Abstract:
Arrays of resonator sensors include an active wafer array comprising a plurality of active wafers, a first end cap array coupled to a first side of the active wafer array, and a second end cap array coupled to a second side of the active wafer array. Thickness shear mode resonator sensors may include an active wafer coupled to a first end cap and a second end cap. Methods of forming a plurality of resonator sensors include forming a plurality of active wafer locations and separating the active wafer locations to form a plurality of discrete resonator sensors. Thickness shear mode resonator sensors may be produced by such methods.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a divisional of U.S. patent application Ser. No. 13/350,577, filed Jan. 13, 2012, pending, and entitled “Thickness Shear Mode Resonator Sensors and Methods of Forming a Plurality of Resonator Sensors,” which application claims the benefit of U.S. Provisional Patent Application Ser. No. 61/432,433, filed Jan. 13, 2011 and entitled “Sensors for Measuring At Least One of Pressure and Temperature, Sensor Arrays and Related Methods,” the disclosure of each of which is hereby incorporated herein in its entirety by this reference. 
     
    
     TECHNICAL FIELD 
       [0002]    Embodiments of the present disclosure relate to sensors for measurement of at least one of a pressure and temperature and, more particularly, to quartz resonator sensors for measurement of at least one of a pressure and temperature and related methods thereof. 
       BACKGROUND 
       [0003]    Thickness shear mode quartz resonator sensors (also interchangeably called quartz resonator transducers) have been used successfully in the down-hole environment of oil and gas wells for several decades and are still an accurate means of determining bottom-hole pressure and temperature. Quartz resonator pressure and temperature sensors typically have a crystal resonator located inside a housing exposed to ambient bottom-hole fluid pressure and temperature. Electrodes on the resonator element coupled to a high frequency power source drive the resonator and result in shear deformation of the crystal resonator. The electrodes also detect the resonator response to at least one of pressure and temperature and are electrically coupled to conductors extending to associated power and processing electronics isolated from the ambient environment. Ambient pressure and temperature are transmitted to the resonator, via a substantially incompressible fluid within the housing, and changes in the resonator frequency response are sensed and used to determine the pressure and/or temperature and interpret changes in same. For example, a quartz resonator sensor, as disclosed in U.S. Pat. Nos. 3,561,832 and 3,617,780, includes a cylindrical design with the resonator formed in a unitary fashion in a single piece of quartz. End caps of quartz are attached to close the structure. 
         [0004]    Generally, a thickness shear mode quartz resonator sensor assembly may include a first sensor in the form of a primarily pressure sensitive quartz crystal resonator exposed to ambient pressure and temperature, a second sensor in the form of a temperature sensitive quartz crystal resonator exposed only to ambient temperature, a third reference crystal in the form of quartz crystal resonator exposed only to ambient temperature, and supporting electronics. The first sensor changes frequency in response to changes in applied external pressure and temperature with a major response component being related to pressure changes, while the output frequency of the second sensor is used to temperature compensate temperature-induced frequency excursions in the first sensor. The reference crystal, if used, generates a reference signal, which is only slightly temperature-dependent, against or relative to which the pressure- and temperature-induced frequency changes in the first sensor and the temperature-induced frequency changes in the second sensor can be compared. Means for such comparison as known in the art include frequency mixing or using the reference frequency to count the signals for the first and second sensors. 
         [0005]    Prior art devices of the type referenced above including one or more thickness shear mode quartz resonator sensors exhibit a high amount of accuracy even when implemented in an environment such as a down-hole environment exhibiting high pressures and temperatures. However, such thickness shear mode quartz resonator sensors may be relatively expensive to fabricate, as each sensor must be individually manufactured. These relatively expensive quartz resonator sensors may not be economically practical for implementation in applications that would benefit from their relatively higher accuracy and ability to operate in a relatively wider range of temperatures and pressures as compared to other less expensive, less accurate and less robust sensors such as strain or piezoresistive gages. 
       BRIEF SUMMARY 
       [0006]    In some embodiments, the present disclosure includes an array of resonator sensors including an active wafer array comprising a plurality of unsingulated active wafers, a first unsingulated end cap array coupled to a first side of the active wafer array, and a second unsingulated end cap array coupled to a second side of the active wafer array. Each unsingulated active wafer comprises a resonating portion wherein the resonating portion of each unsingulated active wafer is out of contact with each of the first and second unsingulated end cap arrays. 
         [0007]    In some embodiments, the present disclosure includes a plurality of thickness shear resonator sensors produced by a process including forming a plurality of active wafer locations in a first sheet of material comprising locating a central portion of each active wafer of the plurality of active wafer locations, bounding the plurality of active wafer locations about the central portions thereof to form a first cavity on a first side of each central portion and a second cavity on a second side of each central portion to form an array of resonator sensors, and separating the array of resonator sensors. 
         [0008]    In yet additional embodiments, the present disclosure includes a method of forming a plurality of resonator sensors. The method includes forming a plurality of active wafer locations in a unitary structure, coupling a plurality of first end cap structures to a first side of the unitary structure, coupling a plurality of second end cap structures to a second, opposing side of the unitary structure, and separating the plurality of active wafer locations laterally between the end cap structures to form a plurality of discrete resonator sensors. 
         [0009]    In yet additional embodiments, the present disclosure includes a method of forming a plurality of resonator sensors. The method includes forming a plurality of active wafer locations in a first sheet of material comprising locating a central portion of each active wafer of the plurality of active wafer locations, bounding the plurality of active wafer locations about the central portions thereof to form a first cavity on a first side of each central portion and a second cavity on a second side of each central portion to form an array of resonator sensors, and separating the array of resonator sensors to form a plurality of discrete resonator sensors. 
         [0010]    In yet additional embodiments, the present disclosure includes a thickness shear mode resonator sensor. The thickness shear mode resonator sensor includes an active wafer comprising a resonating element and a first end cap coupled to a first side of the active wafer where at least one surface of the active wafer and at least one surface of the first end cap form a first cavity between the resonating element of the active wafer and the first end cap. The thickness shear mode resonator sensor also includes a second end cap coupled to a second, opposing side of the active wafer where at least one surface of the active wafer and at least one surface of the second end cap form a second cavity between the resonating element of the active wafer and the second end cap. The active wafer exhibits a substantially quadrilateral cross section taken in a direction along an interface of the active wafer and at least one of the first end cap and the second end cap. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]    While the specification concludes with claims particularly pointing out and distinctly claiming what are regarded as embodiments of the present disclosure, various features and advantages of embodiments of the disclosure may be more readily ascertained from the following description of example embodiments of the disclosure provided with reference to the accompanying drawings, in which: 
           [0012]      FIG. 1  is a perspective view of resonator sensor in accordance with an embodiment of the present disclosure; 
           [0013]      FIG. 2  is a perspective cutaway view of an active wafer of the resonator sensor shown in  FIG. 1 ; 
           [0014]      FIG. 3  is a cross-sectional side view of the resonator sensor shown in  FIG. 1 ; 
           [0015]      FIG. 4  is a cross-sectional side view of a resonator sensor in accordance with another embodiment of the present disclosure; 
           [0016]      FIG. 5  is a cross-sectional side view of a resonator sensor in accordance with yet another embodiment of the present disclosure; 
           [0017]      FIG. 6  is a cross-sectional side view of a resonator sensor in accordance with yet another embodiment of the present disclosure; 
           [0018]      FIG. 7  is a top view of an active wafer of a resonator sensor in accordance with yet another embodiment of the present disclosure; 
           [0019]      FIG. 8  is a top view of an array of active wafers for use in resonator sensors in accordance with yet another embodiment of the present disclosure; 
           [0020]      FIG. 9  is a top view of a portion of the array of active wafers shown in  FIG. 8 ; 
           [0021]      FIG. 10  is a cross-sectional side view of an array of resonator sensors in accordance with yet another embodiment of the present disclosure; and 
           [0022]      FIG. 11  is a cross-sectional side view of the array of resonator sensors shown in  FIG. 10  that have been separated to form individual resonator sensors. 
       
    
    
     DETAILED DESCRIPTION 
       [0023]    In the following detailed description, reference is made to the accompanying drawings that depict, by way of illustration, specific embodiments in which the disclosure may be practiced. However, other embodiments may be utilized, and structural, logical, and configurational changes may be made without departing from the scope of the disclosure. The illustrations presented herein are not meant to be actual views of any particular sensor or component thereof, but are merely idealized representations that are employed to describe embodiments of the present disclosure. The drawings presented herein are not necessarily drawn to scale. Additionally, elements common between drawings may retain the same numerical designation. 
         [0024]    It is noted that in some of the drawings presented herein, embodiments of resonator sensors and components thereof are shown as being at least partially transparent in order to facilitate description of embodiments of the present disclosure. However, it is understood that materials (e.g., quartz) used to form the resonator sensors and components thereof may be transparent, opaque, variations therebetween, or combinations thereof. 
         [0025]      FIG. 1  is a perspective view of a resonator sensor according to the present disclosure. As shown in  FIG. 1 , the resonator sensor such as, for example, a quartz resonator sensor  100  includes an active wafer  102  at least partially disposed in a housing  104 . A portion of the active wafer  102  may be bounded on sides thereof. For example, the housing  102  may include two end caps (e.g., a first end cap  106  end and a second end cap  108 ) and the active wafer  102  may disposed between the end caps  106 ,  108  forming the housing  104 . An actively vibrating portion of the active wafer  102  (e.g., a resonating portion  114  ( FIG. 2 )) includes a cavity on both sides enabling the portion of the active wafer  102  to resonate (e.g., displace, vibrate, etc.) when electrically driven at one or more selected frequencies. For example, the active wafer  102  may include a recessed portion  110  forming a central portion of the active wafer  102  (e.g., a resonating portion  114  ( FIG. 2 )) having a thickness that is less than a thickness of an adjacent portion of the active wafer  102  (e.g., the outer portion  116  ( FIG. 2 )). In some embodiments, active wafer  102  may include a recessed portion  110  on opposing sides of the active wafer  102  (e.g., opposing faces of the active wafer  102 ). 
         [0026]    In some embodiments, the resonator sensor  100  may have a substantially cuboidal shape. For example, the resonator sensor  100  may exhibit a first substantially quadrilateral (e.g., square) cross-sectional shape and a second substantially quadrilateral cross-sectional shape in a direction substantially transverse to the first cross section. It is noted that, while the embodiment of  FIG. 1  illustrates a resonator sensor  100  having a substantially quadrilateral cross-sectional shape, in other embodiments, a resonator sensor may be formed in other geometries (e.g., a circular or disc cross-sectional shape, a polygonal cross-sectional shape, etc.). For example, a resonator sensor may be formed in a substantially cylindrical shape (e.g., the resonator sensor may be somewhat similar to those shown in the above-referenced U.S. Pat. Nos. 3,561,832 and 3,617,780). In an embodiment, resonator sensors  100  initially formed with a substantially quadrilateral cross-section as described herein may subsequently be formed, for example by grinding on a lathe, into a substantially cylindrical shape. As used herein, the term “substantially cylindrical” does not exclude one or more flats on the exterior of the resonator, and specifically includes shapes having an arcuate outer surface comprising one or more radii, such as ellipsoidal shapes. 
         [0027]      FIG. 2  is an enlarged, perspective cutaway view of the active wafer  102 . As shown in  FIG. 2 , the active wafer  102  may include a first recessed portion  110  formed in a first face of the active wafer  102  and a second recessed portion  111  in a second, opposing face of the active wafer  102 . The one or more recessed portions  110 ,  111  may form a resonating portion  114 , which may also be characterized as a resonator element, of the active wafer  102 . In other words, the active wafer  102  may comprise an inverted mesa structure having the resonating portion  114  formed by the first and second recessed portions  110 ,  111  in the center region of the active wafer  102  and a thicker outer portion  116  surrounding the resonating portion  114 . In some embodiments, the first recessed portion  110  may be substantially aligned with the second recessed portion  111 . For example and as shown in  FIG. 2 , the recessed portions  110 ,  111  are substantially aligned with each other (e.g., each point on the outer boundary of the recessed portion  110  is substantially collinear to a similar point of the recessed portion  111 ). 
         [0028]    In some embodiments, portions of the active wafer  102  may be removed to form the recessed portions  110 ,  111 . For example, portions of the active wafer  102  may be removed using an etching process, an abrasive planarization process such as, for example, a chemical-mechanical polishing (CMP) process, or a combination thereof. Etching processes may include, for example, removing portions of the material using a mask (e.g., through photolithography patterning or the like) and a reactive ion (i.e., plasma) etching process or removing the material using a mask and an isotropic wet chemical etching process. It is noted that the particular composition of the gases used to generate the reactive ions, the particular composition of the chemical etchant, and the operating parameters of the etching process may be selected based on the composition of the mask, the material to be etched, and the surrounding materials. 
         [0029]    It is noted that the removal techniques discussed above may be utilized to form recesses in other portions of the resonator sensor, for example, one or more of the end caps as discussed below. 
         [0030]    The active wafer  102  may include one or more electrodes formed thereon. For example, electrodes  112 ,  113  may be provided on the opposing recessed portions  110 ,  111  forming the resonating portion  114  of the active wafer  102 . The electrodes  112 ,  113  may be formed on the active wafer by, for example, deposition techniques (e.g., chemical vapor deposition (CVD), physical vapor deposition (PVD), atomic layer deposition (ALD), sputtering, thermal evaporation, or plating). In some embodiments, the electrodes  112 ,  113  may be formed from gold with an intermediate layer of chromium between the gold and the quartz active wafer  102  to enhance adhesion. As known in the art, the electrodes  112 ,  113  are provided to excite vibrational behavior in the resonating portion  114  of the active wafer  102 , and are electrically coupled by conductors (not shown in  FIG. 2 ) to a high-frequency driving electronics, as is conventional. 
         [0031]    Referring still to  FIG. 2 , the resonating portion  114  may be a flat resonator (i.e., plano-plano). In other embodiments, a resonating portion  114  or a portion thereof may comprise other shapes such as, for example, plano-convex, etc. In plano-convex resonators, the outer portion  116  surrounding the resonating portion  114  of the active wafer  102  on each side of the active wafer  102  may be substantially flat to enable coupling to the end caps  106 ,  108 . 
         [0032]      FIG. 3  is a cross-sectional side view of the resonator sensor  100 . As shown in  FIG. 3 , the end caps  106 ,  108  may be coupled to the active wafer  102  by, for example, an adhesive or bonding process (e.g., a fused glass frit  118 ). The recessed portions  110 ,  111  of the active wafer  102  and the end caps  106 ,  108  form cavities  120 ,  121  on opposing sides of the resonating portion  114  that enable the resonating portion  114  to vibrate freely. The electrodes  112 ,  113  may include a portion (e.g., conductive traces  122 ,  123 ) extending along the active wafer  102  (e.g., along the resonating portion  114  and the outer portion  116 ) to an outer portion of the resonator sensor  100  to enable electrical connection between the electrodes  112 ,  113  and, for example, an electronics assembly. In some embodiments, the fused glass frit  118  formed between one or more end caps  106 ,  108  and the active wafer  102  proximate to the conductive traces  122 ,  123  may not extend to an outer surface of the resonator sensor  100 . Stated in another way, a recess  124  may be formed in the glass frit  118  proximate the outer portion of a joint formed between one or more end caps  106 ,  108  and the active wafer  102  such that the conductive traces  122 ,  123  may be partially exposed at an outer portion of the resonator sensor  100  to enable electrical connection thereto. 
         [0033]      FIG. 4  is a cross-sectional side view of a resonator sensor  200  in accordance with another embodiment of the present disclosure. It is noted that the cross-sectional side view of a resonator sensor  200  is taken in direction transverse to the cross-sectional side view of the resonator sensor  100  shown in  FIG. 3 . As shown in  FIG. 4 , the resonator sensor  200  may be somewhat similar to the resonator sensor  100  and may include similar elements and methods of forming as shown and described above with reference to  FIGS. 1 through 3 . For example, the resonator sensor  200  may include an active wafer  202 , housing  204 , end caps  206 ,  208 , and electrodes  212 ,  213 . The active wafer  202  of the resonator sensor  200  may include a first recessed portion  210  formed in a face of the active wafer  202  such that the active wafer  202  includes a resonating portion  214  and a relatively thicker outer portion  216 . A second recessed portion  211  may be formed in a face of the one of the end caps (e.g., end cap  206 ). The recessed portions  210 ,  211  may form cavities  220 ,  221  on opposing sides of the resonating portion  214  of the active wafer  202  to enable the resonating portion  214  to vibrate or otherwise displace under a force applied thereto. One or more of the electrodes  212 ,  213  may include a conductive trace  222  extending along the active wafer (e.g., along the resonating portion  214  and the outer portion  216 ). 
         [0034]      FIG. 5  is a cross-sectional side view of a resonator sensor  300  in accordance with another embodiment of the present disclosure. Similar to  FIG. 4 , the cross-sectional side view of a resonator sensor  300  is taken in direction transverse to the cross-sectional side view of the resonator sensor  100  shown in  FIG. 3 . As shown in  FIG. 5 , the resonator sensor  300  may be somewhat similar to the resonator sensors  100  and  200  and may include similar elements and methods of forming as shown and described above with reference to  FIGS. 1 through 4 . For example, the resonator sensor  300  may include an active wafer  302 , housing  304 , end caps  306 ,  308 , and electrodes  312 ,  313 . A first recessed portion  310  may be formed in a face of the one of the end caps  306 . A second recessed portion  311  may be formed in a face of an opposing end cap  308 . The active wafer  302  of the resonator sensor  300  may include a resonating portion  314  and an outer portion  316  having substantially the same thickness. The recessed portions  310 ,  311  formed in the end caps  306 ,  308  may form cavities  320 ,  321  on opposing sides of the resonating portion  314  of the active wafer  302  to enable the resonating portion  314  to vibrate or otherwise displace under a force applied thereto. One or more (e.g., both) of the electrodes  312 ,  313  may include conductive traces  322  extending along the active wafer  302  (e.g., along the resonating portion  314  and the outer portion  316 ). 
         [0035]      FIG. 6  is a cross-sectional side view of a resonator sensor  350  in accordance with yet another embodiment of the present disclosure. The cross-sectional side view of a resonator sensor  350  is taken in direction similar to that of the cross-sectional side view of the resonator sensor  100  shown in  FIG. 3 . As shown in  FIG. 6 , the resonator sensor  350  may be somewhat similar to the resonator sensors  100 ,  200 , and  300  and may include similar elements and methods of forming as shown and described above with reference to  FIGS. 1 through 5 . For example, the resonator sensor  350  may include an active wafer  352 , housing  354 , end caps  356 ,  358 , and electrodes  362 ,  363 . First recessed portions  360  may be formed in a face of both of the end caps  356 . Second recessed portions  361  may be formed in two, opposing faces of the active wafer  352  such that the active wafer  352  includes a resonating portion  364  and a relatively thicker outer portion  366 . The recessed portions  360  formed in the end caps  356 ,  358  and the recessed portions  361  formed in active wafer  352  may form cavities  370 ,  371  on opposing sides of the resonating portion  364  of the active wafer  352  to enable the resonating portion  364  to vibrate or otherwise displace under a force applied thereto. One or more (e.g., both) of the electrodes  362 ,  363  may include conductive traces  372  extending along the active wafer  352  (e.g., along the resonating portion  364  and the outer portion  366 ). 
         [0036]    In some embodiments, the components of resonator sensors  100 ,  200 ,  300 , and  350  may be fabricated from single crystal quartz, for example, from quartz plates cut to exhibit an AT-cut, BT-cut, or other suitable orientation. In some embodiments, the resonator sensors  100 ,  200 ,  300 , and  350  may include methods of fabrication, orientations, electronic assemblies, housings, reference sensors, and components similar to the sensors and transducers disclosed in, for example, U.S. Pat. No. 5,471,882 to Wiggins, U.S. Pat. No. 4,550,610 to EerNisse, and U.S. Pat. No. 3,561,832 to Karrer et al., the disclosure of each of which is hereby incorporated herein in its entirety by this reference. For example, dimensional characteristics of components of resonator sensors  100 ,  200 ,  300 , and  350  (e.g., dimensions of the end caps, active wafer, cavities, recesses, etc.) may be varied to adjust the pressure and/or temperature sensitivity thereof, by adjusting the stress experienced by the center portion of resonating portion responsive to application of external pressure to the resonator sensors. In some embodiments, the resonator sensors  100 ,  200 ,  300 , or  350  may be implemented in a transducer including drive and signal processing electronics similar to those described in, for example, U.S. Pat. No. 5,231,880 to Ward et al., the disclosure of which is hereby incorporated herein in its entirety by this reference, or any other suitable arrangement. 
         [0037]      FIG. 7  is a top view of an active wafer such as, for example, active wafer  102 . As shown in  FIG. 7 , the active wafer  102  may include a recessed portion  110  formed therein, a resonating portion  114 , an outer portion  116 , and electrode  112  formed on the resonating portion  114 . The electrode  112  may include a conductive trace  122  extending from the resonating portion  114  to an edge of the active wafer  102 . In some embodiments, a tab  126  may be formed proximate an edge of the active wafer  102  (e.g., formed along an edge of the active wafer  102 ). The tab  126  may be electrically connected to the electrode  112  via the conductive trace  122  to enable an electronics assembly to be connected to the electrode  112  via the tab  126  proximate the edge of the active wafer  102 . In some embodiments, the tab  126  may be disposed on the active wafer  102  (e.g., over or under the conductive trace  122 ) by, for example, the deposition techniques described above. In some embodiments, a tab  126  may be formed from gold with an intermediate layer of chromium between the gold and the quartz active wafer  102  to enhance adhesion. In some embodiments, a portion of the tab  126  may overlap the recessed portion  110  of the active wafer  102 . It is noted that while the embodiment of  FIG. 7  illustrates one side (e.g., a first side) of the active wafer  102 , another side may be substantially similar to the side shown in  FIG. 7 . For example, a second, opposing side of the active wafer  102  may be similar to the first side shown in  FIG. 7 ; however, the second side may be a substantially mirror image of the first side (e.g., as shown in  FIG. 3 ). 
         [0038]    In some embodiments, the active wafer  102  may be substantially square, having a length of approximately 0.240 inch (approximately 6.096 millimeters) on each side. The active wafer  102  may have a thickness of approximately 0.004 inch (approximately 0.1016 millimeter). 
         [0039]    In some embodiments, the resonating portion  114  (i.e., the recessed portion  110 ) and the electrode  112  may be formed to have a substantially circular shape. For example, the resonating portion  114  may have a diameter of between approximately 0.110 inch and 0.150 inch (approximately between 2.794 millimeters and 3.81 millimeters) and the electrode  112  may have a diameter of between approximately 0.050 inch and 0.090 inch (approximately between 1.27 millimeters and 2.286 millimeters). 
         [0040]    In some embodiments and as discussed above with reference to  FIG. 3 , a recess  124  may be formed in the adhesive or bonding layer (e.g., the glass frit  118 ) adjacent a periphery of the sensor assembly. The recess  124  may expose a portion of the tab  126  for forming electrical connection between the electrode  112  and an electronics assembly via the tab  126 . 
         [0041]      FIG. 8  is a top view of an array of unsingulated active wafers for use in resonator sensors in accordance with yet another embodiment of the present disclosure. As shown in  FIG. 8 , an array  400  including a plurality of active wafers  402  may be formed as a unitary structure (e.g., a plate or sheet of cultured quartz having a thickness of, for example, approximately 0.004 inch (approximately 0.1016 millimeter)). In some embodiments, the plurality of active wafers  402  of the array  400  may include the elements, features, and methods of forming of the active wafers  102 ,  202 ,  302  described above with reference to  FIGS. 1 through 7 . For example, as shown in  FIG. 9 , the plurality of active wafers  402  of the array  400  may include recessed portions  410  formed therein, resonating portions  414 , outer portions  416 , electrodes  412 , and tabs  426 . In some embodiments, as represented by a portion of array  400  shown in dashed lines, a recess  424  may be formed (e.g., in the adhesion layer, in the array, in the end caps, etc.) to expose portions of the tabs  426  for electrical connection thereto. For example, during adhesion or bonding of the array  400  to one or more ends caps (e.g., end caps  106 ,  108  (FIG.  1 )), the recess  424  may be formed at a corner portion of two or more active wafers  402  such that one recess  424  of the array  400  may provide two to four individual recesses in the separate active wafers  402 . 
         [0042]      FIG. 10  is a cross-sectional side view of an array of resonator sensors in accordance with yet another embodiment of the present disclosure. As shown in  FIG. 10 , an array  500  including a plurality of quartz resonator sensors  501  may be formed as a unitary structure. For example, the array  500  including the plurality of quartz resonator sensors  501  may be formed from an array of active wafers  502  (e.g., array  400  of active wafers  402  as shown and described with reference to  FIGS. 8 and 9 ). The array  500  including the plurality of quartz resonator sensors  501  may include one or more arrays of end caps  506 ,  508 , each array being formed as a unitary structure (e.g., one or more plates of cultured quartz a thickness of, for example, approximately 0.070 inch (approximately 1.778 millimeters)). In some embodiments, the ratio of the thickness of at least one of the end caps  506 ,  508  to the thickness of the active wafers  502  may be 10:1 or greater (e.g., 15:1, 17.5:1, 20:1, etc.). 
         [0043]    As shown in  FIG. 10 , the array  500  including the plurality of quartz resonator sensors  501  may be separated (e.g., singulated) to form individual resonator sensors  501  ( FIG. 11 ). For example, the array  500  including the plurality of quartz resonator sensors  501  may be separated along dashed lines  503  (e.g., separated along a plane transverse to interfaces between the array  400  of active wafers  402  and the arrays of end caps  506 ,  508 ). The array  500  including the plurality of quartz resonator sensors  501  may be separated through a processes such as, for example, a dicing process (e.g., a diamond-edged dicing saw), a scribing and breaking process, laser cutting, or any other suitable singulation or cutting process. 
         [0044]      FIG. 11  is a cross-sectional side view of the array  500  of resonator sensors  501  that have been separated to form individual resonator sensors  501 . The resonator sensors  501  may include any of the elements, features, and methods of forming discussed above with reference to  FIGS. 1 through 9 . 
         [0045]    Embodiments of the current disclosure may be particularly useful in forming and providing resonator sensors (e.g., quartz resonator sensors) having a relatively simplified design such as a resonator sensor having an active wafer including an inverted mesa design. Such resonator sensors may enable the production thereof in quantities greater than one. In other words, multiple sensors may be fabricated simultaneously out of sheets or plates of quartz and may be subsequently separated to form individual resonator sensors. 
         [0046]    While the disclosure may be susceptible to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and have been described in detail herein. However, it should be understood that the disclosure is not intended to be limited to the particular forms disclosed. Rather, the disclosure encompasses all modifications, variations, combinations, and alternatives falling within the scope of the disclosure as defined by the following appended claims and their legal equivalents.