Abstract:
A pressure sensing element may include a diaphragm and a stepped cavity. The pressure sensing element may include a plurality of piezoresistors, which are operable to generate an electrical signal based on an amount of deflection of the diaphragm in response to a sensed pressure of the fluid. The pressure sensing element may be mounted onto a housing substrate using an adhesive so that a portion of the adhesive is attached to walls of a first cavity and to a step surface of the stepped cavity to redistribute thermally induced stresses on the pressure sensing element. The stepped cavity may be included in a MEMS pressure sensing element to reduce or eliminate thermal noise, such as temperature coefficient of offset voltage output (TCO).

Description:
BACKGROUND 
     Embodiments of the invention relate to a microelectromechanical system (MEMS) pressure sensing element having a stepped cavity at the backside for reducing or eliminating thermal noise induced by thermal stresses, such as the temperature coefficient of offset voltage output (TCO). 
     MEMS pressure sensors are generally known. One type of pressure sensor is a differential pressure sensor, which includes a silicon pressure sensing element that is anodically bonded to a glass pedestal and 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 to sense the stresses that are applied to the resistors. The glass pedestal is incorporated between the pressure sensing element and the adhesive such that the stresses resulting from the difference in thermal expansion among the pressure sensing element, the adhesive, and the housing substrate 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 among the pressure sensing element, the adhesive, and the housing substrate. 
     An example of the pressure sensor discussed above is shown in  FIG. 1  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 the cross-sectional view of  FIG. 1 . 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 in the micron range, 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  and  22 . 
     The deflections on 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-crystal 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 . 
     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. 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 as p− resistors, 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 mounting the pressure sensing element  12  to the housing substrate  18  with the adhesive  16 . However, the difference in thermal expansion among the housing substrate  18 , the adhesive  16 , and the pressure sensing element  12  has resulted in unwanted stresses being applied to the pressure sensing element  12 , which then disrupts 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  FIG. 1  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 and 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; and 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 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. 
     It is difficult for an ASIC to compensate for a high TCO, 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 because the stress difference in the X and Y directions on each of the four resistors will be amplified. The difference between the offset voltage outputs at the low and high temperatures will, therefore, increase and so will 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 would be desirable to eliminate the glass pedestal. A pressure sensing element without a glass pedestal would also improve wire bonding stability and reliability. Therefore, a pressure sensor that does not have a glass pedestal and that has low TCO noise would advance the state of the art. 
     BRIEF SUMMARY 
     In accordance with embodiments of the invention, a pressure sensing element may include a diaphragm and a stepped cavity. The pressure sensing element may include a plurality of piezoresistors, which are operable to generate an electrical signal based on an amount of deflection of the diaphragm in response to a sensed pressure of the fluid. The pressure sensing element may be mounted onto a housing substrate using an adhesive so that a portion of the adhesive is attached to walls of a first cavity and to a step surface of the stepped cavity to redistribute thermally induced stresses on the pressure sensing. The stepped cavity may be included in a MEMS pressure sensing element to reduce or eliminate thermal noise, such as temperature coefficient of offset voltage output (TCO). 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         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 prior art distributed Wheatstone bridge on the pressure sensing element. 
         FIG. 4  is a perspective view of a section of a pressure sensing device, according to embodiments of the invention. 
         FIG. 5  is a perspective bottom view of a pressure sensing element used as part of a pressure sensing device, according to embodiments of the invention. 
         FIG. 6  is a perspective view of a quarter of a pressure sensing element used as part of a pressure sensing device, according to embodiments of the invention. 
         FIG. 7  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 pressure sensing device and a pressure sensing device according to embodiments of the invention. 
         FIG. 8  is a cross-sectional view of a pressure sensing device for backside absolute pressure sensing, according to another embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     The following description of embodiment(s) is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses. 
     A pressure sensing element according to embodiments of the invention is shown in  FIGS. 4-6 . The pressure sensing element can further comprise a cap as shown in  FIG. 8  generally at  1100 . The sensor  100  includes a pressure sensing element  112 , an adhesive  114 , and a housing substrate  116 .  FIG. 6  depicts a perspective view of a quarter of the pressure sensing element with a center  160  of the diaphragm  126 . The pressure sensing element  112  shown in  FIGS. 4-6  and  FIG. 8  is made from silicon, and is mounted 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 stepped cavity  120 , which is formed as part of the pressure sensing element  112 . In one embodiment, the stepped cavity  120  is formed using a dry etch, deep reactive ion etches (DRIE), but it is within the scope of the invention that other processes may be used. The stepped cavity  120  as shown in  FIGS. 5 ,  6 , and  8  is formed into the base surface  146 , by the walls  121  of the first cavity  621 , the step surface  144 , the walls  122  of the second cavity  622 , and the bottom surface  124  of the diaphragm  126 . In this way, the step surface may be considered as both an upper surface of the first cavity and a base surface into which the second cavity is formed. The stepped cavity  120  is located approximately at the center of the base surface of the pressure sensing element  112 . According to some embodiments, each of the wall surfaces  121 A- 121 D and  122 A- 122 D is substantially perpendicular to the diaphragm  126 , and the step surface  144  is substantially parallel to the diaphragm. In other embodiments, the wall surfaces may not be substantially perpendicular to the diaphragm, or the step surface may not be substantially parallel to the diaphragm. 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 type of picture-frame Wheatstone bridge  36  as the one 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  as shown in  FIG. 4 . The pressure in the stepped cavity  120  changes as a result of a pressure change of a fluid in the aperture  118 . 
     The deflections on 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 . 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.  2 A- 2 B, and the 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 a respective side of the diaphragm  126 . 
     In this embodiment, the Wheatstone bridge 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 located near a side  46  of the top surface  128  of the pressure sensing element  112 . The pressure sensing element in this embodiment also includes a fiducial  48  which is used for orienting the pressure sensing element 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 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         n 
                       
                     
                   
                   = 
                   
                     ( 
                     
                       
                         
                           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 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         n 
                       
                     
                   
                 
               
               
                 
                   ( 
                   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. A thermal mismatch exists among the pressure sensing element  112 , the adhesive 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 
                         
                           i 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           n 
                         
                       
                       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 
             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. Referring to the coordinate system as shown in  FIG. 2A , 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 
                           
                             i 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             n 
                           
                         
                       
                       2 
                     
                     × 
                     
                       1 
                       4 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         4 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             Sxx 
                             - 
                             Syy 
                           
                           ) 
                         
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     V out  is thus a function of the sum of the differential stresses, (Sxx−Syy) on all of the four resistors. According to Equation 5, when the pressure sensor device is under 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 thermal 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 coefficients 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 the stepped cavity, shown generally at  120 . In this way, the stepped cavity  120  eliminates the need for the glass pedestal  14 , thereby advantageously reducing the cost of the pressure sensor  100 . 
     The depth  148  of the stepped cavity  120  is generally from about one quarter to two-thirds of the thickness  150  of the pressure sensing element  112 , and is preferably about one-third to one-half of the thickness  150  of the pressure sensing element  112 . The thickness  150  of the pressure sensing element  112  is about 0.525 mm, and the first cavity of the stepped cavity  120  is generally in the range of 1.4 to 1.6 mm, and is preferably about 1.58 mm. Numeral  158  shows half a width of the first cavity in  FIG. 4 . 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 0.78 mm. 
     The walls of the first cavity  121 A- 121 D and the walls of the second cavity  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 stepped cavity  120  creates a hold-down force on the step surface  144  by the inner fillet  172  of adhesive and more uniformly holds down the area surrounding the diaphragm  126  above the step surface  144 , redistributes the thermal stresses induced by the adhesive  114  and the housing substrate  116 , and significantly compresses the resistors  36 A- 36 D in the direction perpendicular to the diaphragm  126  (Sxx), while gently compressing 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 compressive stresses in both the X and Y directions. 
     During assembly, the pressure sensing element  112  is attached to the housing substrate  116  using the adhesive  114 . A scenario that presents an extreme TCO case is when, as the pressure sensing element  112  is placed onto the adhesive  114 , the adhesive  114  partially fills the first cavity  621  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  FIG. 4 . 
     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 stepped cavity  120  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 . 
     Since the curing temperature is at 150° C., the thermal stress components Sxx and Syy are trivial because there is very little thermal mismatch. However, the thermal stress components Sxx and Syy are significant at −40° C. because the thermal mismatch is significant.  FIG. 7  shows at −40° C. a comparison of the stress components Sxx and Syy between a pressure sensor having the stepped cavity  120 , and a pressure sensor which does not have the stepped cavity  120 . In  FIG. 7 , reference numeral  176  shows the stress components Sxx and Syy on each of the four resistors  36  without a stepped cavity added to the pressure sensing element  112 . For convenience, Resistors  36 A- 36 D are named R 1 , R 2 , R 3 , and R 4 , respectively. The stress differences (Sxx−Syy) on the four resistors are all positive. Thus the sum of all (Sxx−Syy) on all four resistors is greatly positive and results in a positive voltage of 14.03 mV. At 150° C., the thermal stress components Sxx and Syy on each resistor are trivial, and the stress difference (Sxx−Syy) on each resistor is near zero. The same is true for the sum of stress differences on all four resistors. Hence the offset voltage output at 150° C. is approximately zero. Based on the definition of TCO, the value of TCO is calculated as −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. 7  shows that (Sxx−Syy) 1 , (Sxx−Syy) 2 , and (Sxx−Syy) 3  are all slightly positive except that (Sxx−Syy) 4  is slightly negative. Thus the sum of all of these smaller (Sxx−Syy) on all four resistors is slightly positive and results in a positive voltage of 0.89 mV. The sum of all (Sxx−Syy) is significantly reduced, and so the offset voltage output at −40° C. is minimized to a small positive value. TCO is thus reduced to a small negative value at −4.69 uV/° C. 
     Another embodiment of the invention is shown at  1100  in  FIG. 8 , 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  is made of glass, the cap  180  could 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 media. This allows the pressure sensor  1100  shown in  FIG. 8  to measure a backside absolute pressure, whereas the pressure sensor  100  shown in the previous embodiments measures 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 foregoing description is for purposes of illustration only. The true scope of the invention is defined by the appurtenant claims.