Abstract:
A miniature microphone comprising a diaphragm compliantly suspended over an enclosed air volume having a vent port is provided, wherein an effective stiffness of the diaphragm with respect to displacement by acoustic vibrations is controlled principally by the enclosed air volume and the port. The microphone may be formed using silicon microfabrication techniques and has sensitivity to sound pressure substantially unrelated to the size of the diaphragm over a broad range of realistic sizes. The diaphragm is rotatively suspend for movement through an arc in response to acoustic vibrations, for example by beams or tabs, and has a surrounding perimeter slit separating the diaphragm from its support structure. The air volume behind the diaphragm provides a restoring spring force for the diaphragm. The microphone&#39;s sensitivity is related to the air volume, perimeter slit, and stiffness of the diaphragm and its mechanical supports, and not the area of the diaphragm.

Description:
RELATED APPLICATIONS 
       [0001]    The present invention is related to co-pending U.S. patent application Ser. No. 10/689,189, for ROBUST DIAPHRAGM FOR AN ACOUSTIC DEVICE, filed Oct. 20, 2003, Ser. No. 11/198,370 for COMB SENSE MICROPHONE, filed Aug. 5, 2005, Ser. No. 11/335,137 for OPTICAL SENSING IN A DIRECTIONAL MEMS MICROPHONE, filed Jan. 19, 2006, and Ser. No. 11/343,564 for SURFACE MICROMACHINED MICROPHONE, filed Jan. 31, 2006, all of which are included herein in their entirety by reference. 
     
    
     FUNDED RESEARCH 
       [0002]    This work is supported in part by Grant No. 1035968 from the National Institutes of Health. The Government may have certain rights in this invention. 
     
    
     FIELD OF THE INVENTION 
       [0003]    The present invention relates to the field of miniature non-directional microphones, particular, to miniature microphones having high sensitivity and good low frequency response characteristics. 
       BACKGROUND OF THE INVENTION 
       [0004]    Small microphones that can be manufactured with low cost are highly desirable components in many portable electronic products. In current design approaches, however, the small size of the microphone results in diminished sensitivity to sound, and in particular poor sensitivity to low frequencies. As a result, great care must be taken in the design to maximize sensitivity, which generally adds to the complexity and cost of the device. 
         [0005]    The conventional approach to creating small microphones is to fabricate a thin, lightweight diaphragm that vibrates in response to minute sound pressures. The motion of the diaphragm is usually transduced into an electronic signal through capacitive sensing, where changes in capacitance are detected between the moving diaphragm and a fixed backplate electrode. As the size of the diaphragm is reduced, however, in an attempt to make a small, low-cost microphone, the stiffness of the diaphragm is generally increased. This increased stiffness causes a marked reduction in its ability to deflect in response to fluctuating sound pressures. This increased stiffness with decreasing size is a fundamental challenge in the design of small microphones. An additional challenge in the design of microphones comes from the use of a backplate electrode to achieve capacitive sensing. To obtain an electronic readout, it is necessary to apply a biasing electric voltage between the backplate and the diaphragm. This will result in a force that is proportional to the square of the voltage (and hence is independent of its polarity) that always acts to attract the flexible diaphragm toward the fixed backplate. Because the output of the electronic circuit will be proportional to the biasing voltage used, one is tempted to use as high a voltage as possible to increase sensitivity. However, great care must be taken to ensure that the resulting attractive force is not sufficient to collapse the diaphragm into the backplate. To avoid this potentially catastrophic situation, one may use a diaphragm that has a higher stiffness so it can resist the attractive force, but this also results in reduced acoustic sensitivity. Achieving a compromise between increased electronic sensitivity through the use of a high bias voltage and avoiding diaphragm collapse is one of the most challenging aspects of microphone design. 
         [0006]    Because microphones are generally designed to respond to sound pressures using a pressure-sensitive diaphragm, it is important to ensure that the pressure due to sound acts on only one side, or face of the diaphragm otherwise the pressures acting on the two sides will cancel. (In some cases, this cancellation property is used to advantage, especially where the microphone can be designed such that undesired sounds are cancelled while desired sounds are not). In addition, because the diaphragm is also subjected to relatively large atmospheric pressure changes, it is important to incorporate a small vent to equalize static pressures on the two sides of the diaphragm. Depending on the size of the enclosure around the back-side of the diaphragm and the size of the pressure-equalizing vent, the low-frequency response of the diaphragm will also be reduced by the vent. In small microphones, the air volume behind the diaphragm is generally quite small and as a result, motion of the diaphragm can cause a significant change in the volume of the air. The air thus becomes compressed or expanded as the diaphragm moves, which results in a respective increase or decrease in its pressure. This pressure creates a restoring force on the diaphragm and could be viewed as an equivalent linear air spring having a stiffness that increases as the nominal volume of air is reduced. The combined effects of the diaphragm&#39;s mechanical stiffness, the pressure-equalizing vent, and the equivalent air spring of the back volume need to be considered very carefully in designing microphones that are small, have good sensitivity and respond at low audio frequencies 
         [0007]    When a microphone is sensing small differences in the air pressure (i.e., sound waves), both large and small diaphragms will, in principle, be equally capable of picking up low frequencies. The lower limiting frequency (LLF) of a pressure microphone is typically controlled by a small pressure equalization vent that prevents the microphone diaphragm from responding to changes in the ambient barometric pressure. The vent typically acts as an acoustic low cut filter (i.e., a high-pass filter) whose cut-off frequency depends on the vent dimensions (e.g., diameter and length). As a sound pressure wave passes the microphone, longer wavelengths (lower frequencies) will tend to equalize pressure around the diaphragm and thus cancel their response. 
       SUMMARY OF THE INVENTION 
       [0008]    In accordance with the present invention, there is provided a miniature, generally non-directional microphone that maintains both good sensitivity and low-frequency response as the surface area of the microphone&#39;s diaphragm is reduced. A preferred implementation of the microphone provides a silicon diaphragm formed using silicon microfabrication techniques and has sensitivity to sound pressure substantially unrelated to the size (e.g., sensing area) of the diaphragm. 
         [0009]    In the preferred embodiment, the diaphragm is rotatively suspended by two stiff beams and has a surrounding perimeter slit separating the diaphragm from its support structure. Air in a back volume behind the diaphragm provides a restoring spring force for the diaphragm. The relationship of the volume of air in the back volume, the perimeter slit characteristics, and the effective stiffness of the diaphragm (generally determined by the stiffness of the beams supporting the diaphragm for rotational displacement in response to acoustic waves) determine the microphone&#39;s sensitivity. 
         [0010]    In accordance with a preferred embodiment, the present invention provides a tiny microphone diaphragm that is dramatically less stiff than what can be achieved with previous approaches. Therefore, the responsivity is increased. 
         [0011]    A preferred embodiment in accordance with the present invention avoids imposing a large force between the diaphragm and the backplate due to a sensing voltage, and employs a different transduction approach, which does not require mechanical stiffness of the out-of-plane motion of the diaphragm to avoid collapse. Preferably, a significant electrostatic force component from the sensing voltage is disposed in the plane of the diaphragm, and thus has a lower tendency to displace the diaphragm. 
         [0012]    The permitted use of a highly flexible diaphragm in accordance with preferred embodiments of the present invention causes the overall sensitivity to be less dependent on the diaphragm&#39;s stiffness and the size of the vent than that of prior approaches. 
         [0013]    The microphone according to the present invention preferably has a sensing membrane displacement which is approximately (within, e.g., 5%) proportional to the pressure and volume of a back space, and inversely proportional to an area of a slit which viscously equalizes the pressure of the back space with the environment, e.g., PV/A, and, for example, providing a ±3 dB amplitude response over at least one octave, and preferably ±6 dB amplitude response over a range of 6 octaves, e.g., 100 to 3200 Hz. Of course, the microphone may have far better performance, e.g., ±3 dB amplitude response from 50 to 10 kHz, and/or a displacement which is proportional to PV/A within 1% or better. It is noted that the electrical performance of the transducer may differ from the mechanical performance, and indeed electronic techniques are available for correcting mechanical deficiencies, separate from the performance criteria discussed above. Likewise, the electrical components may be a limiting or controlling factor in the accuracy of the output. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]    A complete understanding of the present invention may be obtained by reference to the accompanying drawings, when considered in conjunction with the subsequent detailed description, in which: 
           [0015]      FIGS. 1A and 1B  are side, cross-sectional and top schematic views, respectively, of an omni-directional microphone in accordance with the invention; 
           [0016]      FIG. 2  is a schematic, plan view of a miniature microphone diaphragm; 
           [0017]      FIGS. 3A-3E  are schematic representations of the fabrication process steps of the microphone diaphragm of  FIGS. 1A ,  1 B, and  2 ; 
           [0018]      FIG. 4  is a plan view of the microphone of  FIGS. 1A and 1B  having interdigitated comb sense fingers; and 
           [0019]      FIG. 5  is a plan view of a microphone having a tab support system and interdigitated comb sense fingers. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0020]    The motion of a diaphragm of a typical microphone results in a fluctuation in the net volume (at standardized temperature and pressure) of air in a region behind the diaphragm. The compression and expansion of the air in this region due to the diaphragm&#39;s motion results in a linear restoring force that effectively stiffens the diaphragm and reduces its response to sound. This stiffness acts in parallel with the mechanical stiffness of the diaphragm, which, in small microphones and particularly in silicon microphones, is normally much greater than the stiffness of the air in the back volume. 
         [0021]    The present invention permits a diaphragm to be designed such that its mechanical stiffness is much less than that resulting from the compression of air or fluid in the back volume, even though the diaphragm is fabricated out of a very stiff material such as silicon. 
         [0022]    Unlike typical microphone diaphragms that are supported around their entire perimeter, the diaphragm according to a preferred embodiment of the present invention is supported only by flexible pivots around a small portion of its perimeter, and is separated from the surrounding substrate by a narrow slit around the remainder of its perimeter. U.S. patent application Ser. No. 10/689,189, expressly incorporated herein by reference, describes a microphone diaphragm that is supported on flexible pivots. The pivots may be designed to have nearly any desired stiffness. Because the area of silicon is reduced, its corresponding contribution to the effective stiffness of the diaphragm, representing the extent of its movement in response to acoustic pressure waves of various amplitudes, is reduced. Therefore, the back-volume effective stiffness, which roughly corresponds to Δp=nRT/ΔV (ideal gas law equation), and the contribution from the slit, will control the effective stiffness. 
         [0023]    Referring first to  FIGS. 1A and 1B , there are shown side, cross-sectional and top schematic views, respectively, of a microphone diaphragm in accordance with the present invention, generally at reference number  100 . The inventive microphone  100  is typically formed in silicon using micromachining operations as are well known to those of skill in the art. It is noted that materials other than silicon may be used to form the diaphragm, and the techniques other than the silicon micromachining techniques may be employed, as appropriate or desired. 
         [0024]    A silicon chip or wafer  102  has been processed (e.g., micromachined) to form a thin diaphragm  104  supported by a pivot  106 . Diaphragm  104  is separated from silicon wafer  102  by a slit  110  disposed between the outer edge  105  of diaphragm  104  and silicon wafer  102 . Slit  110  typically extends around substantially the entire perimeter  105  of diaphragm  104 . 
         [0025]    A back volume  108  is formed behind diaphragm  104  in silicon wafer  102 . Typically, silicon wafer  102  is mounted on a substrate  112  that may seal a portion of back volume  108 . The back volume  108  is defined, for example, by a recess in the substrate  112  which communicates with the slit  110 , and provides sufficient depth to allow movement of the diaphragm  104  in response to acoustic waves. 
         [0026]    By proper design of the flexible pivots  106  and the dimensions of the slit  110 , the overall stiffness of the diaphragm  104  is determined by the dimensions of the volume of air behind the diaphragm  104  (i.e., back volume  108 ) rather than by the material properties or the dimensions of the pivots  106 . The flexible pivots  106  are provided with sufficient compliance (e.g., the stress-strain relationship) such that they do not impose a dominant force on the diaphragm  104 , with respect to slit  110  and the fluid or gas in the back volume  108 , to substantially control the overall stiffness. Of course, there may be instances where a stiffness contribution from the flexible pivots  106  or other elements may be desired, for example to provide mechanical frequency response control, which may be implemented without departing from the spirit of the invention. 
         [0027]    An approximate model for the mechanical sensitivity of a miniature microphone, for example the microphone of  FIGS. 1A and 1B , has been developed. The diaphragm  104  of the miniature microphone is assumed to be supported in such a way that the structural connection (e.g., pivots  106 ) of the diaphragm  104  to the surrounding substrate  102  is extremely compliant. The effective stiffness of the diaphragm  104  is therefore primarily determined by the air volume  108  therebehind. 
         [0028]    In order to achieve this high structural compliance, it is assumed that the diaphragm  104  is typically supported at only a small fraction of its perimeter, leaving a narrow gap of slit  110  around most of the perimeter  105 . This approximate model includes the effects of the air in both the back volume  108  behind the diaphragm  104  and in narrow slit  110  around the diaphragm&#39;s perimeter  105 . The air in the back volume  108  acts like a spring. Due to the narrowness of the slit  110 , viscous forces control the flow of air therethrough. It has been found that the slit  110  and back volume  108  have a pronounced effect on the response of the diaphragm  104 . The model shows that by proper design of the compliance of the diaphragm  104  and the dimensions of the surrounding slit  110 , the mechanical response to incident sound, not shown, has good sensitivity over the audible frequency range, over a large range of sizes of diaphragm  104 . This makes it feasible to produce microphones that are substantially smaller than those possible using currently available technology. 
         [0029]    In analyzing the inventive technology, consider first, a conventional microphone diaphragm (i.e., a diaphragm having no surrounding slit) consisting of an impermeable plate or membrane that is supported around its entire perimeter. Assume that the pressure in the air behind the microphone diaphragm does not vary due to the incident sound. In this case, the diaphragm response may be modeled as a linear second order oscillator: 
         [0000]        m{umlaut over (x)}+kx+C{dot over (x)}=−PA   (1) 
         [0000]    where m is the diaphragm mass, x is the displacement of the diaphragm, k is the effective mechanical stiffness, C is the viscous damping coefficient, and P is the pressure due to the applied sound field. Assume that a positive pressure at the diaphragm&#39;s exterior results in a force in the negative direction. If the resonant frequency, ω 0 =√{square root over (k/m)}, is above the highest frequency of interest, then the mechanical sensitivity is s m ≈A/k. 
         [0030]    In the preferred microphone  100  according to the present invention, if the dimensions of the air chamber back volume  108  behind the diaphragm  104  are much smaller than the wavelength of sound, it may be assumed that the air pressure in the back volume  108  is independent of location. The air in this volume  108  will then act like a linear spring. The fluctuating pressure in the back volume  108  (V), due to a fluctuation in the volume, dV, resulting from the outward motion of the diaphragm  104 , x, is: 
         [0000]        P   d =ρ 0   c   2   dV/V=−ρ   0   c   2   Ax/V   (2) 
         [0000]    where ρ 0  is the density of air and c is the sound speed. The negative sign results from the fact that an outward, or positive motion of the diaphragm  104  increases the volume of back volume  108  and thus reduces the internal pressure therein. This pressure in the back volume  108  exerts a force on the diaphragm given by: 
         [0000]        F   d   =P   d   *A=−ρ   0   c   2   A   2   x/V=−K   d   x   (3) 
         [0000]    where 
         [0000]        K   d =ρ 0   c   2   A   2   /V   (4) 
         [0000]    is the equivalent spring constant of the air in N/m. 
         [0031]    The force due to the air in the back volume  108  adds to the restoring force due to the mechanical stiffness of the diaphragm  104 . Including the air in the back volume  108 , equation (1) becomes: 
         [0000]        m{umlaut over (x)}+kx+K   d   x+C{dot over (x)}=−PA   (5) 
         [0000]    so that the mechanical sensitivity now becomes s m ≈A/(k+K d ). 
         [0032]    The effect of the air in the slit  110  must also be considered. The air in the slit  110  around diaphragm  104  is forced to move due to the fluctuating pressures both within the back volume  108  space behind the diaphragm  104  and in the external sound field. Again, assume that the dimensions of these volumes of moving air are much less than the wavelength of sound so that they can be represented by a single lumped mass, m a . An outward displacement of the air in the slit  110 , x a , causes a change in volume of the air in the back volume  108  given by −A α x a  and a corresponding pressure given by: 
         [0000]        P   αα =−ρ 0   c   2   A   α   x   α   /V   (6) 
         [0000]    where A a  is the area of the slit upon which the pressure acts. 
         [0033]    The pressure due to the motion of the air in the slit  110  applies a restoring force on the mass of air in the slit  110  given by: 
         [0000]        F   αα =ρ 0   c   2   A   α   2   s   α   /V=−K   αα   x   α   (7) 
         [0000]    where 
         [0000]        K   αα =ρ 0   c   2   A   α   2   /V.   (8) 
         [0034]    The pressure due to the motion of the air in the slit  110  also exerts a force on the diaphragm  104  given by: 
         [0000]        F   dα   =P   d   A   α =−ρ 0   c   2   AA   α   x/V=−K   dα   x   (9) 
         [0000]    where 
         [0000]        K   dα =ρ 0   c   2   AA   α   /V   (10) 
         [0035]    Likewise, the pressure due to the motion of the diaphragm  104  in equation (2) produces a force on the air in the slit  110  that is given by: 
         [0000]        F   dα   =P   d   A   α =−ρ 0   c   2   AA   α   x/V=−K   dα   x   (11) 
         [0000]    where K dα =K αd  as given in equation (10). 
         [0036]    Because the air in the slit  110  is squeezed through a relatively small opening, the effects which result in a velocity dependent restoring force on the air in the slit  110  must be accounted for, 
         [0000]        F   υ   =−c   υ   {dot over (x)}   α   (12) 
         [0000]    where c v  is a viscous damping coefficient that depends on the details of the airflow. 
         [0037]    Finally, the externally applied force on the air in the slit  110  due to the incident sound field is: 
         [0000]      F α =−PA α   (13) 
         [0038]    Summing the forces on the moving elements of the system gives the following pair of governing equations: 
         [0000]        m{umlaut over (x)} +( k+K   d ) x+K   αd   x   α   +C{dot over (x)}=−PA    
         [0000]        m   α   {umlaut over (x)}   α   +K   αα   x   α   +K   dα   x+C   υ   {dot over (x)}   α   =−PA   α   (14) 
         [0039]    Response due to harmonic sound fields may also be considered. If it is assumed that the sound pressure is harmonic with frequency ω then let P(t)=Pe iωt , x(t)=Xe iωt  and x α (t)=X α e iωt . Equations (14) can be solved to give the steady-state response relative to the amplitude of the pressure. This is expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
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         [0040]    The response of the microphone diaphragm  104  is then: 
         [0000]    
       
         
           
             
               
                 
                   
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         [0041]    Note that equations (8) and (10) give AK αα =A α K αd  so that equation (16) becomes: 
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         [0042]    The ω dependence in the numerator of this expression of equation (17) clearly shows that the response has a high-pass filter characteristic. The cut-off frequency of the high-pass response is given by: 
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         [0000]    Note that for sufficiently large c v , equation (17) becomes: 
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         [0000]    in which case the response behaves as if the enclosure is sealed with an equivalent stiffness k+K d . 
         [0043]    Another important special case occurs if the diaphragm&#39;s mechanical stiffness is significantly less than the stiffness of the air behind the diaphragm, k&lt;&lt;K d  in equation (17). In this case, equation (17) becomes: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
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                                       a 
                                     
                                   
                                   + 
                                   
                                     
                                       i 
                                       ^ 
                                     
                                      
                                     
                                         
                                     
                                      
                                     ω 
                                      
                                     
                                         
                                     
                                      
                                     
                                       c 
                                       v 
                                     
                                   
                                 
                                 ) 
                               
                             
                             - 
                             
                               
                                 K 
                                 ad 
                               
                               * 
                               
                                 K 
                                 da 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             - 
                             
                               A 
                                
                               
                                 ( 
                                 
                                   
                                     
                                       ω 
                                       2 
                                     
                                      
                                     
                                       m 
                                       a 
                                     
                                   
                                   + 
                                   
                                     
                                       i 
                                       ^ 
                                     
                                      
                                     
                                         
                                     
                                      
                                     ω 
                                      
                                     
                                         
                                     
                                      
                                     
                                       c 
                                       v 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       - 
                                       
                                         ω 
                                         2 
                                       
                                     
                                      
                                     m 
                                   
                                   + 
                                   
                                     
                                       i 
                                       ^ 
                                     
                                      
                                     
                                         
                                     
                                      
                                     ω 
                                      
                                     
                                         
                                     
                                      
                                     C 
                                   
                                 
                                 ) 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       - 
                                       
                                         ω 
                                         2 
                                       
                                     
                                      
                                     
                                       m 
                                       a 
                                     
                                   
                                   + 
                                   
                                     
                                       i 
                                       ^ 
                                     
                                      
                                     
                                         
                                     
                                      
                                     ω 
                                      
                                     
                                         
                                     
                                      
                                     
                                       c 
                                       v 
                                     
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               
                                 K 
                                 aa 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       - 
                                       
                                         ω 
                                         2 
                                       
                                     
                                      
                                     
                                       m 
                                       a 
                                     
                                   
                                   + 
                                   
                                     
                                       i 
                                       ^ 
                                     
                                      
                                     
                                         
                                     
                                      
                                     ω 
                                      
                                     
                                         
                                     
                                      
                                     C 
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               
                                 K 
                                 d 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       - 
                                       
                                         ω 
                                         2 
                                       
                                     
                                      
                                     
                                       m 
                                       a 
                                     
                                   
                                   + 
                                   
                                     
                                       i 
                                       ^ 
                                     
                                      
                                     
                                         
                                     
                                      
                                     ω 
                                      
                                     
                                         
                                     
                                      
                                     
                                       c 
                                       v 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
         [0044]    If attention is limited to the lower frequencies where terms that are proportional to ω 2  may be neglected, equation (20) becomes: 
         [0000]    
       
         
           
             
               
                 
                   
                     X 
                     / 
                     P 
                   
                   = 
                   
                     
                       - 
                       
                         
                           
                             - 
                             A 
                           
                            
                           
                               
                           
                            
                           i 
                            
                           
                               
                           
                            
                           ω 
                            
                           
                               
                           
                            
                           
                             c 
                             v 
                           
                         
                         
                           
                             
                               K 
                               aa 
                             
                              
                             
                               ( 
                               
                                 i 
                                  
                                 
                                     
                                 
                                  
                                 ω 
                                  
                                 
                                     
                                 
                                  
                                 C 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               K 
                               d 
                             
                              
                             
                               i 
                               ^ 
                             
                              
                             
                                 
                             
                              
                             ω 
                              
                             
                                 
                             
                              
                             
                               c 
                               v 
                             
                           
                         
                       
                     
                     = 
                     
                       
                         - 
                         
                           Ac 
                           v 
                         
                       
                       
                         
                           
                             K 
                             aa 
                           
                            
                           C 
                         
                         + 
                         
                           
                             K 
                             d 
                           
                            
                           
                             c 
                             v 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
         [0045]    If the viscous damping in the system is dominated by the viscous damping of the air in the slit  110 , c v &gt;&gt;C. If when this is true, by using equations (4) and (8), equation (21) becomes: 
         [0000]    
       
         
           
             
               
                 
                   
                     X 
                     / 
                     P 
                   
                   = 
                   
                     
                       
                         
                           - 
                           
                             Ac 
                             v 
                           
                         
                         
                           
                             K 
                             d 
                           
                            
                           
                             c 
                             v 
                           
                         
                       
                       ≈ 
                       
                         
                           - 
                           A 
                         
                         
                           K 
                           d 
                         
                       
                     
                     = 
                     
                       
                         
                           - 
                           A 
                         
                         
                           ( 
                           
                             
                               ρ 
                               0 
                             
                              
                             
                               c 
                               2 
                             
                              
                             
                               
                                 A 
                                 2 
                               
                               / 
                               V 
                             
                           
                           ) 
                         
                       
                       = 
                       
                         - 
                         
                           V 
                           
                             
                               ρ 
                               0 
                             
                              
                             
                               c 
                               2 
                             
                              
                             A 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
         [0046]    In this case, the mechanical sensitivity of the microphone is no longer determined by the structural features of the diaphragm  104  or its material properties. The stiffness and resulting sensitivity are determined substantially by the properties of the air spring behind the diaphragm  104 . Consequently, a very small microphone may be designed wherein diaphragm area A is made small while holding the size of the back volume  108  V constant. This produces the added benefit of increasing the microphone&#39;s sensitivity. Also, if the depth of back volume  108  is d, and the other back volume dimensions are equal to the length and width of the diaphragm  140 , then V=dA. Equation (22) then becomes: 
         [0000]    
       
         
           
             
               
                 
                   
                      
                     
                       X 
                       / 
                       P 
                     
                      
                   
                   = 
                   
                     - 
                     
                       d 
                       
                         
                           ρ 
                           0 
                         
                          
                         
                           c 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
         [0047]    For air ρ 0 c 2 ≈1.4×10 5 . Sensitivity is independent of area A of the diaphragm  104  so that very small diaphragms may be effective. If the microphone is fabricated using silicon microfabrication techniques, as discussed herein below, and the depth of the back volume  108  is equal to the thickness of the wafer  102 , then a typical depth is d=500 μm. The magnitude of the mechanical sensitivity is then |X/P|≈3.5 nm/Pascal. 
         [0048]    Note that this sensitivity is achieved when the diaphragm&#39;s mechanical stiffness is much less than that of the air spring so that k&lt;&lt;K d . 
         [0049]    Referring now to  FIG. 2 , there is shown a schematic, plan view of a miniature microphone diaphragm, generally at reference number  200 . Assume that diaphragm  200  is fabricated out of a film of polycrystalline silicon having a thickness, h. The main part of the diaphragm  200  is a rectangular plate  202  having a first dimension L ω ,  204 , and a second dimension L b    206 . The diaphragm  200  is supported only at the ends of the rectangular support beams  207 , each having dimensions W  208  by L  210 . While a more detailed analysis might be useful in identifying details of the design, the following analysis identifies the dominant parameters in the design and gives an estimate of the feasibility of constructing a diaphragm  200  that is sufficiently flexible so that equation (22) is valid. 
         [0050]    In this approximate model, assume that the rectangular diaphragm rotates like a rigid body about the y axis  212 . The two support beams  206  behave like linear restoring torsional springs having a total torsional stiffness that may be estimated by: 
         [0000]    
       
         
           
             
               
                 
                   
                     k 
                     t 
                   
                   ≈ 
                   
                     
                       2 
                        
                       β 
                        
                       
                           
                       
                        
                       
                         GWh 
                         3 
                       
                     
                     L 
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where β≈⅓ and G is the shear modulus of the material. Assuming that the polysilicon layer is linearly isotropic, the shear modulus may be calculated from 
         [0000]    
       
         
           
             
               G 
               = 
               
                 E 
                 
                   2 
                    
                   
                     ( 
                     
                       1 
                       + 
                       γ 
                     
                     ) 
                   
                 
               
             
             , 
           
         
       
     
         [0000]    where E is Young&#39;s modulus of elasticity (E≈170×10 9  N/m 2  for polysilicon) and γ is Poisson&#39;s ratio (γ≈0.3). Assuming that the diaphragm is thin so that h is much smaller than L ω   204  and L b    206 , the mass moment of inertia of the diaphragm  200  about they axis may be approximated by: 
         [0000]    
       
         
           
             
               
                 
                   
                     I 
                     yy 
                   
                   = 
                   
                     
                       
                         L 
                         w 
                       
                        
                       h 
                        
                       
                           
                       
                        
                       ρ 
                        
                       
                           
                       
                        
                       
                         l 
                         b 
                         3 
                       
                     
                     3 
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where ρ is the volume density of the material. For polysilicon, ρ≈2300 kg/m 3 . 
         [0051]    The response of the diaphragm  200  due to an incident sound pressure P in terms of rotation θ, about the pivot (i.e., the y-axis) may be written as: 
         [0000]        I   yy   {umlaut over (θ)}+k   t   θ=PAL   b /2  (26) 
         [0000]    where A=L ω L b  is the area of the diaphragm  200  that is acted on by the sound pressure P, and L b /2 is the distance between the center of the diaphragm  200  and the pivot. In order to convert the rotational representation of equation (26) into one that uses the displacement x as the generalized coordinate, as in equation (5), note that x=θL b /2 or θ=2x/L b . Replacing θ with x allows equation (26) to be rewritten as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           I 
                           yy 
                         
                          
                         2 
                          
                         
                           
                             x 
                             ¨ 
                           
                           / 
                           
                             L 
                             b 
                           
                         
                       
                       + 
                       
                         
                           k 
                           t 
                         
                          
                         2 
                          
                         
                           x 
                           / 
                           
                             L 
                             b 
                           
                         
                       
                     
                     = 
                     
                       
                         PAL 
                         b 
                       
                       / 
                       2 
                     
                   
                    
                   
                     
 
                   
                    
                   or 
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             I 
                             yy 
                           
                            
                           
                             ( 
                             
                               2 
                               
                                 L 
                                 b 
                               
                             
                             ) 
                           
                         
                         2 
                       
                        
                       
                         x 
                         ¨ 
                       
                     
                     + 
                     
                       
                         
                           
                             k 
                             t 
                           
                            
                           
                             ( 
                             
                               2 
                               
                                 L 
                                 b 
                               
                             
                             ) 
                           
                         
                         2 
                       
                        
                       x 
                     
                   
                   = 
                   PA 
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
         
       
     
         [0052]    Comparing equations (5) and (28) gives the equivalent mass as: 
         [0000]    
       
         
           
             
               
                 
                   m 
                   = 
                   
                     
                       
                         I 
                         yy 
                       
                        
                       
                         ( 
                         
                           2 
                           
                             L 
                             b 
                           
                         
                         ) 
                       
                     
                     2 
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
           
         
       
     
         [0053]    Similarly, the equivalent stiffness is: 
         [0000]    
       
         
           
             
               
                 
                   k 
                   = 
                   
                     
                       
                         k 
                         t 
                       
                        
                       
                         ( 
                         
                           2 
                           
                             L 
                             b 
                           
                         
                         ) 
                       
                     
                     2 
                   
                 
               
               
                 
                   ( 
                   30 
                   ) 
                 
               
             
           
         
       
     
         [0054]    Equations (24) and (30) allow the mechanical stiffness of the diaphragm supports to be estimated, which may then be compared to the stiffness of the air in the back volume, K d . For a design in which L=100 μm, L=250 μm, L b =250 μm, W=5 μm, h=1 μm, d=500 μm, the equivalent stiffness of the diaphragm from equations (24) and (30) is k≈14 N/m while the effective stiffness of the air in the back volume  108  is K d =17.5 N/m. The mechanical stiffness of this design, k, is clearly negligible compared to the stiffness of the air spring, K d . In general, the permissible ratio of K d /k is dependent on the environment of use and the associated requirements, but for most applications, a ratio of 20-1,000 will be preferred. For example, it is preferred that the structural stiffness of the support k be less than 10% of the effective stiffness defined by the air spring K d , and more preferably less than 5%, and most preferably less than 1%. The microphone may have a usable range over the audio band, 20 Hz to 20 kHz, though there is no particular limit on the invention imposed by the limits of human hearing, and the frequency response may therefore extend, for example, from 1 Hz to ultrasonic frequencies, e.g., 25 kHz and above, in accordance with the design parameters set forth above, for technical applications. In a typical consumer electronic device, a preferred acoustic bandwidth (±3 dB) is about 40 Hz-3.2 kHz, more preferably about 30 Hz to 8 kHz. In many cases, the transducer and associated electronics will limit the effective response of the sensor, rather than the diaphragm intrinsic response, and indeed band-limiting may be a design feature of the transducer. 
         [0055]    Based on the foregoing, preliminary estimate, the assumptions behind equations (22) and (23) are not difficult to realize. The magnitude of the mechanical sensitivity may then be estimated from equation (23) to be |X/P≈13.5 nm/Pascal. 
         [0056]    It is also possible to mount the diaphragm  501  for linear movement instead of rotational movement, by providing a set of tabs  502  spaced about its periphery as shown in  FIG. 5 . Likewise, a cantilever support will allow rotational movement of the diaphragm with a different placement of supporting structures than the torsional bars. The diaphragm  501  shown in  FIG. 5  also includes an optional slit  503  of width wg. This may be included to greatly reduce the effect of intrinsic stress on the tabs  502  that support the diaphragm  501 . The Diaphragm  501  displacement may be sensed, for example, by a set of interdigital finger electrodes  504 . 
         [0057]    The supporting structures for the diaphragm  200  are not limited to having a length equal to the width of the slit  110 , but rather may themselves have adjacent or underlying reliefs to provide supports of sufficient length to achieve a desired stiffness. 
         [0058]    Therefore, while a preferred embodiment comprises hinges disposed at one edge of the diaphragm, it is also possible to provide alternate supporting structures which do not substantially contribute to the effective stiffness of the diaphragm. 
         [0059]    Referring now to  FIGS. 3A-3E , a practical microphone as described hereinabove may be fabricated using silicon microfabrication techniques. The fabrication process begins with a bare silicon wafer  300 ,  FIG. 3A . 
         [0060]    A sacrificial layer  302  is deposited or formed on an upper surface of silicon wafer  300  as may be seen in  FIG. 3B . Sacrificial layer  302  is typically silicon dioxide, but, other materials that may be readily removed may be used. Such materials are known to those of skill in the silicon microfabrication arts and are not further discussed herein. A layer  304  of structural material such as polysilicon is deposited over sacrificial layer  302 . Layer  304  ultimately forms the microphone diaphragm  104  ( FIGS. 1A ,  1 B). It is also possible to obtain a similar construction where the diaphragm material is made of stress-free single crystal silicon by using a silicon-on-insulator (SOI) wafer. 
         [0061]    As may be seen in  FIG. 3C , the diaphragm material (i.e., structural layer  304 ) is next patterned and etched to create slits  306  that isolate the diaphragm  310  from the remainder of structural layer  304 . 
         [0062]    As may be seen in  FIG. 3D , a backside through-wafer etch is next performed to create the back volume of air behind the diaphragm  310 . 
         [0063]    Finally, as may be seen in  FIG. 3E , sacrificial layer  302  is removed to separate diaphragm  310  from the remainder of the structure. 
         [0064]    The motion of diaphragm  310  may be converted into an electronic signal in many ways. For example, comb sense fingers, not shown, may be disposed on the perimeter of diaphragm  310 . Comb sense fingers are described in detail in U.S. patent application Ser. No. 11/198,370 for COMB SENSE MICROPHONE, filed Aug. 5, 2005, expressly incorporated herein by reference. Advantageously, the sensing elements for the diaphragm  310  movement are formed using the silicon wafer  300  and/or structural layer  304  as supports for conducting materials, and/or these may be processed by standard semiconductor processing techniques for form functional doped and/or insulating regions, and/or integrated electronic devices may be formed therein. For example, a transducer excitation circuit and/or amplifier may be integrated into the silicon wafer  300 , to directly provide a buffered output. 
         [0065]      FIG. 4  shows a possible arrangement wherein interdigitated comb sense fingers  402  are incorporated in the microphone diaphragm  404 . A bias voltage or modulated voltage waveform may be applied to the microphone diaphragm  404  through the interdigitated comb sense fingers  402  to utilize capacitive sensing as the means to develop an output voltage. Because the electrostatic forces between the comb sense fingers on the diaphragm and the corresponding fingers on the substrate has a substantial component coplanar with the diaphragm, the effect on diaphragm stiffness is attenuated. Likewise, the force component normal to the surface does not tend to displace the diaphragm far from the home position, though during operation, the respective comb sense fingers should be displaced from each other to avoid signal nulls. The displaced position of the comb fingers can be imposed by the stress gradient through the thickness of the fingers. It is well known that stress gradients cause out of plane displacements in flexible structures. Another method of imposing a controllable out of plane displacement, or offset of the comb fingers, is to apply a bias voltage between the wafer substrate material and the diaphragm fingers. This will cause the diaphragm to deflect relative to the fingers that are firmly attached to the surrounding substrate. 
         [0066]    In alternate embodiments, optical sensing may be used to convert diaphragm motion into an electrical signal. Optical sensing is described in U.S. patent application Ser. No. 11/335,137 for OPTICAL SENSING IN A DIRECTIONAL MEMS MICROPHONE, filed Jan. 19, 2006, expressly incorporated herein by reference. 
         [0067]    It will be recognized by those of skill in the art that numerous other methods may be utilized to generate an electrical signal representative of the motion of the diaphragm into an electrical signal. Consequently, the invention is not limited to the methods chosen for purposes of disclosure. Rather, the invention covers any and all methods for generating an output signal representing sounds or acoustic vibrations which act upon the diaphragm. 
         [0068]    Since other modifications and changes varied to fit particular operating requirements and environments will be apparent to those skilled in the art, this invention is not considered limited to the example chosen for purposes of this disclosure, and covers all changes and modifications which does not constitute departures from the true spirit and scope of this invention. 
         [0069]    Having thus described the invention, what is desired to be protected by Letters Patent is presented in the subsequently appended claims.