Patent Publication Number: US-2022212918-A1

Title: Vibration sensor

Description:
GOVERNMENT FUNDING 
     This invention was made with government support under DGE1256260 awarded by the National Science Foundation. The government has certain rights in the invention. 
    
    
     FIELD 
     This invention relates generally to sensors, and more particularly, to piezoelectric micro-electro-mechanical system (MEMS) vibration sensors. 
     BACKGROUND 
     Piezoelectric MEMS vibration sensors can be used in a wide array of applications, such as consumer electronics, activity trackers, or biomedical devices, to cite a few examples. in one particular example, a piezoelectric MEMS vibration sensor can be used in an auditory prosthetic device. Only about 20% of people who could benefit from a hearing aid use one. This low uptake could be due to issues relating to appearance, discomfort, and technical issues (e.g., acoustic feedback and poor performance in noisy environments). With many cochlear implants, the external processor must be removed during sleeping, bathing, or exercise. Completely implantable systems, on the other hand, would use natural outer ear and ear canal function, and would be able to provide more realistic representations of natural hearing. However, some implantable systems involve undesirable disarticulation of the ossicular chain, or their sensor performance is impacted by tissue variation. Thus, complete implantation without irreversible alteration of the ossicular chain is desirable. Additionally, with most piezoelectric MEMS vibration sensors, including those used for auditory prostheses, it is desirable to achieve an appropriately high sensitivity over a wide frequency range. 
     SUMMARY 
     According to one embodiment, there is provided a sensor, comprising: a frame; a beam array con a plurality of beams; and a plurality of masses. Each beam of the plurality of beams has an anchored end and an unanchored end. Each beam is coupled to the frame at the anchored end. The unanchored end of each bears is coupled to a respective mass of the plurality of masses. 
     According to various implementations, the sensor may further include the following features or any technically-feasible combination of some or all of these features:
         the beam array has a xylophonic shape;   each mass has a mass thickness, and each mass thickness has a xylophonic variation that corresponds to the xylophonic shape of the beam array;   each beam includes a cantilevered bimorph multi-layer structure;   one or more beams of the plurality of beams includes an exposed body portion that is located between an electrode and the respective mass;   a size of each mass of the plurality of masses correlates with a length of each beam of the plurality of beams;   a center of gravity for each mass in the plurality of masses is vertically aligned with a neutral axis, lies above the neutral axis, or lies below the neutral axis of each beam of the plurality of beams;   each beam of the plurality of beams is configured to minimize a variation in a voltage sensitivity for a limited frequency range;   each beam of the plurality of beams has a resonant frequency, and the resonant frequency of each beam corresponds to a sensitivity peak in a limited frequency range; and/or   two or more beams of the plurality of beams have different resonant frequencies.       

     According to another embodiment, there is provided a sensor, comprising: a frame and a beam array comprising a plurality of beams. Each beam of the plurality of beams is configured to minimize a variation in a voltage output for a limited frequency range. 
     According to various implementations, the sensor may further include the following features or any technically-feasible combination of some or all of these features:
         each beam of the plurality of beams has an anchored end and an unanchored end, wherein each beam is coupled to the frame at the anchored end and a mass is coupled to each beam of the plurality of beams at the unanchored end; and/or   each beam of the plurality of beams has a resonant frequency, and wherein the resonant frequency of each beam corresponds to a sensitivity peak in the limited frequency range.       

     According to another embodiment, there is provided a sensor, comprising: a frame and a beam array comprising a plurality of beams. Each beam of the plurality of beams has a resonant frequency, wherein the resonant frequency of each beam corresponds to a sensitivity peak in a limited frequency range. 
     According to various implementations, the sensor may further include the following features or any technically-feasible combination of some or all of these features:
         each beam of the plurality of beams has an anchored end and an unanchored end, wherein each beam is coupled to the frame at the anchored end and a mass is coupled to each beam of the plurality of beams at the unanchored end; and/or   each beam of the plurality of beams is configured to minimize a variation in a voltage sensitivity for the limited frequency range.       

     According to another embodiment, there is provided a sensor, comprising: a frame and a beam array comprising a plurality of beams. Two or more beams of the plurality of beams have different resonant frequencies. 
     According to various implementations, the sensor may further include the following features or any technically-feasible combination of some or all of these features:
         each beam of the plurality of beams has an anchored end and an unanchored end, wherein each beam is coupled to the frame at the anchored end and a mass is coupled to each beam of the plurality of beams at the unanchored end;   each beam of the plurality of beams has a resonant frequency and the resonant frequency of each beam corresponds to a sensitivity peak in a limited frequency range; and/or   each beam of the plurality of beams is configured to minimize a variation in a voltage sensitivity for a limited frequency range       

    
    
     
       DRAWINGS 
       Example embodiments will hereinafter be described in conjunction with the appended drawings, wherein like designations denote like elements, and wherein: 
         FIG. 1  is a cross-section, schematic representation of a sensor in accordance with one embodiment; 
         FIG. 2  is a perspective view of a sensor in accordance with another embodiment; 
         FIG. 3  is a top view of a sensor in accordance with another embodiment; 
         FIG. 4  is a top view of a sensor in accordance with yet another embodiment; 
         FIG. 5  is a graph of sensitivity with respect to frequency for a desired outcome of an embodiment: 
         FIGS. 6-8  graphically represent comparisons between a single-resonance MEMS sensor and two embodiments of a multi-resonant MEMS sensor, with  FIG. 6  comparing sensitivity,  FIG. 7  comparing phase, and  FIG. 8  comparing input referred noise; and 
         FIG. 9  is cross-section, schematic representation of a sensor in accordance with another embodiment; 
         FIG. 10  is a top view of the top electrode from the sensor of  FIG. 9 ; 
         FIGS. 11-13  graphically represent comparisons between a reference MEMS sensor and two embodiments of a multi-resonant MEMS sensor, with  FIG. 11  comparing sensitivity,  FIG. 12  comparing phase, and  FIG. 13  comparing input referred noise; and 
         FIGS. 14-16  graphically represent comparisons between a reference MEMS sensor and two other embodiments of a multi-resonant MEMS sensor, with  FIG. 14  comparing sensitivity,  FIG. 15  comparing phase, and  FIG. 16  comparing input referred noise. 
     
    
    
     DESCRIPTION 
     A piezoelectric MEMS vibration sensor is described herein that is capable of achieving an appropriately high sensitivity over a wide frequency range, so as to satisfy certain input referred noise (IRN) design limits, which are typically application dependent. In one particular application, the MEMS sensor is used as an implantable, multi-resonant accelerometer fir an auditory prosthetic device. However, other implementations and applications are certainly possible, including but not limited to, sensors for consumer electronics, other biomedical devices, activity trackers, or other applications where vibration sensing is useful. The MEMS sensor described herein includes a beam array comprising a plurality of beans, each beam having an anchored end attached to a frame and an unanchored end attached to a mass. The MEMS sensor is a multi-resonant vibration sensor having particular beam and electrode structures, as well as particularly numbered and/or dimensioned beam-mass pairs, that tailor the magnitude and smoothness of the voltage output over a desired range of frequencies. 
       FIG. 1  is a cross-section, schematic representation of a sensor  10 . The sensor  10  is a multi-resonant MEMS vibration sensor. The sensor  10  includes a beam array  12  having a plurality of beams  14  (only one beam  14  is shown in the cross-section schematic of  FIG. 1 ). Each beam  14  includes an anchored end  16  and an unanchored end  18 . The anchored end  16  is a portion of the beam  14  that is secured or otherwise attached to a frame  20 , and the unanchored end  18  includes a mass  22 . Advantageously, each beam  14  includes a multi-layer structure  24 . The multi-layer structure  24  includes a body  26 , which is advantageously a piezoelectric body  26  having a top side  28  and a bottom side  30 . A first electrode  32  is situated on the bottom side  30  of the body  26 , and a second electrode  34  is situated on the top side  28  of the body  26 . This embodiment of the multi-layer structure  24  also includes a passive substrate layer  35 ; however, the multi-layer structure  24  may be different than what is illustrated, as shown in the alternate, example embodiment illustrated in  FIG. 9 . Various electronics  36  can be used to connect the beam array  12 , via the frame  20 , to a printed circuit board (PCB)  38 . The electronics  36  can include any operable components such as transistors, amplifiers, etc., and will most likely depend on the desired application For the sensor  10 . The PCB  38  can be attached to a protective package (sealing the MEMS sensor  10  inside this package) and the transducer can be sensitive to the motion of the PCB in either the transverse or in plane direction. 
       FIG. 2  shows one example of a beam array  12  that is structured to provide a multi-resonant sensor  10 . In the illustrated embodiment, the beam array  12  has a xylophonic shape, wherein the beam  14   a  is the longest, and each beam  14   b - 14   h  gets progressively shorter in length. The change in beam length (L B  as shown in  FIG. 1 ) between the beams  14   a - 14   h  may be exponential (see e.g.,  FIG. 3 ), or it may be linear (see e.g.,  FIG. 4 ). The xylophonic variation in beam length L B  can help provide the sensor  10  with multi-resonant performance, as will be detailed further below. In some embodiments, the beam array  12  may not follow the xylophonic variation, as the mix in beam length L B  may be more randomized than the ascending/descending arrangement shown. For example, the beam array  12  can include one or more long beams followed by one or more shorter beams, then followed by one or more additional longer beams. 
     Each beam  14  is a single, physically isolated beam that is electrically interconnected with the other beams in the array  12  to produce the overall sensor  10  having desired sensitivity characteristics. Each beam  14  may have a straight, rectangular shape as shown. In other embodiments, the beams  14  may have some other operable shape. The beam thickness T B  can range from 0.5 microns to 8 microns, inclusive, to cite one example range; however, the thickness may be different and will likely depend on a number of factors, including the materials for the various layers  26 ,  32 ,  34 , the manufacturing technique, etc. Further, although the layers  26 ,  32 ,  34  are schematically illustrated as having the same or a similar thickness, it is possible for this to vary (e.g., the body  26  may be the thickest or thinnest layer, with the electrodes  32 ,  34  having a different thickness than the body  26 ). Advantageously, the piezoelectric body  26  is manufactured to be as thin as possible (e.g., approximately 0.5 microns) while maintaining good piezoelectric film quality. While the sensor  10  includes advantageous variations in beam length L B , the thickness T B  of the beams  14  is generally the same front beam to beam, given the desired manufacturing/patterning method. 
     The beams  14  each include an anchored end  16  and an unanchored end  18  (in  FIGS. 2-4 , only one beam  14   a,  is labeled to show the anchored end  16  and unanchored end  18  for clarity purposes). The anchored end  16  is coupled to the frame  20 , and the unanchored end  18  is coupled to a separate mass  22 . As shown more particularly in  FIG. 1 , the anchored end  16  can include an overlap area  40  that at least partially overlaps the frame  20 . Similarly, the unanchored end  18  can include an overlap area  42  that at least partially overlaps the mass  22 . The overlap areas  40 ,  42  may be also included in the other embodiments, although they are not particularly illustrated in the other figures and often will comprise the entire area on top of the mass  20  and nearly all of the upper surface area of the frame  20 . The overlap areas  40 ,  42  may be a product of the manufacturing process, such as a deep reactive ion etching (DRIE) process. The size of the overlap areas  40 ,  42  may be greater than what is schematically illustrated in  FIG. 1  as well. For example, the overlap area  40 ,  42  can make up all or a greater proportion of the top area or surface of the frame  20  and/or mass  22 , respectively. In the embodiments illustrated in  FIGS. 2-4 , the anchored ends  16  of each beam  14  are generally aligned with respect to an edge portion  44  of the frame  20 . The unanchored ends  18  are advantageously not aligned, and instead can follow the xylophonic variation of the beam array  12 . 
     The frame  20  and a mass  22  are coupled with the anchored end  16  and the unanchored end  18 , respectively, of each beam  14 . The frame  20  and each mass  22  are advantageously portions of an etched silicon substrate; however, other materials are certainly possible. The frame  20  is situated between the beam array  12  and the PCB  38 , and it serves as the main structural support for the beam array  12 . The dimensions of the frame  20  will vary depending on the desired application for the sensor  10 . The frame  20  has a connection surface  46  that includes patterned electrical connections  48 ,  50  with associated output pads  52 ,  54  for connecting to the other electronics  36 . The electrical connections  48 ,  50  can be series, parallel, or some combination of both series and parallel. In some embodiments, inversion of the signal can be used to obtain the sum and/or difference of voltage outputs from the individual beams  14 . Thus, the electrical connections  48 ,  50  can provide final corrections to the output voltage of the sensor  10  by connecting the plurality of beams  14  in series and/or in parallel, as well as determining which outputs are summed and which are differenced. For example, the sensor  10  can achieve better sensitivity by summing the outputs, but it may be advantageous in other embodiments to vary which outputs are summed and which are differenced. In other embodiments, each beam&#39;s output could be digitally sampled by the electrical readout circuitry and then digitally added or subtracted over different frequency ranges, depending on the application. 
     Each mass  22  is a proof mass attached at the unanchored end  18  of each beam  14 . The mass  22  helps dictate the resonant frequency of each beam  14 , and accordingly, the size and shape of each mass  22  can be tailored to achieve a desired resonant frequency response. With reference to  FIG. 1 , each mass  22  has a length L M  and thickness T M . These dimensions may be chosen to impact the frequency response of the beam  14 . In some embodiments, the size of the mass  22  may correlate with the length L B  of each beam  14 , such that larger masses (whether by length, thickness, some combination thereof, etc.) are included with longer beams and smaller masses are included with shorter beams. An example of this embodiment is shown with respect to the beam array  12  shown in  FIG. 2 . In this embodiment, the relative mass thicknesses T M  have the same xylophonic variation as the size of the beams  14  themselves, in that the thickness T M  of each mass  22  increases as the beam length L B  increases. To help ensure adequate sensor performance, each mass  22  has a thickness T M  that is less than a thickness T F  of the frame  20 . It may be helpful to align the center of mass of each proof mass  22  to the point where it connects at the unanchored end  18  to the neutral axis NA of each beam  14 . The location of the neutral axis NA is somewhere within the beam  14 , and will depend on the material properties of the beam and the layers that make up the beam. For example, in  FIG. 1 , the neutral axis NA depends on the thickness of the passive substrate  35  and piezoelectric body  26 . 
     Advantageously, each mass  22  has a width W M  that coincides with the width of the beam W B , as designated, for example, in the top view of  FIG. 3 . As with the length L M  and thickness T M , it is possible for the mass width W M  to vary from beam to beam to impact the resonant frequency response. In the  FIG. 3  embodiment, the width W M  of each mass increases as the length L B  of each beam  14  decreases. Given the varying widths W M  in  FIG. 3 , this also impacts the spacing between beams. For example, the spacing between beams  14   a  and  14   b  is greater than the spacing between any of the other beam pairs, such as beams  14   g  and  14   h.  In the  FIG. 4  embodiment, the width W M  of each mass stays constant, but the length L M  of each mass  22  increases as the beam length L B  decreases. In this embodiment, the spacing between beams  14  is constant. Varying the width of the beams W B  can change the capacitance of each beam  14 . 
     Each beam  14  includes a multi-layer structure  24 . The multi-layer structure  24  may be a cantilevered bimorph or a cantilevered multimorph. A cantilevered biomorph multi-layer structure  24  can be advantageous, as the bending of each bimorph structure produces a measurable voltage that can be used to determine displacement or acceleration, and cantilevering can reduce the influence of material residual stress on the device bandwidth. A bimorph consisting of two piezoelectric layers (see  FIG. 9  haying two piezoelectric body layers  26   a,    26   b ), would also have three electrode layers, such that it further includes a middle electrode layer  37 , while a bimorph with one piezoelectric body layer  26  and one passive substrate  35  (see  FIG. 1 ) would have four total layers (one piezoelectric, one passive substrate, and two electrodes). The multi-layer structure  24  generally includes a piezoelectric body  26  that is at least partially located between the first electrode  32  and the second electrode  34 . The multi-layer structure  24  may have more layers than what is particularly illustrated in the figures. The multi-layer structure  24  may also include one or more layers having a different functionality than the illustrated layers, such as spacer layers and/or shielding layers (e.g., a parylene layer, a silicon dioxide layer, etc.). To those practiced in the art, it is known that there will be a trade-off between the location of the neutral axis NA of the beam  14 , sensitivity, and noise. The neutral axis NA will occur somewhere between the upper and lower surfaces of the multi-laver structure  24 . 
     The body  26  of the multi-layer structure  24  comprises a piezoelectric material. In one example embodiment, the piezoelectric material is aluminum nitride (AlN), and in an even more particular embodiment, the piezoelectric material is a scandium-doped AlN. The use of scandium-doped AlN may be advantageous because it can help increase sensitivity of the sensor  10  without overly increasing the IRN. Other piezoelectric materials are certainly possible, including but not limited to lead zirconate titanate (PZT), zinc oxide (ZnO), polyvinylidene fluoride (PVDF), or Pb(Mg 1/3 Nb 2/3 )O 3 —PbTiO 3  (PMN-PT). While the piezoelectric body  26  is illustrated as stopping directly at the edge portion  44  of the frame  20 , if the sensor  10  is patterned, the body layer may extend further across the frame and/or the substrate, as it may not be necessary to etch off the material on inactive areas. The piezoelectric body  26 , at least in the cantilevered beam area, can be fully sandwiched or covered by each of the first and second electrode layers  32 ,  34 , as shown in the beam  14   a  in  FIG. 2  or in all of the beams  14  in  FIG. 3 . Alternatively, the first and/or second electrode layers  32 ,  34  may only partially cover the piezoelectric body  26 . 
     A first electrode  32  is situated on the bottom side  30  of the body  26 , and a second electrode  34  is situated on the top side  28  of the body  26 . Each electrode  32 ,  34  in the illustrated embodiments is patterned or deposited on or beneath the piezoelectric body  26 . A metal-based material such as molybdenum can advantageously be used for the electrodes  32 ,  34 , or another operable material such as platinum or aluminum, to cite a few examples. As shown in  FIG. 2 , the amount of electrode coverage (defined at least partially by the electrode length L E ) can be chosen for a particular capacitance and voltage output. Accordingly, the embodiments illustrated in  FIGS. 2 and 4  have an exposed body portion  56  that is located between the first and/or second electrode  32 ,  34  and the mass  22 . The size of the exposed body portion  56  may vary in no particular order, as shown in  FIG. 2 . However, in  FIG. 4 , the length of the exposed body portion  56  decreases exponentially from  56   a - 56   h , and the length of each exposed body portion  56  generally tracks the xylophonic distribution of the beam array  12  (e.g., ascending/descending). For example, the exponential decrease in the electrode length L E  shown in  FIG. 4 , however, occurs when the beam length L B  decreases linearly. In some embodiments, the beam length L B  and the electrode length L E  both decrease exponentially, or both decrease linearly. In yet another embodiment, the beam length L B  may decrease exponentially while the electrode length L E  decreases linearly. 
     Instead of the structure of the exposed body portion  56  schematically illustrated in  FIGS. 2 and 4 , it is possible, and likely in many embodiments, that except for a break portion  39 , as shown in  FIGS. 9 and 10 , the entire flexible body layer  26  of the piezoelectric material  26  would be covered by the metal electrode  34 , although some portion of the beam  14  may be uncovered, This leaves a floating electrode portion  41 . At the anchored end  16 , electrical vias connect the electrodes  32 ,  34 ,  37  to the traces  48 ,  50  which then go to respective pads  52 ,  54 . The middle electrode  37 , which is included in this embodiment of the multi-layer structure  24 , is typically not broken (i.e., does not include break portion  39 ), and is continuous. The teachings with respect to the exposed body portion  56  may also be applicable to the floating electrode portion  41 . It is also possible to have a break portion that extends along the length of the beam  14  (e.g., generally orthogonal to the break portion  39  illustrated in  FIG. 10 ). 
     The components and structure of the beam array  12  are chosen to help improve the low-frequency IRN of the multi-resonant sensor  10 . It is desirable to have an appropriately high sensitivity over a wide frequency range so as to achieve certain IRN design limits for particular applications.  FIG. 5  graphically illustrates example sensitivity with respect to frequency. There are two scenarios, the first is where the resonant region serves to extend the low frequency sensitivity region ( 58   a,  which traditionally ends at the resonance of the sensor, as discussed later with regard to a single resonance case  64 ). The second is when a handpass region is created over the resonant frequency range ( 58   b ). The limited frequency range could be both  58   a  and  58   b  (together discussed as just  58 , with  58   a  representing a below resonance sensitivity and  58   b  representing a resonance region sensitivity), or just one or the other. It is possible to increase the sensitivity in the range  58   a,  as seen in  FIG. 6  and represented by dotted line  63 , depending on whether the signals are summed or differenced. This can cause a higher or lower sensitivity in the range  58   a , and thus it may be possible to take advantage of the sensitivity in the low frequency range  58   a.  It can be advantageous to try and make the sensitivity in the region  58   a  the same or within some percentage of the sensitivity in the region  58   b.  In some embodiments, each beam  14   a - 14   h  is configured such that its resonant frequency corresponds to a sensitivity peak  62   a - 62   h  in the range  58   b.  More particularly, the beam  14   a  shown in  FIG. 2  can be configured to have a resonant frequency corresponding to the sensitivity peak  62   a,  the beam  14   b  can be configured to have a resonant frequency corresponding to the sensitivity peak  62   b,  etc. 
     The frequency range  58  will depend on a number of factors, one of the prominent factors being the desired application for the multi-resonant MEMS sensor  10 . in an auditory prosthesis accelerometer, the limited frequency range in one example is about 100 Hz to 8 kHz. Also, as detailed above, the limited frequency range  58  may also be chosen based on the magnitude or presence of sensitivity variation. Other factors may be used to help dictate the scope of the frequency range needed to achieve the particular IRN design limits or resolution for the desired application. In some embodiments, beam array  12  is configured to minimize a variation in a voltage output over the limited frequency range  58 . Having a sensor  10  with the proper number and dimensions of beam-mass pairs  14 ,  22  mounted to the frame  20 , as well as the necessary electrode size L E  and electrical connections  48 ,  50 , can help tailor this variation in voltage output, in terms of magnitude and/or smoothness, over the frequency range  58  (e.g., magnitude with respect to range  58   a,  and smoothness with regard to range  58   b ). Resonant frequency placement and damping can be controlled to minimize the amount of ripple in the bandwidth or frequency range  58   b  of interest. The number of beams and the damping can control the ripple magnitude  62   a - h . While it can be a challenge to simultaneously achieve a required sensor size, frequency range, and IRN, for instance in the auditory prosthesis realm, it is possible to improve the IRN by increasing sensitivity, which can be done in some embodiments, with a lower resonant frequency. 
       FIGS. 6-8  illustrate results from preliminary analytic studies, in which beam arrays  12  comprising ten parallel-connected beams  14  were shown to improve the IRN.  FIGS. 6 and 7  show a sensitivity and phase comparison between a single resonance case  64  that would typically be designed to cover the frequency range  58  of interest. For the single resonance case  64 , the ten beams are all 50 microns long and 100 microns wide, and each mass is 50 microns long, 100 microns tall, and 100 microns wide. The beams are connected in parallel. The comparison cases  66 ,  68  each have ten beams, each beam being 100 microns wide with the same mass dimensions as the single resonance case  64 . However, with the multi-resonant comparison cases  66 ,  68 , the shortest beam is 50 microns long and the longest beam is 950 microns (stepping up in increments of 100 microns). The comparison case  66  sums the outputs, whereas the comparison case  68  takes alternating sums and differences of the outputs. In the studies, a damping factor (e.g., 10% or 1−i*0.1) was used with the elastic properties to model damping.  FIGS. 6 and 7  help illustrate that the multi-resonant comparison cases  66 ,  68  provide an increased sensitivity from about 0 to 8 kHz. 
       FIG. 8  illustrates the IRN comparison between the single resonance case  64  and the multi-resonant comparison cases  66 ,  68 . For the auditory prosthesis application, the single resonance case  64  only achieves the required resolution above approximately 1 kHz. The multi-resonant comparison cases  66 ,  68  both also achieve the necessary IRN down to 100 Hz. The noise for the multi-resonant comparison cases  66 ,  68  was calculated by combining all of the capacitances in parallel. At 100 Hz, the summed case  66  is approximately 45 dB lower than the single resonance case  64 . This is a significant improvement of the low-frequency IRN. 
     Further development of the preliminary analytic studies illustrated in  FIGS. 6-8  involved increasing the number of beams in the beam array from ten to sixteen. The additional beams were included with dimensions that place the resonant frequencies in the gaps of the examples in  FIGS. 6-8 . The sixteen beams were 62.5 microns wide and still ranged from 50 to 950 microns long. Adding the extra beams, with the extra beams filling the resonant frequency gaps, helped smooth and decrease the sensitivity ripple or oscillation described above. Further, there was a significant improvement in IRN over the frequency range of interest. 
       FIGS. 11-13  illustrate additional results from preliminary analytic studies, in which beam arrays  12  comprised five parallel-connected beams  14  that are each 100 microns wide. In each of  FIGS. 11-13 , a reference sensor case  74  is compared with a summed case  76  and a difference case  78  (summed with alternating polarity). The difference case  78  illustrates a band-pass type bandwidth, and the summed case  76  is included, as with  FIGS. 6-8 , to illustrate the potential extension of the sensor bandwidth. The beams  14  increase in 50 micron length increments from 400 microns to 600 microns. They are completely electrode covered and identical in all remaining dimensions (including mass dimensions of 50 microns long, 100 microns wide, and 100 microns tall) and have 10% damping. The reference sensor case  74  is a 150 micron long, 500 micron wide beam with a 50 micron long, 500 micron wide, and 100 micron tall mass that is designed for a 3 dB bandwidth that is as large (or larger) than the bandwidth of the multi-resonant implementations. Typically, the sensors are designed with a bandwidth that is defined by the 3 dB point—the frequency at which the sensitivity has increased to 3 dB more than the low-frequency asymptote value. Over this range the sensor response is essentially linear. This demonstrates the highest sensitivity that could be achieved for a single-resonance sensor. 
       FIGS. 11-13  provide an example of what is theoretically illustrated in  FIG. 5 . The closely spaced resonant frequencies of each beam  14  in the beam array  12  help to smooth out the frequency response. The curve  78  would desirably have an extended range with minimized ripple over the resonant frequency region. The curve  76  illustrates a band of increased sensitivity that can be smoothed by the choice of resonant frequency location. Over this particular frequency band, the IRN will be decreased, which is advantageous. 
       FIGS. 14-16  also illustrate additional results from preliminary analytic studies, in which beam arrays  12  comprised five beams  14 , as with  FIGS. 11-13 . However, in this example, overlap of the piezoelectric electrode layer  32  on the frame  20  at the base or anchored end  16  of each beam  14  was included, to serve as a stray capacitance that will decrease the voltage output from the sensor  10 . Further, series connections of multiple electrodes on a surface of a subset of the beams were used to increase the voltage output (increase the sensitivity) of the beam  14 . These tools can be used to smooth the ripple since the amplitude of the overall frequency response can be tuned, including the resonant frequency peak amplitude. The reference sensor case  84  is the same as in  FIGS. 11-13 , but both the summed case  86  and difference case  88  have a decreased voltage output generated by the beam, resulting from the overlap of the electrode materials on the top of the frame and/or mass. This allows for scaling of the sensitivity result. Additionally, these examples include series connections of two electrodes, although there could be more, on a single beam structure. This series connection increases the sensitivity, contributing to the result scaling. 
     It is to be understood that the foregoing description is of one or more preferred example embodiments of the invention. The invention is not limited to the particular embodiment(s) disclosed herein, but rather is defined solely by the claims below. Furthermore, the statements contained in the foregoing description relate to particular embodiments and are not to be construed as limitations on the scope of the invention or on the definition of terms used in the claims, except where a term or phrase is expressly defined above. Various other embodiments and various changes and modifications to the disclosed embodiment will become apparent to those skilled in the art. All such other embodiments, changes, and modifications are intended to come within the scope of the appended claims. 
     As used in this specification and claims, the terms “for example,” “e.g.,” “for instance,” and “such as,” and the verbs “comprising,” “having,” “including,” and their other verb forms, when used in conjunction with a listing of one or more components or other items, are each to be construed as open-ended, meaning that the listing is not to be considered as excluding other, additional components or items. Other terms are to be construed using their broadest reasonable meaning unless they are used in a context that requires a different interpretation.