only a case where a separation distance between the through-holes  30  adjacent to each other in the X axis direction and the Y axis direction is identical in all of the through-holes  30  but also a case where some separation distances are slightly (for example, about 10% or less) deviated relative to other separation distances in consideration of an error which may occur in manufacturing. Similarly, the term “square shape” includes not only a case of a complete square shape but also a case where a shape slightly deviated relative to a square shape, for example, four corners are not squared and are chamfered or rounded, at least one corner is deviated from 90°, or a length of at least one side is different from lengths of other sides, in consideration of an error which may occur in manufacturing. The phrase “occupancy proportions being the same” includes not only a case where occupancy proportions of the plurality of through-holes  30  match each other in the first mass  321 , the base part  322 ′, and the torque generation part  322 ″ but also, for example, a case where an occupancy proportion is slightly (for example, about ±5% or less) is deviated in consideration of an error which may occur in manufacturing. 
     Next, design of the through-hole  30 , more specifically, design of the through-hole  30  in a region overlapping the electrodes  8  will be described in detail. The through-holes  30  are provided to control damping of a gas when the movable body  32  swings. As illustrated in  FIG.  4   , damping includes inside-hole damping of a gas penetrating through the through-hole  30  and squeeze film damping between the movable body  32  and the substrate  2 . In a case where a size of the through-hole  30  is increased, a gas easily passes therethrough, and thus the inside-hole damping can be reduced. In a case where an occupancy proportion of the through-hole  30  is increased, a facing area between the movable body  32  and the substrate  2  is reduced, and thus the squeeze film damping can be reduced. However, a reduction of the facing area between the movable body  32  and the substrate  2  leads to a reduction of the mass of the torque generation part  322 ″, and thus measurement sensitivity for the acceleration Az is reduced. Conversely, in a case where a size of the through-hole  30  is reduced, and thus an occupancy proportion thereof is reduced, a facing area between the movable body  32  and the substrate  2  is increased, and thus the mass of the torque generation part  322 ″ is increased. Therefore, measurement sensitivity for the acceleration Az is improved, but damping is increased. As mentioned above, the measurement sensitivity and the damping have a trade-off relationship, and, thus, in the related art, both thereof are hardly compatible. 
     In contrast, in the physical quantity sensor  1 , the measurement sensitivity and the damping can be made compatible by devising design of the through-hole  30 . Hereinafter, this will be described in detail. 
     The measurement sensitivity of the physical quantity sensor  1  is proportional to (A) 1/h 2  in a case where a gap between the movable body  32 , and the first fixed electrode  81  and the second fixed electrode  82  is indicated by h, (B) a facing area between the movable body  32 , and the first fixed electrode  81  and the second fixed electrode  82 , (C) spring rigidity (which is proportional to a length H of the through-hole in the Z axis direction when a thickness of a structural body is uniform) of the support beam  33 , and (D) the mass of the torque generation part  322 ″. In the physical quantity sensor  1 , first, H, h, and a facing area between the movable body  32 , and the first fixed electrode  81  and the second fixed electrode  82  required to obtain a necessary measurement sensitivity, that is, an occupancy proportion of the through-hole  30  is determined in a state in which damping is disregarded. Consequently, the electrostatic capacitors Ca and Cb having necessary sizes are formed, and thus the physical quantity sensor  1  can obtain a sufficient measurement sensitivity. 
     Here, an occupancy proportion of the plurality of through-holes  30  in the first mass  321 , the base part  322 ′, and the torque generation part  322 ″ is not particularly limited, but is preferably, for example, 75% or more, more preferably 78% or more, and most preferably 82% or more. Consequently, a measurement sensitivity and damping can be easily made compatible. 
     In a case where an occupancy proportion of the through-holes  30  in the movable body  32  is determined, next, design for damping is performed. As a new technical concept of minimizing damping without changing a sensitivity, in the physical quantity sensor  1 , the plurality of through-holes  30  are designed such that a difference between the inside-hole damping and the squeeze film damping illustrated in  FIG.  4    is reduced as much as possible, and, preferably, the inside-hole damping is the same as the squeeze film damping. As mentioned above, in a case where a difference between the inside-hole damping and the squeeze film damping is reduced as much as possible, damping can be reduced, and, in a case where the inside-hole damping is the same as the squeeze film damping, damping is minimized. Thus, according to the physical quantity sensor  1 , it is possible to effectively reduce damping while maintaining a measurement sensitivity to be sufficiently high. 
     Here, in a case where a length of the through-hole along the Z axis direction is indicated by H [m], a length of ½ of a length of the movable body  32  along the Y axis direction is indicated by a [m], a length of the movable body  32  along the X axis direction is indicated by L [m], a gap between the electrodes  8  (for example, a fixed electrode) of the substrate  2  and the movable body  32  is indicated by h [m], a length of one side of the square shape of the through-hole  30  is indicated by S 0  [m], a gap between the through-holes  30  adjacent to each other is indicated by S 1  [m], a viscous resistance (viscosity coefficient) of a gas filling the storage space S is indicated by μ [kg/ms], and damping occurring in the movable body  32  is indicated by C [N·s/m], C is expressed by the following Equation (1). 
     
       
         
           
             
               
                 
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     Here, the parameters used in Equation (1) are expressed by Equations (2) to (8) as follows. 
     
       
         
           
             
               
                 
                   
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                         S 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                       
                       + 
                       
                         S 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     
                       π 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     r 
                     0 
                   
                   = 
                   
                     0.547 
                     × 
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     The length H of the through-hole  30  in the Z axis direction, that is, a thickness of the movable body  32  is not particularly limited, but is preferably, for example, 5.0 μm or more and 80.0 μm or less. Consequently, the movable body  32  which is sufficiently thin can be obtained while maintaining mechanical strength. Therefore, it is possible to miniaturize the physical quantity sensor  1 . The gap h between the electrodes  8  and the movable body  32  is not particularly limited, but is preferably, for example, 1.0 μm or more and 3.5 μm or less. Consequently, it is possible to sufficiently increase sizes of the electrostatic capacitors Ca and Cb while sufficiently securing a movable range of the movable body  32 . The length S 0  is not particularly limited, differs depending on the lengths a and L, but is preferably, for example, 5 μm or more and 40 μm or less, and is more preferably 10 μm or more and 30 μm or less. 
     Here, an inside-hole damping component included in Equation (1) is expressed by the following Expression (9), and a squeeze film damping component is expressed by the following Expression (10). 
                   2   ⁢           ⁢   aL   ⁢           ⁢         8   ⁢           ⁢   μ   ⁢           ⁢   H         β   2     ⁢     r   0   2         ⁡     [     1   -       l   a     ⁢     tanh   ⁡     (     a   l     )           ]               (   9   )               2   ⁢           ⁢   aL   ⁢           ⁢       8   ⁢           ⁢   μ   ⁢           ⁢   H         β   2     ⁢     r   0   2         ⁢       (       3   ⁢           ⁢     r   0   4     ⁢     K   ⁡     (   β   )           16   ⁢           ⁢     Hh   3         )     ⁡     [     1   -       l   a     ⁢     tanh   ⁡     (     a   l     )           ]               (   10   )               
Therefore, the damping C is minimized by causing the above Expression (9) to be the same as the above Expression (10), that is, by using dimensions of H, h, S 0 , and S 1  satisfying the following Equation (11).
 
     
       
         
           
             
               
                 
                   
                     
                       3 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         r 
                         0 
                         4 
                       
                       ⁢ 
                       
                         K 
                         ⁡ 
                         
                           ( 
                           β 
                           ) 
                         
                       
                     
                     
                       16 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         Hh 
                         3 
                       
                     
                   
                   = 
                   1 
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     The length S 0  of one side of the through-hole  30  satisfying the above Equation (11) is indicated by S 0 min, the gap S 1  between the through-holes  30  adjacent to each other is indicated by S 1 min, the damping C when S 0 min and S 1 min are assigned to the above Equation (1), that is, a minimum value of the damping C is indicated by Cmin. 
     Damping also depends on accuracy required for the physical quantity sensor  1 , but the damping can be sufficiently reduced by ranges of S 0  and S 1  when H and h are fixed (constant) satisfying the following Expression (12). In other words, in a case of damping within the damping minimum value Cmin+50%, since damping can be sufficiently reduced, a measurement sensitivity within a desired bandwidth can be maintained, and noise can be reduced. The following Expression (13) is preferably established, the following Expression (14) is more preferably established, and the following Expression (15) is most preferably established. Consequently, the above-described effect can be remarkably exhibited.
 
 C≤ 1.5× C min  (12)
 
 C≤ 1.4× C min  (13)
 
 C≤ 1.3× C min  (14)
 
 C≤ 1.2× C min  (15)
 
       FIG.  5    is a graph illustrating a relationship between the length S 0  of one side of the through-hole  30  and damping. H and h are fixed (constant), and a ratio of S 1 /S 0  is 1 such that a sensitivity is constant (this indicates that an opening ratio is not changed even though the length S 0  is changed). From the graph, the damping in the above Equation (1) may be divided into the squeeze film damping in the above Expression (10) and the inside-hole damping in the above Expression (9), and it can be seen that the inside-hole damping is dominant in a region in which S 0  is smaller than S 0 min, and the squeeze film damping is dominant in a region in which S 0  is larger than S 0 min. S 0  satisfying the above Expression (12) is in a range from S 0 ′ on the side smaller than S 0 min to S 0 ″ on the side larger than S 0 min. In the range from S 0 min to S 0 ′, a change in damping for a dimension variation of S 0  is greater than in the range from S 0 min to S 0 ″, and thus dimension accuracy is necessary. Therefore, S 0  may be employed in the range from S 0 min to S 0 ″ such that dimension accuracy can be alleviated. This is also the same for a case where the above Expressions (13) to (15) are established. 
     A relationship between S 0  and S 1  is not particularly limited, but preferably establishes the following Expression (16), more preferably establishes the following Expression (17), and most preferably establishes the following Expression (18). Such a relationship is established, and thus the through-holes  30  can be formed in the movable body  32  with good balance.  FIG.  6    is a graph illustrating a relationship among S 1 /S 0 , and a sensitivity ratio and a minimum damping ratio. The sensitivity ratio is a ratio with a sensitivity at S 1 /S 0 =1, and the minimum damping ratio is a ratio with minimum damping at S 1 /S 0 =1. 
     As can be seen from the graph, at S 1 /S 0 &gt;3, an increase ratio of the sensitivity ratio has a saturation tendency, and the minimum damping ratio has a considerable increase tendency. Therefore, Expressions (16) to (18) are established, and thus damping can be sufficiently reduced while making a measurement sensitivity sufficiently high.
 
0.25≤ S 1/ S 0≤3.00  (16)
 
0.6≤ S 1/ S 0≤2.40  (17)
 
0.8≤ S 1/ S 0≤2.0  (18)
 
     Hereinafter, a detailed description will be made of simulation or test verification related to the dimension ratio S 1 /S 0  in the process of deriving the ranges in the above Expressions (16) to (18).  FIGS.  7  to  15    illustrate plotting of values of a hole size and an inter-hole distance as S 0 min and S 1 min in a range of H from 5 to 80 μm, a range of h from 1.0 to 3.5 μm, and a range of S 1 /S 0  from 0.25 to 3.0 μm. In a case where S 0  and S 1  are respectively summarized in a transverse axis and a longitudinal axis of a graph based on S 0 min and S 1 min obtained in  FIGS.  7  to  15   , this leads to a graph in  FIG.  16   . As examples,  FIG.  17    illustrates S 0 min and S 1 min when S 1 /S 0  is 0.25, H is 5 μm, and h is 1.0 to 3.5 μm, and  FIG.  18    illustrates S 0 min and S 1 min when S 1 /S 0  is 0.25, H is 80 μm, and h is 1.0 to 3.5 μm. It can be seen from  FIGS.  17  and  18    that dimensions of S 0 min and S 1 min tend to increase as H or h increases. 
     Here,  FIG.  19    illustrates ranges of all points of S 0 min and S 1 min in a range of H from 5 to 80 μm, a range of h from 1.0 to 3.5 μm, and a range of S 1 /S 0  from 0.25 to 3.0. An arrow A direction is defined in the range of S 1 /S 0 , and an arrow B direction is defined in the ranges of H and h. As an example, conditions of S 0 min and S 1 min when S 1 min/S 0 min is 0.25 to 3, H is 20 μm, and h is 1.0 to 3.5 μm are as illustrated in  FIG.  20   .  FIG.  21    illustrates respective regions in which S 1 min/S 0 min is restricted by the ranges in the above Expressions (16) to (18) at H=5 to 80 μm and h=1.0 to 3.5 μm. 
     S 0 min and S 1 min have been described hitherto, but S 0  and S 1  giving the ranges of the above Expressions (12) to (15) include the peripheries of S 0 min and S 1 min in an image, for example, when H is 20 μm, and h is 3.5 μm, and thus a range Q in  FIG.  22    is obtained, so that only two sides are spread as a whole. 
     As mentioned above, the physical quantity sensor  1  has been described. The physical quantity sensor  1  includes, as described above, the substrate  2 , the movable body  32  facing the substrate  2 , the fixed part  31  fixed to the substrate  2 , and the support beam  33  coupling the movable body  32  to the fixed part  31 . The movable body  32  is displaceable with the support beam  33  as the rotation axis J, and includes, in a plan view, the first mass  321  located on one side of the X axis direction (second direction) orthogonal to the Y axis direction (first direction) which is a direction along the rotation axis J with respect to the rotation axis J, the second mass  322  located on the other side of the X axis direction with respect to the rotation axis J, and the connection portion  323  which connects the first mass  321  to the second mass  322 . Each of the first mass  321  and the second mass  322  has a plurality of through-holes  30  which penetrate through the movable body  32  in the Z axis direction (third direction) orthogonal to the X axis direction and the Y axis direction and each of which has a square shape as an opening shape. The physical quantity sensor  1  establishes the above Expression (12). Consequently, the plurality of through-holes  30  are appropriately designed, and thus damping can be sufficiently reduced while maintaining a favorable measurement sensitivity. Therefore, it is possible to provide the physical quantity sensor  1  which has a favorable measurement sensitivity and can secure a desired frequency bandwidth. 
     As described above, the physical quantity sensor  1  preferably establishes the above Expression (13), more preferably establishes the above Expression (14), and most preferably establishes the above Expression (15). Consequently, it is possible to provide the physical quantity sensor  1  which can notably exhibit the above-described effect, has a favorable measurement sensitivity, and can secure a desired frequency bandwidth. 
     As described above, the physical quantity sensor  1  preferably establishes the above Expression (16), more preferably establishes the above Expression (17), and most preferably establishes the above Expression (18). Consequently, it is possible to sufficiently reduce damping while sufficiently increasing a measurement sensitivity. 
     Regarding design of the through-hole  30 , a description has been made of a case where a cross-sectional shape of the through-hole  30  is a square shape, but the same effect can also be achieved in a case where a cross-sectional shape of the through-hole  30  is a circular shape. Specifically, this case is a case where a circular through-hole has a value in the above Equation (8) as a radius, and has twice the value in the above Equation (7) as a distance between through-hole centers. The same effect can be achieved even in a case where a cross-sectional shape of the through-hole  30  is a polygonal shape (for example, a triangular shape, a quadrangular shape other than a square shape, and a polygonal shape of a pentagonal shape or more) having an area variation within ±25% with respect to an area of a square shape in an optimal condition (when S 0 =S 0 min). 
     Second Embodiment 
     Next, a description will be made of a physical quantity sensor device according to a second embodiment of the present disclosure. 
       FIG.  23    is a sectional view illustrating a physical quantity sensor device according to a second embodiment of the present disclosure. 
     As illustrated in  FIG.  23   , a physical quantity sensor device  5000  includes the physical quantity sensor  1  and a semiconductor element  5900  (circuit element). The semiconductor element  5900  is bonded to the upper surface of the lid  5  via a die attach material DA (bonding member). The semiconductor element  5900  is electrically coupled to the electrode pad P of the physical quantity sensor  1  via a bonding wire BW 1 . The semiconductor element  5900  includes, as necessary, for example, a drive circuit which applies a drive voltage to the element assembly  3 , a measurement circuit which measures the acceleration Az based on an output from the element assembly  3 , and an output circuit which converts a signal from the measurement circuit into a predetermined signal which is then output. 
     As mentioned above, the physical quantity sensor device  5000  has been described. The physical quantity sensor device  5000  includes the physical quantity sensor  1  and the semiconductor element  5900  (circuit element). Thus, it is possible to achieve the effect of the physical quantity sensor  1 , and thus to provide the physical quantity sensor device  5000  with high reliability. 
     Third Embodiment 
     Next, a description will be made of a physical quantity sensor device according to a third embodiment of the present disclosure. 
       FIG.  24    is a sectional view illustrating a physical quantity sensor device according to a third embodiment of the present disclosure. 
     A physical quantity sensor device  5000  according to the present embodiment is the same as the physical quantity sensor device  5000  according to the second embodiment except that a package  5100  is further provided. In the following description, regarding of the physical quantity sensor device  5000  according to the third embodiment, a difference from the second embodiment will be focused, and the same contents will not be described. In  FIG.  24   , the same constituent element as that in the second embodiment is given the same reference numeral. 
     As illustrated in  FIG.  24   , the physical quantity sensor device  5000  includes the package  5100  storing the physical quantity sensor  1  and the semiconductor element  5900  (circuit element). Thus, the package  5100  can appropriately protect the physical quantity sensor  1  and the semiconductor element  5900  from impact, dust, heat, moisture (water), and the like. 
     The package  5100  includes a cavity-like base  5200 , and a lid  5300  bonded to an upper surface of the base  5200 . The base  5200  has a depression  5210  which is open to the upper surface. The depression  5210  includes a first depressed part  5211  which is open to the upper surface of the base  5200  and a second depressed part  5212  which is open to a bottom surface of the first depressed part  5211 . 
     On the other hand, the lid  5300  has a tabular shape, and is bonded to the upper surface of the base  5200  so as to close the opening of the depression  5210 . As mentioned above, the opening of the depression  5210  is closed by the lid  5300 , so that a storage space S 2  is formed in the package  5100 , and the physical quantity sensor  1  and the semiconductor element  5900  are stored in the storage space S 2 . A method of bonding the base  5200  to the lid  5300  is not particularly limited, and, in the present embodiment, seam welding using a seam ring  5400  is used. 
     The storage space S 2  is air-tightly sealed. An atmosphere of the storage space S 2  is not particularly limited, and is preferably the same as, for example, an atmosphere of the storage space S of the physical quantity sensor  1 . Consequently, even if the airtightness of the storage space S is broken, and thus the storage spaces S and S 2  communicate with each other, the atmosphere of the storage space S can be maintained without any change. Thus, it is possible to reduce a change in a measurement characteristic of the physical quantity sensor  1  due to a change in the atmosphere of the storage space S, and thus to exhibit a stable measurement characteristic. 
     A constituent material of the base  5200  is not particularly limited, and various ceramics such as alumina, zirconia, or titania may be used. A constituent material of the lid  5300  is not particularly limited, and a member having a linear expansion coefficient similar to that of a constituent material of the base  5200  may be used. For example, in a case where the above-described ceramic is used as a constituent material of the base  5200 , an alloy such as Kovar is preferably used. 
     The base  5200  includes a plurality of internal terminals  5230  disposed in the storage space S 2  and a plurality of external terminals  5240  disposed on a bottom surface thereof. Each internal terminal  5230  is electrically coupled to a predetermined external terminal  5240  via an internal wire (not illustrated) disposed in the base  5200 . 
     The physical quantity sensor  1  is fixed to the bottom surface of the depression  5210  via a die attach material DA, and the semiconductor element  5900  is disposed on the upper surface of the physical quantity sensor  1  via the die attach material DA. The physical quantity sensor  1  is electrically coupled to the semiconductor element  5900  via a bonding wire BW 1 , and the semiconductor element  5900  is electrically coupled to the internal terminals  5230  via a bonding wire BW 2 . 
     Fourth Embodiment 
     Next, a description will be made of a composite sensor device according to a fourth embodiment of the present disclosure. 
       FIG.  25    is a plan view illustrating a composite sensor device according to a fourth embodiment of the present disclosure.  FIG.  26    is a sectional view of the composite sensor device illustrated in  FIG.  25   . 
     As illustrated in  FIGS.  25  and  26   , a composite sensor device  4000  includes a base substrate  4100 , a semiconductor element  4200  (circuit element) attached to an upper surface of the base substrate  4100  via a die attach material DA (resin adhesive), an acceleration sensor  4300  (first physical quantity sensor) and an angular velocity sensor  4400  (second physical quantity sensor) attached to an upper surface of the semiconductor element  4200  via a die attach material DA, and a resin package  4500  covering the semiconductor element  4200 , the acceleration sensor  4300 , and the angular velocity sensor  4400 . The acceleration sensor  4300  is a three-axis acceleration sensor which can separately measure accelerations in three axes (the X axis, the Y axis, and the Z axis) orthogonal to each other. The angular velocity sensor  4400  is a three-axis angular velocity sensor which can separately measure angular velocities in three axes (the X axis, the Y axis, and the Z axis) orthogonal to each other. The physical quantity sensor according to the present disclosure may be used as the acceleration sensor  4300  and the angular velocity sensor  4400 . 
     The base substrate  4100  is provided with a plurality of connection terminals  4110  on an upper surface thereof, and is provided with a plurality of external terminals  4120  on a lower surface thereof. Each connection terminal  4110  is electrically coupled to a corresponding external terminal  4120  via an internal wire or the like (not illustrated) disposed in the base substrate  4100 . The semiconductor element  4200  is disposed on the upper surface of the base substrate  4100 . 
     The semiconductor element  4200  includes, as necessary, for example, a drive circuit which drives the acceleration sensor  4300  and the angular velocity sensor  4400 , an acceleration measurement circuit which separately measures an acceleration in the X axis direction, an acceleration in the Y axis direction, and an acceleration in the Z axis direction based on outputs from the acceleration sensor  4300 , an angular velocity measurement circuit which separately measures an angular velocity about the X axis, an angular velocity about the Y axis, and an angular velocity about the Z axis based on outputs from the angular velocity sensor  4400 , and an output circuit which converts a signal from each of the acceleration measurement circuit and the angular velocity measurement circuit into a predetermined signal which is then output. 
     The semiconductor element  4200  is electrically coupled to the acceleration sensor  4300  via bonding wires BW 3 , electrically coupled to the angular velocity sensor  4400  via bonding wires BW 4 , and electrically coupled to the connection terminals  4110  of the base substrate  4100  via bonding wires BW 5 . The acceleration sensor  4300  and the angular velocity sensor  4400  are disposed side by side on the upper surface of the semiconductor element  4200 . 
     As mentioned above, the composite sensor device  4000  has been described. As described above, the composite sensor device  4000  includes the acceleration sensor  4300  (first physical quantity sensor), and the angular velocity sensor  4400  (second physical quantity sensor) which measures a physical quantity which is different from that of the acceleration sensor  4300 . Consequently, it is possible to provide the composite sensor device  4000  which can measure different kinds of physical quantities and thus has high convenience. Particularly, in the present embodiment, the first physical quantity sensor is the acceleration sensor  4300  which measures accelerations, and the second physical quantity sensor is the angular velocity sensor  4400  which measures angular velocities. Thus, for example, it is possible to provide the composite sensor device  4000  which may be used for a motion sensor and thus has considerably high convenience. 
     Disposition of the acceleration sensor  4300  and the angular velocity sensor  4400  is not particularly limited, and, for example, the acceleration sensor  4300  and the angular velocity sensor  4400  may be attached to the upper surface of the base substrate  4100  with the semiconductor element  4200  interposed therebetween. With this configuration, it is possible to reduce a height of the composite sensor device  4000 . 
     Fifth Embodiment 
     Next, a description will be made of an inertial measurement unit according to a fifth embodiment of the present disclosure. 
       FIG.  27    is an exploded perspective view illustrating an inertial measurement unit according to a fifth embodiment of the present disclosure.  FIG.  28    is a perspective view of a substrate of the inertial measurement unit illustrated in  FIG.  27   . 
     An inertial measurement unit (IMU)  2000  illustrated in  FIG.  27    is an inertial measurement unit which detects an attitude or a behavior (moment of inertia) of a motion object (mounting apparatus) such as an automobile or a robot. The inertial measurement unit  2000  functions as a so-called six-axis motion sensor including a three-axis acceleration sensor and a three-axis angular velocity sensor. 
     The inertial measurement unit  2000  is a cuboid of which a planner shape is substantially a square shape. Screw holes  2110  as fixation parts are formed near two vertexes located in a diagonal direction of the square shape. The inertial measurement unit  2000  may be mounted to a mounting surface of a mounting object such as an automobile by inserting two screws into the two screw holes  2110 . The inertial measurement unit  2000  may be reduced to a size so as to be mountable on, for example, a smart phone or a digital camera through selection of components or a design change. 
     The inertial measurement unit  2000  includes an outer case  2100 , a bonding member  2200 , and a sensor module  2300 , and has a configuration in which the sensor module  2300  is inserted into the outer case  2100  via the bonding member  2200 . The sensor module  2300  has an inner case  2310  and a substrate  2320 . 
     An outer shape of the outer case  2100  is a cuboidal shape of which a planar shape is substantially a square shape in the same manner as the entire shape of the inertial measurement unit  2000 , and the screw holes  2110  are formed near two vertexes located in the diagonal direction of the square. The outer case  2100  has a box shape, and stores the sensor module  2300  therein. 
     The inner case  2310  is a member supporting the substrate  2320 , and has a shape accommodate inside the outer case  2100 . The inner case  2310  is provided with a depression  2311  for preventing contact with the substrate  2320  or an opening  2312  for exposing a connector  2330  which will be described later. The inner case  2310  is bonded to the outer case  2100  via the bonding member  2200  (for example, a packing impregnated with an adhesive). A lower surface of the inner case  2310  is bonded to the substrate  2320  via an adhesive. 
     As illustrated in  FIG.  28   , the connector  2330 , an angular velocity sensor  2340   z  measuring an angular velocity about the Z axis, an acceleration sensor  2350  measuring an acceleration in each of the X axis direction, the Y axis direction, and the Z axis direction, and the like are mounted on an upper surface of the substrate  2320 . An angular velocity sensor  2340   x  measuring an angular velocity about the X axis, and an angular velocity sensor  2340   y  measuring an angular velocity about the Y axis are mounted on a side surface of the substrate  2320 . The physical quantity sensor of the present embodiment may be used as the sensors  2340   z ,  2340   x ,  2340   y , and  2350 . 
     A control IC  2360  is mounted on a lower surface of the substrate  2320 . The control IC  2360  is a micro controller unit (MCU), has a storage section including a nonvolatile memory or an A/D converter built thereinto, and controls each element of the inertial measurement unit  2000 . The storage section stores a program for defining an order and contents for measuring acceleration and angular velocity, a program for digitalizing measured data to be incorporated into packet data, accompanying data, and the like. A plurality of other electronic components are mounted on the substrate  2320 . 
     As mentioned above, the inertial measurement unit  2000  has been described. As described above, the inertial measurement unit  2000  includes angular velocity sensors  2340   z ,  2340   x , and  2340   y , and the acceleration sensor  2350  as physical quantity sensors, and the control IC  2360  (control circuit) controlling driving of the sensors  2340   z ,  2340   x ,  2340   y , and  2350 . 
     Consequently, it is possible to achieve the effect of the physical quantity sensor of the present disclosure, and thus to provide the inertial measurement unit  2000  with high reliability. 
     Sixth Embodiment 
     Next, a description will be made of a vehicle positioning apparatus according to a sixth embodiment of the present disclosure. 
       FIG.  29    is a block diagram illustrating the entire system of a vehicle positioning apparatus according to a sixth embodiment of the present disclosure.  FIG.  30    is a diagram illustrating an operation of the vehicle positioning apparatus illustrated in  FIG.  29   . 
     A vehicle positioning apparatus  3000  illustrated in  FIG.  29    is an apparatus which is mounted on a vehicle and is used to perform positioning of the vehicle. A vehicle is not particularly limited, and may be any of a bicycle, an automobile (including a four-wheeled vehicle and a motorcycle), an electric train, an airplane, and a ship, and, in the present embodiment, a four-wheeled vehicle will be described. The vehicle positioning apparatus  3000  includes an inertial measurement unit (IMU)  3100 , a calculation processing section (calculation processor)  3200 , a GPS reception section  3300 , a reception antenna  3400 , a position information acquisition section  3500 , a position combination section  3600 , a processing section (processor)  3700 , a communication section  3800 , and a display section  3900 . The inertial measurement unit  2000  may be used as the inertial measurement unit  3100 . 
     The inertial measurement unit  3100  includes a three-axis acceleration sensor  3110  and a three-axis angular velocity sensor  3120 . The calculation processing section  3200  receives acceleration data from the acceleration sensor  3110  and receives angular velocity data from the angular velocity sensor  3120 , performs inertial navigation calculation process on the data, and outputs inertial navigation positioning data (data including acceleration and an attitude of the vehicle). 
     The GPS reception section  3300  receives a signal (a GPS carrier wave; a satellite signal on which position information is superimposed) from a GPS satellite via the reception antenna  3400 . The position information acquisition section  3500  outputs GPS positioning data indicating a position (latitude, longitude, and altitude), velocity, and an azimuth of the vehicle positioning apparatus  3000  (vehicle) based on the signal received by the GPS reception section  3300 . 
     The GPS positioning data includes status data indicating a reception state, a reception time, and the like. 
     The position combination section  3600  calculates a position of the vehicle, specifically, a position where the vehicle is traveling on the ground based on the inertial navigation positioning data output from the calculation processing section  3200  and the GPS positioning data output from the position information acquisition section  3500 . For example, in a case where positions of the vehicle included in the GPS positioning data are the same as each other, but attitudes of the vehicle are different from each other due to the influence of an inclination of the ground, the vehicle travels at different positions on the ground, as illustrated in  FIG.  30   . Thus, an accurate position of the vehicle cannot be calculated by using only the GPS positioning data. Therefore, the position combination section  3600  calculates a position where the vehicle travels on the ground by using the inertial navigation positioning data (particularly, data regarding an attitude of the vehicle). The determination can be relatively easily performed through calculation using a trigonometric function (an inclination θ for a vertical direction). 
     Position data output from the position combination section  3600  is subjected to a predetermined process in the processing section  3700 , and is displayed on the display section  3900  as a positioning result. The position data may be transmitted to an external apparatus via the communication section  3800 . 
     As mentioned above, the vehicle positioning apparatus  3000  has been described. As described above, the vehicle positioning apparatus  3000  includes the inertial measurement unit  3100 , the GPS reception section  3300  (reception section) which receives a satellite signal on which position information is superimposed from a positioning satellite, the position information acquisition section  3500  (acquisition section) which acquires position information of the GPS reception section  3300  based on the received satellite signal, the calculation processing section  3200  (operating section) which calculates an attitude of a vehicle based on inertial navigation positioning data (inertial data) output from the inertial measurement unit  3100 , and the position combination section  3600  (calculation section) which calculates a position of the vehicle by correcting the position information based on the calculated attitude. Consequently, it is possible to achieve the effect of the inertial measurement unit  2000  and thus to provide the vehicle positioning apparatus  3000  with high reliability. 
     Seventh Embodiment 
     Next, a description will be made an electronic apparatus according to a seventh embodiment of the present disclosure. 
       FIG.  31    is a perspective view illustrating an electronic apparatus according to a seventh embodiment of the present disclosure. 
     A laptop type personal computer  1100  illustrated in  FIG.  31    is an apparatus to which an electronic apparatus of the present embodiment is applied. The personal computer  1100  is configured with a main body section  1104  including a keyboard  1102  and a display unit  1106  including a display section  1108 , and the display unit  1106  is rotatably supported with respect to the main body section  1104  via a hinge structure section. The personal computer  1100  includes the physical quantity sensor  1 , and a control circuit  1110  (control section (controller)) which performs control based on a measurement signal output from the physical quantity sensor  1 . 
     Such a personal computer  1100  (electronic apparatus) includes the physical quantity sensor  1 , and the control circuit  1110  (control section) which performs control based on a measurement signal output from the physical quantity sensor  1 . Thus, it is possible to achieve the effect of the physical quantity sensor  1  and thus to realize high reliability. 
     Eighth Embodiment 
     Next, a description will be made of an electronic apparatus according to an eighth embodiment of the present disclosure. 
       FIG.  32    is a perspective view illustrating an electronic apparatus according to an eighth embodiment of the present disclosure. 
     A mobile phone  1200  (including a PHS) illustrated in  FIG.  32    is a phone to which an electronic apparatus of the present embodiment is applied. The mobile phone  1200  includes an antenna (not illustrated), a plurality of operation buttons  1202 , an earpiece  1204 , and a mouthpiece  1206 , and a display section  1208  is disposed between the operation buttons  1202  and the earpiece  1204 . The mobile phone  1200  includes the physical quantity sensor  1 , and a control circuit  1210  (control section (controller)) which performs control based on a measurement signal output from the physical quantity sensor  1 . 
     Such a mobile phone  1200  (electronic apparatus) includes the physical quantity sensor  1 , and the control circuit  1210  (control section) which performs control based on a measurement signal output from the physical quantity sensor  1 . Thus, it is possible to achieve the effect of the physical quantity sensor  1  and thus to realize high reliability. 
     Ninth Embodiment 
     Next, a description will be made of an electronic apparatus according to a ninth embodiment of the present disclosure. 
       FIG.  33    is a perspective view illustrating an electronic apparatus according to a ninth embodiment of the present disclosure. 
     A digital still camera  1300  illustrated in  FIG.  33    is a phone to which an electronic apparatus of the present embodiment is applied. The digital still camera  1300  includes a case  1302 , and a display section  1310  is provided on a rear surface of the case  1302 . The display section  1310  performs display based on an imaging signal generated by a CCD, and functions as a view finder which displays a subject as an electronic image. A light reception unit  1304  which includes an optical lens (imaging optical system), a CCD, and the like is provided on a front surface side (the rear surface side in  FIG.  33   ) of the case  1302 . When a photographer confirms a subject image displayed on the display section  1310  and presses a shutter button  1306 , an imaging signal of the CCD at this point is transmitted to and stored in a memory  1308 . The digital still camera  1300  includes the physical quantity sensor  1 , and a control circuit  1320  (control section (controller)) which performs control based on a measurement signal output from the physical quantity sensor  1 . The physical quantity sensor  1  is used for, for example, camera shaking correction. 
     The digital still camera  1300  (electronic apparatus) includes the physical quantity sensor  1 , and a control circuit  1320  (control section (controller)) which performs control based on a measurement signal output from the physical quantity sensor  1 . Thus, it is possible to achieve the effect of the physical quantity sensor  1  and thus to realize high reliability. 
     The electronic apparatus according to the present disclosure is applicable not only to the personal computer and the mobile phone of the above-described embodiments and the digital still camera of the present embodiment but also to, for example, a smart phone, a tablet terminal, a watch (including a smart watch), an ink jet type ejection apparatus (for example, an ink jet printer), a laptop type personal computer, a television set, a wearable terminal such as a head mounted display (HMD), a video camera, a video tape recorder, a car navigation apparatus, a pager, an electronic organizer (including a communication function), an electronic dictionary, an electronic calculator, an electronic gaming machine, a word processor, a workstation, a videophone, a security television monitor, electronic binoculars, a POS terminal, a medical apparatus (for example, an electronic thermometer, a sphygmomanometer, a blood glucose monitoring system, an electrocardiographic apparatus, an ultrasonic diagnostic apparatus, or an electronic endoscope), a fish-finder, various measurement apparatuses, an apparatus for mobile terminal base station, meters and gauges (for example, meters and gauges of vehicles, aircrafts, and ships), a flight simulator, and a network server. 
     Tenth Embodiment 
     Next, a description will be made of a portable electronic apparatus according to a tenth embodiment of the present disclosure. 
       FIG.  34    is a plan view illustrating a portable electronic apparatus according to a tenth embodiment of the present disclosure.  FIG.  35    is a functional block diagram illustrating a schematic configuration of the portable electronic apparatus illustrated in  FIG.  34   . 
     A wristwatch type activity meter  1400  (activity tracker) illustrated in  FIG.  34    is a wrist apparatus to which a portable electronic apparatus of the present embodiment is applied. The activity meter  1400  is mounted on a part (subject) such as a user&#39;s wrist via a band  1401 . The activity meter  1400  is provided with a display section  1402  performing digital display, and can perform wireless communication. A physical quantity sensor according to the present embodiment of the present disclosure is incorporated into the activity meter  1400  as an acceleration sensor  1408  measuring acceleration or an angular velocity sensor  1409  measuring angular velocity. 
     The activity meter  1400  includes a case  1403  in which the acceleration sensor  1408  and the angular velocity sensor  1409  are accommodated, a processing section (processor)  1410  which is accommodated in the case  1403  and processes data output from the acceleration sensor  1408  and the angular velocity sensor  1409 , the display section  1402  which is accommodated in the case  1403 , and a light transmissive cover  1404  which closes an opening of the case  1403 . A bezel  1405  is provided outside the light transmissive cover  1404 . A plurality of operation buttons  1406  and  1407  are provided on a side surface of the case  1403 . 
     As illustrated in  FIG.  35   , the acceleration sensor  1408  measures respective accelerations in three axial directions which intersect (ideally, orthogonal to) each other, and outputs signals (acceleration signal) corresponding to magnitudes and directions of the measured three-axis accelerations. The angular velocity sensor  1409  measures respective angular velocities in three axial directions which intersect (ideally, orthogonal to) each other, and outputs signals (angular velocity signals) corresponding to magnitudes and directions of the measured three-axis angular velocities. 
     A liquid crystal display (LCD) configuring the display section  1402  displays, according to various measurement modes, for example, position information using a GPS sensor  1411  or a geomagnetic sensor  1412 , motion information such as a movement amount or a motion amount using the acceleration sensor  1408  or the angular velocity sensor  1409 , biological information such as a pulse rate using a pulse sensor  1413 , or time information such as the current time. An environment temperature using a temperature sensor  1414  may be displayed. 
     A communication section  1415  performs various pieces of control for establishing communication between a user terminal and an information terminal (not illustrated). The communication section  1415  is configured to include a transceiver conforming to a short-range radio communication standard such as Bluetooth (registered trademark) (including Bluetooth Low Energy (BTLE)), Wireless Fidelity (Wi-Fi) (registered trademark), Zigbee (registered trademark), near field communication (NFC), or ANT+ (registered trademark), and a connector conforming to a communication bus standard such as Universal Serial Bus (USB). 
     The processing section (processor)  1410  is configured with, for example, a micro processing unit (MPU), a digital signal processor (DSP), or an application specific integrated circuit (ASIC). The processing section  1410  performs various processes based on a program stored in a storage section  1416  and a signal which is input from an operation section  1417  (for example, the operation buttons  1406  and  1407 ). The processes in the processing section  1410  include, for example, a data process on an output signal from each of the GPS sensor  1411 , the geomagnetic sensor  1412 , a pressure sensor  1418 , the acceleration sensor  1408 , the angular velocity sensor  1409 , the pulse sensor  1413 , the temperature sensor  1414 , and a clocking section  1419 , a display process of displaying an image on the display section  1402 , a sound output process of outputting sounds from a sound output section  1420 , a communication process of performing communication with an information terminal via the communication section  1415 , and a power control process of supplies power to each section from a battery  1421 . 
     The activity meter  1400  may have at least the following functions. 
     1. Distance: A total distance is measured from measurement starting by using a highly accurate GPS function. 
     2. Pace: The current traveling pace is displayed through pace distance measurement. 
     3. Average speed: An average speed is calculated from average speed traveling starting to the current time, and is displayed. 
     4. Elevation: Elevation is measured and displayed by using the GPS function. 
     5. Stride: Strides are measured even in a tunnel or the like which GPS electric waves do not reach, and are displayed. 
     6. Pitch: The number of steps per minute is measured and displayed. 
     7. Pulse rate: A pulse rate is measured by using the pulse sensor, and is displayed. 
     8. Gradient: A gradient of the ground is measured and displayed in training or trailing in a mountainous region. 
     9. Auto lap: Lap measurement is automatically performed in a case where a user runs a predetermined distance or a predetermined time set in advance. 
     10. Motion calorie consumption: Calorie consumption is displayed. 
     11. Number of steps: A sum of the number of steps from motion starting is displayed. 
     The activity meter  1400  (portable electronic apparatus) includes the physical quantity sensor  1 , the case  1403  in which the physical quantity sensor  1  is accommodated, the processing section  1410  which is accommodated in the case  1403  and processes data output from the physical quantity sensor  1 , the display section  1402  which is accommodated in the case  1403 , and the light transmissive cover  1404  which closes the opening of the case  1403 . Thus, it is possible to achieve the effect of the physical quantity sensor  1  and thus to realize high reliability. 
     As described above, the activity meter  1400  includes the GPS sensor  1411  (satellite positioning system), and can thus measure a movement distance or a movement trajectory of a user. Thus, it is possible to provide the highly convenient activity meter  1400 . 
     The activity meter  1400  may be widely applied to a running watch, a runner&#39;s watch, a multi-sports compatible runner&#39;s watch such as duathlon and triathlon, an outdoor watch, and a satellite positioning system, for example, a GPS watch with a GPS. 
     In the above description, a global positioning system (GPS) has been described as a satellite positioning system, but other global navigation satellite systems (GNSS) may be used. For example, one, or two or more satellite positioning systems such as a European geostationary-satellite navigation overlay service (EGNOS), a quasi zenith satellite system (QZSS), a global navigation satellite system (GLONASS), GALILEO, and a Beidou navigation satellite system (BeiDou) may be used. As at least one of the satellite positioning systems, a satellite-based augmentation system (SBAS) such as a wide area augmentation system (WAAS) or a European geostationary-satellite navigation overlay service (EGNOS) may be used. 
     Eleventh Embodiment 
     Next, a description will be made of a vehicle according to an eleventh embodiment of the present disclosure. 
       FIG.  36    is a perspective view illustrating a vehicle according to an eleventh embodiment of the present disclosure. 
     An automobile  1500  illustrated in  FIG.  36    is an automobile to which a vehicle according to the present disclosure is applied. In  FIG.  36   , the automobile  1500  includes at least one system  1510  among an engine system, a brake system, and a keyless entry system. The physical quantity sensor  1  is built into the automobile  1500 , and a posture of a car body  1501  can be detected by using the physical quantity sensor  1 . A measurement signal in the physical quantity sensor  1  is supplied to a control device  1502 . The control device  1502  may control the system  1510  based on the signal. 
     Such an automobile  1500  (vehicle) includes the physical quantity sensor  1 , and the control device  1502  (control section (controller)) which performs control based on a measurement signal output from the physical quantity sensor  1 . Thus, it is possible to achieve the effect of the physical quantity sensor  1  and thus to realize high reliability. The automobile  1500  includes at least one system  1510  among an engine system, a brake system, and a keyless entry system, and the control device  1502  controls the system  1510  based on a measurement signal. Consequently, it is possible to control the system  1510  with high accuracy. 
     The physical quantity sensor  1  is widely applicable to electronic control units (ECUs) such as a car navigation system, a car air conditioner, an antilock brake system (ABS), an air bag, a tire pressure monitoring system (TPMS), engine control, and a battery monitor of a hybrid car or an electric car. 
     A vehicle is not limited to the automobile  1500 , and is applicable to, for example, an airplane, a rocket, an artificial satellite, a ship, an automated guided vehicle (AGV), a bipedal robot, and an unmanned aircraft such as a drone. 
     As mentioned above, although the physical quantity sensor, the physical quantity sensor device, the composite sensor device, the inertial measurement unit, the vehicle positioning apparatus, the portable electronic apparatus, the electronic apparatus, and the vehicle according to the embodiments have been described in detail, the present disclosure is not limited thereto, and a configuration of each part may be replaced with any configuration having the same function. Any other configuration may be added to the present disclosure. The above-described embodiments may be combined with each other as appropriate. 
     In the embodiments, a description has been made of a configuration in which the physical quantity sensor measures an acceleration, but a physical quantity measured by the physical quantity sensor is not particularly limited, and may be, for example, an angular velocity or pressure.