Patent Publication Number: US-2010126270-A1

Title: Inertia force sensor

Description:
TECHNICAL FIELD 
     The present invention relates to an inertial force sensor used in various electronic devices for attitude control or navigation of mobile objects, such as aircrafts, automobiles, robots, marine vehicles, or vehicles. 
     BACKGROUND ART 
       FIG. 30  is a plan view of sensor element  151  of a conventional acceleration sensor disclosed in Patent Document 1.  FIGS. 31 and 32  are sectional views of sensor element  151  on line  31 - 31  and line  32 - 32 , respectively. 
     The conventional acceleration sensor includes sensor element  151  for detecting acceleration, and a processor for processing an acceleration output from sensor element  151  to detect the acceleration. Sensor element  151  includes supporter  154  and mounters  159 . Supporter  154  supports weights  152 . Mounters  159  are connected to supporter  154  via flexible portions  156 , and allow sensor element  151  to be mounted on a mounting board. 
     Flexible portions  156  have an arm shape and arranged in cross about supporter  154 . Flexible portions  156  and supporter  154  are arranged in a single straight line. 
     Flexible portions  156  include strain-sensitive resistors  158 . The resistances of strain-sensitive resistors  158  change according to the deformation of flexible portions  156  bent with the motion of weights  152 . The changes are output as an acceleration signal. 
     Then, an operation of the conventional acceleration sensor will be described.  FIG. 33  is a sectional view of sensor element  151  on line  32 - 32  shown in  FIG. 30  receiving an acceleration. 
     An X-axis, a Y-axis, and a Z-axis perpendicular to each other are defined as shown in  FIGS. 30 ,  32 , and  33 . Four flexible portions  156  are arranged along the X-axis and the Y-axis about supporter  154 . When an acceleration, for example, along the X-axis is applied, weights  152  receive forces in the direction of the acceleration. As a result, one of two flexible portions  156  arranged along the X-axis is bent in a positive direction of the Z-axis, and the other flexible portions  156  are bent in a negative direction of the Z-axis. Thus, flexible portions  156  are bent such that weights  152  rotate about center axis  154 A of supporter  154  parallel to the Y-axis. Two strain-sensitive resistors  158  on two flexible portions  156  are also bent in the positive and negative directions of the Z-axis according to the bending of flexible portions  156 , thereby changing the resistances of strain-sensitive resistors  158 . Strain-sensitive resistors  158  of sensor element  151  output the changes of the resistances as the acceleration signal. The processor detects the acceleration based on the signal. 
     This acceleration sensor is arranged such that the X-axis and the Y-axis match with directions of an acceleration to be detected so as to be installed in an attitude control device or a navigation device in mobile objects, such as vehicles. 
     In acceleration sensor  151 , since flexible portions  156  having the arm shape are arranged in cross about supporter  154 , the motion of weights  152  is restricted by flexible portions  156  arranged in the direction of the acceleration. When an acceleration occurs in the X-axis shown in  FIG. 33 , weights  152  is displaced along the X-axis, but the motion of weights  152  is restricted by flexible portions  156  arranged along the X-axis. This causes weights  152  to rotate about supporter  154  (center axis  154 A) with respect to the Y-axis so as to bend flexible portions  156 . The bending, however, is small since the force applied in a linear direction to weights  152  is converted into a force in a rotational direction. As a result, strain-sensitive resistors  158  of flexible portions  156  have small changes in resistances, and provide low detection sensitivity. 
       FIG. 34  is a sectional view of another conventional acceleration sensor  502  disclosed in Patent Document 2. Acceleration sensor  502  includes case  440  having a cylindrical shape, weight  441  having a circular column shape placed in case  440 , and four pairs of electrodes  442  facing each other provided on weight  441  and in case  440 . Case  440  has a bottom surface having recess  443  therein. Boss  444  of weight  441  is inserted in recess  443  to support weight  441 . 
       FIG. 35  is a plan view of electrodes  442 . Electrodes  442  are arranged on respective surfaces of weight  441  and case  440  facing each other. 
     An operation of acceleration sensor  502  will be described below. When weight  441  is displaced due to an acceleration, a gap between electrodes  442  changes, and accordingly, changes the capacitance between electrodes  442 . The acceleration is detected based on the change of the capacitance. Acceleration sensor  502  is placed such that electrodes  442  face each other in a direction perpendicular to the direction of the acceleration to be detected so as to be installed in an attitude control device or a navigation device in mobile objects, such as vehicles. 
     In acceleration sensor  502 , a capacitance is also produced between electrodes  442  adjacent to the surface of case  440  or the surface of weight  441 . This capacitance generates noise which causes detection error of acceleration, and hence decreases the detection accuracy. 
     Patent Document 1: JP10-48243A 
     Patent Document 2: JP2002-55117A 
     SUMMARY OF THE INVENTION 
     An inertial force sensor includes a weight, a first fixing portion linked to the weight, a second fixing portion linked to the weight via the first fixing portion, a first electrode on a first surface of the weight, a second electrode facing the first electrode, and first and second elastic portions elastically deforming so as to displace the weight. The first elastic portion displaces the weight along an X-axis but not along any of a Y-axis and a Z-axis. The second elastic portion displaces the first fixing portion along the Y-axis but not along any of the X-axis and the Z-axis. 
     This inertial force sensor detects an acceleration at high sensitivity. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an exploded perspective view of a sensor element of an inertial force sensor according to Exemplary Embodiment  1  of the present invention. 
         FIG. 2  is a sectional view of the inertial force sensor on line  2 - 2  shown in  FIG. 1 . 
         FIG. 3  is a sectional view of the inertial force sensor on line  3 - 3  shown in  FIG. 1 . 
         FIG. 4  is a perspective view of the inertial force sensor according to Embodiment 1. 
         FIG. 5  is a sectional view of the inertial force sensor according to Embodiment 1. 
         FIG. 6  is a sectional view of the inertial force sensor according to Embodiment 1. 
         FIG. 7  is a sectional view of the inertial force sensor according to Embodiment 1. 
         FIG. 8  is a sectional view of the inertial force sensor according to Embodiment 1. 
         FIG. 9A  is an exploded perspective view of an inertial force sensor according to Exemplary Embodiment 2 of the invention. 
         FIG. 9B  is a perspective view of a sensor element of the inertial force sensor according to Embodiment 2. 
         FIG. 10  is a sectional view of the inertial force sensor on line  10 - 10  shown in  FIG. 9A . 
         FIG. 11  is a sectional view of the inertial force sensor on line  11 - 11  shown in  FIG. 9A . 
         FIG. 12  is a sectional view of the inertial force sensor according to Embodiment 2. 
         FIG. 13  is a sectional view of the inertial force sensor according to Embodiment 2. 
         FIG. 14  is a sectional view of the inertial force sensor according to Embodiment 2. 
         FIG. 15  is a sectional view of the inertial force sensor according to Embodiment 2. 
         FIG. 16A  is an exploded perspective view of an inertial force sensor according to exemplary Embodiment 3 of the invention. 
         FIG. 16B  is a perspective view of a sensor element of the inertial force sensor according to Embodiment 3. 
         FIG. 17  is a sectional view of the inertial force sensor on line  17 - 17  shown in  FIG. 16A . 
         FIG. 18  is a sectional view of the inertial force sensor on line  18 - 18  shown in  FIG. 16A . 
         FIG. 19  is a plan view of the inertial force sensor according to Embodiment 3. 
         FIG. 20  is a plan view of the inertial force sensor according to Embodiment 3. 
         FIG. 21  is a sectional view of the inertial force sensor according to Embodiment 3. 
         FIG. 22  is a sectional view of the inertial force sensor according to Embodiment 3. 
         FIG. 23  is a sectional view of the inertial force sensor according to Embodiment 3. 
         FIG. 24  is a sectional view of the inertial force sensor according to Embodiment 3. 
         FIG. 25  is an exploded perspective view of an inertial force sensor according to Exemplary Embodiment 4 of the invention. 
         FIG. 26  is a sectional view of the inertial force sensor according to Embodiment 4. 
         FIG. 27  is a sectional view of the inertial force sensor according to Embodiment 4. 
         FIG. 28  is a plan view of the inertial force sensor according to Embodiment 4. 
         FIG. 29  is a plan view of the inertial force sensor according to Embodiment 4. 
         FIG. 30  is a plan view of a conventional acceleration sensor. 
         FIG. 31  is a sectional view of the acceleration sensor on lines  31 - 31  shown in  FIG. 30 . 
         FIG. 32  is a sectional view of the acceleration sensor pm line  32 - 32  shown in  FIG. 30 . 
         FIG. 33  is a sectional view of the acceleration sensor shown in  FIG. 30 . 
         FIG. 34  is a plan view of another conventional acceleration sensor. 
         FIG. 35  is a plan view of electrodes of the acceleration sensor shown in  FIG. 34 . 
     
    
    
     REFERENCE NUMERALS 
     
         
           103 A Weight (First Weight) 
           103 B Weight (Second Weight) 
           103 C Weight (Third Weight) 
           103 D Weight 
           104  Fixing Portion (First Fixing Portion) 
           105  Substrate (First Substrate) 
           106  Fixing Portion (Second Fixing Portion) 
           109  Elastic Portion (First Elastic Portion) 
           110 A Arm 
           110 B Arm 
           110 C Arm 
           110 D Arm 
           111  Elastic Portion (Second Elastic Portion) 
           113 A Slit 
           113 B Slit 
           114  Opposed Electrode Unit (First Opposed Electrode Unit) 
           114 A Electrode (First Electrode) 
           114 B Electrode (Second Electrode) 
           116  Opposed Electrode Unit (Second Opposed Electrode Unit) 
           116 A Electrode (Third Electrode) 
           116 B Electrode (Fourth Electrode) 
           118  Opposed Electrode Unit (Second Opposed Electrode Unit) 
           118 A Electrode (Third Electrode) 
           118 B Electrode (Fourth Electrode) 
           203 A Weight (First Weight) 
           203 B Weight (Second Weight) 
           204  Fixing Portion (First Fixing Portion) 
           205  Substrate (First Substrate) 
           206  Fixing Portion (Second Fixing Portion) 
           209  Elastic Portion (First Elastic Portion) 
           210 A Arm 
           210 B Arm 
           210 C Arm 
           210 D Arm 
           211  Elastic Portion (Second Elastic Portion) 
           214  Opposed Electrode Unit (First Opposed Electrode Unit) 
           214 A Electrode (First Electrode) 
           214 B Electrode (Second Electrode) 
           215  Substrate (Second Substrate) 
           216  Opposed Electrode Unit (Second Opposed Electrode Unit) 
           216 A Electrode (Third Electrode) 
           216 B Electrode (Fourth Electrode) 
           217  Opposed Electrode Unit (Second Opposed Electrode Unit) 
           217 A Electrode (Third Electrode) 
           217 B Electrode (Fourth Electrode) 
           218  Opposed Electrode Unit (Third Opposed Electrode Unit, Fifth Opposed Electrode Unit) 
           218 A Electrode (Fifth Electrode, Ninth Electrode) 
           218 B Electrode (Sixth Electrode, Tenth Electrode) 
           219  Opposed Electrode Unit (Fourth Opposed Electrode Unit) 
           219 A Electrode (Seventh Electrode) 
           219 B Electrode (Eighth Electrode) 
           221  Opposed Electrode Unit (Sixth Opposed Electrode Unit) 
           221 A Electrode (Eleventh Electrode) 
           221 B Electrode (Twelfth Electrode) 
           213 A Slit 
           213 B Slit 
           303 A Weight (First Weight) 
           303 B Weight (Second Weight) 
           303 C Weight (Third Weight) 
           303 D Weight 
           304  Fixing Portion (First Fixing Portion) 
           306  Fixing Portion (Second Fixing Portion) 
           305  Substrate (First Substrate) 
           310 A Arm 
           310 B Arm 
           310 C Arm 
           310 D Arm 
           314 A Electrode (First Electrode) 
           314 B Electrode (Second Electrode) 
           314 C Electrode (Second Electrode) 
           314 X Opposed Electrode Unit (First Opposed Electrode Unit) 
           314 Y Opposed Electrode Unit (First Opposed Electrode Unit) 
           315  Substrate (Second Substrate) 
           316 A Electrode (Third Electrode) 
           316 B Electrode (Fourth Electrode) 
           316 C Electrode 
           316 X Opposed Electrode Unit (Second Opposed Electrode Unit) 
           316 Y Opposed Electrode Unit 
           317 A Electrode (Third Electrode) 
           317 B Electrode (Fourth Electrode) 
           317 C Electrode 
           317 X Opposed Electrode Unit (Second Opposed Electrode Unit) 
           317 Y Opposed Electrode Unit 
           318 A Electrode (Fifth Electrode) 
           318 B Electrode 
           318 C Electrode (Sixth Electrode) 
           318 X Opposed Electrode Unit 
           318 Y Opposed Electrode Unit (Third Opposed Electrode Unit) 
           319 A Electrode (Seventh Electrode) 
           319 B Electrode (Eighth Electrode) 
           319 C Electrode 
           319 X Opposed Electrode Unit (Fourth Opposed Electrode Unit) 
           319 Y Opposed Electrode Unit 
           321 A Electrode (Eleventh Electrode) 
           321 B Electrode 
           321 C Electrode (Twelfth Electrode) 
           321 X Opposed Electrode Unit 
           321 Y Opposed Electrode Unit (Sixth Opposed Electrode Unit) 
           309  Elastic Portion (First Elastic Portion) 
           311  Elastic Portion (Second Elastic Portion) 
           313 A Slit 
           313 B Slit 
           430  Grounding Electrode (First Grounding Electrode) 
           440  Grounding Electrode (Second Grounding Electrode) 
           1001  Inertial Force Sensor 
           1001 A Object 
           1002  Inertial Force Sensor 
           1002 A Object 
           1003  Inertial Force Sensor 
           1003 A Object 
           1004  Inertial Force Sensor 
         X X-Axis (Second Axis) 
         Y Y-Axis (Third Axis) 
         Z Z-Axis (First Axis) 
       
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     Exemplary Embodiment 1 
       FIG. 1  is an exploded perspective view of sensor element  101  of inertial force sensor  1001  according to Exemplary Embodiment 1 of the present invention.  FIGS. 2 and 3  are sectional views of sensor element  101  on line  2 - 2  and line  3 - 3  shown in  FIG. 1 , respectively. Inertial force sensor  1001  can detect an acceleration and an angular velocity. 
     A Z-axis, an X-axis, and a Y-axis, a first axis, a second axis, and a third axis, perpendicular to each other are defined as shown in  FIG. 1 . Two arms  108  extend from supporter  112  along the X-axis and are connected to fixing portion  104  having a frame shape. Supporter  112  is joined to fixing portion  104  via arms  108 . Arms  108  extend perpendicularly to fixing portion  104 . Four arms  110 A to  110 D extend from supporter  112  along the Y-axis and are connected to four weights  103 A to  103 D, respectively. Arms  108  and  110 A to  110 D are flexible and constitute a flexible portion together with supporter  112 . The flexible portion is connected to fixing portion  104 . Weights  103 A to  103 D are linked to fixing portion  104  via the flexible portion. Arms  108  are much thinner and hence more flexible than arms  110 A to  110 D. Weights  103 A to  103 D have surfaces  1103 A to  1103 D facing substrate  105 . 
     Electrodes  114 A,  116 A,  118 A, and  120 A are provided on surfaces  1103 A,  1103 B,  1103 C, and  1103 D of weights  103 A,  103 B,  103 C and  103 D, respectively. Substrate  105  is attached to fixing portion  104 . Substrate  105  has surface  105 A facing weights  103 A to  103 D along the Z-axis. Electrodes  114 B,  116 B,  118 B, and  120 B provided on surface  105 A of substrate  105  face electrodes  114 A,  116 A,  118 A, and  120 A along the Z-axis, respectively, and are spaced from electrodes  114 A,  116 A,  118 A, and  120 A, respectively. Electrodes  114 A and  114 B providing a capacitance between the electrodes constitute opposed electrode unit  114 . Electrodes  116 A and  116 B providing a capacitance between the electrodes constitute opposed electrode unit  116 . Electrodes  118 A and  118 B providing a capacitance between the electrodes constitute opposed electrode unit  118 . Electrodes  120 A and  120 B providing a capacitance between the electrodes constitute opposed electrode unit  120 . Electrodes  114 A and  116 A are arranged along the X-axis. Electrodes  114 B and  116 B are arranged along the X-axis. Thus, opposed electrode units  114  and  116  are arranged along the X-axis. Electrodes  118 A and  120 A are arranged along the X-axis. Electrodes  118 B and  120 B are arranged along the X-axis. Thus, opposed electrode units  118  and  120  are arranged along the X-axis. Electrodes  114 A and  118 A are arranged along the Y-axis. Electrodes  114 B and  118 B are arranged along the Y-axis. Thus, opposed electrode units  114  and  118  are arranged along the Y-axis. Electrodes  116 A and  120 A are arranged along the Y-axis. Electrodes  116 B and  120 B are arranged along the Y-axis. Thus, opposed electrode units  116  and  120  are arranged along the Y-axis. 
     Arm  110 A extending from supporter  112  includes extension  1110 A extending from supporter  112  along the Y-axis, extension  3110 A extending in parallel with extension  1110 A along the Y-axis, and connecting portion  2110 A connecting between extensions  1110 A and  3110 A, thus having substantially a U-shape. Connecting portion  2110 A extends from extension  1110 A along the X-axis. Extension  3110 A is connected to weight  103 A. Arm  110 B extending from supporter  112  includes extension  1110 B extending from supporter  112  along the Y-axis, extension  3110 B extending in parallel with extension  1110 B along the Y-axis, and connecting portion  2110 B connecting between extensions  1110 B and  3110 B, thus having substantially a U-shape. Connecting portion  2110 B extends from extension  1110 B along the X-axis in a direction opposite to the direction in which connecting portion  2110 A of arm  110 A extends. Extension  3110 B is connected to weight  103 B. Arm  110 C extending from supporter  112  includes extension  1110 C extending from supporter  112  along the Y-axis, extension  3110 C extending in parallel with extension  1110 C along the Y-axis, and connecting portion  2110 C connecting between extensions  1110 C and  3110 C, thus having substantially a U-shape. Connecting portion  2110 C extends from extension  1110 C along the X-axis in a direction identical to the direction in which connecting portion  2110 A of arm  110 A extends. Extension  3110 C is connected to weight  103 C. Arm  110 D extending from supporter  112  includes extension  1110 D extending from supporter  112  along the Y-axis, extension  3110 D extending in parallel with extension  1110 D along the Y-axis, and connecting portion  2110 D connecting between extensions  1110 D and  3110 D, thus having substantially a U-shape. Connecting portion  2110 D extends from extension  1110 D along the X-axis in a direction opposite to the direction in which connecting portion  2110 C of arm  110 C extends. Extension  3110 D is connected to weight  103 D. Extensions  1110 A to  1110 D and  3110 A to  3110 D of arms  110 A to  110 D extend perpendicularly to fixing portions  104  and  106 . 
     Arms  108  and supporter  112  are arranged substantially on a single straight line. Extensions  1110 A and  1110 B of arms  110 A and  110 B extend in the same direction from supporter  112 . Extensions  1110 C and  1110 D of arms  110 C and  110 D extend in the same direction from supporter  112  and in the direction opposite to the direction in which extensions  1110 A and  1110 B of arms  110 A and  110 B extends. 
     Weights  103 A to  103 D are arranged inside the frame shape of fixing portion  104 . Fixing portion  104  is linked to fixing portion  106  via fixing arm  107 , and placed inside fixing portion  106 . Arms  108  and supporter  12  are arranged substantially on the single straight line. Arms  18  are arranged symmetrically to each other with respect to center  101 A of sensor element  101 . Arms  110 A to  110 D are arranged symmetrically to each other with respect to center  101 A of sensor element  101 . Arms  108  and  110 A to  110 D function as a linking unit for linking weights  103 A to  103 D to fixing portion  104 . Fixing arm  107  functions as a linking unit for linking fixing portion  104  to fixing portion  106 . 
     Fixing portion  104  includes elastic portions  109  which elastically deform only along the X-axis, that is, which do not substantially deform along any of the Y-axis and the Z-axis. Fixing arm  107  extends along the Y-axis. Fixing portion  106  includes elastic portions  111  which elastically deform only along the Y-axis, that is, which do not substantially deform along any of the X-axis and the Z-axis. Fixing portion  106  is arranged to be mounted to mounting substrate  1001 A, an object. 
     Elastic portions  109  are implemented by slits  113 A which is provided in fixing portion  104  and which extend along the Y-axis. Elastic portions  111  are implemented by slits  113 B which is provided in fixing portion  106  and which extend along the X-axis. 
     Driving electrode  122  which drives and vibrates weight  103 C is provided on arm  110 C. Detecting electrode  124  which detects the vibration of arm  110 D is provided on arm  110 D. Sensing electrodes  126  and  128 , which sense strain on arms  110 A and  110 B are provided on arms  110 A and  110 B, respectively. Driving electrode  122  includes a lower electrode on arm  110 C, a piezoelectric layer on the lower electrode, and an upper electrode on the piezoelectric layer. Similarly, electrode  124  ( 126 ,  128 ) includes a lower electrode on arm  110 D ( 110 A,  110 B), a piezoelectric layer on the lower electrode, and an upper electrode on the piezoelectric layer. 
     Opposed electrode units  114 ,  116 ,  118 , and  120 , driving electrode  122 , detecting electrode  124 , and sensing electrodes  126  and  128  are connected to fixing portion  106  via signal lines and electrically connected to circuit patterns on mounting substrate  1001 A via, e.g. bonding wires at ends of the signal lines. Opposed electrode units  114 ,  116 ,  118 , and  120 , driving electrode  122 , detecting electrode  124 , and sensing electrodes  126  and  128  are connected to processor  161  via the signal lines and mounting substrate  1001 A. 
     An operation of sensor element  101  of inertial force sensor  1001  to detect an angular velocity will be described below.  FIG. 4  is a perspective view of sensor element  101 . Arm  110 C extending from supporter  112  together with weight  103 C connected to arm  110 C has a natural resonance frequency. When an alternating-current (AC) voltage having the resonance frequency is applied between the upper and lower electrodes of driving electrode  122  from a driving power source, arm  110 C causes weight  103 C to vibrate in direction  1901 C along the X-axis at the resonance frequency. Arms  110 A,  110 B, and  110 D extending from supporter  112 , and weights  103 A,  103 B, and  103 D connected to arms  110 A,  110 B, and  110 D have the same natural resonance frequency as arm  110 C and weight  103 C. Since supporter  112  is linked to fixing portion  104  via flexible arm  8 , when arm  110 C and weight  103 C vibrate at the resonance frequency, the vibration propagates to arms  110 A,  110 B, and  110 D via supporter  112  to vibrate weights  103 A,  103 B, and  103 D at the resonance frequency in directions  1901 A,  1901 B, and  1901 D, respectively, along the X-axis. Detecting electrode  124  feeds back a voltage which changes according to the vibration of arm  110 D to the driving power source. The driving power source determines the amplitude, the frequency, and the phase of the AC voltage applied to driving electrode  122  based on the voltage fed back so that arm  110 D can vibrate by a constant amplitude, thereby vibrating arms  110 A to  110 D by the constant amplitude at the resonance frequency. 
     An operation of sensor element  1  will be described below in which angular velocity  1001 B counterclockwise with respect to the Z-axis, that is, in the direction causing weight  103 A to approach weight  103 C, is applied while weights  103 A to  103 D vibrate in directions  1901 A to  1901 D, respectively, along the X-axis. When weights  103 A to  103 D vibrate, Coriolis force is generated in directions  1902 A to  1902 D which are along the Y-axis and perpendicular to directions  1901 A to  1901 D, respectively, thereby producing arms  110 A to  110 D to have strains. Sensing electrodes  126  and  128  output voltages according to the strains produced in arms  110 A and  110 B. Processor  161  detects angular velocity  1001 B based on the voltages. 
     An operation of inertial force sensor  1001  to detect an acceleration will be described below. 
     First, an operation of inertial force sensor  1001  to detect an acceleration along the X-axis will be described below.  FIG. 5  is a sectional view of sensor element  101  on line  2 - 2  shown in  FIG. 1  when no acceleration is applied along the X-axis. Electrodes  114 A and  114 B have ends  1114 A and  1114 B directed in the same direction along the X-axis. Electrodes  116 A and  116 B have ends  1116 A and  1116 B directed in the same direction along the X-axis. Ends  1114 A and  1114 B face ends  1116 A and  1116 B, respectively. When no acceleration is applied, end  1114 A of electrode  114 A deviates slightly from end  1114 B of electrode  114 B in direction D 101  along the X-axis, and end  1116 A of electrode  116 A deviates slightly from end  1116 B of electrode  116 B in direction D 102  opposite to direction D 101 . Similarly, when no acceleration is applied, ends of electrodes  118 A and  118 B directed in the same direction deviate slightly from each other along the X-axis. Ends of electrodes  120 A and  120 B directed in the same direction deviate slightly from each other in a direction opposite to the direction in which the ends of electrodes  118 A and  118 B deviates along the X-axis. Electrodes  114 A and  114 B have ends  3114 A and  3114 B side opposite to ends  1114 A and  1114 B, respectively, along the X-axis. When no acceleration is applied, end  3114 A of electrode  114 A deviates slightly from end  3114 B of electrode  114 B in direction D 101  along the X-axis. Electrodes  116 A and  116 B have ends  3116 A and  3116 B opposite to ends  3116 A and  3116 B, respectively, along the X-axis. When no acceleration is applied, end  3116 A of electrode  116 A deviates slightly from end  3116 B of electrode  116 B in direction D 102 . 
       FIG. 6  is a sectional view of sensor element  101  on line  2 - 2  shown in  FIG. 1  when an acceleration along the X-axis. When acceleration  1001 C in direction D 101  along the X-axis is applied, a force along the X-axis due to acceleration  1001 C deforms elastic portions  109  along the X-axis but not along any of the Y-axis and the Z-axis while the force is not converted into a rotational force. As a result, ends  1114 A and  1116 A of electrodes  114 A and  116 A are displaced relatively with respect to ends  1114 B and  1116 B of electrodes  114 B and  116 B by large distance W 101  along the X-axis. Similarly, the ends of electrodes  118 A and  120 A are displaced relatively with respect to the ends of electrodes  118 B and  120 B by large distance W 101  along the X-axis. Acceleration  1001 C displaces weights  103 A and  103 B along the X-axis, and changes the capacitances of opposed electrode units  114  and  116  by amounts different from each other. Similarly, the acceleration displaces weights  103 C and  103 D along the X-axis, and changes the capacitances of opposed electrode units  118  and  120  by amounts different from each other. 
     Next, an operation of inertial force sensor  1001  to detect an acceleration along the Y-axis will be described below.  FIG. 7  is a sectional view of sensor element  101  on line  3 - 3  shown in  FIG. 1  when no acceleration is applied along the Y-axis. Electrodes  114 A and  114 B have ends  2114 A and  2114 B directed in the same direction along the Y-axis. Electrodes  118 A and  118 B have ends  2118 A and  2118 B directed in the same direction along the Y-axis. Ends  2114 A and  2114 B face ends  2118 A and  2118 B, respectively. When no acceleration is applied, end  2114 A of electrode  114 A deviates slightly from end  2114 B of electrode  114 B in direction D 103  along the Y-axis. End  2118 A of electrode  118 A deviates slightly from end  2118 B of electrode  118 B along the Y-axis in direction D 104  opposite to direction D 103 . Similarly, when no acceleration is applied, ends of electrodes  116 A and  116 B directed in the same direction deviate slightly from each other along the Y-axis. Ends of electrodes  120 A and  120 B directed in the same direction deviate slightly from each other in a direction opposite to the direction in which the ends of electrodes  116 A and  116 B deviate along the Y-axis. Electrodes  114 A and  114 B have ends  4114 A and  4114 B opposite to ends  2114 A and  2114 B, respectively, along the Y-axis. When no acceleration is applied, end  4114 A of electrode  114 A deviates slightly from end  4114 B of electrode  114 B in direction D 103  along the Y-axis. Electrodes  118 A and  118 B have ends  4118 A and  4118 B opposite to ends  2118 A and  2118 B, respectively, along the Y-axis. When no acceleration is applied, end  4118 A of electrode  118 A deviate slightly from end  4118 B of electrode  118 B in direction D 104 . 
       FIG. 8  is a sectional view of sensor element  101  on line  3 - 3  shown in  FIG. 1  when an acceleration along the Y-axis is applied. When acceleration  1001 D in direction D 103  along the Y-axis is applied, a force along the Y-axis due to acceleration  1001 D deforms elastic portions  111  along the Y-axis but not along any of the Y-axis and the Z-axis while the force is not converted into a rotational force. The force displaces ends  2114 A and  2118 A of electrodes  114 A and  118 A relatively with respect to ends  2114 B and  2118 B of electrodes  114 B and  118 B by large distance W 102  along the Y-axis. Similarly, the force displaces the ends of electrodes  114 A and  120 A relatively with respect to the ends of electrodes  114 B and  120 B by large distance W 102  along the Y-axis. Acceleration  1001 D displaces weights  103 A and  103 C along the Y-axis, and changes the capacitance of opposed electrode units  114  and  118  by amounts different from each other. Similarly, acceleration  1001 D displaces weights  103 B and  103 D along the Y-axis, and the capacitances of opposed electrode units  116  and  120  by amounts different from each other. 
     Thus, the capacitances of opposed electrode units  114 ,  116 ,  118 , and  120  change according to accelerations  1001 C and  1001 D along the X-axis and the Y-axis. Processor  161  can detect accelerations  1001 C and  1001 D based on the changes of the capacitances. 
     Sensor element  101  can detect acceleration  1001 C along the X-axis since elastic portions  109  deform along the X-axis but not along any of the Y-axis and the Z-axis. Sensor element  101  can detect acceleration  1001 D along the Y-axis since elastic portions  111  deform along the Y-axis but not along any of the X-axis and the Z-axis. Thus, sensor element  101  can detect acceleration  1001 C along the X-axis and acceleration  1001 D along the Y-axis at high sensitivity independently without mutual interference. 
     The amount of the change of the capacitance of opposed electrode unit  114  due to acceleration  1001 C is different from the amount of the change of the capacitance of opposed electrode unit  116  due to acceleration  1001 C. Similarly, the amount of the change of the capacitance of opposed electrode unit  118  due to acceleration  1001 C is different from the amount of the change of the capacitance of opposed electrode unit  120  due to acceleration  1001 C. For example, when acceleration  1001 C directed in the negative direction of the X-axis is applied, as shown in  FIG. 6 , opposed electrode units  114  and  118  decrease their capacitances, and opposed electrode units  116  and  120  increase their capacitance. When an acceleration in the positive direction of the X-axis is applied, weights  103 A to  103 D are displaced in the direction opposite to the direction shown in  FIG. 6 . Therefore, opposed electrode units  114  and  118  increase their capacitances, and opposed electrode units  116  and  120  decrease their capacitances. As a result, processor  161  connected to sensor element  101  can determine, based on the capacitances of opposed electrode units  114 ,  116 ,  118 , and  120 , whether weights  103 A to  103 D are displaced in the positive direction or in the negative direction of the X-axis based on the capacitances of opposed electrode units  114 ,  116 ,  118 , and  120 . Similarly, when acceleration  1001 D directed in the negative direction of the Y-axis is applied, as shown in  FIG. 8 , opposed electrode units  114  and  116  decrease their capacitances, and opposed electrode units  118  and  120  increase their capacitances. When an acceleration directed in the positive direction of the Y-axis is applied, weights  103 A to  103 D are displaced in the direction opposite to the direction shown in  FIG. 8 . Therefore, opposed electrode units  114  and  116  increase their capacitances, and opposed electrode units  118  and  120  decrease their capacitances. As a result, processor  161  can determine, based on the capacitances of opposed electrode units  114 ,  116 ,  118 , and  120 , whether weights  103 A to  103 D have been displaced in the positive direction or the negative direction of the Y-axis. 
     Single sensor element  101  can detect both the acceleration and the angular velocity, and allows inertial force sensor  1001  to have a small footprint and a small size. 
     Elastic portions  109  which deform along the X-axis but not along any of the Y-axis and the Z-axis are provided at fixing portion  104  of sensor element  101  of inertial force sensor  1001 . Alternatively, elastic portions  109  may be provided at arms  108  functioning as the linking unit of the inertial force sensor according to Embodiment 1. Elastic portions  111  which deform along the Y-axis but not along any of the X-axis and the Z-axis are provided at fixing portion  106  of sensor element  101 . Alternatively, elastic portions  111  may be provided at fixing arm  107  functioning as the linking unit of the inertial force sensor according to Embodiment 1. 
     Driving electrode  122 , detecting electrode  124 , and sensing electrodes  126  and  128  for detecting the angular velocity may have shapes and positions other than those described above. 
     Electrodes  114 A,  116 A,  118 A, and  120 A are largely displaced in the direction of the acceleration with respect to electrodes  114 B,  116 B,  118 B, and  120 B without causing the force due to the acceleration to be converted into a rotational force. Inertial force sensor  1001  according to Embodiment 1 detects the acceleration at high sensitivity accordingly. 
     Exemplary Embodiment 2 
       FIG. 9A  is an exploded perspective view of sensor element  201  of inertial force sensor  1002  according to Exemplary Embodiment 2 of the present invention.  FIG. 9B  is a perspective view of sensor element  201 .  FIGS. 10 and 11  are sectional views of sensor element  201  on line  10 - 10  and line  11 - 11  shown in  FIG. 9A , respectively. Inertial force sensor  1002  can detect an acceleration and an angular velocity. 
     A Z-axis, the X-axis, and the Y-axis, a first axis, a second axis, and a third axis perpendicular to each other, are defined as shown in  FIGS. 9A and 9B . Two arms  208  extend from supporter  212  along the X-axis and connected to fixing portion  204  having a frame. Supporter  212  is joined to fixing portion  204  via arms  208 . Arms  208  extend perpendicular to fixing portion  204 . Four arms  210 A to  210 D extend from supporter  212  along the Y-axis and are connected to four weights  203 A to  203 D, respectively. Arms  208  and  210 A to  210 D are flexible and constitute a flexible portion together with supporter  212 . The flexible portion is connected to fixing portion  204 . Weights  203 A to  203 D are linked to fixing portion  204  via the flexible portion. Weights  203 A to  203 D have surfaces  1203 A to  1203 D facing substrate  205 , and have surfaces  2203 A to  2203 D which face substrate  215  and which are opposite to surfaces  1203 A to  1203 D, respectively. Arms  208  are much thinner and hence more flexible than arms  210 A to  210 D. 
     Electrodes  214 A,  216 A,  218 A and  220 A are provided on surfaces  1203 A,  1203 B,  1203 C, and  1203 D of weights  203 A,  203 B,  203 C, and  203 D, respectively. Electrodes  217 A,  219 A,  221 A, and  223 A are provided on surfaces  2203 A,  2203 B,  2203 C, and  2203 D of weights  203 A,  203 B,  203 C, and  203 D, respectively. Substrates  205  and  215  are attached to fixing portion  204 . Substrate  205  has surface  205 A facing surfaces  1203 A to  1203 D of weights  203 A to  203 D along the Z-axis. Electrodes  214 B,  216 B,  218 B, and  220 B facing electrodes  214 A,  216 A,  218 A and  220 A along the Z-axis are provided on surface  205 A of substrate  205 , and are spaced from electrodes  214 A,  216 A,  218 A and  220 A, respectively. Electrodes  214 A and  214 B having a capacitance between the electrodes constitute opposed electrode unit  214 . Electrodes  216 A and  216 B having a capacitance between the electrodes constitute opposed electrode unit  216 . Electrodes  218 A and  218 B having a capacitance between the electrodes constitute opposed electrode unit  218 . Electrodes  220 A and  220 B having a capacitance between the electrodes constitute opposed electrode unit  220 . Electrodes  214 A and  216 A are arranged along the X-axis, and electrodes  214 B and  216 B are also arranged along the X-axis. Thus, opposed electrode units  214  and  216  are arranged along the X-axis. Electrodes  218 A and  220 A are arranged along the X-axis, and electrodes  218 B and  220 B are also arranged along the X-axis. Thus, opposed electrode units  218  and  220  are arranged along the X-axis. Electrodes  214 A and  218 A are arranged along the Y-axis, and electrodes  214 B and  218 B are also arranged along the Y-axis. Thus, opposed electrode units  214  and  218  are arranged along the Y-axis. Electrodes  216 A and  220 A are arranged along the Y-axis, and electrodes  216 B and  220 B are also arranged along the Y-axis. Thus, opposed electrode units  216  and  220  are arranged along the Y-axis. Substrate  215  has surface  215 A facing surfaces  2203 A to  2203 D of weights  203 A to  203 D along the Z-axis. Electrodes  217 B,  219 B,  221 B, and  223 B facing electrodes  217 A,  219 A,  221 A, and  223 A along the Z-axis are provided on surface  215 A of substrate  215  electrodes  217 B,  219 B,  221 B, and  223 B, and are spaced from electrodes  217 A,  219 A,  221 A, and  223 A, respectively. Electrodes  217 A and  217 B having a capacitance between the electrodes constitute opposed electrode unit  217 . Electrodes  219 A and  219 B having a capacitance between the electrodes constitute opposed electrode unit  219 . Electrodes  221 A and  221 B having a capacitance between the electrodes constitute opposed electrode unit  221 . Electrodes  223 A and  223 B having a capacitance between the electrodes constitute opposed electrode unit  223 . Electrodes  217 A and  219 A are arranged along the X-axis, and electrodes  217 B and  219 B are also arranged along the X-axis. Thus, opposed electrode units  217  and  219  are arranged along the X-axis. Electrodes  221 A and  223 A are arranged along the X-axis, and electrodes  221 B and  223 B are also arranged along the X-axis. Thus, opposed electrode units  221  and  223  are arranged along the X-axis. Electrodes  217 A and  221 A are arranged along the Y-axis, and electrodes  217 B and  221 B are also arranged along the Y-axis. Thus, opposed electrode units  217  and  221  are arranged along the Y-axis. Electrodes  219 A and  223 A are arranged along the Y-axis, and electrodes  219 B and  223 B are also arranged along the Y-axis. Thus, opposed electrode units  219  and  223  are arranged along the Y-axis. 
     Arm  210 A extending from supporter  212  includes Extension  1210 A extending from supporter  212  along the Y-axis, extension  3210 A extending in parallel with extension  1210 A along the Y-axis, and connecting portion  2210 A connecting between extensions  1210 A and  3210 A, and thus, has substantially a U-shape. Connecting portion  2210 A extends from extension  1210 A along the X-axis. Extension  3210 A is connected to weight  203 A. Arm  210 B extending from supporter  212  includes Extension  1210 B extending from supporter  212  along the Y-axis, extension  3210 B extending in parallel with extension  1210 B along the Y-axis, and connecting portion  2210 B connecting between extensions  1210 B and  3210 B, and thus, has substantially a U-shape. Connecting portion  2210 B extends from extension  1210 B along the X-axis in a direction opposite to connecting portion  2210 A of arm  210 A. Extension  3210 B is connected to weight  203 B. Arm  210 C extending from supporter  212  includes Extension  1210 C extending from supporter  212  along the Y-axis, extension  3210 C extending in parallel with extension  1210 C along the Y-axis, and connecting portion  2210 C connecting between extensions  1210 C and  3210 C, and thus, has substantially a U-shape. Connecting portion  2210 C extends from extension  1210 C along the X-axis in a direction identical to the direction in which connecting portion  2210 A of arm  210 A extends. Extension  3210 C is connected to weight  203 C. Arm  210 D extending from supporter  212  includes Extension  1210 D extending from supporter  212  along the Y-axis, extension  3210 D extending in parallel with extension  1210 D along the Y-axis, and connecting portion  2210 D connecting between extensions  1210 D and  3210 D, and thus, has substantially a U-shape. Connecting portion  2210 D extends from extension  1210 D along the X-axis in a direction opposite to connecting portion  2210 C of arm  210 C. Extension  3210 D is connected to weight  203 D. Extensions  1210 A to  1210 D and  3210 A to  3210 D of arms  210 A to  210 D extend perpendicularly to fixing portions  204  and  206 . 
     Arms  208  and supporter  212  are arranged substantially in a single straight line. Extensions  1210 A and  1210 B of arms  210 A and  210 B extend in the same direction from supporter  212 . Extensions  1210 C and  1210 D of arms  210 C and  210 D extend in the same direction from supporter  212  and in the direction opposite to the direction in which extensions  1210 A and  1210 B of arms  210 A and  210 B extend. 
     Weights  203 A to  203 D are arranged inside the frame shape of fixing portion  204 . Fixing portion  204  is linked to fixing portion  206  via fixing arm  207 , and placed inside fixing portion  206 . Arms  208  and supporter  212  are arranged substantially in a single straight line, and arms  208  are arranged symmetrically to each other with respect to center  201 A of sensor element  201 . Arms  210 A to  210 D are arranged symmetrically to each other with respect to center  201 A of sensor element  201 . Arms  208  and  210 A to  210 D function as a linking unit for linking weights  203 A to  203 D to fixing portion  204 . Fixing arm  207  functions as a linking unit for linking fixing portion  204  to fixing portion  206 . 
     Fixing portion  204  includes elastic portions  209  which elastically deform only along the X-axis, that is, elastic portions  209  do not substantially deform along any of the Y-axis and the Z-axis. Fixing arm  207  extends along the Y-axis. Fixing portion  206  includes elastic portions  211  which elastically deform only along the Y-axis, that is, elastic portions  211  do not substantially deform along any of the X-axis and the Z-axis. Fixing portion  206  is arranged to be mounted to mounting substrate  1002 A, an object. 
     Elastic portions  209  are implemented by slits  213 A which are provided in fixing portion  204  and which extend along the Y-axis. Elastic portions  211  are implemented by slits  213 B which are provided in fixing portion  206  and extend along the X-axis. 
     Driving electrode  222  is provided on arm  210 C and drives and vibrates weight  203 C. Detecting electrode  224  is provided on arm  210 D and detects the vibration of arm  210 D. Sensing electrodes  226  and  228  are provided on arms  210 A and  210 B, and sense the strains of arms  210 A and  210 B, respectively. Driving electrode  222  includes a lower electrode provided on arm  210 C, a piezoelectric layer provided on the lower electrode, and an upper electrode provided on the piezoelectric layer. Similarly, each of detecting electrode  224  and sensing electrodes  226  and  228  include a lower electrode provided on each of arms  210 D,  210 A, and  210 B, respectively, a piezoelectric layer provided on the lower electrode, and an upper electrode provided on the piezoelectric layer. 
     Opposed electrode units  214 ,  216 ,  217 ,  218 ,  219 ,  220 ,  221 , and  223 , driving electrode  222 , detecting electrode  224 , and sensing electrodes  226 ,  228  are connected out to fixing portion  206  via signal lines and electrically connected to circuit patterns on mounting substrate  1002 A with, e.g. bonding wire at ends of the signal lines. Opposed electrode units  214 ,  216 ,  217 ,  218 ,  219 ,  220 ,  221 , and  223 , driving electrode  222 , detecting electrode  224 , and sensing electrodes  226 ,  228  are connected to processor  261  via the signal lines and mounting substrate  1002 A. 
     Inertial force sensor  1002  including driving electrode  222 , detecting electrode  224 , and sensing electrodes  226 ,  228  can detect the angular velocity about the Z-axis similarly to inertial force sensor  1001  including driving electrode  122 , detecting electrode  124 , and sensing electrodes  126 ,  128  according to Embodiment 1 shown in  FIG. 4 . 
     An operation of inertial force sensor  1002  to detect an acceleration will be described. 
     First, an operation of inertial force sensor  1002  to detect an acceleration along the X-axis will be described below.  FIG. 12  is a sectional view of sensor element  201  on line  10 - 10  shown in  FIG. 9A  when no acceleration along the X-axis is applied. Electrodes  214 A and  214 B have ends  1214 A and  1214 B directed in the same direction along the X-axis. Electrodes  216 A and  216 B have ends  1216 A and  1216 B directed in the same direction along the X-axis and facing ends  1214 A and  1214 B, respectively. When no acceleration is applied, end  1214 A of electrode  214 A deviates slightly from end  1214 B of electrode  214 B in direction D 201  along the X-axis, and end  1216 A of electrode  216 A deviates slightly from end  1216 B of electrode  216 B in direction D 202  opposite to direction D 201 . Similarly, when no acceleration is applied, ends of electrodes  218 A and  218 B directed in the same direction deviate slightly from each other along the X-axis, and ends of electrodes  220 A and  220 B directed in the same direction deviate slightly from each other in a direction opposite to the direction in which the ends of electrodes  218 A and  218 B deviate along the X-axis. Electrodes  217 A and  217 B have ends  1217 A and  1217 B directed in the same direction, and electrodes  219 A and  219 B have ends  1219 A and  1219 B directed in the same direction and facing ends  1217 A and  1217 B, respectively. When no acceleration is applied, end  1217 A of electrode  217 A deviates slightly from end  1217 B of electrode  217 B in direction D 201 , and end  1219 A of electrode  219 A deviates slightly in direction D 202 . Similarly, when no acceleration is applied, ends of electrodes  221 A and  221 B directed in the same direction deviate slightly from each other along the X-axis, and ends of electrodes  223 A and  223 B directed in the same direction deviate slightly from each other in a direction opposite to the direction in which the ends of electrodes  221 A and  221 B deviate along the X-axis. Electrodes  214 A and  214 B have ends  3214 A and  3214 B opposite to ends  1214 A and  1214 B along the X-axis. When no acceleration is applied, end  3214 A of electrode  214 A deviates slightly from end  3214 B of electrode  214 B in direction D 201  along the X-axis. Electrodes  216 A and  216 B have ends  3216 A and  3216 B opposite to ends  3216 A and  3216 B along the X-axis, respectively. When no acceleration is applied, end  3216 A of electrode  216 A deviates slightly from end  3216 B of electrode  216 B in direction D 202 . Electrodes  217 A and  217 B have ends  3217 A and  3217 B opposite to ends  1217 A and  1217 B along the X-axis, respectively. When no acceleration is applied, end  3217 A of electrode  217 A deviates slightly from end  3217 B of electrode  217 B in direction D 201  along the X-axis. Electrodes  219 A and  219 B have ends  3219 A and  3219 B side opposite to ends  3219 A and  3219 B along the X-axis. When no acceleration is applied, end  3219 A of electrode  219 A deviates slightly from end  3219 B of electrode  219 B in direction D 202 . 
       FIG. 13  is a sectional view of sensor element  201  on line  10 - 10  shown in  FIG. 9A  when an acceleration along the X-axis is applied. When acceleration  1002 C directed in direction D 201  along the X-axis is applied, a force along the X-axis due to acceleration  1002 C deforms elastic portions  209  along the X-axis but not along any of the Y-axis and the Z-axis while acceleration  1002 C is not converted into a rotational force. The force displaces ends  1214 A and  1216 A of electrodes  214 A and  216 A relatively with respect to ends  1214 B and  1216 B of electrodes  214 B and  216 B by distance W 201  along the X-axis. Similarly, the force displaces the ends of electrodes  218 A and  220 A relatively with respect to the ends of electrodes  218 B and  220 B by distance W 201  along the X-axis. When weights  203 A and  203 B are displaced along the X-axis due to acceleration  1002 C, the capacitance of opposed electrode unit  214  changes by an amount different from an amount of the change of the capacitance of opposed electrode unit  216 . Similarly, when weights  203 C and  203 D are displaced along the X-axis, the capacitance of opposed electrode unit  218  changes by an amount different from an amount of the change of the capacitance of opposed electrode unit  220 . Similarly, the force displaces ends  1217 A and  1219 A of electrodes  217 A and  219 A relatively with respect to ends  1217 B and  1219 B of electrodes  217 B and  219 B by distance W 201  along the X-axis. Similarly, the ends of electrodes  221 A and  223 A are displaced relatively with respect to the ends of electrodes  221 B and  223 B by distance W 201  along the X-axis. When weights  203 A and  203 B are displaced along the X-axis due to acceleration  1002 C, the capacitance of opposed electrode unit  217  changes by an amount different from the amount of the change of the capacitance of opposed electrode unit  219 . Similarly, when weights  203 C and  203 D are displaced along the X-axis, the capacitance of opposed electrode unit  221  changes by an amount different from the amount of the change of the capacitance of opposed electrode unit  223 . 
     Next, an operation of inertial force sensor  1002  to detect the acceleration along the Y-axis will be described below.  FIG. 14  is a sectional view of sensor element  201  on line  10 - 10  shown in  FIG. 9A  when no acceleration along the Y-axis is applied. Electrodes  214 A and  214 B have ends  2214 A and  2214 B directed in the same direction along the Y-axis, and electrodes  218 A and  218 B have ends  2218 A and  2218 B directed in the same direction along the Y-axis and facing ends  2214 A and  2214 B, respectively. When no acceleration is applied, end  2214 A of electrode  214 A deviates slightly from end  2214 B of electrode  214 B in direction D 203  along the Y-axis, and end  2218 A of electrode  218 A deviates slightly from end  2218 B of electrode  218 B in direction D 204  opposite to direction D 203 . Similarly, when no acceleration is applied, ends of electrodes  216 A and  216 B directed in the same direction deviate slightly from each other along the Y-axis, and ends of electrodes  220 A and  220 B directed in the same direction deviate slightly from each other in a direction opposite to the direction in which the ends of electrodes  218 A and  218 B deviate along the Y-axis. Electrodes  217 A and  217 B have ends  2217 A and  2217 B directed in the same direction, and electrodes  221 A and  221 B have ends  2221 A and  2221 B directed in the same direction and facing ends  2217 A and  2217 B, respectively. When no acceleration is applied, end  2217 A of electrode  217 A deviates slightly from end  2217 B of electrode  217 B in direction D 203 , and end  2221 A of electrode  221 A deviates slightly in direction D 204 . Similarly, when no acceleration is applied, the ends of electrodes  219 A and  219 B directed in the same direction deviate slightly from each other along the Y-axis, and the ends of electrodes  223 A and  223 B directed in the same direction deviate slightly from each other in the direction opposite to the direction in which the ends of electrodes  219 A and  219 B deviate along the Y-axis. Electrodes  214 A and  214 B have ends  4214 A and  4214 B opposite to ends  2214 A and  2214 B along the Y-axis. When no acceleration is applied, end  4214 A of electrode  214 A deviates slightly from end  4214 B of electrode  214 B in direction D 203  along the Y-axis. Electrodes  218 A and  218 B have ends  4218 A and  4218 B opposite to ends  2218 A and  2218 B along the Y-axis. When no acceleration is applied, end  4218 A of electrode  218 A deviates slightly from end  4218 B of electrode  218 B in direction D 204 . Electrodes  217 A and  217 B have ends  4217 A and  4217 B opposite to ends  2217 A and  2217 B along the Y-axis. When no acceleration is applied, end  4217 A of electrode  217 A deviates slightly from end  4217 B of electrode  217 B in direction D 203  along the Y-axis. Electrodes  221 A and  221 B have ends  4221 A and  4221 B opposite to ends  2221 A and  2221 B along the Y-axis. When no acceleration is applied, end  4221 A of electrode  221 A deviates slightly from end  4221 B of electrode  221 B in direction D 204 . 
       FIG. 15  is a sectional view of sensor element  201  on line  10 - 10  shown in  FIG. 9A  when an acceleration along the Y-axis is applied. When acceleration  1002 D directed in direction D 203  along the Y-axis is applied, a force along the Y-axis due to acceleration  1002 D deforms elastic portions  209  along the Y-axis but not along any of the Y-axis and the Z-axis while the force is not converted into a rotational force. The force displaces ends  2214 A and  2218 A of electrodes  214 A and  218 A relatively with respect to ends  2214 B and  2218 B of electrodes  214 B and  218 B by distance W 202  along the Y-axis. Similarly, the force displaces the ends of electrodes  216 A and  220 A relatively with respect to the ends of electrodes  216 B and  220 B by distance W 202  along the Y-axis. When weights  203 A and  203 C are displaced along the Y-axis due to acceleration  1002 D, the capacitance of opposed electrode unit  214  changes by an amount different from an amount of the change of the capacitance of opposed electrode unit  218 . Similarly, when weights  203 B and  203 D are displaced along the Y-axis, the capacitance of opposed electrode unit  216  changes by an amount different from an amount of the change of the capacitance of opposed electrode unit  220 . Similarly, the force displaces ends  2217 A and  2221 A of electrodes  217 A and  221 A relatively with respect to ends  2217 B and  2221 B of electrodes  217 B and  221 B by distance W 202  along the Y-axis. Similarly, the force displaces the ends of electrodes  219 A and  223 A relatively with respect to the ends of electrodes  219 B,  223 B by distance W 202  along the Y-axis. When weights  203 A and  203 C are along the Y-axis due to acceleration  1002 D, the capacitance of opposed electrode unit  217  changes by an amount different from an amount of the change of the capacitance of opposed electrode unit  221 . Similarly, when weights  203 B and  203 D are displaced along the Y-axis, the capacitance of opposed electrode unit  219  changes by an amount different from an amount of the change of the capacitance of opposed electrode unit  223 . 
     Thus, accelerations  1002 C and  1002 D along the X-axis and the Y-axis changes the capacitances of opposed electrode units  214 ,  216 ,  217 ,  218 ,  219 ,  220 ,  221 , and  223 . Processor  261  can detect accelerations  1002 C and  1002 D based on the changes of the capacitances. 
     Sensor element  201  can detect acceleration  1002 C along the X-axis since elastic portions  209  deform along the X-axis but not along any of the Y-axis and the Z-axis. Sensor element  201  can detect acceleration  1002 D along the Y-axis since elastic portions  211  deform along the Y-axis but not along any of the X-axis and the Z-axis. Thus, sensor element  201  can detect acceleration  1002 C along the X-axis and acceleration  1002 D along the Y-axis at high sensitivity independently without mutual interference. 
     Acceleration  1002 C changes the capacitances of opposed electrode units  214  and  216  by the amounts different from each other, and changes the capacitances of opposed electrode units  218  and  220  by the amounts different from each other. Acceleration  1002 C changes the capacitances of opposed electrode units  217  and  219  by the amounts different from each other, and changes the capacitances of opposed electrode units  221  and  223  by the amounts different from each other. For example, when acceleration  1002 C directed in the negative direction of the X-axis is applied, as shown in  FIG. 13 , opposed electrode units  214 ,  217 ,  218 , and  221  decrease their capacitances, and opposed electrode units  216 ,  219 ,  219 , and  223  increase their capacitances. When an acceleration directed in the positive direction of the X-axis is applied, weights  203 A to  203 D are displaced in a direction opposite to the direction shown in  FIG. 13 . Therefore, opposed electrode units  214 ,  217 ,  218 , and  221  increase their capacitances, and opposed electrode units  216 ,  219 ,  220 , and  223  decrease their capacitances. Processor  261  connected to sensor element  201  can determine, based on the capacitances of opposed electrode units  214 ,  216 ,  217 ,  218 ,  219 ,  220 ,  221 , and  223 , whether weights  203 A to  203 D are displaced in the positive direction or the negative direction of the X-axis. Similarly, when acceleration  1002 D directed in the negative direction of the Y-axis is applied, as shown in  FIG. 15 , opposed electrode units  214 ,  217 ,  216 , and  219  decrease their capacitances, and opposed electrode units  218 ,  220 ,  221 , and  223  increase their capacitances. When an acceleration directed in the positive direction of the Y-axis is applied, weights  203 A to  203 D are displaced in a direction opposite to the direction shown in  FIG. 15 . Therefore, opposed electrode units  214 ,  217 ,  216 , and  219  increase their capacitances, and opposed electrode units  218 ,  220 ,  221 , and  223  decrease their capacitances. Processor  261  can determine, based on the capacitances of opposed electrode units  214 ,  216 ,  217 ,  218 ,  219 ,  220 ,  221 , and  223 , whether weights  203 A to  203 D are displaced in the positive direction or the negative direction of the Y-axis. 
     In inertial force sensor  1002 , when weights  203 A to  203 D are displaced in the positive direction of the Z-axis, electrodes  214 A,  216 A,  218 A, and  220 A approach electrodes  214 B,  216 B,  218 B, and  220 B, whereas electrodes  217 A,  219 A,  221 A and  223 A are displaced away from electrodes  217 B,  219 B,  221 B, and  223 B. When weights  203 A to  203 D are displaced in the negative direction of the Z-axis, electrodes  214 A,  216 A,  218 A, and  220 A are displaced away from electrodes  214 B,  216 B,  218 B, and  220 B, whereas electrodes  217 A,  219 A,  221 A, and  223 A approach electrodes  217 B,  219 B,  221 B, and  223 B. Thus, the displacement of weights  203 A to  203 D along the Z-axis does not change the sum of the distance between electrodes  214 A and  214 B and the distance between electrodes  217 A and  217 B, the sum of the distance between electrodes  216 A and  216 B and the distance between electrodes  219 A and  219 B, the sum of the distance between electrodes  218 A and  218 B and the distance between electrodes  221 A and  221 B, and the sum of the distance between electrodes  220 A and  220 B and the distance between electrodes  223 A and  223 B. Thus, the displacement of weights  203 A to  203 D along the Z-axis does not change a combined capacitance of opposed electrode units  214  and  217 , a combined capacitance of opposed electrode units  216  and  219 , a combined capacitance of opposed electrode units  218  and  221 , or a combined capacitance of opposed electrode units  220  and  223  so much. Thus, inertial force sensor  1002  can detect accelerations  1002 C and  1002 D accurately based on these combined capacitances. 
     Single sensor element  201  which can detect both the acceleration and the angular velocity allows inertial force sensor  1002  to have a small footprint and a small size. 
     Elastic portions  209  which deform along the X-axis but not along any of the Y-axis and the Z-axis are placed at fixing portion  204  of sensor element  201  of inertial force sensor  1002 . Alternatively, elastic portions  209  may be placed at arms  208  functioning as the linking unit of the inertial force sensor according to Embodiment 2. Elastic portions  211  which deform along the Y-axis but not along any of the X-axis and the Z-axis are placed at fixing portion  206  of sensor element  201 . Alternatively, elastic portions  211  may be placed at fixing arm  207  functioning as the linking unit of the inertial force sensor according to Embodiment 2. 
     Driving electrode  222 , detecting electrode  224 , and sensing electrodes  226  and  228  for detecting the angular velocity may have shapes and positions other than those described above. 
     Electrodes  214 A,  216 A,  217 A,  218 A,  219 A,  220 A,  221 A, and  223 A are largely displaced in the direction of the acceleration with respect to electrodes  214 B,  216 B,  217 B,  218 B,  219 B,  220 B,  221 B, and  223 B without causing the force due to the acceleration to be converted into a rotational force. Thus, inertial force sensor  1002  according to Embodiment 2 detects the acceleration at high sensitivity. 
     Exemplary Embodiment 3 
       FIG. 16A  is an exploded perspective view of sensor element  301  of inertial force sensor  1003  according to Exemplary Embodiment 3 of the present invention.  FIG. 16B  is a perspective view of sensor element  301 .  FIGS. 17 and 18  are sectional views of sensor element  301  on line  17 - 17  and line  18 - 18  shown in  FIG. 16A , respectively. Inertial force sensor  1003  can detect an acceleration and an angular velocity. 
     A Z-axis, an X-axis, and a Y-axis, a first axis, a second axis, and a third axis perpendicular to each other are defined as shown in  FIGS. 16A and 16B . Two arms  308  extend from supporter  312  along the X-axis and are connected to fixing portion  304  having a frame shape. Supporter  312  is joined to fixing portion  304  via arms  308 . Arms  308  extend perpendicularly to fixing portion  304 . Four arms  310 A to  310 D extend from supporter  312  along the Y-axis and are connected to four weights  303 A to  303 D, respectively. 
     Arms  308  and  310 A to  310 D and supporter  312  are flexible and constitute a flexible portion. The flexible portion is connected to fixing portion  304 . Weights  303 A to  303 D are linked to fixing portion  304  via the flexible portion. Weights  303 A to  303 D have surfaces  1303 A to  1303 D facing substrate  305 , and have surfaces  2303 A to  2303 D which face substrate  315  and which are opposite to surfaces  1303 A to  1303 D, respectively. Arms  308  are much thinner and hence more flexible than arms  310 A to  310 D. 
     Electrodes  314 A,  316 A,  318 A and  320 A are provided on surfaces  1303 A,  1303 B,  1303 C, and  1303 D of weights  303 A,  303 B,  303 C, and  303 D, respectively. Electrodes  317 A,  319 A,  321 A and  323 A are provided on surfaces  2303 A,  2303 B,  2303 C, and  2303 D of weights  303 A,  303 B,  303 C, and  303 D, respectively. Substrates  305  and  315  are attached to fixing portion  304 . Substrate  305  has surface  305 A facing surfaces  1303 A to  1303 D of weights  303 A to  303 D along the Z-axis. Electrodes  314 B,  316 B,  318 B, and  320 B facing electrodes  314 A,  316 A,  318 A, and  320 A, along the Z-axis are provided on surface  305 A of substrate  305  and are spaced from electrodes  314 B,  316 B,  318 B, and  320 B, respectively. Electrodes  314 C,  316 C,  318 C, and  320 C facing electrodes  314 A,  316 A,  318 A, and  320 A along the Z-axis are provided on substrate  305  and are spaced from electrodes  314 A,  316 A,  318 A, and  320 A, respectively. Electrodes  314 A and  314 B having a capacitance between the electrodes constitute opposed electrode unit  314 X. Electrodes  316 A and  316 B having a capacitance between the electrodes constitute opposed electrode unit  316 X. Electrodes  318 A and  318 B having a capacitance between the electrodes constitute opposed electrode unit  318 X. Electrodes  320 A and  320 B having a capacitance between the electrodes constitute opposed electrode unit  320 X. Electrodes  314 A and  316 A are arranged along the X-axis, and electrodes  314 B and  316 B are also arranged along the X-axis. Thus, opposed electrode units  314 X and  316 X are arranged along the X-axis. Electrodes  318 A and  320 A are arranged along the X-axis, and electrodes  318 B and  320 B are also arranged along the X-axis. Thus, opposed electrode units  318 X and  320 X are arranged along the X-axis. Electrodes  314 A and  314 C having a capacitance between the electrodes constitute opposed electrode unit  314 Y. Electrodes  316 A and  316 C having a capacitance between the electrodes constitute opposed electrode unit  316 Y. Electrodes  318 A and  318 C having a capacitance between the electrodes constitute opposed electrode unit  318 Y. Electrodes  320 A and  320 C having a capacitance between the electrodes constitute opposed electrode unit  320 Y. Electrodes  314 A and  318 A are arranged along the Y-axis, and electrodes  314 C and  318 C are also arranged along the Y-axis. Thus, opposed electrode units  314 Y and  318 Y are arranged along the Y-axis. Electrodes  316 A and  320 A are arranged along the Y-axis, and electrodes  316 C and  320 C are also arranged along the Y-axis. Thus, opposed electrode units  316 Y and  320 Y are arranged along the Y-axis. Substrate  315  has surface  315 A facing surfaces  2303 A to  2303 D of weights  303 A to  303 D along the Z-axis. Electrodes  317 B,  319 B,  321 B, and  323 B facing electrodes  317 A,  319 A,  321 A, and  323 A along the Z-axis are provided on surface  315 A of substrate  315  electrodes  317 B,  319 B,  321 B, and  323 B, and are spaced from electrodes  317 A,  319 A,  321 A, and  323 A, respectively. Electrodes  317 C,  319 C,  321 C, and  323 C facing electrodes  317 A,  319 A,  321 A, and  323 A along the Z-axis are provided on substrate  315  and are spaced from electrodes  317 C,  319 C,  321 C, and  323 C, respectively. Electrodes  317 A and  317 B having a capacitance between the electrodes constitute opposed electrode unit  317 X. Electrodes  319 A and  319 B having a capacitance between the electrodes constitute opposed electrode unit  319 X. Electrodes  321 A and  321 B having a capacitance between the electrodes constitute opposed electrode unit  321 X. Electrodes  323 A and  323 B having a capacitance between the electrodes constitute opposed electrode unit  323 X. Electrodes  317 A and  319 A are arranged along the X-axis, and electrodes  317 B and  319 B are arranged along the X-axis. Thus, opposed electrode units  317 X and  319 X are arranged along the X-axis. Electrodes  321 A and  323 A are arranged along the X-axis, and electrodes  321 B and  323 B are arranged along the X-axis. Thus, opposed electrode units  321 X and  323 X are arranged along the X-axis. Electrodes  317 A and  317 C having a capacitance between the electrodes constitute opposed electrode unit  317 Y. Electrodes  319 A and  319 C having a capacitance between the electrodes constitute opposed electrode unit  319 Y. Electrodes  321 A and  321 C having a capacitance between the electrodes constitute opposed electrode unit  321 Y. Electrodes  323 A and  323 C having a capacitance between the electrodes constitute opposed electrode unit  323 Y. Electrodes  317 A and  321 A are arranged along the Y-axis, and electrodes  317 C and  321 C are arranged along the Y-axis. Thus, opposed electrode units  317 Y and  321 Y are arranged along the Y-axis. Electrodes  319 A and  333 A are arranged along the Y-axis, and electrodes  319 C,  323 C are also arranged along the Y-axis. Thus, opposed electrode units  319 Y and  323 Y are arranged along the Y-axis. 
     Arm  310 A extending from supporter  312  includes extension  1310 A extending from supporter  312  along the Y-axis, extension  3310 A extending in parallel with extension  1310 A along the Y-axis, and connecting portion  2310 A connecting between extensions  1310 A and  3310 A, and thus has substantially a U-shape. Connecting portion  2310 A extends from extension  1310 A along the X-axis. Extension  3310 A is connected to weight  303 A. Arm  310 B extending from supporter  312  includes extension  1310 B extending from supporter  312  along the Y-axis, extension  3310 B extending in parallel with extension  1310 B along the Y-axis, and connecting portion  2310 B connecting between extensions  1310 B and  3310 B, and thus, has substantially a U-shape. Connecting portion  2310 B extends from extension  1310 B along the X-axis in a direction opposite to the direction in which connecting portion  2310 A of arm  310 A extends. Extension  3310 B is connected to weight  303 B. Arm  310 C extending from supporter  312  includes extension  1310 C extending from supporter  312  along the Y-axis, extension  3310 C extending in parallel with extension  1310 C along the Y-axis, and connecting portion  2310 C connecting between extensions  1310 C and  3310 C, and thus, has substantially a U-shape. Connecting portion  2310 C extends from extension  1310 C along the X-axis in a direction identical to the direction in which connecting portion  2310 A of arm  310 A extends. Extension  3310 C is connected to weight  303 C. Arm  310 D extending from supporter  312  includes extension  1310 D extending from supporter  312  along the Y-axis, extension  3310 D extending in parallel with extension  1310 D along the Y-axis, and connecting portion  2310 D connecting between extensions  1310 D and  3310 D, and thus, has substantially a U-shape. Connecting portion  2310 D extends from extension  1310 D along the X-axis in a direction opposite to the direction in which connecting portion  2310 C of arm  310 C extends. Extension  3310 D is connected to weight  303 D. Extensions  1310 A to  1310 D and  3310 A to  3310 D of arms  310 A to  310 D extend perpendicularly to fixing portions  304  and  306 . 
     Arms  308  and supporter  312  are arranged substantially in a single straight line. Extension  1310 A and  1310 B of arms  310 A and  310 B extend in the same direction from supporter  312 . 
     Extensions  1310 C and  1310 D of arms  310 C and  310 D extend in the same direction from supporter  312 , and in the direction opposite to extensions  1310 A and  1310 B of arms  310 A and  310 B extends. 
     Weights  303 A to  303 D are arranged inside the frame shape of fixing portion  304 . Fixing portion  304  is linked to fixing portion  306  via fixing arm  307 , and placed inside fixing portion  306 . Arms  308  and supporter  12  are arranged substantially in a single straight line. Arms  308  are arranged symmetrically to each other with respect to center  301 A of sensor element  301 . Arms  310 A to  310 D are arranged symmetrically to each other with respect to center  301 A of sensor element  301 . Arms  308  and  310 A to  310 D function as a linking unit for linking weights  303 A to  303 D to fixing portion  304 . Fixing arm  307  functions as a linking unit for linking fixing portion  304  to fixing portion  306 . 
     Fixing portion  304  includes elastic portions  309  which elastically deform only along the X-axis, that is, which do not substantially deform along any of the Y-axis and the Z-axis. Fixing arm  307  extends along the Y-axis. Fixing portion  306  includes elastic portions  311 , which elastically deform only along the Y-axis, that is, which do not substantially deform along the X or Z-axis. Fixing portion  306  is arranged to be mounted to mounting substrate  1003 A, an object. 
     Elastic portions  309  are implemented by slits  313 A which are provided in fixing portion  304  and extend along the Y-axis. Elastic portions  311  are implemented by slits  313 B which are provided in fixing portion  306  and which extend along the X-axis. Driving electrode  322  which drives and vibrates weight  303 C is provided on arm  310 C. Detecting electrode  324  which detects the vibration of arm  310 D is provided on arm  310 D. Sensing electrodes  326  and  328  which sense strains on arms  310 A and  310 B are provided on arms  310 A and  310 B, respectively. Driving electrode  322  includes a lower electrode provided on arm  310 C, a piezoelectric layer provided on the lower electrode, and an upper electrode provided on the piezoelectric layer. Similarly, each of detecting electrodes  324 ,  326 , and  328  include a lower electrode provided on each of arms  310 D,  310 A, and  310 B, respectively, a piezoelectric layer provided on the lower electrode, and an upper electrode provided on the piezoelectric layer. 
     Opposed electrode units  314 X,  314 Y,  316 X,  316 Y,  317 X,  317 Y,  318 X,  318 Y,  319 X,  319 Y,  320 X,  320 Y,  321 X,  321 Y,  323 X, and  323 Y, driving electrode  322 , detecting electrode  324 , and sensing electrodes  326 ,  328  are connected to fixing portion  306  via signal lines, and electrically connected to circuit patterns on mounting substrate  1003 A with e.g., bonding wire at ends of the signal lines. Opposed electrode units  314 X,  314 Y,  316 X,  316 Y,  317 X,  317 Y,  318 X,  318 Y,  319 X,  319 Y,  320 X,  320 Y,  321 X,  321 Y,  323 X, and  323 Y, driving electrode  322 , detecting electrode  324 , and sensing electrodes  326  and  328  are connected to processor  361  via the signal lines and mounting substrate  1003 A. 
     Inertial force sensor  1003  including driving electrode  322 , detecting electrode  324 , and sensing electrodes  326 ,  328  can detect an angular velocity about the Z-axis similarly to inertial force sensor  1001  including driving electrode  122 , detecting electrode  124 , and sensing electrodes  126  and  128  according to Embodiment 1 shown in  FIG. 4 . 
     An operation of inertial force sensor  1002  to detect an acceleration will be described below. 
       FIGS. 19 and 20  are plan views of sensor element  301 .  FIG. 19  shows positional relationship of electrodes  314 A,  314 B,  314 C,  316 A,  316 B,  316 C,  318 A,  318 B,  318 C,  320 A,  320 B, and  320 C.  FIG. 20  shows positional relationship of electrodes  317 A,  317 B,  317 C,  319 A,  319 B,  319 C,  321 A,  321 B,  321 C,  323 A,  323 B, and  323 C. 
     First, an operation of inertial force sensor  1003  to detect an acceleration along the X-axis will be described below.  FIG. 21  is a sectional view of sensor element  301  on line  21 - 21  shown in  FIGS. 19 and 20  when there no acceleration along the X-axis is applied. Electrodes  314 A and  314 B have ends  1314 A and  1314 B directed in the same direction along the X-axis. Electrodes  316 A and  316 B have ends  1316 A and  1316 B directed in the same direction along the X-axis and facing ends  1314 A and  1314 B, respectively. When no acceleration is applied, ends  1314 A of electrode  314 A deviates slightly from end  1314 B of electrode  314 B in direction D 301  along the X-axis, and end  1316 A of electrode  316 A deviates slightly from end  1316 B of electrode  316 B in direction D 302  opposite to direction D 301 . Similarly, electrodes  318 A and  318 B have ends  1318 A and  1318 B directed in the same direction along the X-axis, and electrodes  320 A and  320 B have ends  1320 A and  1320 B directed in the same direction along the X-axis and facing ends  1318 A and  1318 B, respectively. When no acceleration is applied, end  1318 A of electrode  318 A deviates slightly from end  1318 B of electrode  318 B in direction D 301  along the X-axis, and end  1320 A of electrode  320 A deviates slightly from end  1320 B of electrode  320 B in direction D 302 . 
     Electrodes  317 A and  317 B have ends  1317 A and  1317 B directed in the same direction. Electrodes  319 A and  319 B have ends  1319 A and  1319 B directed in the same direction and facing ends  1317 A and  1317 B, respectively. When no acceleration is applied, end  1317 A of electrode  317 A deviates slightly from end  1317 B of electrode  317 B in direction D 301 , and end  1319 A of electrode  319 A deviates slightly in direction D 302 . Similarly, electrodes  321 A and  321 B have ends  1321 A and  1321 B directed in the same direction. Electrodes  323 A and  323 B have ends  1323 A and  1323 B directed in the same direction and facing ends  1321 A and  1321 B. When no acceleration is applied, end  1321 A of electrode  321 A deviates slightly from end  1321 B of electrode  321 B in direction D 301 , and end  1323 A of electrode  323 A deviates slightly in direction D 302 . Electrodes  314 A and  314 B have ends  3314 A and  3314 B opposite to ends  1314 A and  1314 B along the X-axis, respectively. When no acceleration is applied, end  3314 A of electrode  314 A deviates slightly from end  3314 B of electrode  314 B in direction D 301  along the X-axis. Electrodes  316 A and  316 B have ends  3316 A and  3316 B opposite to ends  3316 A and  3316 B along the X-axis, respectively. When no acceleration is applied, end  3316 A of electrode  316 A deviates slightly from end  3316 B of electrode  316 B in direction D 302 . Electrodes  317 A and  317 B have ends  3317 A and  3317 B opposite to ends  1317 A and  1317 B along the X-axis, respectively. When no acceleration is applied, end  3317 A of electrode  317 A deviates slightly from end  3317 B of electrode  317 B in direction D 301  along the X-axis. Electrodes  319 A and  319 B have ends  3319 A and  3319 B opposite to ends  3319 A and  3319 B along the X-axis, respectively. When no acceleration is applied, end  3319 A of electrode  319 A deviates slightly from end  3319 B of electrode  319 B in direction D 302 . 
       FIG. 22  is a sectional view of sensor element  301  on line  21 - 21  shown in  FIGS. 19 and 20  when an acceleration along the X-axis is applied. When acceleration  1003 C directed in direction D 301  along the X-axis is applied, a force along the X-axis due to acceleration  1003 C deforms elastic portions  309  along the X-axis nut not along any of the Y-axis and the Z-axis while the force is not converted into a rotational force. The force displaces ends  1314 A and  1316 A of electrodes  314 A and  316 A relatively with respect to ends  1314 B and  1316 B of electrodes  314 B and  316 B by distance W 301  along the X-axis. Similarly, the force displaces ends of electrodes  318 A and  320 A relatively with respect to ends of electrodes  318 B and  320 B by distance W 301  along the X-axis. When weights  303 A and  303 B are displaced along the X-axis due to acceleration  1003 C, the capacitance of opposed electrode unit  314 X changes by an amount different from an amount of the change of the capacitance of opposed electrode unit  316 X. Similarly, when weights  303 C and  303 D are displaced along the X-axis, the capacitance of opposed electrode unit  318 X changes by an amount different from an amount of the change of the capacitance of opposed electrode unit  320 X. Similarly, the force displaces ends  1317 A and  1319 A of electrodes  317 A and  319 A relatively with respect to ends  1317 B and  1319 B of electrodes  317 B and  319 B by distance W 301  along the X-axis. Similarly, the force displaces ends of electrodes  321 A and  323 A relatively with respect to the ends of electrodes  321 B and  323 B by distance W 301  along the X-axis. When weights  303 A and  303 B are displaced along the X-axis due to acceleration  1003 C, the capacitance of opposed electrode unit  317 X changes by an amount different from an amount of the change of the capacitance of opposed electrode unit  319 X. Similarly, when weights  303 C and  303 D are displaced along the X-axis, the capacitance of opposed electrode unit  321 X changes by an amount different from an amount of the change of the capacitance of opposed electrode unit  323 X. 
     Processor  361  detects acceleration  1003 C along the X-axis based on the amount of the change of the difference between a combined capacitance of opposed electrode units  314 X,  318 X,  317 X, and  321 X and a combined capacitance of opposed electrode units  316 X,  320 X,  319 X, and  323 X. 
     Next, an operation of inertial force sensor  1003  to detect an acceleration along the Y-axis will be described below.  FIG. 23  is a sectional view of sensor element  301  on line  23 - 23  shown in  FIGS. 19 and 20  when no acceleration along the Y-axis is applied. Electrodes  314 A and  314 C have ends  2314 A and  2314 C directed in the same direction along the Y-axis. Electrodes  316 A and  316 C have ends  2316 A and  2316 C directed in the same direction along the Y-axis and facing ends  2314 A and  2314 C, respectively. When no acceleration is applied, end  2314 A of electrode  314 A deviates slightly from end  2314 C of electrode  314 C in direction D 303  along the Y-axis, and end  2316 A of electrode  316 A deviates slightly from end  2316 C of electrode  316 C in direction D 304  opposite to direction D 303 . Similarly, electrodes  318 A and  318 C have ends  2318 A and  2318 C directed in the same direction along the Y-axis. Electrodes  320 A and  320 C have ends  2320 A and  2320 C directed in the same direction along the Y-axis and facing ends  2318 A and  2318 C. When no acceleration is applied, end  2318 A of electrode  318 A deviates slightly from end  2318 C of electrode  318 C in direction D 303  along the Y-axis, and end  2320 A of electrode  320 A deviates slightly from end  2320 C of electrode  320 C in direction D 304 . Electrodes  317 A and  317 C have ends  2317 A and  2317 C directed in the same direction. Electrodes  319 A and  319 C have ends  2319 A and  2319 C directed in the same direction face ends  2317 A and  2317 C, respectively. When no acceleration is applied, end  2317 A of electrode  317 A deviates slightly from end  2317 C of electrode  317 C in direction D 303 , and end  2319 A of electrode  319 A deviates slightly in direction D 304 . Similarly, electrodes  321 A and  321 C have ends  2321 A and  2321 C directed in the same direction. Electrodes  323 A and  323 C have ends  2323 A and  2323 C directed in the same direction face ends  2321 A and  2321 C, respectively. When no acceleration is applied, end  2321 A of electrode  321 A deviates slightly from end  2321 C of electrode  321 C in direction D 303 , and end  2323 A of electrode  323 A deviates slightly in direction D 304 . Electrodes  314 A and  314 C have ends  4314 A and  4314 C opposite to ends  2314 A and  2314 C along the Y-axis, respectively. When no acceleration is applied, end  4314 A of electrode  314 A deviates slightly from end  4314 C of electrode  314 C in direction D 303  along the Y-axis. Electrodes  318 A and  318 C have ends  4318 A and  4318 C opposite to ends  2318 A and  2318 C along the Y-axis, respectively. When no acceleration is applied, end  4318 A of electrode  318 A deviates slightly from end  4318 C of electrode  318 C in direction D 304 . Electrodes  317 A and  317 C have ends  4317 A and  4317 C opposite to ends  2317 A and  2317 C along the Y-axis, respectively. When no acceleration is applied, end  4317 A of electrode  317 A deviates slightly from end  4317 C of electrode  317 C in direction D 303  along the Y-axis. Electrodes  321 A and  321 C have ends  4321 A and  4321 C opposite to ends  2321 A and  2321 C along the Y-axis, respectively. When no acceleration is applied, end  4321 A of electrode  321 A deviates slightly from end  4321 C of electrode  321 C in direction D 304 . 
       FIG. 24  is a sectional view of sensor element  301  on line  23 - 23  shown in  FIGS. 19 and 20  when an acceleration along the Y-axis is applied. When acceleration  1003 D directed in direction D 303  along the Y-axis is applied, a force along the Y-axis due to acceleration  1003 D deforms elastic portions  311  along the Y-axis, and do not deform along any of the X-axis and the Z-axis while the force is not converted into a rotational force. The force displaces ends  2314 A and  2316 A of electrodes  314 A and  316 A relatively with respect to ends  2314 C and  2316 C of electrodes  314 C and  316 C by distance W 302  along the Y-axis. Similarly, the force displaces ends of electrodes  318 A and  320 A relatively with respect to the ends of electrodes  318 C and  320 C by distance W 302  along the Y-axis. When weights  303 A and  303 C are displaced along the Y-axis due to acceleration  1003 D, the capacitances of opposed electrode unit  314 Y changes by an amount different from an amount of the change of the capacitances of opposed electrode unit  316 Y. Similarly, when weights  303 D and  303 D are displaced along the Y-axis, the capacitances of opposed electrode unit  318 Y changes by an amount different from an amount of the change of the capacitances of opposed electrode unit  320 Y. Similarly, the force displaces ends  2317 A and  2319 A of electrodes  317 A and  319 A relatively with respect to ends  2317 C and  2319 C of electrodes  317 C and  319 C by distance W 302  along the Y-axis. Similarly, the force displaces ends of electrodes  321 A and  323 A relatively with respect to the ends of electrodes  321 C and  323 C by distance W 302  along the Y-axis. When weights  303 A and  303 C are displaced along the Y-axis due to acceleration  1003 D, the capacitances of opposed electrode unit  317 Y changes by an amount different from an amount of the change of the capacitances of opposed electrode unit  319 Y. Similarly, when weights  303 D and  303 D are displaced along the Y-axis, the capacitances of opposed electrode unit  321 Y changes by an amount different from an amount of the change of the capacitances of opposed electrode unit  323 Y 
     Processor  361  detects acceleration  1003 D along the Y-axis based on the amount of the change of the difference between a combined capacitance of opposed electrode units  314 Y,  316 Y,  317 Y, and  319 Y and a combined capacitance of opposed electrode units  318 Y,  320 Y,  321 Y, and  323 Y. 
     Sensor element  301  can detect acceleration  1003 C along the X-axis since elastic portions  309  deform along the X-axis but not along any of the Y-axis and the Z-axis. Sensor element  301  can detect acceleration  1003 D along the Y-axis since elastic portions  311  deform along the Y-axis but not along any of the X-axis and the Z-axis. Thus, sensor element  301  can detect acceleration  1003 C along the X-axis and acceleration  1003 D along the Y-axis at high sensitivity independently without mutual interference. 
     The amounts of the changes of the capacitances of opposed electrode units  314 X and  316 X due to acceleration  1003 C are different from each other. The amounts of the changes of the capacitances of opposed electrode units  318 X and  320 X due to acceleration  1003 C are different from each other. The amounts of the changes of the capacitances of opposed electrode units  317 X and  319 X due to acceleration  1003 C are different from each other. The amounts of the changes of the capacitances of opposed electrode units  321 X and  323 X due to acceleration  1003 C are different from each other. For example, when acceleration  1003 C directed in a negative direction of the X-axis, as shown in  FIG. 22 , opposed electrode units  314 X,  317 X,  318 X, and  321 X decrease their capacitances, and opposed electrode units  316 X,  319 X,  319 X, and  323 X increase their capacitances. When an acceleration directed in the positive direction of the X-axis is applied, weights  303 A to  303 D are displaced in a direction opposite to the direction shown in  FIG. 22 . Therefore, opposed electrode units  314 X,  317 X,  318 X, and  321 X decrease their capacitances, and opposed electrode units  316 X,  319 X,  320 X, and  323 X decrease their capacitances. Processor  361  connected to sensor element  301  can determine, based on the capacitances of opposed electrode units  314 X,  316 X,  317 X,  318 X,  319 X,  320 X,  321 X, and  323 X, whether weights  303 A to  303 D have been displaced in the positive direction or the negative direction of the X-axis. Similarly, when acceleration  1003 D directed in the negative direction of the Y-axis, as shown in  FIG. 24 , opposed electrode units  314 Y,  317 Y,  316 Y, and  319 Y decrease their capacitances, and opposed electrode units  318 Y,  320 Y,  321 Y, and  323 Y increase their capacitances. When acceleration directed in the positive direction of the Y-axis, weights  303 A to  303 D are displaced in a direction opposite to the direction shown in  FIG. 24 . Therefore, opposed electrode units  314 Y,  317 Y,  316 Y, and  319 Y increase their capacitances, and opposed electrode units  318 Y,  320 Y,  321 Y, and  323 Y decrease their capacitances. Processor  361  can distinguish, based on the capacitances of opposed electrode units  314 Y,  316 Y,  317 Y,  318 Y,  319 Y,  320 Y,  321 Y, and  323 Y, whether weights  303 A to  303 D are displaced in the positive direction or the negative direction of the Y-axis. 
     In inertial force sensor  1003 , when weights  303 A to  303 D are displaced in the positive direction of the Z-axis, electrodes  314 A,  316 A,  318 A, and  320 A approach electrodes  314 B,  314 C,  316 B,  316 C,  318 B,  318 C,  320 B, and  320 C, whereas electrodes  317 A,  319 A,  321 A, and  323 A are displaced away from electrodes  317 B,  317 C,  319 B,  319 C,  321 B,  321 C,  323 B, and  323 C. When weights  303 A to  303 D are displaced in the negative direction of the Z-axis, electrodes  314 A,  316 A,  318 A, and  320 A are displaced away from electrodes  314 B,  314 B,  316 B,  316 B,  318 B,  318 C,  320 B, and  320 C, whereas electrodes  317 A,  319 A,  321 A, and  323 A approach electrodes  317 B,  317 C,  319 B,  319 C,  321 B,  321 C,  323 B, and  323 C. Thus, the displacement of weights  303 A to  303 D along the Z-axis does not change any of the sum of the distance between electrodes  314 A and  314 B and the distance between electrodes  317 A and  317 B, the sum of the distance between electrodes  314 A and  314 C and the distance between electrodes  317 A and  317 C, the sum of the distance between electrodes  316 A and  316 B and the distance between electrodes  319 A and  319 B, the sum of the distance between electrodes  316 A and  316 C and the distance between electrodes  319 A and  319 C, the sum of the distance between electrodes  318 A and  318 B and the distance between electrodes  321 A and  321 B, the sum of the distance between electrodes  318 A and  318 C and the distance between electrodes  321 A and  321 C, the sum of the distance between electrodes  320 A and  320 B and the distance between electrodes  323 A and  323 B, and the sum of the distance between electrodes  320 A and  320 C and the distance between electrodes  323 A and  323 C. As a result, the displacement of weights  303 A to  303 D along the Z-axis does not change any of a combined capacitance of opposed electrode units  314 X and  317 X, a combined capacitance of opposed electrode units  314 Y and  317 Y, a combined capacitance of opposed electrode units  316 X and  319 X, a combined capacitance of opposed electrode units  316 Y and  319 Y, a combined capacitance of opposed electrode units  318 X and  312 X, a combined capacitance of opposed electrode units  318 Y and  321 Y, a combined capacitance of opposed electrode units  320 X and  323 X, and a combined capacitance of opposed electrode units  320 Y and  323 Y Thus, inertial force sensor  1003  can detect accelerations  1003 C and  1003 D accurately based on these combined capacitances. 
     Single sensor element  301  which can detect both the acceleration and the angular velocity allows inertial force sensor  1003  to have a small footprint and a small size. 
     Elastic portions  309  which deform along the X-axis but not along any of the Y-axis and the Z-axis are placed at fixing portion  304  of sensor element  301  of inertial force sensor  1003 . Alternatively, elastic portions  309  may be placed at arms  308  functioning as the linking unit of the inertial force sensor according to Embodiment 3. Elastic portions  311  which deform along the Y-axis but not along any of the X-axis and the Z-axis are placed at fixing portion  306  of sensor element  301 . Alternatively, elastic portions  311  may be placed at fixing arm  307  functioning as the linking unit of the inertial force sensor according to Embodiment 3. 
     Driving electrode  322 , detecting electrode  324 , and sensing electrodes  326 ,  328  for detecting the angular velocity may have shapes and positions other than those described above. 
     Electrodes  314 A,  316 A,  317 A,  318 A,  319 A,  320 A,  321 A, and  323 A are largely displaced in the direction of the acceleration with respect to electrodes  314 B,  314 C,  316 B,  316 C,  317 B,  317 C,  318 B,  318 C,  319 B,  319 C,  320 B,  320 C,  321 B,  321 C,  323 B, and  323 C without causing the force due to the acceleration to be converted into rotational force. Thus, inertial force sensor  1003  according to Embodiment 3 detects the acceleration at high sensitivity. 
     Exemplary Embodiment 4 
       FIG. 25  is an exploded perspective view of sensor element  401  of inertial force sensor  1004  according to Exemplary Embodiment 4 of the present invention. In  FIG. 25 , components identical to those of sensor element  301  of inertial force sensor  1003  shown in  FIG. 16A  according to Embodiment 2 are denoted by the same reference numerals, and their description will be omitted. Sensor element  401  includes electrodes  414 B,  414 C,  416 B,  416 C,  417 B,  417 C,  418 B,  418 C,  419 B,  419 C,  420 B,  420 C,  421 B,  421 C,  423 B, and  423 C instead of electrodes  314 B,  314 C,  316 B,  316 C,  317 B,  317 C,  318 B,  318 C,  319 B,  319 C,  320 B,  320 C,  321 B,  321 C,  323 B, and  323 C of sensor element  301  according to Embodiment 3 shown in  FIG. 16A . Sensor element  401  further includes grounding electrodes  430  and  440  provided on surfaces  305 A and  315 A of substrates  305  and  315 , respectively. Grounding electrodes  430  and  440  are arranged to be grounded. Inertial force sensor  1004  includes opposed electrode units  414 X,  414 Y,  416 X,  414 Y,  417 X,  417 Y,  418 X,  418 Y,  419 X,  419 Y,  420 X,  420 Y,  421 X,  421 Y,  423 X, and  423 Y instead of opposed electrode units  314 X,  314 Y,  316 X,  314 Y,  317 X,  317 Y,  318 X,  318 Y,  319 X,  319 Y,  320 X,  320 Y,  321 X,  321 Y,  323 X, and  323 Y of inertial force sensor  1003  according to Embodiment 3. 
     Grounding electrode  430  is formed on an area of surface  305 A of substrate  305  excluding areas having electrodes  414 B,  414 C,  416 B,  416 C,  418 B,  418 C,  420 B, and  420 C provided thereon. In other words, grounding electrode  430  is formed on an entire area of surface  305 A positioned between electrodes  414 B,  414 C,  416 B,  416 C,  418 B,  418 C,  420 B, and  420 C and away from these electrodes and surrounding these electrodes individually. Grounding electrode  440  is formed on an area of surface  315 A of substrate  315  excluding areas having electrodes  417 B,  417 C,  419 B,  419 C,  421 B,  421 C,  423 B, and  423 C provided thereon. In other words, grounding electrode  440  is formed on an entire area of surface  315 A positioned between electrodes  417 B,  417 C,  419 B,  419 C,  421 B,  421 C,  423 B, and  423 C, away from these electrodes, and surrounding these electrodes individually. 
     Electrodes  314 A and  414 B facing each other and having a capacitance between the electrodes constitute opposed electrode unit  414 X. Electrodes  316 A and  416 B facing each other and having a capacitance between the electrodes constitute opposed electrode unit  416 X. Electrodes  317 A and  417 B facing each other and having a capacitance between the electrodes constitute opposed electrode unit  417 X. Electrodes  318 A and  418 B facing each other and having a capacitance between the electrodes constitute opposed electrode unit  418 X. Electrodes  319 A and  419 B facing each other and having a capacitance between the electrodes constitute opposed electrode unit  419 X. Electrodes  320 A and  420 B facing each other and having a capacitance between the electrodes constitute opposed electrode unit  420 X. Electrodes  321 A and  421 B facing each other and having a capacitance between the electrodes constitute opposed electrode unit  421 X. Electrodes  323 A and  423 B facing each other and having a capacitance between the electrodes constitute opposed electrode unit  423 X. Electrodes  314 A and  414 C facing each other and having a capacitance between the electrodes constitute opposed electrode unit  414 Y. Electrodes  316 A and  416 C facing each other and having a capacitance between the electrodes constitute opposed electrode unit  416 Y. Electrodes  317 A and  417 C facing each other and having a capacitance between the electrodes constitute opposed electrode unit  417 Y. Electrodes  318 A and  418 C facing each other and having a capacitance between the electrodes constitute opposed electrode unit  418 Y. Electrodes  319 A and  419 C facing each other and having a capacitance between the electrodes constitute opposed electrode unit  419 Y. Electrodes  320 A and  420 C facing each other and having a capacitance between the electrodes constitute opposed electrode unit  420 Y. Electrodes  321 A and  421 C facing each other and having a capacitance between the electrodes constitute opposed electrode unit  421 Y. Electrodes  323 A and  423 C facing each other and having a capacitance between the electrodes constitute opposed electrode unit  423 Y. 
     Inertial force sensor  1004  which includes driving electrode  322 , detecting electrode  324 , and sensing electrodes  326  and  328  can detect an angular velocity about the Z-axis similarly to inertial force sensor  1001  including driving electrode  122 , detecting electrode  124 , and sensing electrodes  126 ,  128  according to Embodiment 1 shown in  FIG. 4 . 
       FIGS. 26 and 27  are sectional views of sensor element  401 . Grounding electrode  430  surrounds electrodes  414 B,  414 C,  416 B,  416 C,  418 B,  418 C,  420 B, and  420 C individually and is positioned between these electrodes. Grounding electrode  440  surrounds electrodes  417 B,  417 C,  419 B,  419 C,  421 B,  421 C,  423 B, and  423 C individually and is positioned between these electrodes. 
       FIG. 26  shows sensor element  401  when no acceleration along the X-axis is applied. Ends  1314 A and  1414 B of electrodes  314 A and  414 B directed in the same direction along the X-axis face ends  1316 A and  1416 B of electrodes  316 A and  416 B directed in the same direction along the X-axis, respectively. When no acceleration is applied, end  1314 A of electrode  314 A deviates slightly from end  1414 B of electrode  414 B in direction D 402  along the X-axis, and end  1316 A of electrode  316 A deviates slightly from end  1416 B of electrode  416 B in direction D 401  opposite to direction D 402 . Similarly, ends  1318 A and  1418 B of electrodes  318 A and  418 B directed in the same direction along the X-axis face ends  1320 A and  1420 B of electrodes  320 A and  420 B directed in the same direction along the X-axis, respectively. When no acceleration is applied, end  1318 A of electrode  318 A deviates slightly from end  1418 B of electrode  418 B in direction D 402  along the X-axis, and end  1320 A of electrode  320 A deviates slightly from end  1420 B of electrode  420 B in direction D 401 . Ends  1317 A and  1417 B of electrodes  317 A and  417 B directed in the same direction face ends  1319 A and  1419 B of electrodes  319 A and  419 B directed in the same direction, respectively. When no acceleration is applied, end  1317 A of electrode  317 A deviates slightly from end  1417 B of electrode  417 B in direction D 402 , and end  1319 A of electrode  319 A deviates slightly displaced in direction D 401 . Similarly, ends  1321 A and  1321 B of electrodes  321 A and  321 B directed in the same direction face ends  1323 A and  1323 B of electrodes  323 A and  323 B directed in the same direction, respectively. When no acceleration is applied, end  1321 A of electrode  321 A deviates slightly from end  1321 B of electrode  321 B in direction D 402 , and end  1323 A of electrode  323 A deviates slightly in direction D 401 . Electrodes  314 A and  414 B have ends  3314 A and  3414 B opposite to ends  1314 A and  1414 B along the X-axis, respectively. When no acceleration is applied, end  3314 A of electrode  314 A deviates slightly from end  3414 B of electrode  414 B in direction D 402  along the X-axis. Electrodes  316 A and  416 B have ends  3316 A and  3416 B opposite to ends  1316 A and  1416 B along the X-axis, respectively. When no acceleration is applied, end  3316 A of electrode  316 A deviates slightly from end  3416 B of electrode  416 B in direction D 401 . Electrodes  317 A and  417 B have ends  3317 A and  3417 B opposite to ends  1317 A and  1417 B along the X-axis, respectively. When no acceleration is applied, end  3317 A of electrode  317 A deviates slightly from end  3417 B of electrode  417 B in direction D 402  along the X-axis. Electrodes  319 A and  419 B have ends  3319 A and  3419 B opposite to ends  1319 A and  1419 B along the X-axis, respectively. When no acceleration is applied, end  3319 A of electrode  319 A deviates slightly from end  3419 B of electrode  419 B in direction D 401 . 
     When an acceleration along the X-axis is applied, inertial force sensor  1004  can detect the acceleration similarly to inertial force sensor  1003  according to Embodiment 3. In inertial force sensor  1004 , the direction in which electrodes  414 B,  416 B,  417 B,  418 B,  419 B,  420 B,  421 B, and  423 B deviate from electrodes  314 A,  316 A,  317 A,  318 A,  319 A,  320 A,  321 A, and  323 A, respectively, is opposite to the direction in which electrodes  314 B,  316 B,  317 B,  318 B,  319 B,  320 B,  321 B, and  323 B deviate from electrodes  314 A,  316 A,  317 A,  318 A,  319 A,  320 A,  321 A, and  323 A, respectively, of inertial force sensor  1003  according to Embodiment 3 shown in  FIG. 21 . When the acceleration is applied, the capacitances of opposed electrode units  414 X,  416 X,  417 X,  418 X,  419 X,  420 X,  421 X, and  423 X change reversely to the change of the capacitances of opposed electrode units  314 X,  316 X,  317 X,  318 X,  319 X,  320 X,  321 X, and  323 X of inertial force sensor  1003  according to Embodiment 3. Besides this, inertial force sensor  1004  can detect the acceleration along the X-axis similarly to inertial force sensor  1003 , thus providing the same effects. 
       FIG. 27  shows sensor element  401  when no acceleration along the Y-axis is applied. Ends  2314 A and  2414 C of electrodes  314 A and  414 C directed in the same direction along the Y-axis face ends  2316 A and  2416 C of electrodes  316 A and  416 C directed in the same direction along the Y-axis, respectively. When no acceleration is applied, end  2314 A of electrode  314 A deviates slightly from end  2414 C of electrode  414 C in direction D 403  along the Y-axis, and end  2316 A of electrode  316 A deviates slightly from end  2416 C of electrode  416 C in direction D 404  opposite to direction D 403 . Similarly, ends  2318 A and  2418 C of electrodes  318 A and  418 C directed in the same direction along the Y-axis respectively face ends  2320 A and  2420 C of electrodes  320 A and  420 C directed in the same direction along the Y-axis, respectively. When is no acceleration is applied, end  2318 A of electrode  318 A deviates slightly from end  2418 C of electrode  418 C in direction D 403  along the Y-axis, and end  2320 A of electrode  320 A deviates slightly from end  2420 C of electrode  420 C in direction D 404 . Ends  2317 A and  2417 C of electrodes  317 A and  417 C directed in the same direction face ends  2319 A and  2419 C of electrodes  319 A and  419 C directed in the same direction, respectively. When no acceleration is applied, end  2317 A of electrode  317 A deviates slightly from end  2417 C of electrode  417 C in direction D 403 , and end  2319 A of electrode  319 A deviates slightly from end  2317 C of electrode  317 C in direction D 404 . Similarly, ends  2321 A and  2321 C of electrodes  321 A and  321 C directed in the same direction face ends  2323 A and  2323 C of electrodes  323 A and  323 C directed in the same direction, respectively. When no acceleration is applied, end  2321 A of electrode  321 A deviates slightly displaced from end  2321 C of electrode  321 C in direction D 403 , and end  2323 A of electrode  323 A deviates slightly in direction D 404 . Electrodes  314 A and  414 C have ends  4314 A and  4414 C opposite to ends  2314 A and  2414 C along the Y-axis, respectively. When no acceleration is applied, end  3314 A of electrode  314 A deviates slightly from end  4414 C of electrode  414 C in direction D 403  along the Y-axis. Electrodes  316 A and  416 C have ends  3316 A and  4416 C opposite to ends  2316 A and  2416 C along the Y-axis, respectively. When no acceleration is applied, end  3316 A of electrode  316 A deviates slightly from end  4416 C of electrode  416 C in direction D 404 . Electrodes  317 A and  417 C have ends  3317 A and  4417 C opposite to ends  2317 A and  2417 C along the Y-axis, respectively. When no acceleration is applied, end  3317 A of electrode  317 A deviates slightly from end  4417 C of electrode  417 C in direction D 403  along the Y-axis. Electrodes  319 A and  419 C have ends  3319 A and  4419 C opposite to ends  3319 A and  4419 C along the Y-axis, respectively. When no acceleration is applied, end  3319 A of electrode  319 A deviates slightly from end  4419 C of electrode  419 C in direction D 404 . 
     When an acceleration along the Y-axis is applied, inertial force sensor  1004  can detect the acceleration similarly to inertial force sensor  1003  according to Embodiment 3, providing the same effects. 
       FIG. 28  is a plan view of the electrodes provided on substrate  305 . Lands  432  which is arranged to have the signal lines connected thereto to mount inertial force sensor  1004  are provided around sensor element  401 . Electrodes  414 B,  414 C,  416 B,  416 C,  418 B,  418 C,  420 B, and  420 C provided on surface  305 A of substrate  305  are coupled to grounding electrode  430  via capacitances C 101  to C 112 . Electrodes  414 C,  416 C,  418 C, and  420 C adjacent to each other are coupled to each other via capacitances C 121  to C 124 . Electrodes  414 B,  416 B,  418 B, and  420 B are coupled to lands  432  via capacitances C 125  to C 128 . Electrodes  414 C,  416 C,  418 C, and  420 C face electrodes  414 A,  416 A,  418 A, and  420 A which are displaced independently from each other. Lands  432  are connected to processor  461  which is outside sensor element  401 . Capacitances C 125  to C 128  may cause noise on electrodes  414 B,  416 B,  418 B, and  420 B. However, capacitances C 101  to C 112  produced by grounding electrode  430  reduce capacitances C 125  to C 128 , accordingly reducing the noise. 
       FIG. 29  is a plan view of electrodes on substrate  315 . Lands  442  which is arranged to have the signal lines connected thereto to mount inertial force sensor  1004  are provided around sensor element  401 . Electrodes  417 B,  417 C,  419 B,  419 C,  421 B,  421 C,  423 B, and  423 C provided on surface  305 A of substrate  305  are coupled to grounding electrode  430  via capacitances C 201  to C 212 . Electrodes  417 C,  419 C,  421 C, and  423 C adjacent to each other are coupled to each other via capacitances C 221  to C 224 . Electrodes  417 B,  419 B,  421 B, and  423 B are coupled to lands  442  via capacitances C 225  to C 228 . Electrodes  417 C,  419 C,  421 C, and  423 C face electrodes  417 A,  419 A,  421 A, and  423 A which are displaced independently from each other, respectively. Lands  442  are connected to processor  461  which is outside sensor element  401 . Since inertial force sensor  1004  detects the acceleration based on the capacitances between the electrodes, capacitances C 225  to C 228  may cause a noise on electrodes  417 B,  419 B,  421 B, and  423 B. However, capacitances C 201  to. C 212  produced by grounding electrode  430  can reduce capacitances C 225  to  0228 , thereby reducing the noise. Thus, inertial force sensor  1004  according to Embodiment 4 does not generate errors due to the noise, and detect the acceleration at high sensitivity accurately. 
     INDUSTRIAL APPLICABILITY 
     This inertial force sensor can detect an acceleration at high sensitivity and is suitable for various electronic devices.