Patent Publication Number: US-7903830-B2

Title: Push-pull capacitive micro-machined ultrasound transducer array

Description:
BACKGROUND 
     The present embodiments relate to electrostatic transducers (i.e., capacitive micro-machined ultrasound transducers (CMUTs)). 
     An element of a CMUT transduces between electrical and acoustic energy. The element includes a plurality of membranes  12  (see  FIG. 1 ) formed on a silicon substrate  14 . Each membrane  12  is adjacent a single gap  16 . An electrode is adjacent to the membrane  12 , and another electrode is on the other side of the single gap  16 . A DC voltage applied to the electrode adjacent the membrane  12  biases the membrane  12 . Variation in electrical potential between the electrodes causes the membrane  12  to flex into and out of the gap  16 . The flexing generates acoustic energy. Acoustic reflections cause the membrane  12  to flex, causing variation in electrical potential. 
     The force on the membrane  12  may be represented by: 
               F   =         ɛ   0     ·   Area   ·       (       V   dc     +     V   ac       )     2         2   ⁢       (     d   -   w     )     2           ,         
where V dc  is the DC bias voltage, ε 0  is a constant representing the permittivity of free space, V ac  is the AC voltage signal, d is an initial gap or separation, and w is the AC displacement from an equilibrium position. The membrane displacement, which determines the output pressure, responds proportionally to the force at low frequencies. An estimate of nonlinear distortion is possible by analyzing the equation above for electrostatic force. The voltage-squared term in the numerator dominates the nonlinear distortion since the AC displacement, w, is usually much smaller than the total gap distance, d. Second harmonics are generated, and are roughly proportional to the ratio of V ac /V dc  for small AC displacements (i.e., w&lt;&lt;d). Second harmonics generated by a transducer may be undesired, especially in imaging modes that attempt to isolate 2 nd  harmonics generated in tissue or by contrast agent microbubbles. CMUTs designed for high pressure output can have AC displacements that are significant fractions of the nominal gap thickness. In this case, there will be additional nonlinear terms that produce both even and odd harmonics.
 
     As the membrane  12  deflects and the spacing between capacitor plates (i.e., electrodes) reduces, the electrostatic force increases. At some amount of displacement, the electrostatic force overwhelms the restoring spring force of the membrane  12 , causing the membrane to contact the substrate and hindering further movement. When parallel, rigid plates are assumed with a linear membrane restoring force, this distance is about ⅓ of the moveable gap  16  at low frequencies. This often restricts the maximum DC bias voltage and AC drive voltages that can be applied to the CMUT. 
     BRIEF SUMMARY 
     By way of introduction, the preferred embodiments described below include methods, transducers, elements and systems for electrostatic transduction. Gaps and electrodes on both sides of a membrane provide push-pull operation. Since electrostatic force is attractive, the use of “push” in “push-pull” herein represents the AC voltage configuration so that one electrode supplies a reduction in force while the other electrode supplies an increase in force on the membrane, with some components of the forces acting in opposite directions on the membrane. The membrane is oriented to flex or move in a direction of acoustic propagation. A surface connected to the membrane may better expose the movement to the acoustic medium in the push-pull arrangement. The surface may be used for push-pull operation without requiring electrodes on opposite sides of the membrane. 
     In a first aspect, a capacitive micro-machined ultrasound transducer element is provided. A membrane is operable to flex at ultrasound frequencies. A first electrode is associated with the membrane. A first gap is on a first side of the membrane. A second electrode is opposite the first gap from the membrane. A second gap is on a second side of the membrane. The second side is opposite the first side of the membrane. A third electrode is opposite the second gap from the membrane. The membrane is operable to flex in a direction substantially parallel to a direction of acoustic propagation generated by the flexing. 
     In a second aspect, a method is provided for transducing between electrical and ultrasound energies. Ultrasound energy is generated with an electrostatic membrane in a push-pull arrangement in response to flexing of the membrane generally facing a medium to be scanned. Electrical energy is generated with the electrostatic membrane in the push-pull arrangement. 
     In a third embodiment, a capacitive micro-machined ultrasound transducer array has a plurality of elements. Each element has a membrane with a membrane electrode, a substrate with a substrate electrode, and a gap between the membrane and the substrate. An improvement includes an additional electrode separated from the membrane by an additional gap in each element. The additional electrode and the additional gap are on an opposite side of the membrane than the gap and substrate electrode. The membrane is substantially orthogonal to a direction of acoustic propagation from the transducer. 
     In a fourth aspect, a capacitive micro-machined ultrasound transducer element is provided. A membrane is operable to move at ultrasound frequencies. A surface is spaced from and connected with the membrane. A structure extends at least partially between the membrane and the surface. A first electrode is associated with the membrane and the surface. Second and third electrodes are on opposite sides of the structure. The second electrode is adjacent to the membrane across a first gap, and the third electrode is adjacent the surface across a second gap. 
     The present invention is defined by the following claims, and nothing in this section should be taken as a limitation on those claims. Further aspects and advantages of the invention are discussed below in conjunction with the preferred embodiments and may be later claimed independently or in combination. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The components and the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. Moreover, in the figures, like reference numerals designate corresponding parts throughout the different views. 
         FIG. 1  is a graphical representation of a prior art electrostatic transducer; 
         FIG. 2  is a graphical representation of one embodiment of a push-pull arrangement; 
         FIG. 3  is a cross-sectional view of one embodiment of a push-pull electrostatic transducer; 
         FIG. 4  is another cross-sectional view of another embodiment of a push-pull electrostatic transducer; 
         FIG. 5  is a cross-sectional view of yet another embodiment of a push-pull electrostatic transducer; 
         FIG. 6  is another graphical representation of another embodiment of a push-pull arrangement; 
         FIG. 7  is a graphical representation of one example transmit waveform; 
         FIG. 8  is a graphical representation of a spectral response of the transmit waveform of  FIG. 7 ; 
         FIG. 9  is a graphical representation showing an example difference in membrane velocity between a push-pull electrostatic transducer and a single gap electrostatic transducer; 
         FIG. 10  is a graphical representation of the spectral responses associated with the membrane velocities and transducers of  FIG. 9 ; and 
         FIG. 11  is a graphical representation of exemplary membrane velocity for a push-pull electrostatic transducer and a single gap electrostatic transducer with a voltage associated with collapse of the single gap electrostatic transducer. 
     
    
    
     DETAILED DESCRIPTION OF THE DRAWINGS AND PRESENTLY PREFERRED EMBODIMENTS 
     Electrostatic actuation of CMUT transducers with a single gap for a membrane produces harmonic distortion due to nonlinearities. The nonlinear distortion may be reduced by using a push-pull actuation scheme in which a moving conductor between two driven plates experiences a simultaneous repulsive (push) force and an attractive (pull) force. The membrane motion is substantially parallel to the direction of acoustic propagation. 
     In tissue harmonic imaging (THI), the output signal from the transducer may be more effective if very little frequency content is generated at the harmonic frequency. The receiving transducer may detect harmonic signals generated by the tissue rather than the transmitting transducer. A push-pull CMUT may provide more effective harmonic imaging. 
     Push-pull operation may allow an increase in output pressures. For example, THI relies on nonlinear propagation and reflection, so the harmonic information may be weak as compared to the transmitted information. For sufficient signal-to-noise ratio, higher transmit pressures are desired. Transducers capable of producing high output pressures during transmit may generate greater harmonic signals within the tissue. With single gap CMUTs, obtaining high output pressure with low harmonic distortion are competing or conflicting objectives. The electrostatic force between two plates is proportional to the square of the voltage (or similarly, the electric field) between them. Large ratios of AC to DC voltages (or equivalently electric fields) required for high output pressure increase the levels of harmonic distortion. Push-pull operation may provide more effective THI. A push-pull design may mitigate the harmonic distortion in transmit operation by canceling the voltage-squared terms for the electrostatic force on the membranes, making the electrostatic force on the moving membrane plate almost linearly related to the driving voltage signal. In addition, the displacement of the moving member of the push-pull electrostatic transducer may be stable over a wider range of travel. 
     In one embodiment, a top surface of the moving structure component is exposed to the acoustic medium. An “I-beam” membrane structure allows the placement of conductive plates on either side of the moving conductor while still exposing a large area of the moving structure to the acoustic medium. Ultrasound may be transmitted in the direction of motion of the membrane. Other embodiments may be provided with or without the “I-beam” structure or the top surface. 
     A capacitive micro-machined ultrasound transducer (CMUT) array has a plurality of elements. The elements are arranged as a one-dimensional, two-dimensional, or other multi-dimensional array. The CMUT is formed using CMOS, micro-electro mechanical processes or other semiconductor manufacturing processes. For example, deposition, sputtering, plating, etching, printing, patterning, wafer bonding, sacrificial etching, or other now known or later developed processes form the micro-structures and/or electrical structures. 
     Each element has a plurality of membranes, such as tens, hundreds or thousands of membranes.  FIG. 2  shows one graphic representation of a bi-directional driving configuration representing a portion of membrane structure for a CMUT element. The element includes an electrode  22  associated with a membrane  12 , an electrode  24  associated with a substrate  14 , a gap  16  between the membrane electrode  22  and the substrate electrode  24 , an additional electrode  20 , and an additional gap  18  between the membrane electrode  22  and the additional electrode  20 . Additional, different or fewer components may be provided. 
     The substrate  14  is silicon, but other materials may be used. The substrate  14  is processed to form the membrane  12  and gaps  16 ,  18 . The membrane  12  may be deposited on the substrate  14  with subsequent etching away of material to form the gaps  16 ,  18 . The membrane  12  may be formed in the substrate  14  by etching away material to form the gaps  16 ,  18 . The membrane  12  is semiconductor material or other deposited or grown material, such as silicon nitride or wafer bonded silicon. The thickness, material and size of the membrane  12  provide a desired or sufficient stiffness. The gaps  16 ,  18  have sufficient depth to avoid undesired or provide desired “bottoming out” of the membrane  12  during operation with a DC bias voltage. 
     The electrodes  20 ,  22 ,  24  are conductive materials, such as metal or doped silicon. For example, the electrodes  20 ,  22 ,  24  are deposited metal, such as aluminum, copper, silver or gold. As another example, the electrodes  20 ,  22 ,  24  are formed from semiconductor material. The electrodes  20 ,  22 ,  24  are each formed from the same material, but may be formed from different materials. 
     The electrode  22  is associated with the membrane  12 . The membrane electrode  22  is formed on the membrane  12 , such as depositing the electrode  22  on one or both sides of the membrane  12 . The electrode  22  is immediately adjacent the membrane  12 , but one or more layers of material, such as insulators, may separate the electrode  22  and the membrane  12 . In another embodiment, the membrane  12  forms the electrode  22 , such as the membrane  12  being electrically conductive. 
     The electrodes  20  and  24  are formed on opposite sides of the membrane  12  across different gaps  16 ,  18 . The electrodes  20  and  24  are part of or in the substrate  14  or are deposited on the substrate  14 . The electrodes  20  and  24  are associated with more rigid structure than the membrane  12 , such as the substrate  14 , thicker structures, stiffer material, or supported structures. For example, one or more stiffening ribs, honeycomb pattern, support posts, or other supports make the structure more rigid than the membrane  12 . The electrodes  20  and  24  and corresponding structure are relatively fixed as compared to the membrane  12 . The mass of the buried membrane  12  and beam or disk  34  may be reduced to raise potential bending mode resonances by forming small holes, voids, or using a porous material. This may create a stiff structure with low mass. 
     The gaps  16 ,  18  are on opposite sides of the membrane  12 . The gaps  16 ,  18  have a same or different depths, d 1  and d 2 . The gaps  16 ,  18  and corresponding membrane  12  may have the same or different shapes and/or dimensions. The gaps  16 ,  18  may connect together through one or more channels or holes or may be separate. One gap  16  is between the membrane  12  and the base substrate  14 . The other gap  18  is between the membrane  12  and other material, such as the substrate  14  or deposited/grown material. 
     The electrode  20  and corresponding gap  18  are in addition to the gap  16  and the electrode  24  on the opposite side of the membrane  12 . The membrane  12  separates or defines the two gaps  16 ,  18 . The two gaps  16 ,  18  and corresponding electrodes  20 ,  24  apply electrostatic forces for movement of the membrane  12 . The gaps  16 ,  18  also allow movement of the membrane  12  in response to electrical or acoustic energy. 
     The membrane  12  is operable to flex at ultrasound frequencies, such as being sized and shaped to resonate or flex in response to waveforms at 1-20 MHz, such as 1-10 MHz. The membrane  12 , gaps  16 ,  18  and electrodes  20 ,  22 ,  24  are oriented relative to a face of the transducer, acoustic window, and/or the direction of acoustic propagation. In one embodiment, the membrane  12  is oriented for a 3-1 mode of operation or flexes in a direction perpendicular to a direction of propagation (see U.S. Published application Ser. No. 2007/0071272 (Ser. No. 11/236,700, file Sep. 26, 2005), the disclosure of which is incorporated herein by reference). 
     In other embodiments, the membrane  12  flexes or moves in a direction substantially parallel to a direction of acoustic propagation generated by the flexing. The membrane  12  moves towards or away from the electrodes  20 ,  24  and is generally orthogonal to a direction of acoustic propagation. The acoustic energy generated by the membrane  12  travels from the membrane  12  in the direction of movement, such as represented by the arrows in  FIG. 1 . The membrane  12  may be treated as a point source with the acoustic energy generally propagating in a divergent pattern (see the radiating lines of transmitted ultrasound in  FIG. 1 ). The direction of propagation is treated as the center of the divergent pattern or is generally parallel with the motion of the membrane  12 . Substantially or generally in the direction of acoustic propagation is used to account for the divergent nature of the acoustic energy. 
     In a push-pull design, the moveable electrode  22  is positioned between two fixed electrodes  20 ,  24  which are driven with voltage signals having opposite phase or polarity as shown in  FIG. 2 . A DC bias is placed on the center electrode  22  through a large resistor designed to keep the charge on the center electrode  22  roughly constant. The product of the resistance and the capacitance between the electrodes is large (e.g., two or three times larger) than the (frequency) −1  of the AC signal, such as the resistor being 100 M ohms or 1 G ohm. The resistor is formed in the substrate  14  or is a separate component. As an alternative to the resistor and DC bias voltage, a charge is trapped or stored and insulated on the membrane  12  during fabrication, such as provided for electrets. 
     The equations below have been simplified to demonstrate approximately how the second harmonic generated by the voltage-squared term disappears in push-pull operation. The actual potential on the center electrode  22  depends on the movements of charge through the bias resistor, but this effect is neglected in the simplifications below. The force on the center plate due to one fixed electrode (neglecting charge movements) is: 
                 F   ⁢           ⁢   1     =         -     ɛ   0       ·   Area   ·       (       V   dc     -     V   ac       )     2         2   ⁢       (       d   1     +   w     )     2           ,         
where the positive force and positive displace w are to the right. The force on the center plate due to the other fixed electrode is:
 
               F   ⁢           ⁢   2     =           ɛ   0     ·   Area   ·       (       V   dc     +     V   ac       )     2         2   ⁢       (       d   2     -   w     )     2         .           
The total (sum) force is the sum of F 1  and F 2 . If the initial spacing d 1  and d 2  between the fixed plates and the moving center plate are equal, such that d 1 =d 2 =d, then many quadratic terms cancel from the expression for total force. In this case, the total force on the moving electrode is roughly Ftotal≈2·ε 0 ·Area·V dc ·V ac /d 2 . The total force may be proportional to the driving signal V ac , rather than having a strong dependence on the square of the driving signal as in single gap CMUT actuation. This expression also assumes that the displacement w is small relative to the distances d 1  and d 2  so that the charges on the electrodes do not vary significantly.
 
     The push-pull CMUT may become unstable at high voltages (or electric fields), as the electrostatic force overwhelms the restoring spring force. However, the maximum low-frequency voltage that can be applied to the push-pull CMUT may be approximately 30% higher than a single gap CMUT. The greater electric field allows slightly higher electric fields, increasing the electrostatic force and the obtainable output pressures from the transducer proportionally. 
       FIG. 3  shows a cross-section view of one embodiment of a CMUT in a push-pull arrangement. The membrane  12 , substrate  14 , gaps  16 ,  18  and electrodes  20 ,  22  and  24  provide push-pull operation of the transducer. The substrate electrode  24  and additional electrode  20  are each a circular disk shape with a non-conductive cutout or center, but may be divided into two or more electrically interconnected sections or may be a conductive disk with no cutout. While shown extending to the edges of the gap  16 , the electrodes  20 ,  24  may be smaller or larger. 
     The membrane  12  includes the membrane electrode  22 . For example, the membrane electrode  22  is deposited or formed on a bottom side of the membrane  12  as a solid disk, on the top of the membrane  12  as a disk with a cutout, or as part of the membrane  12  with any spatial extent. The membrane electrode  22  has a same or different shape and size as the substrate electrode  24  and/or additional electrode  20 . 
     The membrane  12  connects to or is supported by the substrate  14  or another structure connected with the substrate  14 . The connection is around the entire or portions of the outer edges of the membrane  12 . When the membrane  12  flexes or moves, the center of the membrane  12  moves to a greater extent than the supported edges. Alternatively or additionally, other portions of the membrane  12  are supported or connected to the substrate  14 . 
     The additional electrode  20  is formed on or in a disk or beams  34  of substrate material. Other material may be used. The disk or beams  34  are flat, but may include ribs or other supporting structures for relative rigidity. The disk or beams  34  form one or more holes, apertures, gaps or channels of any size or shape. 
     The membrane  12  connects, with one or more pillars  30 , to a surface  32  exposable to or closer to an acoustic medium. The pillar  30  extends from the membrane  12  to the surface  32  through the one or more apertures in the disk or beams  34 . As shown in an elevation, depth cross-section in  FIG. 3 , the membrane  12 , pillar  30  and top surface  32  form an “I-beam” structure. The top surface  32  is a disk, but other shapes may be used. The top surface  32  is thicker than the membrane  12 , but may be a same or thinner thickness. The top surface  32  and pillar  30  are of a same material as the membrane  12 , but may be different materials. The pillar  30  is a cylinder, but may be any desired shape (e.g., cubic or plate-like). Other structures than “I-beam” may be used for transferring membrane motion to a location adjacent to the acoustic medium. 
     The top surface  32  moves in response to the flexing or movement of the membrane  12 . The two relatively fixed electrodes  20 ,  24  above and below the moving membrane  12  are driven with AC voltage signals of the same or different magnitude and substantially opposite polarity. The membrane electrode  22  is DC biased or contains a fixed charge. The structural motion of the membrane  12  translates to the top surface  32 , such as shown by the arrows parallel with a direction of acoustic propagation. As the membrane  12  moves up and down (i.e., towards and away from the electrodes  20 ,  24 ), the top surface  32  also moves up and down (i.e., towards and away from the acoustic medium). Because the moving membrane  12  is responsible for producing the ultrasonic pressure, exposure of the top surface  32  may provide more efficient transfer of acoustic energy. Being adjacent to the acoustic medium includes having insulating, matching, lens, and/or window layers between the top surface  32  and the acoustic medium. The top surface may be exposed to fluid (e.g., air or liquid), tissue, and/or coupling gel. 
     Alternatively, the membrane  12  is provided without the pillar  30  and/or the top surface  32 . Acoustic energy propagates through holes in the beams or disk  34  or through substrate material enclosing the gap  18 . 
       FIG. 4  shows an alternative embodiment of the “I-beam” arrangement. The membrane  12  connects with the substrate  14  at the edges  42 . Alternatively, the membrane  12  is adjacent, slideably contacts or is spaced from the substrate  14  at the edges  42 . The top surface  32  connects to the beams or disk  34 , the substrate  14  or other structure. The connection is along portions or the entire circumference  40  of the top surface. For the entire circumference  40  with or without any inset, the gaps  16 ,  18  are sealed from contamination and squeeze-film effects that could otherwise hinder membrane motion. As the membrane  12  moves, the top surface  32  flexes or moves. The edges or circumference  40  is held in position, but the top surface  32  bows inwards and outwards. Alternatively, a bellows structure may be used to seal the gaps  16 ,  18  and avoid squeeze-film effects while connecting the membrane  12  and allowing the edges  40  more freedom of movement. In another alternative, no connection is provided, such as allowing the membrane  12 , pillar  30  and top surface  32  to float in the substrate  14  and beams or disk  34 , with the shape of the membrane  12 , pillar  30  and top surface  32  relative to the substrate structure maintaining the relative position. 
       FIG. 5  shows another alternative embodiment of the “I-beam” arrangement. One or more additional membranes  50  are provided between pairs of gaps. The additional membranes  50  and corresponding gaps are stacked along the acoustic propagation direction within the substrate  14 . The additional layers electrically connect in parallel. The top electrodes associated with each membrane  12 ,  50  electrically connect, and the bottom electrodes associated with each membrane  12 ,  50  electrically connect. The membrane electrodes  22  also electrically connect. Independent connections may be used, such as to apply relative phasing and/or amplitude weighting for the different layers. The disk or beams  34  for lower layer or membranes  12  include a top electrode  20  for a lower membrane  50  and a lower electrode  24  for a higher membrane. 
     Each membrane  12 ,  50  contributes to movement of the top surface  32 . Additional pillars connect between the membranes  12 ,  50 . The interconnected membranes  12 ,  50  apply force to the top surface  32 . Two membranes  12 ,  50  operating with push-pull may effectively double the net force for the same applied voltages as compared to the arrangements of  FIGS. 3 and 4 . Additional membrane layers may form a comb-like structure in cross-section to further increase the force or lower the drive voltages. One or more layers may be associated with a single gap structure. 
     Push-pull operation of the CMUT provides a method for transducing between electrical and ultrasound energies. Referring to  FIG. 2 , a bias voltage is applied to the membrane conductor  22  (i.e., electrostatic membrane). The bias voltage is a constant voltage relative to the AC signal or ultrasound energy. The bias may vary, such as providing different levels of bias for transmit and receive operations. The bias voltage is provided through a large resistor to limit fluctuations of charge during reception or transmission events. Alternatively, a stored or trapped charge biases the membrane  12 . 
     Ultrasound energy is generated with the electrostatic membrane  12  in the push-pull arrangement. AC voltage signals are applied with opposite phase (i.e., 180 degrees out of phase) to the electrodes  20 ,  24  across the gaps  16 ,  18  from the membrane  12 . Other phases may be used, such as substantially opposite phase or other phase relationships. The AC signals for the different electrodes  20 ,  24  are generated by separate signal sources or beamformer channels. Alternatively, a same AC voltage source applies a signal to a center-tapped transformer. The transformer generates the AC voltage signals with the desired phase relationship for each fixed electrode  20 ,  24  from the single AC voltage source. 
     The difference in potential between the membrane electrode  22  and the substrate electrode  24  increase the attractive force (“pulls”) and decreases the attractive force in the opposite direction (“pushes”) on the membrane  12 . The difference in potential between the membrane electrode  22  and the additional electrode  20  pulls and pushes the membrane  12 . With opposite phasing, the membrane is moved in a same direction by the two potential differences. The opposite polarity or different potential across gaps  16 ,  18  on opposite sides of the membrane  12  cause the membrane  12  to flex or move. The electrostatic membrane  12  is pushed in a first direction and pulled in the same direction as a function of electrical energy. In response, the electrostatic membrane  12  moves. Variation in the AC signals causes variation in the movement. 
     In one embodiment, movement of the membrane  12  is transferred to move another structure, such as a surface  32  exposed to or closer to a medium to be scanned. The surface  32  is spaced from the membrane  12 . The transfer is by direct connection, but indirect transfer may be used, such as with a gear, lever or belt. Alternatively, no transfer is provided. For example, the acoustic energy is generated by the membrane  12  without another surface  32 . The energy propagates through a grid or other acoustically transparent structure holding the additional electrode  20 . 
     The membrane  12  and/or top surface  32  ( FIG. 3 ) face a medium to be scanned. The membrane  12  and/or top surface  32  are orthogonal to the direction of acoustic propagation, such as lying in plane on top of the substrate  14  or parallel with the top of the substrate  14  for propagation of acoustic energy away from the top of the substrate. The acoustic propagation is substantially parallel with the direction of movement or flexing of the membrane  12 . Other orientations may be provided. 
     Electrical energy is generated with the electrostatic membrane  12  in the push-pull arrangement. As the membrane  12  moves in response to acoustic energy, variation in electrical potential is created across the gaps  16 ,  18 . Electrical signals on opposite sides of the membrane  12  are generated by the variation. The electrical signals are processed separately, such as being amplified and/or phased separately. Alternatively, the signals are combined, such as summed by electrical connection. 
     In one embodiment, the received electrical energy is used as an analog signal representing the acoustic energy. Alternatively, bottoming-out or collapse of the membrane  12  against one or both gaps  16 ,  18  is used as a digital signal representing the acoustic energy. Different gap distances or bias levels may be used to cause different membranes  12  to collapse at different acoustic energy levels, allowing digital detection of acoustic echo amplitude. 
       FIG. 6  shows an alternative electrical arrangement to  FIG. 2 . The locations of application of the AC and DC voltages are switched. The DC bias voltages and resistors are provided on the relatively fixed, substrate and additional electrodes  20 ,  24 . The AC signal is applied to the membrane electrode  22 . 
       FIGS. 7-11  represent a numerical simulation of a push-pull CMUT structure of  FIG. 2  as compared to a single gap CMUT structure. The membrane  12  is treated as a lumped mass-spring-damper system driven by electrostatic forcing function: m{umlaut over (w)}+b{dot over (w)}+kw=F e , where m is the mass, b is the damping, k is the spring constant, w is the displacement, and “dot” denotes time-derivative. For the single gap CMUT, the electrostatic force is represented as: 
               F   e     =         ɛ   0     ⁢         A   el     ⁡     (       V   dc     +     V   ac       )       2         2   ⁢       (       d   1     -   w     )     2               
where A el  is the electrode area and d 1  is the gap spacing.
 
     To simplify the equations for the push-pull system, the moving membrane is assumed to be initially charged to V dc , and then disconnected from the bias source to maintain this charge. In addition, all charge movements on the electrodes are neglected, and the membrane is assumed to move as a rigid plate. These simplifications reduce the accuracy of the simulation, but still illustrate operation of the push-pull CMUT. For the push-pull CMUT, the electrostatic force, in the case of constant charge, is given by: 
               F   e     =         q   1   2     -     q   2   2         2   ⁢     ɛ   0     ⁢     A   el               
where the charges on the fixed electrodes # 1  and # 2  are given by
 
               q   1     =           C   1     ⁢     C   2           C   1     +     C   2         ⁢     (         q   0       C   2       -     2   ⁢     V   ac         )                     q   2     =           C   1     ⁢     C   2           C   1     +     C   2         ⁢     (         q   0       C   1       +     2   ⁢     V   ac         )             
where q 0 =q 1 +q 2  and the capacitances C 1  and C 2  between the center membrane and the fixed electrodes are:
 
     
       
         
           
             
               C 
               1 
             
             = 
             
               
                 
                   ɛ 
                   0 
                 
                 ⁢ 
                 
                   A 
                   el 
                 
               
               
                 
                   d 
                   1 
                 
                 + 
                 w 
               
             
           
         
       
       
         
           
             
               C 
               2 
             
             = 
             
               
                 
                   ɛ 
                   0 
                 
                 ⁢ 
                 
                   A 
                   el 
                 
               
               
                 
                   d 
                   2 
                 
                 - 
                 w 
               
             
           
         
       
     
     The following values are assumed in the numerical simulations of  FIGS. 7-11 . Other values may be used, such as for membrane resonance at 2-8 MHz. Membrane and gap spacing parameters are: k=307.44e3 (N/m), m=5.67e-11 (kg), b=1.5e6 (kg/s), ε 0 =8.85e-12 (F/m), A el =1539.85e-12 (m 2 ), and d 1 =d 2 =0.216e-6 (m). This membrane  12  naturally resonates at 11.7 MHz. The bias and driving voltages are: V dc =180 (V) and AC voltage (Vac) peak amplitude of 100 (V). This value of V dc  provides an initial total charge q 0  of 2.27e-11 C on the center electrode  22  of the push-pull transducer. The driving frequency is centered at 5.9 MHz, which is about half the membrane resonant frequency. 
       FIG. 7  shows an example AC drive voltage signal, V ac . The signal is a Gaussian shaped sinusoidal signal, but may have other envelopes, carriers (e.g., bipolar or unipolar square wave), and/or number of cycles.  FIG. 8  shows the spectrum of the signal of  FIG. 7 . This voltage signal has most of its frequency content centered around 5.9 MHz, and very little harmonic content between 11 MHz and 12 MHz. 
     The AC drive voltage signal is applied to the membrane  12  for the signal gap CMUT and to the fixed electrodes in opposite polarity of the push-pull transducer. The output pressure is roughly proportional to the membrane velocity. The membrane velocity is determined through solution of the respective equations in the single gap and push-pull drive cases.  FIG. 9  shows the membrane velocity for the push-pull and single gap CMUTs. Because the CMUT is driven at half the frequency of natural resonance, the second-order nonlinearity is accentuated by the single gap CMUT, and the velocity waveform appears distorted (see the positive peaks of the single gap, conventional CMUT). 
       FIG. 10  shows the spectra for the velocity waveforms of  FIG. 9 . The harmonic content of the membrane velocity is different. The spectral peak of each transducer&#39;s velocity spectrum is normalized to 0 dB. The harmonic content of the push-pull transducer is more than 50 dB lower (similar to the levels of the input signal) than the harmonic content of the fundamental driving frequency. However, the single gap, conventional CMUT shows nonlinearities that are less than 10 dB down from the fundamental. The second order harmonic distortion caused by the transducer may be less or almost completely eliminated through push-pull operation. 
       FIG. 11  shows another advantage of the push-pull arrangement. Larger voltages may be applied for push-pull operation. The larger voltages may collapse the single gap CMUT, but not the push-pull CMUT. For example, the AC amplitude of the driving signal is increased from 100 V to 200 V. Once the envelope reaches a threshold voltage, the single gap CMUT collapses, as represented by the membrane velocity extending off the graph. The membrane movement becomes out-of-phase with the AC signal due to collapse. The push-pull transducer may still operate, and the membrane velocity is approximately doubled. The push-pull CMUT may also collapse for even higher voltages. 
     In another embodiment, the membrane electrode  22  extends into or on the top surface  32 . Separate electrodes at the same or different potential may be used. The substrate electrode  24  is positioned on the beam or disk  34  structure opposite the electrode  20  (e.g., the electrode  20  on the bottom and the electrode  24  on the top). The electrode  20  is adjacent to the membrane  12  across a first gap, and the electrode  24  is adjacent the top surface  32  across a second gap. Adjacent is used for relative description and may include intervening structures. The AC signals are applied to the membrane electrode  22 , and the electrodes  20 ,  24  on the structure of the beam or disk  34  have opposite polarity DC potential. The AC signal may be applied to the membrane electrode  22  in an alternative embodiment. This structure may operate in push-pull because the electrostatic forces operate in opposite directions on the overall moving structure (i.e., the membrane  12 , the top surface  32  and the pillar  30 ). The electrostatic forces are applied to different parts of the moving structure. Since the forces on either side of the structure of the beam or disk  34  are opposite each other, there may be less tendency to bend or deflect compared to the structure of  FIG. 3 . The upper electrode  24  on the structure of the beam or disk  34  and the membrane electrode  22  on the top surface  32  may be used for a “receive” operation without push-pull, and all the electrodes  20 ,  22 ,  24  may be used as a push-pull CMUT. 
     While the invention has been described above by reference to various embodiments, it should be understood that many changes and modifications can be made without departing from the scope of the invention. For example, the invention could find application in any electrostatic acoustic sensor, particularly in applications where a reduction in nonlinear distortion is desirable. 
     It is therefore intended that the foregoing detailed description be regarded as illustrative rather than limiting, and that it be understood that it is the following claims, including all equivalents, that are intended to define the spirit and scope of this invention.