Abstract:
An MEMS pressure sensor is designed to reduce or eliminate thermal noise, such as temperature offset voltage output. The pressure sensor includes a pressure sensing element having a diaphragm, and a cavity formed as part of the pressure sensing element, where the cavity receives a fluid such that the diaphragm at least partially deflects. The pressure sensing element also includes a plurality of piezoresistors, which are operable to generate a signal based on the amount of deflection in the diaphragm. At least one trench is integrally formed as part of the pressure sensing element, and an adhesive connects the pressure sensing element to the at least one substrate such that at least a portion of the adhesive is attached to the trench and redistributes thermally induced stresses on the pressure sensing element such that the thermally induced noise is substantially eliminated.

Description:
FIELD OF THE INVENTION 
     Embodiments of the invention relate to a microelectromechanical system (MEMS) pressure sensing element having a trench at the backside for reducing or eliminating the effect of thermally induced stresses or thermal noise, such as temperature offset voltage output. 
     BACKGROUND OF THE INVENTION 
     MEMS pressure sensors are generally known. One type of pressure sensor is a differential pressure sensor which includes a pressure sensing element made of silicon which is anodically bonded to a glass pedestal, and the glass pedestal is mounted to a housing substrate using an adhesive. Many differential pressure sensors are used in applications in which the sensors are exposed to varying temperatures. This causes the sensing element, the glass pedestal, the adhesive, and the housing substrate to expand and contract in response to the temperature changes. 
     The pressure sensing element includes four piezoresistors or resistors positioned in what is known as a “Wheatstone Bridge” configuration. The adhesive expands and contracts at a different rate in relation to the pressure sensing element, which can cause stress to be applied to the resistors, affecting the pressure reading detected by the pressure sensing element. The glass pedestal is incorporated between the pressure sensing element and the adhesive such that the stresses resulting from the difference in thermal expansion between the pressure sensing element and the adhesive are isolated by the glass pedestal. The glass pedestal and the pressure sensing element have slightly different coefficients of thermal expansion, and therefore expand and contract at a lower different rate when exposed to varying temperatures. The glass pedestal essentially acts as a buffer to isolate the stresses resulting from the different expansion and contraction rates between the glass pedestal and the adhesive. 
     An example of the pressure sensor discussed above is shown in  FIGS. 1-2B  generally at  10 . The sensor  10  includes a pressure sensing element  12 , a glass pedestal  14 , an adhesive  16 , and a housing substrate  18 . The pressure sensing element  12  shown in  FIG. 1  is made from silicon, and is anodically bonded to the glass pedestal  14 . The adhesive  16  is used to bond the glass pedestal  14  to the housing substrate  18 . 
     Formed as part of the housing substrate  18  is a first aperture  20 , and formed as part of the glass pedestal  14  is a second aperture  22 , which is in substantial alignment with the first aperture  20 . The second aperture  22  is in fluid communication with a cavity, shown generally at  24 , where the cavity  24  is formed as part of the pressure sensing element  12 . The pressure sensing element  12  includes four angular inner surfaces, where only a first angular inner surface  26  and a second angular inner surface  28  are depicted in  FIG. 1 , because  FIG. 1  is a cross-sectional view. Each of the four angular inner surfaces terminates into a bottom surface  30 , which is part of a diaphragm  32 . The pressure sensing element  12  also includes a top surface  34 , and there is a picture frame transducer or picture frame Wheatstone bridge  36  doped onto the top surface  34  of the pressure sensing element  12 . At least a thermal oxide layer and passivation layers are formed to protect the circuitry. The picture frame Wheatstone bridge  36  is formed by four p− piezoresistors  36 A- 36 D as shown in  FIG. 2B . The four piezoresistors  36 A- 36 D may also be formed as a distributed Wheatstone bridge  38 A- 38 D as shown in  FIG. 3  for pressure sensing. 
     The diaphragm  32  is relatively thin, and the thickness of the diaphragm  32  depends upon the pressure range. The diaphragm  32  deflects upwardly and downwardly in response to pressure applied to the bottom surface  30 , and the top surface  34  of the diaphragm  32 . The pressure in the cavity  24  changes as a result of a pressure change of fluid flowing into and out of the apertures  20 , 22 . 
     The deflections in the top surface  34  also deform the picture frame Wheatstone bridge  36 , which is doped onto the top surface  34  of the pressure sensing element  12 . The pressure sensing element  12  is made of a single crystalline silicon (Si). On the top of the pressure sensing element  12 , four p− piezoresistors  36 A- 36 D are formed and connected to each other by p+ interconnectors  40  to form the picture frame Wheatstone bridge  36  for pressure sensing as shown in  FIGS. 2A-2B . 
     Merriam-Webster&#39;s Collegiate Dictionary 11 th  Edition defines a Wheatstone bridge as an electrical bridge consisting of two branches of a parallel circuit joined by a galvanometer and used for determining the value of an unknown resistance in one of the branches. As used herein, the term Wheatstone bridge refers to the circuit topology shown in  FIG. 2A-2B , namely the parallel connection of two series-connected resistors. 
       FIGS. 2A-2B  represent a top view of the piezoresistive pressure sensing element  12  with the picture frame Wheatstone bridge  36 , which is doped on the diaphragm  32 . The diaphragm  32  has dimensions of 780 μm×780 μm. The thickness of the diaphragm  32  is generally in the range of about 5 μm to 20 μm, and as shown in  FIGS. 2A-2B , is about 9 μm. The picture frame Wheatstone bridge  36  is processed using conventional techniques to form four resistors  36 A- 36 D on the top surface of the pressure sensing element  12 . The resistors  36 A- 36 D are formed of a p− material, embodiments of which are well-known to those of ordinary skill in the semiconductor art. Electrical interconnects  40  made of p+material connected to the bottom of bond pads  42 A- 42 D are also formed on the top surface  34  of the pressure sensing element  12 . Each interconnect  40  provides an electrical connection between two resistors in order to connect the resistors to each other to form a piezoresistive Wheatstone bridge circuit. 
     The four interconnects  40  are shown as part of the pressure sensing element  12 . Each interconnect  40  extends outwardly from a point or node  44  between two of the four resistors  36  next to each other, and connects to the bottom of a metal bond pad  42 . Each bond pad  42  is located near a side  46  of the top surface  34  of the pressure sensing element  12 . Each interconnect  40  thus terminates at and connects to a bond pad  42 . 
       FIG. 2A  also shows an orientation fiducial  48  on the top surface  34 . The fiducial  48  is a visually perceptible symbol or icon the function of which is simply to enable the orientation of the pressure sensing element  12 . 
     Each bond pad  42  has a different label or name that indicates its purpose. The first bond pad  42 A and the second bond pad  42 B receive an input or supply voltage for the Wheatstone bridge circuit. Those two bond pads  42 A, 42 B are denominated as V p  and V n , respectively. The other two bond pads  42 C, 42 D are output signal nodes denominated as S p  and S n , respectively. 
     Many attempts have been made to simplify the construction of this type of pressure sensor  10  by eliminating the glass pedestal  14 , and directly connecting the pressure sensing element  12  to the housing substrate  18  with the adhesive  16 . However, the difference in thermal expansion between the adhesive  16  and the pressure sensing element  12  has resulted in unwanted stresses being applied to the pressure sensing element  12 , which then disrupt each of the resistors  36 A- 36 D, causing an inaccurate pressure reading by the pressure sensing element  12 . 
     More particularly, both experimental measurement and computer simulations of the structure depicted in  FIGS. 1-2B  show that connecting the pressure sensing element  12  directly to the housing substrate  18  creates offset voltage output and its variation over an operating temperature range due to asymmetrical thermal stresses on the resistors  36 A- 36 D. Elimination of the glass pedestal  14  causes one of the resistors  36 A through  36 D to deform or stressed, or to change its resistance value asymmetrically with respect to the other resistors leading to an offset voltage output variation in an operating temperature range in the output of the pressure sensing element  12 . 
     The offset voltage output variation over an operating temperature is called temperature coefficient of offset voltage output (TCO) and defined as follows:
 
TCO=(Vo at 150° C.−Vo at −40° C.)/190° C.
 
Where Vo at 150° C.: offset voltage output at 150° C. without pressure applied
 
     Vo at −40° C.: offset voltage output at −40° C. without pressure applied 
     The pressure sensing element  12  is commonly used with an application-specific integrated circuit (ASIC). The ASIC is, among other things, used for amplifying and calibrating the signal received from the pressure sensing element  12 . It is desirable to keep the TCO between −50 uV/° C. and 50 uV/° C. so the ASIC is better able to handle any thermal noise. 
     The high TCO is difficult for an ASIC to compensate, especially when the adhesive  16  is not symmetrically dispensed. If the adhesive is not symmetrically dispensed, this can further reduce the accuracy of the sensor. The stress difference in the X and Y directions on each of the four resistors is amplified, thus the offset voltage outputs increase, as well as the TCO. That is why the glass pedestal  14  shown in  FIG. 1  is used to isolate the thermal stresses. In order to reduce cost and simplify the manufacturing process, it is desirable to eliminate the glass pedestal. A pressure sensing element without a glass pedestal also improves wire bonding stability and reliability. Therefore, there is a need for a type of pressure sensor which does not have a glass pedestal, but has a low TCO noise. 
     SUMMARY OF THE INVENTION 
     In some embodiments, a pressure sensor is designed to reduce or eliminate thermally induced stresses or thermal noise, such as temperature offset voltage output. The pressure sensor includes a pressure sensing element having a diaphragm, and a cavity formed as part of the pressure sensing element, where the cavity receives a fluid such that the diaphragm at least partially deflects. The pressure sensor also includes a plurality of piezoresistors connected to the pressure sensing element, which are operable to generate a signal based on the amount of deflection in the diaphragm. A top surface is formed as part of the pressure sensing element, and the plurality of piezoresistors are doped to the top surface. A plurality of outer surfaces is also formed as part of the pressure sensing element, such that each of the plurality of outer surfaces terminates into the top surface. At least one substrate is operable for supporting the pressure sensing element. 
     At least one trench is integrally formed as part of the pressure sensing element, and an adhesive connects the pressure sensing element to the at least one substrate such that at least a portion of the adhesive is disposed in the trench and redistributes thermally induced stresses on the piezoresistors such that the thermally induced stresses are substantially eliminated. 
     Further areas of applicability of the present invention will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will become more fully understood from the detailed description and the accompanying drawings, wherein: 
         FIG. 1  is a cross-sectional view of a prior art pressure sensor; 
         FIG. 2A  is a top view of a piezoresistive pressure sensing element used with a prior art pressure sensor; 
         FIG. 2B  is an enlarged view of the pressure sensing element shown in  FIG. 2A , which shows a picture frame Wheatstone bridge; 
         FIG. 3  is a top view of a distributed Wheatstone bridge on the pressure sensing element; 
         FIG. 4  is a perspective view of a section of a semiconductor sensing device, according to embodiments of the present invention; 
         FIG. 5  is a perspective bottom view of a pressure sensing element used as part of a semiconductor sensing device, according to embodiments of the present invention; 
         FIG. 6  is a perspective bottom view of a section of a pressure sensing element used as part of a semiconductor sensing device, according to embodiments of the present invention; 
         FIG. 7  is a perspective view of a pressure sensing element and an adhesive used as part of a semiconductor sensing device, according to embodiments of the present invention; 
         FIG. 8  is a graph representing the comparison and improvement in reduction of thermal stress difference in the X and Y directions on each resistor between a prior art semiconductor sensing device and a semiconductor sensing device, according to embodiments of the present invention; 
         FIG. 9  is a perspective view of a section of a semiconductor sensing device, according to another embodiment of the present invention; 
         FIG. 10  is a perspective view of a section of a semiconductor sensing device, according to another embodiment of the present invention; and 
         FIG. 11  is a cross-sectional view of a semiconductor sensing device for backside absolute pressure sensing, according to another embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The following description of the preferred embodiment(s) is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses. 
     A pressure sensor according to embodiments of the present invention is shown in  FIGS. 4-11 , generally at  100 . The sensor  100  includes a pressure sensing element  112 , an adhesive  114 , and a housing substrate  116 . The pressure sensing element  112  shown in  FIGS. 4-7  is made from silicon, and is connected to the housing substrate  116  using the adhesive  114 . 
     Formed as part of the housing substrate  116  is an aperture  118 . The aperture  118  is in fluid communication with a cavity, shown generally at  120 , where the cavity  120  is formed as part of the pressure sensing element  112 . In one embodiment, the cavity  120  is formed using a dry etch, deep reactive ion etch (DRIE), but it is within the scope of the invention that other processes may be used. The pressure sensing element  112  includes a plurality of substantially vertical inner surfaces  122 A- 122 D. Each of the inner surfaces  122 A- 122 D terminates into a bottom surface  124 , which is part of a diaphragm  126 . Each of the inner surfaces  122 A- 122 D is substantially perpendicular to the diaphragm  126 . The pressure sensing element  112  also includes a top surface  128 , and there is a picture frame Wheatstone bridge, shown generally at  36 , doped onto the top surface  128  of the pressure sensing element  112 , which is the same picture frame Wheatstone bridge  36  shown in  FIGS. 2A-2B . 
     The diaphragm  126  is relatively thin, and the thickness of the diaphragm  126  depends upon the pressure range. The diaphragm  126  deflects upwardly and downwardly in response to pressure applied to the bottom surface  124 , and the top surface  128  of the diaphragm  126  deflects in response to pressure changes in the cavity  120  and on the top surface  128  as shown in  FIG. 4 . The pressure in the cavity  120  changes as a result of a pressure change of a fluid in the aperture  118 . 
     The deflections in the top surface  128  also deform the picture frame Wheatstone bridge  36 . The deflections of the top surface  128  of the diaphragm  126  deform the picture frame Wheatstone bridge  36  doped onto the top surface  128  of the pressure sensing element  112 , which is made of a single crystalline silicon (Si) in a similar manner to the pressure sensing element  12  shown in  FIG. 1 . On the top surface  128  of the pressure sensing element  112 , four piezoresistors are formed and connected to each other to form a Wheatstone bridge for pressure sensing as shown in  FIGS. 2A and 2B . In this embodiment, the Wheatstone bridge is a picture frame Wheatstone bridge  36 , and is configured as shown in  FIG. 2A-2B , and all four resistors  36 A- 36 D are located near one side of the diaphragm  126 . However, it is within the scope of the invention that the Wheatstone bridge may be configured as a distributed Wheatstone bridge circuit, shown in  FIG. 3 , where each resistor  38 A- 38 D is located near each side of the diaphragm  126 . 
     In this embodiment, the Wheatstone bridge still includes the plurality of resistors  36 A- 36 D, the plurality of electrical interconnects  40 , the plurality of bond pads  42 , and the nodes  44 . With this embodiment, the bond pads  42  are again located near a side  46  of the top surface  128  of the pressure sensing element  112 . The Wheatstone bridge in this embodiment also includes a fiducial  48  which used for orienting the Wheatstone bridge during assembly. 
     A Wheatstone bridge circuit has two input nodes and two output nodes. The transfer function, which is the ratio of the output voltage to the input voltage, can be expressed as shown in Eq. 1 below. 
     
       
         
           
             
               
                 
                   
                     
                       V 
                       out 
                     
                     
                       V 
                       in 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         
                           R 
                           3 
                         
                         
                           
                             R 
                             3 
                           
                           + 
                           
                             R 
                             4 
                           
                         
                       
                       - 
                       
                         
                           R 
                           2 
                         
                         
                           
                             R 
                             1 
                           
                           + 
                           
                             R 
                             2 
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Rearranging the transfer function terms provides an equation for the output voltage V out  as a function of the input voltage V in  and values of the resistors in the Wheatstone bridge. Equation 2 below thus expresses the output voltage as a function of the input voltage and the values of the resistors that comprise the Wheatstone bridge circuit. 
     
       
         
           
             
               
                 
                   
                     V 
                     out 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             R 
                             3 
                           
                           
                             
                               R 
                               3 
                             
                             + 
                             
                               R 
                               4 
                             
                           
                         
                         - 
                         
                           
                             R 
                             2 
                           
                           
                             
                               R 
                               1 
                             
                             + 
                             
                               R 
                               2 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       V 
                       in 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     It can be seen from Eq. 2 that the output voltage changes as the resistors&#39; values change induced by pressure, temperature change, thermal mismatch, etc. One type of thermal mismatch exists between the pressure sensing element  112  and the housing substrate  116 , which has an effect on the output voltage. 
     Equation 3 below expresses the output voltage as a function of the fluctuations in resistance values. 
     
       
         
           
             
               
                 
                   
                     V 
                     out 
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       4 
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           
                             ∂ 
                             
                               V 
                               out 
                             
                           
                           
                             ∂ 
                             
                               R 
                               i 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         R 
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     Expanding Equation 3 into Equation 4 below shows that V out  will vary with changes in each of the resistors R 1  through R 4 . 
     
       
         
           
             
               
                 
                   
                     V 
                     out 
                   
                   = 
                   
                     
                       
                         V 
                         in 
                       
                       4 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               R 
                               1 
                             
                           
                           
                             R 
                             1 
                           
                         
                         - 
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               R 
                               2 
                             
                           
                           
                             R 
                             2 
                           
                         
                         + 
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               R 
                               3 
                             
                           
                           
                             R 
                             3 
                           
                         
                         - 
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               R 
                               4 
                             
                           
                           
                             R 
                             4 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     For a piezoresistive device, the ratio of the resistance change versus the resistance for each resistor can be expressed as follows: 
     
       
         
           
             
               
                 Δ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   R 
                   i 
                 
               
               
                 R 
                 i 
               
             
             = 
             
               
                 
                   π 
                   44 
                 
                 2 
               
               ⁢ 
               
                 ( 
                 
                   
                     σ 
                     i 
                     L 
                   
                   - 
                   
                     σ 
                     i 
                     T 
                   
                 
                 ) 
               
             
           
         
       
     
     σ i   L : longitudinal stress on the resistor i 
     where 
     σ i   T : transverse stress on the resistor i 
     and the value of piezoresistive coefficient, π 44  is approximately 1.381/GPa with a boron doping density of 1.8E15/cm^3. 
     Equation 4 shows that the value for the ratio of the resistance change versus the resistance for each resistor is dependent on the longitudinal and transverse stresses on each resistor. If the longitudinal stresses on Resistor  1  and  3  are aligned to be perpendicular to the edge of the diaphragm, then the transverse stresses on Resistor  2  and  4  is also perpendicular to the edge of the diaphragm. The stress perpendicular to the edge of the diaphragm is denominated as Sxx. In this condition, the transverse stresses on Resistor  1  and  3  and the longitudinal stresses on Resistor  2  and  4  will be parallel to the edge of the diaphragm. The stress parallel to the edge of the diaphragm is denominated as Syy. Therefore, Equation 4 can be re-written as Equation 5 below. 
     
       
         
           
             
               
                 
                   
                     V 
                     out 
                   
                   = 
                   
                     
                       
                         
                           π 
                           44 
                         
                         ⁢ 
                         
                           V 
                           in 
                         
                       
                       2 
                     
                     × 
                     
                       1 
                       4 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         4 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             Syy 
                             - 
                             Sxx 
                           
                           ) 
                         
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     V out  is thus a function of the sum of the differential stresses, (Sxx−Syy) on all the four resistors. According to Equation 5, when the pressure sensor device is under the pressure, the stress perpendicular to the diaphragm on each resistor, Sxx is higher than the stress parallel to the diaphragm on each resistor, Syy. Therefore the pressure sensor device has a high sensitivity. In order to minimize the noise, however, it is desirable to keep the voltage output, or the offset voltage output in this condition as low as possible, and preferably zero for the noise induced by the thermal stress. Based on Equation 5, it is apparent that if thermally-induced stresses Sxx and Syy can be equalized or the sum of (Sxx−Syy) can be reduced to zero, the offset voltage output becomes zero due to the cancellation of the stresses. Once the offset voltage outputs are reduced to approximately zero at different temperature levels, the TCO is essentially zero. 
     The operating temperature range of the sensor  100  is between about −40° C. and about +150° C. The difference in the coefficient of thermal expansion between the pressure sensing element  112 , the adhesive  114 , and the housing substrate  116  creates an imbalance among the stresses applied to the various resistors  36 . This imbalance is corrected by a trench, shown generally at  144 . Because of the trench  144 , the sensor  100  also does not require the glass pedestal  14  shown in  FIG. 1 , reducing the overall cost of the sensor  100 . The trench  144  extends along a base surface  146  of the pressure sensing element  112 . The depth  148  of the trench  144  is generally from about one-tenth to one-half of the height  150  of the pressure sensing element  112 , and is preferably about one-third to one-half of the height  150  of the pressure sensing element  112 . The height  150  of the pressure sensing element  112  is about 0.525 mm, and the width  152  of the trench  144  is generally in the range of 0.1 to 0.5 mm, and is preferably about 0.225 mm. The pressure sensing element  112  is essentially square-shaped, and the width  154  of each side of the pressure sensing element  112  is about 2.06 mm, and the width  156  of each side of the diaphragm  126  is about 0.780 mm. 
     The trench  144  is located at a distance  158  from the center  160  of the pressure sensing element  112 . The distance  158  is calculated from the center  162  of the trench  144  to the center  160  of the pressure sensing element  112 . The distance  158  from the center  160  of the pressure sensing element  112  to the center  162  of the trench  144  is generally about 0.575 mm to 0.800 mm. The overall width  164  of the bottom surface  146  is about 0.640 mm, and is located at a distance  166  of about 0.390 mm from the center  160  of the pressure sensing element  112 . 
     The inner surfaces  122 A- 122 D being substantially vertical provide for the pressure sensing element  112  to be made smaller compared to the pressure sensing element  12  shown in  FIG. 1 , which is an improvement over the design which includes the angled surfaces  26 , 28  shown in  FIG. 1 . The reduced size of the pressure sensing element  112  allows for installation and use in a wider arrangement of locations, such as location where space or weight is limited. The incorporation of the trench  144  relaxes the stiffness of the silicon pressure sensing element  112 , redistributes the thermal stresses induced by the adhesive  114 , and significantly compresses the resistors  36 A- 36 D in the direction perpendicular to the diaphragm  126  (Sxx), while gently compresses the resistors  36 A- 36 D in the direction parallel to the diaphragm  126  (Syy). The diaphragm  126 , especially in the area of the picture frame Wheatstone bridge  36 , experiences more equally planar compressive stresses in both the X and Y directions. 
     During assembly, the pressure sensing element  112  is connected to the housing substrate  116  using the adhesive  114 . As the pressure sensing element  112  is placed onto the adhesive  114 , the adhesive  114  fills the trench  144  and at least partially surrounds two of the substantially vertical outer surfaces  174  on two opposite sides of the pressure sensing element  112 . The adhesive  114  provides a secure connection between the housing substrate  116  and the pressure sensing element  112 . During assembly, the adhesive  114  is deformable and when assembled, the adhesive  114  has an outer fillet portion  168 , a base portion  170 , and an inner fillet portion  172 . The portion of the adhesive  114  that surrounds two of the outer surfaces  174  is the outer fillet portion  168 , best shown in  FIGS. 4 and 7  for one of the worst TCO cases. 
     When the sensor  100  is used in operation, and exposed to various temperatures, the pressure sensing element  112 , the adhesive  114 , and the housing substrate  116  have different coefficients of thermal expansion, and therefore expand and contract at different rates. The trench  144  is used to offset the various stresses which result from the difference in rates of thermal expansion of the pressure sensing element  112 , the adhesive  114 , and the housing substrate  116 . 
       FIG. 8  shows a comparison of the stress components Sxx and Syy between a pressure sensor having the trench  144 , and a pressure sensor which does not have the trench  144 . In  FIG. 8 , reference numeral  176  shows the stress components Sxx and Syy on each of the four resistors  36  without a trench  144  added to the pressure sensing element  112 . Resistors  36 A- 36 D which are named R 1 , R 2 , R 3 , and R 4  respectively, (Syy−Sxx) 1  and (Syy−Sxx) 3  as well as both (Syy−Sxx) 2  and (Syy−Sxx) 4  are all negative. Thus the sum of all small (Syy−Sxx) on all four resistors is greatly negative, generating a TCO of −73.83 uV/° C. 
     Experimental and computer simulations show that the TCO is approximately proportional to the offset voltage output at −40° C. In order to reduce or minimize the TCO, it is important to reduce or minimize the offset voltage output at −40° C. Numeral  178  in  FIG. 8  shows that all (Syy−Sxx) on resistors R 1  through R 3   36 A through  36 C turn into small negative from positive, and the (Syy−Sxx) on resistor R 4   36 D drops but still remains positive. The sum of all (Syy−Sxx) is virtually cancelled out and so the offset voltage output at −40° C. is minimized to a small negative value. TCO is thus reduced to a small negative value at −0.02 uV/° C. 
     The pressure sensing element  112  is also able to compensate for different variations as well. Referring to  FIG. 9 , the pressure sensing element  112  is shown with the trench  144 . However, the adhesive  114  has not completely filled the trench  144 , compared to the completely filled trench  144  shown in  FIG. 4 . However, even if the trench  144  is not completely filled with the adhesive  144 , the trench  144  being partially filled with adhesive  114  shows an improvement over the prior art pressure sensing element  12  which has no trench. The pressure sensing element  112  shown in  FIG. 9  has a TCO of −32.45 uV/° C. 
     An alternate embodiment of the present invention is shown in  FIG. 10 , with like numbers referring to like elements. In this embodiment, the depth  148  of the trench  144  is reduced, and the pressure sensing element  112  has a TCO of −13.53 uV/° C., which is still an improvement over a pressure sensing element which does not have a trench  144 . 
     Another alternate embodiment of the present invention is shown at  1100  in  FIG. 11 , with like numbers referring to like elements. In this embodiment, a cap  180  is attached to the top surface  128  of the pressure sensing element  112 . In some embodiments, the cap  180  may be made of silicon or glass, such as borosilicate glass. In this embodiment, the cap  180  is made of silicon and fusion bonded to the top surface  128  of the pressure sensing element  112 . However, if the cap  180  were made of glass, the cap  180  would be anodically bonded to the top surface  128  of the pressure sensing element  112 . 
     The cap  180  includes a chamber, shown generally at  182 , located between sidewalls  184 . The cap  180  is bonded to the top surface  128  of the pressure sensing element  112  such that the chamber  182  is a vacuum chamber, which functions as a zero pressure reference when the diaphragm  126  is exposed to the environment. This allows the pressure sensor  1100  shown in  FIG. 11  to measure an absolute pressure, whereas the pressure sensor  100  shown in the previous embodiments measure differential pressure. The length and width of the chamber  182  is at least as large as the length and width of the diaphragm  126 . The cap  180  isolates the diaphragm  126  from the media from the top side and protects the diaphragm  126  from harsh environments, reducing the probability of damage occurring to the circuitry on the top surface  128  of the pressure sensing element  112 . 
     The description of the invention is merely exemplary in nature and, thus, variations that do not depart from the gist of the invention are intended to be within the scope of the invention. Such variations are not to be regarded as a departure from the spirit and scope of the invention.