Abstract:
Temperature compensation is performed using a computation program for temperature compensation, a computation processing, and a sensor. Deformation in a diaphragm caused by a pressure change due to the temperature of the gas in a cavity is cancelled out, and deformation of the diaphragm is minimized within the target temperature range, thereby allowing an optimum temperature compensation to be performed. The temperature compensation in a capacitance-type sensor executes calculation steps which include including a calculation step (S 17 ) of acquiring the amount of change ΔC′ in capacitance. A parameter ΔC′ is obtained, through which it is possible to determine the degree of compensation for the deformation in the diaphragm section caused by a pressure change due to the temperature changes of the gas in the hermetically sealed space.

Description:
TECHNICAL FIELD 
       [0001]    The present invention relates to a method for temperature compensation in a sensor, a computation program for the method for temperature compensation, a computation processing device carrying out a computation process of the computation program, and a sensor that is subjected to the temperature compensation. 
       BACKGROUND ART 
       [0002]    A semiconductor pressure sensor conventionally includes a micro-cavity and a thin diaphragm that covers a surface of the micro-cavity, and serves as a pressure gauge by measuring a change in a resistance formed on a surface of the diaphragm resulting from deformation of the diaphragm caused by external pressure, or with another electrode provided on the opposite pole, measuring a change in the capacitance between the diaphragm and the counter electrode. 
         [0003]    In a pressure sensor configured as described above, in cases where the inside of the cavity is vacuumed and sealed, the deformation of the diaphragm is caused by a difference between outside pressure and vacuum pressure. That is, the pressure sensor corresponds to an absolute pressure sensor. On the other hand, in cases where a gas of a certain pressure is sealed in the cavity, the deformation of the diaphragm is caused by a difference between the outside pressure and the pressure of the gas in the cavity. That is, the pressure sensor is a relative pressure sensor. Even though it suffers from difficulty in keeping the inside of the cavity in vacuum, the absolute pressure sensor with the inside of the cavity vacuumed and sealed advantageously facilitates temperature compensation for a pressure sensor because the effect of the temperature-dependent contraction of the internal gas is negligible. On the other hand, since the inside of the cavity is sealed in vacuum, the diaphragm is already significantly deformed under an outside pressure of, for example, 1 atm. Thus, for the pressure sensor used at about 1 atm, it is disadvantageously difficult to use a thinner diaphragm to increase pressure sensitivity. 
         [0004]    On the other hand, as an example of the relative pressure sensor, a capacitive pressure sensor is well-known which has a diaphragm portion that is deformable depending on pressure, which is a type of physical quantity, as typified by Patent Literature 1. Patent Literature 1 discloses a capacitive pressure sensor including a sensor chip having a first substrate with an electrode portion formed thereon and a second substrate with a diaphragm portion that is deformable depending on pressure formed thereon, a cavity portion formed in such a way that the diaphragm portion is associated with the electrode portion so as to face each other via a gap, and a sealing material externally sealing the cavity portion, the first substrate and the second substrate being bonded together, a gap width of the gap being changed depending on a difference between a pressure to be measured applied to the diaphragm portion and a pressure in the cavity portion so that the pressure difference is detected based on a change in the capacitance between the diaphragm portion and the electrode portion caused by the change in the gap width, wherein the capacitive pressure sensor further has a closure member that closes an inside of the cavity portion. 
       CITATION LIST 
     Patent Literature 
       [0000]    
       
         [Patent Literature 1] Japanese Patent Laid-Open No. 10-19709 
       
     
       SUMMARY OF INVENTION 
     Technical Problem 
       [0006]    The relative pressure sensor has an advantage in particular when outside air of about 1 atm is to be measured with a gas of about 1 atm sealed in the cavity. In this case, since the difference in pressure between the sealed gas and the outside air is small and the deformation of the diaphragm is insignificant, a thinner diaphragm can be provided, enabling an increase in sensitivity at about 1 atm. However, disadvantageously, since a gas is sealed in the cavity, a change in the temperature in the cavity varies the internal pressure, hindering deformation associated with the temperature of the diaphragm from being compensated for, as defined by the combined gas law. 
         [0007]    Thus, an object of the present invention is to provide a method for temperature compensation in a sensor, a computation program for the method for temperature compensation, a computation processing device carrying out a computation process of the computation program, and a sensor in which optimum temperature compensation can be achieved by cancelling out deformation of a diaphragm caused by a change in pressure associated with the temperature of a gas in the cavity (thermal expansion of the gas sealed in the cavity) to suppress the deformation of the diaphragm within an intended temperature range. 
       Solution to Problem 
       [0008]    (1) The present invention provides a method for temperature compensation in a sensor including a substrate with a first electrode portion formed on one surface, a conductive portion formed on the one surface of the substrate via an insulator layer, a diaphragm portion formed on a surface of the conductive portion opposite to the surface of the conductive portion on which the insulator layer is formed, the diaphragm portion being deformable depending on pressure, and a temperature compensation member formed on a surface of the diaphragm portion opposite to the surface of the diaphragm portion on which the conductive portion is formed, the sensor internally having a closed space, a part of the closed space being formed along an inner circumferential surface of the conductive portion and the surface of the diaphragm portion on which the conductive portion is formed, wherein the temperature compensation member compensates for deformation of the diaphragm portion caused by thermal expansion of a gas sealed in the closed space. 
         [0009]    The configuration in (1) can achieve optimum temperature compensation by cancelling out the deformation of the diaphragm portion caused by a change in pressure associated with the temperature of the gas in the closed space (thermal expansion of the gas sealed in the closed space) to suppress the deformation of the diaphragm portion within an intended temperature range. 
         [0010]    Moreover, the configuration in (1) carries out effective temperature compensation to allow a sensor with a thin diaphragm to be designed and produced, thus enabling an increase in the sensitivity of the sensor. 
         [0011]    The “compensation for the deformation of the diaphragm portion” in the present invention includes completely zeroing the amount of deformation of the diaphragm portion and approximating the amount of deformation of the diaphragm portion to zero. 
         [0012]    (2) In the method for temperature compensation in the sensor in (1), preferably, the sensor is configured as a capacitive sensor including the substrate, the ring-like conductive portion having an inner diameter of 2R 2  and an outer diameter of 2R 3 , the diaphragm portion formed on the surface of the conductive portion opposite to the surface of the conductive portion on which the insulator layer is formed, the diaphragm portion being shaped like a circular plate that is deformable depending on pressure and having an outer diameter of 2R 3 , the temperature compensation member being a ring-shaped temperature compensation ring that has an inner diameter of 2R 1  and an outer diameter of 2R 3 , and a part of the closed space being formed by the inner circumferential surface of the conductive portion and the surface of the diaphragm portion on which the conductive portion is formed, and the method includes a computation step (1) of dividing, based on Timoshenko&#39;s symmetric circular plate theory, a composite circular plate configured such that center axes of the conductive portion, the diaphragm portion, and the temperature compensation ring align with one another into a first segment including a portion with a radius of 0 to R 1  based on the center axis of the diaphragm portion, a second segment including a portion with a radius of R 1  to R 2  based on the center axes of the diaphragm portion and the temperature compensation ring, and a third segment including a portion with a radius of R 2  to R 3  based on the center axes of the conductive portion, the diaphragm portion, and the temperature compensation ring, 
         [0013]    a computation step (2) of determining, based on Kirchhoff&#39;s circular plate theory, strains ∈ 0   rr  and ∈ 0   θθ  of a reference plane (z=0) in a stacking direction of the first to third segments (a direction of a Z axis) shown below in Formulae (5) and (6), using Formulae (1) to (4) shown below and representing relations between strains ∈ rr  and ∈ θθ  and displacements κ r  and κ θ , in a radial direction (a direction of an r axis) and a circumferential direction (θ), 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     1 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     ɛ 
                     rr 
                   
                   = 
                   
                     
                       ɛ 
                       rr 
                       0 
                     
                     + 
                     
                       z 
                        
                       
                           
                       
                        
                       
                         κ 
                         r 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     2 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     ɛ 
                     θθ 
                   
                   = 
                   
                     
                       ɛ 
                       θθ 
                       0 
                     
                     + 
                     
                       z 
                        
                       
                           
                       
                        
                       
                         κ 
                         θ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     3 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     κ 
                     r 
                   
                   = 
                   
                     
                       
                         - 
                         
                           
                              
                             2 
                           
                            
                           ω 
                         
                       
                        
                       
                         / 
                       
                        
                       
                          
                         
                           r 
                           2 
                         
                       
                     
                     = 
                     
                       
                         - 
                         
                            
                           θ 
                         
                       
                        
                       
                         / 
                       
                        
                       
                          
                         r 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     4 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     κ 
                     θ 
                   
                   = 
                   
                     
                       
                         - 
                         
                           ( 
                           
                             1 
                             / 
                             r 
                           
                           ) 
                         
                       
                        
                       
                         ( 
                         
                           
                              
                             ω 
                           
                            
                           
                             / 
                           
                            
                           
                              
                             r 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       - 
                       
                         ( 
                         
                           θ 
                            
                           
                             / 
                           
                            
                           r 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     5 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     ɛ 
                     rr 
                     0 
                   
                   = 
                   
                     
                        
                       
                         u 
                         0 
                       
                     
                     
                        
                       r 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     6 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     ɛ 
                     θθ 
                     0 
                   
                   = 
                   
                     
                       u 
                       0 
                     
                     r 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0014]    a computation step (3) of inputting Young&#39;s modulus E and Poisson&#39;s ratio ν to Formula (7) shown below to determine a matrix [Q], 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     7 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     [ 
                     Q 
                     ] 
                   
                   = 
                   
                     
                       E 
                       
                         1 
                         - 
                         
                           v 
                           2 
                         
                       
                     
                      
                     
                       { 
                       
                         
                           
                             1 
                           
                           
                             v 
                           
                         
                         
                           
                             v 
                           
                           
                             1 
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0015]    a computation step (4) of inputting the matrix [Q], the strains ∈ 0   rr  and ∈ 0   θθ , the displacements κ r  and κ θ , a coefficient of thermal expansion α, and a temperature difference ΔT (a difference between a reference temperature T 0  in an initial state during compensation for deformation of the diaphragm portion and a temperature T 1  resulting from a change) to a constitutive equation for stress on a linearly elastic symmetric circular plate with traverse isotropy shown below in Formula (8) to determine a stress σ rr  in the radial direction (the direction of the r axis) and a stress σ θθ  in the circumferential direction (θ), 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     8 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     { 
                     
                       
                         
                           
                             σ 
                             rr 
                           
                         
                       
                       
                         
                           
                             σ 
                             θθ 
                           
                         
                       
                     
                     } 
                   
                   = 
                   
                     
                       [ 
                       Q 
                       ] 
                     
                      
                     
                       ( 
                       
                         
                           { 
                           
                             
                               
                                 
                                   ɛ 
                                   rr 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   ɛ 
                                   θθ 
                                   0 
                                 
                               
                             
                           
                           } 
                         
                         + 
                         
                           Z 
                            
                           
                             { 
                             
                               
                                 
                                   
                                     κ 
                                     r 
                                   
                                 
                               
                               
                                 
                                   
                                     κ 
                                     θ 
                                   
                                 
                               
                             
                             } 
                           
                         
                         - 
                         
                           { 
                           
                             
                               
                                 
                                   αΔ 
                                    
                                   
                                       
                                   
                                    
                                   T 
                                 
                               
                             
                             
                               
                                 
                                   αΔ 
                                    
                                   
                                       
                                   
                                    
                                   T 
                                 
                               
                             
                           
                           } 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0016]    a computation step (5) of inputting the matrix [Q] to Formulae (9) to (11) shown below to compute matrixes [A], [B], and [D], 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     9 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     [ 
                     A 
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               A 
                               11 
                             
                           
                           
                             
                               A 
                               12 
                             
                           
                         
                         
                           
                             
                               A 
                               21 
                             
                           
                           
                             
                               A 
                               22 
                             
                           
                         
                       
                       ] 
                     
                     = 
                     
                       
                         ∫ 
                         
                           z 
                           1 
                         
                         
                           z 
                           2 
                         
                       
                        
                       
                         
                           [ 
                           Q 
                           ] 
                         
                          
                         
                             
                         
                          
                         
                            
                           z 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     10 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     [ 
                     B 
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               B 
                               11 
                             
                           
                           
                             
                               B 
                               12 
                             
                           
                         
                         
                           
                             
                               B 
                               21 
                             
                           
                           
                             
                               B 
                               22 
                             
                           
                         
                       
                       ] 
                     
                     = 
                     
                       
                         ∫ 
                         
                           z 
                           1 
                         
                         
                           z 
                           2 
                         
                       
                        
                       
                         
                           [ 
                           Q 
                           ] 
                         
                          
                         z 
                          
                         
                             
                         
                          
                         
                            
                           z 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     11 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     [ 
                     D 
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               D 
                               11 
                             
                           
                           
                             
                               D 
                               12 
                             
                           
                         
                         
                           
                             
                               D 
                               21 
                             
                           
                           
                             
                               D 
                               22 
                             
                           
                         
                       
                       ] 
                     
                     = 
                     
                       
                         ∫ 
                         
                           z 
                           1 
                         
                         
                           z 
                           2 
                         
                       
                        
                       
                         
                           [ 
                           Q 
                           ] 
                         
                          
                         
                           z 
                           2 
                         
                          
                         
                             
                         
                          
                         
                            
                           z 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0017]    a computation step (6) of inputting the matrix [Q], the coefficient of thermal expansion α, and the temperature difference ΔT (the difference between the reference temperature T 0  in the initial state during the compensation for the deformation of the diaphragm portion and the temperature T 1  resulting from the change) to Formulae (12) and (13) shown below to compute matrices [N T ] and [M T ], 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     12 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             N 
                             r 
                             T 
                           
                         
                       
                       
                         
                           
                             N 
                             θ 
                             T 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       ∫ 
                       
                         z 
                         1 
                       
                       
                         z 
                         2 
                       
                     
                      
                     
                       
                         
                           [ 
                           Q 
                           ] 
                         
                          
                         
                           [ 
                           
                             
                               
                                 
                                   αΔ 
                                    
                                   
                                       
                                   
                                    
                                   T 
                                 
                               
                             
                             
                               
                                 
                                   αΔ 
                                    
                                   
                                       
                                   
                                    
                                   T 
                                 
                               
                             
                           
                           ] 
                         
                       
                        
                       
                           
                       
                        
                       
                          
                         z 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     13 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             M 
                             r 
                             T 
                           
                         
                       
                       
                         
                           
                             M 
                             θ 
                             T 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       ∫ 
                       
                         z 
                         1 
                       
                       
                         z 
                         2 
                       
                     
                      
                     
                       
                         
                           [ 
                           Q 
                           ] 
                         
                          
                         
                           [ 
                           
                             
                               
                                 
                                   αΔ 
                                    
                                   
                                       
                                   
                                    
                                   T 
                                 
                               
                             
                             
                               
                                 
                                   αΔ 
                                    
                                   
                                       
                                   
                                    
                                   T 
                                 
                               
                             
                           
                           ] 
                         
                       
                        
                       z 
                        
                       
                           
                       
                        
                       
                          
                         z 
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0018]    a computation step (7) of inputting, to Formula (14) shown below, the amount of initial deformation ω 0 ′(r) of the diaphragm portion corresponding to the reference temperature T 0  and the reference pressure P 0  in the initial state during the compensation for the deformation of the diaphragm portion, and a distance g between the surface of the diaphragm portion on which the conductive portion is formed and an opposite surface of the substrate opposite to the surface of the diaphragm portion on which the conductive portion is formed, to compute a volume V 0  in the closed space in the initial state, 
         [0000]      [Formula 14] 
         [0000]        V   0 =∫ 0   R     2   2π r ( g+ω   0 ′( r )) dr   (14)
 
         [0019]    a computation step (8) of inputting a pressure P C  in the closed space, the reference pressure P 0 , the volume V 0  in the closed space in the initial state, the reference temperature T 0 , the temperature T 1  resulting from the change, and a volume V 1  (assumed value) in the closed space resulting from thermal expansion to Formula (15) shown below to compute a resultant pressure (a difference between the pressure P C  in the closed space and the reference temperature P 0  of an environment) P of the diaphragm portion, 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     15 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   P 
                   = 
                   
                     
                       
                         
                           P 
                           c 
                         
                          
                         
                           V 
                           0 
                         
                          
                         
                           T 
                           1 
                         
                       
                       
                         
                           T 
                           0 
                         
                          
                         
                           V 
                           1 
                         
                       
                     
                     - 
                     
                       P 
                       0 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
         [0020]    a computation step (9) of inputting a dielectric constant ∈ 0  of vacuum, a relative dielectric constant (a ratio between a dielectric constant of a medium and the dielectric constant of vacuum) ∈ r , the amount of initial deformation ω 0 ′(r), and the distance g to Formula (16) shown below to compute a capacitance C 0 ′ corresponding to the amount of initial deformation ω 0 ′(r), 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     16 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     C 
                     0 
                     ′ 
                   
                   = 
                   
                     
                       ∫ 
                       0 
                       
                         R 
                         2 
                       
                     
                      
                     
                       
                         
                           
                             ɛ 
                             0 
                           
                            
                           
                             ɛ 
                             r 
                           
                            
                           2 
                            
                           π 
                            
                           
                               
                           
                            
                           r 
                         
                         
                           ( 
                           
                             g 
                              
                             
                               
                                 ω 
                                 0 
                                 ′ 
                               
                                
                               
                                 ( 
                                 r 
                                 ) 
                               
                             
                           
                           ) 
                         
                       
                        
                       
                           
                       
                        
                       
                          
                         r 
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
         [0021]    a computation step (10) of inputting Formulae (1) to (6) shown above to Formulae (17) and (18) shown below to obtain Formula (19) shown below and representing a resultant force N r  in the first to third segments in the radial direction (the direction of the r axis), Formula (20) shown below and representing a resultant force N θ  in the first to third segments in the circumferential direction (θ), Formula (21) shown below and representing a resultant moment M r  in the first to third segments in the radial direction (the direction of the r axis), and Formula (22) shown below and representing a resultant moment M θ  in the first to third segments in the circumferential direction (θ), 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     17 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     { 
                     
                       
                         
                           
                             N 
                             r 
                           
                         
                       
                       
                         
                           
                             N 
                             0 
                           
                         
                       
                     
                     } 
                   
                   = 
                   
                     
                       [ 
                       A 
                       ] 
                     
                      
                     
                       ( 
                       
                         
                           { 
                           
                             
                               
                                 
                                   ɛ 
                                   rr 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   ɛ 
                                   θθ 
                                   0 
                                 
                               
                             
                           
                           } 
                         
                         + 
                         
                           
                             [ 
                             B 
                             ] 
                           
                            
                           
                             { 
                             
                               
                                 
                                   
                                     κ 
                                     r 
                                   
                                 
                               
                               
                                 
                                   
                                     κ 
                                     0 
                                   
                                 
                               
                             
                             } 
                           
                         
                         - 
                         
                           { 
                           
                             
                               
                                 
                                   N 
                                   r 
                                   T 
                                 
                               
                             
                             
                               
                                 
                                   N 
                                   θ 
                                   T 
                                 
                               
                             
                           
                           } 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     18 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     { 
                     
                       
                         
                           
                             M 
                             r 
                           
                         
                       
                       
                         
                           
                             M 
                             θ 
                           
                         
                       
                     
                     } 
                   
                   = 
                   
                     
                       [ 
                       B 
                       ] 
                     
                      
                     
                       ( 
                       
                         
                           { 
                           
                             
                               
                                 
                                   ɛ 
                                   rr 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   ɛ 
                                   θθ 
                                   0 
                                 
                               
                             
                           
                           } 
                         
                         + 
                         
                           
                             [ 
                             D 
                             ] 
                           
                            
                           
                             { 
                             
                               
                                 
                                   
                                     κ 
                                     r 
                                   
                                 
                               
                               
                                 
                                   
                                     κ 
                                     θ 
                                   
                                 
                               
                             
                             } 
                           
                         
                         - 
                         
                           { 
                           
                             
                               
                                 
                                   M 
                                   r 
                                   T 
                                 
                               
                             
                             
                               
                                 
                                   M 
                                   θ 
                                   T 
                                 
                               
                             
                           
                           } 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     19 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     N 
                     r 
                   
                   = 
                   
                     
                       
                         A 
                         
                           11 
                            
                           
                               
                           
                         
                       
                        
                       
                         
                            
                           
                             
                               u 
                               0 
                             
                              
                             
                               ( 
                               r 
                               ) 
                             
                           
                         
                         
                            
                           r 
                         
                       
                     
                     + 
                     
                       
                         A 
                         12 
                       
                        
                       
                         
                           
                             u 
                             0 
                           
                            
                           
                             ( 
                             r 
                             ) 
                           
                         
                         r 
                       
                     
                     - 
                     
                       
                         B 
                         11 
                       
                        
                       
                         
                            
                           
                             θ 
                              
                             
                               ( 
                               r 
                               ) 
                             
                           
                         
                         
                            
                           r 
                         
                       
                     
                     - 
                     
                       
                         B 
                         12 
                       
                        
                       
                         
                           θ 
                            
                           
                             ( 
                             r 
                             ) 
                           
                         
                         r 
                       
                     
                     - 
                     
                       N 
                       r 
                       T 
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     20 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     N 
                     θ 
                   
                   = 
                   
                     
                       
                         A 
                         21 
                       
                        
                       
                         
                            
                           
                             
                               u 
                               0 
                             
                              
                             
                               ( 
                               r 
                               ) 
                             
                           
                         
                         
                            
                           r 
                         
                       
                     
                     + 
                     
                       
                         A 
                         22 
                       
                        
                       
                         
                           
                             u 
                             0 
                           
                            
                           
                             ( 
                             r 
                             ) 
                           
                         
                         r 
                       
                     
                     - 
                     
                       
                         B 
                         21 
                       
                        
                       
                         
                            
                           
                             θ 
                              
                             
                               ( 
                               r 
                               ) 
                             
                           
                         
                         
                            
                           r 
                         
                       
                     
                     - 
                     
                       
                         B 
                         22 
                       
                        
                       
                         
                           θ 
                            
                           
                             ( 
                             r 
                             ) 
                           
                         
                         r 
                       
                     
                     - 
                     
                       N 
                       θ 
                       T 
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     21 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     M 
                     r 
                   
                   = 
                   
                     
                       
                         B 
                         11 
                       
                        
                       
                         
                            
                           
                             
                               u 
                               0 
                             
                              
                             
                               ( 
                               r 
                               ) 
                             
                           
                         
                         
                            
                           r 
                         
                       
                     
                     + 
                     
                       
                         B 
                         12 
                       
                        
                       
                         
                           
                             u 
                             0 
                           
                            
                           
                             ( 
                             r 
                             ) 
                           
                         
                         r 
                       
                     
                     - 
                     
                       
                         D 
                         11 
                       
                        
                       
                         
                            
                           
                             θ 
                              
                             
                               ( 
                               r 
                               ) 
                             
                           
                         
                         
                            
                           r 
                         
                       
                     
                     - 
                     
                       
                         D 
                         12 
                       
                        
                       
                         
                           θ 
                            
                           
                             ( 
                             r 
                             ) 
                           
                         
                         r 
                       
                     
                     - 
                     
                       M 
                       r 
                       T 
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     22 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     M 
                     θ 
                   
                   = 
                   
                     
                       
                         B 
                         21 
                       
                        
                       
                         
                            
                           
                             
                               u 
                               0 
                             
                              
                             
                               ( 
                               r 
                               ) 
                             
                           
                         
                         
                            
                           r 
                         
                       
                     
                     + 
                     
                       
                         B 
                         22 
                       
                        
                       
                         
                           
                             u 
                             0 
                           
                            
                           
                             ( 
                             r 
                             ) 
                           
                         
                         r 
                       
                     
                     - 
                     
                       
                         D 
                         21 
                       
                        
                       
                         
                            
                           
                             θ 
                              
                             
                               ( 
                               r 
                               ) 
                             
                           
                         
                         
                            
                           r 
                         
                       
                     
                     - 
                     
                       
                         D 
                         22 
                       
                        
                       
                         
                           θ 
                            
                           
                             ( 
                             r 
                             ) 
                           
                         
                         r 
                       
                     
                     - 
                     
                       M 
                       θ 
                       T 
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
         [0022]    a computation step (11) of inputting the resultant force N r  in the first to third segments in the radial direction (the direction of the r axis), the resultant force N θ  in the first to third segments in the circumferential direction (θ), the resultant moment M r  in the first to third segments in the radial direction (the direction of the r axis), the resultant moment M θ  in the first to third segments in the circumferential direction (θ), a transverse shear force Q r , and the resultant pressure (the difference between the pressure in the closed space and the reference pressure of the environment) P of the diaphragm portion to Formulae (23) to (25) shown below, to determine a balanced equation for an axial symmetric circular plate represented in Formula (26) shown below, 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     23 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                          
                         
                           N 
                           r 
                         
                       
                       
                          
                         r 
                       
                     
                     + 
                     
                       
                         
                           N 
                           r 
                         
                         - 
                         
                           N 
                           0 
                         
                       
                       r 
                     
                   
                   = 
                   0 
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     24 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Q 
                     r 
                   
                   = 
                   
                     
                       
                          
                         
                           M 
                           r 
                         
                       
                       
                          
                         r 
                       
                     
                     + 
                     
                       
                         
                           M 
                           r 
                         
                         - 
                         
                           M 
                           θ 
                         
                       
                       r 
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     25 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                          
                         
                           Q 
                           r 
                         
                       
                       
                          
                         r 
                       
                     
                     + 
                     P 
                     + 
                     
                       
                         Q 
                         r 
                       
                       r 
                     
                   
                   = 
                   0 
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     26 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         1 
                         r 
                       
                        
                       
                         
                            
                           
                               
                           
                         
                         
                            
                           r 
                         
                       
                        
                       
                         ( 
                         
                           
                             r 
                              
                             
                               
                                  
                                 
                                   M 
                                   r 
                                 
                               
                               
                                  
                                 r 
                               
                             
                           
                           + 
                           
                             M 
                             r 
                           
                           + 
                           
                             M 
                             θ 
                           
                         
                         ) 
                       
                     
                     + 
                     P 
                   
                   = 
                   0 
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
         [0023]    a computation step (12) of inputting Formulae (19) to (22) shown above to Formulae (23) and (26) shown above to obtain relational expressions (27) and (28) shown below, 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     27 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                            
                           2 
                         
                          
                         
                           θ 
                            
                           
                             ( 
                             r 
                             ) 
                           
                         
                       
                       
                          
                         
                           r 
                           2 
                         
                       
                     
                     + 
                     
                       
                         1 
                         r 
                       
                        
                       
                         
                            
                           
                             θ 
                              
                             
                               ( 
                               r 
                               ) 
                             
                           
                         
                         
                            
                           r 
                         
                       
                     
                     - 
                     
                       
                         θ 
                          
                         
                           ( 
                           r 
                           ) 
                         
                       
                       
                         r 
                         2 
                       
                     
                   
                   = 
                   
                     Pr 
                     
                       2 
                        
                       
                         D 
                         11 
                         * 
                       
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     28 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                            
                           2 
                         
                          
                         
                           
                             u 
                             0 
                           
                            
                           
                             ( 
                             r 
                             ) 
                           
                         
                       
                       
                          
                         
                           r 
                           2 
                         
                       
                     
                     + 
                     
                       
                         1 
                         r 
                       
                        
                       
                         
                            
                           
                             
                               u 
                               0 
                             
                              
                             
                               ( 
                               r 
                               ) 
                             
                           
                         
                         
                            
                           r 
                         
                       
                     
                     - 
                     
                       
                         
                           u 
                           0 
                         
                          
                         
                           ( 
                           r 
                           ) 
                         
                       
                       
                         r 
                         2 
                       
                     
                   
                   = 
                   
                     
                       
                         Pr 
                          
                         
                             
                         
                          
                         β 
                       
                       
                         2 
                          
                         
                           D 
                           11 
                           * 
                         
                       
                     
                      
                     
                       ( 
                       
                         β 
                         = 
                         
                           
                             
                               B 
                               11 
                             
                              
                             
                               / 
                             
                              
                             
                               A 
                               11 
                             
                              
                             
                               
 
                             
                              
                             and 
                              
                             
                               
 
                             
                              
                             
                               D 
                               11 
                               * 
                             
                           
                           = 
                           
                             
                               D 
                               11 
                             
                             - 
                             
                               
                                 B 
                                 11 
                                 2 
                               
                                
                               
                                 / 
                               
                                
                               
                                 A 
                                 11 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
         
       
     
         [0024]    a computation step (13) of carrying out two integration processes on Formulae (27) and (28) shown above to obtain Formulae (29) and (30) shown below, 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     29 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     θ 
                      
                     
                       ( 
                       r 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         b 
                         1 
                       
                        
                       r 
                     
                     + 
                     
                       
                         b 
                         2 
                       
                       r 
                     
                     + 
                     
                       
                         1 
                         
                           D 
                           11 
                           * 
                         
                       
                        
                       
                         ( 
                         
                           
                             Pr 
                             3 
                           
                           16 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     30 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       u 
                       0 
                     
                      
                     
                       ( 
                       r 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         a 
                         1 
                       
                        
                       r 
                     
                     + 
                     
                       
                         a 
                         2 
                       
                       r 
                     
                     + 
                     
                       
                         β 
                         
                           D 
                           11 
                           * 
                         
                       
                        
                       
                         ( 
                         
                           
                             Pr 
                             3 
                           
                           16 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   30 
                   ) 
                 
               
             
           
         
       
     
         [0025]    a computation step (14) of carrying out an integration process on Formula (29) shown above to compute an amount of deformation ω (1)  of the diaphragm portion in the first segment shown below in Formula (31), an amount of deformation ω (2)  of the diaphragm portion in the second segment shown below in Formula (32), and an amount of deformation ω (3)  of the diaphragm portion in the third segment shown below in Formula (33), 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     31 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       ω 
                       
                         ( 
                         1 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           Pr 
                           4 
                         
                         
                           64 
                            
                           
                             D 
                             11 
                             
                               * 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                           
                         
                       
                       + 
                       
                         
                           
                             b 
                             1 
                             
                               ( 
                               1 
                               ) 
                             
                           
                            
                           
                             r 
                             2 
                           
                         
                         2 
                       
                       + 
                       
                         c 
                         
                           ( 
                           1 
                           ) 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     0 
                     ≤ 
                     r 
                     ≤ 
                     
                       R 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   31 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     32 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       ω 
                       
                         ( 
                         2 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           Pr 
                           4 
                         
                         
                           64 
                            
                           
                             D 
                             11 
                             
                               * 
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                           
                         
                       
                       + 
                       
                         
                           
                             b 
                             1 
                             
                               ( 
                               2 
                               ) 
                             
                           
                            
                           
                             r 
                             2 
                           
                         
                         2 
                       
                       + 
                       
                         
                           b 
                           2 
                           
                             ( 
                             2 
                             ) 
                           
                         
                          
                         
                           ln 
                            
                           
                             ( 
                             r 
                             ) 
                           
                         
                       
                       + 
                       
                         c 
                         
                           ( 
                           2 
                           ) 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     
                       R 
                       1 
                     
                     ≤ 
                     r 
                     ≤ 
                     
                       R 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   32 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     33 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       ω 
                       
                         ( 
                         3 
                         ) 
                       
                     
                     = 
                     0 
                   
                   , 
                   
                     
                       R 
                       2 
                     
                     ≤ 
                     r 
                     ≤ 
                     
                       R 
                       3 
                     
                   
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
           
         
       
     
         [0026]    a computation step (15) of inputting the amount of deformation ω (1)  and ω (2)  and the distance g to Formula (34) shown below to compute the volume V 1  in the closed space resulting from the thermal expansion, 
         [0000]      [Formula 34] 
         [0000]        V   1 =∫ 0   R     1   2π r ( g+ω   (1) ) dr+∫   0   R     3   2π r ( g+ω   (2) ) dr   (34)
 
         [0027]    a computation step (16) of inputting the volume V 1  to Formulae (31) and (32) shown above to compute a capacitance C′ shown below in Formula (35) and corresponding to the amounts of deformation ω (1)  and ω (2) , and 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     35 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     C 
                     ′ 
                   
                   = 
                   
                     
                       
                         ∫ 
                         0 
                         
                           R 
                           1 
                         
                       
                        
                       
                         
                           
                             
                               ɛ 
                               0 
                             
                              
                             
                               ɛ 
                               r 
                             
                              
                             2 
                              
                             π 
                              
                             
                                 
                             
                              
                             r 
                           
                           
                             ( 
                             
                               g 
                               + 
                               
                                 
                                   ω 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                  
                                 
                                   ( 
                                   r 
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                          
                         
                             
                         
                          
                         
                            
                           r 
                         
                       
                     
                     + 
                     
                       
                         ∫ 
                         
                           R 
                           1 
                         
                         
                           R 
                           2 
                         
                       
                        
                       
                         
                           
                             
                               ɛ 
                               0 
                             
                              
                             
                               ɛ 
                               r 
                             
                              
                             2 
                              
                             π 
                              
                             
                                 
                             
                              
                             r 
                           
                           
                             ( 
                             
                               g 
                               + 
                               
                                 
                                   ω 
                                   
                                     ( 
                                     2 
                                     ) 
                                   
                                 
                                  
                                 
                                   ( 
                                   r 
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                          
                         
                             
                         
                          
                         
                            
                           r 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   35 
                   ) 
                 
               
             
           
         
       
     
         [0028]    a computation step (17) of inputting the capacitances C 0 ′ and C′ to Formula (36) shown below to determine an amount of change in capacitance ΔC′, the computation steps (1) to (17) being carried out in order. 
         [0000]      [Formula 36] 
         [0000]      Δ C′=C′−C′   0   (6)
 
         [0029]    The configuration in (2) allows obtainment of the amount of change in capacitance ΔC′, more specifically, the parameter ΔC′ enabling determination of the degree of compensation for the deformation of the diaphragm portion caused by the thermal expansion of the gas sealed in the closed space. Thus, the deformation of the diaphragm portion can be compensated for more accurately than in the conventional art simply by applying the result of optimization of the parameter ΔC′ to the capacitive sensor. As a result, in detecting a change in the capacitance between the diaphragm portion and both the first electrode portion and the conductive portion based on the deformation of the diaphragm portion, the capacitive sensor can detect the change in capacitance more accurately than in the conventional art. Here, “optimization of the parameter ΔC′” includes completely zeroing the parameter ΔC′ and approximating the parameter ΔC′ to zero. 
         [0030]    (3) In the method for temperature compensation in the sensor in (1) or (2), preferably, the conductive portion is a second electrode portion for detecting a change in the capacitance between the diaphragm portion and both the first electrode portion and the second electrode portion based on the deformation of the diaphragm portion. 
         [0031]    The configuration in (3) allows the deformation of the diaphragm portion to be compensated for more accurately than in the conventional art simply by applying the result of optimization of the parameter ΔC′ to the capacitive sensor. As a result, in detecting a change in the capacitance between the diaphragm portion and both the first electrode portion and the second electrode portion based on the deformation of the diaphragm portion, the capacitive sensor can detect the change in capacitance more accurately than in the conventional art. 
         [0032]    (4) In the method for temperature compensation in the sensor in (3), preferably, the sensor includes a barrier metal layer containing at least platinum and formed between the second electrode portion and the insulator layer, the barrier metal layer having an inner circumferential surface forming a part of the closed space. Here, the “barrier metal” refers to a material such as metal which exerts the following advantageous effects: the material (1) allows a dense film to be formed and produces a barrier effect against reaction between a wiring material and a silicon substrate, (2) is bonded well to metal and an insulating film, (3) can be micromachined by dry etching, and (4) offers reduced resistance. 
         [0033]    The configuration in (4) applies the result of optimization of the parameter ΔC′ to the capacitive sensor. Thus, the capacitive sensor configured to enjoy the barrier metal effect of the barrier metal layer can also detect a change in the capacitance between the diaphragm portion and both the first electrode portion and the conductive portion more accurately than in the conventional art. 
         [0034]    (5) In the method for temperature compensation in the sensor in (2), preferably, the conductive portion is a sealing ring portion formed on a surface of the diaphragm portion opposite to the surface of the diaphragm portion on which the temperature compensation ring is formed, and the sensor includes a ring-like second electrode portion formed between the sealing ring portion and the insulator layer to detect a change in the capacitance between the diaphragm portion and both the first electrode portion and the second electrode portion based on the deformation of the diaphragm portion. 
         [0035]    The configuration in (5) applies the result of optimization of the parameter ΔC′ to the capacitive sensor. Thus, while configured to enjoy an effect enabling possible leakage of the gas in the closed space to be more reliably prevented by using the sealing ring to seal the portion between the diaphragm portion and the second electrode portion, the capacitive sensor can also detect a change in the capacitance between the diaphragm portion and both the first electrode portion and the second electrode portion more accurately than in the conventional art. 
         [0036]    (6) In the method for temperature compensation in the sensor in (5), preferably, the second electrode portion and the sealing ring portion of the sensor are bonded together by a gold-gold bonding. 
         [0037]    The configuration in (6) applies the result of optimization of the parameter ΔC′ to the capacitive sensor. Thus, while configured to enjoy an effect enabling reliability of an electric connection between the second electrode portion and the sealing ring portion to be improved, the capacitive sensor can also detect a change in the capacitance between the diaphragm portion and both the first electrode portion and the second electrode portion more accurately than in the conventional art. 
         [0038]    (7) In the method for temperature compensation in the sensor in (2), preferably, the sensor includes a ring-like barrier metal layer containing at least platinum and formed on a surface of the diaphragm portion opposite to the surface of the diaphragm portion on which the temperature compensation ring is formed, and a ring-like second electrode portion formed between the barrier metal layer and the insulator layer to detect a change in the capacitance between the diaphragm portion and both the first electrode portion and the second electrode portion based on the deformation of the diaphragm portion, and when the barrier metal layer includes a single layer, the conductive portion is the barrier metal layer, and when the barrier metal layer includes a plurality of layers, the conductive portion is a layer included in the barrier metal layer and which is closest to the diaphragm portion. 
         [0039]    The configuration in (7) applies the result of optimization of the parameter ΔC′ to the capacitive sensor. Thus, the capacitive sensor configured to enjoy the barrier metal effect of the barrier metal layer can also detect a change in the capacitance between the diaphragm portion and both the first electrode portion and the second electrode portion more accurately than in the conventional art. 
         [0040]    (8) The present invention provides a computation program for carrying out a computation process for a method for temperature compensation in a sensor including a substrate with a first electrode portion formed on one surface, a conductive portion formed on the one surface of the substrate via an insulator layer, a diaphragm portion formed on a surface of the conductive portion opposite to the surface of the conductive portion on which the insulator layer is formed, the diaphragm portion being deformable depending on pressure, and a temperature compensation member formed on a surface of the diaphragm portion opposite to the surface of the diaphragm portion on which the conductive portion is formed, the sensor internally having a closed space, a part of the closed space being formed along an inner circumferential surface of the conductive portion and the surface of the diaphragm portion on which the conductive portion is formed, wherein the temperature compensation member compensates for deformation of the diaphragm portion caused by thermal expansion of a gas sealed in the closed space. 
         [0041]    The configuration in (8) allows effects similar to the effects of the configuration in (1) to be enjoyed. 
         [0042]    (9) A computation processing device according to the present invention carries out a computation process in accordance with the computation program according to claim  8 . 
         [0043]    The configuration in (9) allows effects similar to the effects of the configuration in (8) to be enjoyed. 
         [0044]    (10) The present invention provides a sensor including a substrate with a first electrode portion formed on one surface, a conductive portion formed on the one surface of the substrate via an insulator layer, a diaphragm portion formed on a surface of the conductive portion opposite to the surface of the conductive portion on which the insulator layer is formed, the diaphragm portion being deformable depending on pressure, and a temperature compensation member formed on a surface of the diaphragm portion opposite to the surface of the diaphragm portion on which the conductive portion is formed, the sensor internally having a closed space, a part of the closed space being formed along an inner circumferential surface of the conductive portion and the surface of the diaphragm portion on which the conductive portion is formed, wherein the temperature compensation member compensates for deformation of the diaphragm portion caused by thermal expansion of a gas sealed in the closed space. 
         [0045]    The configuration in (10) allows effects similar to the effects of the configuration in (1) to be enjoyed. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0046]      FIG. 1  is a schematic diagram of a capacitive sensor to which the results of computations in a method for temperature compensation in a sensor according to a first embodiment of the present invention are applied, wherein  FIG. 1(   a ) is a plan view of the capacitive sensor, and  FIG. 1(   b ) is a cross-sectional view of the capacitive sensor taken along line A-A in  FIG. 1(   a ). 
           [0047]      FIG. 2  is a diagram illustrating a general principle for compensation for the amount of deformation of a diaphragm portion, wherein  FIG. 2(   a ) shows a state before compensation and  FIG. 2(   b ) shows a state after the compensation. 
           [0048]      FIG. 3  is a flowchart showing computation steps of the method for temperature compensation in the sensor according to the first embodiment of the present invention. 
           [0049]      FIG. 4  is a flowchart showing computation steps of the method for temperature compensation in the sensor according to the first embodiment of the present invention. 
           [0050]      FIG. 5  is a flowchart showing computation steps of the method for temperature compensation in the sensor according to the first embodiment of the present invention. 
           [0051]      FIG. 6  is a diagram illustrating a computation process of dividing a composite circular plate into a first segment to a third segment based on the Timoshenko&#39;s symmetric circular plate theory, wherein  FIG. 6(   a ) shows a state before the division, and  FIG. 6(   b ) shows a state after the division. 
           [0052]      FIG. 7  is a schematic diagram of a capacitive sensor to which the results of computations in a method for temperature compensation in a sensor according to a second embodiment of the present invention are applied, wherein  FIG. 7(   a ) is a plan view of the capacitive sensor, and  FIG. 7(   b ) is a cross-sectional view of the capacitive sensor taken along line B-B in  FIG. 7(   a ). 
           [0053]      FIG. 8  is a flowchart showing computation steps of the method for temperature compensation in the sensor according to the second embodiment of the present invention. 
           [0054]      FIG. 9  is a flowchart showing computation steps of the method for temperature compensation in the sensor according to the second embodiment of the present invention. 
           [0055]      FIG. 10  is a flowchart showing computation steps of the method for temperature compensation in the sensor according to the second embodiment of the present invention. 
           [0056]      FIG. 11  is a schematic diagram of a capacitive sensor to which the results of computations in a method for temperature compensation in a sensor according to a third embodiment of the present invention are applied, wherein  FIG. 11(   a ) is a plan view of the capacitive sensor, and  FIG. 11(   b ) is a cross-sectional view of the capacitive sensor taken along line C-C in  FIG. 11(   a ). 
           [0057]      FIG. 12  is a flowchart showing computation steps of the method for temperature compensation in the sensor according to the third embodiment of the present invention. 
           [0058]      FIG. 13  is a flowchart showing computation steps of the method for temperature compensation in the sensor according to the third embodiment of the present invention. 
           [0059]      FIG. 14  is a flowchart showing computation steps of the method for temperature compensation in the sensor according to the third embodiment of the present invention. 
           [0060]      FIG. 15  is a schematic diagram of a capacitive sensor to which the results of computations in a method for temperature compensation in a sensor according to a fourth embodiment of the present invention are applied, wherein  FIG. 15(   a ) is a plan view of the capacitive sensor, and  FIG. 15(   b ) is a cross-sectional view of the capacitive sensor taken along line D-D in  FIG. 15(   a ). 
           [0061]      FIG. 16  is a flowchart showing computation steps of the method for temperature compensation in the sensor according to the fourth embodiment of the present invention. 
           [0062]      FIG. 17  is a flowchart showing computation steps of the method for temperature compensation in the sensor according to the fourth embodiment of the present invention. 
           [0063]      FIG. 18  is a flowchart showing computation steps of the method for temperature compensation in the sensor according to the fourth embodiment of the present invention. 
           [0064]      FIG. 19  is a block diagram showing a computation processing device according to a fifth embodiment of the present invention. 
           [0065]      FIG. 20  is a flowchart showing computation steps of a computation program and a computation processing device for a method for temperature compensation in a sensor according to the fifth embodiment of the present invention. 
           [0066]      FIG. 21  is a flowchart showing computation steps of the computation program and the computation processing device for the method for temperature compensation in the sensor according to the fifth embodiment of the present invention. 
           [0067]      FIG. 22  is a flowchart showing computation steps of the computation program and the computation processing device for the method for temperature compensation in the sensor according to the fifth embodiment of the present invention. 
           [0068]      FIG. 23  is a schematic diagram of the sensor according to a variation of the fourth embodiment of the present invention, wherein  FIG. 23(   a ) is a plan view, and  FIG. 23(   b ) is a cross-sectional view taken along line E-E in  FIG. 23(   a ). 
           [0069]      FIG. 24  is a schematic diagram of a sensor according to a variation of the fourth embodiment of the present invention, wherein  FIG. 24(   a ) is a plan view, and  FIG. 24(   b ) is a cross-sectional view taken along line F-F in  FIG. 24(   a ). 
           [0070]      FIG. 25  is a schematic diagram of a sensor according to a variation of the first embodiment of the present invention, wherein  FIG. 25(   a ) is a plan view, and  FIG. 25(   b ) is a cross-sectional view taken along line G-G in  FIG. 25(   a ). 
           [0071]      FIG. 26  is a schematic diagram of a sensor according to a variation of the first embodiment of the present invention, wherein  FIG. 26  (and  FIG. 26(   b ) is a cross-sectional view taken along line H-H in  FIG. 26(   a ). 
       
    
    
     DESCRIPTION OF EMBODIMENTS 
     First Embodiment 
       [0072]    A method for temperature compensation in a sensor according to a first embodiment of the present invention will be described below with reference to  FIG. 1  to  FIG. 6 . 
         [0073]    (Configuration of a Capacitive Sensor  100 ) 
         [0074]    As shown in  FIG. 1(   a ) and  FIG. 1(   b ), a capacitive sensor (a sensor)  100  to which the results of computations in a method for temperature compensation in the capacitive sensor are applied includes a substrate  1 , an insulator layer  2 , a first electrode portion  3 , a second electrode portion (conductive portion)  4 , a diaphragm portion  5 , a temperature compensation ring (temperature compensation member)  6 , and a closed space  7 . 
         [0075]    The substrate  1  is formed of a semiconductor such as silicon and has a circular recess  1   a  in a substantially central portion of the substrate  1 . 
         [0076]    The insulator layer  2  is a layer formed of an insulator such as silicon dioxide and is formed on one surface of the substrate  1 . The insulator layer  2  also has a circular penetration portion  2   a  formed in a substantially central portion thereof so as to align with the recess  1   a  in the substrate  1  and such a generally rectangular penetration portion  2   b  as shown in  FIG. 1(   a ). 
         [0077]    The first electrode portion  3  is formed as a barrier metal layer containing at least platinum and includes three layers, that is, a layer located closest to the substrate  1  and formed of titanium, a layer located furthest from the substrate  1  and formed of gold, and a layer located between these two layers and formed of platinum. 
         [0078]    The second electrode portion  4  is formed of gold and shaped like a ring on a surface of the insulator layer  2  opposite to a surface of the insulator layer  2  on which the substrate  1  is formed. In a variation, the second electrode portion  4  may be formed of a metal material such as silver or copper. 
         [0079]    The diaphragm portion  5  is formed of silicon and is deformable under a pressure applied by atmospheric pressure. In a variation, the diaphragm portion  5  may be formed of a semiconductor material other than silicon. 
         [0080]    The temperature compensation ring  6  is formed of aluminum and shaped like a ring on a surface of the diaphragm portion  5  opposite to a surface of the diaphragm portion  5  on which the second electrode portion  4  is formed. In a variation, the temperature compensation ring  6  may be a metal material with a high coefficient of thermal expansion instead of aluminum. 
         [0081]    The closed space  7  forms an atmospheric environment suitable for detection of the pressure applied to the diaphragm portion  5 . The closed space  7  is formed by being surrounded by an inner surface of the recess  1   a , an inner circumferential surface of the penetration portion  2   a , an inner circumferential surface of the second electrode portion  4 , and the surface of the diaphragm portion  5  on which the second electrode portion  4  is formed. 
         [0082]    (Operation of the Capacitive Sensor  100 ) 
         [0083]    Now, operation of the capacitive sensor  100  will be described. When a pressure based on atmospheric pressure is applied to the diaphragm portion  5  of the capacitive sensor  100 , the diaphragm portion  5  is deformable depending on the pressure. The pressure is measured by detecting a change in the capacitance between the diaphragm portion  5  and both the first electrode portion  3  and the second electrode portion  4 . 
         [0084]    (Principle for Compensation for the Amount of Deformation of the Diaphragm Portion  5 ) 
         [0085]    Now, a general principle for compensation for the amount of deformation of the diaphragm portion  5  will be described with reference to  FIG. 2 . A distance g in  FIG. 2(   a ) to  FIG. 2(   c ) indicates the distance between the surface of the diaphragm portion  5  on which the second electrode portion  4  is formed and an opposite surface of the recess  1   a  opposite to the surface of the diaphragm portion  5  on which the second electrode portion  4  is formed. 
         [0086]    First, in a state before compensation shown in  FIG. 2(   a ) and in an initial state in an environment with a reference temperature T 0  and a reference pressure P 0 , the diaphragm portion  5  is deformed to a state shown by a solid line in  FIG. 5 . The amount of initial deformation of the diaphragm portion  5  is ω 0 (r). A capacitance C 0  is generated between the diaphragm portion  5  and both the first electrode portion  3  and the second electrode portion  4  in association with the amount of initial deformation ω 0 (r). Then, the following are assumed. When the reference pressure remains the initial pressure P 0  and only the reference temperature changes from the initial temperature T 0  to a temperature T, the diaphragm portion  5  is deformed to a state shown by a dotted line in  FIG. 2(   a ), the amount of deformation of the diaphragm portion  5  changes from the amount of initial deformation ω 0 (r) to an amount of deformation ω(r), and the capacitance generated between the diaphragm portion  5  and both the first electrode portion  3  and the second electrode portion  4  changes from the initial capacitance C 0  to C. Under these assumptions, the amount of change ΔC in capacitance can be expressed by Formula (37) shown below. In Formula (37), a coefficient ∈ 0  represents the dielectric constant of vacuum and a coefficient ∈ r  represents a relative dielectric constant (the ratio between the dielectric constant of a medium and the dielectric constant of vacuum). 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     37 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Δ 
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                     C 
                   
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                   ( 
                   37 
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         [0087]    Then, in a state after compensation shown in  FIG. 2(   b ) and in an initial state in an environment with the reference temperature T 0  and the reference pressure P 0 , the diaphragm portion  5  is deformed to a state shown by a solid line in  FIG. 2(   b ). The amount of initial deformation of the diaphragm portion  5  is ω 0 ′(r). A capacitance C′ 0  is generated between the diaphragm portion  5  and both the first electrode portion  3  and the second electrode portion  4  in association with the amount of initial deformation ω 0 ′(r). Then, the following are assumed. When the reference pressure remains the initial pressure P 0  and only the reference temperature changes from the initial temperature T 0  to a temperature T, the diaphragm portion  5  is deformed to a state shown by a dotted line in  FIG. 2(   b ), the amount of deformation of the diaphragm portion  5  changes from the amount of initial deformation ω 0 ′(r) to an amount of deformation ω′(r), and the capacitance generated between the diaphragm portion  5  and both the first electrode portion  3  and the second electrode portion  4  changes from the initial capacitance C′ 0  to C′. Under these assumptions, the amount of change ΔC′ in capacitance can be expressed by Formula (38) shown below. In Formula (38), the coefficient ∈ 0  represents the dielectric constant of vacuum and the coefficient ∈ r  represents the relative dielectric constant (the ratio between the dielectric constant of a medium and the dielectric constant of vacuum). 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     38 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
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                   38 
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         [0088]    Formula 38 indicates that the parameter ΔC′ may be set to zero in order to completely compensate for deformation of the diaphragm portion  5 , that is, to completely zero a difference in the amount of deformation of the diaphragm portion  5  (=the amount of initial deformation ω 0 ′(r)−the amount of deformation ω′(r)). This in turn indicates that the parameter ΔC′ enables the degree of compensation for the deformation of the diaphragm portion  5  to be determined. 
         [0089]      FIG. 2(   c ) shows a comparative example for the general principle for compensation shown in  FIG. 2(   a ) and  FIG. 2(   b ) and shows the result of optimization of the parameter ΔC′ obtained by computations in the method for temperature compensation according to the first embodiment, more specifically, the result of setting the parameter ΔC′ to zero, and thus, the result of completely zeroing the amount of deformation of the diaphragm portion  5 . In this state, the distance g is maintained between the surface of the diaphragm portion  5  on which the second electrode portion  4  is formed and an inner surface of the recess  1   a  opposite to the surface of the diaphragm portion  5  on which the second electrode portion  4  is formed. In a variation, the amount of deformation of the diaphragm portion  5  may be approximated to zero by setting the parameter ΔC′ to a value approximate to zero. 
         [0090]    (Computation Steps of the Method for Temperature Compensation in the Sensor According to the First Embodiment) 
         [0091]    Now, the computation steps of the method for temperature compensation in the capacitive sensor will be described with reference to  FIG. 3  to  FIG. 6 . The purpose of each of the computation steps is to compute the deformation of the diaphragm portion  5  associated with temperature. The pressure in the closed space  7  varies depending on temperature, and thus, the deformation of the diaphragm portion  5  is calculated based on the relation between temperature and pressure. 
         [0092]    First, in a computation step S 1  shown in  FIG. 3 , based on the Timoshenko&#39;s symmetric circular plate theory, a composite circular plate configured such that center axes of the second electrode portion  4 , the diaphragm portion  5 , and the temperature compensation ring  6  align with one another (see  FIG. 6(   a )) is divided into a first segment (1) including a portion with a radius of 0 to R 1  based on the center axis of the diaphragm portion  5 , a second segment (2) including a portion with a radius of R 1  to R 2  based on the center axes of the diaphragm portion  5  and the temperature compensation ring  6 , and a third segment (3) including a portion with a radius of R 2  to R 3  based on the center axes of the second electrode portion  4 , the diaphragm portion  5 , and the temperature compensation ring  6  (see  FIG. 6(   b )), as shown in  FIG. 6 . 
         [0093]    An alternate long and short dash line in  FIG. 6(   a ) and  FIG. 6(   b ) shows an axis passing through the center axis P (the position of a radius of 0) of the second electrode portion  4 , the diaphragm portion  5 , and the temperature compensation ring  6  and extending along a stacking direction of the second electrode portion  4 , the diaphragm portion  5 , and the temperature compensation ring  6 . Thicknesses tg, ts, and to in  FIG. 6(   a ) and  FIG. 6(   b ) represent the respective thicknesses of the second electrode portion  4 , the diaphragm portion  5 , and the temperature compensation ring  6 . A temperature difference ΔT in  FIG. 6(   a ) and  FIG. 6(   b ) represents a difference between the reference temperature T 0  and the temperature T. A resultant pressure P in  FIG. 6(   a ) and  FIG. 6(   b ) represents a difference between the pressure P C  in the closed space  7  and the reference pressure P 0  of the environment. R 1  in  FIG. 6(   a ) and  FIG. 6(   b ) denotes the radius of the inner diameter (2R 1 ) of the temperature compensation ring  6 . Similarly, R 2  in  FIG. 6(   a ) and  FIG. 6(   b ) denotes the radius of the inner diameter (2R 2 ) of the second electrode portion  4 . Similarly, R 3  in  FIG. 6(   a ) and  FIG. 6(   b ) denotes the radius of the outer diameter (2R 3 ) of the second electrode portion  4 , the diaphragm portion  5 , and the temperature compensation ring  6 . In this case, the second electrode portion  4 , the diaphragm portion  5 , and the temperature compensation ring  6  are formed using gold, silicon, and aluminum, respectively, as a material. 
         [0094]    Then, in a computation step S 2 , based on Kirchhoff&#39;s circular plate theory, strains ∈ 0   rr  and ∈ 0   θθ  of a reference plane (z=0), shown in Formulae (5) and (6) shown above, in the stacking direction of the first to third segments (1) to (3) are determined using Formulae (1) to (4) shown above and representing the relations between strains ∈ rr  and ∈ θθ  and displacements κ r  and κ θ  in a radial direction (the direction of an r axis) and a circumferential direction (θ). 
         [0095]    Then, in a computation step S 3 , Young&#39;s modulus E and Poisson&#39;s ratio ν are input to Formula (7) shown above to determine a matrix [Q]. 
         [0096]    Then, in a computation step S 4 , a stress σ rr  in the radial direction (the direction of the r axis) and a stress σ θθ  in the circumferential direction (θ) are determined by inputting the matrix [Q], the strains ∈ 0   rr  and ∈ 0   θθ , the displacements κ r  and κ θ , a coefficient of thermal expansion α, and a temperature difference ΔT (a difference between a reference temperature T 0  in an initial state during compensation for deformation of the diaphragm portion  5  and a temperature T 1  resulting from a change) to a constitutive equation for stress on a linearly elastic symmetric circular plate with traverse isotropy shown in Formula (8) shown above. 
         [0097]    Then, in a computation step S 5 , the matrix [Q] is input to Formulae (9) to (11) shown above to compute matrices [A], [B], and [D]. 
         [0098]    Then, in a computation step S 6 , matrices [N T ] and [M T ] are respectively computed by inputting the matrix [Q], the coefficient of thermal expansion α, and the temperature difference ΔT (the difference between the reference temperature T 0  in the initial state during the compensation for the deformation of the diaphragm portion and the temperature T 1  resulting from the change) to Formulae (12) and (13) shown above. 
         [0099]    Then, in a computation step S 7 , a volume V 0  in the closed space  7  in the initial state is computed by inputting, to Formula (14) shown above, the amount of initial deformation ω 0 ′(r) of the diaphragm portion  5  corresponding to the reference temperature T 0  and the reference pressure P 0  in the initial state during the compensation for the deformation of the diaphragm portion  5 , and the distance g between the surface of the diaphragm portion  5  on which the second electrode portion  4  is formed and an opposite surface of the recess  1   a  opposite to the surface of the diaphragm portion  5  on which the second electrode portion  4  is formed. 
         [0100]    Then, in a computation step S 8 , a resultant pressure of the diaphragm portion  5  (the difference between the pressure P C  in the closed space  7  and the reference pressure P 0  of the environment) P is computed by inputting the pressure P C  in the closed space, the reference pressure P 0 , the volume V 0  in the closed space  7  in the initial state, the reference temperature T 0 , the temperature T 1  resulting from the change, and a volume V 1  (assumed value) in the closed space resulting from thermal expansion to Formula (15) shown above. 
         [0101]    Then, in a computation step S 9 , a capacitance C 0 ′ corresponding to the amount of initial deformation ω 0 ′(r) is computed by inputting the dielectric constant ∈ 0  of vacuum, the relative dielectric constant (the ratio between the dielectric constant of a medium and the dielectric constant of vacuum) ∈ r , the amount of initial deformation ω 0 ′(r), and the distance g to Formula (16) shown above. 
         [0102]    Then, in a computation step S 10 , Formulae (1) to (6) shown above are input to Formulae (17) and (18) shown above to obtain Formula (19) shown above representing a resultant force N r  in the first segment (1) to the third segment (3) in the radial direction (the direction of the r axis), Formula (20) shown above representing a resultant force N θ  in the first segment (1) to the third segment (3) in the circumferential direction (θ), Formula (21) shown above representing a resultant moment M r  in the first segment (1) to the third segment (3) in the radial direction (the direction of the r axis), and Formula (22) shown below representing a resultant moment M θ  in the first segment (1) to the third segment (3) in the circumferential direction (θ). Here, reference characters A 11 , A 12 , B 11 , and B 12  in Formula (19) represent components of the matrices [A] and [B] shown in Formulae (9) and (10) shown above. Reference character N r   T  represents a resultant force exerted in the radial direction (the direction of the r axis) at the temperature T. Reference characters A 21 , A 22 , B 21 , and B 22  in Formula (20) represent components of the matrices [A] and [B] shown in Formulae (9) and (10) shown above. Reference character N θ   T  represents a resultant force exerted in the circumferential direction (θ) at the temperature T. Reference characters B 11 , B 12 , D 11 , and D 12  in Formula (21) represent components of the matrices [B] and [D] shown in Formulae (10) and (11) shown above. Reference character M r   T  represents a resultant moment exerted in the radial direction (the direction of the r axis) at the temperature T. Reference characters B 21 , B 22 , D 21 , and D 22  in Formula (22) represent components of the matrices [B] and [D] shown in Formulae (10) and (11) shown above. Reference character M θ   T  represents a resultant moment exerted in the circumferential direction (θ) at the temperature T. 
         [0103]    Then, in a computation step S 11 , a balanced equation for an axial symmetric circular plate represented in Formula (26) shown above is determined by inputting the resultant force N r  in the first segment (1) to the third segment (3) in the radial direction (the direction of the r axis), the resultant force N θ  in the first segment (1) to the third segment (3) in the circumferential direction (θ), the resultant moment M r  in the radial direction (the direction of the r axis), the resultant moment M θ  in the circumferential direction (θ), a transverse shear force Q r , and the resultant pressure (the difference between the pressure P C  in the closed space  7  and the reference temperature P 0  of the environment) P of the diaphragm portion  5  to Formulae (23) to (25) shown above. 
         [0104]    Then, in a computation step S 12 , Formulae (19) to (22) shown above are input to Formulae (23) and (26) shown above to obtain relational expressions (27) and (28) shown above. Here, reference character D* 11  in Formulae (27) and (28) represents a parameter acquired using the respective components A 11 , B 11 , and D 11  of the matrices [A], [B], and [D] as shown in Formula (28). Similarly, reference numeral β in Formula (28) represents a parameter acquired using the respective components A 11  and B 11  of the matrices [A] and [B] as shown in Formula (28) shown above. 
         [0105]    Then, in a computation step S 13 , two integration processes are carried out on Formulae (27) and (28) shown above to obtain common solutions for a gradient θ(r) of a normal direction displacement shown in  FIG. 29 ) shown above and a displacement u 0 (r) shown in Formula 30 shown above. Here, reference characters a 1  and a 2  in Formula (30) and reference characters b 1  and b 2  shown in Formula (29) represent coefficients. 
         [0106]    Then, in a computation step S 14 , an integration step is carried out on Formula (29) shown above to compute the amount of deformation ω (1)  of the diaphragm portion  5  in the first segment (1) shown above in Formula (31), the amount of deformation ω (2)  of the diaphragm portion  5  in the second segment (2) shown above in Formula (32), and the amount of deformation ω (3)  of the diaphragm portion  5  in the third segment (3) shown above in Formula (33). Reference characters D* 11   (1) , b 1   (1) , and c (1)  in Formula (31) represent coefficients resulting from the integration process. Similarly, reference characters D* 11   (2) , b 1   (2) , b 2   (2) , and c (2)  in Formula (32) represent coefficients resulting from the integration process. Thus, the coefficients b 1   (1) , c (1) , b 1   (2) , b 2   (2) , and c (2)  are calculated based on a condition of continuity and a condition of constraint for each of the segments of the composite circular plate. 
         [0107]    Then, in a computation step S 15 , the amount of deformation ω (1)  and ω (2)  of the diaphragm portion  5  and the distance g are input to Formula (34) shown above to compute the volume V 1  in the closed space  7  resulting from the thermal expansion. 
         [0108]    Then, in a computation step S 16 , the volume V 1  in the closed space  7  resulting from the thermal expansion is input to Formulae (31) and (32) shown above to compute a capacitance C′ shown in Formula (35) shown above and corresponding to the amounts of deformation ω (1)  and ω (2)  of the diaphragm portion  5 . 
         [0109]    Then, in a computation step S 17 , the capacitances C 0 ′ and C′ are input to Formula (36) shown above to determine an amount of change in capacitance ΔC′. 
         [0110]    The above-described configuration can achieve the optimum temperature compensation by cancelling out the deformation of the diaphragm portion  5  caused by a change in pressure associated with the temperature of the gas in the closed space  7  (the thermal expansion of the gas sealed in the closed space  7 ) to suppress the deformation of the diaphragm portion  5  within an intended temperature range. 
         [0111]    Moreover, the above-described configuration carries out effective temperature compensation to allow the capacitive sensor  100  with the thin diaphragm portion  5  to be designed and produced, thus enabling an increase in the sensitivity of the capacitive sensor  100 . 
         [0112]    Moreover, the above-described configuration can provide the parameter ΔC′, which enables determination of the degree of compensation for the deformation of the diaphragm portion  5  caused by the thermal expansion of the gas sealed in the closed space  7 . Thus, the deformation of the diaphragm portion  5  can be compensated for more accurately than in the conventional art simply by applying the result of optimization of the parameter ΔC′ to the capacitive sensor. As a result, in detecting a change in the capacitance between the diaphragm portion  5  and both the first electrode portion  3  and the second electrode portion  4  based on the deformation of the diaphragm portion  5 , the capacitive sensor  100  can detect the change in capacitance more accurately than in the conventional art. Here, “optimization of the parameter ΔC′” includes completely zeroing the parameter ΔC′ and approximating the parameter ΔC′ to zero. Furthermore, the “compensation for the deformation of the diaphragm portion  5 ” includes completely zeroing the amount of deformation of the diaphragm portion  5  by setting zero for the parameter ΔC′, and approximating the amount of deformation of the diaphragm portion  5  to zero by setting a value approximate to zero for the parameter ΔC′. 
       Second Embodiment 
       [0113]    Now, a method for temperature compensation in a sensor according to a second embodiment of the present invention will be described with reference to  FIG. 7  to  FIG. 10 . Portions  21  to  27  (some of the portions are not shown in the drawings) of a capacitive sensor  200  to which the results of computations in the method for temperature compensation according to the second embodiment are applied are similar to the portions  1  to  7 , respectively, of the capacitive sensor  100  to which the results of computations in the method for temperature compensation according to the first embodiment are applied. Thus, description of the portions  21  to  27  may be omitted. 
         [0114]    (Configuration of the Capacitive Sensor  200 ) 
         [0115]    As shown in  FIG. 7 , the capacitive sensor (the sensor)  200  includes a substrate  21 , an insulator layer  22 , a first electrode portion  23 , a second electrode portion (conductive portion)  24 , a diaphragm portion  25 , a temperature compensation ring (temperature compensation member)  26 , and a closed space  27  which are similar to the corresponding portions of the capacitive sensor  100 , as well as a first barrier metal layer  28 . 
         [0116]    The first barrier metal layer  28  contains at least platinum and is formed between the second electrode portion  24  and the insulator layer  22  like a ring similar to the second electrode portion  24 . The first barrier metal layer  28  includes two layers, a layer  28   a  located closest to the insulator layer  22  and formed of titanium and a layer  28   b  located closest to the second electrode portion  24  and formed of platinum. An inner circumferential surface of the first barrier metal layer  28  forms the closed space  27  along with an inner surface of a recess  21   a , an inner circumferential surface of a penetration portion  22   a , an inner circumferential surface of the second electrode portion  24 , and a surface of the diaphragm portion  25  on which the second electrode portion  24  is formed. 
         [0117]    (Operation of the Capacitive Sensor  200 ) 
         [0118]    Now, operation of the capacitive sensor  200  will be described. When a pressure based on atmospheric pressure is applied to the diaphragm portion  25  of the capacitive sensor  200 , the diaphragm portion  25  is deformable depending on the pressure. The pressure is measured by detecting a change in the capacitance between the diaphragm portion  25  and both the first electrode portion  23  and the second electrode portion  24 , the change being caused by the deformation. 
         [0119]    (Computation Steps of the Method for Temperature Compensation in the Sensor According to the Second Embodiment) 
         [0120]    Now, computation steps of the method for temperature compensation in the capacitive sensor will be described with reference to  FIG. 8  to  FIG. 10 . The second embodiment carries out steps S 201  to S 217  in order which are similar to the computation steps S 1  to S 17  of the method for temperature compensation according to the first embodiment. 
         [0121]    This configuration applies the result of optimization of the parameter ΔC′ to the capacitive sensor  200 . Thus, the capacitive sensor  200 , configured to enjoy the barrier metal effect of the first barrier metal layer  28 , can also detect a change in the capacitance between the diaphragm portion  25  and both the first electrode portion  23  and the second electrode portion  24  more accurately than in the conventional art. 
       Third Embodiment 
       [0122]    Now, a method for temperature compensation in a sensor according to a third embodiment of the present invention will be described with reference to  FIG. 11  to  FIG. 14 . Portions  31  to  37  (some of the portions are not shown in the drawings) of a capacitive sensor  300  to which the results of computations in the method for temperature compensation according to the third embodiment are applied are similar to the portions  1  to  7 , respectively, of the capacitive sensor  100  to which the results of computations in the method for temperature compensation according to the first embodiment are applied. Thus, description of the portions  31  to  37  may be omitted. 
         [0123]    (Configuration of the Capacitive Sensor  300 ) 
         [0124]    As shown in  FIG. 11 , the capacitive sensor (the sensor)  300  includes a substrate  31 , an insulator layer  32 , a first electrode portion  33 , a second electrode portion  34 , a diaphragm portion  35 , a temperature compensation ring (temperature compensation member)  36 , and a closed space  37  which are similar to the corresponding portions of the capacitive sensor  100 , as well as a sealing ring portion (conductive portion)  38 . 
         [0125]    The sealing ring portion  38  is formed of a metal material such as gold, platinum, or titanium, has an inner diameter of 2R 2  and an outer diameter of 2R 3 , and is formed between the diaphragm portion  35  and the second electrode portion  34  to prevent a gas sealed in the closed space  37  from leaking. In this case, the second electrode portion  34  and the sealing ring portion  38  are preferably bonded together by a gold-gold bonding. An inner circumferential surface of the sealing ring portion  38  forms the closed space  37  along with an inner surface of a recess  31   a , an inner circumferential surface of a penetration portion  32   a , an inner circumferential surface of the second electrode portion  34 , and a surface of the diaphragm portion  35  on which the sealing ring portion  38  is formed. 
         [0126]    (Operation of the Capacitive Sensor  300 ) 
         [0127]    Now, operation of the capacitive sensor  300  will be described. When a pressure based on atmospheric pressure is applied to the diaphragm portion  35  of the capacitive sensor  300 , the diaphragm portion  35  is deformable depending on the pressure. The pressure is measured by detecting a change in the capacitance between the diaphragm portion  35  and both the first electrode portion  33  and the second electrode portion  34 , the change being caused by the deformation. 
         [0128]    (Computation Steps of the Method for Temperature Compensation in the Sensor According to the Third Embodiment) 
         [0129]    Now, computation steps of the method for temperature compensation in the capacitive sensor will be described with reference to  FIG. 12  to  FIG. 14 . Computation steps S 302  to S 317  of the method for temperature compensation according to the third embodiment are similar to the computation steps S 2  to S 17 , respectively, of the method for temperature compensation according to the first embodiment. Thus, only the computation step S 301  will be described in detail. 
         [0130]    First, in the computation step S 301 , based on the Timoshenko&#39;s symmetric circular plate theory, a composite circular plate configured such that center axes of the sealing ring portion  38 , the diaphragm portion  35 , and the temperature compensation ring  36  align with one another is divided into a first segment (1) including a portion with a radius of 0 to R 1  based on the center axis of the diaphragm portion  35 , a second segment (2) including a portion with a radius of R 1  to R 2  based on the center axes of the diaphragm portion  35  and the temperature compensation ring  36 , and a third segment (3) including a portion with a radius of R 2  to R 3  based on the center axes of the sealing ring portion  38 , the diaphragm portion  35 , and the temperature compensation ring  36 . 
         [0131]    Then, the computation steps S 302  to S 317  are sequentially carried out to finish the computation steps of the method for temperature compensation in the capacitive sensor. 
         [0132]    The above-described configuration applies the result of optimization of the parameter ΔC′ to the capacitive sensor  300 . Thus, while configured to enjoy an effect enabling possible leakage of the gas in the closed space  37  to be more reliably prevented by using the sealing ring portion  38  to seal the portion between the diaphragm portion  35  and the second electrode portion  34 , the capacitive sensor  300  can also detect a change in the capacitance between the diaphragm portion  35  and both the first electrode portion  33  and the second electrode portion  34  more accurately than in the conventional art. 
         [0133]    Moreover, the above-described configuration applies the result of optimization of the parameter ΔC′ to the capacitive sensor  300 . Thus, while configured to enjoy an effect enabling reliability of an electric connection between the second electrode portion  34  and the sealing ring portion  38  to be improved when the second electrode portion  34  and the sealing ring portion  38  are bonded together by a gold-gold bonding, the capacitive sensor  300  can also detect a change in the capacitance between the diaphragm portion  35  and both the first electrode portion  33  and the second electrode portion  34  more accurately than in the conventional art. 
       Fourth Embodiment 
       [0134]    Now, a method for temperature compensation in a sensor according to a fourth embodiment of the present invention will be described with reference to  FIG. 15  to  FIG. 18 . Portions  41  to  47  (some of the portions are not shown in the drawings) of a capacitive sensor  400  to which the results of computations in the method for temperature compensation according to the fourth embodiment are applied are similar to the portions  1  to  7 , respectively, of the capacitive sensor  100  to which the results of computations in the method for temperature compensation according to the first embodiment are applied. Thus, description of the portions  41  to  47  may be omitted. 
         [0135]    (Configuration of the Capacitive Sensor  400 ) 
         [0136]    As shown in  FIG. 15 , the capacitive sensor (the sensor)  400  includes a substrate  41 , an insulator layer  42 , a first electrode portion  43 , a second electrode portion  44 , a diaphragm portion  45 , a temperature compensation ring (temperature compensation member)  46 , and a closed space  47  which are similar to the corresponding portions of the capacitive sensor  100 , as well as a sealing ring portion  48  and a second barrier metal layer  49 . 
         [0137]    The sealing ring portion  48  is formed of gold and provided between the diaphragm portion  45  and the second electrode portion  44 , more specifically, on a surface of the second electrode portion  44  opposite to a surface of the second electrode portion  44  on which the insulator layer  42  is formed, thus preventing a gas sealed in the closed space  47  from leaking. 
         [0138]    The second barrier metal layer  49  contains at least platinum, has an inner diameter of 2R 2  and an outer diameter of 2R 3 , and is formed between the diaphragm portion  45  and the sealing ring  48  like a ring similar to the sealing ring  48 . The second barrier metal layer  49  includes two layers, a layer  49   a  located closest to the sealing ring  48  and formed of platinum and a layer (conductive portion)  49   b  located closest to the diaphragm portion  45  and formed of titanium. An inner circumferential surface of the second barrier metal layer  49  forms the closed space  47  along with an inner circumferential surface of the sealing ring portion  48 , an inner surface of a recess  41   a , an inner circumferential surface of a penetration portion  42   a , an inner circumferential surface of the second electrode portion  44 , and a surface of the diaphragm portion  45  on which the second barrier metal layer  49  is formed. 
         [0139]    (Operation of the Capacitive Sensor  400 ) 
         [0140]    Now, operation of the capacitive sensor  400  will be described. When a pressure based on atmospheric pressure is applied to the diaphragm portion  45  of the capacitive sensor  400 , the diaphragm portion  45  is deformable depending on the pressure. The pressure is measured by detecting a change in the capacitance between the diaphragm portion  45  and both the first electrode portion  43  and the second electrode portion  44 , the change being caused by the deformation. 
         [0141]    (Computation Steps of the Method for Temperature Compensation in the Sensor According to the Fourth Embodiment) 
         [0142]    Now, computation steps of the method for temperature compensation in the capacitive sensor will be described with reference to  FIG. 16  to  FIG. 18 . Computation steps S 402  to S 417  of the method for temperature compensation according to the fourth embodiment are similar to the computation steps S 2  to S 17 , respectively, of the method for temperature compensation according to the first embodiment. Thus, only the computation step S 401  will be described in detail. 
         [0143]    First, in the computation step S 401 , based on the Timoshenko&#39;s symmetric circular plate theory, a composite circular plate configured such that center axes of a layer  49   b  of the second barrier metal layer  49  which is closest to the diaphragm portion  45 , the diaphragm portion  45 , and the temperature compensation ring  46  align with one another is divided into a first segment (1) including a portion with a radius of 0 to R 1  based on the center axis of the diaphragm portion  45 , a second segment (2) including a portion with a radius of R 1  to R 2  based on the center axes of the diaphragm portion  45  and the temperature compensation ring  46 , and a third segment (3) including a portion with a radius of R 2  to R 3  based on the center axes of the layer  49   b  of the second barrier metal layer  49  which is closest to the diaphragm portion  45 , the diaphragm portion  45 , and the temperature compensation ring  46 . 
         [0144]    Then, the computation steps S 402  to S 417  are sequentially carried out to finish the computation steps of the method for temperature compensation member in the capacitive sensor. 
         [0145]    The above-described configuration applies the result of optimization of the parameter ΔC′ to the capacitive sensor  400 . Thus, the capacitive sensor  400 , configured to enjoy the barrier metal effect of the second barrier metal layer  49 , can also detect a change in the capacitance between the diaphragm portion  45  and both the first electrode portion  43  and the second electrode portion  44  more accurately than in the conventional art. 
         [0146]    Moreover, the above-described configuration applies the result of optimization of the parameter ΔC′ to the capacitive sensor. Thus, while configured to enjoy an effect enabling reliability of an electric connection between the second electrode portion  44  and the sealing ring portion  48  to be improved when the second electrode portion  44  and the sealing ring portion  48  are bonded together by a gold-gold bonding, the capacitive sensor  400  can also detect a change in the capacitance between the diaphragm portion  45  and both the first electrode portion  43  and the second electrode portion  44  more accurately than in the conventional art. 
       Fifth Embodiment 
       [0147]    Now, with reference to  FIG. 19  to  FIG. 22 , a description will be given which concerns a computation program for a method for temperature compensation in a sensor and a computation processing device carrying out a computation process of the computation program, according to a fifth embodiment of the present invention. 
         [0148]    (Configuration of a Computation Processing Device  500 ) 
         [0149]    As shown in  FIG. 19 , a personal computer (computation processing device)  500  includes a display  51  that displays images, a keyboard  52  via which commands, numerical values, and the like are input, and a control device  53 . 
         [0150]    The control device  53  has a CPU  54  that controls devices in the personal computer  500 , a hard disk  55 , and a drive device  56 . A CD-ROM  57  is removably installed in the drive device  56 . 
         [0151]    (Operation of the Computation Processing Device  500 ) 
         [0152]    After the CD-ROM  57  is installed in the drive device  56 , a program stored in the CD-ROM  57  (a computation program according to the fifth embodiment) is downloaded into the hard disk  55  in response to an instruction input via the keyboard  52 . 
         [0153]    (Computation Steps of the Computation Processing Device According to the Fifth Embodiment) 
         [0154]    Now, computation steps of the computation processing device according to the fifth embodiment will be described with reference to  FIG. 20  to  FIG. 22 . The computation steps shown in  FIG. 20  to  FIG. 22  are implemented by the CPU  54  by executing the program stored in the hard disk  55 . The fifth embodiment carries out steps S 501  to S 507  in order which are similar to the computation steps S 1  to S 17  of the method for temperature compensation according to the first embodiment. 
         [0155]    According to the above-described configuration, the personal computer  500  specifically executes the computation program according to the fifth embodiment to enjoy effects similar to the effects of the first embodiment. 
         [0156]    The present invention is not limited to the above-described embodiments. The embodiments may be varied based on the spirits of the present invention without departing from the scope of the present invention. For example, as shown in  FIG. 23 , in a capacitive sensor  600  including a substrate  61 , an insulator layer  62 , a first electrode portion  63 , a second electrode portion  64 , a diaphragm portion  65 , a temperature compensation ring  66 , a sealing ring portion  68 , and a second barrier metal layer  69  ( 69   a  and  69   b ) which are similar to the corresponding components of the capacitive sensor  400 , a first barrier metal layer  60  may be formed which contains at least platinum and includes two layers, a layer  60   a  formed between the second electrode portion  64  and the insulator layer  62  like a ring similar to the second electrode portion  64 , the layer  60   a  formed of titanium being located closest to the insulator layer  62 , and a layer  60   b  formed of platinum and located closest to the second electrode portion  64 . In this case, an inner circumferential surface of the first barrier metal layer  60  forms a closed space  67  along with an inner circumferential surface of the second barrier metal layer  69 , an inner circumferential surface of the sealing ring portion  68 , an inner surface of a recess  61   a , an inner circumferential surface of a penetration portion  62   a , an inner circumferential surface of the second electrode portion  64 , and a surface of the diaphragm portion  65  on which the second barrier metal layer  69  is formed. Thus, the result of optimization of the parameter ΔC′ is applied to the capacitive sensor  600 . Therefore, the capacitive sensor  600 , configured to enjoy the barrier metal effect of the first barrier metal layer  60 , can also detect a change in the capacitance between the diaphragm portion  65  and both the first electrode portion  63  and the second electrode portion  64  more accurately than in the conventional art. 
         [0157]    In the example described above in the first to fifth embodiments, the Timoshenko&#39;s symmetric circular plate theory is applied to a composite circular plate with three layers including a layer closest to a diaphragm portion, the diaphragm portion, and a temperature compensation ring to obtain the parameter ΔC′, which enables determination of the degree of compensation for deformation of the diaphragm portion. However, the embodiments are not limited to this. The Timoshenko&#39;s symmetric circular plate theory may be applied to a composite circular plate with four or more layers including the three layers, the layer closest to the diaphragm portion, the diaphragm portion, and the temperature compensation ring, and an additional layer other than the layer closest to the diaphragm portion, the diaphragm portion, and the temperature compensation ring, to obtain the parameter ΔC′, which enables determination of the degree of compensation for the deformation of the diaphragm portion. 
         [0158]    In the example described above in the fourth embodiment, the second barrier metal layer  49  includes a plurality of layers, that is, the layer  49   a  formed of platinum and located closest to the sealing ring  48  and the layer  49   b  formed of titanium and located closest to the diaphragm portion  45 . However, the embodiments are not limited to this. As shown in  FIG. 24 , in a capacitive sensor  700  including a substrate  71 , an insulator layer  72 , a first electrode portion  73 , a second electrode portion  74 , a diaphragm portion  75 , a temperature compensation ring  76 , a closed space  77 , and a sealing ring portion  78  which are similar to the corresponding portions of the capacitive sensor  400 , the second barrier metal layer may have a single layer configuration including only a layer  79   a  formed of platinum. In this case, in the above-described computation step S 401  (see  FIG. 16 ), a composite circular plate configured such that the center axes of the layer  79   a , the diaphragm portion  75 , and the temperature compensation ring  76  align with one another is divided into a first segment (1) including a portion with a radius of 0 to R 1  based on the center axis of the diaphragm portion  75  (the position where the radius r is zero), a second segment (2) including a portion with a radius of R 1  to R 2  based on the center axes of the diaphragm portion  75  and the temperature compensation ring  76 , and a third segment (3) including a portion with a radius of R 2  to R 3  based on the center axes of the layer  79   a , the diaphragm portion  75 , and the temperature compensation ring  76 , based on the Timoshenko&#39;s symmetric circular plate theory as is the case with the fourth embodiment. 
         [0159]    In the example described above in the first embodiment, the temperature compensation ring  6  is shaped like a ring on the surface of the diaphragm portion  5  opposite to the surface of the diaphragm portion  5  on which the second electrode portion  4  is formed. However, the embodiments are not limited to this. By way of example, as shown in  FIG. 25(   a ) and  FIG. 25(   b ), in a capacitive sensor  800  including a substrate  81 , an insulator layer  82 , a first electrode portion  83 , a second electrode portion  84 , a diaphragm portion  85 , and a closed space  87  which are similar to the corresponding portions of the capacitive sensor  100 , temperature compensation members  86  each shaped generally like a rectangular parallelepiped may be arranged at every 90° along a circumferential direction of the diaphragm portion  85 , on the surface of the diaphragm portion  85  opposite to the surface of the diaphragm portion  85  on which the second electrode portion  84  is formed. In this example, as shown in  FIG. 25(   a ), a radially outward end surface of the temperature compensation member  86  is shaped identically to an outer circumferential surface of the diaphragm portion  85  (a thick line portion in  FIG. 25(   a )) as viewed in a stacking direction of the substrate  81  and the insulator layer  82 . The temperature compensation member  86  may be disposed at any position and have any shape provided that the temperature compensation member  86  is in a condition optimum for temperature compensation. This also applies to the capacitive sensors  200  to  400  according to the other embodiments (the second to fourth embodiments). 
         [0160]    In the example described above in the first embodiment, the temperature compensation ring  6  is formed on the surface of the diaphragm portion  5  opposite to the surface of the diaphragm portion  5  on which the second electrode portion  4  is formed. However, the embodiments are not limited to this. By way of example, as shown in  FIG. 26(   a ) and  FIG. 26(   b ), in a piezo-resistive physical quantity sensor (a sensor)  900  including a substrate  91 , an insulator layer  92 , a first electrode portion  93 , a second electrode portion  94 , a diaphragm portion  95 , and a closed space  97  which are similar to the corresponding portions of the capacitive sensor  100 , sets of a temperature compensation member  96  and a piezo element  98  shaped generally like rectangular parallelepipeds may be arranged at every 90° along a circumferential direction of the diaphragm portion  95 , on the surface of the diaphragm portion  95  opposite to the surface of the diaphragm portion  95  on which the second electrode portion  94  is formed. In this example, as shown in  FIG. 26(   a ), radially outward end surfaces of the temperature compensation member  96  and the piezo element  98  are shaped identically to an outer circumferential surface of the diaphragm portion  95  (a thick line portion in  FIG. 26(   a )) as viewed in a stacking direction of the substrate  91  and the insulator layer  92 . The piezo-resistive physical quantity sensor  900  uses the piezo element  98 , having a resistance value varying depending on strain of the diaphragm portion  95 , to detect the value of a pressure applied to the diaphragm portion  95 . Changes in the resistance value can be detected based on outputs from the first electrode portion  93  and the second electrode portion  94 . A material for the piezo element  98  may be a piezoelectric material such as PZT (lead zirconate titanate). This also applies to the other embodiments (the second to fourth embodiments). 
         [0161]    Furthermore, in the first to fifth embodiments described above, the conductive portion (electrode portion) is shaped like a circular ring, the diaphragm portion is shaped like a circle, and the temperature compensation member is a temperature compensation ring so that the shapes of the conductive portion, the diaphragm portion, and the temperature compensation member correspond to one another. However, the present invention is not limited to this combination. For example, for compensation for the deformation of the diaphragm portion caused by thermal expansion of a gas sealed in the closed space, the conductive portion (electrode portion) and the temperature compensation member may be shaped like rectangular rings and the diaphragm portion may be shaped like a rectangle so that the shapes of the conductive portion, the temperature compensation member, and the diaphragm portion correspond to one another. Of course, the conductive portion, the diaphragm portion, and the temperature compensation member may have any shapes provided that the conductive portion, the diaphragm portion, and the temperature compensation member are formed to compensate for the deformation of the diaphragm portion caused by thermal expansion of the gas sealed in the closed space. 
       REFERENCE SIGNS LIST 
       [0000]    
       
         
           
               1 ,  21 ,  31 ,  41 ,  61 ,  71 ,  81 ,  91 : Substrate 
               100 ,  200 ,  300 ,  400 ,  600 ,  700 ,  800 : Capacitive sensor (sensor) 
               1   a ,  21   a ,  31   a ,  41   a ,  61   a : Recess 
               2 ,  22 ,  32 ,  42 ,  62 ,  72 ,  82 ,  92 : Insulator layer 
               2   a ,  2   b ,  22   a ,  32   a ,  42   a ,  62   a : Penetration portion 
               3 ,  23 ,  33 ,  43 ,  63 ,  73 ,  83 ,  93 : First electrode portion 
               4 ,  24 ,  34 ,  44 ,  64 ,  74 ,  84 ,  94 : Second electrode portion 
               5 ,  25 ,  35 ,  45 ,  65 ,  75 ,  85 ,  95 : Diaphragm portion 
               6 ,  26 ,  36 ,  46 ,  66 ,  76 : Temperature compensation ring (temperature compensation member) 
               7 ,  27 ,  37 ,  47 ,  67 ,  77 ,  87 ,  97 : Closed space 
               28 ,  28   a ,  28   b ,  60 ,  60   a ,  60   b : First barrier metal layer 
               38 ,  48 ,  68 ,  78 : Sealing ring portion 
               49 ,  49   a ,  49   b ,  69 ,  69   a ,  69   b ,  79   a : Second barrier metal layer 
               51 : Display 
               52 : Keyboard 
               53 : Control device 
               54 : CPU 
               55 : Hard disk 
               56 : Drive device 
               57 : CD-ROM 
               86 ,  96 : Temperature compensation member 
               98 : Piezo element 
               500 : Personal computer (computation processing device) 
               900 : Piezo-resistive physical quantity sensor (sensor)