Abstract:
A micro electromechanical system (MEMS) includes a substrate, a first curved surface located at a position above a surface of the substrate, and a second curved surface generally opposite to the first curved surface along a first axis parallel to the surface of the substrate, wherein the first curved surface is movable along the first axis in a direction toward the second curved surface.

Description:
[0001]    This application claims the benefit of U.S. Provisional Application No. 61/557,767, filed Nov. 9, 2011, the entire contents of which is herein incorporated by reference. 
     
    
     FIELD 
       [0002]    The present disclosure relates to semiconductor devices and, more particularly, to semiconductor devices incorporating sensors. 
       BACKGROUND 
       [0003]    Micro-electromechanical systems referred to herein as “MEMS” or “MEMS devices”, integrate electrical and mechanical components on the same silicon substrate using microfabrication technologies. The electrical components are fabricated using integrated circuit processes, while the mechanical components are fabricated using micromachining processes compatible with the integrated circuit processes. This combination makes it possible to fabricate an entire electromechanical system on a silicon substrate using standard manufacturing processes. 
         [0004]    A common application of MEMS devices is the design and manufacture of sensors. These sensors have proven to be effective solutions in various applications due to the sensitivity, spatial and temporal resolutions, and lower power requirements exhibited by MEMS devices. Consequently, MEMS sensors, such as inertial sensors, gyroscopes and pressure sensors, have been developed for use in a wide variety of applications. 
         [0005]    MEMS inertial sensors are useful for measuring both static and dynamic acceleration. In particular, MEMS inertial sensors may be used to sense the orientation and position of a device. One type of MEMS inertial sensor includes a proof mass supported above a substrate anchor by a spring. The substrate anchor defines a cavity in which the proof mass is movably positioned. The spring positions the proof mass in a neutral position within the cavity. When the substrate anchor accelerates, the proof mass moves from the neutral position relative the substrate anchor, but remains within the cavity. The spring constant of the spring, among other factors, determines the amount of movement exhibited by the proof mass in response to acceleration of the substrate anchor. The travel span of the proof mass within the cavity is referred to as a displacement range. Electrical leads may be connected to the substrate anchor and the proof mass. Acceleration of the substrate anchor can be sensed by measuring the capacitance between the substrate anchor and the proof mass. 
         [0006]    Some known MEMS inertial sensors incorporate one or more positioning features to limit and to define the displacement range of the proof mass within the cavity. If the sensor is subjected to a force that exceeds a threshold force, the proof mass may move to a position of maximum displacement. The positioning features ensure the proof mass remains properly positioned within the cavity even after the proof mass has been moved to a position of maximum displacement. Furthermore, positioning features prevent the proof mass from moving to a position that breaks, fractures, or otherwise damages the spring. 
         [0007]    In the past, positioning features were implemented with a flat surface on the substrate anchor and a corresponding flat surface on the proof mass. These flat surfaces contact each other when the proof mass is moved to a position of maximum displacement. Although positioning features having flat surfaces effectively limit and define the maximum displacement of the proof mass, stiction may occur as a result of contact between the flat surfaces. 
         [0008]    The term “stiction”, as used herein, refers to the force that must be overcome to move a first object that is in physical contact with a second object. In general, stiction increases in relation to the surface area of the contact region between the first and second objects. As applied to MEMS having positioning features with flat contact surfaces, stiction may occur as a result of large external physical shocks, such as drop tests, and spring-mass resonant frequency excitation, etc. As reported by G. J. O&#39;Brian, D. J. Monk, and L. Lin, “A Stiction Study Via Capacitance-Voltage (C-V) Plot Electrostatic Actuation/Latching”, American Society of Mechanical Engineering MEMS, Vol. 1, pp. 275-280 (1999), electrostatic self-test actuation of MEMS inertial sensors is also an event that may result in stiction. 
         [0009]    Stiction may cause a MEMS inertial sensor to generate false measurements or become inoperable. In particular, some stiction causing events may cause the proof mass to adhere permanently to the substrate anchor, thereby resulting in the MEMS ceasing to sense acceleration. Other stiction causing events, however, may cause the proof mass to adhere temporarily to the substrate anchor, which may result in the MEMS inaccurately sensing acceleration. Therefore, both temporary and permanent adhesion of the proof mass to the substrate anchor as a result of stiction may cause a MEMS inertial sensor to generate false measurements. 
         [0010]    Accordingly, a MEMS inertial sensor subject to less stiction between the substrate anchor and the proof mass would be beneficial. 
       SUMMARY 
       [0011]    A micro electromechanical system (MEMS) in one embodiment includes a substrate, a first curved surface located at a position above a surface of the substrate, and a second curved surface generally opposite to the first curved surface along a first axis parallel to the surface of the substrate, wherein the first curved surface is movable along the first axis in a direction toward the second curved surface. 
         [0012]    In accordance with another embodiment, an accelerometer for a micro electromechanical system (MEMS) includes a substrate, a proof mass at a position above a surface of the substrate and with a first curved surface located on a first side of the proof mass, and a travel stop with a second curved surface generally opposite to the first curved surface, wherein the first curved surface is movable in a direction toward the second curved surface. 
         [0013]    In accordance with another embodiment, a method of forming an accelerometer for a micro electromechanical system (MEMS) includes, forming a substrate, forming a proof mass with a first curved surface on a first side of the proof mass at a position above a surface of the substrate, and forming a first travel stop fixed in position with respect to the substrate and including a second curved surface generally opposite to the first curved surface, wherein the proof mass is movable in a direction toward the first travel stop. 
     
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         [0014]    Features of the device and method disclosed herein will become apparent to those skilled in the art from the following description with reference to the figures, in which: 
           [0015]      FIG. 1  depicts a perspective view of a micro electromechanical system (“MEMS”) having proof mass positioning features that include concave followers on a proof mass and convex travel stops on an anchor; 
           [0016]      FIG. 2  depicts a cross sectional view of the MEMS along line  2 - 2  of  FIG. 1 ; 
           [0017]      FIG. 3  depicts a top plan view of the MEMS of  FIG. 1 ; 
           [0018]      FIG. 4  depicts a partial top plan view of a positioning feature of the MEMS of  FIG. 1 , the proof mass being in a neutral position; 
           [0019]      FIG. 5  depicts a partial top plan view of a positioning feature of the MEMS of  FIG. 1 , the proof mass being in a position of maximum negative displacement along the x-axis; 
           [0020]      FIG. 6  depicts a partial top plan view of a positioning feature of the MEMS of  FIG. 1 , the proof mass being in a position of maximum negative displacement along the y-axis; 
           [0021]      FIG. 7  depicts a top plan view of an embodiment of a MEMS having proof mass positioning features that include concave followers on a proof mass and convex travel stops on an anchor; 
           [0022]      FIG. 8  depicts a top plan view of an embodiment of a MEMS having proof mass positioning features that include concave followers on an anchor and convex travel stops on a proof mass; 
           [0023]      FIG. 9  depicts a top plan view of an embodiment of a MEMS having proof mass positioning features that include rectangular followers on a proof mass and convex travel stops on an anchor; 
           [0024]      FIG. 10  depicts a top plan view of a mask for forming a MEMS having proof mass positioning features that include a first element and a second element separated by a submicron gap; 
           [0025]      FIG. 11  depicts a top plan view of a MEMS formed with the mask of  FIG. 10 ; 
           [0026]      FIG. 12  depicts a top plan view of a mask for forming a MEMS having proof mass positioning features that include a first element and a second element separated by a submicron gap; 
           [0027]      FIG. 13  depicts a top plan view of a MEMS formed with the mask of  FIG. 12 ; 
           [0028]      FIG. 14  depicts a schematic view of a MEMS tunneling tip accelerometer; and 
           [0029]      FIG. 15  depicts a partial top plan view of a mask for forming a first and second tip of the tunneling tip accelerometer of  FIG. 14 . 
       
    
    
     DESCRIPTION 
       [0030]    For the purpose of promoting an understanding of the principles of the device and method described herein, reference will now be made to the embodiments illustrated in the figures and described in the following written specification. It is understood that no limitation to the scope of the device and method is thereby intended. It is further understood that the device and method includes any alterations and modifications to the illustrated embodiments and includes further applications of the principles of the device and method as would normally occur to one skilled in the art to which this device and method pertains. 
         [0031]    An exemplary embodiment of a micro electromechanical system (“MEMS”)  100  is depicted in  FIG. 1 . The MEMS  100  is configured to sense acceleration. In particular, when the MEMS  100  accelerates in a direction having a component along the z-axis, the MEMS  100  generates an electrical output related to the acceleration. 
         [0032]    The MEMS  100  includes a substrate  108 , a wall  112 , and a proof mass  116 . The substrate  108  defines a surface  120  in an x-y plane that is generally normal, i.e. perpendicular, to the z-axis. The wall  112  is coupled to the substrate  108  and extends above the surface  120  along the z-axis. The wall  112  may be formed from the same material as the substrate  108 , and, in some embodiments, may be integral with the substrate  108 . Alternatively, the wall  112  may be a material different from the substrate  108  that is deposited on the surface  120  and bonded to the substrate  108 . As illustrated in  FIG. 1 , the wall  112  is formed about the proof mass  116  as a unitary section of material; however, the wall  112  may also be formed about the proof mass  116  as sections of material separated by one or more spaces. The wall  112  and the surface  120  define a cavity  124 . The cavity  124  has a length along the y-axis, a width along the x-axis, and a depth along the z-axis. 
         [0033]    The proof mass  116  is positioned in the cavity  124  to move relative the substrate  108  in response to the MEMS  100  accelerating in a direction having a component along the z-axis. 
         [0034]    The proof mass  116  may be formed from a material different from the substrate  108 . A spring  126  ( FIG. 2 ) suspends the proof mass  116  above the substrate  108 , as described below. The proof mass  116  has a length along the y-axis, a width along the x-axis, and a height along the z-axis. The length and width of the proof mass  116  are less than the length and width of the cavity  124  to permit the proof mass  116  to move within the cavity  124  along the x-axis, y-axis, and z-axis. 
         [0035]    The MEMS  100  is described in further detail with reference to  FIGS. 2 and 3 . As shown in the cross-sectional view of  FIG. 2 , the MEMS  100  includes a spring  126  and a retaining element  128 . The spring  126  suspends the proof mass  116  above the surface  120  in a neutral position. The proof mass  116  is illustrated in the neutral position in  FIGS. 1-4 . The spring constant of the spring  126  is related to the degree of displacement exhibited by the proof mass  116  in response to acceleration of the MEMS  100 . In particular, a MEMS  100  having a spring  126  with a spring constant of a low magnitude may have a lower acceleration threshold than a MEMS  100  having a spring  126  with a spring constant of a greater magnitude. As used herein, the term “acceleration threshold” refers to a minimum acceleration the MEMS  100  is configured to sense. The spring  126  returns the proof mass  116  to the neutral position when the MEMS  100  ceases to accelerate and when the acceleration of the MEMS  100  falls below the acceleration threshold. The retaining element  128  (not illustrated in  FIGS. 1 and 3 ) forms an upper boundary of the cavity  124  and is generally parallel to the surface  120 . The retaining element  128  prevents the proof mass  116  from exiting the cavity  124  as a result of the MEMS  100  accelerating in a direction having a component along the minus z-axis direction. 
         [0036]    The MEMS  100  includes positioning features  132  to limit the movement of the proof mass  116  relative the substrate  108  in directions along the x-axis and the y-axis. The positioning features  132  include a travel stop  134  and a follower  136 . As shown in  FIGS. 1 and 3 , the follower  136  is formed on the proof mass  116  and the travel stop  134  is formed on the wall  112 ; however, in other embodiments, the follower  136  is formed on the wall  112  and the travel stop  134  is formed on the proof mass  116 . In each embodiment, the follower  136  contacts the travel stop  134  when the proof mass  116  moves to a position of maximum displacement along the x-axis and/or the y-axis. 
         [0037]    The positioning features  132  are described in further detail with reference to  FIGS. 4-6 . The followers  136  include a dimple  138  and a mouth  140 . The dimple  138  defines a curved surface having a radius  142 . The curved surface of the dimple  138  is positioned above the surface  120  of the substrate  108  and is a generally concave surface in the x-y plane. The mouth  140  defines the outer edge of the dimple  138 . The mouth  140  has a length  150  that extends from a lower edge of the dimple  138  to an upper edge of the dimple  138 . The travel stops  134  include a post  144  having a head  146  and a neck  147 . The head  146  is connected to the end of the neck  147 . The head  146  defines a curved surface that is a generally convex surface in the x-y plane. The curved surface of the head  146  has a radius  148 . The radius  142  and the radius  148  are non-equal, and, in particular, the radius  142  is greater than the radius  148 . 
         [0038]    As shown in  FIG. 4 , when the proof mass  116  is in the neutral position, the travel stop  134  is positioned in the dimple  138 . When the proof mass  116  is moved to a point of maximum displacement along the x-axis, apex  151  of the head  146  contacts apex  152  of the dimple  138 , as shown in  FIG. 5 . As used herein, the term “apex” refers to the deepest point of the dimple  138  and the highest point of the head  146 . Because the radius  142  is greater than the radius  148 , contact between the apex  151  and the apex  152  is a point contact. When the proof mass  116  is moved to a point of maximum displacement along the y-axis, the neck  147  contacts the mouth  140  at a point contact, as shown in  FIG. 6 . When the proof mass  116  is moved to a position between a point of maximum displacement along the x-axis and a point of maximum displacement along the y-axis the head  146  contacts the dimple  138  at a point contact between the apex  152  and the mouth  140 . 
         [0039]    The positioning features  132  limit the motion of the proof mass  116  along the x-axis and the y-axis to fixed distances. Specifically, the positioning features  132  on the left and right sides of the MEMS  100  limit the motion of the proof mass  116  along the y-axis to a distance  154  ( FIG. 6 ). In particular, the distance  154  is equal to the length  150  minus a thickness  156  of the neck  147 . Furthermore, the positioning features  132  on the left and right sides of the MEMS  100  limit the motion of the proof mass  116  along the x-axis to a distance  160 . Specifically, when the proof mass  116  is in the neutral position, a gap  162  separates the head  146  from the dimple  138 . The distance  160  is equal to two times the length of the gap  162 . The positioning features  132  on the upper and lower sides of the MEMS  100  limit the motion of the proof mass  116  along the x-axis to the distance  154  and limit the motion of the proof mass  116  along the y-axis to the distance  160 . 
         [0040]    The MEMS  100  may be formed with a reduced number of positioning features  132 . Referring again to  FIG. 3 , the positioning features  132  on the left side of the MEMS  100  address over travel in the minus x-axis direction and the plus and minus y-axis directions, while the positioning features  132  on the right side of the MEMS  100  address over travel in the plus x-axis direction and the plus and minus y-axis directions. Accordingly, the MEMS  100  may address over travel of the proof mass  116  in each direction in the x-y plane with one positioning feature  132  on the left side of the MEMS  100  and one positioning feature  132  on the right side of the MEMS  100 . Furthermore, the positioning feature  132  on the top side of the MEMS  100  addresses over travel in the plus and minus x-axis directions and the plus y-axis direction, while the positioning feature  132  on the bottom side of the MEMS  100  addresses over travel in the plus and minus x-axis directions and the minus y-axis direction. Therefore, the MEMS  100  may also address over travel of the proof mass  116  in each direction of the x-y plane with one positioning feature  132  on the top side of the MEMS  100  and one positioning feature  132  on the bottom side of the MEMS  100 . 
         [0041]    The positioning features  132  are configured to reduce stiction between the travel stop  134  and the follower  136  because a first curved surface having a radius smaller than a second curved surface necessarily contacts the second curved surface at a single point that is tangential to both curved surfaces. In particular, as shown in  FIG. 5 , the apex  151  of the head  146  contacts the apex  152  of the dimple  138  when the proof mass  116  has been moved to a position of maximum negative displacement along the x-axis. Similarly, as shown in  FIG. 6 , the head  146  contacts the mouth  140  when the proof mass  116  has been moved to a position of maximum positive displacement along the y-axis. In order to satisfy the tangent point contact region the radius  142  and the radius  148  are non-equal. The reduced surface area of the contact region reduces stiction between the follower  136  and the travel stop  134  as compared to known flat travel stops. Accordingly, the MEMS  100  has a reduced stiction threshold and, therefore, may be configured to measure a very small acceleration. 
         [0042]    Referring now to  FIG. 7 , another embodiment of a MEMS  200  is illustrated. The MEMS  200  includes a substrate  204 , a wall  208 , and a proof mass  212 . The substrate  204  defines a surface  216  in the x-y plane that is generally normal, i.e. perpendicular, to the z-axis. The wall  208  is coupled to the substrate  204  and extends above the surface  216  along the z-axis. The wall  208  and the surface  216  define a cavity  220  having a length along the y-axis, a width along the x-axis, and a depth along the z-axis. The proof mass  212  is positioned in the cavity  220  to move relative the substrate  204  in response to the MEMS  200  accelerating in a direction having a component along the z-axis. 
         [0043]    The MEMS  200  includes positioning features  224  to limit the movement of the proof mass  212  relative the substrate  204  in directions along the x-axis and the y-axis. In particular, the MEMS  200  includes four additional positioning features  224  as compared to the MEMS  100 . The additional positioning features  224  reduce the force exerted upon any one positioning feature  224  during periods of external physical shock, such as, but not limited to, drop tests, electrostatic self-test actuation, and spring-mass resonant frequency excitation. 
         [0044]    Another embodiment of a MEMS  300  is shown in  FIG. 8 . The MEMS  300  includes a substrate  304 , a wall  308 , and a proof mass  312 . The substrate  304  defines a surface  316  in the x-y plane that is generally normal, i.e. perpendicular, to the z-axis. The wall  308  is coupled to the substrate  304  and extends above the surface  316  along the z-axis. The wall  308  and the surface  316  define a cavity  320  having a length along the y-axis, a width along the x-axis, and a depth along the z-axis. The proof mass  312  is positioned in the cavity  320  to move relative the substrate  304  in response to the MEMS  300  accelerating in a direction having a component along the z-axis. 
         [0045]    The MEMS  300  includes positioning features  324  to limit the movement of the proof mass  312  relative the substrate  304  in directions along the x-axis and the y-axis. The positioning features  324  include a follower  328  and a post  332 . Some of the followers  328  are formed on the wall  308  and some of the followers  328  are formed on the proof mass  312 . Similarly some of the posts  332  are formed on the wall  308  and some of the posts  332  are formed on the proof mass  312 . The MEMS  300  has the same stiction threshold reducing benefits as described with reference to the MEMS  100 . 
         [0046]    With reference to  FIG. 9 , another embodiment of a MEMS  400  is illustrated. The MEMS  400  includes a substrate  404 , a wall  408 , and a proof mass  412 . The substrate  404  defines a surface  416  in the x-y plane that is generally normal, i.e. perpendicular, to the z-axis. The wall  408  is coupled to the substrate  404  and extends above the surface  416  along the z-axis. The wall  408  and the surface  416  define a cavity  420  having a length along the y-axis, a width along the x-axis, and a depth along the z-axis. The proof mass  412  is positioned in the cavity  420  to move relative the substrate  404  in response to the MEMS  400  accelerating in a direction having a component along the z-axis. 
         [0047]    The MEMS  400  includes positioning features  424  to limit the movement of the proof mass  412  relative the substrate  404  in directions along the x-axis and the y-axis. The positioning features  424  include a follower  428  and a travel stop  432 . The travel stop  432  includes a head  436  having a curved surface. The followers  428  include a rectangular region  440  instead of a dimple  138 . The positioning features  424  limit the over travel of the proof mass  412  in directions along both the x-axis and the y-axis. Additionally, the positioning features  424  reduce the contact area between the wall  408  and the proof mass  412  when the proof mass  412  has been moved to a position of maximum displacement. For instance, when the proof mass  412  has been moved to a position of maximum displacement along the x-axis, an apex  444  of the head  436  contacts a single point of the rectangular region  440 . When the proof mass  412  has been moved to a position of maximum displacement along the x-axis and y-axis, however, the head  436  contacts the rectangular region  440  at discrete contact points. Thus the stiction threshold is reduced as compared to known flat positioning features. In another embodiment (not illustrated) the travel stop  432  is on the proof mass  412  and the follower  428  having a rectangular region  440  is on the wall  408 . 
         [0048]    The MEMS  100  may be formed according to the following process. First the substrate  108  is formed. In one embodiment, the substrate  108  is formed on a silicon wafer. Next, the surface  120  is etched, or otherwise micromachined, on the substrate  108 . The term “etching” as used herein, includes wet chemical etching, vapor etching, and dry etching, among other forms of etching and micromachining. While the surface  120  is shown to be in the same x-y plane as the remainder of the substrate  108 , the surface  120  may also be formed below the remainder of the substrate  108  in a well. 
         [0049]    Next, material to form the spring  126  is deposited on the surface  120 . A sacrificial layer of oxide may be formed on the surface  120  around the spring  126 . Thereafter, material to form the wall  112  and the proof mass  116  is deposited on the surface  120 , such that the material to form the proof mass  116  is deposited on the sacrificial layer and suspended above the surface  120 . The material forming the proof mass  116  bonds to the spring  126 . The material forming the wall  112  bonds to the surface  120 . Next, a mask is deposited over the material. The mask the outlines and defines at least the wall  112 , the proof mass  116 , and the positioning features  132 . 
         [0050]    Subsequently, the material unencumbered by the mask is etched away to form the wall  112 , the proof mass  116 , and the positioning features  132 . Additionally, the sacrificial layer, if one is present, is also etched away to separate the proof mass  116  from the surface  120  and to permit the spring  126  to support the proof mass  116  in the neutral position. The process may also include forming the retaining element  128  to seal the proof mass  116  within the cavity  124 . Furthermore, a first electrical lead may be coupled to the surface  120 , and a second electrical lead may be coupled to the proof mass  116 . In some embodiments, the spring  126  may function as the second electrical lead. 
         [0051]    In operation, the MEMS  100  senses acceleration in a direction having a component along the z-axis. In one embodiment, acceleration is sensed by measuring the capacitance between the surface  120  and the proof mass  116  with a capacitance measuring device coupled to first and second electrical leads. In particular, the proof mass  116  is shown in the neutral position slightly separated from the surface  120 , resulting in a capacitance between the proof mass  116  and the surface  120 . If the MEMS  100  were to accelerate downward along the z-axis, the proof mass  116  would move upward relative the surface  120 . The capacitance measured between the proof mass  116  and the surface  120  decreases as the distance between the proof mass  116  and the surface  120  increases. The change in capacitance is related to the acceleration of the MEMS  100 . 
         [0052]    An exemplary mask  500  for forming a MEMS is illustrated in  FIG. 10 . The mask  500  is configured to form the MEMS  502  of  FIG. 11 . The MEMS  502  of  FIG. 11  includes a substrate  530 , a wall  534 , and a proof mass  538 . The substrate  530  defines a surface  542  in the x-y plane that is generally normal, i.e. perpendicular, to the z-axis. The wall  534  is coupled to the substrate  530  and extends above the surface  542  along the z-axis. The wall  534  and the surface  542  define a cavity  546  having a length along the y-axis, a width along the x-axis, and a depth along the z-axis. The proof mass  538  is positioned in the cavity  546  to move relative the substrate  530  in response to the MEMS  502  accelerating in a direction having a component along the z-axis. The MEMS  502  includes numerous positioning features  550  each having a wall element  554  and a proof mass element  558 . 
         [0053]    The mask  500  ( FIG. 10 ) is used with a lateral silicon etch process to form submicron gaps  562  ( FIG. 11 ) between the wall elements  554  and the proof mass elements  558 . As shown in  FIG. 10 , the mask  500  is configured to form numerous types of positioning features  550 . In particular, the mask  500  includes wall element mask portions  560  and proof mass element mask portions  564 . The portions  560  and the portions  564  are bridged together at point  568  such that the portion  560  contacts the portion  564 . During the lateral silicon etching process, however, some of the material extending under the portions  560 ,  564  and under the point  568  is etched, thereby forming and separating the wall element  554  from the proof mass element  558 . The degree of lateral etching that occurs under the portions  560 ,  564  and under the point  568  is controlled by the area of the point  568 , as shown by the submicron gaps  562  of  FIG. 11 . The submicron gaps  562  are arranged from smallest (top) to largest (bottom). The mask  600  of  FIG. 12  is also configured to form a MEMS  604  ( FIG. 13 ) using a lateral silicon etch process. The mask  600  includes positioning feature mask portions  608  that produce various widths of submicron gaps  616 , as shown in the positioning features  612  in the MEMS  604  of  FIG. 13 . The submicron gaps  616  are arranged from smallest (top) to largest (bottom). 
         [0054]    Lateral silicon etching may be used to form the MEMS tunneling tip accelerometer  700 , shown in  FIG. 14 . Tunneling tip accelerometers are discussed in references including C. H. Liu and T. W. Kenny, “A High Precision, Wide Bandwidth Micromachined Tunneling Accelerometer”, Journal of Microelectromechanical Systems, Vol. 10, No. 3, pp. 425-433 (2001); and P. G. Hartwell, F. M. Bertsch, K. L. Turner, and N. C. MacDonald, “Single Mask Lateral Tunneling Accelerometer”, Microelectromechanical Systems Conference (1998). In the accelerometer  700  of  FIG. 14 , the proof mass  704  is supported by springs  708 . The accelerometer  700  includes a first convex surface in the x-y plane, referred to as tip  712 , and a second convex surface in the x-y plane, referred to as tip  716 . A tunneling current flows from tip  712  to tip  716 . The tunneling current is measured between pads  720  and  724 . An electrostatic force feedback is applied to pads  728  and  732  to maintain a tunneling tip gap  736  and also to ensure stable tunneling current for a wide range of external acceleration input stimulus amplitudes. The field concentration of the accelerometer  700  is maximized at the tip location illustrated in  FIG. 14 . In some embodiments, a localized thermal oxidation may be applied to the tips  712 ,  716 . 
         [0055]    The tips  712 ,  716  of the accelerometer  700  may be formed by the following process. First, mask portion  750  of  FIG. 15  is applied over a region of semiconductor material deposited on a substrate. The mask portion  750  includes tip masks  754 ,  758  that are bridged together. Next, a lateral etching process removes a portion of the semiconductor material extending under the mask portion  750 . In particular, after the lateral etching process, the submicron gap  736  is formed between the tips  712 ,  716 , even though the tip masks  754 ,  758  are bridged together. 
         [0056]    The device and method described herein have been illustrated and described in detail in the figures and foregoing description, the same should be considered as illustrative and not restrictive in character. It is understood that only the preferred embodiments have been presented and that all changes, modifications, and further applications that come within the spirit of the device and method described herein are desired to be protected.