Patent Publication Number: US-2023134722-A1

Title: Monolithic ultrasonic flow meter and particle detection system

Description:
TECHNICAL FIELD 
     This description relates to the field of ultrasonic systems. More particularly, but not exclusively, this description relates to flow meters and particle detection in ultrasonic systems. 
     BACKGROUND 
     Flow meters may be used to measure flow speeds of fluids in a wide variety of applications. The fluids may include pure water, seawater, polluted or dirty water, petrochemicals, industrial fluids such as acidic solutions, alkaline solutions, and solvents, agricultural fluids such as milk or fertilizer, and fluids used in health care, such as drugs, saline solutions, and blood. Ultrasonic flow meters utilize ultrasonic waves, which are acoustic waves having frequencies above 20 kilohertz (kHz). 
     SUMMARY 
     This description described an ultrasonic transducer formed on a substrate including a semiconductor material, with an interconnect region on the substrate. The ultrasonic transducer includes an array of first ferroelectric resonators and an array of second ferroelectric resonators, both in the interconnect region, with ultrasonic reflectors in the interconnect region at one end of the array of first ferroelectric resonators and at one end of the array of second ferroelectric resonators. The ultrasonic transducer further includes a transmitter circuit including first active components in the semiconductor material, configured to actuate the first ferroelectric resonators to provide a transmitted ultrasonic signal, and a detector circuit including second active components in the semiconductor material, configured to detect a received ultrasonic signal acquired by the second ferroelectric resonators. 
     This description described an ultrasonic fluid flow measurement system including an ultrasonic transducer formed on a substrate including a semiconductor material, with an interconnect region on the substrate. The ultrasonic transducer includes an array of first ferroelectric resonators and an array of second ferroelectric resonators, both in the interconnect region. The ultrasonic transducer further includes a transmitter circuit including first active components in the semiconductor material, coupled to the array of first ferroelectric resonators. The transmitter circuit is configured to actuate the first ferroelectric resonators to emit an ultrasonic signal into a fluid flow channel acoustically coupled to the ultrasonic transducer. The ultrasonic transducer further includes a detector circuit including second active components in the semiconductor material, coupled to the array of second ferroelectric resonators. The detector circuit is configured to provide a detection signal corresponding to acquisition of a second ultrasonic signal from the fluid flow channel, by the second ferroelectric resonators. 
     This description described an ultrasonic fluid flow measurement system including an ultrasonic transducer formed on a substrate including a semiconductor material, with an interconnect region on the substrate. The ultrasonic transducer includes an array of first ferroelectric resonators and an array of second ferroelectric resonators, both in the interconnect region. The array of first ferroelectric resonators and the array of second ferroelectric resonators are parallel to a fluid boundary surface of a fluid flow channel attached to the ultrasonic transducer. The ultrasonic transducer further includes a transmitter circuit including first active components in the semiconductor material coupled to the array of first ferroelectric resonators. The transmitter circuit is configured to actuate the first ferroelectric resonators to emit an ultrasonic signal into the fluid flow channel. The ultrasonic transducer further includes a detector circuit including second active components in the semiconductor material, coupled to the array of second ferroelectric resonators. The detector circuit is configured to provide a detection signal corresponding to detection of a reflection of the ultrasonic signal from the fluid flow channel, by the second ferroelectric resonators 
     This description described an ultrasonic fluid flow measurement system including a first ultrasonic transducer and a second ultrasonic transducer. The first ultrasonic transducer is formed on a first substrate including a first semiconductor material, with a first interconnect region on the first substrate. The first ultrasonic transducer includes an array of first ferroelectric resonators in the first interconnect region, configured parallel to a first fluid boundary surface of a fluid flow channel attached to the first ultrasonic transducer. The first ultrasonic transducer further includes a transmitter circuit including first active components in the first semiconductor material, coupled to the array of first ferroelectric resonators. The transmitter circuit is configured to actuate the first ferroelectric resonators to emit an ultrasonic signal into the fluid flow channel. The second ultrasonic transducer is formed on a second substrate including a second semiconductor material, with a second interconnect region on the second substrate. The second ultrasonic transducer includes an array of second ferroelectric resonators in the second interconnect region, configured parallel to a second fluid boundary surface of the fluid flow channel. The second ultrasonic transducer is attached to the fluid flow channel. The second ultrasonic transducer further includes a detector circuit including second active components in the second semiconductor material, coupled to the array of second ferroelectric resonators. The detector circuit is configured to provide a detection signal corresponding to detection of a transmission of the ultrasonic signal through the fluid flow channel, by the second ferroelectric resonators. 
    
    
     
       BRIEF DESCRIPTION OF THE VIEWS OF THE DRAWINGS 
         FIG.  1 A  and  FIG.  1 B  are a top view and a cross section of an example ultrasonic transducer. 
         FIG.  2 A  and  FIG.  2 B  are a top view and a cross section of another example ultrasonic transducer. 
         FIG.  3 A  and  FIG.  3 B  are a top view and a cross section of a further example ultrasonic transducer. 
         FIG.  4    is a cross section of an example ultrasonic transducer, showing details of ferroelectric resonators. 
         FIG.  5    is a cross section of an example ultrasonic fluid flow measurement system. 
         FIG.  6    is a chart depicting example waveforms of the transmitted ultrasonic signals and the received ultrasonic signals, described in reference to  FIG.  5   . 
         FIG.  7    is a chart depicting example frequency spectra of the transmitted ultrasonic signals and the received ultrasonic signals, described in reference to  FIG.  5    and  FIG.  6   . 
         FIG.  8    is a cross section of another example ultrasonic fluid flow measurement system. 
         FIG.  9    is a chart depicting example waveforms of the transmitted ultrasonic signals and the received ultrasonic signals, described in reference to  FIG.  8   . 
         FIG.  10    is a cross section of another example ultrasonic fluid flow measurement system. 
         FIG.  11    is a chart depicting example waveforms of the transmitted ultrasonic signals and the received ultrasonic signals, described in reference to  FIG.  10   . 
         FIG.  12    is a cross section of another example ultrasonic fluid flow measurement system. 
         FIG.  13    depicts a cutaway view of an example ultrasonic fluid flow measurement system. 
         FIG.  14    depicts a cutaway view of another example ultrasonic fluid flow measurement system. 
         FIG.  15    depicts another example ultrasonic fluid flow measurement system. 
     
    
    
     DETAILED DESCRIPTION 
     The drawings are not necessarily drawn to scale. This description is not limited by the illustrated ordering of acts or events, as some acts or events may occur in different orders and/or concurrently with other acts or events. Furthermore, some illustrated acts or events are optional. 
     Although some embodiments illustrated herein are shown in two-dimensional views with various regions having depth and width, those regions may illustrate a portion of a device that is actually a three-dimensional structure. Accordingly, those regions have three dimensions, including length, width and depth, when fabricated on an actual device. 
     In one aspect of this description, an ultrasonic transducer is formed on a substrate that includes a semiconductor material, and an interconnect region is formed on the substrate. An array of first ferroelectric resonators and an array of second ferroelectric resonators are formed in the interconnect region. Ultrasonic reflectors are formed in the interconnect region proximate to at least one end of the array of first ferroelectric resonators and proximate to at least one end of the array of second ferroelectric resonators. A transmitter circuit including first active components is formed in the semiconductor material and the interconnect region. The transmitter circuit is configured to actuate the first ferroelectric resonators, that is, to apply a potential difference across opposite surfaces of ferroelectric material in the first ferroelectric resonators, to provide a transmitted ultrasonic signal. A detector circuit including second active components is formed in the semiconductor material and the interconnect region. The detector circuit is configured to detect a received ultrasonic signal acquired by the second ferroelectric resonators. The received ultrasonic signal is the transmitted ultrasonic signal after transmission through a fluid. 
     In another aspect of this description, an ultrasonic fluid flow measurement system includes an ultrasonic transducer. The ultrasonic transducer includes a substrate with a semiconductor material, and an interconnect region on the substrate. The ultrasonic transducer includes an array of first ferroelectric resonators and an array of second ferroelectric resonators, both formed in the interconnect region. The ultrasonic transducer further includes a transmitter circuit configured to actuate the first ferroelectric resonators to emit a transmitted ultrasonic signal into a fluid flow channel. The transmitter circuit is coupled to the array of first ferroelectric resonators. The transmitter circuit includes first active components formed in the semiconductor material. The ultrasonic transducer further includes a detector circuit configured to provide a detection signal corresponding to acquisition of a received ultrasonic signal from the fluid flow channel, by the second ferroelectric resonators. The detector circuit is coupled to the array of second ferroelectric resonators. The detector circuit includes second active components formed in the semiconductor material. In one version of this aspect, the received ultrasonic signal may be a reflection of the transmitted ultrasonic signal. In another version, the ultrasonic fluid flow measurement system may include a second ultrasonic transducer, and the transmitted ultrasonic signal may be detected by the second ultrasonic transducer after passing through the fluid flow channel, while the received ultrasonic signal may be transmitted from the second ultrasonic transducer through the fluid flow channel. The ultrasonic fluid flow measurement system may be configured to operate in a pulse-echo mode, a doppler mode, or a combined pulse-echo and doppler mode. 
     In a further aspect of this description, an ultrasonic fluid flow measurement system includes an ultrasonic transducer. The ultrasonic transducer is attached to a fluid flow channel during fluid flow measurements. The ultrasonic transducer includes a substrate with a semiconductor material, and an interconnect region on the substrate. The ultrasonic transducer includes an array of first ferroelectric resonators and an array of second ferroelectric resonators, both in the interconnect region. The array of first ferroelectric resonators and the array of second ferroelectric resonators are parallel to an adjacent fluid boundary surface of the fluid flow channel. The ultrasonic transducer includes a transmitter circuit and a detector circuit. The transmitter circuit includes first active components in the semiconductor material coupled to the array of first ferroelectric resonators. The detector circuit includes second active components in the semiconductor material, coupled to the array of second ferroelectric resonators. The transmitter circuit is configured to actuate the first ferroelectric resonators to emit an ultrasonic signal into the fluid flow channel. The detector circuit is configured to provide a detection signal corresponding to detection of a reflection of the ultrasonic signal from the fluid flow channel, by the second ferroelectric resonators. The ultrasonic fluid flow measurement system may optionally include a user interface coupled to the ultrasonic transducer. 
     In another aspect of this description, an ultrasonic fluid flow measurement system includes a first ultrasonic transducer and a second ultrasonic transducer. The first ultrasonic transducer and the second ultrasonic transducer are attached to a fluid flow channel during fluid flow measurements. The first ultrasonic transducer includes a first substrate with a first semiconductor material, and a first interconnect region on the first substrate. The first ultrasonic transducer includes an array of first ferroelectric resonators and an array of second ferroelectric resonators, both in the first interconnect region. The array of first ferroelectric resonators and the array of second ferroelectric resonators are parallel to an adjacent first fluid boundary surface of the fluid flow channel. The first ultrasonic transducer includes a first transmitter circuit and a first detector circuit. The first transmitter circuit includes first active components in the first semiconductor material coupled to the array of first ferroelectric resonators. The first detector circuit includes second active components in the first semiconductor material, coupled to the array of second ferroelectric resonators. The first transmitter circuit is configured to actuate the first ferroelectric resonators to emit a first ultrasonic signal into the fluid flow channel. The first detector circuit is configured to provide a first detection signal corresponding to detection of a second ultrasonic signal from the fluid flow channel, by the second ferroelectric resonators. The second ultrasonic transducer includes a second substrate with a second semiconductor material, and a second interconnect region on the second substrate. The second ultrasonic transducer includes an array of third ferroelectric resonators and an array of fourth ferroelectric resonators, both in the second interconnect region. The array of third ferroelectric resonators and the array of fourth ferroelectric resonators are parallel to an adjacent second fluid boundary surface of the fluid flow channel. The second ultrasonic transducer includes a second transmitter circuit and a second detector circuit. The second transmitter circuit includes third active components in the second semiconductor material coupled to the array of third ferroelectric resonators. The second detector circuit includes fourth active components in the second semiconductor material, coupled to the array of fourth ferroelectric resonators. The second transmitter circuit is configured to actuate the third ferroelectric resonators to emit the second ultrasonic signal into the fluid flow channel. The second detector circuit is configured to provide a second detection signal corresponding to detection of the first ultrasonic signal from the fluid flow channel, by the fourth ferroelectric resonators. 
     For the purposes of this description, the term “ultrasonic” refers to frequencies above 20 kHz. The term “ferroelectric” refers to materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. Ferroelectric materials used in the ultrasonic transducers described herein are piezoelectric, that is, the ferroelectric materials generate potential differences in response to externally applied force, and generate forces in response to externally applied potential differences. 
     Terms such as top, bottom, over, and above may be used in this description. These terms do not limit the position or orientation of a structure or element, but they provide spatial relationships between structures or elements. For the purposes of this description, the term “lateral” refers to a direction parallel to a plane of a corresponding array of ferroelectric resonators. 
     The following commonly assigned patent applications include related material, and are incorporated herein by reference but are not admitted to be prior art with respect to this description by their mention in this section: U.S. patent application Ser. No. 17/463,013, titled “ACOUSTIC WAVEGUIDE WITH DIFFRACTION GRATING”, filed Aug. 31, 2021, and U.S. patent application Ser. No. 16/590,354, titled “HIGH FREQUENCY CMOS ULTRASONIC TRANSDUCER”, filed Oct. 1, 2019, published as U. S. Patent Application Publication 2021/0099237 A1. 
       FIG.  1 A  and  FIG.  1 B  are a top view and a cross section of an example ultrasonic transducer  100 . Referring to  FIG.  1 A , the ultrasonic transducer  100  includes a substrate  102 . The substrate  102  may be a singulated portion of a semiconductor wafer, such as a bulk silicon wafer or a silicon-on-insulator (SOI) wafer, by way of example. Other manifestation of the substrate  102  are within the scope of this example. The substrate  102  includes a semiconductor material  104 , such as monocrystalline silicon. The ultrasonic transducer  100  includes an interconnect region  106  formed on the substrate  102 . The interconnect region  106  includes several interconnect levels, not shown, with each interconnect level including metal interconnect lines. The interconnect region  106  further includes metal vias that connect the metal interconnect lines of sequential interconnect levels, and contacts that connect the metal interconnect lines of a first interconnect level with active components formed in the semiconductor material  104 . 
     The ultrasonic transducer  100  includes an array of first ferroelectric resonators  108  formed in the interconnect region  106 . The ultrasonic transducer  100  includes an array of second ferroelectric resonators  110  formed in the interconnect region  106 . In this example, the array of first ferroelectric resonators  108  may be arranged parallel to the array of second ferroelectric resonators  110 , as depicted in  FIG.  1 A . The ultrasonic transducer  100  includes ultrasonic reflectors  112  at both ends of the array of first ferroelectric resonators  108  and at both ends of the array of second ferroelectric resonators  110 . The ultrasonic reflectors  112  are formed in the interconnect region  106 , and may include ferroelectric resonators similar to the first ferroelectric resonators  108  and the second ferroelectric resonators  110 . 
     The ultrasonic transducer  100  includes a transmitter circuit  114 . The transmitter circuit  114  includes first active components  116  formed in the semiconductor material  104 . The transmitter circuit  114  is coupled to the array of first ferroelectric resonators  108 , as indicated in  FIG.  1 A . The transmitter circuit  114  may be coupled to the array of first ferroelectric resonators  108  through the metal interconnect lines and metal vias of the interconnect region  106 . 
     The ultrasonic transducer  100  includes a detector circuit  118 . The detector circuit  118  includes second active components  120  formed in the semiconductor material  104 . The detector circuit  118  is coupled to the array of second ferroelectric resonators  110 , as indicated in  FIG.  1 A . The detector circuit  118  may be coupled to the array of second ferroelectric resonators  110  through the metal interconnect lines and metal vias of the interconnect region  106 . 
     The ultrasonic transducer  100  includes a microelectronic package  122  which contains the substrate  102  and the interconnect region  106 . The microelectronic package  122  of this example includes external leads  124 . The external leads  124  may be parts of a lead frame assembly, by way of example. The transmitter circuit  114  and the detector circuit  118  are coupled to the external leads  124 , though wire bonds  126  in this example, as depicted in  FIG.  1 A . Other structures for coupling the transmitter circuit  114  and the detector circuit  118  to the external leads  124 , such as solder bump bonds, are within the scope of this example. The microelectronic package  122  of this example includes a package material  128  that surrounds the substrate  102 , the interconnect region  106 , and the wire bonds  126 , and holds the external leads  124  in place. The package material  128  may include epoxy, and may include filler particles to reduce a thermal expansion coefficient of the package material  128 . Other compositions of the package material  128  are within the scope of this example. 
     Referring to  FIG.  1 B , the second ferroelectric resonators  110  may be configured as capacitors with ferroelectric material  130  between plates of the capacitors. The ferroelectric material  130  may include, by way of example, lead zirconium titanate or lead lanthanum zirconium titanate. The first ferroelectric resonators  108  of  FIG.  1 A , which are out of the plane of  FIG.  1 B , include the ferroelectric material  130 , and may have structure similar to the second ferroelectric resonators  110 . 
     The transmitter circuit  114  of  FIG.  1 A  is configured to actuate the first ferroelectric resonators  108  to provide a transmitted ultrasonic signal  132 . In this example, the transmitted ultrasonic signal  132  may be emitted through a top surface  134  of the interconnect region  106 , as indicated in  FIG.  1 B . The top surface  134  of the interconnect region  106  is located opposite from a bottom surface  136  of the substrate  102 . In this example, the transmitted ultrasonic signal  132  may include a first signal beam  132   a  and a second signal beam  132   b . The first signal beam  132   a  may be emitted from the ultrasonic transducer  100  at a first angle  138   a  from a perpendicular direction to a plane of the first ferroelectric resonators  108  and the second ferroelectric resonators  110 . The second signal beam  132   b  may be emitted from the ultrasonic transducer  100  at a second angle  138   b  from the perpendicular direction, opposite from the first signal beam  132   a . The second angle  138   b  may be equal in magnitude to the first angle  138   a . The first signal beam  132   a  and the second signal beam  132   b  may extend in a plane containing an axis of the first ferroelectric resonators  108  and the perpendicular direction to the plane of the first ferroelectric resonators  108  and the second ferroelectric resonators  110 . 
     The detector circuit  118  of  FIG.  1 A  is configured to detect a received ultrasonic signal  140  acquired by the second ferroelectric resonators  110  and provide a detection signal corresponding to the received ultrasonic signal  140 . The received ultrasonic signal  140  of this example may be the transmitted ultrasonic signal  132  after transmission through a fluid, not shown in  FIG.  1 B . The received ultrasonic signal  140  of this example may include a first signal component  140   a  which is a reflection of the first signal beam  132   a  after transmission through the fluid, and may include a second signal component  140   b  which is a reflection of the second signal beam  132   b  after transmission through the fluid. 
       FIG.  2 A  and  FIG.  2 B  are a top view and a cross section of another example ultrasonic transducer  200 . Referring to  FIG.  2 A , the ultrasonic transducer  200  includes a substrate  202 . The substrate  202  may be manifested as any of the examples described in reference to the substrate  102  of  FIG.  1 A . Other manifestation of the substrate  202  are within the scope of this example. The substrate  202  includes a semiconductor material  204 , such as monocrystalline silicon. The ultrasonic transducer  200  includes an interconnect region  206  formed on the substrate  202 . The interconnect region  206  includes several interconnect levels with metal interconnect lines, metal vias, and contacts as described in reference to the interconnect region  106  of  FIG.  1 A . 
     The ultrasonic transducer  200  of this example includes an array of first ferroelectric resonators  208  and an array of second ferroelectric resonators  210 , both formed in the interconnect region  206 . In this example, the first ferroelectric resonators  208  and the second ferroelectric resonators  210  comprise the same ferroelectric resonators. In this example, the arrays of first and second ferroelectric resonators  208  and  210  may be arranged in a single row, as depicted in  FIG.  2 A . The ultrasonic transducer  200  includes ultrasonic reflectors  212  at both ends of the arrays of first and second ferroelectric resonators  208  and  210 . The ultrasonic reflectors  212  are formed in the interconnect region  206 , and may include ferroelectric resonators similar to the first and second ferroelectric resonators  208  and  210 . 
     The ultrasonic transducer  200  includes a transmitter circuit  214  which includes first active components  216  formed in the semiconductor material  204 . The ultrasonic transducer  200  includes a detector circuit  218  which includes second active components  220  formed in the semiconductor material  204 . The transmitter circuit  214  is coupled to the array of first ferroelectric resonators  208  through a multiplexer  242 , as indicated in  FIG.  2 A . The multiplexer  242  includes third active components  244  formed in the semiconductor material  204 . The detector circuit  218  is coupled to the array of second ferroelectric resonators  210  through the multiplexer  242 , as indicated in  FIG.  2 A . 
     The ultrasonic transducer  200  includes a microelectronic package  222  which contains the substrate  202  and the interconnect region  206 . The microelectronic package  222  of this example includes external leads  224 , which may be parts of a lead frame assembly, by way of example. The transmitter circuit  214 , the detector circuit  218 , and the multiplexer  242  are coupled to the external leads  224 , though wire bonds  226  in this example, as depicted in  FIG.  2 A . Other structures for coupling the transmitter circuit  214 , the detector circuit  218 , and the multiplexer  242  to the external leads  224 , such as solder bump bonds, are within the scope of this example. The microelectronic package  222  of this example includes a package material  228  that surrounds the substrate  202 , the interconnect region  206 , and the wire bonds  226 , and holds the external leads  224  in place. The package material  228  may have a composition as described in reference to the package material  128  of  FIG.  1 A . Other compositions of the package material  228  are within the scope of this example. 
     Referring to  FIG.  2 B , the first and second ferroelectric resonators  208  and  210  may be configured as capacitors with ferroelectric material  230  between plates of the capacitors. The ferroelectric material  230  may have a composition as described in reference to the ferroelectric material  130  of  FIG.  1 B . 
     The transmitter circuit  214  of  FIG.  2 A  is configured to actuate the first ferroelectric resonators  208  to provide a transmitted ultrasonic signal  232 . In this example, the transmitted ultrasonic signal  232  may be emitted through a bottom surface  236  of the substrate  202 , as indicated in  FIG.  2 B . The bottom surface  236  of the substrate  202  is located opposite from a top surface  234  of the interconnect region  206 . In this example, the transmitted ultrasonic signal  232  may include a first signal beam  232   a  and a second signal beam  232   b . The first signal beam  232   a  may be emitted from the ultrasonic transducer  200  at a first angle  238   a  from a perpendicular direction to a plane of the first ferroelectric resonators  208  and the second ferroelectric resonators  210 . The second signal beam  232   b  may be emitted from the ultrasonic transducer  200  at a second angle  238   b  from the perpendicular direction, opposite from the first signal beam  232   a . The second angle  238   b  may be equal in magnitude to the first angle  238   a . The first signal beam  232   a  and the second signal beam  232   b  may extend in a plane containing an axis of the first ferroelectric resonators  208  and the perpendicular direction to the plane of the first ferroelectric resonators  208  and the second ferroelectric resonators  210 . 
     The detector circuit  218  of  FIG.  2 A  is configured to detect a received ultrasonic signal  240  acquired by the second ferroelectric resonators  210  and provide a detection signal corresponding to the received ultrasonic signal  240 . The received ultrasonic signal  240  of this example may be the transmitted ultrasonic signal  232  after transmission through a fluid, not shown in  FIG.  2 B . The received ultrasonic signal  240  of this example may include a first signal component  240   a  which is a reflection the first signal beam  232   a  after transmission through the fluid, and may include a second signal component  240   b  which is a reflection of the second signal beam  232   b  after transmission through the fluid. 
       FIG.  3 A  and  FIG.  3 B  are a top view and a cross section of a further example ultrasonic transducer  300 . Referring to  FIG.  3 A , the ultrasonic transducer  300  includes a substrate  302 . The substrate  302  may be manifested as any of the examples described in reference to the substrate  102  of  FIG.  1 A . Other manifestations of the substrate  302  are within the scope of this example. The substrate  302  includes a semiconductor material  304 , such as monocrystalline silicon. The ultrasonic transducer  300  includes an interconnect region  306  formed on the substrate  302 . The interconnect region  306  includes several interconnect levels with metal interconnect lines, metal vias, and contacts as described in reference to the interconnect region  106  of  FIG.  1 A . 
     The ultrasonic transducer  300  of this example includes an array of first ferroelectric resonators  308  and an array of second ferroelectric resonators  310 , both formed in the interconnect region  306 . In this example, the array of first ferroelectric resonators  308  may be arranged parallel to the array of second ferroelectric resonators  310 , as depicted in  FIG.  3 A . In this example, the array of first ferroelectric resonators  308  may be arranged in a two subarrays, a first subarray  346   a  of the first ferroelectric resonators  308  and a second subarray  346   b  of the first ferroelectric resonators  308 , with a transmitter grating  348  between the two subarrays  346   a  and  346   b , as depicted in  FIG.  3 A . Similarly, the array of second ferroelectric resonators  310  may be arranged in a two subarrays, a first subarray  350   a  of the second ferroelectric resonators  310  and a second subarray  350   b  of the second ferroelectric resonators  310 , with a receiver grating  352  between the two subarrays  350   a  and  350   b , as depicted in  FIG.  3 A . The transmitter grating  348  and the receiver grating  352  are formed in the interconnect region  306 , and may include ferroelectric resonators similar to the first and second ferroelectric resonators  308  and  310 . The ultrasonic transducer  300  includes ultrasonic reflectors  312  at both ends of the arrays of first and second ferroelectric resonators  308  and  310 . The ultrasonic reflectors  312  are formed in the interconnect region  306 , and may include ferroelectric resonators similar to the first and second ferroelectric resonators  308  and  310 . 
     The ultrasonic transducer  300  includes a first transmitter circuit  314   a  which includes first active components  316   a  formed in the semiconductor material  304 , and a second transmitter circuit  314   b  which includes second active components  316   b  formed in the semiconductor material  304 . The first transmitter circuit  314   a  is coupled to the first subarray  346   a  of the first ferroelectric resonators  308 , for example, through the metal interconnect lines and metal vias of the interconnect region  306 . The second transmitter circuit  314   b  is coupled to the second subarray  346   b  of the first ferroelectric resonators  308  in a manner similar to the first transmitter circuit  314   a.    
     The ultrasonic transducer  300  includes a first detector circuit  318   a  which includes third active components  320   a  formed in the semiconductor material  304 , and a second detector circuit  318   b  which includes fourth active components  320   b  formed in the semiconductor material  304 . The first detector circuit  318   a  is coupled to the first subarray  350   a  of the second ferroelectric resonators  310 , for example, through the metal interconnect lines and metal vias of the interconnect region  306 . The second detector circuit  318   b  is coupled to the second subarray  350   b  of the second ferroelectric resonators  310  in a manner similar to the first detector circuit  318   a.    
     The ultrasonic transducer  300  includes a microelectronic package  322  which contains the substrate  302  and the interconnect region  306 . The microelectronic package  322  of this example includes external leads  324 , shown in  FIG.  3 B , which may be solder bumps, by way of example. The first transmitter circuit  314   a , the second transmitter circuit  314   b , the first detector circuit  318   a , and the second detector circuit  318   b  are coupled to the external leads  324  through the metal interconnect lines and metal vias of the interconnect region  306 , in this example. The microelectronic package  322  of this example includes a package material  328  that surrounds the substrate  302  and the interconnect region  306 , and provides support for the external leads  324 . The package material  328  may have a composition as described in reference to the package material  128  of  FIG.  1 A . Other compositions of the package material  328  are within the scope of this example. 
     Referring to  FIG.  3 B , the first and second ferroelectric resonators  308  and  310  may be configured as capacitors with ferroelectric material  330  between plates of the capacitors. The ferroelectric material  330  may have a composition as described in reference to the ferroelectric material  130  of  FIG.  1 B . 
     The first transmitter circuit  314   a  of  FIG.  3 A  is configured to actuate the first subarray  346   a  to produce a first transmitted signal component, and the second transmitter circuit  314   b  of  FIG.  3 A  is configured to actuate the second subarray  346   b  to produce a second transmitted signal component. The first and second transmitted signal components combine in the transmitter grating  348  to provide a transmitted ultrasonic signal  332 . In this example, the transmitted ultrasonic signal  332  may be emitted through a bottom surface  336  of the substrate  302 , as indicated in  FIG.  3 B . The bottom surface  336  of the substrate  302  is located opposite from a top surface  334  of the interconnect region  306 . The transmitted ultrasonic signal  332  is emitted at a transmission angle  338  from a perpendicular direction to a plane of the first ferroelectric resonators  308  and the second ferroelectric resonators  310 . The transmission angle  338  depends on a first phase of the first transmitted signal component with respect to a second phase of the second transmitted signal component. The first transmitter circuit  314   a  may actuate the first subarray  346   a  to provide the first transmitted signal component with the first phase and the second transmitter circuit  314   b  may actuate the second subarray  346   b  to provide the second transmitted signal component with the second phase, to provide a desired value of the transmission angle  338 . The first phase and the second phase may be varied with respect to each other during emission of the transmitted ultrasonic signal  332 , so that the transmission angle  338  varies with time. In one version of this example, the first phase may be constant across all the first ferroelectric resonators  308  in the first subarray  346   a , and the second phase may be constant across all the first ferroelectric resonators  308  in the second subarray  346   b . In another version, the first phase may be varied across all the first ferroelectric resonators  308  in the first subarray  346   a , so that separate instances of the first ferroelectric resonators  308  in the first subarray  346   a  are provided with different values of the first phase, and similarly for the second phase. 
     The first detector circuit  318   a  of  FIG.  3 A  is configured to detect a received ultrasonic signal  340  acquired by the first subarray  350   a  of the second ferroelectric resonators  310  and provide a first detection signal corresponding to the received ultrasonic signal  340 . 
     A received ultrasonic signal  340  induces vibrations in the receiver grating  352  which provides a first received signal component to the first subarray  350   a  of the second ferroelectric resonators  310 , and provides a second received signal component to the second subarray  350   b  of the second ferroelectric resonators  310 . The first detector circuit  318   a  of  FIG.  3 A  is configured to detect the first received signal component acquired by the first subarray  350   a  of the second ferroelectric resonators  310  and provide a first detection signal corresponding to the first received signal component. The second detector circuit  318   b  of  FIG.  3 A  is configured to detect the second received signal component acquired by the second subarray  350   b  of the second ferroelectric resonators  310  and provide a second detection signal corresponding to the first received signal component. The first received signal component has a first phase and the second received signal component has a second phase. A reception angle  354  of the received ultrasonic signal  340  from the perpendicular direction to a plane of the first ferroelectric resonators  308  and the second ferroelectric resonators  310  may be determined from the first and second phases of the first and second received signal components. The received ultrasonic signal  340  of this example may be the transmitted ultrasonic signal  332  after transmission through a fluid, not shown in  FIG.  3 B . 
       FIG.  4    is a cross section of an example ultrasonic transducer  400 , showing details of ferroelectric resonators  408 . The ultrasonic transducer  400  may be implemented in any of the ultrasonic transducers  100 ,  200 , and  300  described in reference to  FIG.  1 A  and  FIG.  1 B ,  FIG.  2 A  and  FIG.  2 B , and  FIG.  3 A  and  FIG.  3 B , respectively. The ultrasonic transducer  400  includes a substrate  402 . The substrate  402  may be manifested as any of the examples described in reference to the substrate  102  of  FIG.  1 A . Other manifestations of the substrate  402  are within the scope of this example. The substrate  402  includes a semiconductor material  404 , such as monocrystalline silicon. The substrate  402  may include field oxide  410 , depicted in  FIG.  4    with a shallow trench isolation (STI) structure, having angled sides extending into the semiconductor material  404 . Alternatively, the field oxide  410  may have a local oxidation of silicon (LOCOS) structure with tapered edges commonly referred to as “birds&#39; beaks”. The ultrasonic transducer  400  includes active components, not shown in  FIG.  4   , such as transistors, in the substrate  402 . 
     The ultrasonic transducer  400  includes an interconnect region  406  on the substrate  402 . The ferroelectric resonators  408  are located in the interconnect region  406 . The ultrasonic transducer  400  of this example includes lower bias lines  412  of polycrystalline silicon  414 , commonly referred to as “polysilicon”, on the field oxide  410 . The polysilicon  414  may be doped to improve a sheet resistance of the lower bias lines  412 . The lower bias lines  412  have metal silicide  416  on the polysilicon  414  to further improve the sheet resistance of the lower bias lines  412 . The metal silicide  416  may include titanium silicide, cobalt silicide, nickel silicide, or tungsten silicide, by way of example. Sidewalls  418  may be formed on sides of the polysilicon  414 , to facilitate fabrication of transistors having the polysilicon  414  for gates. The sidewalls  418  may include silicon nitride, for example. 
     The interconnect region  406  includes a pre-metal dielectric (PMD) layer  420  over the substrate  402  and the lower bias lines  412 . The PMD layer  420  is electrically non-conductive, and may include one or more sublayers of dielectric material. By way of example, the PMD layer  420  may include a PMD liner, not shown, of silicon nitride, on the substrate  402  and the lower bias lines  412 . The PMD layer  420  may also include a planarized layer, not shown, of silicon dioxide-based dielectric material such as silicon dioxide, phosphosilicate glass (PSG), fluorinated silicate glass (FSG), or borophosphosilicate glass (BPSG), on the PMD liner. The PMD layer  420  may further include a PMD cap layer, not shown, of silicon nitride, silicon carbide, or silicon carbonitride, suitable for an etch-stop layer of a chemical-mechanical polish (CMP) stop layer, on the planarized layer. Other layer structures and compositions for the PMD layer  420  are within the scope of this example. The ultrasonic transducer  400  includes a lower hydrogen barrier  422  formed on the PMD layer  420 . The lower hydrogen barrier  422  reduces hydrogen diffusion into the ferroelectric resonators  408  from the PMD layer  420 . The lower hydrogen barrier  422  is electrically non-conductive and may include aluminum oxide or silicon nitride, by way of example. The lower hydrogen barrier  422  may be between 10 and 50 nanometers thick. 
     Contacts  424  of the ultrasonic transducer  400  are formed through the lower hydrogen barrier  422  and the PMD layer  420 , making electrical connections to the lower bias lines  412 . The contacts  424  are electrically conductive, and may include titanium adhesion layers on the lower bias lines  412  and the PMD layer  420 , titanium nitride liners on the titanium adhesion layers, and tungsten cores on the titanium nitride liners. In some versions of this example, the contacts  424  may have lengths significantly greater than widths, as depicted in  FIG.  4   , wherein each of the lower bias lines  412  makes an electrical connection with a single, separate, instance of the contacts  424 , which extends along the lower bias line  412 . In other versions, the contacts  424  may have lengths equal to widths, and a plurality of the contacts  424  may connect to each of the lower bias lines  412 . 
     Each of the ferroelectric resonators  408  includes a lower plate  426  formed on the lower hydrogen barrier  422 , making electrical connections to the contacts  424 . The lower plate  426  may include titanium aluminum nitride and iridium, by way of example. Each of the ferroelectric resonators  408  includes a ferroelectric material  428  on the lower plate  426 . The ferroelectric material  428  may have any of the compositions described in reference to the ferroelectric material  130  of  FIG.  1 B . Each of the ferroelectric resonators  408  includes an upper plate  430  on the ferroelectric material  428 . The upper plate  430  may include titanium aluminum nitride and iridium, by way of example. The upper plate  430  and the lower plate  426  may have similar compositions. The ultrasonic transducer  400  includes an upper hydrogen barrier  432  formed over the ferroelectric resonators  408 . The upper hydrogen barrier  432  is electrically non-conductive and may have a composition and thickness similar to the lower hydrogen barrier  422 . 
     The interconnect region  406  includes a first inter-level dielectric (ILD) layer  434  over the upper hydrogen barrier  432  The first ILD layer  434  is electrically non-conductive. The first ILD layer  434  may include one or more dielectric layers, such as an etch stop layer of silicon nitride, a planarized main dielectric layer of silicon dioxide-based material, and a cap layer of silicon carbonitride, by way of example. Other layer structures and compositions for the first ILD layer  434  are within the scope of this example. 
     The interconnect region  406  includes first vias  436  formed through the first ILD layer  434  and the upper hydrogen barrier  432  to make electrical connections to the upper plates  430 . The first vias  436  are electrically conductive. In some versions of this example, the first vias  436  may have lengths significantly greater than widths, as depicted in  FIG.  4   , wherein a single, separate, instance of the first vias  436  makes an electrical connection with each of the lower bias lines  412 , which extends along the upper plate  430 . In other versions, the first vias  436  may have lengths equal to widths, and a plurality of the first vias  436  may connect to each of the upper plates  430 . In some versions of this example, the first vias  436  may include tantalum nitride barriers and copper fill metal, formed by a damascene process. In other versions, the first vias  436  may include titanium adhesion layers on the upper plate  430  and the first ILD layer  434 , titanium nitride liners on the titanium adhesion layers, and tungsten cores on the titanium nitride liners. Other structures and compositions for the first vias  436  are within the scope of this example. 
     The interconnect region  406  includes a first intra-metal dielectric (IMD) layer  438  formed on the first ILD layer  434 , and first interconnect lines  440  formed on the first vias  436  and laterally surrounded by the first IMD layer  438 . The first IMD layer  438  is electrically non-conductive, and includes one or more silicon dioxide-based dielectric materials. The first interconnect lines  440  are electrically conductive, and may include primarily aluminum with an adhesion layer of titanium nitride and a cap layer of titanium nitride, or may include primarily copper with a barrier liner of tantalum nitride, by way of example. Other compositions and structures for the first IMD layer  438  and the first interconnect lines  440  are within the scope of this example. A plurality of the first interconnect lines  440  are electrically connected to the ferroelectric resonators  408  through the first vias  436 . 
     The interconnect region  406  includes a second ILD layer  442  over the first IMD layer  438  and the first interconnect lines  440 . The interconnect region  406  further includes a second IMD layer  444  formed on the second ILD layer  442 , and second interconnect lines  446  laterally surrounded by the second IMD layer  444 . A plurality of the second interconnect lines  446  may overlie the first interconnect lines  440  that are electrically connected to the ferroelectric resonators  408 , as indicated in  FIG.  4   , which may facilitate acoustically coupling an ultrasonic signal from the ferroelectric resonators  408  through a top surface  448  of the interconnect region  406 . The second IMD layer  444  is electrically non-conductive, and may have a composition and structure similar to the first IMD layer  438 . The second interconnect lines  446  may have a composition and structure similar to the first interconnect lines  440 . Other compositions and structures for the second IMD layer  444  and the second interconnect lines  446  are within the scope of this example. 
     The interconnect region  406  includes a third ILD layer  450  over the second IMD layer  444  and the second interconnect lines  446 . The interconnect region  406  further includes a third IMD layer  452  formed on the third ILD layer  450 , and third interconnect lines  454  laterally surrounded by the third IMD layer  452 . The third IMD layer  452  is electrically non-conductive, and may have a composition and structure similar to the second IMD layer  444 . The third interconnect lines  454  may have a composition and structure similar to the second interconnect lines  446 . Other compositions and structures for the third IMD layer  452  and the third interconnect lines  454  are within the scope of this example. In this example, the interconnect region  406  may be free of the third interconnect lines  454  directly over the ferroelectric resonators  408 , as indicated in  FIG.  4   . 
     The interconnect region  406  may include additional interconnect levels above the third IMD layer  452  and the third interconnect lines  454 , with each interconnect level having an ILD level, an IMD level on the ILD level, and interconnect lines on the ILD level, surrounded by the IMD level. The interconnect region  406  further includes a protective overcoat (PO) layer over all the interconnect levels, extending to the top surface  448  of the interconnect region  406 . The PO layer  456  includes one or more layers of dielectric material, such as silicon dioxide, silicon nitride, silicon oxynitride, aluminum oxide, and polyimide. The PO layer  456  may have openings, not shown, for bond pads, not shown; the bond pads provide external connections for the active components in the substrate  402 . The ultrasonic transducer  400  may include a package material, similar to the package material  128  of  FIG.  1 A  and  FIG.  1 B , not shown in  FIG.  4   , surrounding the substrate  402  and the interconnect region  406 . The ultrasonic transducer  400  may further include external leads, similar to the external leads  124  of  FIG.  1 A , not shown in  FIG.  4   , that are electrically connected to the bond pads. 
       FIG.  5    is a cross section of an example ultrasonic fluid flow measurement system  500 . The ultrasonic fluid flow measurement system  500  includes an ultrasonic transducer  502 . The ultrasonic transducer  502  includes an array of ferroelectric resonators  504 . The ultrasonic transducer  502  may be similar to any of the ultrasonic transducers  100 ,  200 , and  300  described in reference to  FIG.  1 A  and  FIG.  1 B ,  FIG.  2 A  and  FIG.  2 B , and  FIG.  3 A  and  FIG.  3 B , respectively. The ultrasonic transducer  502  is acoustically coupled to a fluid flow channel  506 . The ultrasonic transducer  502  may be acoustically coupled to the fluid flow channel  506  through an ultrasonic coupling material  508  such as an ultrasonic gel or an adhesive. The ultrasonic transducer  502  may be removably coupled to the fluid flow channel  506  or may be permanently attached to the fluid flow channel  506 . During operation of the ultrasonic fluid flow measurement system  500 , a fluid  510  may be flowing through the fluid flow channel  506 . The fluid flow channel  506  has a fluid boundary surface  512  which contacts the fluid  510 . The array of ferroelectric resonators  504  is parallel to the fluid boundary surface  512 . 
     The fluid  510  contains particles  514  which flow with the fluid  510 . The particles  514  thus have velocities with respect to the ultrasonic transducer  502 , as indicated schematically in  FIG.  5   . During operation of the ultrasonic fluid flow measurement system  500 , the ultrasonic transducer  502  may provide a first transmitted ultrasonic signal  516   a . The first transmitted ultrasonic signal  516   a  is transmitted into the fluid  510  at a first angle  518   a  to a perpendicular direction from the fluid boundary surface  512 . The first transmitted ultrasonic signal  516   a  may be reflected off one or more of the particles  514 , referred to as first reflecting particles  514   a , to provide a first received ultrasonic signal  520   a  which is acquired by the ultrasonic transducer  502 . In the configuration depicted in  FIG.  5   , the first reflecting particles  514   a  are decreasing a first separation between the first reflecting particles  514   a  and the ultrasonic transducer  502 , so a frequency of the first received ultrasonic signal  520   a  has a higher frequency than the first transmitted ultrasonic signal  516   a , due to the Doppler effect. A first speed of the first reflecting particles  514   a  in the fluid  510  may be estimated using a difference in the frequency of the first received ultrasonic signal  520   a  and the first transmitted ultrasonic signal  516   a . In one version of this example, the first and second transmitted ultrasonic signals  516   a  and  516   b  may be provided as continuous signals at a constant frequency. In another version of this example, the first and second transmitted ultrasonic signals  516   a  and  516   b  may be provided as transmitted bursts, and a first time period between transmission of the first transmitted ultrasonic signal  516   a  by the ultrasonic transducer  502  and acquisition of the first received ultrasonic signal  520   a  by the ultrasonic transducer  502  is a function of the first separation between the first reflecting particles  514   a  and the ultrasonic transducer  502 , a speed of the first transmitted ultrasonic signal  516   a  in the fluid  510 , and a speed of the first received ultrasonic signal  520   a  in the fluid  510 . The first separation between the first reflecting particles  514   a  and the ultrasonic transducer  502  may be estimated using the first time period between transmission of the first transmitted ultrasonic signal  516   a  and acquisition of the first received ultrasonic signal  520   a , the speed of the first transmitted ultrasonic signal  516   a , and the speed of the first received ultrasonic signal  520   a.    
     Also during operation of the ultrasonic fluid flow measurement system  500 , the ultrasonic transducer  502  may provide a second transmitted ultrasonic signal  516   b . The second transmitted ultrasonic signal  516   b  is transmitted into the fluid  510  at a second angle  518   b  to the perpendicular direction from the fluid boundary surface  512 . The second transmitted ultrasonic signal  516   b  may be reflected off one or more of the particles  514 , referred to as second reflecting particles  514   b , to provide a second received ultrasonic signal  520   b  which is acquired by the ultrasonic transducer  502 . In the configuration depicted in  FIG.  5   , the second reflecting particles  514   b  are increasing a separation between the second reflecting particles  514   b  and the ultrasonic transducer  502 , so a frequency of the second received ultrasonic signal  520   b  has a lower frequency than the second transmitted ultrasonic signal  516   b , due to the Doppler effect. 
       FIG.  6    is a chart  600  depicting example waveforms of the transmitted ultrasonic signals  516   a  and  516   b  and the received ultrasonic signals  520   a  and  520   b , described in reference to  FIG.  5   . In this example, the first transmitted ultrasonic signal  516   a  may be provided as transmitted bursts  602  of pulses at an average transmitted frequency f t , separated by quiescent periods  604 . The second transmitted ultrasonic signal  516   a  may be provided as transmitted bursts  602  and quiescent periods  604 , concurrent with the first transmitted ultrasonic signal  516   a.    
     The first received ultrasonic signal  520   a  may be manifested as first received bursts  606  of pulses at a first average received frequency f r1  that is higher than the average transmitted frequency f t  of the transmitted bursts  602  of the first transmitted ultrasonic signal  516   a . A detector circuit of the ultrasonic transducer  502  of  FIG.  5    is configured to provide a first detection signal corresponding to the first received bursts  606 . The first detection signal may be a frequency shift signal corresponding to a difference between the average transmitted frequency f t a nd the first average received frequency f r1 . A speed v 1  of the first reflecting particles  514   a  of  FIG.  5    may be estimated using equation 1: 
         v   1   =c   1 ×( f   r1   −f   t )/[2× f   t ×sin(θ 1 )]  Equation 1
 
     Where: 
     C 1  is the average speed of the first transmitted ultrasonic signal  516   a  and the first received ultrasonic signal  520   a  in the fluid  510 , and 
     θ 1  is the first angle  518   a  of the first transmitted ultrasonic signal  516   a , shown in  FIG.  5   . 
     The second received ultrasonic signal  520   b  may be manifested as second received bursts  608  of pulses at a second average received frequency f r2  that is lower than the average transmitted frequency f t  of the transmitted bursts  602  of the second transmitted ultrasonic signal  516   b . The detector circuit of the ultrasonic transducer  502  is configured to provide a second detection signal corresponding to the second received bursts  608 . The second detection signal may be a frequency shift signal corresponding to a difference between the average transmitted frequency f t  and the second average received frequency f r2 . A speed v 2  of the second reflecting particles  514   b  of  FIG.  5    may be estimated using equation 2: 
         v   2   =c   2 ×( f   r2   −f   t )/[2× f   t ×sin(θ 2 )]  Equation 2
 
     Where: 
     C 2  is the average speed of the second transmitted ultrasonic signal  516   b  and the second received ultrasonic signal  520   b  in the fluid  510 ; generally, c 2  and c 2  are equal, and 
     θ 2  is the second angle  518   b  of the second transmitted ultrasonic signal  516   b , shown in  FIG.  5   . 
     Other methods for estimating the speeds v 1  and v 2  are within the scope of this example. The method described in reference to  FIG.  6    may also be used to count the particles  514  of  FIG.  5    as the particles  514  flow by the ultrasonic transducer  502 , by counting the received bursts  606  and  608 . 
       FIG.  7    is a chart  700  depicting example frequency spectra of the transmitted ultrasonic signals  516   a  and  516   b  and the received ultrasonic signals  520   a  and  520   b , described in reference to  FIG.  5   . In this example, the first and second transmitted ultrasonic signals  516   a  and  516   b  may be provided as continuous signals or bursts. The first transmitted ultrasonic signal  516   a  has a first transmitted bandwidth  702  at the average ultrasonic frequency f t . The first transmitted bandwidth  702  may reflect shaping of the transmitted bursts  602  of  FIG.  6   . Similarly, the second transmitted ultrasonic signal  516   b  has a second transmitted bandwidth  704  at the average ultrasonic frequency f t . The first received ultrasonic signal  520   a  has a second received bandwidth  704  at the first average received frequency f r1 . The first received bandwidth  706  is larger than the first transmitted bandwidth  702 , due at least in part to variations in the speed v 1  of the first reflecting particles  514   a  of  FIG.  5   . Similarly, the second received bandwidth  708  is larger than the second transmitted bandwidth  704 , due at least in part to variations in the speed v 2  of the second reflecting particles  514   b  of  FIG.  5   . 
       FIG.  8    is a cross section of another example ultrasonic fluid flow measurement system  800 . The ultrasonic fluid flow measurement system  800  includes an ultrasonic transducer  802 . The ultrasonic transducer  802  includes an array of ferroelectric resonators  804 . The ultrasonic transducer  802  may be similar to the ultrasonic transducer  300  described in reference to  FIG.  3 A  and  FIG.  3 B , for example. The ultrasonic transducer  802  is acoustically coupled to a fluid flow channel  806 . During operation of the ultrasonic fluid flow measurement system  800 , a fluid  810  may be flowing through the fluid flow channel  806 . The fluid flow channel  806  has a fluid boundary surface  812  which contacts the fluid  810 . The array of ferroelectric resonators  804  is parallel to the fluid boundary surface  812 . 
     The fluid  810  contains a particles  814 , including a reflecting particle  814   a  which flows with the fluid  810  at speed v, as indicated schematically in  FIG.  8   . During operation of the ultrasonic fluid flow measurement system  800 , the ultrasonic transducer  802  may provide a first transmitted ultrasonic signal  816   a  at a first angle  818   a  at a first time t 1 . The first angle  818   a  is determined with respect to a perpendicular direction from the fluid boundary surface  812 . The first transmitted ultrasonic signal  816   a  may be reflected off the reflecting particles  814   a  to provide a first received ultrasonic signal  820   a  which is acquired by the ultrasonic transducer  802  after a first delay time Δt 1 . A distance r 1  between the ultrasonic transducer  802  and the reflecting particles  814   a  at the time t 1  may be estimated using equation 3: 
         r   1   =Δt   1   ×c/ 2  Equation 3
 
     Where C is the average speed of the first transmitted ultrasonic signal  516   a  and the first received ultrasonic signal  520   a  in the fluid  510  at rest. 
     At a later time t 2 , the ultrasonic transducer  802  may provide a second transmitted ultrasonic signal  816   b  at a second angle  818   b . In  FIG.  8   , the second angle  818   b  is zero, that is, the second transmitted ultrasonic signal  816   b  is directed along the perpendicular direction from the fluid boundary surface  812 . The second transmitted ultrasonic signal  816   b  may be reflected off the reflecting particles  814   a  to provide a second received ultrasonic signal  820   b  which is acquired by the ultrasonic transducer  802  after a second delay time Δt 2 . A distance r 2  between the ultrasonic transducer  802  and the reflecting particles  814   a  at the time t 2  may be estimated using equation 3 by substituting Δt 2  for Δt 1 . 
     A speed v p  of the reflecting particles  814   a  may be estimated using equation 4: 
         v   p =[ r   2  sin(θ 2 )− r   1  sin(θ 1 )]/( t   2   −t   1 )  Equation 4
 
     Where: 
     θ 1  is the first angle  818   a  of the first transmitted ultrasonic signal  816   a , shown in  FIG.  8   , and 
     θ 2  is the second angle  818   b  of the second transmitted ultrasonic signal  816   b , shown in  FIG.  8   . 
     Other methods for estimating the distances r 1  and r 2  and estimating the speed v p  using the delay times Δt 1  and Δt 2  and the angles  818   a  and  818   b  are within the scope of this example. 
       FIG.  9    is a chart  900  depicting example waveforms of the transmitted ultrasonic signals  816   a  and  816   b  and the received ultrasonic signals  820   a  and  820   b , described in reference to  FIG.  8   . In this example, the first transmitted ultrasonic signal  816   a  may be provided as a burst of pulses at time t 1 , followed by the second transmitted ultrasonic signal  816   a , also manifested as a burst of pulses, at time t 2 , separated by a and quiescent period. 
     The first received ultrasonic signal  820   a  may be manifested as a first burst of pulses, received at time t 1 +Δt 1 , that is, the first received ultrasonic signal  820   a  is received after the delay Δt 1 , as indicated in  FIG.  9   . Similarly, the second received ultrasonic signal  820   b  may be manifested as a second burst of pulses, received at time t 2 +Δt 2 , as indicated in  FIG.  9   . A detector circuit of the ultrasonic transducer  802  of  FIG.  8    is configured to provide a first detection signal corresponding to the first received ultrasonic signal  820   a . The first detection signal may be a first delay time signal corresponding to the time difference Δt 1  between emission of the first transmitted ultrasonic signal  816   a  and detection of the first received ultrasonic signal  820   a . Similarly, the detector circuit is configured to provide a second detection signal corresponding to the second received ultrasonic signal  820   b ; the first detection signal may be a second delay time signal corresponding to the time difference Δt 2  between emission of the second transmitted ultrasonic signal  816   b  and detection of the second received ultrasonic signal  820   b.    
     The method described in reference to  FIG.  9    may also be used to count the particles  814  of  FIG.  8    as the particles  814  flow by the ultrasonic transducer  802 , by counting the received ultrasonic signals  820   a  and  820   b.    
       FIG.  10    is a cross section of another example ultrasonic fluid flow measurement system  1000 . The ultrasonic fluid flow measurement system  1000  of this example includes a first ultrasonic transducer  1002   a  and a second ultrasonic transducer  1002   b . The first ultrasonic transducer  1002   a  includes a first array of ferroelectric resonators  1004   a , and the second ultrasonic transducer  1002   b  includes a second array of ferroelectric resonators  1004   b . The ultrasonic transducers  1002   a  and  1002   b  may be similar to any of the ultrasonic transducers  100 ,  200 , and  300  described in reference to  FIG.  1 A  and  FIG.  1 B ,  FIG.  2 A  and  FIG.  2 B , and  FIG.  3 A  and  FIG.  3 B , respectively. The first ultrasonic transducer  1002   a  and the second ultrasonic transducer  1002   b  are acoustically coupled to opposite sides of a fluid flow channel  1006 , and laterally displaced from each other, as depicted in  FIG.  10   . During operation of the ultrasonic fluid flow measurement system  1000 , a fluid  1010  may be flowing at speed v through the fluid flow channel  1006 . The fluid flow channel  1006  has a first fluid boundary surface  1012   a  adjacent to the first ultrasonic transducer  1002   a , and a second fluid boundary surface  1012   b  adjacent to the second ultrasonic transducer  1002   b . The fluid  1010  contacts the first fluid boundary surface  1012   a  and the second fluid boundary surface  1012   b . The first array of ferroelectric resonators  1004   a  is parallel to the first fluid boundary surface  1012   a , and the second array of ferroelectric resonators  1004   b  is parallel to the second fluid boundary surface  1012   b . The first fluid boundary surface  1012   a  is separated from the second fluid boundary surface  1012   b  by a distance w  1022  in a direction perpendicular to the first fluid boundary surface  1012   a  and the second fluid boundary surface  1012   b.    
     During operation of the ultrasonic fluid flow measurement system  1000 , the first ultrasonic transducer  1002   a  provides a first transmitted ultrasonic signal  1016   a  at a first angle  1018   a  toward the second ultrasonic transducer  1002   b , at a first time t 1 . The first angle  1018   a  is determined with respect to a perpendicular direction from the first fluid boundary surface  1012   a . The first transmitted ultrasonic signal  1016   a  provides a first received ultrasonic signal  1020   a  which is acquired by the second ultrasonic transducer  1002   b  after a first delay time Δt 1 . The first transmitted ultrasonic signal  1016   a  travels in a direction that is partially aligned with the flow of the fluid  1010 , so that the first delay time Δt 1  is less than a delay time when the fluid  1010  is not moving in the fluid flow channel  1006 . 
     Also during operation of the ultrasonic fluid flow measurement system  1000 , the second ultrasonic transducer  1002   b  provides a second transmitted ultrasonic signal  1016   b  at a second angle  1018   b  toward the first ultrasonic transducer  1002   a , at a second time t 2 . The second angle  1018   b  is determined with respect to a perpendicular direction from the second fluid boundary surface  1012   b , and is equal to the first angle  1018   b  when the first fluid boundary surface  1012   a  is parallel to the second fluid boundary surface  1012   b . The second transmitted ultrasonic signal  1016   b  provides a second received ultrasonic signal  1020   b  which is acquired by the first ultrasonic transducer  1002   a  after a second delay time Δt 2 . The second transmitted ultrasonic signal  1016   b  travels in a direction that is partially opposite to the flow of the fluid  1010 , so that the second delay time Δt 2  is greater than the delay time when the fluid  1010  is not moving in the fluid flow channel  1006 . 
       FIG.  11    is a chart  1100  depicting example waveforms of the transmitted ultrasonic signals  1016   a  and  1016   b  and the received ultrasonic signals  1020   a  and  1020   b , described in reference to  FIG.  10   . In this example, the first transmitted ultrasonic signal  1016   a  may be provided as a burst of pulses at time t 1 , which provides the first received ultrasonic signal  1020   a  after the first time delay Δt 1 . Similarly, the second transmitted ultrasonic signal  1016   b  may be provided as a burst of pulses at time t 2 , which provides the second received ultrasonic signal  1020   b  after the second time delay Δt 2 . 
     For the case when the first fluid boundary surface  1012   a  and the second fluid boundary surface  1012   b  of  FIG.  10    are parallel, the speed v of the fluid  1010  through the fluid flow channel  1006  may be estimated using Equation 5: 
         v =[ w /(2×sin(θ)×sin(θ))]×[(Δ t   2   −Δt   10 )/(Δ t   2   ×Δt   1 )]  Equation 5
 
     Where θ is the first angle  1018   a  and the second angle  1018   b.    
       FIG.  12    is a cross section of another example ultrasonic fluid flow measurement system  1200 . The ultrasonic fluid flow measurement system  1200  of this example includes a first ultrasonic transducer  1202   a  and a second ultrasonic transducer  1202   b . The first ultrasonic transducer  1202   a  and a second ultrasonic transducer  1202   b  may optionally be joined by a connection structure  1224 , as indicated in  FIG.  12   . The first ultrasonic transducer  1202   a  includes a first array of ferroelectric resonators  1204   a , and the second ultrasonic transducer  1202   b  includes a second array of ferroelectric resonators  1204   b . The ultrasonic transducers  1202   a  and  1202   b  may be similar to any of the ultrasonic transducers  100 ,  200 , and  300  described in reference to  FIG.  1 A  and  FIG.  1 B ,  FIG.  2 A  and  FIG.  2 B , and  FIG.  3 A  and  FIG.  3 B , respectively. The first ultrasonic transducer  1202   a  and the second ultrasonic transducer  1202   a  are acoustically coupled to a first side of a fluid flow channel  1206 , and laterally displaced from each other, as depicted in  FIG.  12   . During operation of the ultrasonic fluid flow measurement system  1200 , a fluid  1210  may be flowing through the fluid flow channel  1206 . The fluid flow channel  1206  has a first fluid boundary surface  1212   a  adjacent to the first ultrasonic transducer  1202   a  and a second fluid boundary surface  1212   b  adjacent to the second ultrasonic transducer  1202   b . The first fluid boundary surface  1212   a  and the second fluid boundary surface  1212   b  are located on a same side of the fluid flow channel  1206 . The fluid flow channel  1206  has a third fluid boundary surface  1212   c  located opposite from the first fluid boundary surface  1212   a  and the second fluid boundary surface  1212   b . The fluid  1210  contacts the first fluid boundary surface  1212   a , the second fluid boundary surface  1212   b , and the third fluid boundary surface  1212   c . The first array of ferroelectric resonators  1204   a  and the second array of ferroelectric resonators  1204   b  are parallel to the first fluid boundary surface  1212   a  and the second fluid boundary surface  1212   b , respectively. The first fluid boundary surface  1212   a  and the second fluid boundary surface  1212   b  are parallel to the third fluid boundary surface  1212   c.    
     During operation of the ultrasonic fluid flow measurement system  1200 , the first ultrasonic transducer  1202   a  provides a first transmitted ultrasonic signal  1216   a  at a first angle  1218   a  through the fluid  1210  toward the third fluid boundary surface  1212   c . The first transmitted ultrasonic signal  1216   a  reflects off the third fluid boundary surface  1212   c  and travels through the fluid  1210  toward the second ultrasonic transducer  1202   b . The first angle  1218   a  is determined with respect to a perpendicular direction from the first fluid boundary surface  1212   a . The first transmitted ultrasonic signal  1216   a  provides a first received ultrasonic signal  1220   a  which is acquired by the second ultrasonic transducer  1202   b  after a first delay time Δt 1 . The first transmitted ultrasonic signal  1216   a  travels in a direction that is partially aligned with the flow of the fluid  1210 , so that the first delay time Δt 1  is less than a delay time when the fluid  1210  is not moving in the fluid flow channel  1206 . 
     Also during operation of the ultrasonic fluid flow measurement system  1200 , the second ultrasonic transducer  1202   b  provides a second transmitted ultrasonic signal  1216   b  at a second angle  1218   b  toward the third fluid boundary surface  1212   c . The second transmitted ultrasonic signal  1216   b  reflects off the third fluid boundary surface  1212   c  and travels through the fluid  1210  toward the first ultrasonic transducer  1202   a . The second angle  1218   b  is determined with respect to a perpendicular direction from the second fluid boundary surface  1212   b , and is equal to the first angle  1218   b . The second transmitted ultrasonic signal  1216   b  provides a second received ultrasonic signal  1220   b  which is acquired by the first ultrasonic transducer  1202   a  after a second delay time Δt 2 . The second transmitted ultrasonic signal  1216   b  travels in a direction that is partially opposite to the flow of the fluid  1210 , so that the second delay time Δt 2  is greater than the delay time when the fluid  1210  is not moving in the fluid flow channel  1206 . 
     A speed of the fluid  1210  though the fluid flow channel  1206  may be estimated using the first delay time Δt 1  and the second delay time Δt 2 , in a manner analogous to the method described in reference to  FIG.  10    and  FIG.  11   . Having the first ultrasonic transducer  1202   a  and the second ultrasonic transducer  1202   b  joined by the connection structure  1224  may advantageously facilitate installation of the ultrasonic fluid flow measurement system  1200 . 
       FIG.  13    depicts a cutaway view of an example ultrasonic fluid flow measurement system  1300 . The ultrasonic fluid flow measurement system  1300  includes an ultrasonic transducer  1302  having an array of ferroelectric resonators  1304 . The ultrasonic transducer  1302  may be similar to any of the ultrasonic transducers  100 ,  200 , and  300  described in reference to  FIG.  1 A  and  FIG.  1 B ,  FIG.  2 A  and  FIG.  2 B , and  FIG.  3 A  and  FIG.  3 B , respectively. The ultrasonic fluid flow measurement system  1300  of this example includes a fluid flow channel  1306  permanently attached to the ultrasonic transducer  1302 . The ultrasonic transducer  1302  may extend through a portion of the fluid flow channel  1306 , so that the ultrasonic transducer  1302  is exposed to a fluid  1310  flowing through the fluid flow channel  1306  during operation of the ultrasonic fluid flow measurement system  1300 . A surface of the ultrasonic transducer  1302  that is exposed in the fluid flow channel  1306  provides a fluid boundary surface  1312  parallel to the array of ferroelectric resonators  1304 . The ultrasonic fluid flow measurement system  1300  may operate as described in reference to either of the ultrasonic fluid flow measurement systems  500  or  800 , described in reference to  FIG.  5    through  FIG.  7   , or  FIG.  8    and  FIG.  9   , respectively. 
     The ultrasonic fluid flow measurement system  1300  may include an interface board  1326  which provides connections to the ultrasonic transducer  1302 . The interface board  1326  may include communication circuitry which enable communication of the ultrasonic fluid flow measurement system  1300  with a user interface  1328 , depicted in  FIG.  13    as a laptop computer. Other manifestations of the user interface  1328  are within the scope of this example. The ultrasonic fluid flow measurement system  1300  may communicate with the user interface  1328  through a communication channel  1330 , which may be implemented as a wiring cable, a fiber optic cable, a cellular phone channel, or a wireless channel using a protocol such as IEEE 802.15.1, commonly referred to as Bluetooth, or IEEE 802.11, commonly referred to as WiFi or WLAN. Other modes of communication for the communication channel  1330  between the ultrasonic fluid flow measurement system  1300  and the user interface  1328  are within the scope of this example. 
       FIG.  14    depicts a cutaway view of another example ultrasonic fluid flow measurement system  1400 . The ultrasonic fluid flow measurement system  1400  includes an ultrasonic transducer  1402  having an array of ferroelectric resonators  1404 . The ultrasonic transducer  1402  may be similar to any of the ultrasonic transducers  100 ,  200 , and  300  described in reference to  FIG.  1 A  and  FIG.  1 B ,  FIG.  2 A  and  FIG.  2 B , and  FIG.  3 A  and  FIG.  3 B , respectively. The ultrasonic transducer  1402  is acoustically coupled to a fluid flow channel  1406 ; the ultrasonic transducer  1402  may be permanently or removably attached to the fluid flow channel  1406 . 
     The fluid flow channel  1406  has a fluid boundary surface  1412  adjacent to, and parallel to, the array of ferroelectric resonators  1404 . The fluid flow channel  1406  of this example has an fluid inlet  1432 , a first fluid outlet  1434 , and a second fluid outlet  1436 . During operation of the ultrasonic fluid flow measurement system  1400 , a fluid  1410  flows into the fluid flow channel  1406  through the fluid inlet  1432 , and flows out of the fluid flow channel  1406  through the first fluid outlet  1434  and the second fluid outlet  1436 . The fluid  1410  includes particles  1438  that flow with the fluid  1410  through the fluid flow channel  1406 . The ultrasonic transducer  1402  is located proximate to a junction between the fluid inlet  1432 , the first fluid outlet  1434 , and the second fluid outlet  1436 , so as to enable the ultrasonic transducer  1402  to measure speeds of the particles  1438  in the fluid inlet  1432  and in the first fluid outlet  1434 , in the second fluid outlet  1436 , or in both the first fluid outlet  1434  and the second fluid outlet  1436 . The ultrasonic fluid flow measurement system  1400  may operate as described in reference to either of the ultrasonic fluid flow measurement systems  500  or  800 , described in reference to  FIG.  5    through  FIG.  7   , or  FIG.  8    and  FIG.  9   , respectively. 
     The ultrasonic fluid flow measurement system  1400  may communicate with a user interface  1428 , depicted in  FIG.  14    as a handheld device such as a smart phone. Other manifestations of the user interface  1428  are within the scope of this example. The ultrasonic fluid flow measurement system  1400  may communicate with the user interface  1428  through a communication channel  1430 , which may be implemented as any of the examples described in reference to the communication channel  1330  of  FIG.  13   . Other modes of communication between the ultrasonic fluid flow measurement system  1400  and the user interface  1428  are within the scope of this example. 
       FIG.  15    depicts another example ultrasonic fluid flow measurement system  1500 . The ultrasonic fluid flow measurement system  1500  of this example may be used to measure flow of blood in a live subject  1540 . The ultrasonic fluid flow measurement system  1500  includes an ultrasonic transducer  1502  having an array of ferroelectric resonators  1504 . The ultrasonic transducer  1502  may be similar to any of the ultrasonic transducers  100 ,  200 , and  300  described in reference to  FIG.  1 A  and  FIG.  1 B ,  FIG.  2 A  and  FIG.  2 B , and  FIG.  3 A  and  FIG.  3 B , respectively. The ultrasonic transducer  1502  is acoustically coupled to a fluid flow channel  1506 ; the ultrasonic transducer  1502  of this example is manifested as an artery of the live subject  1540 , as indicated in  FIG.  15   . The ultrasonic fluid flow measurement system  1500  may operate as described in reference to either of the ultrasonic fluid flow measurement systems  500  or  800 , described in reference to  FIG.  5    through  FIG.  7   , or  FIG.  8    and  FIG.  9   , respectively. The ultrasonic fluid flow measurement system  1500  may communicate with a user interface  1528 , depicted in  FIG.  15    as a remote server. Other manifestations of the user interface  1528  are within the scope of this example. The ultrasonic fluid flow measurement system  1500  may communicate with the user interface  1528  through a communication channel  1530 , which may be implemented as any of the examples described in reference to the communication channel  1330  of  FIG.  13   . Other modes of communication between the ultrasonic fluid flow measurement system  1500  and the user interface  1528  are within the scope of this example. Modifications are possible in the described embodiments, and other embodiments are possible, within the scope of the claims.