Abstract:
MEMS based sensors, particularly capacitive sensors, potentially can address critical considerations for users including accuracy, repeatability, long-term stability, ease of calibration, resistance to chemical and physical contaminants, size, packaging, and cost effectiveness. Accordingly, it would be beneficial to exploit MEMS processes that allow for manufacturability and integration of resonator elements into cavities within the MEMS sensor that are at low pressure allowing high quality factor resonators and absolute pressure sensors to be implemented. Embodiments of the invention provide capacitive sensors and MEMS elements that can be implemented directly above silicon CMOS electronics.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This patent application claims the benefit of U.S. Provisional Patent Application U.S. 62/020,049 filed Jul. 2, 2014 entitled “Methods and Devices for Microelectromechanical Sensors”, the entire contents of which are included by reference. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention relates to MEMS sensors and more particularly to absolute pressure MEMS capacitive sensors which may be manufactured directly over or in conjunction with silicon based CMOS electronics. 
       BACKGROUND OF THE INVENTION 
       [0003]    Microelectromechanical systems (MEMS) are small integrated devices or systems that combine electrical and mechanical components. The components can range in size from the sub-micrometer level to the millimeter level, and there can be any number, from one, to few, to potentially thousands or millions, in a particular system. Historically MEMS devices have leveraged and extended the fabrication techniques developed for the silicon integrated circuit industry, namely lithography, doping, deposition, etching, etc. to add mechanical elements such as beams, gears, diaphragms, and springs to silicon circuits either as discrete devices or in combination with integrated silicon electronics. Whilst the majority of development work has focused on silicon (Si) electronics additional benefits may be derived from integrating MEMS devices onto other existing electronics platforms such as silicon germanium (SiGe), gallium arsenide (GaAs) and, indium phosphide (InP) for RF circuits and future potential electronics platforms such as organic based electronics, nanocrystals, etc. 
         [0004]    Examples of MEMS device application today include inkjet-printer cartridges, accelerometers, miniature robots, micro-engines, locks, inertial sensors, micro-drives, micro-mirrors, micro actuators, optical scanners, fluid pumps, transducers, chemical sensors, pressure sensors, and flow sensors. New applications are emerging as the existing technology is applied to the miniaturization and integration of conventional devices. These systems can sense, control, and activate mechanical processes on the micro scale, and function individually or in arrays to generate effects on the macro scale. The micro fabrication technology enables fabrication of large arrays of devices, which individually perform simple tasks, or in combination can accomplish complicated functions. 
         [0005]    MEMS have become a successful sensing and actuating technology. Because of their extensive optical, electrical to mechanical functionalities, MEMS devices are suited to applications in many different fields of science and engineering. However, because of this vast range of functionality, MEMS fabrication processes, unlike the microelectronics industry, are difficult to gear towards general applications. As a result most processes are aimed at the fabrication of a few devices, and usually performance of the devices is hindered by process variability. As MEMS devices are typically sensing weak analog signals, for example pressure, acceleration, vibration, magnetic or electric fields, with capacitive based elements, there is considerable benefit in being able to integrate analog front-end electronics to buffer, amplify and process these weak electronic signals and either facilitate their direct processing, such as with RF signals, or their digitization for sensing and measurements applications. 
         [0006]    MEMS sensors, like other sensors, are transducers or converters that measure a physical quantity and convert it into a signal which can be read. Typically, that reading is by an electronic instrument which converts the signal to a measurement based upon the sensitivity of the sensor, its calibration data, and other corrections. Included within the many types of sensors are those relating to sound, acoustics, vibration, chemicals, humidity, pressure, fluid flow, position, displacement, force, level, temperature, proximity, and acceleration. For each type of sensor, different sensing mechanisms exist which may for example be targeted to different dynamic ranges, speed, accuracy, etc. Amongst these capacitive sensing constitutes a very important means of monitoring many environmental conditions in an effective and reliable manner as well as having applications in areas including, but not limited to, gas sensing, thickness measurements, haptic interfaces, heating, ventilation, and air conditioning system monitoring, and displacement measurements. Accordingly, capacitive sensors have major applications in the consumer, industrial, automotive and medical fields. One such capacitive sensor being pressure. 
         [0007]    Capacitive based pressure sensors are based upon the variation of capacitance arising from pressure induced membrane displacement where the membrane represents one of the two electrodes constituting the electrical capacitor. However, whilst easily deployed for relative pressure measurements the implementation of absolute pressure sensors has within the prior art caused significant issues due to the issues of providing a reference pressure and/or reference pressure element through sealing. Accordingly, it would be beneficial to provide a capacitance based pressure sensor realized with a high vacuum cavity without requiring a sealing technique. It would be further beneficial for the capacitance based pressure sensor to provide increased reproducibility through thickness control of the layer(s) within the sensor forming the mechanical membrane. 
         [0008]    However, in essentially all applications, the important considerations for selecting a MEMS sensor include: 
         [0009]    Accuracy; 
         [0010]    Repeatability; 
         [0011]    Long-term stability; 
         [0012]    Ease of calibration; 
         [0013]    Size; 
         [0014]    Packaging; and 
         [0015]    Cost effectiveness. 
         [0016]    MEMS sensors require electronic circuits to either provide excitation and/or bias signals, as in the instance of MEMS resonators, or to convert the MEMS sensor output to a signal for use by other electronics. Silicon CMOS electronics has become the predominant technology in analog and digital integrated circuits. This is essentially because of the unparalleled benefits available from CMOS in the areas of circuit size, operating speed, energy efficiency and manufacturing costs which continue to improve from the geometric downsizing that comes with every new generation of semiconductor manufacturing processes. In respect of MEMS systems, CMOS is particularly suited as digital and analog circuits can be designed in CMOS technologies with very low power consumption. This is due, on the digital side, to the fact that CMOS digital gates dissipate power predominantly during operation and have very low static power consumption. This power consumption arising from the charging and discharging of various load capacitances within the CMOS gates, mostly gate and wire capacitance, but also transistor drain and transistor source capacitances, whenever they are switched. On the analog side, CMOS processes also offers power savings by offering viable operation with sub-1V power supplies and with μA-scale bias currents. 
         [0017]    Accordingly, it would be beneficial whilst designing MEMS resonators and absolute pressure sensors it would be beneficial to establish their designs such that they are compatible with combining the CMOS and MEMS technologies into a single integrated circuit. It would be further beneficial for the processes of manufacturing MEMS resonators and absolute pressure sensors to support the integration of other capacitive sensors for other measurands within a single die and for the MEMS elements to be implemented directly atop silicon CMOS electronics (i.e. above integrated circuits, or above-IC) thereby minimizing footprint, cost, and parasitics. 
         [0018]    Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures. 
       SUMMARY OF THE INVENTION 
       [0019]    It is an object of the present invention to mitigate limitations within the prior art relating to MEMS sensors and more particularly to absolute pressure MEMS capacitive sensors which may be manufactured directly over or in conjunction with silicon based CMOS electronics. 
         [0020]    In accordance with an embodiment of the invention there is provided a MEMS device comprising a membrane formed within a device layer, an upper cavity formed within a top layer, and a lower cavity formed within a handling layer. 
         [0021]    In accordance with an embodiment of the invention there is provided a MEMS device comprising:
   a plurality of first sensors, each first sensor comprising   
 
         [0023]    a first membrane of a first predetermined thickness formed within a device layer; 
         [0024]    an upper cavity formed within a top layer; and 
         [0025]    an opening formed within a handling layer; and
   a plurality of second sensors, each second sensor comprising:   
 
         [0027]    a second membrane of a second predetermined thickness formed within the device layer; 
         [0028]    an upper cavity formed within the top layer; and 
         [0029]    an opening formed within the handling layer; wherein
   the plurality of first sensors and the plurality of second sensors are concurrently formed and represent a plurality of first pressure sensors and a plurality of second pressure sensors respectively.   
 
         [0031]    Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0032]    Embodiments of the present invention will now be described, by way of example only, with reference to the attached Figures, wherein: 
           [0033]      FIG. 1  depicts a MEMS absolute pressure sensor according to an embodiment of the invention; 
           [0034]      FIG. 2  depicts an array of MEMS absolute pressure sensors according to an embodiment of the invention; 
           [0035]      FIG. 3A  depicts schematically the MEMS absolute pressure sensor according to an embodiment of the invention acting as a capacitive transducer in conjunction with an Op-Amp based capacitance to voltage converter and it&#39;s equivalent circuit in  FIG. 3B ; 
           [0036]      FIG. 4  depicts the development methodology for establishing MEMS devices according to embodiments of the invention; 
           [0037]      FIG. 5  depicts the calibration curve for a MEMS absolute pressure sensors according to an embodiment of the invention; 
           [0038]      FIG. 6  depicts a MEMS absolute pressure sensor according to an embodiment of the invention after formation of the absolute pressure side of the sensor and deposition of the protective coating for post-processing; 
           [0039]      FIGS. 7A and 7B  depict the MEMS absolute pressure sensor according to an embodiment of the invention after deep etching of the handling wafer to expose the device layer and etching of the device layer to form the sensor membrane respectively; 
           [0040]      FIG. 8  depicts the calibration curve for a MEMS absolute pressure sensors according to an embodiment of the invention; 
           [0041]      FIG. 9  depicts modal analysis of a MEMS absolute pressure sensor according to an embodiment of the invention; 
           [0042]      FIGS. 10A to 10F  depict a process flow for fabricating MEMS sensors according to embodiments of the invention; 
           [0043]      FIG. 11  depicts an exemplary integration methodology for MEMS pressure sensors according to an embodiment of the invention; and 
           [0044]      FIG. 12  depicts alternate membrane designs for M&lt;EMS pressure sensors according to embodiments of the invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0045]    The present invention is directed to MEMS sensors and more particularly to absolute pressure MEMS capacitive sensors which may be manufactured directly over or in conjunction with silicon based CMOS electronics. 
         [0046]    The ensuing description provides exemplary embodiment(s) only, and is not intended to limit the scope, applicability or configuration of the disclosure. Rather, the ensuing description of the exemplary embodiment(s) will provide those skilled in the art with an enabling description for implementing an exemplary embodiment. It being understood that various changes may be made in the function and arrangement of elements without departing from the spirit and scope as set forth in the appended claims. 
         [0047]    A. Pressure Sensor 
         [0048]    Miniaturized pressure sensors are among the most mass-produced MEMS devices in the recent years and find its applications in different areas including automotive, and aerospace, energy and biomedical applications. As discussed supra it would be beneficial to realize a capacitive sensor constituting of a high vacuum cavity without any post-fabrication sealing requirements providing an absolute pressure sensor with improved manufacturing yields whilst controlling the membrane thickness forming the mechanical test specimen. Accordingly, embodiments of the invention exploit both bulk micromachining and surface micromachining in order to provide a MEMS pressure sensor offering:
       Effective control of the membrane thickness and consequently a perfect predictable response of the theoretical calculations;   Good encapsulation of the cavity without any need of create holes to allow for the sealing technique;   Small gap between the two electrodes, which increases the DC capacitance value, and consequently the sensor sensitivity. The small gap is highly precise and well controlled by means of spacer layer; and   Higher vacuum in the cavity increasing hence the quality factor Q, the frequency range of the measurement for dynamic measurement and ultimately the reliability of the sensor.       
 
         [0053]    A1. Theoretical Analysis 
         [0054]    A1.A Static Modeling: 
         [0055]    The design of the MEMS capacitive pressure sensor is based on two electrodes forming an electrical capacitor. As depicted in  FIG. 1  the bottom electrode is a circular membrane undergoing distributed pressure load where if the cavity pressure between the two electrodes is close to vacuum allowing thus absolute measurement. To avoid the short-circuiting problem, a vertical insulating oxide of approximately 5 μm width is used on the top cap. As depicted in  FIG. 2  an array of capacitance based pressure sensors may be implanted within a single sensor die increasing both the magnitude of the capacitance and the pressure induced capacitance variation. 
         [0056]    Referring to  FIG. 3A  the capacitive MEMS pressure sensor is depicted coupled to an operational amplifier (Op-Amp) based capacitance to voltage converter. The equivalent circuit for such a combination being depicted in  FIG. 3B  wherein the output voltage is given by Equations (1A) to (1C). 
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         [0057]    A1.B Dynamic Modeling: 
         [0058]    The dynamic modeling takes into account the dynamic measurement of the pressure in order to deduce the frequency range over which the sensor can sustain its metrology specifications. In this context the objective is to identify the mechanical impedance i.e. the equivalent spring coefficient constant. k eq , equivalent mass, m eff , and damping coefficient, b eq . If we consider p(t)=p m  sin(ωt)−p 0           {dot over (p)}=p m ω cos(ωt) then the output voltage defined in Equation (6C) can be re-written as Equations (2A) and (2B). 
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         [0059]    With respect to damping coefficient expression then based upon the Reynold&#39;s equation 
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         [0000]    where η is the dynamic viscosity. In cylindrical coordinates, as in this case with cylindrical coordinates, then we get Equation (3). As a result the mechanical impedance can be expressed by its basic parameters as given by Equations (4A) to (4C) respectively. 
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         [0060]    A1.C Sensor Sensitivities: 
         [0061]    Based upon the expression of the capacitance in terms of the applied pressure then it is possible to deduce the expression of the electrical signal in terms of pressure as described by Equation (5). 
         [0000]    
       
         
           
             
               
                 
                   
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         [0062]    Accordingly, the capacitance of the MEMS sensor is given by Equation (6) wherein if we subsequently let 
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                  
                 dr 
               
             
           
         
       
     
         [0000]    we derive Equations (7). Then letting 
         [0000]    
       
         
           
             x 
             = 
             
               
                 
                   
                     u 
                     0 
                   
                   d 
                 
                  
                 X 
               
             
           
         
       
     
         [0000]    we derive Equation (8). 
         [0000]    
       
         
           
             
               
                 
                   C 
                   = 
                   
                     
                       
                         ∫ 
                         0 
                         
                           α 
                            
                           
                               
                           
                            
                           R 
                         
                       
                        
                       
                         
                           
                             
                               ɛ 
                               0 
                             
                              
                             2 
                              
                             π 
                              
                             
                                 
                             
                              
                             r 
                           
                           
                             d 
                             - 
                             
                               u 
                                
                               
                                 ( 
                                 r 
                                 ) 
                               
                             
                           
                         
                          
                         
                             
                         
                          
                         
                            
                           r 
                         
                       
                     
                     = 
                     
                       
                         ∫ 
                         0 
                         
                           α 
                            
                           
                               
                           
                            
                           R 
                         
                       
                        
                       
                         
                           
                             
                               ɛ 
                               0 
                             
                              
                             2 
                              
                             π 
                              
                             
                                 
                             
                              
                             r 
                           
                           
                             d 
                             - 
                             
                               
                                 u 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     
                                       ( 
                                       
                                         r 
                                         R 
                                       
                                       ) 
                                     
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                          
                         
                             
                         
                          
                         
                            
                           r 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     ⇒ 
                     C 
                   
                   = 
                   
                     
                       ∫ 
                       
                         1 
                         - 
                         
                           α 
                           2 
                         
                       
                       1 
                     
                      
                     
                       
                         
                           
                             ɛ 
                             0 
                           
                            
                           π 
                            
                           
                               
                           
                            
                           
                             R 
                             2 
                           
                         
                         
                           d 
                            
                           
                             ( 
                             
                               1 
                               - 
                               
                                 
                                   ( 
                                   
                                     
                                       u 
                                       0 
                                     
                                     d 
                                   
                                   ) 
                                 
                                  
                                 
                                   X 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                       
                        
                       
                           
                       
                        
                       
                          
                         r 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     ⇒ 
                     C 
                   
                   = 
                   
                     
                       
                         
                           
                             ɛ 
                             0 
                           
                            
                           π 
                            
                           
                               
                           
                            
                           
                             R 
                             2 
                           
                         
                         
                           d 
                            
                           
                             
                               
                                 u 
                                 0 
                               
                               d 
                             
                           
                         
                       
                        
                       
                         
                           ∫ 
                           
                             
                               
                                 
                                   u 
                                   0 
                                 
                                 d 
                               
                                
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     α 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 u 
                                 0 
                               
                               d 
                             
                           
                         
                          
                         
                           1 
                           
                             ( 
                             
                               1 
                               - 
                               
                                 x 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                     
                     = 
                     
                         
                     
                      
                     
                       
                         
                           
                             C 
                             0 
                           
                           
                             2 
                              
                             
                               
                                 
                                   u 
                                   0 
                                 
                                 d 
                               
                             
                           
                         
                          
                         
                           [ 
                           
                             arg 
                              
                             thx 
                           
                           ] 
                         
                       
                       
                         
                           
                             
                               u 
                               0 
                             
                             d 
                           
                            
                           
                             ( 
                             
                               1 
                               - 
                               
                                 α 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             u 
                             0 
                           
                           d 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0063]    Accordingly, solving this we derive Equations (9A) and (9B) which yields Equations (10) and (11) and hence the sensitivity is defined by Equations (12) and (13). 
         [0000]    
       
         
           
             
               
                 
                   C 
                   = 
                   
                     
                       
                         C 
                         0 
                       
                       
                         2 
                          
                         
                           
                             
                               u 
                               0 
                             
                             d 
                           
                         
                       
                     
                      
                     
                       Ln 
                        
                       
                         ( 
                         
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   
                                     
                                       u 
                                       0 
                                     
                                     d 
                                   
                                 
                               
                               ) 
                             
                              
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       
                                         α 
                                         2 
                                       
                                     
                                     ) 
                                   
                                    
                                   
                                     
                                       
                                         u 
                                         0 
                                       
                                       d 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   
                                     
                                       u 
                                       0 
                                     
                                     d 
                                   
                                 
                               
                               ) 
                             
                              
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   
                                     + 
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           α 
                                           2 
                                         
                                       
                                       ) 
                                     
                                   
                                    
                                   
                                     
                                       
                                         u 
                                         0 
                                       
                                       d 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     9 
                      
                     A 
                   
                   ) 
                 
               
             
             
               
                 
                   C 
                   = 
                   
                     
                       
                         C 
                         0 
                       
                       
                         2 
                          
                         α 
                          
                         
                           
                             
                               u 
                               0 
                             
                             d 
                           
                         
                       
                     
                      
                     
                       Ln 
                        
                       
                         ( 
                         
                           
                             ( 
                             
                               1 
                               + 
                               
                                 
                                   α 
                                   2 
                                 
                                  
                                 
                                   
                                     
                                       u 
                                       0 
                                     
                                     d 
                                   
                                 
                               
                               + 
                               
                                 
                                   α 
                                   2 
                                 
                                  
                                 
                                   
                                     u 
                                     0 
                                   
                                   d 
                                 
                               
                               - 
                               
                                 
                                   u 
                                   0 
                                 
                                 d 
                               
                             
                             ) 
                           
                           
                             ( 
                             
                               1 
                               - 
                               
                                 
                                   u 
                                   0 
                                 
                                 d 
                               
                               + 
                               
                                 
                                   α 
                                   2 
                                 
                                  
                                 
                                   
                                     u 
                                     0 
                                   
                                   d 
                                 
                               
                               - 
                               
                                 
                                   α 
                                   2 
                                 
                                  
                                 
                                   
                                     
                                       u 
                                       0 
                                     
                                     d 
                                   
                                 
                               
                             
                             ) 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     9 
                      
                     B 
                   
                   ) 
                 
               
             
             
               
                 
                   C 
                   = 
                   
                     
                       C 
                       0 
                     
                      
                     
                       ( 
                       
                         1 
                         + 
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 α 
                                 2 
                               
                               + 
                               
                                 
                                   α 
                                   4 
                                 
                                 3 
                               
                             
                             ) 
                           
                            
                           
                             
                               u 
                               0 
                             
                             d 
                           
                         
                         + 
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 α 
                                 2 
                               
                               + 
                               
                                 2 
                                  
                                 
                                   α 
                                   4 
                                 
                               
                               - 
                               
                                 
                                   α 
                                   8 
                                 
                                 5 
                               
                             
                             ) 
                           
                            
                           
                             
                               ( 
                               
                                 
                                   u 
                                   0 
                                 
                                 d 
                               
                               ) 
                             
                             2 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     S 
                     
                       C 
                       / 
                       P 
                     
                   
                   = 
                   
                     
                       
                         
                           C 
                           0 
                         
                          
                         
                           ( 
                           
                             1 
                             - 
                             
                               α 
                               2 
                             
                             + 
                             
                               
                                 α 
                                 4 
                               
                               3 
                             
                           
                           ) 
                         
                       
                        
                       
                         1 
                         d 
                       
                        
                       
                         
                           R 
                           4 
                         
                         
                           64 
                            
                           D 
                         
                       
                     
                     = 
                     
                       
                         
                           C 
                           0 
                         
                          
                         K 
                          
                         
                           1 
                           d 
                         
                          
                         
                           
                             R 
                             4 
                           
                           
                             64 
                              
                             D 
                           
                         
                          
                         
                             
                         
                          
                         with 
                          
                         
                             
                         
                          
                         K 
                       
                       = 
                       
                         1 
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           S 
                           
                             V 
                             / 
                             P 
                           
                         
                         = 
                           
                          
                         
                           
                             δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               out 
                             
                           
                           
                             δ 
                              
                             
                                 
                             
                              
                             P 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           | 
                           
                             N 
                              
                             
                               
                                  
                                 
                                   
                                     u 
                                     0 
                                   
                                   = 
                                   0 
                                 
                               
                                
                               
                                 
                                   
                                     
                                       u 
                                       . 
                                     
                                     0 
                                   
                                   P 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       R 
                                       f 
                                     
                                     / 
                                     
                                       C 
                                       f 
                                     
                                   
                                   ) 
                                 
                               
                                
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               C 
                               0 
                             
                              
                             
                               ( 
                               
                                 
                                   V 
                                   in 
                                 
                                 d 
                               
                               ) 
                             
                           
                            
                           
                             
                               π 
                                
                               
                                   
                               
                                
                               
                                 r 
                                 a 
                                 2 
                               
                                
                               
                                 1 
                                 
                                   
                                     C 
                                     f 
                                   
                                    
                                   ω 
                                 
                               
                             
                             
                               
                                 
                                   K 
                                   e 
                                 
                                 ω 
                               
                                
                               
                                 
                                   
                                     ( 
                                     
                                       1 
                                       + 
                                       
                                         
                                           ( 
                                           
                                             ω 
                                             
                                               ω 
                                               0 
                                             
                                           
                                           ) 
                                         
                                         2 
                                       
                                     
                                     ) 
                                   
                                   + 
                                   
                                     
                                       ( 
                                       
                                         2 
                                          
                                         ξ 
                                          
                                         
                                           ω 
                                           
                                             ω 
                                             0 
                                           
                                         
                                       
                                       ) 
                                     
                                     2 
                                   
                                   + 
                                   
                                     Z 
                                     m 
                                     ′ 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   
                     S 
                     
                       V 
                       / 
                       P 
                     
                   
                   = 
                   
                     
                       
                         
                           C 
                           0 
                         
                          
                         
                           ( 
                           
                             
                               V 
                               in 
                             
                             d 
                           
                           ) 
                         
                       
                        
                       
                         
                           π 
                            
                           
                               
                           
                            
                           
                             r 
                             a 
                             2 
                           
                            
                           
                             1 
                             
                               
                                 C 
                                 f 
                               
                                
                               ω 
                             
                           
                         
                         
                           
                             K 
                             e 
                           
                           ω 
                         
                       
                     
                     = 
                     
                       
                         
                           
                             C 
                             0 
                           
                           
                             C 
                             f 
                           
                         
                          
                         
                           ( 
                           
                             
                               V 
                               in 
                             
                             d 
                           
                           ) 
                         
                          
                         
                           
                             π 
                              
                             
                                 
                             
                              
                             
                               r 
                               a 
                               2 
                             
                           
                           
                             64 
                              
                             D 
                              
                             
                               π 
                               
                                 r 
                                 a 
                                 2 
                               
                             
                           
                         
                       
                       = 
                       
                         
                           
                             C 
                             0 
                           
                           
                             C 
                             f 
                           
                         
                          
                         
                           ( 
                           
                             
                               V 
                               in 
                             
                             d 
                           
                           ) 
                         
                          
                         
                           
                             π 
                              
                             
                                 
                             
                              
                             
                               r 
                               a 
                               4 
                             
                           
                           
                             64 
                              
                             D 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0064]    A2. Design. 
         [0065]    The methodology adopted by the inventors was based on a common prototyping methodology for MEMS sensors, which as depicted in  FIG. 4 , involves the usual steps from the initial concept through to the prototype including steps of design, electro-mechanical simulation (using Coventorware CAD software), verifying the sensor characteristics that fit well the desired metrology specifications, fabrication, post-processing and finally sensor calibration. The center of the sensor membrane has a displacement that is directly proportional to the pressure load. This deformation is then converted into electrical capacitance which will be linearized in order to get a linear relationship between the pressure measurement and the output voltage. 
         [0066]    In order to obtain a linear relationship the inventors only use the first order expansion of Equation (10) where u 0  is proportional to the applied pressure. C 0  is the capacitance of the un-deformed membrane and is given by 
         [0000]    
       
         
           
             
               C 
               0 
             
             = 
             
               
                 
                   
                     
                       ɛ 
                       0 
                     
                      
                     
                       ( 
                       
                         α 
                          
                         
                             
                         
                          
                         R 
                       
                       ) 
                     
                   
                   2 
                 
                  
                 π 
               
               d 
             
           
         
       
     
         [0000]    and α is the dimensionless parameter controlling the effective radius of the upper electrode and its choice depends on the fabrication design rules check (DRC). Preliminary simulation results were deduced and a depicted in  FIG. 5  over a range of pressures from 1 atmosphere (approximately 101 kPa) to 120 kPa where good linearity can be seen. 
         [0067]    Within the modelling and design iteration process the ratio of u 0 /d         1. This leads to Equations (14) and (15). Through the design process the inventors choose the lowest d and for each couple (R, h) chose designs that fit with the required specification of δp. In order to calculate the couple (R, h) the mechanical sensitivity is fixed by setting S mec =U max /P max , then the value of R is fixed, which in turn is dependent upon the available die area. The resulting value of h is calculated using Equation (16). 
         [0000]    
       
         
           
             
               
                 
                   
                     S 
                     
                       C 
                       / 
                       P 
                     
                   
                   = 
                   
                     
                       
                         
                           C 
                           0 
                         
                         
                           3 
                            
                           d 
                         
                       
                        
                       
                         
                           
                             R 
                             4 
                           
                            
                           12 
                            
                           
                             ( 
                             
                               1 
                               - 
                               
                                 v 
                                 2 
                               
                             
                             ) 
                           
                         
                         
                           64 
                            
                           
                             Eh 
                             3 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           
                             ɛ 
                             0 
                           
                            
                           π 
                            
                           
                               
                           
                            
                           12 
                            
                           
                             ( 
                             
                               1 
                               - 
                               
                                 v 
                                 2 
                               
                             
                             ) 
                           
                         
                         
                           192 
                            
                           
                             Ed 
                             2 
                           
                         
                       
                        
                       
                         
                           R 
                           6 
                         
                         
                           h 
                           3 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                   
                     δ 
                      
                     
                         
                     
                      
                     p 
                   
                   = 
                   
                     
                       
                         δ 
                          
                         
                             
                         
                          
                         C 
                       
                       
                         S 
                         
                           C 
                           / 
                           P 
                         
                       
                     
                     = 
                     
                       δ 
                        
                       
                           
                       
                        
                       
                         C 
                          
                         
                           ( 
                           
                             
                               
                                 192 
                                  
                                 
                                   Ed 
                                   2 
                                 
                               
                               
                                 ɛ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   π12 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       
                                         v 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                              
                             
                               
                                 h 
                                 3 
                               
                               
                                 R 
                                 6 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                   
                     S 
                     mec 
                   
                   = 
                   
                     
                       
                         
                           
                             12 
                              
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   v 
                                   2 
                                 
                               
                               ) 
                             
                           
                           
                             64 
                              
                             E 
                           
                         
                          
                         
                           
                             R 
                             4 
                           
                           
                             h 
                             3 
                           
                         
                       
                       ⇒ 
                       h 
                     
                     = 
                     
                       
                         
                           12 
                            
                           
                             ( 
                             
                               1 
                               - 
                               
                                 v 
                                 2 
                               
                             
                             ) 
                           
                            
                           
                             R 
                             4 
                           
                         
                         
                           64 
                            
                           
                             ES 
                             mec 
                           
                         
                       
                       3 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
         [0068]    Subsequently, for each couple (R, h) the ratio is checked in order to if it&#39;s in the hypothesis to consider the circle shape as membrane. Finally, the resolution is checked in terms of measured pressure. 
         [0069]    A3. Fabrication 
         [0070]    A3.A Design Cross-Section. 
         [0071]    Referring to  FIGS. 6 ,  7 A and  7 B there are depicted cross-sections of the MEMS pressure sensor upon completion of the fabrication process and after post-fabrication processing wherein the sensor membrane is exposed, such as depicted in  FIG. 2 . Referring initially to  FIG. 6  the MEMS pressure sensor according to embodiments of the invention is depicted in cross-section after formation of the absolute pressure side of the sensor and deposition of the protective coating for post-processing. Accordingly, the cross-section depicts a handling layer at the bottom which has a 30 μm deep trench etched. Disposed upon this is the device layer, with thickness 30 μm, and then atop these is disposed top layer which includes metallization and importantly the 2 μm deep trench which forms in combination with the device layer the reference side of the pressure sensor. Where the top layer is attached to the device layer under vacuum then the deflection of the membrane is dependent solely upon the pressure on the membrane and hence the pressure sensor is an absolute pressure sensor. This latter cavity is formed using direct fusion bonding process with the top layer and device layer, which are a pair of silicon wafers. In order to fabricate the two electrodes for the capacitor without any short circuit, an insulating layer of oxide will fill all the top cavity depth, thus the upper electrode can be maintained and surrounded by the oxide material. 
         [0072]    As depicted in  FIG. 6  after formation of the three layer stack the device is protected with a protective layer, e.g. silicon nitride (Si 3 N 4 ), prior to the post-processing stages. As depicted upper contacts are aluminum-copper (AlCu) with an in-situ doped polysilicon (ISDP) underlying layer. 
         [0073]    Formation of the membrane is performed during post-fabrication processing once the handling wafer, device layer, and top layer have been assembled together. Accordingly, the post-processing to yield the device cross-section depicted in  FIGS. 6 ,  7 A and  7 B respectively, comprising
       Etching the handling wafer to the silicon oxide layer of the patterned cavity; and   Etching of the handling wafer and the device (structure) layer to expose the device layer and form the membrane.       
 
         [0076]    Beneficially, the post-processing sequence does not require any alignment marks on the backside, thereby avoiding the requirement for a photolithography process and there is no requirement for a hard etch mask for the deep reactive ion etching of the handling and device layers wherein approximately 232 μm of material is removed from the geometry. Accordingly, there are no requirements for any plasma enhanced chemical vapour deposition (PECVD) oxide/nitride deposition or low temperature oxide (LTO) deposition and its subsequent dry or wet etching. This process is suited to forming devices such as pressure sensors for a range of applications. Accordingly, the topside of the device is protected initially, for example with thick PECVD silicon nitride, silicon oxide or silicon oxynitride. Alternatively, a thick polymer coating may be employed for protection. There are a range of different process configurations to achieve the desired post-processing, including, for example, purely wet etching, purely dry etching, and combination dry/wet etching. Exemplary processes for each of these are presented below. 
         [0077]    Wet Etching: 
         [0078]    Accordingly, the first post-processing step is a wet etching process using potassium hydroxide (KOH) or tetramethylammonium hydroxide (TMAH) in order to etch down the handling wafer until the oxide layer deposited onto the handling wafer within the recesses/trenches/pits is reached. Within the structure depicted in  FIG. 6  this requires the removal of approximately 232 μm of silicon wafer. At this point the oxide layer is removed, for example, using a dry etching process with trifluoromethane (CHF3). Now the device layer is etched using TMAH or KOH in order to create the thin membrane layer. As this etching is through bulk silicon high reproducibility can be achieved. 
         [0079]    Dry Etching: 
         [0080]    In this process dry etching of the handling wafer is initially performed until the oxide layer, e.g. approximately 232 μm of silicon wafer for the structure depicted in  FIG. 6 . At this point the oxide layer is removed, for example, using a dry etching process with trifluoromethane (CHF3). Finally, deep etching of the device layer with a special recipe DRIE process is undertaken to provide highly controlled etching in order to attain the desired precision and uniformity of the membrane thickness. 
         [0081]    Dry and Wet Etching A: 
         [0082]    In this process dry etching of the handling wafer is initially performed until the oxide layer, e.g. approximately 232 μm of silicon wafer for the structure depicted in  FIG. 6 . At this point the oxide layer is removed, for example, using a dry etching process with trifluoromethane (CHF3). Finally the device layer is etched using TMAH or KOH in order to create the thin membrane layer. 
         [0083]    Dry and Wet Etching B: 
         [0084]    In this process a wet etching process using potassium hydroxide (KOH) or tetramethylammonium hydroxide (TMAH) in order to etch down the handling wafer until the oxide layer deposited onto the handling wafer within the recesses/trenches/pits is reached. Within the structure depicted in  FIG. 6  this requires the removal of approximately 232 μm of silicon wafer. Finally, deep etching of the device layer with a special recipe DRIE process is undertaken to provide highly controlled etching in order to attain the desired precision and uniformity of the membrane thickness. 
         [0085]    Referring to  FIGS. 6 ,  7 A and  7 B then it can be seen that the initial structure, according to an embodiment of the invention, comprises a 90 μm top layer, 30 μm device layer, and approximately 275 μm handling layer. Post-fabrication after post-fabrication processing the handling wafer has been thinned to approximately 30 μm whilst the device layer has been thinned to form the circular membrane approximately 5 μm thick. 
         [0086]    A3.B Exemplary Process Sequence 
         [0087]    FIG.  10 A—exemplary process flow wherein three sub-process flows for handling wafer, device wafer, and through silicon vias (TSVs) are employed. Subsequent to completion of the handling wafer processes this is then bonded to the device wafer by wafer-wafer bonding. This assembly then undergoes additional combined handling and device wafer processing. In the third process flow TSVs are implemented as required in the top layer wherein this is then bonded to the handling/device wafer combination. 
         [0088]      FIG. 10B  there is depicted an image of a handling wafer lower cavity pattern, e.g. 30 μm recess. 
         [0089]      FIG. 10C  depicts the handling wafer bonded to the device wafer, typically, 30 μm thick, wherein the device wafer may have been pre-processed to form other MEMS structures that will be formed as part of the final die. Such MEMS structures, may include, but are not limited to, temperature sensors, humidity sensors, gas sensors, and accelerometers, see for example El-Gamal et al in “Methods and Systems for Humidity and Pressure Sensor Overlay Integration with Electronics” (U.S. Patent Publication 2014/0,125,359). 
         [0090]      FIG. 10D  wherein through silicon vias (TSV) are fabricated together with the upper sense cavity, typically for example 2 μm-5 μm. 
         [0091]      FIG. 10E  wherein the TSV wafer has the upper cavity formed, typically 30 μm deep, followed by formation of the metallization for electrical contacts. Additionally, the handling/device wafer is bonded to the TSV wafer via wafer-wafer bonding with establishment of the interconnect metallization. 
         [0092]      FIG. 10F  depicts an exploded view of final assembled stack for MEMS pressure sensor according to an embodiment of the invention. 
         [0093]    It would be evident that the MEMS pressure sensor described with respect to embodiments of the invention may be formed simultaneously/concurrently with other MEMS devices exploiting the same three layer design methodology of handling layer (bottom layer), device layer and top layer (TSV layer). By the addition of a photolithography process prior to etching the openings within the handling wafer through which the MEMS pressure sensors are formed then the handling wafer thickness over the remaining regions is maintained. 
         [0094]    Accordingly, considering such a process flow the resulting structure is a device layer having active elements disposed between upper and lower cavities formed within the top and handling layers respectively. The environment at the time of bonding these top, device and handling layers together allows the environment within the cavity or cavities to be controlled. In the instance the membrane within the device layer is as large as the cavity then two cavities are formed but in the instance that the membrane is not then there is a single cavity with the membrane (i.e. beam) disposed within. Accordingly, a resonator beam may be packaged within a hermetic very low pressure environment for a high quality factor or a cavity sealed at very low pressure on one side of the membrane for an absolute pressure sensor. 
         [0095]    It would be evident that formation of a beam resonator within a cavity and absolute pressure sensor may be made within the same device using the designs described supra wherein in the absolute pressure sensor the handling wafer is processed to remove the silicon opening the lower cavity to ambient whereas in the resonator case the silicon is not removed. 
         [0096]    Referring to first and second cross-sections  1200 A and  1200 B in  FIG. 12  alternate membrane designs are depicted for pressure sensors according to embodiments of the invention. Referring to first cross-section  1200 A then a “bossed” membrane as defined by the inventors is depicted wherein the membrane on the device layer is formed by an annular ring of thin silicon with a thicker central “boss” region. In contrast, in second cross-section  1200 B in  FIG. 12  an “interdigitated” membrane within the device layer and an “interdigitated” body within the top layer increase the effective surface area wherein external pressure deforms the central “interdigitated” membrane within the device layer through the annular thin “living hinge” such that the vertical “fingers” on the device layer move relative to the “fingers” on the top layer. 
         [0097]    A3. C CMOS Electronics Integration 
         [0098]    Referring to  FIG. 11  there is depicted an exemplary integration methodology for MEMS pressure sensors according to an embodiment of the invention wherein a fabricated array/die/wafer of MEMS pressure sensors  1110  is flipped and aligned relative to a CMOS electronics  1120  die/wafer. These are then brought together under conditions that the contact bumps, e.g. Au/Sn on the CMOS electronics  1120  die/wafer join to the metallization on the MEMS pressure sensors  1110 , e.g. Au/Sn as well, to form a bond and electrical contact. 
         [0099]    A4. Simulation and Results 
         [0100]    Referring to Table 1 there are listed the design parameters for a MEMS pressure sensor fabricated according to an embodiment of the invention. The calibration curve derived for this MEMS sensor is depicted in  FIG. 8  over the range 0.05 MPa≦P≦2.50 MPa. In  FIG. 9  with first to third images  900 A to  900 C there are depicted the results of electromechanical simulations on the MEMS pressure sensor. First image  900 A depicts the fundamental mode of the membrane whilst second and third images  900 B and  900 C respectively depict the first order modes of the membrane. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Pressure Sensor Specification 
               
             
          
           
               
                   
                 Parameter 
                 Value 
               
               
                   
                   
               
             
          
           
               
                   
                 Gap (μm) 
                 2 
               
               
                   
                 Radius (μm) 
                 180 
               
               
                   
                 Thickness (μm) 
                 12 
               
               
                   
                 Sensitivity (pF/kPa) 
                 4.96 × 10 −4   
               
               
                   
                 Resolution (δC = 10 fF) kPa 
                 20.2 
               
               
                   
                 Equivalent Mass m eff  (kg) 
                 1.40 × 10 −9   
               
               
                   
                 Equivalent Spring Constant 
                 47100 
               
               
                   
                 Damping Coefficient b eff  (N/m) 
                 1.13 × 10 −2   
               
               
                   
                 Natural Frequency (kHz) 
                 922.920 
               
               
                   
                   
               
             
          
         
       
     
         [0101]    Beneficially, embodiments of the invention provide a fabrication process which is designed to be fully compatible with monolithic integration above CMOS electronics, and other electronics technologies that can withstand the low processing temperatures of embodiments of the invention. Beneficially this provides:
       direct integration over the electronics;   improved system performance through reduced parasitic effects;   reduced die size;   increased electronics selection freedom, allowing for use of high performance technological nodes   reduced package footprint and thickness;   self-aligned processing;   lower sensor fabrication costs through batch processing;   integral reference elements; and   integral heaters and/or temperature stabilization.       
 
         [0111]    Referring to  FIG. 2  it would be evident that in the die depicted nine pressure sensors are concurrently fabricated. Optionally, a first subset of the elements may be processed with membranes, i.e. forming pressure sensors, and a second subset of the elements may be processed without membranes such that they form reference pressure elements. Optionally, the process flows described and depicted may be modified to provide for two or more membrane thicknesses such that a plurality of pressure sensors with different pressure ranges are concurrently formed from the process flow(s). As the capacitance of capacitors in parallel is directly additive the interconnection of a group of pressure sensors may be implemented within the MEMS die directly. 
         [0112]    The foregoing disclosure of the exemplary embodiments of the present invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many variations and modifications of the embodiments described herein will be apparent to one of ordinary skill in the art in light of the above disclosure. The scope of the invention is to be defined only by the claims appended hereto, and by their equivalents. 
         [0113]    Further, in describing representative embodiments of the present invention, the specification may have presented the method and/or process of the present invention as a particular sequence of steps. However, to the extent that the method or process does not rely on the particular order of steps set forth herein, the method or process should not be limited to the particular sequence of steps described. As one of ordinary skill in the art would appreciate, other sequences of steps may be possible. Therefore, the particular order of the steps set forth in the specification should not be construed as limitations on the claims. In addition, the claims directed to the method and/or process of the present invention should not be limited to the performance of their steps in the order written, and one skilled in the art can readily appreciate that the sequences may be varied and still remain within the spirit and scope of the present invention.