Patent Publication Number: US-2023146578-A1

Title: High sensitivity silicon piezoresistor force sensor

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation application of co-pending U.S. patent application Ser. No. 16/573,500, filed Sep. 17, 2019, which is a continuation of U.S. patent application Ser. No. 15/388,483, filed Dec. 22, 2016, which are incorporated herein by reference. 
    
    
     BACKGROUND 
     In many industrial areas it is necessary to accurately measure the magnitude of a force. Force sensors can be used to measure a force or a pressure. Various designs can be used and can rely on a displacement of a component or a stress-field applied to a stress-sensitive element or component to measure the presence of a force and/or an amount of the force present on the sensor. Force sensors can experience forces above their designed operating ranges (e.g., overforce situations), which can result in damage to the force sensors. 
     SUMMARY 
     In an embodiment, a sense die may comprise a chip comprising a slab; one or more sense elements supported by the slab, wherein the ratio of the width of the slab to the distance between the one or more sense elements is at least 2/1; one or more bond pads supported by a first side of the chip, each of the one or more bond pads electrically coupled to at least one of the one or more sense elements; a structural frame disposed on the first side of the chip, wherein the structural frame is disposed at least partially about the slab; and one or more electrical contacts extending through the structural frame, wherein the one or more electrical contacts are electrically coupled to the one or more bond pads. 
     In an embodiment, a method of sensing a force using a sense die may comprise providing a sense die comprising a chip having a slab formed thereon; applying a force to the slab of the sense die; and determining the magnitude of the force applied to the slab via one or more sense elements attached to the slab, wherein the ratio of the width of the slab to the distance between the one or more sense elements is greater than approximately 2/1. 
     In an embodiment, a sense die may comprise a chip comprising a slab; an actuation element configured to contact the slab at or near the center of the slab, and configured to apply a force to the slab; and one or more sense elements supported by the slab, wherein the ratio of the width of the slab to the distance between the one or more sense elements is greater than approximately 2/1, and wherein the distance between the sense elements is centered on the contact point between the actuation element and the slab. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present disclosure, reference is now made to the following brief description, taken in connection with the accompanying drawings and detailed description, wherein like reference numerals represent like parts. 
         FIG.  1    illustrates a schematic cross-section of a sense die according to an embodiment of the disclosure. 
         FIGS.  2 A- 2 C  illustrate cross-sectional views of an actuation element, a slab and a sense die according to embodiments of the disclosure. 
         FIGS.  3 A- 3 C  illustrate a stress map of a surface of a sense die according to an embodiment of the disclosure. 
         FIGS.  4 A- 4 B  illustrate the relationships between load on the sense die, location of the sense elements, and sensor output according to an embodiment of the disclosure. 
         FIG.  5    illustrates the relationship between contact radius and load on the sense die according to an embodiment of the disclosure. 
         FIGS.  6 A- 6 B  illustrate cross sectional views of a sense die that illustrate the relationship between contact radius and load on the sense die according to an embodiment of the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     It should be understood at the outset that although illustrative implementations of one or more embodiments are illustrated below, the disclosed systems and methods may be implemented using any number of techniques, whether currently known or not yet in existence. The disclosure should in no way be limited to the illustrative implementations, drawings, and techniques illustrated below, but may be modified within the scope of the appended claims along with their full scope of equivalents. 
     The following brief definition of terms shall apply throughout the application: 
     The term “comprising” means including but not limited to, and should be interpreted in the manner it is typically used in the patent context; 
     The phrases “in one embodiment,” “according to one embodiment,” and the like generally mean that the particular feature, structure, or characteristic following the phrase may be included in at least one embodiment of the present invention, and may be included in more than one embodiment of the present invention (importantly, such phrases do not necessarily refer to the same embodiment); 
     If the specification describes something as “exemplary” or an “example,” it should be understood that refers to a non-exclusive example; 
     The terms “about” or “approximately” or the like, when used with a number, may mean that specific number, or alternatively, a range in proximity to the specific number, as understood by persons of skill in the art field; and 
     If the specification states a component or feature “may,” “can,” “could,” “should,” “would,” “preferably,” “possibly,” “typically,” “optionally,” “for example,” “often,” or “might” (or other such language) be included or have a characteristic, that particular component or feature is not required to be included or to have the characteristic. Such component or feature may be optionally included in some embodiments, or it may be excluded. 
     Embodiments of the disclosure include systems and methods for improving the signal output from a sense die configured to detect force applied to the sense die. Embodiments of the disclosure may comprise piezoresistive elements unusually close to the center of the die, where the load-bearing actuation element makes contact to the die face. Through stress mapping of the surface of the sense die, it was discovered that there is a small localized area of very high signal-generating stress near the actuation element. When piezoresistive elements are implanted in this location, die sensitivities can be up to 100 times greater or higher than traditional locations for the piezoresistive elements. Because the small areas of high stress constitute a localized contact phenomenon, no anisotropic etch is needed to form a diaphragm, and therefore a “slab” die can be used. Using a slab die may have the advantage of significantly higher proof loads (i.e. higher overload protection), while at the same time reducing cost because it is no longer necessity to complete the anisotropic etch. Additionally, this method of positioning the piezoresistive elements may allow for a smaller die to be used, which may lower costs as well. 
     Typical uses of piezoresistive elements position the piezoresistive elements at or near the center edge of a formed diaphragm. Typical force sensors may use a stress field that is relatively distant from the contact point between the actuation element and the sense die (or the load point). Embodiments of the disclosure may use a localized stress field very near the load point. This localized stress field may be much higher in magnitude than the typically used distant stress field, leading to higher die output for a given load. 
     A technical benefit of the described method of positioning the piezoresistive elements may include much higher die output for a given load. Additionally, since a full wafer thickness may be used, no specifically-defined diaphragm is required, and therefore the proof load is significantly higher. Also, the costs of the sense die may be reduced because no etch steps are required to form a diaphragm, no specially patterned adhesive is required under the die (just a continuous layer rather than a “picture frame” pattern with an unsupported central area), and a smaller die can be used (costs are proportional to the size of a die, where even a 30% reduction is die side length may translates to a cost reduction of up to 50%). The same general design and orientation of the piezoresistive elements may be similar to a traditional pressure or force sensor, but the location of the piezoresistive elements may be adjusted. 
       FIG.  1    illustrates an embodiment of a typical sense die  100  according to some embodiments that can be used to detect a force, including a pressure. As shown, the sense die  100  can include a diaphragm or slab  102 , and a substrate  140  located near a first surface  103  of the sensor. The slab  102  may comprise one or more sense elements  120 ,  124  connected to one or more electrical contacts  106 . The sense elements  120 ,  124  may be located on a second surface  105  of the slab  102 . Optionally, a sidewall  108  can be attached to a portion of a second surface  105  of the sensor. An actuation element  110  can be present within a cavity  112  formed by the sidewall  108  and can serve to transfer a force to the second surface  105  of the slab  102 . In some embodiments, the slab  102  may comprise a solid slab. In some embodiments, the slab  102  may be attached to the substrate  140  via an adhesive  142 . 
     The sense die  100  may be formed from silicon or other semiconductor material. While the sense die  100  is described with respect to being formed from silicon, it should be understood that other materials can also be used. In an embodiment, the sense die  100  can begin as a silicon chip and be processed to form the sense die  100 , as described in more detail herein. In some embodiments, the silicon chip may include a recess formed on the first surface  103  to form a diaphragm  102 . A variety of micro-fabrication techniques including, but not limited to, lithography techniques, wet etching techniques, and dry etching techniques may be used to form the recess. In some embodiments, the diaphragm  102  may be fabricated on the sense die  100  by back-side etching of a silicon die (e.g., with a KOH etching technique, deep reactive ion etching, or other etching technique). However, it is contemplated that any suitable process may be used, as desired. The diaphragm  102  may have a height or thickness that is less than the thickness of the edges of the sense die  100 , thereby forming the diaphragm  102 . 
     The diaphragm or slab  102  is configured to flex in response (or at least have some elastic response) to an applied force, creating stress fields that extend through the one or more sense elements  120  and  124 , thereby allowing the applied force to be determined. In some embodiments, the elastic response of the slab  102  may be microscopic in nature. In some embodiments, the applied force can be present in the form of a differential pressure across the slab  102 . In some embodiments, an actuation element  110  may be in contact with the second surface  105  of the slab  102  to transfer a force to the slab  102 . The actuation element  110  can comprise a mechanical coupling between an exterior force and the slab  102 . In some aspects, the actuation element  110  can comprise a mechanical actuation element configured to transfer a force to the slab  102 . In some embodiments, the actuation element  110  may include a spherical object (such as the sphere shown in  FIG.  1   ), a pin, an extender, a button, any other activation device, and/or a combination thereof. It may be appreciated that other types of actuators may be utilized, such as, for example, slidable mounted plungers or shafts, point of contact type components other than spherical objects, and/or “T”-shaped transfer mechanisms, in accordance with alternative embodiments. If desired, only a portion of an outer surface of the actuation element  110  may be spherical in shape or take on a particular shape. The actuation element  110  may be made of any material. For example, the actuation element  110  may be formed from stainless steel, a polymer, a ceramic, jeweled, another suitable metal, and/or another suitable material. In some cases, the actuation element  110  may include a stainless steel ball bearing. It is contemplated, however, that other generally spherical and other shaped elements may be used as or as part of the actuation element  110 , if desired, including polymer based objects. 
     The deflection resulting from a force applied on the diaphragm through an applied pressure and/or through the actuation element  110  may generally result in the deflection of the slab  102 . The slab  102  may be configured to detect a deflection that is predominantly in a direction perpendicular to the plane of the slab  102 . In this sense, the sense die  100  is configured to measure a uniaxial force that is provided normal to the plane of sense die  100 . 
     The sense die  100  may have one or more sensing elements  120  and  124  disposed on or adjacent to the slab  102 , such as piezoresistive sensing elements or components formed using suitable fabrication or printing techniques. For example, starting with the silicon sense die  100 , standard pattern, implant, diffusion, and/or metal interconnect processes may be used to form one or more elements  120  and  124  on a surface  103 ,  105  of the sense die  100 . For example, one or more piezoresistive sense elements  120  and  124  may be formed on the slab  102 . The piezoresistive sense elements  120  and  124  may be configured to have an electrical resistance that varies according to an applied mechanical stress (e.g. deflection of the slab  102 ). The piezoresistive elements  120  and  124  can thus be used to convert the applied force or pressure into an electrical signal. In some instances, the piezoresistive components may include a silicon piezoresistive material; however, other non-silicon materials may be used. 
     One or more bond pads  130  and  134  may be formed on the upper surface  105  of the sense die  100  and adjacent to the slab  102 . Metal, diffusion, or other interconnects may be provided to interconnect the one or more piezoresistive sensor elements  120  and  124  and the one or more bond pads  130  and  134 . As shown in  FIG.  1   , one or more of the piezoresistive sensor elements  120  and  124  can be electrically coupled to one or more of the bond pads  130  and  134 . 
     In some embodiments, the sense elements  120  and  124  may comprise a plurality of sense elements, for example two sense elements, three sense elements, four sense elements, or more. Similarly, the bond pads  130  and  134  may comprise a plurality of bond pads, for example two bond pads, three bond pads, four bond pads, or more.  FIG.  1    indicates typical locations for the piezoresistive elements  120  and  124 . These locations may be selected to be within an area of the slab  102 , where the slab  102  experiences forces from the contact with the actuation element  110 . 
     Embodiments of the disclosure describe a sense die  100  where the piezoresistive elements are located much closer to the contact area between the actuation element  110  and the slab  102  (or diaphragm), than a typical sense die. 
       FIGS.  2 A- 2 C  illustrate cross-sectional views of an actuation element  210  (which may comprise a ball bearing) and a slab  202  of a sense die  200 . The actuation element  210  may comprise a spheroid shape. The actuation element  210  may contact and apply pressure to a contact area  220  between the actuation element  210  and the slab  202 . The slab  202  may comprise a first surface  203 , which may be attached to a structural frame  204 . The slab  202  may comprise a second surface  205  configured to contact the actuation element  210 . 
     In some embodiments, the actuation element  210  may comprise stainless steel. In some embodiments, the actuation element  210  may comprise glass, sapphire, or another similar material. In some embodiments, the total length of the sense die  200  may be reduced by approximately 20% to 30% compared to a typical sense die  200 . 
       FIG.  2 A  illustrates a sense die  200  comprising a slab  202  attached to a substrate  240  via an adhesive layer  242 . The slab  202  may comprise sense elements  250  located on the surface  205  of the slab  202 . The distance between the sense elements  250  is indicated by distance  260 . The width of the slab  202  is indicated by width  262 . 
     In the embodiment shown in  FIG.  2 B , the slab  202  may comprise an etched cavity  230  on the first surface  203  of the slab  202 . However, in other embodiments, such as  FIGS.  2 A and  2 C , the slab  202  may not be etched. In other words, the slab  202  may not comprise any thinned areas or cavities on either surface  203  and  205  of the slab  202 . 
       FIG.  2 C  illustrates a double cross-section of the slab  202 , illustrating a quarter view of the slab  202  and actuation element  210 . The slab  202  may comprise four sense element  250  located about the contact point  220  between the slab  202  and the actuation element  210 . 
     In some embodiments, the sense elements  250  may be closer together than in a typical sense die. In some embodiments, the distance  260  between the sense elements  250  may be centered on the contact point  220  between the actuation element  210  and the slab  202 . 
     Referring to  FIG.  2 A , in some embodiments, the ratio between the width  262  of the slab  202  and the distance  260  between the sense elements  250  may be greater than approximately 3/1. In some embodiments, the ratio between the width  262  of the slab  202  and the distance  260  between the sense elements  250  may be greater than approximately 5/1. In some embodiments, the ratio between the width  262  of the slab  202  and the distance  260  between the sense elements  250  may be greater than approximately 7/1. In some embodiments, the ratio between the width  262  of the slab  202  and the distance  260  between the sense elements  250  may be greater than approximately 11/1. In some embodiments, the ratio between the width  262  of the slab  202  and the distance  260  between the sense elements  250  may be less than approximately 20/1. In some embodiments, the sense elements  250  may not touch one another. 
     In some embodiments, the location of the sense elements  250  may be chosen based on the anticipated stress at a particular location on the surface  205  of the slab  202 . 
     Referring to  FIGS.  3 A- 3 C , a stress map  300  is shown illustrating the stress fields resulting from a force applied to the second surface  205  of the slab  202  by the actuation element  210 . The slab  202  and actuation element  210  are shown above. The stress map  300  may comprise a plot of the difference between stress in the x direction (Sx) and stress in the y direction (Sy) or Sx-Sy. The largest values, both positive and negative, may indicate the locations on the surface  205  of the slab where the stress is the highest in one direction. These areas may be called “hotspots” or high stress areas. The stress field generated on the surface  205  at the hotspots  302  and  304  may be significantly greater than the stress field generated at other areas of the surface  205 . The hotspots  302  and  304  may create an ideal location for a piezoresistive element to be placed on the surface  205 , where the piezoresistive element may detect the stress created at that location. The hotspots  302  and  304  may be located closer to the contact area  220  than typical locations for piezoresistive elements. 
     The stress map  300  shown in  FIGS.  3 A- 3 B  may be cross-sectioned to show a quarter of the total surface  205  of the slab  202 , wherein the corner  310  illustrates the center of the contact area  220  (as shown above) between the actuation element and the slab. Referring to  FIG.  3 C , a full stress map  300  may comprise up to four hotspots  302 ,  304 ,  306 , and  308  surrounding the center  310  of the contact area  220  between the actuation element and the slab. The typical locations for piezoresistive elements are indicated by “x”  322 ,  324 ,  326 , and  328 . 
     Using the information from the stress map  300  shown in  FIGS.  3 A- 3 C , the piezoresistive elements (such as  120  and  124  described above) may be placed within one of the hotspots  302 ,  304 ,  306 , and  308  indicated by the stress map  300 . While the stress at the typical locations  322 ,  324 ,  326 , and  328  for the piezoresistive elements may be within an area that will detect stress on the slab surface  205 , the hotspots  302 ,  304 ,  306 , and  308  may produce significantly higher outputs, thereby improving the accuracy and sensitivity of the piezoresistive elements. For example, Sx-Sy stress at the typical locations  322 ,  324 ,  326 , and  328  for piezoresistive elements may be approximately ±70 megapascal (MPa), and stress in the hotspots  302 ,  304 ,  306 , and  308  may be approximately ±1400 MPa (approximately 20 times higher than the typical stress readings). The increased stress reading may produce an increased signal output for the piezoresistive elements. 
     Unlike a typical pressure sensor comprising an anisotropic etch, the Sx-Sy stress peak measured on the surface  205  of the slab moves outward radially from the contact area  220  as the load on the surface  205  is increased. In other words, the hotspots may change in location based on the magnitude of the force applied to the slab via the actuation element. For example, the distance from the center  310  at which the hotspot occurs may increase as the magnitude of the force increases. This concept may be illustrated by the following graphs and figures. 
     Piezoresistive elements located at different positions with respect to the center of the surface  205  were evaluated at a range of forces applied to the surface  205 . The results are show in the graphs of  FIGS.  4 A- 4 B . As an example, the locations ranged from approximately 39 microns (μm) from the center to approximately 310 μm from the center. 
     Referring to  FIG.  4 A , the sensor output in millivolts (mV) is plotted against the load applied to the slab in Newtons (N). Each line indicates a different location for the piezoresistive elements, measured in radians from the center of the contact area between the slab and the actuation element. The traditional location of the piezoresistive elements is also plotted, for reference, wherein the distance from the center is higher in a traditional sensor. For each line on the graph, the sensor output builds as the load increases until the Sx-Sy peak passes through the location of the piezoresistive element, and then then the output drops off. Sensor function may be optimal before the peak in the lines. 
     Referring to  FIG.  4 B , the graph illustrates the results show in  FIG.  4 A  that have been normalized using a standard of the traditional sensor location output (at a distance of 890 μm), where the results for each of the locations have been divided by the standard. The graph shown in  FIG.  4 B  illustrates that the sensor output may be relatively constant before the peak (for that location), and may be usable for determining stress on the slab at that location. 
     For most sensor applications, it may be possible to estimate the range of the load expected for a particular application. Using the graphs and the estimated load (in N), an optimal location for the piezoresistive elements may be chosen. For example, if the expected load is less than 5 N, the location for the piezoresistive elements may be chosen to be at a distance of between approximately 30 to 80 μm from the center. As another example, if the expected load is between 10 and 20 N, the location for the piezoresistive elements may be chosen to be at a distance of between approximately 100 to 120 μm from the center. 
     Referring to  FIG.  5   , an additional graph illustrates the approximate relationship between the contact radius between the flat surface of the slab and the curved surface of the spherical actuation element, and the estimated load that will be applied to the sense die. As the load increases, what is initially a point contact between the slab and the actuation element, widens out into circular contact.  FIG.  5    is a plot of the radius of that circle of contact vs. force applied by the actuation element. In some embodiments, it may be desirable to locate the sense elements outside the contact radius, to avoid contact between the actuation element and the sense elements. However, in some embodiments, the actuation element may contact one or more of the sense elements during the use life of the sense die. 
     To further evaluate the effect of locating the piezoresistive elements closer to the center of a slab, sense die were analyzed to solve for the generated signal. At approximately 1 N force applied to the slab, the signal from a piezoresistive element located at the typical location of 890 μm from the center may produce approximately 3.6 mV. When the location of the piezoresistive element was changed to 310 μm from the center, the signal may rise to approximately 27.3 mV (approximately 7.6 times the typical output). When the location of the piezoresistive element was changed to 150 μm from the center, the signal may rise to approximately 87.2 mV (approximately 246 times the typical output). 
     Additionally, it may be desirable to provide accurate measurements for forces lower than 1 N. Force detection in this low range may typically be difficult to achieve with adequate over-load protection. To further evaluate the effect of locating the piezoresistive elements closer to the center of a slab, sense dies were tested to determine the generated signal in force ranges of approximately 1 N (100 g), approximately 0.1 N (10 g), approximately 0.01 N, and approximately 0.001 N. 
     As described above, the closer a piezoresistive element is location to the center (i.e. the smaller the distance from the center), the higher the sensitivity of the output signal. In the following results, the closest location for the piezoresistive element was approximately 150 μm from the center. For a force range of 0.1 N, at a location of 150 μm from the center, the sensor output may be approximately 8.8 mV. 
     As the force ranges decrease below 1 N, it may be proportionally harder to develop sufficient output signal. Therefore, the use of piezoresistive elements positioned closer to the center of the slab may allow for improved signal output for lower force ranges. 
       FIGS.  6 A- 6 B  further illustrate the relationship between the contact radius, i.e. the distance from the center  310  of the slab  202  at which the piezoresistive element is located, and the estimated load that will be applied to the sense die. In  FIG.  6 A , the force applied to the actuation element  210  is approximately 25 N. The contact radius to the first hotspot  302  is indicated by distance  602 . Similarly, the contact radius to the second hotspot  304  is indicated by distance  604 . 
     In  FIG.  6 B , the force applied to the actuation element  210  is increased to approximately 100 N. The distance  602  to the first hotspot  302  has increased accordingly. Similarly, the distance  604  to the second hotspot  304  has increased accordingly. Therefore, the optimal location for the piezoresistive elements to be located at or near a hotspot  302  and  304  depends on the amount of force that is anticipated to be applied to the slab  202 . 
     The sensitivity (measured in mV/V) of the sense elements described above was determined via modeling, and then compared to a standard or typical sensor. The different locations of the sense elements were compared to one another as well. In some embodiments, the sensitivity ratio (when compared to a typical sensor) may be greater than approximately 1/1. In some embodiments, the sensitivity ratio may be greater than approximately 5/1. In some embodiments, the sensitivity ratio may be greater than approximately 10/1. In some embodiments, the sensitivity ratio may be greater than approximately 20/1. In some embodiments, the sensitivity ratio may be greater than approximately 25/1. 
     In a first embodiment, a sense die may comprise a chip comprising a slab; one or more sense elements supported by the slab, wherein the ratio of the width of the slab to the distance between the one or more sense elements is at least 2/1; one or more bond pads supported by a first side of the chip, each of the one or more bond pads electrically coupled to at least one of the one or more sense elements; a structural frame disposed on the first side of the chip, wherein the structural frame is disposed at least partially about the slab; and one or more electrical contacts extending through the structural frame, wherein the one or more electrical contacts are electrically coupled to the one or more bond pads. 
     A second embodiment can include the sense die of the first embodiment, wherein the sense elements comprise piezoresistive elements. 
     A third embodiment can include the sense die of the first or second embodiments, further comprising an actuation element configured to contact the slab at or near the center of the slab. 
     A fourth embodiment can include the sense die of the third embodiment, wherein the distance between the sense elements is centered on the contact point between the slab and the actuation element. 
     A fifth embodiment can include the sense die of any of the first to fourth embodiments, wherein the ratio of the width of the slab to the distance between the one or more sense elements is greater than approximately 5/1. 
     A sixth embodiment can include the sense die of any of the first to fifth embodiments, the ratio of the width of the slab to the distance between the one or more sense elements is greater than approximately 10/1. 
     A seventh embodiment can include the sense die of any of the first to sixth embodiments, wherein the locations of the one or more sense elements are determined by mapping the force on the slab applied by the actuation element, and identifying one or more hotspots on the slab where the force is higher than the surrounding areas. 
     An eighth embodiment can include the sense die of any of the first to seventh embodiments, wherein the locations of the one or more sense elements are determined by determining a correlation between the estimated force that will be applied to the slab and the desired location for sense elements on the slab. 
     In a ninth embodiment, a method of sensing a force using a sense die may comprise providing a sense die comprising a chip having a slab formed thereon; applying a force to the slab of the sense die; and determining the magnitude of the force applied to the slab via one or more sense elements attached to the slab, wherein the ratio of the width of the slab to the distance between the one or more sense elements is greater than approximately 2/1. 
     A tenth embodiment can include the method of the ninth embodiment, further comprising determining a correlation between the estimated force that will be applied to the slab and the desired location for sense elements on the slab. 
     An eleventh embodiment can include the method of the tenth embodiment, wherein as the estimated force increases, the desired location for the sense elements increases in distance from the center of the slab. 
     A twelfth embodiment can include the method in of any of the ninth to eleventh embodiments, wherein applying a force comprises contacting the slab with an actuation element. 
     A thirteenth embodiment can include the method of the twelfth embodiment, wherein the distance between the sense elements is centered on the contact point between the slab and the actuation element. 
     A fourteenth embodiment can include the method of any of the ninth to thirteenth embodiments, wherein the ratio of the width of the slab to the distance between the one or more sense elements is greater than approximately 5/1. 
     A fifteenth embodiment can include the method of the any of the ninth to fourteenth embodiments, further comprising mapping the force on the slab applied by the actuation element; identifying one or more hotspots on the slab where the force is higher than the surrounding areas; and determining the location for a piezoresistive element to be located on the slab based on the location of the hotspots. 
     In a sixteenth embodiment, a sense die may comprise a chip comprising a slab; an actuation element configured to contact the slab at or near the center of the slab, and configured to apply a force to the slab; and one or more sense elements supported by the slab, wherein the ratio of the width of the slab to the distance between the one or more sense elements is greater than approximately 2/1, and wherein the distance between the sense elements is centered on the contact point between the actuation element and the slab. 
     A seventeenth embodiment can include the sense die of the sixteenth embodiment, wherein the sense elements comprise piezoresistive elements. 
     An eighteenth embodiment can include the sense die of the sixteenth or seventeenth embodiments, wherein the ratio of the width of the slab to the distance between the one or more sense elements is greater than approximately 5/1. 
     A nineteenth embodiment can include the sense die of any of the sixteenth to eighteenth embodiments, wherein the ratio of the width of the slab to the distance between the one or more sense elements is less than approximately 20/1. 
     A twentieth embodiment can include the sense die of any of the sixteenth to nineteenth embodiments, wherein the sense elements are located at or near hotspots identified on the surface of the slab by force mapping. 
     While various embodiments in accordance with the principles disclosed herein have been shown and described above, modifications thereof may be made by one skilled in the art without departing from the spirit and the teachings of the disclosure. The embodiments described herein are representative only and are not intended to be limiting. Many variations, combinations, and modifications are possible and are within the scope of the disclosure. Alternative embodiments that result from combining, integrating, and/or omitting features of the embodiment(s) are also within the scope of the disclosure. Accordingly, the scope of protection is not limited by the description set out above, but is defined by the claims which follow, that scope including all equivalents of the subject matter of the claims. Each and every claim is incorporated as further disclosure into the specification and the claims are embodiment(s) of the present invention(s). Furthermore, any advantages and features described above may relate to specific embodiments, but shall not limit the application of such issued claims to processes and structures accomplishing any or all of the above advantages or having any or all of the above features. 
     Additionally, the section headings used herein are provided for consistency with the suggestions under 37 C.F.R. 1.77 or to otherwise provide organizational cues. These headings shall not limit or characterize the invention(s) set out in any claims that may issue from this disclosure. Specifically and by way of example, although the headings might refer to a “Field,” the claims should not be limited by the language chosen under this heading to describe the so-called field. Further, a description of a technology in the “Background” is not to be construed as an admission that certain technology is prior art to any invention(s) in this disclosure. Neither is the “Summary” to be considered as a limiting characterization of the invention(s) set forth in issued claims. Furthermore, any reference in this disclosure to “invention” in the singular should not be used to argue that there is only a single point of novelty in this disclosure. Multiple inventions may be set forth according to the limitations of the multiple claims issuing from this disclosure, and such claims accordingly define the invention(s), and their equivalents, that are protected thereby. In all instances, the scope of the claims shall be considered on their own merits in light of this disclosure, but should not be constrained by the headings set forth herein. 
     Use of broader terms such as “comprises,” “includes,” and “having” should be understood to provide support for narrower terms such as “consisting of,” “consisting essentially of,” and “comprised substantially of” Use of the terms “optionally,” “may,” “might,” “possibly,” and the like with respect to any element of an embodiment means that the element is not required, or alternatively, the element is required, both alternatives being within the scope of the embodiment(s). Also, references to examples are merely provided for illustrative purposes, and are not intended to be exclusive. 
     While several embodiments have been provided in the present disclosure, it should be understood that the disclosed systems and methods may be embodied in many other specific forms without departing from the spirit or scope of the present disclosure. The present examples are to be considered as illustrative and not restrictive, and the intention is not to be limited to the details given herein. For example, the various elements or components may be combined or integrated in another system or certain features may be omitted or not implemented. 
     Also, techniques, systems, subsystems, and methods described and illustrated in the various embodiments as discrete or separate may be combined or integrated with other systems, modules, techniques, or methods without departing from the scope of the present disclosure. Other items shown or discussed as directly coupled or communicating with each other may be indirectly coupled or communicating through some interface, device, or intermediate component, whether electrically, mechanically, or otherwise. Other examples of changes, substitutions, and alterations are ascertainable by one skilled in the art and could be made without departing from the spirit and scope disclosed herein.