Abstract:
An accelerometer is fabricated as a MEMS device and includes an array of capacitive electrode plates mechanically coupled to a common proof mass. 
     The proof mass is constrained to move or vibrate in the plane parallel to the first array of plates. The capacitance between the first array of plates is measured with respect to additional arrays of capacitive plates inter-digitated in a comb like pattern.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
   The present application claims priority to the U.S. Provisional Patent Application filed on Feb. 21, 2006, entitled “Accelerometer” and having Ser. No. 60/775,530. 

   BACKGROUND OF INVENTION 
   The present invention relates to micro-mechanical electrical systems (MEMS) type device for measuring vibration and movement, and more particularly to a MEMS accelerometer. 
   MEMS type devices for use as sensors and accelerometers are well known. Such devices are generally fabricated on a silicon or related planar substrate by semi-conductor manufacturing type methods, such as the use of photoresists, masks and various etching processes to fabricate a proximity sensor that includes a suspended proof mass member and means to measure the deflection of the proof mass suspending means. Such devices have inherent limitations on the minimum size, detection limit, sensitivity and the like, largely due to the means used for detecting the deflection of the proof mass. 
   In particular, as attempts have been made to miniaturize accelerometer devices for diverse applications using the technology prior to this applicants invention important aspects of performance have been compromised. In particular, it has been difficult for the prior art devices to achieve both a low noise floor and the required capacitive sensitivity. 
   Although accelerometers with a noise floor of less than 1 μg/√Hz have been reported they include a very large proof mass in the order of several square millimeters. In particular, there has been an unmet need for accelerometer devices with a size of less than about 1.5×1.5 mm, and more preferably less than about 1 mm×1 mm. 
   It is therefore a first object of the present invention to provide an accelerometer with a reduced minimum detection limit. 
   It is another object of the invention to provide an accelerometer with smaller physical dimensions than the prior art. 
   It is still a further object to provide an accelerometer having the above attributes with a higher sensitivity. 
   It is also an object of the invention to provide an accelerometer subject to lower mechanical noise. 
   A still further and additional object of the invention is to provide the aforementioned benefits in an accelerometer that can be fabricated using standard silicon on insulator (SOI) fabrication techniques generally known in he semiconductor industry to reduce manufacturing costs. 
   It is still a further object of the invention to provide a means to combine multiple accelerometers in a configuration for the simultaneous measurement acceleration in three dimensions. 
   It is still a further object of the invention to provide an accelerometer which doesn&#39;t require vacuum packaging in order to operate, thus enabling the benefits of lower packaging costs, smaller packaging size and stability of operation. 
   SUMMARY OF INVENTION 
   In the present invention, the first object is achieved by fabricating on a substantially planar substrate a proof mass frame supported on the substrate by a plurality of planar spring elements. A one or more capacitive plates is attached to and distributed with the proof mass frame while two or more arrays of capacitive plates are supported on the substrate in a cooperative inter-digitated comb like orientation. The capacitive plates are arranged with respect to the proof mass frame such that the movement of the frames permitted by the planar spring causes a change in the overlap area between stationary and moving electrodes. 
   A second aspect of the invention is characterized in that the capacitive plates are arrayed in a manner that capacitive plates disposed on opposite sides of the plates in a first array are connected to opposite poles of a power supply to form a differential circuit for eliminating noise. 
   A third aspect of the invention is characterized in the arrays of capacitive plates connected to opposite poles of a power supply that are separately and remotely inter-digitated with the capacitive plates in the first array to facilitate fabricating a MEMS device with electrical isolation between each of the arrays connected to opposite poles of the power supply. 
   An additional aspect of the invention is the processing of the SOI wafer from two sides resulting in an increased mass of the rotor (moving part). This facilitates in increasing the capacitive sensitivity and decreases the thermo-dynamical noise. 
   The above and other objects, effects, features, and advantages of the present invention will become more apparent from the following description of the embodiments thereof taken in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF DRAWINGS 
       FIG. 1A  is a plan view of a portion of an operative accelerometer. 
       FIG. 1B  is a cross section elevation of the portion of the accelerometer shown in  FIG. 1A  at section line B-B. 
       FIG. 1C  is a projection though the elevation orthogonal to that shown in  FIG. 1B . 
       FIG. 2  is schematic illustration showing a preferred circuit diagram for use with the accelerometer of  FIG. 1 . 
       FIG. 3A  is a plan view of an alternative embodiment of the operative accelerometer deploying an array of capacitive plates and planar springs. 
       FIG. 3B  is a cross section elevation of the portion of the accelerometer shown in  FIG. 3A  at section line B-B. 
       FIG. 3C  is a projection though the elevation orthogonal to that shown in  FIG. 3B . 
       FIG. 4  is a cross section elevation of a three dimensional accelerometer device deploying the accelerometer component shown in  FIG. 3 . 
       FIG. 5  is a cross-sectional elevation of the SOI structure used to fabricate the accelerometer. 
       FIG. 6  is a plan view of one embodiment of the accelerometer as fabricated from the SOI in  FIG. 5 . 
       FIG. 7  is a cross-sectional elevation of the accelerometer of  FIG. 6  taken a reference line A-A in  FIG. 6 . 
       FIG. 8  is a cross-sectional elevation of the accelerometer of  FIG. 6  taken a reference line B-B in  FIG. 6 . 
       FIG. 9A  is a plan view of the moving components and the capacitive circuit in another embodiment of the invention as fabricated from the SOI in  FIG. 6 , with the scale in microns. 
       FIG. 9B  is an enlarged partial view of the lower spring portion of the accelerometer shown in  FIG. 9A . 
       FIG. 9C  is an enlarged partial view of the central portion of the spring portion shown  9 B. 
       FIG. 9D  is an enlarged partial view of the right most portion of the spring portion shown  9 B. 
       FIG. 9E  is an enlarged partial view of the right most portion a single spring fold shown in  FIG. 9D . 
       FIG. 10A  is a schematic diagram of the function elements of the device in  FIG. 9A  that correspond to the circuit diagram in  FIG. 10B   
       FIG. 11A  is a partial plan view of the same device in  FIG. 9A  with reference line B-B to indicate the position of the portion shown in section in  FIG. 11B   
       FIG. 11B  is a cross-sectional elevation of the accelerometer of  FIG. 9  taken a reference line B-B- in  FIG. 11A . 
       FIG. 12  is a graph comparing the performance of the device in  FIG. 9  against alternative devices, not all of which are prior art. 
   

   DETAILED DESCRIPTION 
   Referring to  FIGS. 1 through 12 , wherein like reference numerals refer to like components in the various views, there is illustrated therein a new and improved accelerometer, generally denominated  100  herein. 
   In accordance with the present invention, the operative principles will first be illustrated with reference to  FIG. 1 , which illustrates a portion of the operative accelerometer  100  that includes a substrate  110  which supports a pair of capacitive plates  160  and  150  that extend upward therefrom. As will be illustrated in other embodiments, the capacitive plates can be connected to the substrate in alternative configurations, provided that in general they are disposed orthogonal to the plane of the substrate. Generally, capacitive plates  160  and  150  are electrically isolated from each other, as shown in the circuit diagram  200  of  FIG. 2 . A third capacitive plate  140  is suspended above the substrate  110  in a parallel orientation between capacitive plates  150  and  160  by a proof mass frame  120 , via bridge  127 . The proof mass frame  120  is attached to and supported above substrate  110  by planar springs. The planar spring  130  is preferably a leaf spring having multiple junctions with a plurality of planar segments that lie perpendicular to the substrate  110 . Preferably as shown, four planar leaf springs  130  are distributed at corners of the proof mass frame  120 , being coupled thereto at junctions  130   a . The opposite end  130   b  of each leaf spring  130  is a post that extends downward to connect with the substrate. Thus, each of the parallel or straight segment  132  of each leaf spring are free to move due to flexure at the interconnecting folds or joints  131 . Arrow  105  shows the direction of movement of the proof mass frame  120  as permitted by planar springs  130 . 
   The planar springs  130  confine the movement of proof mass frame  120  to the direction of Arrow  105  such that as the proof mass frame moves or vibrates above the substrate the capacitive plate  140  move between and parallel to the surrounding capacitive plates  150  and  160  disposed on opposite and generally diagonal sides thereof. 
   Thus, the acceleration of proof mass  120  urges the movement of capacitive plate  140  with respect to the adjacent capacitive plates  150  and  160  such that the degree of movement of proof mass  120  can be determined by the change in capacitance or charge in the operative circuit  200  of  FIG. 2 . 
   The change in capacitance with respect to plates  150  and  160  is best understood with respect to  FIG. 1C , which is a projection showing both plates. The projected overlapping area of plates  140  and  150  is labeled  175 , whereas the overlapping area of plates  140  and  160  is labeled  176 . It show be appreciated that as proof mass moves upward with respect to arrow  105  in  FIG. 1A , overlapping area  175  increases, while overlapping area  176  decreases. In contrast, when proof mass moves downward with respect to arrow  105  in  FIG. 1A , overlapping area  175  decreases, while overlapping area  176  increases. 
   While  FIGS. 1 and 2  illustrate an accelerometer deploying three capacitive plates  140 ,  150  and  160  it should be appreciated that in preferred embodiments, such as will be further discussed with respect to  FIG. 3 , each capacitive plate is replaced with one or more parallel arrays of capacitive plates. However, although the various embodiments illustrate one capacitive plate (or an array of capacitive plates is attached to the proof mass) with the other two capacitive plates (or arrays of capacitive plates) are attached to the substrate it should also be appreciated that the same relative motion between capacitive plates can be achieved in the opposite configuration, e.g., with one capacitive plate (or array of capacitive plates) attached to the substrate, while the other two (or arrays of two) capacitive plates are attached to the proof mass. 
   A preferred operative electrical circuit  200  for the device  100  of  FIG. 1  is shown in  FIG. 2 . Capacitive plate  140  (or the array  240  shown in  FIG. 3 ) that moves with respect to the substrate  110  is connected to one input terminal  221  of amplifier  220 . The other input terminal  222  of amplifier  220  is grounded. Each of the adjacent fixed capacitive plates  160  and  150  (or arrays  250  and  260  shown in  FIG. 3 ) that interact with capacitive plate  140  are connected to opposite polarity terminals of the DC power supply  210 . Amplifier  220  has an output terminal  223 . 
   When the moving capacitive plate  140  is in nominal position  140 ′ shown in  FIG. 2 , the electrostatic charging from each of the oppositely charged plates  160  and  150  are balanced, hence no current flows to amplifier  220 , resulting in zero output at terminal  223 . However, as the plate  140  moves downward as shown in the Figure, the induced charge of the upper capacitor plate  160  decrease while the opposite induced charge from capacitor plate  150  increase, resulting in a unbalanced charge to plate  140 . The changing charge balance now causes current to flow to amplifier  220  resulting in a measurable voltage change at terminal  223 . 
   It should be appreciated that the method of sensing the movement of proof mass  120  by measuring the change in capacitance between plates  140 ,  150  and  160  has numerous advantages. Such a system of the capacitor electrodes (both proof mass and stationary electrodes) can be viewed as a system of parallel-connected plate capacitors. 
   The capacitance of each pair of electrodes is 
   
     
       
         
           
             
               
                 C 
                 = 
                 
                   
                     
                       ɛ 
                       0 
                     
                     ⁢ 
                     A 
                   
                   h 
                 
               
             
             
               
                 ( 
                 1 
                 ) 
               
             
           
         
       
     
   
   Where ε 0  is the vacuum dielectric permittivity, A is the area of the capacitor plates and h is the distance between the plates. When the proof mass moves, the capacitance between the electrodes changes, the capacitance sensitivity Γ C  is defined as the capacitance change per g of acceleration. 
   
     
       
         
           
             
               
                 
                   
                     Γ 
                     C 
                   
                   = 
                   
                     
                       
                         ∂ 
                         C 
                       
                       
                         ∂ 
                         a 
                       
                     
                     = 
                     
                       
                         
                           
                             ∂ 
                             C 
                           
                           
                             ∂ 
                             x 
                           
                         
                         ⁢ 
                         
                           
                             ∂ 
                             x 
                           
                           
                             ∂ 
                             a 
                           
                         
                       
                       = 
                       
                         
                           
                             ∂ 
                             C 
                           
                           
                             ∂ 
                             x 
                           
                         
                         ⁢ 
                         
                           g 
                           
                             ω 
                             0 
                             2 
                           
                         
                       
                     
                   
                 
                 , 
               
             
             
               
                 ( 
                 2 
                 ) 
               
             
           
         
       
     
   
   where a is acceleration, x is displacement and ω 0  is eigenfrequency of the accelerometer that is assumed to be far above the accelerometer bandwidth. (It is usually expressed in pF/g units) 
   In contrast to the current invention, air gap accelerometer relies on the change in the distance h between to parallel and facing electrodes that overlap in projected area, in such an air gap accelerometer the capacitive sensitivity is 
   
     
       
         
           
             
               
                 
                   Γ 
                   
                     C 
                     ⊥ 
                   
                 
                 = 
                 
                   
                     
                        
                       
                         
                           ∂ 
                           C 
                         
                         
                           ∂ 
                           h 
                         
                       
                        
                     
                     ⁢ 
                     
                       g 
                       
                         ω 
                         0 
                         2 
                       
                     
                   
                   = 
                   
                     
                       C 
                       h 
                     
                     ⁢ 
                     
                       g 
                       
                         ω 
                         0 
                         2 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 3 
                 ) 
               
             
           
         
       
     
   
   The mechanical noises of the novel area change accelerometer will now be compared with that for the conventional air gap type device. The Brownian equivalent of acceleration noise in g/√{square root over (Hz)} is 
   
     
       
         
           
             
               
                 
                   
                     g 
                     
                       n 
                       , 
                       B 
                     
                   
                   = 
                   
                     
                       
                         4 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           K 
                           B 
                         
                         ⁢ 
                         TD 
                       
                     
                     Mg 
                   
                 
                 , 
               
             
             
               
                 ( 
                 5 
                 ) 
               
             
           
         
       
     
   
   where D is the damping coefficient of proof mass M. The damping coefficient for two moving area-changed electrodes, such as is shown in  FIG. 1-4 , is 
   
     
       
         
           
             
               
                 
                   
                     D 
                     1 
                   
                   = 
                   
                     
                       η 
                       0 
                     
                     ⁢ 
                     
                       
                         A 
                         1 
                       
                       h 
                     
                   
                 
                 , 
               
             
             
               
                 ( 
                 6 
                 ) 
               
             
           
         
       
     
   
   where η 0 =22.6×10 −6  Ns/m 2  is the viscosity of the air, A 1  is the plate area, h is the air gap. 
   The damping coefficient for two moving air-gap changed electrodes can be calculated analytically for a limited case of elongated rectangular electrodes for which h&lt;&lt;b&lt;&lt;L 
   
     
       
         
           
             
               
                 
                   D 
                   ⊥ 
                 
                 = 
                 
                   
                     η 
                     eff 
                   
                   ⁢ 
                   
                     
                       
                         b 
                         3 
                       
                       ⁢ 
                       L 
                     
                     
                       h 
                       3 
                     
                   
                 
               
             
             
               
                 ( 
                 7 
                 ) 
               
             
           
         
       
     
   
   where b is the width, L is the length of the electrodes and η eff  is the effective gas viscosity that depends on the gas pressure and the distance between the electrodes h. For example, if h=2 μm then η eff ≈0.83η 0  at the normal pressure. The Eq. (7) could be obtained by integration of the Incompressible Navier-Stocks equation with appropriate boundary conditions. 
   We will now compare the damping coefficients of the area-changed and air gap accelerometers that have the same capacitive sensitivity. 
   Assume that the area-changed accelerometer has N 1  rectangular fingers with width b 1 , length L 1  and distance between the electrodes h and that the air-gap accelerometer has N 2  rectangular fingers with width b 2 , length L 2  and the same distance between the electrodes h 
   From Eq (4) the total capacitive sensitivity of the area-changed accelerometer is 
   
     
       
         
           
             Γ 
             1 
           
           = 
           
             
               N 
               1 
             
             ⁢ 
             
               
                 
                   ɛ 
                   0 
                 
                 ⁢ 
                 
                   L 
                   1 
                 
               
               h 
             
             ⁢ 
             
               g 
               
                 ω 
                 0 
                 2 
               
             
           
         
       
     
   
   From Eq (3) the total capacitive sensitivity of the gap-change accelerometer is 
   
     
       
         
           
             Γ 
             2 
           
           = 
           
             
               N 
               2 
             
             ⁢ 
             
               
                 
                   ɛ 
                   0 
                 
                 ⁢ 
                 
                   b 
                   2 
                 
                 ⁢ 
                 
                   L 
                   2 
                 
               
               
                 h 
                 2 
               
             
             ⁢ 
             
               g 
               
                 ω 
                 0 
                 2 
               
             
           
         
       
     
   
   Equalizing Γ 1  and Γ 2  we have 
   
     
       
         
           
             
               
                 
                   Γ 
                   1 
                 
                 = 
                 
                   
                     
                       Γ 
                       2 
                     
                     ⇒ 
                     
                       
                         N 
                         1 
                       
                       ⁢ 
                       
                         L 
                         1 
                       
                     
                   
                   = 
                   
                     
                       
                         N 
                         2 
                       
                       ⁢ 
                       
                         b 
                         2 
                       
                       ⁢ 
                       
                         L 
                         2 
                       
                     
                     h 
                   
                 
               
             
             
               
                 ( 
                 8 
                 ) 
               
             
           
         
       
     
   
   Now let us calculate the ration D 1 /D ⊥  subject to the condition of Eq. (8). From Eq. (6) and Eq. (7) we have 
   
     
       
         
           
             
               
                 
                   
                     D 
                     1 
                   
                   
                     D 
                     ⊥ 
                   
                 
                 = 
                 
                   
                     
                       
                         
                           N 
                           1 
                         
                         ⁢ 
                         
                           η 
                           0 
                         
                       
                       
                         
                           N 
                           2 
                         
                         ⁢ 
                         
                           η 
                           eff 
                         
                       
                     
                     ⁢ 
                     
                       
                         
                           b 
                           1 
                         
                         ⁢ 
                         
                           L 
                           1 
                         
                         ⁢ 
                         
                           / 
                         
                         ⁢ 
                         h 
                       
                       
                         
                           b 
                           2 
                           3 
                         
                         ⁢ 
                         
                           L 
                           2 
                         
                         ⁢ 
                         
                           / 
                         
                         ⁢ 
                         
                           h 
                           3 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         
                           N 
                           1 
                         
                         ⁢ 
                         
                           η 
                           0 
                         
                       
                       
                         
                           N 
                           2 
                         
                         ⁢ 
                         
                           η 
                           eff 
                         
                       
                     
                     ⁢ 
                     
                       
                         
                           b 
                           1 
                         
                         ⁢ 
                         
                           L 
                           1 
                         
                         ⁢ 
                         
                           h 
                           2 
                         
                       
                       
                         
                           b 
                           2 
                           3 
                         
                         ⁢ 
                         
                           L 
                           2 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 9 
                 ) 
               
             
           
         
       
     
   
   Substituting N 1 L 1  from Eq. (8) into Eq. (9) we get 
   
     
       
         
           
             
               
                 
                   
                     D 
                     1 
                   
                   
                     D 
                     ⊥ 
                   
                 
                 = 
                 
                   
                     
                       
                         η 
                         0 
                       
                       
                         
                           N 
                           2 
                         
                         ⁢ 
                         
                           η 
                           eff 
                         
                       
                     
                     ⁢ 
                     
                       
                         
                           b 
                           1 
                         
                         ⁢ 
                         
                           h 
                           2 
                         
                         ⁢ 
                         
                           N 
                           2 
                         
                         ⁢ 
                         
                           b 
                           2 
                         
                         ⁢ 
                         
                           L 
                           2 
                         
                         ⁢ 
                         
                           / 
                         
                         ⁢ 
                         h 
                       
                       
                         
                           b 
                           2 
                           3 
                         
                         ⁢ 
                         
                           L 
                           2 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         η 
                         0 
                       
                       
                         η 
                         eff 
                       
                     
                     ⁢ 
                     
                       
                         
                           b 
                           1 
                         
                         ⁢ 
                         h 
                       
                       
                         b 
                         2 
                         2 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 10 
                 ) 
               
             
           
         
       
     
   
   Since η eff ≈η 0  at the normal pressure, the ratio D 1 /D ⊥  depends on the widths of the area-changed and the air-gap electrodes b 1  and b 2  respectively and by the electrode gap h and is independent from N 1 , N 2 , L 1 , L 2 . 
   If b 1 =b 2  and b 2 &gt;&gt;h, then D           &lt;&lt;D         . That is for equal electrode width the area-changed accelerometer has smaller damping than air gap changed accelerometer. That is, however, no longer true if the width of the electrodes became comparable with the distance between the electrodes.
   If we assign the typical values for h=1.5 μm and b 1 =b 2 =10 μm, then we get from Eq. (10) 
   
     
       
         
           
             
               
                 
                   
                     D 
                     1 
                   
                   
                     D 
                     - 
                   
                 
                 = 
                 
                   0.18 
                   . 
                 
               
             
             
               
                 ( 
                 11 
                 ) 
               
             
           
         
       
     
   
   Thus, in this example the damping coefficient of the area-changed accelerometer is about 5.5 times smaller than the damping coefficient of the air gap accelerometer while providing the same level of capacitive sensitivity 
   Accordingly, the area change type of accelerometers of the disclosed invention can have a smaller mechanical damping than the conventional type that are sensitive to a change in air gap, yet while providing the same level of capacitive sensitivity. Therefore, capacitive accelerometers working on the inventive area-changed principle could have a smaller proof mass than those working on the prior art air-gap principle. Thus, the ability to reduce the proof mass by a factor of about 16 permits the reduction of the size of MEMS accelerometers to the micrometer-scale range. 
   For an area-change in-plane capacitive accelerometer with complementary metal-oxide-semiconductor (CMOS) readout circuitry, which includes 350 electrodes, a 2 μm gap between electrodes, the mass of the device 3 μg. The estimated device sensitivity is 10 fF/g with total electrode capacitance 0.4 pF. The device has a resonance frequency of 1500 Hz and a mechanical noise floor of 14 μg/√{square root over (Hz)}. It should be appreciated that for the additional and more preferred embodiments the TNEA is 4.5 μg/√{square root over (Hz)}. 
   The damping coefficient was calculated using FEM for the solution of the incompressible Navier-Stokes equation. Capacitance calculations were performed using 3D FEM. 
     FIG. 3  illustrates an alternative embodiment of the inventive accelerometer in which a plurality of arrays of capacitive plates is deployed. 
   In the preferred embodiment shown in  FIG. 3 , the capacitive plates of array  240  are arranged as a plurality of rows extending from opposite sides of the proof mass  120 . The rows of capacitive plates in array  240  are mounted on one or more support arms  123 . The proof mass frame  120  preferably has an H-shape with the horizontal portions  121  between the vertical legs  122  supporting the first set of arrays of capacitive plates. The vertical legs  122 , having a width w which may in this embodiment provide the largest fraction of the proof mass, as opposed to the horizontal portion  122 , the capacitive plates  241  and the capacitive plate array supporting arms  123 . 
   The capacitive plates in the device  100  of  FIG. 3  are arranged in subgroups of type A and subgroups of type B. In this embodiment, two A type subgroups are deployed A, and A′. Each subgroups consists of an array  241  of capacitive plates attached to the proof mass  120  interlaced with the one of the powered array of capacitive plates attached to the substrates  110  as illustrated in circuit  200  of  FIG. 2 . In Subgroups A, and A′ the arrays  241  of capacitive plates is interlaced with capacitive plate arrays  250 . In contrast in each of subgroups B and B′ the  241  arrays  241  of capacitive plates are interlaced with capacitive plate arrays  260 . Although each of the capacitive plate arrays  250  and  260  are physically attached to the substrate  110  they are electrically isolated for connection to opposite terminals of a power supply to form an equivalent to circuit  200  shown in  FIG. 2 . While the insulating structures isolating plate arrays  241 ,  250  and  260  are omitted from the figure for simplicity, it should be understood that when the substrate is electrically conductive, only two of the three plate arrays needs to be insulated therefrom, as the circuit  200  of  FIG. 2  may include substrate  110 . It should be understood that each subgroup may have more than 2 or 3 capacitive plates and that the device may deploy considerably more than two of each type of subgroup. 
   Further in the configuration shown in  FIG. 3 , the proof mass value can be increased by extending the frame width, w, without interference in the movement of the capacitive plates. 
   In contrast to prior art MEMS based capacitor devices that deploy a variable air gap between capacitive plates, this invention largely eliminates potential stiction between capacitive plates, which leads to lost sensitivity and hysteresis. Other inherent advantages of the novel arrangement of the capacitor plates and proof mass shown in  FIGS. 3-11  are that a high capacitor area, for greater sensitivity can be achieved with a relatively small device. 
     FIG. 4  illustrates a three dimensional accelerometer  400  assembled from three of the devices  100  of  FIG. 3  in a mutually orthogonal arrangement thus forming a three-dimensional accelerometer. Thus each of the three accelerometers  100 ,  100 ′ and  100 ″ will independently sense movement and acceleration in an axis orthogonal to each of the other two sensors. Further, each of each of the three accelerometers  100 ,  100 ′ and  100 ″ has its own analog electronics  90 ,  90 ′ and  90 ″ that includes circuit  200  packaged below substrates  110 . In preferred embodiments, the completed device  400  includes digital electronics and in particular a common microprocessor operatively in communication with the analog electronics of each particular accelerometer  100 ,  100 ′ and  100 ′″. It should be appreciated that the alternative embodiments shown in  FIG. 3-11  can be arranged in a like manner. 
     FIG. 5  through  FIG. 11  illustrate more preferred embodiments of the invention that are particularly optimized for the intended use of small scale, yet sensitive accelerometers, and methods for their fabrication from SOI (Silicon On Oxide) substrates.  FIG. 5  is a cross sectional illustration of the SOI substrate  500  in which a relatively thick Si substrate layer  510  is covered by a layer  520  of dielectric silicon oxide about 2 microns thick. The silicon oxide layer  520  is in turn covered by a layer of n or p doped silicon  530 , which is preferable about 45 to 50 microns thick. The lower or handle wafer portion  510  portion of substrate  500  has a thickness of about 350 μm for a total thickness for the SOI substrate  500  of about 400 μm. 
     FIG. 6  is a plan view of one such embodiment of the accelerator device  100  as fabricated in the SOI substrate  500  in  FIG. 5 . Generally, a square or rectangular region or frame  205  confines the proof mass  120  that is free of substrate  510  by removal of the silicon oxide layer  520  in this region. The silicon oxide layer  520  is removed by first defining the MEMS device pattern shown in this view by masking and etching layer  510 . Once the features shown in the plan view are formed, an etchant that preferably attacks silicon oxide over silicon is used to remove the underlying oxide layer  520 , releasing the proof mass as shown in the different sectional view in  FIGS. 7 and 8 . It should be noted that  FIG. 7  corresponds with section reference line A-A to illustrate the static support arms  240  that extend inward form frame  205  and the dynamic support arms  540  that extend out from proof mass  120 . In contrast,  FIG. 8  corresponds to section reference line B-B in  FIG. 6 , illustrating the vertical portion  122  of proof mass  120 , the central of horizontal portion  121  and spring  130  attached to the side  205   a  of frame  205 . Specifically, the static arms  240  extend in from the side of frame  205  that is orthogonal to the side  205   a  attached to the springs  130 . The frame  205  supports multiple arrays of capacitive plates  245  on support arms  240 . The proof mass  120  supports multiple array of capacitive plates  545  on the support arms  540  that extend out from the central portion  121  thereof. 
   Further, as can be seen in the central portion  121  of proof mass of  120  an array of through holes have been formed that extend to the former location of the silicon oxide layer  520 . These holes are formed to permit liquid etchant to reach and thus extract the portion of silicon layer  520  directly beneath the proof mass. Thus, regions of the proof mass  120  are masked to expose a square area of etch holes. Further, at the outer periphery of frame  205  the upper silicon layer  530  in this region is etched down to the silicon oxide layer  520  for electrical isolation of the portion of the support arms  240 , as well as other circuit features, that are intended to form separate parts of the capacitive circuit. Thus, various trenches  610  divide the top silicon layer  510 . Various conductive traces or metallization layers  620  connect to the isolated silicon region around the frame. These traces can be formed on the silicon oxide  520  layer, or can run over additional dielectric layers that are added for this purpose in the well known method of semiconductor device manufacture. Further, the trenches  610  or portion of upper silicon layer  510  can be filled or cover with a one or more dielectric layer so that the traces  620  can run on these layers. 
     FIG. 9A  illustrates in plan view a more preferred embodiment. First it should be noted that while the overall structure of the proof mass is suspended inside the frame as shown in  FIGS. 6-8 , the central portion of the proof mass is now solid. 
   It should be appreciated that the proof mass  120  in the embodiment in  FIG. 5-8  has reduced mass due to the plural holes created so that etchant can completely remove and release the silicon oxide layer  520 . In contrast, the embodiment now shown in  FIG. 9-11  has as a first advantage a heavier proof mass for the same area of capacitive plates because such etch holes are avoided. More significantly, as is evident from the sectional view in  FIG. 11A  the proof mass extends to at least a portion of silicon layer  530  having a solid lower portion  9122 , shown in  FIG. 11 , as well as the upper generally H shaped portion  9121  that suspends the support arms  540  and the dynamic capacitive plates  545  within the central region of frame  205 . The lower portion of  9122  was formed in silicon layer  510  by multiple steps of selective etching through a resist mask applied to the lower surface. The perimeter of the frame is etched longer to penetrate closer or the silicon oxide layer  520 . The square central portion within this perimeter is etched for a shorter period of time to define the bottom of the proof mass  120 . In either this or a separate etch step the silicon oxide layer is penetrated only in the frame region to release the proof mass  120  so that it is only support by springs  130 . Thus, as the silicon oxide layer  520  is not intended to etch laterally for release of the proof mass, no perforations are required in it for etching agent flow and reach all of the silicon oxide layer  520  . The larger proof mass, relative to the high capacitive plate area reduces the noise floor of the device  100 . In addition, the attachment of the additional of proof mass portion  9122  not only permits the increased volume and hence weight of the proof mass but frees up space on the upper surface of the proof mass to fabricate trenches and interconnects circuits that connect different support arms and the associated capacitive plates in a more preferred electrical circuit  1000 , shown in  FIG. 10 . 
   As shown in the plan view in  FIG. 9 , the springs  130  also extend in from side  205   a  of frame  205  where they connect to the vertical sides  122  of “H” shaped proof mass  120 . In this embodiment the spring  130  consists from eight beams with a thickness of 3 microns and a length of 240 microns. Height of the springs is 20 μm. As shown in  FIG. 11A , the springs  130  are situated proximate the bottom of the device layer containing the capacitive plates  245  and  545 . The device layer is etched from layer  510  above for 30 microns and the remaining 20 microns is left for the springs. Preferably the springs  130  are vertical disposed as close as possible to the center of mass of the proof mass structure. 
   It should be understood that depending on the final application and desired device parameters such as the size and structure of the proof mass modified as known to those with ordinary skill of the art. Likewise, in such cases the spring dimension, and spring constant, change with respect to proof mass and desired sensing range. 
   It should also be appreciated that the springs  130  can be inset within proof mass  120  such that the proof mass  120  need not have a literal H shape, but can deviate in other ways that are still intended to be within the scope of the claimed invention. 
   Further, while the static and dynamic support arms in the devices  100  of  FIG. 6-8  have interlaced capacitive plates that interact largely through an area change, the capacitive plates in device  100  of  FIG. 9-11  extend bilaterally from the supports arms, are spaced differently and are connected in a different manner to form the operative device  100  having what is known as a full bridge circuit  1000  illustrated in  FIGS. 10A  and B. First, it can be appreciated that the preferred arrangement of static support arms  240 , the attached capacitive plates  245 , the dynamic support arms  540  (which extend out from the proof mass  120 , and their attached capacitive plates  545  are disposed centrosymmetrically about the geometric center of the MEMS device as seen in a plan view in  FIGS. 6 ,  9 A and  10 A. This full bridge circuit  1000  in combination with the centrosymmetric layout has an advantage of canceling offsets stemming from strains and manufacturing errors and some other first order effects on the device, such as temperature, stress and like variations. 
   As shown in  FIGS. 9A and 10A , the proof mass  120  has support arms  540  that are electrically isolated, to form two types of alternating isolated electrodes, indicated A and B, on both sides of the proof mass. 
   Further, frame  205  now supports two types of alternating support arms  240 , indicated as C and D thus the interleaving of each A and B type of capacitive plates  545  with both a C and D type of static capacitive plates  245  defines four types of capacitor pairs from these combinations: A-C, A-D, B-C and B-D. When the proof mass moves upward the capacitance of pairs A-D and B-C increase, whereas pairs A-C and B-D decrease. The equivalent full bridge type circuit  1000  is shown in  FIG. 10B . As can be more clearly in  FIG. 10A , which is not intended to disclose a particular scale or size, the static capacitive plates  245  now extend orthogonally from support arms  240  bilaterally, that is to opposites sides of support arms  240 . It should be noted that the dynamic support arms  540  now also have capacitive plates  545  that extend from both sides. This configuration enables the full bridge circuit but also increases the capacitive area and reduces damping from air resistance. 
   In this embodiment, as illustrated by the various scale bars in  FIG. 9A-E , the open frame  205  is generally square having the dimensions of about 900 μm×900 μm. The static support arms  240  and dynamic support arms  540  have a length of about 200 μm. Gaps between the static and dynamic arms when the proof mass is at rest and when the springs are fully relaxed is about 2.5 μm. 
   Isolation trenches  610  separate the central portion of the proof mass form the upper and lower spring set. This permits alternating capacitive arms on the proof mass to be connected alternatively to form the full bridge circuit illustrated in  FIG. 10B . The structural organization of isolating the bulk of the proof mass  120  below the interlaced capacitive plates  245  and  545  permits a very dense electrode structure without the need to separate the support arms or electrodes as in the other embodiments. Thus, the capacitive sensitivity and other aspects of the electrical performance of the device  100  are significantly enhanced In particular as this structure is free from the effects of large parasitic capacitance that present in the case of two stationary electrodes near one moving electrode (in the proof mass)—as in the case of the embodiment of  FIG. 6-8 . This permits the fabrication of smaller devices, while keeping our sensitivity and linearity values. It should be appreciated that it is desirable to operate over a linear range. 
     FIG. 9B-E  illustrate the location and size of various stops to prevent planar contact that could lead to stiction either between the springs straight portion  132 , or the springs  130 , portion of the proof mass  120  and the frame  205 . The scale bar surrounding the device is in units of microns. Any enlarged regions have separate scale bars and markings also in micron units. Generally, these stop are protrusion from the planar portions of the spring that would tend to contact each other as well as the proof mass and surrounding frame when the device is accelerated faster than its intended range. These stops prevent large planar area of the device from contacting each other in such circumstances, such contact being likely to lead to sticking of the planar surface. Small size stoppers  135  are added to the fold portion  131  of the springs  130  to avoid stiction between the straight part  132  thereof. Further, another stopper  236  is defined by adjacent channels in the side of frame  205  to prevent stiction of the vertical portion  122  of the proof mass  120  to the frame  205 . Further, a series of four protruding fingers  235  extend outward from the side  205   a  of the frame  205  to prevent the full compression of the springs  130  and the stiction of the long side of the vertical H portion  122  of proof mass  120  with the adjacent frame surface. 
   As shown on the magnified insets over the left and rights portion of  FIG. 9A  (with adjacent scale bar for 20 microns) the support arms have a center to center spacing of 30 microns. The capacitive plates on the support arms have a center to center spacing of about 10 microns. As the capacitive plates are about 4 microns thick, this leaves a capacitive gap between adjacent plates of about 2 microns. However, as the plates have a length of about 18 microns, the nominal distance between the edge of each plate and the adjacent root or gap between plates on the adjacent support arm is about 4 microns, only twice the capacitive gap between parallel plates. Thus when the dynamic support arms move up to the 2.4 microns permitted by stops  235 , the capacitive plates and support arms can approach as close as 1.6 microns, which is less than the 2 micron gap between parallel capacitive plates. When this occurs the overlapping area between capacitive plates increase from about 2 microns to about 4.5 microns. Considering that the capacitive plates are only about 4 microns wide, a short movement of the proof mass by 2.5 microns increase the capacitive area for each electrode pair from about 2 microns to not just 4.5 microns, but about 8.5 microns, the extra 4 microns being the width of the plates. Thus, reducing the width and spacing of the parallel plates results in a very large collective contribution to the change in capacitance upon the movement of proof mass  120  is via both an area and change and a gap change. It has been discovered that such a hybrid effect from this electrode layout provides enhanced capacitive sensitivity at a low level of noise. More specifically, it is preferred that the capacitive plates be arranged on the support arms such that minimum gap between plates and the support arms is at least half the gap between parallel plates. It is more preferred that the capacitive plates be arranged on the support arms such that minimum gap between plates and the support arms is at least 75% the gap between parallel plates. It is most preferable that the that the capacitive plates be arranged on the support arms such that minimum gap between plates and the support arms is at least equal to the gap between parallel plates. 
     FIG. 12  compares a range of alternative devices, not all of which are prior art, against device  100  of  FIG. 9-11  of the present invention. The noise floor and capacitive sensitivity are compared in this X-Y graph to indicated the inherent performance trade offs characteristics of devices that differ from the present invention, which is also on the graph. Although the size or area is not directly plotted it is provided as the area of the MEMS portion of the devices where it could be determined from the publication, as indicated in unit of square millimeters in parenthesis after the authors name. Devices smaller than about 1 mm2 generally have a capacitive sensitivity that is not less than about 50 fF/g Devices that have a lower capacity sensitivity also have a noise floor above about 0.89 μg/√Hz. Further, many of the devices on the plot, other than the present invention, only achieve the stated performance when sealed in a hermetic vacuum package to minimize damping caused by compression of air as the capacitive plates approach each other at close distances. This hermetic package increases the device size substantially. In contrast, the arrangement of capacitive plates in the present invention minimizes such effects substantially so that a vacuum sealed hermetic package is not required. 
   Although accelerometers with a noise floor of less than 1 μg/√Hz have been reported they include a very large proof mass in the order of several square millimeters. To the best of our knowledge, the noise floor for reported small size accelerometers, that is the MEMS area less than about 1 mm2, exceeds 50 μg/√Hz. 
   In contrast, the accelerometer of the present application achieves a Capacitive sensitivity (SEN) of 40 fF/g with a Capacitance noise floor 4.5 μg/√Hz. It achieves this level of performance with a sensing element having an area of about 0.9 mm 2 . This accelerometer  100  fabricated from SOI micromachined capacitive sensing accelerometer with size of the MEMS smaller than 1 mm 2 . This device is thus mechanical noise limited for IC with input reference noise up to 80 nV/√Hz. The resolution of the sensor is 0.1 mg in 400 Hz bandwidth. Further, the present invention is ideally suited for applications that require small size, high resolution and low power consumption (less than 1 mW). 
   While the invention has been described in connection with a preferred embodiment, it is not intended to limit the scope of the invention to the particular form set forth, but on the contrary, it is intended to cover such alternatives, modifications, and equivalents as may be within the spirit and scope of the invention as defined by the appended claims.