Abstract:
A capacitive dynamic quantity sensor includes a semiconductor substrate, a weight, a movable electrode, and two fixed electrodes. The weight is movably supported by the semiconductor substrate. The movable electrode is integrated with the weight. The fixed electrodes are stationarily supported by the semiconductor substrate. The fixed electrodes face the movable electrode to provide a narrow gap and a wide gap and form a detection part having a capacitance. The weight and the movable electrode are displaced relative to the fixed electrodes in response to a dynamic quantity to be detected such that one of the gaps increases while the other decreases. The dynamic quantity is detected on the basis of the variation in the capacitance. One of wide gap electrode surfaces, which define the wide gap, is smaller than narrow gap electrode surfaces, which define the narrow gap, to improve sensor sensitivity.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
   This application is based on and incorporates herein by reference Japanese Patent Application No. 2002-218613 filed on Jul. 26, 2002. 

   BACKGROUND OF THE INVENTION 
   The present invention relates to a capacitive dynamic quantity sensor, a method for manufacturing the capacitive dynamic quantity sensor, and a detector including the capacitive dynamic quantity sensor. 
   For example, a capacitive semiconductor acceleration sensor shown in  FIG. 7A  is such a capacitive dynamic quantity sensor. As shown in  FIGS. 7A and 7B , in the acceleration sensor, a weight  11  is supported by anchors  13 , which are fixed to a semiconductor substrate  1 , through springs  12 . First and second comb-tooth-like movable electrodes  10   a,    10   b  are integrated with the weight  11 . As illustrated in  FIG. 7A , first and second comb-tooth-like fixed electrodes  15   a,    15   b,  which respectively face the first and second movable electrodes  10   a,    10   b,  are supported at one ends thereof by first and second electrode wiring lines  16   a,    16   b.    
   When acceleration is detected, predetermined voltages are applied between movable electrode pad  14  for the movable electrodes  10   a,    10   b  and fixed electrode pads  17   a,    17   b  for the fixed electrodes  15   a,    15   b.  With the voltages, first and second capacitances CS 1  and C 2  are formed respectively between the first movable electrodes  10   a  and the first fixed electrodes  15   a  and between the second movable electrodes  10   b  and the second fixed electrodes  15   b.  CS 1  and CS 2  are expressed by the following equation eq. 1 when no acceleration is applied,
 
 CS 1= CS 2=∈× n×L×h 1×(1 /d 1+1 /d 2)  eq. 1
 
where ∈ is dielectric constant, n is the number of each group of the movable electrodes, L is the effective electrode length, which is the length of the surfaces at which the movable and fixed electrodes face, h 1  is the electrode height, which is the height of the surfaces at which the movable and fixed electrodes face, and d 1  and d 2  are respectively the dimension of the narrow gaps between the electrodes and the dimension of the wide gaps between the electrodes. In the acceleration sensor shown in  FIG. 7A , each of the electrodes has the same effective electrode length L and the same electrode height h 1 .
 
   When the sensor is accelerated, the springs  12  deform to vary the dimensions d 1  and d 2 , or the distances d 1  and d 2  between the movable electrodes  10   a,    10   b  and the fixed electrodes  15   a,    15   b.  However, the dimension d 2  of the wide gaps is sufficiently greater than the dimension d 1  of the narrow gaps, so the first and second capacitances CS 1  and CS 2  vary with the distance variation. Therefore, the acceleration can be measured by detecting the capacitance difference ΔC, or (CS 1 −CS 2 ), between the first and second capacitances CS 1  and CS 2 . 
   Specifically, for example, if the sensor is accelerated to displace the first movable electrodes  10   a  by Δd in the direction shown by arrows in  FIGS. 7A and 7C , the dimension d 1  of the narrow gaps narrow by Δd and the wide gaps d 2  widen by Δd between the first movable electrodes  10   a  and the first fixed electrodes  15   a  to increase the first capacitance CS 1 , as shown in FIG.  7 C. On the other hand, on the cross-section taken along the line VIIC—VIIC in  FIG. 7A , the dimension d 1  of the narrow gaps widens by Δd and the dimension d 2  of the wide gaps narrows by Δd between the second movable electrodes  10   b  and the second fixed electrodes  15   b  to decrease the second capacitance CS 2 . As a result, the capacitance difference ΔC increases. 
   More specifically, when the sensor is accelerated to displace the first movable electrodes  10   a  by Δd in the direction shown by arrows in  FIGS. 7A and 7C , the narrow gaps become (d 1 −Δd) and the wide gaps become (d 2 +Δd) between the first movable electrodes  10   a  and the first fixed electrodes  15   a.  On the other hand, the narrow gaps become (d 1 +Δd) and the wide gaps become (d 2 −Δd) between the second movable electrodes  10   b  and the second fixed electrodes  15   b.  Therefore, from eq. 1, ΔC, or (CS 1 −CS 2 ), can be expressed by the following equation.
 
Δ C=∈×n×L×h 1×[{1/( d   1 −Δ d )+ 1 /( d   2 +Δ d )}−{1/( d   1 +Δ d )+1/( d   2 −Δ d )}] =∈×n×L×h   1 ×2Δ d×{ 1/( d   1   2   −Δd   2 )−1/( d   2   2   −Δd   2 )}
 
   Here, Δd is sufficiently small in comparison with d 1  and d 2 . Therefore, ΔC can be expressed by the following equation eq. 2.
 
Δ C≈∈×n×L×h   1 ×2Δ d× (1 /d   1   2 −1 /d   2   2 )  eq. 2
 
   The sensor sensitivity can be improved by increasing the variation in capacitance per unit acceleration, that is, ΔC in eq. 2. As understood from eq. 2, ΔC can be increased by sufficiently increasing d 2  in comparison with d 1 . 
   However, it is difficult to sufficiently improve the sensor sensitivity by adjusting the distances between the electrodes because the dimension d 2  of the wide gaps is limited by the dimensions of the sensor. 
   SUMMARY OF THE INVENTION 
   The present invention has been made in view of the above aspects with an object to provide a capacitive dynamic quantity sensor having sensitivity higher than the proposed sensor, a method for manufacturing the capacitive dynamic quantity sensor, and a detector including the capacitive dynamic quantity sensor. 
   A capacitive dynamic quantity sensor according to the present invention includes a semiconductor substrate, a weight, a movable electrode, and two fixed electrodes. The weight is movably supported by the semiconductor substrate. The movable electrode is integrated with the weight. The fixed electrodes are stationarily supported by the semiconductor substrate. The fixed electrodes face the movable electrode to provide a narrow gap and a wide gap and form a detection part having a capacitance. The weight and the movable electrode are displaced relative to the fixed electrodes in response to a dynamic quantity to be detected such that one of the gaps increases while the other decreases. The dynamic quantity is detected on the basis of the variation in the capacitance. One of wide gap electrode surfaces, which define the wide gap, is smaller than narrow gap electrode surfaces, which define the narrow gap, to improve sensor sensitivity. 
   The above sensor can be incorporated into a detector with a detection circuit, which outputs a detection signal when the capacitance varies due to the dynamic quantity to be detected. 
   The above sensor can be manufactured by forming the movable electrode and the two fixed electrodes on the semiconductor substrate such that one of the wide gap electrode surfaces becomes smaller than the narrow gap electrode surfaces. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above and other objects, features and advantages of the present invention will become more apparent from the following detailed description made with reference to the accompanying drawings. In the drawings: 
       FIG. 1A  is a schematic plan view of a capacitive semiconductor acceleration sensor according to a first embodiment of the present invention; 
       FIG. 1B  is a schematic cross-sectional view of the sensor in  FIG. 1A  taken along the line IB—IB; 
       FIGS. 2A  to  2 C are schematic cross-sectional views at the cross-section corresponding to that shown in  FIG. 1B , showing a method for manufacturing the sensor of  FIG. 1A ; 
       FIG. 3  is an equivalent circuit diagram for a detection circuit for the sensor of  FIG. 1A ; 
       FIG. 4A  is a partial schematic cross-sectional view of the sensor in  FIG. 1A  taken along the line IB—IB, showing the state that the sensor is not accelerated; 
       FIG. 4B  is a partial schematic cross-sectional view of the sensor in  FIG. 1A  taken along the line IB—IB, showing the state that the sensor is accelerated; 
       FIG. 5A  is a partial schematic cross-sectional view of the sensor in  FIG. 1A  taken along the line VA—VA, showing the state that the sensor is not accelerated; 
       FIG. 5B  is a partial schematic cross-sectional view of the sensor in  FIG. 1A  taken along the line VA—VA, showing the state that the sensor is accelerated; 
       FIG. 6  is a graph that shows the correlation between the capacitance change rate ΔC/ΔC 0  and d 2   2 /d 1   2 ; 
       FIG. 7A  is a schematic plan view of a proposed semiconductor acceleration sensor; 
       FIG. 7B  is a schematic partial cross-sectional view of the sensor in  FIG. 7A  taken along the line VIIB—VIIB, showing the state that no acceleration is applied; and 
       FIG. 7C  is a schematic partial cross-sectional view of the sensor in  FIG. 7A  taken along the line VIIB—VIIB, showing the state that acceleration is applied. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   The present invention will be described in detail with reference to various embodiments. 
   First Embodiment 
   As shown in  FIGS. 1A and 1B , a semiconductor acceleration sensor according to a first embodiment includes a substrate  4 , which has a Silicon-On-Insulator (SOI) structure. The substrate  4  is composed of a semiconductor substrate  1 , or a first semiconductor layer  1 , a second semiconductor layer  2 , and an insulating layer  3 , which is a sacrificial layer made of, for example, silicon oxide. The semiconductor layers  1 ,  2  are made of single crystal silicon. The sensor of  FIGS. 1A and 1B  includes a sensing portion  5 , which has been formed by well-known micromachining technology using semiconductor process technology. 
   As shown in  FIG. 1A , the sensing portion  5  includes a movable unit  6 , first and second fixed units  7 ,  8 , and peripheral portion  9 , which surrounds the movable unit  6  and the fixed units  7 ,  8 . There are predetermined clearances between the movable unit  6 , the fixed units  7 ,  8 , and the peripheral portion  9  to insulate them from one another. 
   The movable unit  6  includes four first comb-tooth-shaped movable electrodes  10   a,  four second comb-tooth-shaped movable electrodes  10   b,  a weight  11 , two rectangular frame-shaped springs  12 , two movable electrode anchors  13 , and a movable electrode pad  14 . The springs  12  are joined to the weight  11 , which is a mass portion on which acceleration acts, and the movable electrode anchors  13 , which are connected to the insulating layer  3 . The movable electrodes  10   a,    10   b  are integrated with the weight  11  to extend from two sides of the eight  11  orthogonally to the longitudinal direction of the weight  11 . The movable electrodes  10   a,    10   b,  the weight  11 , and the springs  12  are spaced apart form the insulating layer  3 . The structure is formed by etching the second semiconductor layer  2  from its surface and consecutively selectively etching the sidewalls of the second semiconductor layer  2  in the proximity of the surface of the insulating layer  3  using selective plasma etching. 
   Each of the springs  12  functions as a spring to expand and shrink along the directions orthogonal to the longitudinal direction thereof. Therefore, the weight  11  and the movable electrodes  10   a,    10   b  move in the direction shown by the arrow in  FIG. 1A  when the sensor is accelerated in that direction and moves back to the original position when the acceleration becomes zero. The movable electrode pad  14  is connected to one of the movable electrode anchors  13  at a predetermined position. The movable electrode pad  14  is used for electrically connecting the movable electrodes  10   a,    10   b  to a C-V converter circuit, which is described later. 
   The first and second fixed units  7 ,  8  respectively include: four comb-tooth-shaped first fixed electrodes  15   a  and four comb-tooth-shaped second fixed electrodes  15   b;  first and second fixed electrode wiring lines  16   a,    16   b;  first and second fixed electrode anchors  18   a,    18   b;  and first and second fixed electrode pads  17   a,    17   b.  The first and second fixed electrode pads  17   a,    17   b  are respectively located on the first and second fixed electrode anchors  18   a,    18   b  for electrically connecting the fixed electrodes  15   a,    15   b  to the C-V converter circuit. The fixed electrode wiring lines  16   a,    16   b  are arranged to be parallel to the longitudinal directions of the weight  11 . The first and second fixed electrodes  15   a,    15   b  respectively extend from the first and second fixed electrode wiring lines  16   a,    16   b  to face respectively parallel the first and second movable electrodes  10   a,    10   b,  which extend from the two side of the weight  11 , such that a predetermined detection gap is formed between the fixed electrodes  15   a,    15   b  and the movable electrodes  10   a,    10   b.    
   The fixed electrode wiring lines  16   a,    16   b  and the fixed electrode anchors  18   a,    18   b  are fixed to the semiconductor substrate  1  with the insulating layer  3  therebetween. The first and second fixed electrodes  15   a,    15   b  are supported at one ends thereof by the first and second fixed electrode wiring lines  16   a,    16   b.  The first movable electrodes  10   a  and the first fixed electrodes  15   a  form a first detection part  19  that provides a first capacitance C 1 , and the second movable electrodes  10   b  and the second fixed electrodes  15   b  form a second detection part  20  that provides a second capacitance CS 2 . 
   As shown in  FIG. 1A , the first movable electrodes  10   a  and the first fixed electrodes  15   a  interleave with each other such that narrow gaps having a dimension of d 1  and wide gaps having a dimension of d 2  are alternately arranged between the first movable electrodes  10   a  and the first fixed electrodes  15   a  when no acceleration is applied. In the same manner, the second movable electrodes  10   b  and the second fixed electrodes  15   b  interleave with each other such that narrow gaps having a dimension of d 1  and wide gaps having a dimension of d 2  are alternately arranged between the second movable electrodes  10   b  and the second fixed electrodes  15   b.    
   As shown in  FIG. 1A , the positional relation between the first movable electrodes  10   a  and the first fixed electrodes  15   a  is different from that between the second movable electrodes  10   b  and the second fixed electrodes  15   b.  More specifically, as illustrated in  FIG. 1A , the narrow gaps of the first detection part  19  and the narrow gaps of the second detection part  20  are on the opposite sides of the axes that are defined by each of the first movable electrodes  10   a  and the corresponding second movable electrode  10   b.  Therefore, for example, if the sensor is accelerated to displace the movable electrodes  10   a,    10   b  in the direction shown by the arrow in  FIG. 1A , the dimension d 1  of the narrow gaps in the first detection part  19  decreases, and the dimension d 2  of the wide gaps in the first detection part increases. On the other hand, the dimension d 1  of the narrow gaps in the second detection part  20  increases, and the dimension d 2  of the wide gaps in the second detection part decreases. 
   Next, a method for manufacturing the semiconductor acceleration sensor of  FIGS. 1A and 1B  will be briefly explained. First, an SOI substrate  4  is prepared, as shown in FIG.  2 A. The substrate  4  is composed of a semiconductor substrate  1 , or a first semiconductor layer  1 , a second semiconductor layer  2 , and an insulating layer  3 , which is made of silicon oxide and located between the first and second semiconductor layers  1 ,  2 . The semiconductor layers  1 ,  2  are made of single crystal silicon. Although a plurality of sensors can be formed from an SOI substrate  4 , the explanation will be made on only one sensor. 
   Then, although not shown in the figure, a movable electrode pad  14  and first and second fixed electrode pads  17   a,    17   b  are formed on the second semiconductor layer  2 . The pads  14 ,  17   a,    17   b  can be formed, for example, by: depositing a highly conductive metal on the entire surface of the second semiconductor layer  2  by a predetermined thickness; and patterning into predetermined shapes using photolithography and etching. Metals such as copper (Cu), aluminum (Al), gold (Au), and silver (Ag) may be used for the pads  14 ,  17   a,    17   b.    
   Then, as shown in  FIG. 2B , an etching mask  21  is formed for forming movable and fixed electrodes  10   a,    10   b,    15   a,    15   b.  Specifically, an etching mask  21  that has openings at the positions where the gaps between the electrodes  10   a,    10   b,    15   a,    15   b  are to be formed is formed in a predetermined area on the second semiconductor layer  2  by photolithography and etching. For example, a silicon nitride film, a silicon oxide film, a metal film, and a photoresist film may be used as the etching mask  21 . 
   After the etching mask  21  is formed, the second semiconductor layer  2  is selectively etched by, for example, plasma etching through the openings of the etching mask  21 , as shown in FIG.  2 C. With the etching, the second semiconductor layer  2  is partially removed below the openings to expose the insulating layer  3 . At the same time, the second semiconductor layer  2  is also removed at the portions located below the electrodes  10   a,    10   b,    15   a,    15   b.  With the etching, a movable unit  6  is formed, and the movable electrodes  10   a,    10   b,  the weight  11 , and the springs  12  of the movable unit  6  become movable. In the above etching, the wide gap electrode surfaces, or the surfaces of the electrodes  10   a,    10   b,    15   a,    15   b  that define wide gaps, are machined such that the electrode surfaces become smaller than the small gap electrode surfaces, or the surfaces of the electrodes  10   a,    10   b,    15   a,    15   b  that define small gaps. 
   Then, the etching mask  21  is removed, and the SOI substrate  4  diced into a plurality of sensor chips to complete the semiconductor acceleration sensor of  FIGS. 1A and 1B . In the above explanation, although only the cross-section taken along line IB—IB of  FIG. 1A  was used, the portion shown by the cross-section taken along the line VA—VA of  FIG. 1A  is formed in the same manner. 
     FIG. 3  is an equivalent circuit diagram for a detection circuit for the sensor of  FIG. 1A , which is included in a detector having a sensor of FIG.  1 A. As shown in  FIG. 3 , the detection circuit includes a C-V converter circuit  22 , or a switched capacitor circuit  22 . The C-V converter circuit  22  converts the capacitance difference (CS 1 −CS 2 ) between the first and second capacitances CS 1  and CS 2  into voltage difference and outputs the voltage difference. The C-V converter circuit  22  includes an operational amplifier  23 , a capacitor  24  having a capacitance Cf, and a switch  25 . 
   The inverting input terminal of the operational amplifier  23  is electrically connected to the movable electrodes  10   a,    10   b  through the movable electrode pad  14 . The capacitor  24  and the switch  25  are connected in parallel between the inverting input terminal and the output terminal of the operational amplifier  23 . A voltage of Vcc/2 is applied from a power source, which is not illustrated in the figure, to the non-inverting input terminal of the operational amplifier  23 . 
   The detection circuit also includes a control circuit, which is not illustrated in the figure. The control circuit inputs a first carrier wave, which has a constant amplitude of Vcc and alternates periodically, from the first fixed electrode pad  17   a  to the first fixed electrodes  15   a  of the first detection part  19 . At the same time, the control circuit inputs a second carrier wave, which has a constant amplitude of Vcc, the phase of which is shifted by 180° from the first carrier wave, from the second fixed electrode pad  17   b  to the second fixed electrodes  15   b  of the second detection part  20 . 
   Therefore, when no acceleration is applied, each potential of the detection parts  19 ,  20  becomes Vcc/2 because the first capacitance CS 1  of the first detection part  19  is substantially equal to the second capacitance CS 2  of the second detection part  20 . The switch  25  in the C-V converter circuit  22  is turned on and off with predetermined timing that is synchronized with the carrier waves. When the switch  25  is off, acceleration is detected. The C-V converter circuit  22  outputs a voltage of Vout in response to the acceleration. Vout is expressed by the following equation eq. 3.
 
 V out=( CS   1   −CS   2 )× Vcc/Cf   eq. 3
 
   When the sensor is accelerated, the ratio of the first capacitance CS 1  to the second capacitance CS 2  varies and Vout, which is proportionate to the capacitive difference (CS 1 −CS 2 ) as understood by eq. 3, is outputted. The outputted voltage is processed by an amplification circuit or low-pass filter, which is not illustrated in the figure, and detected as an acceleration detection signal. 
   Although a voltage of Vcc/2 is applied from a power source, which is not illustrated in the figure, to the non-inverting input terminal of the operational amplifier  23 , a voltage of V 1 , which is not equal to Vcc/2, may be provided in order to create a self-diagnosis function, in which the movable electrode  10   a,    10   b  are forcedly displaced by switching Vcc/2 to V 1  using a switch, which is not illustrated in the figure, with predetermined timing that is synchronized with the carrier waves. 
   As shown in  FIGS. 7A and 7B , the proposed acceleration sensor includes a first detection part  19 , which is made up of the first movable electrodes  10   a  and the first fixed electrodes  15   a,  and a second detection part  20 , which is made up of the second movable electrodes  10   b  and the second fixed electrodes  15   b.  The first movable electrodes  10   a  and the first fixed electrodes  15   a  interleave with each other such that narrow gaps having a dimension of d 1  and wide gaps having a dimension of d 2  are alternately arranged between the first movable electrodes  10   a  and the first fixed electrodes  15   a.  In the same manner, the second movable electrodes  10   b  and the second fixed electrodes  15   b  interleave with each other such that narrow gaps having a dimension of d 1  and wide gaps having a dimension of d 2  are alternately arranged between the second movable electrodes  10   b  and the second fixed electrodes  15   b.    
   In the proposed sensor of  FIGS. 7A and 7B , if each of the electrodes has the same effective electrode length L, which is the length of the surfaces at which the movable and fixed electrodes face, and the same electrode height h 1 , which is the height of the surfaces at which the movable and fixed electrodes face, the first and second capacitances CS 1  and CS 2 , which are formed respectively between the first movable electrodes  10   a  and the first fixed electrodes  15   a  and between the second movable electrodes  10   b  and the second fixed electrodes  15   b,  are expressed by the following equation eq. 4,
 
 CS   1   =CS   2   =∈×n×L×h   1 ×(1 /d   1 + 1   /d   2 )  eq. 4
 
where ∈ is dielectric constant and n is the number of each group of the movable electrodes. When no acceleration is applied, the capacitance difference ΔC, or (CS 1 −CS 2 ), between the first and second capacitances CS 1  and CS 2  is zero.
 
   When the proposed sensor is accelerated, the springs  12  deform to vary the dimensions d 1  and d 2 . If the proposed sensor is accelerated to displace the first movable electrodes  10   a  by Δd in the direction shown by arrows in  FIGS. 7A and 7C , the narrow gaps become (d 1 −Δd) and the wide gaps become (d 2 −Δd) in the first detection part  19  to increase the first capacitance CS 1 . On the other hand, the narrow gaps become (d 1 +Δd) and the wide gaps become (d 2 −Δd) in the second detection part  20  to decrease the second capacitance CS 2 . As a result, the capacitance difference ΔC 0  increases. 
   From eq. 4, ΔC can be expressed by the following equation.
 
Δ C   0   =∈×n×L×h   1 ×[{ 1 /( d   1   −Δd )+1/( d   2 +Δ d )}−{1/( d   1 + Δd )+1/( d   2 −Δ d )}] =∈×n×L×h   1 ×2Δ d×{ 1/( d   1   2   −Δd   2 )−1/( d   2   2   −Δd   2 )}
 
   Here, Δd is sufficiently small in comparison with d 1  and d 2 . Therefore, ΔC 0  can be expressed by the following equation eq. 5.
 
Δ C   0 ≈∈× n×L×h   1 ×2Δ d× (1 /d   1   2 −1 /d   2   2 )  eq. 5
 
   Therefore, the sensor sensitivity, that is, ΔC in eq. 5, can be increased by increasing the value in the parenthesis of eq. 5. The value in the parenthesis of eq. 5 can be increased by sufficiently increasing d 2  in comparison with d 1 . However, it is difficult to sufficiently increase the dimension d 2  of the wide gaps because the dimension d 2  is limited by the dimensions of the sensor. 
   Here, the capacitance formed between a pair of electrodes is proportionate to the area of the electrodes and inversely proportionate to the distance between the electrodes. Therefore, it is possible to increase the variations of the capacitances CS 1  and CS 2  without increasing the dimension d 2  of the wide gaps by decreasing the total area of the electrode surfaces that define the wide gaps in comparison with that defining the narrow gaps. The total area is the sum of the product of the effective electrode length L and the electrode height h 1 , that is, (n×L×h 1 ). 
   Therefore, when the effective electrode length L is constant, it is possible to increase the variations of the capacitances CS 1  and CS 2  by decreasing the electrode height h 1  of the electrode surfaces that define the wide gaps. As a result, the sensor sensitivity can be improved by increasing the variations of the capacitances CS 1  and CS 2 , which correspond to the movement of the movable unit  6 , in the detection parts  19 ,  20  and acquiring the signal that correspond to the difference between the capacitances CS 1  and CS 2 , which vary in the opposite direction, using the C-V converter circuit  22 . 
   As described above, in this embodiment, the sensor sensitivity can be improved by differentiating the electrode height h 1  of the electrode surfaces that define the narrow gaps and the electrode height h 2  of the electrode surfaces that define the wide gaps. 
   As shown in  FIGS. 4A and 5A , when the electrode surfaces that define the wide gaps between the electrodes  10   a,    15   a  of the first detection part  19  and those between the electrodes  10   b,    15   b  of the second detection part  19  have an electrode height of h 2 , the first and second capacitances CS 1  and CS 2  of the first and second detection parts  19 ,  20  are expressed by the following equation eq. 6.
 
 CS   1   =CS   2   =Å×n×L×h   1 ×( h   1   /d   1 + h   2   /d   2 )  eq. 6
 
   In this embodiment, the two electrode surfaces that define each of the wide gaps have an electrode height of h 2 . However, substantially the same effect can be acquired even if only one of the two electrode surfaces has an electrode height of h 2 . 
   For example, when the sensor is accelerated to displace the first movable electrodes  10   a  by Δd in the direction shown by arrows in  FIGS. 4B and 5B , the narrow gaps become (d 1 −Δd) and the wide gaps become (d 2 −Δd) in the first detection part  19  to increase the first capacitance CS 1 . On the other hand, the narrow gaps become (d 1 +Δd) and the wide gaps become (d 2 −Δd) in the second detection part  20  to decrease the second capacitance CS 2 . As a result, the capacitance difference ΔC increases. 
   From eq. 6, ΔC can be expressed by the following equation.
 
Δ C=∈×n×L×h   1 ×[{ h   1 /( d   1 − Δd )+ h   2 /( d   2 +Δ d )}− {h   1 /( d   1 +Δ d )+ h   2 /( d   2 −Δ d )}] =∈×n×L×h   1 ×2Δ d×{h   1 /( d   1   2   −Δd   2 ) − h   2 /( d   2   2   −Δd   2 )}
 
   Here, Δd is sufficiently small in comparison with d 1  and d 2 . Therefore, ΔC can be expressed by the following equation eq. 7.
 
Δ C≈∈×n×L×h   1 ×2Δ d× ( h   1   /d   1   2   −h   2   /d   2   2 )  eq. 7
 
   As understood by comparing eq. 5 with eq. 7, the sensor sensitivity can be increased by machining the electrodes  10   a,    10   b,    15   a,    15   b  to satisfy the following equation eq. 8.
 
h 1 &gt;h 2   eq. 8
 
   The electrodes  10   a,    10   b,    15   a,    15   b  can be machined to satisfy the equation eq. 8, for example, by plasma etching. More specifically, the dimension d 1  of the narrow gaps is set to generate a predetermined micro loading effect when the plasma etching is implemented. Due to the micro loading effect, the etching rate of the second semiconductor layer  2  is slower at the narrow gaps than at the wide gaps. Therefore, when the narrow gaps are completed by the etching, the second semiconductor layer  2  is overetched at the wide gaps to form notches on the sidewalls that define the wide gaps, as shown in FIG.  2 C. As a result, the electrodes  10   a,    10   b,    15   a,    15   b  can be machined to satisfy the equation eq. 8. 
   From the equations eq. 5 and eq. 7, the capacitance change rate ΔC/ΔC 0  is expressed by the following equation eq. 9,
 
 ΔC/ΔC =( X−h   2   /h   1 )/( X− 1)  eq. 9
 
where  X=d   2   2   /d   1   2 .
 
     FIG. 6  is a graph that shows the correlation between the capacitance change rate ΔC/ΔC 0  and d 2   2 /d 1   2 . In  FIG. 6 , symbols ∘, ▴, and □ represent the correlation when h 2 /h 1 =0.25, the correlation when h 2 /h 1 =0.5, and the correlation when h 2 /h 1 =0.75, respectively. The solid line without any symbol represents the correlation when h 2 /h 1 =1.0, that is, when h 2 =h 1 . As understood from  FIG. 6 , the sensor sensitivity can be increased in comparison with the proposed sensor of  FIG. 7A  by making the electrode height h 2  of the wide gap electrode surfaces smaller than the electrode height h 1  of the narrow gap electrode surfaces to increase the capacitance change rate ΔC/ΔC 0 . 
   As described above, in the semiconductor acceleration sensor according to this embodiment, the electrode height h 2  of the wide gap electrode surfaces is smaller than the electrode height h 1  of the small gap electrode surfaces to increase the capacitance change rate ΔC/ΔC 0 . With the structure, the capacitance difference ΔC becomes greater than the capacitance difference ΔC 0  of the proposed sensor, so it is possible to increase the sensor sensitivity. 
   Other Embodiments 
   In the first embodiment, the sensor sensitivity is improved by reducing the electrode height h 2  of the electrode surfaces that define the wide gaps. However, the sensor sensitivity may be improved by reducing the effective electrode length L of the electrode surfaces that define the wide gaps. Alternatively, the electrode height h 2  and the effective electrode length L may be reduced at the same time. 
   In the first embodiment, all the electrode surfaces that define the wide gaps have the same electrode height h 2 . However, it is not necessary that all the electrode surfaces that define the wide gaps should have the same electrode height h 2  as long as at least one electrode surface that defines one wide gap has the electrode height h 2 . 
   The semiconductor acceleration sensor of  FIGS. 1A and 1B  is manufactured by etching the second semiconductor layer  2  from the surface thereof. However, the present invention can be applied to a semiconductor sensor, the diaphragm such as a movable electrode of which is formed by etching the first semiconductor layer  1  of the sensor from its surface, or from its non-insulating-layer side.