Patent Publication Number: US-8526271-B2

Title: Capacitive micromachined ultrasonic transducer with voltage feedback

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of U.S. Provisional Patent Application No. 60/992,027, filed Dec. 3, 2007, the entire disclosure of which is incorporated herein by reference. 
    
    
     BACKGROUND 
     Capacitive micromachined ultrasonic transducers (CMUTs) are electrostatic actuators/transducers, which are widely used in various applications. Ultrasonic transducers can operate in a variety of media including liquids, solids and gas. Ultrasonic transducers are commonly used for medical imaging for diagnostics and therapy, biochemical imaging, non-destructive evaluation of materials, sonar, communication, proximity sensors, gas flow measurements, in-situ process monitoring, acoustic microscopy, underwater sensing and imaging, and numerous other practical applications. A typical structure of a CMUT is a parallel plate capacitor with a rigid bottom electrode and a movable top electrode residing on or within a flexible membrane, which is used to transmit (TX) or receive/detect (RX) an acoustic wave in an adjacent medium. A direct current (DC) bias voltage may be applied between the electrodes to deflect the membrane to an optimum position for CMUT operation, usually with the goal of maximizing sensitivity and bandwidth. During transmission an alternating current (AC) signal is applied to the transducer. The alternating electrostatic force between the top electrode and the bottom electrode actuates the membrane in order to deliver acoustic energy into the medium surrounding the CMUT. During reception an impinging acoustic wave causes the membrane to vibrate, thus altering the capacitance between the two electrodes. 
     Because the electrostatic force in the CMUT is nonlinear, then as the separation space between the two electrodes decreases during actuation, the electrostatic force between the electrodes typically increases at a greater rate than a restorative force of the membrane. Therefore, when the movable electrode displaces to a certain position, e.g., typically one-third of the electrode gap, the restorative force of the membrane is not able to balance the electrostatic force. Any further voltage increase can cause a “pull-in” effect that can result in instability or collapse of the CMUT. Consequently, in order to achieve enough displacement for certain applications, the separation gap between the two electrodes has to be designed to be much larger than the displacement actually required, which can fundamentally limit performance of CMUTs in a conventional operation. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawing figures, in conjunction with the description, serve to illustrate and explain the principles of the best mode presently contemplated. In the figures, the left-most digit of a reference number identifies the figure in which the reference number first appears. In the drawings, like numerals describe substantially similar features and components throughout the several views. 
         FIGS. 1A-1B  illustrate an exemplary schematic model of a system including a theoretical CMUT. 
         FIGS. 2A-2B  illustrate an exemplary implementation of a system including a CMUT with a feedback capacitor. 
         FIG. 3  illustrates another exemplary implementation of a system including a CMUT with a feedback capacitor. 
         FIG. 4  illustrates another exemplary implementation of a system including a CMUT with a feedback capacitor. 
         FIGS. 5A-5C  illustrate exemplary implementations of systems including CMUTs with feedback components. 
         FIG. 6  illustrates a flowchart of an exemplary method for a CMUT with a feedback capacitor. 
         FIG. 7  illustrates another exemplary implementation of a system including a CMUT with a feedback capacitor. 
         FIG. 8  illustrates another exemplary implementation of a system including a CMUT with a feedback capacitor. 
         FIG. 9  illustrates another exemplary implementation of a system including a CMUT with a feedback capacitor. 
         FIG. 10  illustrates another exemplary implementation of a system including a CMUT with a feedback capacitor. 
         FIG. 11  illustrates another exemplary implementation of a system including a CMUT with a feedback capacitor. 
         FIG. 12  illustrates another exemplary implementation of a system including a CMUT with a feedback capacitor. 
         FIG. 13  illustrates another exemplary implementation of a system including a CMUT with a feedback capacitor. 
         FIG. 14  illustrates an exemplary implementation of a system comprising a probe that includes a CMUT with a feedback capacitor. 
         FIG. 15  illustrates another exemplary implementation of a system comprising a probe that includes a CMUT with a feedback capacitor. 
     
    
    
     DETAILED DESCRIPTION 
     In the following detailed description, reference is made to the accompanying drawings which form a part of the disclosure, and in which are shown by way of illustration, and not of limitation, exemplary implementations. Further, it should be noted that while the description provides various exemplary implementations, as described below and as illustrated in the drawings, this disclosure is not limited to the implementations described and illustrated herein, but can extend to other implementations, as would be known or as would become known to those skilled in the art. Reference in the specification to “one implementation”, “this implementation” or “these implementations” means that a particular feature, structure, or characteristic described in connection with the implementations is included in at least one implementation, and the appearances of these phrases in various places in the specification are not necessarily all referring to the same implementation. Additionally, in the description, numerous specific details are set forth in order to provide a thorough disclosure. However, it will be apparent to one of ordinary skill in the art that these specific details may not all be needed in all implementations. In other circumstances, well-known structures, materials, circuits, processes and interfaces have not been described in detail, and/or may be illustrated in block diagram form, so as to not unnecessarily obscure the disclosure. 
     Implementations disclosed herein relate to CMUTs and methods and systems for design and operation of CMUTs that a component (e.g. a capacitor, a resistor, an inductor, etc.) is added to provide a feedback on the voltage applied on the CMUT. Usually the presence of the added component reduces the percentage of the input voltage applied on the CMUT when the capacitance of the CMUT increases. Thus the added component provides a feedback on the percentage of the input voltage applied on the CMUT. The presence of the added component provides a number of advantages, including improving the displacement and output power of the CMUTs without increasing the electrode separation, improving the device reliability for electric shorting or breakdown by decreasing the absolute voltage applied on the CMUT structure, and improving the reception sensitivity by increasing the capacitance of the CMUT structures. In order to efficiently provide a negative feedback on the percentage of the input voltage applied on the CMUT, the electrical value of the added component should be carefully selected so that the component can provide a desired feedback on the voltage applied to the CMUT in the CMUT&#39;s operating frequency region. Implementations may be incorporated into ultrasound systems, transducers, probes, and the like. 
     In order to solve the issues in CMUT operation and improve CMUT performance, some implementations disclosed herein comprise a component which is a capacitor, referred to herein as a feedback capacitor, with a specially selected capacitance placed in series with the CMUT that provides a feedback on the percentage of the input voltage applied on the CMUT during CMUT operation, and especially during operation of a CMUT in a transmission mode (i.e., producing ultrasonic energy). Some exemplary implementations relate to using a feedback capacitor to provide a negative feedback on the percentage of the input voltage applied on the CMUT. For example, in some implementations, the feedback capacitor is a capacitor in series with the CMUT transducer. The series capacitor and the CMUT may form a voltage divider so that an increase of the capacitance of the CMUT decreases the percentage of the input voltage applied on the CMUT. Thus, the series capacitor has a capacitance chosen to provide a predictable level of negative feedback on the voltage applied on the CMUT. Because the feedback capacitor decreases the percentage of the input voltage applied on the CMUT when the membrane displacement, as well as capacitance, increases, the CMUT can operate beyond the limit set by the conventional pull-in effect. Thus the maximum displacement of the CMUT in operation methods and implementations disclosed herein (e.g., in series with a feedback capacitor) may be larger than that of the same CMUT in a conventional operation (without the added feedback capacitor), or the space separating the electrodes may be designed to be substantially smaller to achieve the same maximum displacement as a CMUT with a larger electrode separation in a conventional operation. 
     In some implementations, in order to provide an efficient feedback, the capacitance of the feedback capacitor is comparable to the capacitance of the CMUT so that the input voltage can be meaningfully distributed between the CMUT and the feedback capacitor. In some implementations, the capacitance of the feedback capacitor is within a prescribed range based on the capacitance of the CMUT. Additionally, in some implementations, the feedback capacitor may be configured to be functional only during the CMUT transmission (TX) operation. Further, in some implementations, a bias voltage may be applied to the CMUT having the feedback capacitor. In some implementations, the bias voltage may be applied on the CMUT only in RX operation. In addition, in some implementations, a decoupling capacitor may also be used in the bias circuit which is connected with the CMUT having the feedback capacitor. 
     Other electronic components (e.g., a resistor, an inductor, etc.) with a specified value can be used to replace the feedback capacitor used in some implementations to provide a feedback on the voltage applied on the CMUT. However, unlike the feedback capacitor, the feedback provided by other electronic components may be frequency-dependent, which may not be desirable in some applications. Therefore, while the feedback capacitor, which is not frequency-dependent, is used to illustrate many implementations disclosed herein, it should be noted that implementations using other components to provide the feedback function in CMUT operation are also within the scope of the disclosure. 
       FIG. 1A  illustrates an exemplary system  101  including a schematic model of a theoretical CMUT  100  in transmission operation for illustrating principles of exemplary implementations disclosed herein. The CMUT  100  comprises a fixed electrode  110 , a movable electrode  112 , equivalent springs  114  and spring anchors  116 . The top and bottom electrodes may connect to an interface circuit that includes a first port  120  that receives a transmission input voltage (V TX ) in this implementation and a second port  122  that acts a ground (GND) in this implementation. Usually the first port  120  is connected to the front circuit (not shown) of the CMUT system. The front circuit of the CMUT either applies an actuation signal (V TX ) on the CMUT  100  or detects the reception signal from the CMUT  100 . CMUT  100  is designed with an electrode separation gap “g”  130 , which is the space that exists between the movable electrode  112  and the fixed electrode  110  when the CMUT  100  is in an original position, not activated by a transmission voltage or external acoustic energy. For example, when CMUT  100  is activated by a voltage applied at first port  120 , the movable electrode  112  displaces toward the fixed electrode  110  to a certain displacement position x  132  due to the electrostatic force between the movable electrode  112  and the fixed electrode  110 . When a voltage is applied to displace movable electrode  112  toward the fixed electrode  110 , springs  114  (or equivalent structure) provide a restorative force to return the movable electrode  112  back toward its original position. 
     However, since the electrostatic force in the CMUT is nonlinear, the electrostatic force can increase faster than the restorative force of springs  114  as the separation between the two electrodes becomes smaller. Consequently, at a certain maximum displacement Xm  134 , the restorative force of springs  114  cannot overcome the electrostatic force between the movable electrode  112  and the fixed electrode  110 . Once this maximum displacement point Xm  134  is reached, any further voltage increase may cause the movable electrode  112  to collapse on the fixed electrode  110 . Therefore, the displacement x  132  of the movable electrode needs to be controlled so as to remain smaller than Xm  134  for a normal CMUT operation. Typically, the maximum design displacement Xm  134  is much smaller than the electrode separation gap g  130 . For example, for an ideal parallel plate CMUT in a static actuation, Xm  134  may typically be about one third of separation gap g  130 . Therefore, in conventional designs, in order to achieve sufficient displacement for certain applications, the separation gap g  130  between the fixed and movable electrodes needs to be designed to be much larger than the displacement x  132  actually required to produce the desired amount of acoustic energy. 
       FIG. 1B  shows system  101  as an equivalent circuit of the CMUT  100  in  FIG. 1A . The CMUT  100  is symbolically represented in this implementation as a variable capacitor. The capacitance of the CMUT  100  is proportional to 1/g. In the illustrated implementation, all of the input voltage V TX  may be applied on the CMUT  100 . 
     Since the movable electrode  112  has the displacement, x  132 , smaller than Xm  134  during a normal operation, CMUT  100  in  FIG. 1A  can be conceptually separated into two parts by inserting a virtual floating electrode  111  fixed at Xm  134 , as also shown in  FIG. 1B . Thus, the movable electrode  112  and the floating electrode  111  form another variable capacitor  200  (as shown in system  201  in  FIG. 2A ) and the floating electrode  111  and the fixed capacitor  110  form a constant capacitor  240  (as shown in  FIG. 2A ). As disclosed herein, the circuits in  FIG. 1B  and  FIG. 2A  may have identical electrical and acoustical properties.  FIG. 2B  illustrates a schematic model of an exemplary implementation of the system  201  in  FIG. 2A . A CMUT  200  having a capacitor  240  connected in series. However, the initial capacitance of the CMUT  200  in  FIGS. 2A-2B  is g/Xm times of the initial capacitance of the CMUT  100  in  FIGS. 1A-1B  and the capacitance of the capacitor  240  in  FIGS. 2A-2B  is g/(g−Xm) times of the initial capacitance of the CMUT  100  in  FIGS. 1A-1B . So the capacitances of both the CMUT  200  and the capacitor  240  are larger than that of the CMUT  100  and the total initial capacitance of two series capacitors (i.e., CMUT  200  and capacitor  240 ) in  FIGS. 2A-2B  is the same as the initial capacitance of the CMUT  100  in  FIGS. 1A-1B . 
     Since the acoustic and mechanical properties of the circuits or schematic models in  FIGS. 1A-1B  and  FIGS. 2A-2B  are the same, so in the CMUT  200  in  FIGS. 2A-2B , ideally, the movable electrode  112  can have a maximum displacement Xm that is the same as the whole electrode separation g  230  of the CMUT  200 . Therefore, the relative displacement over the electrode separation of a CMUT  200  with a proper capacitor  240  connected in series can be much larger than that of the same CMUT without a capacitor in series. This is because the feedback capacitor  240  (having a capacitance referred to hereafter as “C F ”) provides a feedback on the percentage of the input voltage applied on the CMUT  200 . In  FIGS. 1A-1B , all input voltage V TX  is applied on the CMUT  100 . However, in  FIGS. 2A-2B , only part of the input voltage (V A ) is applied on the CMUT and rest of the input voltage (V B ) is applied on the feedback capacitor, i.e., V TX =V A +V B . Capacitor  240  and CMUT  200  together form a voltage divider so that an increase of the capacitance, as well as displacement, of the CMUT  200  decreases the percentage of the voltage applied on the CMUT  200 , thus capacitor  240  provides a negative feedback on the voltage applied on the CMUT  200 . Therefore, when connected in series with capacitor  240 , CMUT  200  is able to operate stably well beyond the limits set by the pull-in effect in CMUTs in normal operation (i.e., without a series feedback capacitor). 
     Further, in the implementation of  FIGS. 2A-2B , the CMUT capacitance of CMUT  200  is substantially larger than the capacitance of the theoretical model CMUT  100  of  FIG. 1  for achieving the same displacement x  232  of movable electrode  112 . The larger CMUT capacitance is desirable to improve the performance of the CMUT, for example, when the CMUT is used in a detect/receive mode for detection/reception of acoustic energy. 
     In implementations disclosed herein, capacitor  240  may be any kind of capacitor having a constant capacitance. For example, capacitor  240  may be fabricated directly on a CMUT substrate, such as by using metal or silicon as top and bottom electrodes and using nitride or oxide as the dielectric material. Alternatively, capacitor  240  may be a discrete capacitor component connected to a CMUT transducer designed according to the principles and techniques described herein. 
       FIG. 3  illustrates an exemplary implementation of a system  301  including a CMUT  300  and a feedback capacitor  340  incorporating principles discussed above. The basic structure of CMUT  300  is a flexible membrane capacitive micromachined transducer having a rigid first electrode  310  and a second electrode  312  residing on, or within or as part of a flexible spring element  314 , which may be a flexible membrane or other structure that acts as a spring for enabling second electrode  312  to move toward first electrode  310  when a voltage is applied and then return second electrode  312  to an original position. Spring element  314  and second electrode  312  are separated from first electrode  310  by support anchors  316  to create a transducing separation gap g  330 . CMUT  300  may be used to transmit (TX) or detect (RX) an acoustic wave in an adjacent medium through the deflection of flexible membrane  314 . For example, during transmission an AC signal is applied to CMUT  300  via first port  120 . The alternating electrostatic force between the first electrode  310  and the second electrode  312  actuates the membrane  314  in order to deliver acoustic energy into a medium surrounding the CMUT  300 . Similarly, during reception an impinging acoustic wave vibrates the membrane  314 , thus altering the effective capacitance between the two electrodes  310 ,  312 , and an electronic circuit (not shown) detects and measures this capacitance change for using the CMUT as a sensor. 
     The exemplary CMUT  300  of  FIG. 3  includes feedback capacitor  340  connected in series to one of electrodes  310  or  312 . Feedback capacitor  340  has a capacitance that is preferably approximately equal to or less than an effective capacitance C C  of CMUT  300 , such as within the ranges discussed below. By the inclusion of feedback capacitor  340  in series with the CMUT  300 , while still achieving the similar maximum displacement, separation gap  330  may be able to be designed to be less than one-half to one-third of the size that would be required in a CMUT without feedback capacitor  340 . Feedback capacitor  340  may be fabricated directly on the same CMUT substrate as one of first or second electrodes  310 ,  312 , respectively, or alternatively, capacitor  340  may be connected to CMUT  300  as a discrete capacitor component. 
       FIG. 4  illustrates another implementation of an exemplary system  401  including a CMUT  400  with a feedback capacitor  440  connected in series. CMUT  400  includes a first electrode  410  and a second electrode  412 . CMUT  400  includes an embedded spring element  414 , which may be a flexible membrane or other structure that acts as a spring for enabling second electrode  412  to move toward first electrode  410  and then spring back to an original position. Moreover, spring element  414  may be conductive and be a part of the first electrode  410 . Second electrode  412  may be suspended from spring element  414  by supports  416  to create a transducing separation gap g  430 . CMUT  400  may be operated in a manner similar to that described above for CMUT  300 . 
     The exemplary CMUT  400  of  FIG. 4  includes feedback capacitor  440  connected in series to one of electrodes  410  or  412 . Feedback capacitor  440  has a capacitance that preferably is approximately equal to or less than an effective capacitance C C  of CMUT  400 , such as within the ranges discussed below. By the inclusion of capacitor  440  in series with the CMUT  400 , while still achieving the similar maximum displacement, separation gap  430  is able to be designed to be less than one-half to one-third of the size that would be required in a CMUT in normal operation. Capacitor  440  may be fabricated directly on the same CMUT substrate as one of first or second electrodes  410 ,  412 , respectively, or alternatively, capacitor  440  may be connected to CMUT  400  as a discrete capacitor component. 
       FIG. 5A  is a schematic to depict the basic configuration of a system  501  including a CMUT  500  according to some implementations. A feedback capacitor  540  having a capacitance C F  is connected in series with the CMUT  500  having a capacitance C C . The second port  122  is connected to a GND or a bias source. The first port  120  is connected to the front circuit (not shown) of the CMUT system. The front circuit of the CMUT either applies an actuation signal (V) on the CMUT  500  with a feedback capacitor  540  in series or detects the reception signal from the CMUT  500 . Usually, the implementations of using a feedback capacitor provide more advantages in transmission operation of a CMUT than in detect/receive operation and, therefore, we use the transmission operation to illustrate the implementations in  FIG. 5A . In this case, the input voltage V IN  is the transmission signal V TX . The voltage V A  applied on the CMUT  500  from a transmission signal V TX  can be obtained as: V A =V TX −V B =V TX (1+(C C /C F )) −1 . For a given applied input signal V TX , the voltage V A  applied on the CMUT decreases as the capacitance C C  of the CMUT increases. Therefore the series capacitor  540  provides a negative feedback on the voltage V A  applied on the CMUT  500 . 
     The efficiency of the feedback provided by the feedback capacitor  540  depends on the ratio of C C /C F . Therefore, the capacitance of the series capacitor  540  needs to be selected properly to achieve a desired feedback on the input voltage applied on the CMUT  500 . In some implementations with properly selected feedback capacitor, the feedback on the input voltage applied on the CMUT  500  is able to extend the CMUT operation range beyond that limited by the pull-in effect in normal CMUT operation. Consequently, the CMUT  500  with the feedback capacitor  540  having a capacitance C F  is able to achieve a larger displacement within a predetermined transducing space than the same CMUT in a normal operation (without feedback capacitors) according to the implementations disclosed herein. For example, in a CMUT model with an ideal parallel plate capacitance arrangement, if the feedback capacitor is selected to have a capacitance C F  that is one-half of the capacitance C C  of the CMUT, then there is no pull-in effect and the maximum displacement Xm of the CMUT can be the same as the electrode separation g of the CMUT, as discussed above with reference to  FIGS. 2A and 2B . This enables to design CMUTs having substantially larger capacitance to achieve the same displacement as those designed for a normal CMUT operation, or substantially larger displacements for the same capacitance as those designed for a normal CMUT operation. 
     As discussed above, the sum of the voltage V A  applied on the CMUT  500  and the voltage V B  applied on the feedback capacitor  540  is equal to the applied transmission voltage V TX , i.e., V TX =V A +V B . In some implementations, V B  is comparable to V A  or even larger than V A . Therefore, the voltage (V A ) applied on the CMUT structure disclosed herein is smaller than the voltage (V TX ) applied on the CMUT structure in normal operation. There are some advantages achieved to having a smaller voltage applied on the CMUT when implementations of CMUTs disclosed herein are implemented in an ultrasound system, such as an ultrasound probe. First, in some implementations, the capacitance of the CMUTs can be designed to be larger than that of a CMUT having comparable displacement without a suitable feedback capacitor. Thus, increasing the capacitance C C  of the CMUTs herein can improve the reception performance of the CMUT. Also, an entire transmission voltage V TX  is typically applied on a CMUT in a normal operation (without a feedback capacitor in series). In implementations disclosed herein, however, only a portion of the total voltage (e.g., V A &lt;V TX ) is applied on the CMUT, and the remainder of the voltage (voltage V B ) is applied on the feedback capacitor. This provides a second advantage for some implementations in which the CMUTs serve as ultrasonic transducers that need to be placed in voltage-sensitive locations to emit the ultrasound to a medium or receive ultrasound from a medium. Because the feedback capacitor  540  may be located anywhere in series with the CMUT  500 , the amount of voltage applied to the CMUT itself can be reduced, which can be beneficial to applications where a high voltage is not preferred at the transducer vicinity. 
     Thus, the voltage (V A ) applied on the CMUTs disclosed herein may be much lower than the voltage (V TX ) applied on a CMUT that does not incorporate a feedback capacitor when both are emitting the same ultrasound power. This is beneficial to the electrostatic breakdown issue in CMUTs discussed above because the voltage V A  applied on the CMUT of implementations disclosed herein is much lower. Moreover, the lower voltage applied on the CMUTs with a feedback capacitor disclosed herein allows for a thinner insulation layer in the CMUT to prevent dielectric breakdown when the two electrodes collapse. Although, ideally, the insulation layer may not be needed in some implementations. This improves the reliability of the CMUT because dielectric charging in the insulation layer is minimized or completely eliminated. Therefore, the CMUT disclosed herein (with a feedback capacitor in series) has much better reliability. 
     In some implementations, in order to provide the desired feedback on the voltage applied on the CMUT using the capacitor in series, the capacitance C F  of the feedback capacitor should be comparable with the capacitance C C  of the CMUT, for example, within the same order of magnitude. For instance, the capacitance C F  of the feedback capacitor may be designed to be within the range from 0.1 C C  to 3 C C  (i.e., between 10 and 300 percent of C C ), where C C  stands for the effective baseline capacitance of a CMUT, or more precisely, the capacitance of the CMUT when the CMUT is set for a transmission operation before any change in the capacitance due to input of a transmission voltage V TX . Moreover, in some exemplary implementations, the capacitance C F  of the feedback capacitor may be designed to be within 0.3 C C  to 1 C C  (i.e., between 30 and 100 percent of C C ) for optimum operation. Further, in some implementations, capacitance C C  may include both the CMUT capacitance and any parasitic capacitance if there is a parasitic capacitance existing in certain practical installations or in the CMUT structure itself. 
     Besides using a capacitor, other suitably configured electronic components, e.g., a resistor, an inductor, or the like, may be used in place of the feedback capacitor  540  in  FIG. 5A  to achieve the desired feedback on the input voltage applied on the CMUT  500 . Since the feedback of the components other than a capacitor is frequency-dependent, the value of the electronic component may be selected to have a similar electrical impedance I F  to that of the desired feedback capacitance C F  in the operating frequency of the CMUT  500 . 
       FIG. 5B  illustrates a system  501   b  including a CMUT  500  with a feedback resistor  542  connected in series with CMUT  500 . The feedback resistor  542  is connected with one of two electrodes of the CMUT  500  and has a selected resistance R F . The second port  122  is connected to a GND or a bias source. The first port  120  is connected to the front circuit (not shown) of the CMUT. The front circuit of the CMUT either applies an actuation signal (V IN ) on the CMUT  500  with a feedback resistor  542  in series or detects the reception signal from the CMUT  500 . The voltage V A  applied on the CMUT  500  from a transmission signal V can be obtained as: V A =V in −V B =V in (1+jω C R F C C ) −1 , where j is the imaginary unit and ω C  is the operating frequency of the CMUT. For a given applied input signal V IN , the voltage V A  applied on the CMUT decreases as the capacitance C C  of the CMUT increases. Therefore the series resistor  542  having a properly selected resistance R F  provides a negative feedback on the voltage V A  applied on the CMUT  500 . 
     The efficiency of the feedback provided by the feedback resistor  542  depends on a feedback factor of jω C  R F  C C . Different from using a feedback capacitor discussed above, the feedback factor of using a feedback resistor is a function of the operating frequency ω C  of the CMUT. It is also notable that the feedback factor is an imaginary, so there is a phrase difference between the voltage (V A ) applied on the CMUT and the input voltage (V IN ). This phase difference makes the feedback of the resistor  542  on the CMUT  500  to behave as a damping effect on the CMUT displacement. Therefore, the CMUT with a feedback resistor  542  may have a better bandwidth than the CMUT in normal operation. Thus this approach is especially useful to broaden the bandwidth of a CMUT operating in air as a medium. Therefore, the resistance R F  of the series resistor  542  needs to be selected properly to achieve a desired feedback on the input voltage applied on the CMUT  500  in CMUT in the operating frequency region. For example, in order to achieve the similar absolute feedback effect as a feedback capacitor  540  on the voltage (V A ) applied on the CMUT  500 , the feedback resistor  542  has an impedance Z F =R F  that is of the same order of magnitude as an impedance Z F =1/jω C C C  of CMUT  500  based upon a predetermined operating frequency (ω C ) of CMUT  500 . For example, the impedance of resistor  542  may be between 50 and 300 percent of the impedance of the CMUT  500  at the predetermined operating frequency. 
     Additionally,  FIG. 5C  illustrates system  501   c  including a CMUT  500  having a feedback inductor  544  connected in series with CMUT  500 . The feedback inductor  544  is connected with one of the two electrodes of the CMUT  500 . The second port  122  is connected to a GND or a bias source. The first port  120  is connected to the front circuit (not shown) of the CMUT. The front circuit of the CMUT either applies an actuation signal (V IN ) on the CMUT  500  with a feedback inductor in series or detects the reception signal from the CMUT  500 . The voltage V A  applied on the CMUT  500  from a transmission signal V IN  can be obtained as: V A =V in −V B =V in (1+(−ω C   2 L F C C )) −1 . For an applied input signal V IN , the percentage of the voltage V A  applied on the CMUT increases as the capacitance C C  of the CMUT increases. Therefore the series inductor  544  provides a positive feedback on the voltage V A  applied on the CMUT  500 . 
     The efficiency of the feedback provided by the feedback inductor  544  depends on a feedback factor of −ω C   2 L F  C C . Different from using a feedback capacitor discussed above, the feedback factor of using a feedback inductor  544  is a strong function of the frequency W. It is also notable that the feedback factor is negative so the inductor provides a positive feedback. Thus, the voltage (V A ) applied on the CMUT can be larger than the input voltage (V IN ). The CMUT with the series inductor may have a narrower bandwidth. So this may be useful to applications in which a signal with multiple pulses is needed, e.g., High Intensity Focused Ultrasound (HIFU). The inductance L F  of the series inductor  544  needs to be selected properly to achieve a desired feedback on the input voltage applied on the CMUT  500  in CMUT operating frequency region. For example, in order to achieve the effective feedback effect as a feedback inductor  544  having an inductance L F  on the voltage (V A ) applied on the CMUT  500 , the feedback inductor  544  has an impedance Z F =jω C L F  that is of the same order of magnitude as an impedance Z F =1/jω C C C  of CMUT  500  based upon a predetermined operating frequency (ω C ) of CMUT  500 . For example, the impedance Z F  of inductor  544  may be between 50 and 300 percent of the impedance of the CMUT  500  at the predetermined operating frequency. 
     In the following description and associated drawing figures, feedback capacitors are used to illustrate various implementations disclosed herein, but other feedback components, such as the feedback resistor and feedback inductor discussed above, may be used in the same implementations, taking into account the considerations discussed above. 
       FIG. 6  illustrates a flow chart  600  of an exemplary method for a CMUT including a feedback capacitor according to implementations described herein. Further, it should be noted that this method is entirely exemplary, and the invention is not limited to any particular method. 
     Block  601 : In some implementations, it is first necessary to determine a desired design displacement x of a second electrode toward a first electrode for producing a predetermined amount of acoustic energy when a specified voltage will be applied on the CMUT. 
     Block  602 : Once the desired displacement x is determined, a capacitance C C  that will exist between the first electrode and the second electrode of the CMUT based on the specified transmission voltage can be determined, as discussed above. 
     Block  603 : After the capacitance C C  of the CMUT has been determined, the feedback capacitor can be selected based on the capacitance C C  of the CMUT. As discussed above, in some implementations the feedback capacitor has a capacitance C F  that is less than or approximately equal to the capacitance C C  of the CMUT. In other implementations, the feedback capacitor is chosen within the specific ranges recited above, i.e., between 30 and 100 percent of the capacitance C C  or between 10 and 300 percent of the capacitance C C . 
     Block  604 : The feedback capacitor is placed in series with the CMUT. 
     Block  605 : A transmission voltage is applied to the CMUT and the feedback capacitor to actuate the CMUT. The transmission voltage causes movement of the second electrode toward and away from the first electrode to produce ultrasonic energy. The feedback capacitor applies a feedback on the voltage applied on the CMUT so that the percentage of the transmission voltage applied on the CMUT decreases as the capacitance C C  of the CMUT increases during actuation of the CMUT, and vice versa. 
       FIGS. 7-13  illustrate more detail implementations of the basic configuration shown in  FIG. 5  into different operation methods and configurations of a CMUT.  FIG. 7  illustrates an implementation of a system  701  including a CMUT  700  connected in series with a feedback capacitor  740 . The second port  122  is connected to a GND or a bias source. The first port  120  is connected to the front circuit (not shown) of the CMUT system. The front circuit of the CMUT either applies an actuation signal on the CMUT  700  or detects the reception signal from the CMUT  700 . A switch  760  may be used to short the feedback capacitor  740 , such as during a certain duration of the operation CMUT  700 . For example, switch  760  may be opened during a transmission (TX) operation and closed during a reception (RX) operation to short the circuit, thereby rendering feedback capacitor  740  active during transmission of ultrasonic energy and inactive during reception of ultrasonic energy. During reception operation, a larger CMUT capacitance is desired to drive a detection signal, so the feedback capacitance is desired to be shorted to increase the overall capacitance. Furthermore, even though switch  760  is not shown in the other exemplary configurations described above and also described below, such a switch may be may be added in any of those implementations if desired. The switch illustrated in  FIG. 7  may be a real switch or switch circuit; it may also be any circuit or function box that functions like a switch to include or to exclude the feedback capacitor  740  in certain operation (e.g. TX or RX operation) of the CMUT  700 . 
       FIG. 8  illustrates an implementation of a system  801  including a CMUT  800  connected in series with a feedback capacitor  840 . In this implementation, CMUT  800  is subject to receiving a biasing voltage V Bias  at a third port  824  via a bias circuit  850  including a biasing resistor  826  having a resistance R Bias . Usually, the resistance of a bias resistor is much larger than the impedance of the CMUT. So the presence the bias resistor, as well as the decoupling capacitor introduced later, has minimal impact on the CMUT operation at the operating frequency of the CMUT. Often, an electrical floating operation point/port should be biased to a desired signal source to achieve stable operation, such as when in a detect/receive mode for receiving an acoustic signal. In the implementation of  FIG. 8 , there is an electrical floating point between the CMUT  800  and the feedback capacitor  840  so the CMUT  800  may be biased by a bias source V Bias  at a third port  824 . In some implementations, the bias source may be a DC voltage source, a ground, or any other signal source. In the implementation of  FIG. 8 , a TX/RX switch  860  is included at first port  120  for switching between transmit mode and receive/detect mode. Thus, when switch  860  switches to a TX input terminal  827 , transmission voltage V TX  is able to pass to the CMUT  800 . Alternatively, when switch  860  switches to an RX output terminal  828 , an output current produced by CMUT  800  as a result of receiving or detecting ultrasonic energy is able to be passed to a measuring circuit or the like (not shown). 
     There are various bias methods which can be used for some implementations disclosed herein. TX/RX switch  860  in the implementations and configurations disclosed herein can be any circuit or function box that functions like a switch between transmission (TX) operation and reception (RX) operation. For example, TX/RX switch  860  may be an actual physical switch, may be a protective circuit for preamplification of reception during transmission operations, or some other arrangement that performs the same function. 
       FIG. 8  illustrates an exemplary method to bias CMUT  800  and feedback capacitor  840 . The bias voltage V Bias  that is applied on the CMUT  800  may be delivered through bias resistor  826 . The feedback capacitor  840  is able to perform a feedback function as discussed above, and is also able to perform a DC decoupling function in some implementations so that a DC decouple capacitor is not needed in addition to the feedback capacitor  840 . Further, for all configurations described herein, the biasing resistor having R Bias , which is used to apply the proper bias, may be replaced by a switch. 
     In the implementation of  FIG. 8 , both the feedback capacitor  840  and the bias voltage V Bias  are placed between the CMUT  800  and the TX/RX switch  860 . However,  FIG. 9  illustrates an alternative implementation of a system  901  in which a CMUT  900  receives the bias voltage V Bias  via third port  824  and bias circuit  850 , and a feedback capacitor  940  is located on the other side of TX/RX switch  860  at input terminal  827 , so that feedback capacitor  940  only functions during TX operations. 
       FIG. 10  illustrates another implementation of a system  1001  including a CMUT  1000  in which the bias circuit  850  providing V Bias  is also located on the other side of TX/RX switch  860  at output terminal  828 , so that V Bias    824  only functions during RX operation mode and a feedback capacitor  1040  only functions during transmission mode. 
     Additionally, in the implementation of  FIG. 8 , feedback capacitor  840  is placed between CMUT  800  and TX/RX switch  860 . In that configuration, the operation point of the CMUT is determined by the bias voltage only. However, in other implementations, the feedback capacitor can be placed on the other side of the CMUT, as illustrated in  FIG. 11 . In  FIG. 11 , a system  1101  including a feedback capacitor  1140  and the bias circuit  850  are located between a CMUT  1100  and second port  122 , which also serves as ground in this implementation. The operation point of CMUT  1100  of  FIG. 11  may be determined by the bias voltage V Bias  only, or by both the bias voltage V Bias  and transmission (TX) input signal voltage V TX  when switch  860  is in contact with TX input terminal  827 . 
     Also, in the implementation of  FIG. 9 , the bias circuit  850  is placed between the CMUT  900  and the TX/RX switch  860 . However, as illustrated in  FIG. 12 , the bias voltage V Bias  can be also placed on the other side of the CMUT.  FIG. 12  illustrates an implementation of a system  1201  in which a CMUT  1200  is connected directly to a source of bias voltage through second port  122 , and feedback capacitor  1240  is only connected during a transmission mode. 
       FIG. 13  illustrates an implementation of a system  1301  in which two bias circuits  1350 ,  1351  are placed on the two sides of a CMUT  1300 , respectively. The first bias circuit  1350  having a voltage V Bias1  is provided at a third port  1324  and is applied through a first biasing resistor  1326  having a resistance R Bias1  applied between the CMUT  1300  and a feedback capacitor  1340 . The second bias circuit  1351  having a voltage V Bias2  is provided at a fourth port  1325  and is applied through a second biasing resistor  1327  having a resistance R Bias2  applied on the other side of CMUT  1300 . Further, a decoupling capacitor  1390  may be included on this side of CMUT  1300  between CMUT  1300  and second port  122 . Thus, the implementation of  FIG. 13  includes a decoupling capacitor  1390  in series with CMUT  1300  in addition to feedback capacitor  1340 . For example, decoupling capacitor  1390  is a decoupling capacitor having a capacitance C D  that is typically selected to be much larger than the capacitance C C  of CMUT  1300  (i.e., greater than one order of magnitude so that C D &gt;&gt;C C ), and thus, capacitance C D  is also much larger than the capacitance C F  of feedback capacitor  1340 . Consequently, during a transmission operation by CMUT  1300 , the voltage drop on the decoupling capacitor  1390  is negligible and almost all of the transmission input voltage V TX  is applied on CMUT  1300  and feedback capacitor  1340 . Moreover, in a variation of  FIG. 13 , feedback capacitor  1340  and the first bias circuit  1350  may be placed at the other side of TX/RX switch  860 , similar to the implementation illustrated in  FIG. 10 , so that the feedback capacitor  1340  and the first bias circuit  1350  only function in TX and RX operations, respectively. 
     The CMUTs with feedback capacitors discussed above with reference to  FIGS. 1-13  may be incorporated into a variety of different systems, devices and the like. For example,  FIG. 14  illustrates an exemplary probe  1402  used in an ultrasonic system  1401  according to some implementations. The probe is connected with the rest of the ultrasound system through a cable  1404 , or the like. The implementation of  FIG. 14  includes a CMUT  1400  having a feedback capacitor  1440  connected in series in accordance with the implementations disclosed above. In the implementation of  FIG. 14 , both the CMUT  1400  and the feedback capacitor  1440  are located in the probe  1402  of the ultrasound system. 
     Typically, the CMUT needs to be placed somewhere close to the probe surface to efficiently emit and receive ultrasonic energy. However, it is undesirable to have high voltage present somewhere close to the probe surface for safety considerations. Thus, in the implementation of  FIG. 14 , the CMUT  1400  is located at the probe front surface  1403 . However, the feedback capacitor  1440  can be placed anywhere in the probe which is safe to hold relatively high voltage. Usually, it is preferred to place the feedback capacitor  1440  far from the surface of the probe. In view of these considerations, the CMUT  1400  and the feedback capacitor  1440  can be placed in the separated locations, so the CMUT  1400  is placed on the front surface  1403  of the probe  1402  and the feedback capacitor  1440  can be placed in a location in the probe  1402  which is safe for high voltage, such as within the interior of the probe  1402 , isolated from the surface. In this case, as discussed above, the voltage (V A ) exposed near the probe surface in the implementations disclosed herein is much lower than the total transmission voltage (V TX ) when a CMUT is used in normal operation. 
     Furthermore, in other implementations of an ultrasound system  1501 , as illustrated in the exemplary implementation of  FIG. 15 , a feedback capacitor  1540  may be located remotely from a CMUT  1500  and arranged anywhere in the ultrasound system which is safe for high voltage. In the implementation of  FIG. 15 , CMUT  1500  according to implementations disclosed herein is located in an ultrasound probe  1502 . Feedback capacitor  1540  is located at a separate location in a base unit  1508 , or the like, and is connected in series with the CMUT  1500  via a cable  1504 , or the like. This configuration may be useful, for example, for incorporation into a catheter, other probe type device or similar instruments. Any of the implementations described with reference to  FIGS. 1-13  may be implemented in the systems of  FIGS. 14 and 15 . 
     From the foregoing, it will be apparent that implementations disclosed herein provide for CMUTs that can function on a lower voltage than that required by CMUTs in a normal operation for achieving the same displacement. This is useful when a large voltage may not be available or is not desirable in an implementation of an ultrasound system. For example, there are limitations regarding how high a voltage can be used for a device attached to or inserted into a human body. Further, implementations of the CMUTs disclosed herein are able to have a much smaller separation space or gap between two electrodes. The smaller electrode gap and lower required voltage also can increase the efficiency of the CMUTs during both transmission and receiving modes. 
     Implementations also relate to methods, systems and apparatuses for making and using the CMUTs described herein. Further, it should be noted that the system configurations illustrated in  FIGS. 14 and 15  are purely exemplary of systems in which the implementations may be provided, and the implementations are not limited to a particular hardware configuration. In the description, numerous details are set forth for purposes of explanation in order to provide a thorough understanding of the disclosure. However, it will be apparent to one skilled in the art that not all of these specific details are required. 
     Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims. Additionally, those of ordinary skill in the art appreciate that any arrangement that is calculated to achieve the same purpose may be substituted for the specific implementations disclosed. This disclosure is intended to cover any and all adaptations or variations of the disclosed implementations, and it is to be understood that the terms used in the following claims should not be construed to limit this patent to the specific implementations disclosed in the specification. Rather, the scope of this patent is to be determined entirely by the following claims, along with the full range of equivalents to which such claims are entitled.