Abstract:
A MEMS silicon inertial sensor formed of a mass that is supported and constrained to vibrate in only specified ways. The sensors can be separately optimized from the support, to adjust the sensitivity separate from the bandwidth. The sensor can sense three dimensionally, or can only sense in a single plane.

Description:
This application claims priority from provisional application Ser. Nos. 60/614,858 and 60/614,909, both filed Sep. 30, 2004, the contents of which are herewith incorporated by reference. 

   BACKGROUND 
   Inertial sensors are commonly used in many different applications including vehicle rollover sensors, aircraft sensors, and others. The sensors should be capable being used in many different environments, and be relatively ruggedized. In addition, it is important that the sensors produce output signals which are accurate. Various kinds of environmental noise, of various forms, may effect the accuracy of such sensors. 
   SUMMARY 
   The present application describes the formation of an inertial sensor on a silicon substrate, and in an embodiment is formed using Micro Electro Mechanical Systems or MEMS. An aspect disclosed herein describes mitigating the vibration susceptibility of the sensor. Another aspect describes three-dimensional sensors, and ways of isolating the different orthogonal axes of information. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIGS. 1   a  and  1   b  show respective views of an angular rate sensor of an embodiment; 
       FIG. 2  shows the calculated sensitivity of the sensor as a function of resonant frequency; 
       FIG. 3  shows a piezo resistive element on the sensing element; 
       FIGS. 4   a  and  4   b  show an anti-phase vibration mitigation embodiment; 
       FIG. 5  shows an embodiment using a Wheatstone bridge system; 
       FIG. 6  shows a three-axis accelerometer; 
       FIGS. 7A-7E  show brief processing steps to form the sensor; 
       FIG. 8  illustrates the y-axis acceleration sensing of the accelerometer; 
       FIGS. 9   a - 9 C illustrate the x and z axis acceleration sensing of the accelerometer; 
       FIGS. 10   a - 10   d  illustrate how the Wheatstone bridges can sense the acceleration parameters; and 
       FIGS. 11   a  and  11   b  illustrate shock survival techniques for the sensor. 
   

   DETAILED DESCRIPTION 
   The general structure and techniques, and more specific embodiments which can be used to effect different ways of carrying out the more general goals are described herein. 
   An embodiment is shown in  FIGS. 1 and 2 . The embodiment uses piezo-based driving and sensing, which can be for example piezoelectric driving and piezoelectric or piezoresistive sensing. The rate sensor is formed of silicon, although alternative embodiments may use other semiconductor processable materials. The embodiment forms the sensors using a MEMS technique. 
   An anchor part  100  supports the entire silicon beam-mass structure, and acts as the support for the system. The driving element  110  may include a ZnO piezoelectric film deposited on a Si 3 N 4  beam. In operation, actuating the driving element  110  causes the structure to vibrate in the vertical plane. 
   A decoupling island  120  may decouple the driving part  110  from the sensing parts, which includes a vertical beam  130 , sensing elements  150 ,  155 , and proof mass  140 . The beam  130  connects to a connection surface of the proof mass which is along a surface of the proof mass that faces to the decoupling island. Other surfaces of the mass, which are closest to the edges of the mass, abut against the sensing elements. 
   Vertical supporting beam  130  is connected to the decoupling island  120  to support the proof mass  140 , while allowing the proof mass to move in specified ways. The supporting beams such as  130  effectively forms springs. The supporting beams are columnar in shape, with a rectangular, non-square cross section that defines a thicker thickness, which is in the z direction in  FIG. 1   a , and a thinner thickness in the y direction in  FIG. 1   a . This allows the mass  140  to move in the y direction, thereby flexing the supporting beam  130 . However, movement in the z direction and the x direction is constrained by the vertical beam  130 . 
   The strain on the sensing elements  150 ,  155 , which are located around the vertical beam  130 , indicates the amount of movement of the proof mass. The sensing elements may produce respective output signals which are detected by and analyzed by electronic circuitry shown as  160 . 
   A first embodiment uses piezoresistive sensing to detect the movement.  FIG. 3  shows implanted piezoresistive sensors  320 ,  322  respectively implanted on the beams  150  and  155 . The vibration causes alternate tension and stretching on the sensors. The mode and manner of vibration depends on the resonance of the system. This resonance can be selected to be within a specified range. According to an embodiment, the resonance is selected to be within a range that keeps it within a specified stability control specification, for example, a rollover specification. 
     FIG. 2  illustrates the different sensitivity between the driving mode resonant frequency and the sensing mode resonant frequency. The driving mode resonant frequency of the rate sensor is 477.5 Hz.  FIG. 2  shows how the sensing mode resonant frequency can be selected in the range between 447.6 and 506.7. In an embodiment, a stability control line  200  is selected, and the resonant frequency is maintained between the two edges of that control line. In the exemplary embodiment, the difference between the sensing mode and the driving mode resonant frequency is less than 6.1%, but it should be understood that many different values for this difference are possible. 
   In order to maintain the standards for a rollover application, the system is much more lenient. The area of rollover specification is shown as  205 . In the embodiment, the sensing mode resonant frequency is between 352 and 595 hertz, in order to maintain it within the rollover sensitivity. This only requires a difference between sensing mode and driving mode as being less than 25% or less. 
   Table 1 illustrates a set of structural design parameters that satisfy the specifications for both stability control and rollover applications 
   
     
       
             
           
             
             
             
           
             
             
             
           
         
             
               TABLE 1 
             
           
           
             
                 
             
             
               Structure Design Parameters (for Piezoresistive Sensing) 
             
           
        
         
             
                 
               Structure parameters 
               Design values 
             
             
                 
                 
             
           
        
         
             
                 
               Driving beam length (μm) 
               53.04 
             
             
                 
               Driving beam width (μm) 
               3000 
             
             
                 
               ZnO thickness (μm) 
               0.3 
             
             
                 
               LPCVD SiN thickness (μm) 
               0.1 
             
             
                 
               Decoupling island length (μm) 
               100 
             
             
                 
               Decoupling island width (μm) 
               3000 
             
             
                 
               Decoupling island thickness (μm) 
               530 
             
             
                 
               Tiny beam length (μm) 
               50 
             
             
                 
               Tiny beam width (μm) 
               3 
             
             
                 
               Tiny beam thickness (μm) 
               2 
             
             
                 
               Vertical beam length (μm) 
               2000 
             
             
                 
               Vertical beam width (μm) 
               35 
             
             
                 
               Vertical beam thickness (μm) 
               530 
             
             
                 
               Leg proof mass length (μm) 
               1900 
             
             
                 
               Leg proof mass width (μm) 
               400 
             
             
                 
               Leg proof mass thickness (μm) 
               530 
             
             
                 
               Main proof mass length (μm) 
               3000 
             
             
                 
               Main proof mass width (μm) 
               3000 
             
             
                 
               Main proof mass thickness (μm) 
               530 
             
             
                 
               Driving mode resonant frequency (Hz) 
               477.5 
             
             
                 
               Sensing mode resonant frequency (Hz) 
               502.5 
             
             
                 
               Sensitivity (V/deg/sec) 
               0.00635*V supply   
             
             
                 
                 
             
           
        
       
     
   
   The total size of the sensor chip is 6000 um×3000 um by 530 um. The driving mode resonant frequency is 477.5 Hz. The sensing mode resonant frequency is 502.5. Sensitivity of the angular rate sensor can be up to 0.00635*(V. supply)/degrees/sec. 
   Table 2 illustrates the structural design parameters which allow the piezoelectric sensing to satisfy the specifications for stability control and rollover applications. Again, the total size of the sensor chip is 6000 μm by 3000 μm by 530 μm. The driving mode resonant frequency is 477.5 Hz and the sensing mode resonant frequency is 498 Hz. The sensitivity of the angular rate sensor can be as high as 0.00608*(V.supply/degrees/seconds). 
   
     
       
             
           
             
             
             
           
             
             
             
           
         
             
               TABLE 2 
             
           
           
             
                 
             
             
               Structure Design Parameters (for Piezoelectric Sensing) 
             
           
        
         
             
                 
               Structure parameters 
               Design values 
             
             
                 
                 
             
           
        
         
             
                 
               Driving beam length (μm) 
               53.04 
             
             
                 
               Driving beam width (μm) 
               3000 
             
             
                 
               ZnO thickness (μm) 
               0.3 
             
             
                 
               LPCVD SiN thickness (μm) 
               0.1 
             
             
                 
               Decoupling island length (μm) 
               100 
             
             
                 
               Decoupling island width (μm) 
               3000 
             
             
                 
               Decoupling island thickness (μm) 
               530 
             
             
                 
               Tiny beam length (μm) 
               50 
             
             
                 
               Tiny beam width (μm) 
               10 
             
             
                 
               Tiny beam thickness (μm) 
               2 
             
             
                 
               Vertical beam length (μm) 
               2000 
             
             
                 
               Vertical beam width (μm) 
               34.8 
             
             
                 
               Vertical beam thickness (μm) 
               530 
             
             
                 
               Leg proof mass length (μm) 
               1900 
             
             
                 
               Leg proof mass width (μm) 
               400 
             
             
                 
               Leg proof mass thickness (μm) 
               530 
             
             
                 
               Main proof mass length (μm) 
               3000 
             
             
                 
               Main proof mass width (μm) 
               3000 
             
             
                 
               Main proof mass thickness (μm) 
               530 
             
             
                 
               Driving mode resonant frequency (Hz) 
               477.5 
             
             
                 
               Sensing mode resonant frequency (Hz) 
               498 
             
             
                 
               Sensitivity (V/deg/sec) 
               0.00608*V supply   
             
             
                 
                 
             
           
        
       
     
   
   This system can satisfy the specifications for automotive stability and rollover controls. Moreover, the fundamental resonant frequency of the sensor can be around 500 Hz in order to satisfy the specification that the frequency response should be between 10 and 50 Hz. 
   The sensing signal is from two different elements  150  and  155 . Effectively that sensing signal is a differential mode signal where one beam receives tensile stress and the other beam receives compressive stress. Because of this, the system is not sensitive to vertical vibration and acceleration. These vibrations produce a common mode signal on the two sensing beans which cancel each other out. 
   Another aspect describes embodiments to mitigate the vibration susceptibility of this sensor. 
   A first embodiment takes advantage of the resonance and drives the resonant frequency of the driving mode of the sensor within a specified range that is outside the range of expected vibration and hence provides some vibration independence. For example, the driving mode resonant frequency may be set to around 3000 Hz, taking it about 1000 Hz away from the vibration environment frequency range of 20-2000 Hz. 
   This embodiment may use a PZT film instead of zinc oxide as the piezoelectric driver, to provide a higher d 31 . More specifically, by selecting the sensing mode resonant frequency to be within the range of 2300 to 4000 Hz, this also maintains the frequency outside the specification for automobile stability control. 
   In this embodiment, the difference between the sensing mode and the driving mode resonant frequency is less than 23%. If only the vertical beam is changed, while the other structural parameters are kept the same this can use a vertical beam having a size between 96.6 and 140.4 μm. 
   Table 3 satisfies the specification for both stability control and rollover applications. The total size of the sensor chip is around 6000 μm×3000 μm×530 μm. The targeted driving mode and sensing mode resonant frequencies are around 3000 and 3500 Hz, respectively. The sensitivity of the angular rate sensor can be up to 0.0102*Vsupply/degrees/seconds. 
   
     
       
             
           
             
             
             
           
             
             
             
           
         
             
               TABLE 3 
             
           
           
             
                 
             
             
               Structure design parameters (piezoelectric 
             
             
               driving and piezoresistive sensing). 
             
           
        
         
             
                 
               Structure parameters 
               Design values 
             
             
                 
                 
             
           
        
         
             
                 
               Driving beam length (μm) 
               77.7 
             
             
                 
               Driving beam width (μm) 
               3000 
             
             
                 
               PZT thickness (μm) 
               2 
             
             
                 
               LPCVD SiN thickness (μm) 
               0.93 
             
             
                 
               Decoupling island length (μm) 
               100 
             
             
                 
               Decoupling island width (μm) 
               3000 
             
             
                 
               Decoupling island thickness (μm) 
               530 
             
             
                 
               Tiny beam length (μm) 
               50 
             
             
                 
               Tiny beam width (μm) 
               3 
             
             
                 
               Tiny beam thickness (μm) 
               2 
             
             
                 
               Vertical beam length (μm) 
               2000 
             
             
                 
               Vertical beam width (μm) 
               128 
             
             
                 
               Vertical beam thickness (μm) 
               530 
             
             
                 
               Leg proof mass length (μm) 
               1900 
             
             
                 
               Leg proof mass width (μm) 
               400 
             
             
                 
               Leg proof mass thickness (μm) 
               530 
             
             
                 
               Main proof mass length (μm) 
               3000 
             
             
                 
               Main proof mass width (μm) 
               3000 
             
             
                 
               Main proof mass thickness (μm) 
               530 
             
             
                 
               Driving mode resonant frequency (Hz) 
               3000 
             
             
                 
               Sensing mode resonant frequency (Hz) 
               3500 
             
             
                 
               Sensitivity (V/deg/sec) 
               0.0102*V supply   
             
             
                 
                 
             
           
        
       
     
   
   A second embodiment of vibration independence is explained with reference to  FIGS. 4A and 4B . 
   In-phase oscillations may cause vibrations along the z-axis to be transmitted via the anchor block and from there, into the sensor&#39;s supporting structure. This type and magnitude of vibration could be transmitted into the electronics PCB where it can cause electronic component failures and other undesirable effects. Transmitted vibrations are, therefore undesirable. An embodiment changes the driven oscillation mode to one where each mass is induced to vibrate with a 180 degrees phase shift with respect to each other. That is, both masses will vibrate at the same frequency. However, when one mass is at its maximum deflected position in the +Z direction, the other mass is at its maximum deflected position in the −Z direction. 
     FIGS. 4A and 4B  show a twin mass angular rate sensor which provides anti phase drive vibration mechanisms. Proof masses  405 ,  415  are provided on both sides of the anchor  400 . A first mass  405  is connected to a first sensor  410  and a second mass  415  is connected to a second sensor  420 . The masses  405  and  415  are driven to drive in anti phase modes. Environmental vibration along the z axis can produce extra movement, other than the vibration amplitude. The vibration amplitudes A d1  and A d2  along the z direction of the proof masses  405  and  415  can be described according to equations 1 and 2, respectively:
   A   d1   =A   d   +B   (1)   A   d2   =−A   d   +B   (2) 
where A d  represents the driving amplitude of each proof mass caused by the respective driving element  100  and B represents the extra movement along the z direction on each proof mass caused by the environmental vibration. The extra movement B in one proof mass is in phase with the extra movement in the other proof mass.
 
From equation 1, it follows that:
 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
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   Equation 3 shows that the vibration amplitude produced by the environmental vibration is canceled out, thereby providing vibration independence. 
   Another embodiment shown in  FIG. 5  uses a phase difference detector. The previous embodiments assume the output of the angular rate sensor to be related to the vibration amplitude of the driving mode in the sensing mode and also to be susceptible to environmental vibration. In this embodiment, a new angular rate detecting technique is based on detection of the phase difference. 
   In this embodiment, the driving element  500  uses silicon thin beams  520 ,  522 , in place of the silicon nitride parts used in other embodiments. As in these other embodiments, this embodiment uses resistive sensors  510 ,  512  on the sensing element beams  514 ,  516 , respectively. The additional pair of piezoresistors  520 ,  522  are used as R 3  and R 4 , on the silicon flat beam. 
   The resistors R 1 /R 3  forms a first half Wheatstone bridge, and the resistors R 2 /R 4  form the other half Wheatstone bridge. Each produces an output voltage. In the embodiment, each of the four resistors has a resistance value of R when unstrained. The difference between the base value R, and the strained value, produces the output voltages as follows. 
   The driving amplitude:
 
 X=A   d  sin(ω t )  (4)
 
The sensing amplitude:
 
                 Y   =       A   s     ⁢     cos   ⁡     (     ω   ⁢           ⁢   t     )                 (   5                       A   s     =       ⁢         F   0       k   d       ·       2   ·   Ω   ·     Q   d     ·     ω   d           ω   s   2     ·           (     1   -       ω   d   2       ω   s   2         )     2     +       1     Q   s   2       ·       ω   d   2       ω   s   2                               =       ⁢       A   d     ·       2   ·   Ω   ·     ω   d           ω   s   2     ·           (     1   -       ω   d   2       ω   s   2         )     2     +       1     Q   s   2       ·       ω   d   2       ω   s   2                               =       ⁢       A   d     ·   G   ·   Ω                   (   6   )                     Δ   ⁢           ⁢     R   3       R     =         Δ   ⁢           ⁢     R   4       R     =         π   44     2     ·     S   1     ·     A   d     ·     ω   2     ·     sin   ⁡     (     ω   ⁢           ⁢   t     )             ⁢     
     ⁢         Δ   ⁢           ⁢     R   1       R     =         π   44     2     ·     S   2     ·     A   s     ·     ω   2     ·     cos   ⁡     (     ω   ⁢           ⁢   t     )           ⁢     
     ⁢         Δ   ⁢           ⁢     R   2       R     =       -       π   44     2       ·     S   2     ·     A   s     ·     ω   2     ·     cos   ⁡     (     ω   ⁢           ⁢   t     )                   (   7   )               
The outputs from the two half Wheatstone bridges:
 
                     V     out   ⁢           ⁢   1       =       V   in     ·         Δ   ⁢           ⁢     R   3       -     Δ   ⁢           ⁢     R   1             (     2   +       Δ   ⁢           ⁢     R   3       R       )     ·     (     2   +       Δ   ⁢           ⁢     R   1       R       )             ⁢     
     ⁢       V     out   ⁢           ⁢   2       =       V   in     ·         Δ   ⁢           ⁢     R   4       -     Δ   ⁢           ⁢     R   2             (     2   +       Δ   ⁢           ⁢     R   4       R       )     ·     (     2   +       Δ   ⁢           ⁢     R   2       R       )                     (   8   )               
The phases of V out1  and V out2  when V out1  and V out2  are equal to 0:
 
                     V     out   ⁢           ⁢   1       =       0   ⇒     Δ   ⁢           ⁢     R   3         =         Δ   ⁢           ⁢     R   1       ⇒     β   1       =       ω   ⁢           ⁢     t   1       =     arctan   ⁡     (         S   2     ·     A   s           S   1     ·     A   d         )               ⁢     
     ⁢       V     out   ⁢           ⁢   2       =       0   ⇒     Δ   ⁢           ⁢     R   4         =         Δ   ⁢           ⁢     R   2       ⇒     β   2       =       ω   ⁢           ⁢     t   2       =     -     arctan   ⁡     (         S   2     ·     A   s           S   1     ·     A   d         )                         (   9   )               
The phase difference:
 
   
     
       
         
           
             
               
                 
                   
                     β 
                     1 
                   
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                     2 
                   
                 
                 = 
                 
                   
                     
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                       · 
                       
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                         ⁡ 
                         
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                 ( 
                 10 
                 ) 
               
             
           
         
       
     
   
   The phase difference is proportional to the angular rate Ω and is not related to the vibration amplitude. S 1 , S 2  and G are determined by the structural parameters, driving frequency, resonant frequency of sensing mode, and quality factor. Thus, the phase-difference detecting scheme can reduce the sensitivity to environmental vibrations. 
   Another embodiment describes a three axis accelerometer. The three axis accelerator uses two masses to sense acceleration along three orthogonal axes. The embodiment includes two symmetric parts, each of which includes a proof mass, shown as proof mass  1  ( 600 ) and a proof mass  2  ( 610 ). Each part also includes one vertical beam ( 602  and  612 ), one decoupling island ( 604 ,  614 ), and two sensing beams ( 620 ,  622  and  624 ,  626 ). The sensing beams ( 620 ,  622  and  624 ,  626 ) can sense as described in previous embodiments. In this embodiment, piezoelectric films can be deposited on the sensing beams to allow piezoelectric sensing. The sensing beams  620 ,  622 ,  624 ,  626  sense the movement in the “y” direction, as described herein. 
   Coupling beams  640 ,  642  connect the decoupling island  604  to anchor  650 , which holds the first and second parts together. Analogously, the coupling beams  644 ,  646  connect the other decoupling island  614  to the anchor  650 . The anchor  650  connects to two groups of sensors—a first group sensitive to the x-axis acceleration, and a second group sensitive to the z axis acceleration. These two group of sensors are implemented in sensing beams  671  and  672  coupled between the decoupling island  604  and the anchor  650  and sensing beams  672  and  673  coupled between the decoupling island  614  and the anchor  650 . As shown in  FIGS. 9B and 9C , the sensing beams  671 ,  672 ,  673  and  674  include eight sensing resistors R 1 -R 8  for sensing the accelerations in the x and z directions. The sensing beam  672  includes the first sensing resistor R 1  at one end in contact with the decoupling island  604  and the second sensing resistor R 2  at the other end in contact with the anchor  650 . The sensing beam  673  includes the third sensing resistor R 3  at one end in contact with the anchor  650  and the fourth sensing resistor R 4  at the other end in contact with the decoupling island  614 . The sensing beam  671  includes the fifth sensing resistor R 5  at one end in contact with the decoupling island  604  and the sixth sensing resistor R 6  at the other end in contact with the anchor  650 . The sensing beam  674  includes the seventh sensing resistor R 7  at one end in contact with the anchor  650  and the eighth sensing resistor R 8  at the other end in contact with the decoupling island  614 . Operations of these sensors are illustrated in  FIGS. 9A-9C  and  10 A- 10 D. 
   The supporting beams  640 ,  642 ,  644 ,  646  are separated from the sensing elements  620 ,  622 ,  624 ,  626 . This may optimize the sensing elements and the. supporting beam separately in order to satisfy bandwidth requirements and maximize the sensitivity. Cross axis sensitivity can also be minimized. Tables 4 and 5 show the parameters of an embodiment. 
   
     
       
             
           
             
             
             
           
             
             
             
           
         
             
               TABLE 4 
             
           
           
             
                 
             
             
               Structure design parameters and calculated 
             
             
               output (Y-axis sensing). 
             
           
        
         
             
                 
               Structure parameters 
               Design values 
             
             
                 
                 
             
           
        
         
             
                 
               Tiny beam 3 length (μm) 
               10 
             
             
                 
               Tiny beam 3 width (μm) 
               2 
             
             
                 
               Tiny beam 3 thickness (μm) 
               2 
             
             
                 
               Vertical beam length (μm) 
               2000 
             
             
                 
               Vertical beam width (μm) 
               28 
             
             
                 
               Vertical beam thickness (μm) 
               530 
             
             
                 
               Leg proof mass length (μm) 
               1900 
             
             
                 
               Leg proof mass width (μm) 
               400 
             
             
                 
               Leg proof mass thickness (μm) 
               530 
             
             
                 
               Main proof mass length (μm) 
               3000 
             
             
                 
               Main proof mass width (μm) 
               3000 
             
             
                 
               Main proof mass thickness (μm) 
               530 
             
             
                 
               Resonant frequency (Hz) 
               359.7 
             
             
                 
               Y-axis Sensitivity (mV/g/5 V) 
               1727 
             
             
                 
               Y-axis minimum detectable signal (g) 
               0.0001 
             
             
                 
               Cross-axis sensitivity 
               Close to zero 
             
             
                 
               (X-axis acceleration, Y-axis sensing) 
             
             
                 
               Cross-axis sensitivity 
               Close to zero 
             
             
                 
               (Z-axis acceleration, Y-axis sensing) 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
           
             
             
             
           
         
             
               TABLE 5 
             
           
           
             
                 
             
             
               Structure design parameters and calculated 
             
             
               output (Z-axis and X-axis sensing). 
             
           
        
         
             
                 
               Structure parameters 
               Design values 
             
             
                 
                 
             
           
        
         
             
                 
               Flat beam length (μm) 
               260 
             
             
                 
               Flat beam width (μm) 
               150 
             
             
                 
               Flat beam thickness (μm) 
               12 
             
             
                 
               Tiny beam 1 length (μm) 
               10 
             
             
                 
               Tiny beam 1 width (μm) 
               2 
             
             
                 
               Tiny beam 1 thickness (μm) 
               2 
             
             
                 
               Tiny beam 2 length (μm) 
               10 
             
             
                 
               Tiny beam 2 width (μm) 
               10 
             
             
                 
               Tiny beam 2 thickness (μm) 
               2 
             
             
                 
               Tiny beam 3 length (μm) 
               10 
             
             
                 
               Tiny beam 3 width (μm) 
               2 
             
             
                 
               Tiny beam 3 thickness (μm) 
               2 
             
             
                 
               Vertical beam length (μm) 
               2000 
             
             
                 
               Vertical beam width (μm) 
               28 
             
             
                 
               Vertical beam thickness (μm) 
               530 
             
             
                 
               Leg proof mass length (μm) 
               1900 
             
             
                 
               Leg proof mass width (μm) 
               400 
             
             
                 
               Leg proof mass thickness (μm) 
               530 
             
             
                 
               Main proof mass length (μm) 
               3000 
             
             
                 
               Main proof mass width (μm) 
               3000 
             
             
                 
               Main proof mass thickness (μm) 
               530 
             
             
                 
               Resonant frequency (Hz) 
               207.35 
             
             
                 
               Z-axis Sensitivity (mV/g/5 V) 
               988.5 
             
             
                 
               Z-axis minimum detectable signal (g) 
               0.0002 
             
             
                 
               Cross-axis sensitivity 
               Close to zero 
             
             
                 
               (X-axis acceleration, Z-axis sensing) 
             
             
                 
               Cross-axis sensitivity 
               0.33% 
             
             
                 
               (Y-axis acceleration, Z-axis sensing) 
             
             
                 
               X-axis Sensitivity (mV/g/5 V) 
               148.3 
             
             
                 
               X-axis minimum detectable signal (g) 
               0.0012 
             
             
                 
               Cross-axis sensitivity 
               Close to zero 
             
             
                 
               (Z-axis acceleration, X-axis sensing) 
             
             
                 
               Cross-axis sensitivity 
               2.2% 
             
             
                 
               (Y-axis acceleration, X-axis sensing) 
             
             
                 
                 
             
           
        
       
     
   
   Therefore, in summary, the Three-axis Accelerometer with Piezoresistive Sensing can have the following characteristics:
         (1) input voltage: 5V
           current can be less than 5 mA   
           (2) un-amplified sensitivity:
           X-axis: 148.3 mV/g/5V   Y-axis: 1727 mV/g/5V   Z-axis: 988.5 mV/g/5V   
           (3) Minimum detectable signal:
           X-axis: 0.0012 g   Y-axis: 0.0001 g   Z-axis: 0.0002 g   
           (4) cross-axis sensitivity: &lt;2.2%   (5) Bandwidth: DC-70 Hz   (6) Shock survival: need to include shock protection structure appropriate to the package.       

   The support beams contribute mainly to the resonant frequency of the accelerometer, while the sensing beams affects its sensitivity. This provides the flexibility to optimize the structure parameters of the support beam and sensing beam to maximize the figure of merit (i.e., sensitivity*ω 2 ). 
   For example, the vertical beam  602 ,  612  is the support beam for Y-axis acceleration sensing, while the sensing beams, also called “tiny beams” because of their thin construction in certain embodiments, are on both sides of the vertical beam  620 ,  622 ,  624 ,  626 . 
   The thickness and other structural parameters of the vertical beam  602 ,  612  may be determined by the resonant frequency and bandwidth requirement for a specific application. The thickness of the vertical beam, and also the length and width of the vertical beam, as well as the two sensing beams to some minor degree, may effect the resonant frequency. 
   In the structure-parameter design summarized in Table 4, the width of the vertical beam is chosen to be 28 μm. This vertical beam thickness can be achieved with Deep Reactive Ion Etching (DRIE). The sensitivity is determined by the thickness, length, width and thickness of the tiny sensing beam with trade-off among those parts. 
   Table 5 shows selecting the thickness of the tiny beam to be 2 micron, which can be achieved by using silicon wafers with 2 μm thick N-type epitaxial layer on a P-type substrate. In an alternative embodiment, these may use silicon-on-insulator wafers. Electrochemical etching can be used to etch the P substrate, so that the etching stops exactly at the P-N junction of the epi wafer, leaving a 2 μm thick N-type diaphragm or beams with very good uniformity and repeatability. 
     FIG. 8  illustrates a schematic view of the y axis acceleration. The mass  610  is driven in the y direction  650  by the external acceleration to be detected. The acceleration in the direction of the arrow  650  causes deflection of the supporting beam  612 , and correspondingly causes the sensor  626  to be compressed, and causes the sensor  624  to be stretched. 
   The structure  612  has a rectangular shape to constrain the movement of the mass  610  to the y axis. This forces substantially pure compression on-the sensor  626 ; and substantially pure tension on the other sensor  624 . 
     FIGS. 9   a - 9   c  show a force distribution of the  FIG. 6  tri-axis sensor in sensing accelerations in the x and y directions based on the sensing resistors R 1 -R 8 .  FIG. 9   a  shows an exaggerated view of the results of the force on the sensor. The upper illustration in  FIG. 9   a  shows that the Z axis acceleration causes both masses  600  and  610  on two sides of the anchor  650  to move in an opposite direction of the Z-axis acceleration, and produces symmetric stress distribution between the sensing beams  671  and  672  on one side of the anchor  650  and the sensing beams  673  and  674  on the other side of the anchor  650 . The lower illustration in  FIG. 9   a  shows that the X axis acceleration produces antisymmetric force distribution between the sensing beams  671  and  672  on one side of the anchor  650  and the sensing beams  673  and  674  on the other side of the anchor  650 . Therefore, x-axis acceleration may produce a different distribution of voltages than the z axis acceleration.  FIGS. 9B and 9C  illustrate the sensing resistors R 1 -R 8  at the different locations under a Z-axis acceleration condition and a X-axis acceleration condition, respectively, with resistors labeled as “T” referring to resistors that sense tension, and resistors labeled “C” representing resistors which sense compression. 
     FIGS. 10   a - 10   d  illustrate how these resistances, formed into a Wheatstone Bridge configuration, can be connected to sense the different kinds of acceleration in the X and Z directions.  FIG. 10   a  shows how when x axis acceleration is applied, the output voltage Vout 1  from the resistances R 1 -R 4  that are in the two sensing beams  672  and  673  on two sides of the anchor  650  and are electrically connected in a Wheatstone Bridge configuration is proportional to that acceleration. However, the output voltage from those same resistors R 1 -R 4  is zero when z-axis acceleration is applied, as illustrated in  FIG. 10   b . The Wheatstone bridge formed by resistors R 5 -R 8  produces an output voltage Vout 2  for sensing Z-axis acceleration as shown in  FIGS. 10   c  and  10   d .  FIG. 10   c  shows that, under an acceleration in the Z direction, the Vout 2  is proportional to a z-axis acceleration. The x-axis acceleration causes a 0 output for Vout 2  for the Wheatstone bridge formed by resistors R 5 -R 8 . 
   In order to optimize parameters of the device, a finite element analysis of the device may be carried out for the twin mass structure. When 1 G of acceleration is applied, stresses as high as 390 MPa can be achieved. Sensitivity can be up to 257 mV per G per V, and resonant frequency can be as high as 333 Hz. One G of Y axis acceleration produces minimal stress on the x and z axis. Therefore, there is minimal cross beam sensitivity. 
   The stress on the sensing beams can be up to 180 MPa. Device function and structure may be improved by optimizing the structural parameters such that the asymmetric stress distribution on the beam is minimized. 
   Even higher stresses may cause damage if the stress is high enough to exceed the structural limits of the system  FIGS. 11A and 11B  respectively illustrate in-plane bumpers and out of plane bumpers. For example, 10,000 G&#39;s of shock survival can be obtained through proper in plane and out of plane bumper design. 
     FIGS. 7   a - 7   f  illustrate the device formation, with each figure illustrating both a side view and cross-sectional view of each step. 
     FIG. 7   a  illustrates a first operation. A P type silicon substrate  700  with an epitaxial layer  701  is deposited with a layer of silicon nitride. Low dose boron is implanted in at least one hole  702  in silicon nitride layer  705  to form piezo resistors. The epitaxial layer can be 2-3 μm thick, and can be an n type epitaxial layer on a p type substrate. An electrochemical self etching stop can be used to form the tiny sensing beans in this way. 
   After the initial low dose boron ion implantation, a higher dose boron ion implantation is used to form the ohmic contacts  710  as shown in  FIG. 7B . 
   The low dose boron parts are used as etch stops in  FIG. 7C , to form a thin silicon diaphragm and the tiny sensing beam. 
     FIG. 7E  shows depositing aluminum to form an electrode connection pattern. Finally, deep ion reactive ion etching is used to form the vertical beams and to release the device. 
   The sensors described herein may produce their outputs to be displayed on any kind of display, e.g., an analog dial or a digital display. The outputs may also be processed by one or computers which may be any kind of computer, either general purpose, or some specific purpose computer such as a workstation. The computer may be a Pentium class computer, running Windows XP or Linux, or may be a McIntosh computer. The programs may be written in C, or Java, or any other programming language. The programs may be resident on a storage medium, e.g., magnetic or optical, e.g. the computer hard drive, a removable disk or other removable medium. The programs and the data may also be run over a network. 
   Although only a few embodiments have been disclosed in detail above, other embodiments are possible and are intended to be encompassed within this specification. The specification describes specific examples to accomplish a more general goal that may be accomplished in other way. This disclosure is intended to be exemplary, and the claims are intended to cover any modification or alternative which might be predictable to a person having ordinary skill in the art. 
   For example, the above has described certain parameters with reference to x, y, z orthogonal axes. It should be understood that the parameters can be sensed in different ways. In addition, the above has described different kinds of driving and sensing mechanisms, for example it has described piezo based driving mechanisms, and piezo resistive (as well as piezoelectric) based sensing mechanisms. It should be understood that other driving mechanisms, including magnetic, and other driving mechanisms can be used. Moreover, the sensor can be any kind of sensor. 
   The above has also described an embodiment formed using MEMS, but it should be understood that other formation techniques can be used. 
   Also, only those claims which use the words “means for” are intended to be interpreted under 35 USC 112, sixth paragraph. Moreover, no limitations from the specification are intended to be read into any claims, unless those limitations are expressly included in the claims.