Patent Publication Number: US-2023136347-A1

Title: Method of modifying a resonant frequency in cantilever sensors

Description:
INCORPORATION BY REFERENCE TO ANY PRIORITY APPLICATIONS 
     Any and all applications for which a foreign or domestic priority claim is identified in the Application Data Sheet as filed with the present application are hereby incorporated by reference under 37 CFR 1.57. 
     BACKGROUND 
     Field 
     The present disclosure is directed to cantilever sensors for use with devices, such as piezoelectric microelectromechanical systems (MEMS) microphones, and in particular to cantilever sensors with modified resonance frequency and to a method for modifying the resonance frequency of (e.g., piezoelectric) cantilever sensors. 
     Description of the Related Art 
     A MEMS microphone is a micro-machined electromechanical device used to convert sound pressure (e.g., voice sound) to an electrical signal (e.g., voltage). MEMS microphones are widely used in mobile devices, headsets, smart speakers and other voice-interface devices or systems. Conventional capacitive MEMS microphones suffer from high power consumption (e.g., large bias voltage) and reliability, for example when used in a harsh environment (e.g., when exposed to dust and/or water). 
     Piezoelectric MEMS microphones have been used to address the deficiencies of capacitive MEMS microphones. Piezoelectric MEMS microphones offer a constant listening capability while consuming almost no power (e.g., no bias voltage is needed), are robust and immune to water and dust contamination. Existing piezoelectric MEMS microphones include cantilever MEMS structures, and are mostly based on sputter-deposited thin film piezoelectric structure. Piezoelectric MEMS microphones use piezoelectric cantilever sensors to convert acoustic pressure into electrical signals. 
     SUMMARY 
     Accordingly, there is a need for a method of making a (piezoelectric) cantilever sensor with modified resonant frequency. 
     In accordance with one aspect of the disclosure, a cantilever sensor (e.g., piezoelectric sensor) includes a beam with a sensor or electrode at a proximal end and a tip that extends from the sensor to the distal (unsupported) end of the beam, where the tip is modified to modify (e.g., tune) the resonant frequency of the cantilever sensor. In one implementation, the resonant frequency of the sensor is increased by using a material for the tip with a higher stiffness (e.g., a higher Young&#39;s Modulus) and/or a lower mass or density. In another implementation, the resonant frequency of the cantilever sensor is decreased by using a material for the tip with a lower stiffness (e.g., a lower Young&#39;s Modulus) and/or a higher mass or density. In another implementation, the resonant frequency of the sensor is increased by modifying the shape of the tip to have a higher stiffness in one direction (e.g., in a z direction). 
     In accordance with one aspect of the disclosure, there is a need for an acoustic device with piezoelectric cantilever sensors with modified resonant frequency, for example, a piezoelectric MEMS microphone. 
     In accordance with one aspect of the disclosure, a cantilever sensor with increased resonant frequency is provided. The cantilever sensor comprises a substrate and a beam having a proximal portion attached to the substrate and extending to an unsupported distal end of the beam. An electrode is disposed on or in the proximal portion of the beam, a tip of the beam extending distally of the electrode, where at least a portion of the tip has a greater height in a Z direction transverse to a length of the beam than the proximal portion of the beam. 
     In accordance with another aspect of the disclosure, a piezoelectric microelectromechanical systems (MEMS) microphone is provided. The piezoelectric MEMS microphone comprises a substrate and a plurality of piezoelectric sensors movably coupled to the substrate. Each of the piezoelectric sensors is spaced apart from an adjacent piezoelectric sensor by a gap and includes: a beam having a proximal portion attached to the substrate and extending to an unsupported distal end of the beam, and an electrode disposed on or in the proximal portion of the beam, a tip of the beam extending distally of the electrode. At least a portion of the tip has a greater height in a Z direction transverse to a length of the beam than the proximal portion of the beam. The plurality of piezoelectric sensors are configured to deflect when subjected to sound pressure. 
     In accordance with another aspect of the disclosure, an audio subsystem is provided. The audio subsystem comprises an audio codec and one or more piezoelectric microelectromechanical systems microphones in communication with the audio codec. Each microphone includes: a substrate and a plurality of piezoelectric sensors movably coupled to the substrate, each of the piezoelectric sensors spaced apart from an adjacent piezoelectric sensor by a gap and including a beam having a proximal portion attached to the substrate and extending to an unsupported distal end of the beam, a tip of the beam extending distally of the electrode. At least a portion of the tip has a greater height in a Z direction transverse to a length of the beam than the proximal portion of the beam. 
     In accordance with another aspect of the disclosure, a method of making a cantilever sensor is provided. The method comprises forming or providing a beam extending between a proximal portion and a distal end, and forming or providing an electrode. The method also comprises attaching the electrode to a proximal portion of the beam, a distal portion of the beam between the electrode and distal end defining a tip of the sensor, and attaching the beam to a substrate in cantilever form so that the proximal portion of the beam is anchored to the substrate and the distal end of the beam is unsupported. Forming or providing the beam includes tuning the sensor to a desired resonant frequency by forming at least the tip of the beam of a material having one or both of a density and Young&#39;s modulus that provides the desired resonant frequency. 
     In accordance with another aspect of the disclosure, a method of making a cantilever sensor is provided. The method comprises forming or providing a beam extending between a proximal portion and a distal end, and forming or providing an electrode. The method also comprises attaching the electrode to a proximal portion of the beam, a distal portion of the beam between the electrode and distal end defining a tip of the sensor, and attaching the beam to a substrate in cantilever form so that the proximal portion of the beam is anchored to the substrate and the distal end of the beam is unsupported. Forming or providing the beam includes forming at least the tip of the beam so that it has a greater height in a Z direction transverse to a length of the beam than the proximal portion of the beam to thereby tune a resonant frequency of the sensor. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1 A  is a schematic top view of a substrate and sensors for a piezoelectric MEMS microphone. 
         FIG.  1 B  is a schematic side view of the substrate and sensors for the piezoelectric MEMS microphone of  FIG.  1 A . 
         FIG.  2    is a schematic side view of a cantilever sensor. 
         FIG.  3    is a plot of acoustic response, showing decibels (dB) versus frequency for a piezoelectric cantilever sensor. 
         FIG.  4    is a table graph of resonant frequency, voltage output and deflection relative to density and Young&#39;s Modulus for a cantilever sensor. 
         FIG.  5 A  is a schematic side view of a conventional piezoelectric cantilever sensor. 
         FIG.  5 B  is a schematic transverse cross-sectional view of the conventional piezoelectric cantilever sensor of  FIG.  5 A . 
         FIG.  6 A  is a schematic side view of a cantilever sensor. 
         FIG.  6 B  is a schematic transverse cross-sectional view of the cantilever sensor of  FIG.  6 A . 
         FIG.  7 A  is a schematic side view of a cantilever sensor. 
         FIG.  7 B  is a schematic transverse cross-sectional view of the cantilever sensor of  FIG.  7 A . 
         FIG.  8 A  is a schematic side view of a cantilever sensor. 
         FIG.  8 B  is a schematic transverse cross-sectional view of the cantilever sensor of  FIG.  8 A . 
         FIG.  9 A  is a schematic side view of a cantilever sensor. 
         FIG.  9 B  is a schematic transverse cross-sectional view of the cantilever sensor of  FIG.  9 A . 
         FIG.  10 A  is a flow diagram of a method of tuning a cantilever sensor. 
         FIG.  10 B  is a flow diagram of a method of tuning a cantilever sensor. 
         FIG.  11    is a schematic diagram of an audio subsystem. 
         FIG.  12    is a schematic diagram of an electronic device. 
         FIG.  13    is a schematic diagram of a wireless electronic device. 
     
    
    
     DETAILED DESCRIPTION 
     The following detailed description of certain embodiments presents various descriptions of specific embodiments. However, the innovations described herein can be embodied in a multitude of different ways, for example, as defined and covered by the claims. In this description, reference is made to the drawings were like reference numerals can indicate identical or functionally similar elements. It will be understood that elements illustrated in the figures are not necessarily drawn to scale. Moreover, it will be understood that certain embodiments can include more elements than illustrated in a drawing and/or a subset of the elements illustrated in a drawing. Further, some embodiments can incorporate any suitable combination of features from two or more drawings. 
     Piezoelectric MEMS Microphone 
       FIGS.  1 A- 1 B  show a piezoelectric microelectromechanical systems (MEMS) microphone  10  (hereinafter the “microphone”). The microphone  10  has a substrate  12 . The substrate  12  is optionally made of Silicon and may optionally have additional dielectric, metallic or semiconductor films deposited on it. The microphone  10  can have one or more piezoelectric sensors  14  (hereinafter “sensors”) anchored to the substrate  12  in cantilever form with a gap  16  between adjacent sensors  14 . The microphone  10  converts an acoustic signal to an electrical signal when a sound wave vibrates the sensors  14 . The sensors  14  can be made from one or more layers of material. Optionally, the sensors  14  can be made at least in part of Aluminum Nitride (AlN). In another implementation, the sensors  14  can optionally be made at least in part of Scandium Aluminum Nitride (ScAlN) or other piezoelectric materials. The sensors  14  can include an electrode, which can optionally be made of molybdenum (Mo), titanium nitride (TiN), platinum (Pt) or ruthenium (Ru), in some implementations. The gaps  16  between the sensors  14  allow the sensors  14  to freely move, for airflow F to pass therethrough, and balance the pressure between both sides of the sensors  14 . The gap  16  can be about 100-500 nm wide. The sensors  14  are preferably planar (e.g., flat), but are generally not completely flat due to a material internal stress gradient in the sensors  14 . 
     Resonant Frequency of Cantilever Sensor 
       FIG.  2    shows a cantilever sensor  20  (e.g., a piezoelectric sensor) with a beam  21  (e.g., a triangular beam), a sensing area or electrode  22  on or in a proximal portion of the beam  21  attached to an anchor  24  (e.g., a substrate) and a tip  26  (e.g., of a piezoelectric material) of the beam  21  that extends distally of the sensing area or electrode  22  to a distal unsupported end  28 . In one implementation, the tip  26  is part of a beam that is attached to the anchor  24  and the electrode  22  is disposed over or attached to a proximal end of the beam proximate the anchor  24 . The sensor  20  can generate an electrical signal when it is deflected (e.g., when the tip  26  is deflected) by a force F. In one example, at least a portion of the cantilever sensor  20  (e.g., the tip  26  of the cantilever sensor  20 ) can be deflected when subjected to acoustic pressure. For example, a force applied on the tip  26  will deflect the sensing area or electrode  22 . 
       FIG.  3    shows a plot of acoustic response (e.g., decibels or dB) with frequency for the cantilever sensor  20  and shows the resonant frequency peak m 3  is outside the audio band (e.g., at greater than 20 KHz), but the left side of the resonant frequency peak is inside the audio band. In some implementations, it is preferable to increase the resonant frequency so that the frequency response is substantially linear (e.g., flattened) inside the audio band, as further described below. 
     Modifying the Resonant Frequency of a Cantilever Sensor 
     With reference to  FIGS.  4 - 9 B , the inventors have developed methods for modifying (e.g., increasing, decreasing) the resonant frequency of a cantilever sensor. In some implementations described herein such cantilever sensors can be implemented in a piezoelectric MEMS microphone, such as the microphone  10  in  FIGS.  1 A- 1 B . However, one of skill in the art will recognize that the cantilevered (e.g., piezoelectric) sensors with modified (e.g., increased) resonant frequency in accordance with the methods disclosed herein can be used in various other applications, such as in energy harvesting (e.g., generation of voltage and storage of energy from the movement of the sensor), or as ultrasonic transducers, accelerometers, an optical sensors. 
     The resonant frequency of a cantilever sensor, such as the cantilever sensor  20 , is proportional to the square root of stiffness (k) over mass (m), as shown in the following formula. 
     
       
         
           
             
               f 
               0 
             
             ∝ 
             
               
                 k 
                 m 
               
             
           
         
       
     
     In accordance with this formula, the resonant frequency of a cantilever sensor, such as the cantilever sensor  20 , can be increased by reducing the mass (or density) of at least a portion of the sensor (e.g., of the tip  26  of the sensor  20 ) or by increasing the stiffness (e.g., the Young&#39;s modulus E) of at least a portion of the sensor (e.g., of the tip  26  of the sensor  20 ). Similarly, the resonant frequency can be decreased by increasing the mass (or density) of at least a portion of the sensor (e.g., of the tip  26  of the sensor  20 ) or by reducing the stiffness (e.g., the Young&#39;s modulus E) of at least a portion of the sensor (e.g., of the tip  26  of the sensor  20 ). Therefore, the resonant frequency of the a cantilever sensor, such as the cantilever sensor  20 , can be modified by modifying the mass (e.g., density) or stiffness (e.g., Young&#39;s modulus E) of at least a portion of (e.g., the tip of) the cantilever sensor. 
       FIG.  4    a table graph of resonant frequency, voltage output and deflection for a cantilever sensor, such as the cantilever sensor  20 , varying with density v (e.g., indication of mass) and Young&#39;s modulus E (e.g., indication of stiffness). With reference to  FIGS.  5 A- 5 B , the cantilever sensor  20  used as a baseline for the simulations had the tip  26  made of Aluminum Nitride (AlN) with a length L 1  of the beam  21  of the sensor  20  of approximately 300 um, a length L 2  of the tip  26  of the sensor of approximately 210 um, a height H 1  or thickness of the tip  26  of the sensor of approximately 0.6 um and a width W 1  of the tip  26  of the sensor  20  of approximately 100 um. As shown in  FIG.  5 B , the width W 1  is in a direction transverse to a length L 1  (shown in  FIG.  5 A ) of the beam  21 . The cantilever sensor  20  was determined to have a resonant frequency of 11.3 kHz, an output voltage of 2.07 mV and a maximum deflection of the beam  21  (e.g., of the tip  26  of the beam  21 ) of 61.9 nm, all of which are shown in the middle of the tables in  FIG.  4   . The beam  21  can have a uniform thickness H 1  along its length L 1 . The beam  21  can have a uniform thickness H 1  along its width W 1 . 
     With continued reference to  FIG.  4   , varying the density or varying the Young&#39;s modulus (e.g., to values 20% lower or 20% higher relative to the baseline) for the tip  26  did not have an effect on output voltage, as shown in the middle table in  FIG.  4   , as the output voltage varied no more than 0.01 mV. With respect to the effect on deflection by varying the density or varying the Young&#39;s modulus (e.g., to values 20% lower or 20% higher relative to the baseline) for the tip  26 , varying density did not have a significant effect, but varying Young&#39;s modulus did affect the deflection. As shown in the right table in  FIG.  4   , increasing the Young&#39;s modulus by 20% from the baseline decreased the deflection from 61.9 nm to 60 nm. 
     With respect to the effect on resonant frequency by varying the density or varying the Young&#39;s modulus (e.g., to values 20% lower or 20% higher relative to the baseline) for the tip  26 , varying density and Young&#39;s modulus did have an effect on resonant frequency. As shown in the left table in  FIG.  4   , increasing the Young&#39;s modulus by 20% from the baseline increased the resonant frequency from 11.3 kHz to 11.5 kHz, and decreasing the density by 20% from the baseline increased the resonant frequency from 11.3 kHz to 12.6 kHz. Therefore, one strategy for increasing resonant frequency is to increase the Young&#39;s modulus (e.g., increase stiffness) and decrease the material density for the tip  26 . Similarly, one strategy for decreasing resonant frequency is to decrease the Young&#39;s modulus (e.g., decrease stiffness) and increase the material density for the tip  26 . 
     Modifying the Resonant Frequency of a Cantilever Sensor with Different Materials 
     In one implementation, the resonant frequency for a cantilever sensor (e.g., the cantilever sensor  20 ) can be modified by changing the material used for the beam (e.g., for the tip  26  of the beam  21 ). For example, the resonant frequency for the cantilever sensor (e.g., the cantilever sensor  20 ) can be increased by using a material for the beam  21  (e.g., for the tip  26  of the beam  21 ) with a higher stiffness (e.g., higher Young&#39;s modulus) and/or lower density. For example, as compared with the beam  21  being made of Aluminum Nitride (e.g., having a density of 3255 kg/m 2  and Young&#39;s modulus of 320 GPa), using instead diamond for the beam  21  (e.g., for the tip  26  of the beam  21 ), which has a density of 3500 kg/m 2  and Young&#39;s modulus of 1050 GPa, would increase the resonant frequency of the sensor  20 . Similarly, using instead carbon nanotube for the beam  21  (e.g., for the tip  26  of the beam  21 ), which has a density of 1300 kg/m 2  and Young&#39;s modulus of 1000 GPa, would increase the resonant frequency of the sensor  20 . Similarly, the resonant frequency for the cantilever sensor (e.g., the cantilever sensor  20 ) can be decreased by using a material for the beam  21  (e.g., for the tip  26  of the beam  21 ) with a lower stiffness (e.g., lower Young&#39;s modulus) and/or higher density. 
     Modifying the Resonant Frequency of a Cantilever Sensor with Different Structural Shapes 
     In another implementation, the resonant frequency for a cantilever sensor (e.g., the cantilever sensor  20 ) can be modified by changing the structural shape of the beam (e.g., for the tip  26  of the beam  21 ), such as by changing the shape in one direction (e.g., in a Z direction), for example with a vertical buildup.  FIGS.  6 A- 9 B  show different structural designs for a cantilever sensor that have a higher resonant frequency than the cantilever sensor  20  in  FIGS.  5 A- 5 B , and which have a vertical buildup so the beam (e.g., tip of the beam) has a non-rectangular cross-section transverse to a length of the beam. The cantilever sensors of  FIGS.  6 A- 9 B  can be implemented in a piezoelectric MEMS microphone, such as the microphone  10  in  FIGS.  1 A- 1 B . In other implementations, the cantilever sensors of  FIGS.  6 A- 9 B  can be used in various other applications, such as in energy harvesting (e.g., generation of voltage and storage of energy from the movement of the sensor), or as ultrasonic transducers, accelerometers, an optical sensors. 
       FIG.  6 A  shows a side view of a cantilever sensor  20 A and  FIG.  6 B  shows a cross-sectional view of the cantilever sensor  20 A in a direction transverse to a length of the sensor  20 A. Some of the features of the cantilever sensor  20 A are similar to features of the cantilever sensor  20  in  FIGS.  5 A- 5 B . Thus, reference numerals used to designate the various components of the cantilever sensor  20 A are identical to those used for identifying the corresponding components of the cantilever sensor  20  in  FIGS.  5 A- 5 B , except that an “A” has been added to the numerical identifier. Therefore, the structure and description for the various features of the cantilever sensor  20  in  FIGS.  5 A- 5 B  (e.g., length, width) are understood to also apply to the corresponding features of the cantilever sensor  20 A in  FIGS.  6 A- 6 B , except as described below. 
     The cantilever sensor  20 A differs from the cantilever sensor  20  in that the tip  26 A of the beam  21 A has a corrugated shape, so the beam  21 A (e.g., tip  26 A of the beam  21 A) has a non-rectangular cross-section transverse to a length of the beam  21 A. The corrugated shape of the tip  26 A is provide by a first portion  26 A 1  having a first height H 2  that alternates with a second portion  26 A 2  having a second height H 3  that is greater than the first height, where first portions  26 A 1  are spaced from each other by a first gap distance D 1  and the second portions  26 A 2  are spaced from each other by a second gap distance D 2 . In one implementation, the first and second gap distances D 1 , D 2  can be substantially equal. In another implementation, the second gap distance D 2  can be different (e.g., greater) than the first gap distance D 1 . The first height H 2  can be approximately 0.6 um and the second height H 3  can be approximately 2 um. The corrugated shape of the tip  26 A of the beam  21 A increases a stiffness of the beam  21 A in the Z direction as compared to the beam  21  of the sensor  20 . 
     As compared with the cantilever sensor  20 , which as described above has a resonant frequency of 11.3 kHz, an output voltage of 2.07 mV and a maximum beam deflection of 61.9 nm, the sensor  21 A achieves a resonant frequency of 13.0 kHz, an output voltage of 1.90 mV and a maximum deflection of the beam  21 A (e.g., of the tip  26 A of the beam  21 A) of 57.4 nm. For the sensor  21 A, the resonant frequency can further be modified by changing the stiffness of the tip  26 A, for example the first portions  26 A 1  and second portions  26 A 2 . For example, the second height H 3  can be increased, resulting in increased stiffness for the tip  26 A and increased resonance frequency. In another example, the second height H 3  can be decreased, resulting in decreased stiffness for the tip  26 A and decreased resonance frequency. 
       FIG.  7 A  shows a side view of a cantilever sensor  20 B and  FIG.  7 B  shows a cross-sectional view of the cantilever sensor  20 B in a direction transverse to a length of the sensor  20 B. Some of the features of the cantilever sensor  20 B are similar to features of the cantilever sensor  20  in  FIGS.  5 A- 5 B . Thus, reference numerals used to designate the various components of the cantilever sensor  20 B are identical to those used for identifying the corresponding components of the cantilever sensor  20  in  FIGS.  5 A- 5 B , except that a “B” has been added to the numerical identifier. Therefore, the structure and description for the various features of the cantilever sensor  20  in  FIGS.  5 A- 5 B  (e.g., length, width) are understood to also apply to the corresponding features of the cantilever sensor  20 B in  FIGS.  7 A- 7 B , except as described below. 
     The cantilever sensor  20 B differs from the cantilever sensor  20  in that the tip  26 B of the beam  21 B has (e.g., enhanced) first and second side edges  26 B 1 ,  26 B 2  with a second height H 4  that is greater than a first height H 1  of the remainder of the tip  26 B (e.g., remainder of the tip  26 B between the first and second side edges  26 B 1 ,  26 B 2 ). The beam  21 B (e.g., tip  26 B of the beam  21 B) has a non-rectangular cross-section transverse to a length of the beam  21 B. The first height H 1  can be approximately 0.6 um and the second height H 4  can be approximately 5 um. The shape of the tip  26 B with the first and second side edges  26 B 1 ,  26 B 2  increases a stiffness of the beam  21 B in the Z direction as compared to the beam  21  of the sensor  20 . 
     As compared with the cantilever sensor  20 , which as described above has a resonant frequency of 11.3 kHz, an output voltage of 2.07 mV and a maximum beam deflection of 61.9 nm, the sensor  21 B achieves a resonant frequency of 11.9 kHz, an output voltage of 2.06 mV and a maximum deflection of the beam  21 B (e.g., of the tip  26 B of the beam  21 B) of 54.3 nm. For the sensor  21 B, the resonant frequency can further be modified by changing the stiffness of the tip  26 B, for example the first and second side edges  26 B 1 ,  26 B 2 . For example, the second height H 4  can be increased, resulting in increased stiffness for the tip  26 B and increased resonance frequency. In another example, the second height H 4  can be decreased, resulting in decreased stiffness for the tip  26 B and decreased resonance frequency. 
       FIG.  8 A  shows a side view of a cantilever sensor  20 C and  FIG.  8 B  shows a cross-sectional view of the cantilever sensor  20 C in a direction transverse to a length of the sensor  20 C. Some of the features of the cantilever sensor  20 C are similar to features of the cantilever sensor  20 B in  FIGS.  7 A- 7 B . Thus, reference numerals used to designate the various components of the cantilever sensor  20 C are identical to those used for identifying the corresponding components of the cantilever sensor  20 B in  FIGS.  7 A- 7 B , except that a “C” instead of a “B” has been added to the numerical identifier. Therefore, the structure and description for the various features of the cantilever sensor  20 B in  FIGS.  7 A- 7 B  (e.g., length, width, height) are understood to also apply to the corresponding features of the cantilever sensor  20 C in  FIGS.  8 A- 8 B , except as described below. 
     The cantilever sensor  20 C differs from the cantilever sensor  20 B in that the portion of the beam  21 B between the first and second side edges  26 C 1 ,  26 C 2  has a height or thickness H 5  that is thinner than the thickness or height H 1  of the beam  21 B of the cantilever sensor  20 B. The beam  21 C (e.g., tip  26 C of the beam  21 C) has a non-rectangular cross-section transverse to a length of the beam  21 C. The height or thickness H 5  is approximately 0.3 um as compared to the height or thickness H 1  of approximately 0.6 um for the beam  21 B of the sensor  20 B. The shape of the tip  26 C with the first and second side edges  26 C 1 ,  26 C 2  and thinner beam  21 C increases a stiffness and/or reduces a mass of the beam  21 C in the Z direction as compared to the beam  21 B of the sensor  20 B. 
     As compared with the cantilever sensor  20 B, which as described above has a resonant frequency of 11.9 kHz, an output voltage of 2.06 mV and a maximum beam deflection of 54.3 nm, the sensor  21 C achieves a resonant frequency of 14.9 kHz, an output voltage of 2.10 mV and a maximum deflection of the beam  21 C (e.g., of the tip  26 C of the beam  21 C) of 60.6 nm. For the sensor  21 C, the resonant frequency can further be modified by changing the stiffness of the tip  26 C, for example of the first and second side edges  26 C 1 ,  26 C 2 . For example, the second height H 4  can be increased, resulting in increased stiffness for the tip  26 C and increased resonance frequency. In another example, the second height H 4  can be decreased, resulting in decreased stiffness for the tip  26 C and decreased resonance frequency. Additionally or alternatively, the thickness H 5  can be reduced to decrease weight and increase resonance frequency. 
       FIG.  9 A  shows a side view of a cantilever sensor  20 D and  FIG.  9 B  shows a cross-sectional view of the cantilever sensor  20 D in a direction transverse to a length of the sensor  20 D. Some of the features of the cantilever sensor  20 D are similar to features of the cantilever sensor  20 C in  FIGS.  8 A- 8 B . Thus, reference numerals used to designate the various components of the cantilever sensor  20 D are identical to those used for identifying the corresponding components of the cantilever sensor  20 C in  FIGS.  8 A- 8 B , except that a “D” instead of a “C” has been added to the numerical identifier. Therefore, the structure and description for the various features of the cantilever sensor  20 C in  FIGS.  8 A- 8 B  (e.g., length, width, height) are understood to also apply to the corresponding features of the cantilever sensor  20 D in  FIGS.  9 A- 9 B , except as described below. 
     The cantilever sensor  20 D differs from the cantilever sensor  20 C in that the sensor includes one or more (e.g., a plurality of) ridges  26 D 3  between the first and second side edges  26 D 1 ,  26 D 2 , each of the ridges  26 D 3  having a width W 3 . The beam  21 C (e.g., tip  26 C of the beam  21 C) has a non-rectangular cross-section transverse to a length of the beam  21 C. The ridges  26 D 3  can optionally the same height as the first and second side edges  26 D 1 ,  26 D 2 , and can be spaced from each other (and from the first and second side edges  26 D 1 ,  26 D 2 ) by a gap distance D 3 . The width W 3  of each of the ridges  26 D 3  can in one implementation be equal to the width W 2  of the first and second side edges  26 D 1 ,  26 D 2 . In another implementation, the width W 3  of each of the ridges  26 D 3  can be different (e.g., larger, smaller) than the width W 2  of the first and second side edges  26 D 1 ,  26 D 2 . The shape of the tip  26 D with the first and second side edges  26 D 1 ,  26 D 2  and ridges  26 D 3  decreases a stiffness of the beam  21 D in the Z direction as compared to the beam  21 C of the sensor  20 C. 
     As compared with the cantilever sensor  20 C, which as described above has a resonant frequency of 14.9 kHz, an output voltage of 2.10 mV and a maximum beam deflection of 60.6 nm, the sensor  21 D achieves a resonant frequency of 12.7 kHz, an output voltage of 2.14 mV and a maximum deflection of the beam  21 D (e.g., of the tip  26 D of the beam  21 D) of 50.6 nm. For the sensor  21 D, the resonant frequency can further be modified by changing the stiffness of the tip  26 D, for example of the first side edge  26 D 1 , second side edge  26 D 2  and/or ridges  26 D 3 . For example, the second height H 4  can be increased, resulting in increased stiffness for the tip  26 D and increased resonance frequency. In another example, the second height H 4  can be decreased, resulting in decreased stiffness for the tip  26 D and decreased resonance frequency. 
     Methods of Tuning Resonant Frequency of a Cantilever Sensor 
       FIG.  10 A  shows a method  30  for tuning or modifying the resonant frequency of a cantilever sensor, such as the cantilever sensor  20  described above. The method  30  includes the step  32  of identifying for the desired application the cantilever sensor structure. The method  30  also includes the step  34  of modifying the resonant frequency of the cantilever sensor by forming at least a portion of a beam of the sensor (e.g., forming a tip or distal portion of the beam of the sensor) of a material having a density and/or Young&#39;s modulus that provides the desired resonant frequency. The method  30  includes the step  36  of forming or attaching an electrode to a proximal end of the beam of the sensor. 
       FIG.  10 B  shows a method  50  for tuning or modifying the resonant frequency of a cantilever sensor, such as the cantilever sensor  20  described above. The method  50  includes the step  52  of identifying for the desired application the cantilever sensor structure. The method  50  also includes the step  54  of modifying the resonant frequency of the cantilever sensor by forming at least a portion of a beam of the sensor (e.g., forming a tip or distal portion of the beam of the sensor) with a vertical structure that provides a stiffness or material density that results in the desired resonant frequency in the Z direction. The beam (e.g., tip of the beam) can be formed so that it has a non-rectangular cross-section transverse to a length of the beam. The method  50  includes the step  56  of forming or attaching an electrode to a proximal end of the beam of the sensor. 
     The cantilevered sensors described herein (e.g., cantilevered sensors  20 A,  20 B,  20 C,  20 D) advantageously provide increased performance (e.g., increased resonant frequency) as a cantilever sensor (e.g., cantilever sensor  20 ) having the same length and width. The methods  30 ,  50  in  FIGS.  10 A- 10 B  can be used to tune the resonant frequency for the cantilever sensor. 
       FIG.  11    is a schematic diagram of an audio subsystem  300 . The audio subsystem  300  can include one or more microphones  10 . In one implementation, at least one of the microphone(s)  10  is a piezoelectric MEMS microphone. The microphone(s)  10  can communicate with an audio codec  301 , which can control the operation of the microphone(s)  10 . The audio codec  301  can also communicate with a speaker  302  and control the operation of the speaker  302 . 
       FIG.  12    is a schematic diagram of an electronic device  200  that includes the audio subsystem  300 . The electronic device  200  can optionally have one or more of a processor  210 , a memory  220 , a user interface  230 , a battery  240  (e.g., direct current (DC) battery) and a power management module  250 . Other additional components, such a display and keyboard can optionally be connected to the processor  210 . The battery  240  can provide power to the electronic device  200 . 
     It should be noted that, for simplicity, only certain components of the electronic device  200  are illustrated herein. The control signals provided by the processor  210  control the various components within the electronic device  200 . 
     The processor  210  communicates with the user interface  230  to facilitate processing of various user input and output (I/O), such as voice and data. As shown in  FIG.  12   , the processor  210  communicates with the memory  220  to facilitate operation of the electronic device  200 . 
     The memory  220  can be used for a wide variety of purposes, such as storing data and/or instructions to facilitate the operation of the electronic device  200  and/or to provide storage of user information. 
     The power management system or module  250  provides a number of power management functions of the electronic device  200 . In certain implementations, the power management system  250  includes a PA supply control circuit that controls the supply voltages of power amplifiers. For example, the power management system  250  can change the supply voltage(s) provided to one or more power amplifiers to improve efficiency. 
     As shown in  FIG.  12   , the power management system  250  receives a battery voltage from the battery  240 . The battery  240  can be any suitable battery for use in the electronic device  200 , including, for example, a lithium-ion battery. 
       FIG.  13    is a schematic diagram of a wireless electronic device  200 ′ The wireless electronic device  200 ′ is similar to the electronic device  200  in  FIG.  12   . Thus, reference numerals used to designate the various components of the wireless electronic device  200 ′ are identical to those used for identifying the corresponding components of the electronic device  200  in  FIG.  12   . Therefore, the structure and description above for the various features of the electronic device  200  in  FIG.  12    are understood to also apply to the corresponding features of the wireless electronic device  200 ′ in  FIG.  13   , except as described below. 
     The wireless electronic device  200 ′ differs from the electronic device  200  in that it also includes a transceiver  260  that communicates (e.g., two-way communication) with the processor  210 . Signals, data and/or information received (e.g., wirelessly) by the transceiver  260  (e.g., from a remote electronic device, such a smartphone, tablet computer, etc.) is communicated to the processor  210 , and signals, data and/or information provided by the processor is communicated (e.g., wirelessly) by the transceiver  260  (e.g., to a remote electronic device). Further, the function of the transceiver  260  can be integrated into separate transmitter and receiver components. 
     The wireless electronic device  200 ′ can be used to communicate using a wide variety of communications technologies, including, but not limited to, 2G, 3G, 4G (including LTE, LTE-Advanced, and LTE-Advanced Pro), 5G NR, WLAN (for instance, Wi-Fi), WPAN (for instance, Bluetooth and ZigBee), WMAN (for instance, WiMax), and/or GPS technologies. 
     The transceiver  260  generates RF signals for transmission and processes incoming RF signals received from antennas. It will be understood that various functionalities associated with the transmission and receiving of RF signals can be achieved by one or more components that are collectively represented in  FIG.  13    as the transceiver  260 . In one example, separate components (for instance, separate circuits or dies) can be provided for handling certain types of RF signals. 
     The processor  210  provides the transceiver  260  with digital representations of transmit signals, which the transceiver  260  processes to generate RF signals for transmission. The processor  210  also processes digital representations of received signals provided by the transceiver  260 . 
     While certain embodiments of the inventions have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the disclosure. Indeed, the novel methods and systems described herein may be embodied in a variety of other forms. Furthermore, various omissions, substitutions and changes in the systems and methods described herein may be made without departing from the spirit of the disclosure. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the disclosure. Accordingly, the scope of the present inventions is defined only by reference to the appended claims. 
     Features, materials, characteristics, or groups described in conjunction with a particular aspect, embodiment, or example are to be understood to be applicable to any other aspect, embodiment or example described in this section or elsewhere in this specification unless incompatible therewith. All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and/or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features and/or steps are mutually exclusive. The protection is not restricted to the details of any foregoing embodiments. The protection extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed. 
     Furthermore, certain features that are described in this disclosure in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations, one or more features from a claimed combination can, in some cases, be excised from the combination, and the combination may be claimed as a subcombination or variation of a subcombination. 
     Moreover, while operations may be depicted in the drawings or described in the specification in a particular order, such operations need not be performed in the particular order shown or in sequential order, or that all operations be performed, to achieve desirable results. Other operations that are not depicted or described can be incorporated in the example methods and processes. For example, one or more additional operations can be performed before, after, simultaneously, or between any of the described operations. Further, the operations may be rearranged or reordered in other implementations. Those skilled in the art will appreciate that in some embodiments, the actual steps taken in the processes illustrated and/or disclosed may differ from those shown in the figures. Depending on the embodiment, certain of the steps described above may be removed, others may be added. Furthermore, the features and attributes of the specific embodiments disclosed above may be combined in different ways to form additional embodiments, all of which fall within the scope of the present disclosure. Also, the separation of various system components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the described components and systems can generally be integrated together in a single product or packaged into multiple products. 
     For purposes of this disclosure, certain aspects, advantages, and novel features are described herein. Not necessarily all such advantages may be achieved in accordance with any particular embodiment. Thus, for example, those skilled in the art will recognize that the disclosure may be embodied or carried out in a manner that achieves one advantage or a group of advantages as taught herein without necessarily achieving other advantages as may be taught or suggested herein. 
     Conditional language, such as “can,” “could,” “might,” or “may,” unless specifically stated otherwise, or otherwise understood within the context as used, is generally intended to convey that certain embodiments include, while other embodiments do not include, certain features, elements, and/or steps. Thus, such conditional language is not generally intended to imply that features, elements, and/or steps are in any way required for one or more embodiments or that one or more embodiments necessarily include logic for deciding, with or without user input or prompting, whether these features, elements, and/or steps are included or are to be performed in any particular embodiment. 
     Conjunctive language such as the phrase “at least one of X, Y, and Z,” unless specifically stated otherwise, is otherwise understood with the context as used in general to convey that an item, term, etc., may be either X, Y, or Z. Thus, such conjunctive language is not generally intended to imply that certain embodiments require the presence of at least one of X, at least one of Y, and at least one of Z. 
     Language of degree used herein, such as the terms “approximately,” “about,” “generally,” and “substantially” as used herein represent a value, amount, or characteristic close to the stated value, amount, or characteristic that still performs a desired function or achieves a desired result. For example, the terms “approximately”, “about”, “generally,” and “substantially” may refer to an amount that is within less than 10% of, within less than 5% of, within less than 1% of, within less than 0.1% of, and within less than 0.01% of the stated amount. As another example, in certain embodiments, the terms “generally parallel” and “substantially parallel” refer to a value, amount, or characteristic that departs from exactly parallel by less than or equal to 15 degrees, 10 degrees, 5 degrees, 3 degrees, 1 degree, or 0.1 degree. 
     The scope of the present disclosure is not intended to be limited by the specific disclosures of preferred embodiments in this section or elsewhere in this specification, and may be defined by claims as presented in this section or elsewhere in this specification or as presented in the future. The language of the claims is to be interpreted broadly based on the language employed in the claims and not limited to the examples described in the present specification or during the prosecution of the application, which examples are to be construed as non-exclusive. 
     Of course, the foregoing description is that of certain features, aspects and advantages of the present invention, to which various changes and modifications can be made without departing from the spirit and scope of the present invention. Moreover, the devices described herein need not feature all of the objects, advantages, features and aspects discussed above. Thus, for example, those of skill in the art will recognize that the invention can be embodied or carried out in a manner that achieves or optimizes one advantage or a group of advantages as taught herein without necessarily achieving other objects or advantages as may be taught or suggested herein. In addition, while a number of variations of the invention have been shown and described in detail, other modifications and methods of use, which are within the scope of this invention, will be readily apparent to those of skill in the art based upon this disclosure. It is contemplated that various combinations or subcombinations of these specific features and aspects of embodiments may be made and still fall within the scope of the invention. Accordingly, it should be understood that various features and aspects of the disclosed embodiments can be combined with or substituted for one another in order to form varying modes of the discussed devices.