Patent Publication Number: US-7221241-B2

Title: Method for adjusting the frequency of a MEMS resonator

Description:
RELATED APPLICATION  
   This application is a divisional application of application Ser. No. 10/833,433 (now U.S. Pat. No. 7,102,467), filed Apr. 28, 2004, the contents of which are incorporated herein by reference. 

   BACKGROUND 
   This invention relates to microelectromechanical systems and/or nanoelectromechanical systems (collectively hereinafter “microelectromechanical systems”) and techniques for fabricating microelectromechanical systems; and, more particularly, in one aspect, for adjusting, tune, setting, defining and/or selecting the output frequency of microelectromechanical resonators. 
   Many conventional micromechanical structures are based on the reaction (for example, oscillation, deflection or torsion) of a beam structure to an applied force. Such beam structures are often fabricated from monocrystalline or polycrystalline semiconductors. These materials have excellent mechanical strength and a high intrinsic quality factor. 
   However, manufacturing and material tolerances regarding such micromechanical structures often significantly impact the operation and/or function of the structure. For example, microelectromechanical resonators typically rely upon the bending beam and lateral oscillating beam structures. In this regard, manufacturing and material tolerances tend to lead to large variations of the resonance frequency of such resonators. 
   Notably, the beam structures of conventional resonators are often rectangular in shape and/or cross section. The mechanical stiffness (k M ) of a beam, as calculated with respect to the oscillation direction parallel to the width of the beam (w), is proportional to its Young&#39;s modulus (E) and certain measures of its geometry, including for a beam with a rectangular cross section, length (L) and height (h). That is: 
   
     
       
         
           
             
               
                 
                   k 
                   M 
                 
                 ≈ 
                 
                   
                     E 
                     · 
                     h 
                     · 
                     
                       w 
                       3 
                     
                   
                   
                     L 
                     3 
                   
                 
               
             
             
               
                 EQUATION 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 1 
               
             
           
         
       
     
   
   Setting aside electrostatic forces, the resonance frequency (f) of a beam may thus be defined under these assumptions by the equation: 
   
     
       
         
           
             
               
                 f 
                 ≈ 
                 
                   
                     1 
                     
                       2 
                       · 
                       π 
                     
                   
                   · 
                   
                     
                       
                         k 
                         M 
                       
                       
                         m 
                         eff 
                       
                     
                   
                 
               
             
             
               
                 EQUATION 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 2 
               
             
           
         
       
     
   
   where m eff  is the effective mass for the resonating mode shape of the beam. 
   Thus, as is apparent from EQUATIONS 1 and 2, the dimensions and effective mass of the (moving) beam or electrode of a microelectromechanical resonator, and the capability of precisely and repeatedly controlling such dimensions and mass, are critical to accurately predicting (and/or controlling) the resonance frequency of the resonators. 
   Although conventional processes for manufacturing microelectromechanical resonator are relatively precise, such processes have inherent engineering or processing tolerances. Similarly, the tolerance/range of the material&#39;s characteristics and/or properties produce differences in Young&#39;s modulus, which are difficult to exactly predict, compensate, address and/or predetermine before fabrication. Such manufacturing and material tolerances may lead to relative large frequency variations even between identically designed resonators. Indeed, such frequency variations may be measurable (and likely unacceptable) even between microelectromechanical resonators that undergo identical processing/fabrication, for example, resonators fabricated on the same wafer. 
   There have been many attempts to address the issue of variations in the resonant frequency of a microelectromechanical resonator due to manufacturing and material tolerances. For example, one such technique employs a laser to vaporize material away from an open, unpackaged oscillator. In this technique, prior to packaging, the output frequency of the oscillator is measured. If adjustment is required to provide a particular output frequency, material disposed on the oscillator is removed in order to increase the frequency of the output. (See, for example, Noell et al., “MEMS for Watches”, IEEE, 2004 0-7803-8265-X/04, pages 1–4). Once a suitable frequency is attained, the oscillator is packaged. 
   Another technique employs a laser to “move” a metal material from a nearby “sacrificial” metal layer onto the mechanical structure (comprised of a silicon material) of the microelectromechanical resonator. See, for example, Chiao and Lin, “Post-Packaging Tuning of Microresonators by Pulsed Laser Deposition”, IEEE 2003, 0-7803-7731-1/03, pages 1820–1823. Here, the microelectromechanical resonator is hermitically sealed, via wafer bonding, with a glass wafer cap. The output of a laser is applied through the glass cap and incident on a metal layer disposed in the sealed chamber. The metal material is “blasted” off the cap and onto the oscillator mass. In this way, additional mass is deposited on, for example, the moving beam(s) or electrode(s), which decrease the resonant frequency of the microelectromechanical resonator. 
   Such a configuration, and, in particular, the glass wafer packaging and sacrificial metal layer, may, among other things, adversely impact the vacuum of the microelectromechanical resonator, particularly in view of the evaporation of the metal material within the resonator chamber. Such evaporation may produce unwanted contaminants within the chamber which, in turn, may adversely impact the operation of the resonator. 
   Thus, there is a need for a technique for tuning, setting, defining and/or selecting the output frequency of microelectromechanical resonator that overcomes one, some or all of the shortcomings of conventional techniques. There is a need for a technique that compensates for, and/or addresses, minimizes and/or eliminates the adverse affects of manufacturing and material tolerances of microelectromechanical resonator without contaminating the chamber of the resonator. Notably, it may be advantageous if such a technique does not rely on the incorporation of materials and/or techniques that are incompatible, or difficult to integrate with CMOS circuits. 
   SUMMARY OF THE INVENTION 
   There are many inventions described and illustrated herein. In a first principal aspect, the present invention is a method of adjusting the resonant frequency of a MEMS resonator, having a first resonant frequency. In one embodiment, the MEMS resonator comprises a first substrate anchor including a first electrical contact, a second substrate anchor including a second electrical contact, and a beam structure fixed at a first end by the first substrate anchor and at a second end by the second substrate anchor. The method comprises selecting a first heating current to apply to the first electrical contact and applying the first heating current to the MEMS resonator wherein applying the first heating current includes passing the first heating current from the first electrical contact to the second electrical contact to resistively heat the beam structure (for example, to temperatures that are greater than 300° C., between approximately 900° C. and approximately 1200° C., and/or greater than 1200° C.). In response, the material of the first beam structure changes to provide a second resonant frequency of the MEMS resonator. 
   In one embodiment, the method further includes measuring the first resonant frequency of the MEMS resonator and wherein the first heating current is selected based on the measured first resonant frequency. In another embodiment, the method further includes measuring the second resonant frequency of the MEMS resonator, calculating a second heating current to apply to the first electrical contact, and applying the second heating current to the MEMS resonator wherein applying the second heating current includes passing the second heating current from the first electrical contact to the second electrical contact to resistively heat the beam structure. In response to the second heating current, the material of the first beam structure changes to provide a third resonant frequency of the MEMS resonator. 
   The MEMS resonator may include a beam structure that comprises a multiple beam tuning fork structure, wherein each beam in the multiple beam tuning fork structure comprises a first end fixed by the first substrate anchor and a second end fixed by the second substrate anchor. In one embodiment, the beam structure comprises a high tension area, wherein the high tension area is resistively heated in response to the first electrical current thereby causing the material of the high tension area to change. In another embodiment, the high tension area is heated to a substantially higher temperature than other portions of the beam structure. 
   In another principal aspect, the present invention is a method of adjusting the resonant frequency of a MEMS resonator having a first resonant frequency. The MEMS resonator comprises a first substrate anchor including a first electrical contact, a second substrate anchor including a second electrical contact, and a beam structure fixed at a first end by the first substrate anchor and at a second end by the second substrate anchor. The method comprises applying a first heating current to the MEMS resonator wherein applying the first heating current includes passing the first heating current from the first electrical contact to the second electrical contact to resistively heat the beam structure (for example, to temperatures that are greater than 300° C., between approximately 900° C. and approximately 1200° C., and/or greater than 1200° C.). In response, material of the first beam structure (for example, monocrystalline and/or polycrystalline silicon material) evaporates therefrom to provide a second resonant frequency of the MEMS resonator. 
   The method may further include measuring the first resonant frequency of the MEMS resonator and determining the first heating current based on the measured first resonant frequency. The method may also include measuring the second resonant frequency of the MEMS resonator, determining a second heating current to apply to the first electrical contact, and applying the second heating current to the MEMS resonator wherein applying the second heating current includes passing the second heating current from the first electrical contact to the second electrical contact to resistively heat the beam structure. In response to such heating, the material of the first beam structure changes to provide a third resonant frequency of the MEMS resonator. 
   In yet another principal aspect, the present invention is a method of adjusting the resonant frequency of a MEMS resonator having a first resonant frequency. The MEMS resonator of this aspect of the invention comprises a beam structure and a frequency adjustment structure, wherein the frequency adjustment structure is comprised of polycrystalline silicon and includes first and second electrical contacts. The method comprises applying a first heating current to the frequency adjustment structure wherein applying the first heating current includes passing the first heating current from the first electrical contact to the second electrical contact to resistively heat the frequency adjustment structure (for example, to temperatures that are between approximately 900° C. and approximately 1200° C. and/or greater than 1200° C.). In response to heating the frequency adjustment structure, material of the frequency adjustment structure evaporates therefrom and deposits on the beam structure to provide a second resonant frequency of the MEMS resonator. 
   In one embodiment of this aspect of the invention, the method further includes measuring the first resonant frequency of the MEMS resonator and wherein the first heating current is selected based on the measured first resonant frequency. In another embodiment, the method further includes measuring the second resonant frequency of the MEMS resonator, calculating a second heating current to apply to the first electrical contact, and applying the second heating current to the MEMS resonator wherein applying the second heating current includes passing the second heating current from the first electrical contact to the second electrical contact to resistively heat the beam structure. In response to the second heating current, the material of the first beam structure changes to provide a third resonant frequency of the MEMS resonator. 
   Notably, the frequency adjustment structure may be integrated into a fixed electrode of the MEMS resonator. 
   The beam structure may include at least one high tension area, wherein in response to the first heating current, material of the frequency adjustment structure deposits on the high tension area. Indeed, in one embodiment, a substantial amount of the evaporated material of the frequency adjustment structure deposits on the high tension area. 
   Again, there are many inventions described and illustrated herein. This Summary of the Invention is not exhaustive of the scope of the present inventions. Moreover, this Summary is not intended to be limiting of the present inventions and should not be interpreted in that manner. While certain embodiments, features, attributes and advantages of the inventions have been described in this Summary, it should be understood that many others, as well as different and/or similar embodiments, features, attributes and/or advantages of the present inventions, which are apparent from the description, illustrations and claims, which follow. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the course of the detailed description to follow, reference will be made to the attached drawings. These drawings show different aspects of the present invention and, where appropriate, reference numerals illustrating like structures, components, materials and/or elements in different figures are labeled similarly. It is understood that various combinations of the structures, components, materials and/or elements, other than those specifically shown, are contemplated and are within the scope of the present invention. 
       FIG. 1  illustrates a top view of a resonator, having two oscillating beams that are arranged in a tuning fork beam structure, according to one embodiment of a first aspect of the present invention; 
       FIGS. 2A and 2B  illustrate top views of a resonator, having two oscillating beams that are arranged in a tuning fork beam structure, according to a second embodiments of a first aspect of the present invention; 
       FIG. 3  is a schematic representation of an exemplary configuration to adjust and/or tune the frequency of the output a resonator, according to the first aspect of the present invention; 
       FIG. 4  is a flow diagram of an exemplary tuning technique of the resonator according to the first aspect of the present invention; 
       FIG. 5  illustrates a top view of a resonator, having two oscillating beams that are arranged in a tuning fork beam structure and integrated frequency adjustment structures, according to a first embodiment of a second aspect of the present invention; 
       FIG. 6  illustrates a schematic cross-sectional view of the resonator of  FIGS. 6 and 7 , sectioned along dotted line A–A′; 
       FIG. 7  illustrates a top view of a resonator, having two oscillating beams that are arranged in a tuning fork beam structure and integrated frequency adjustment structures, according to another embodiment of a second aspect of the present invention; 
       FIG. 8A  illustrates a top view of a resonator, having two oscillating beams that are arranged in a tuning fork beam structure and a non-integrated frequency adjustment structures, according to another embodiment of a second aspect of the present invention; 
       FIG. 8B  illustrates a top view of a resonator, having two oscillating beams that are arranged in a tuning fork beam structure and integrated and non-integrated frequency adjustment structures, according to another embodiment of a second aspect of the present invention; 
       FIGS. 9A–9D  are schematic representations of exemplary configurations to adjust and/or tune the frequency of the output a resonator, according to the third aspect of the present invention; 
       FIG. 10  illustrates a schematic cross-sectional view of the resonator of  FIG. 5 , sectioned along dotted lines A–A′, in conjunction with a light source, for example, a laser, to adjust and/or tune the frequency of the output a resonator, according to the third aspect of the present invention; 
       FIG. 11  illustrates a top view of a bulk-type resonator, having an expandable element and two fixed electrodes, according to an embodiment of the present invention; and 
       FIG. 12  illustrates a schematic cross-sectional view of the bulk-type resonator of  FIG. 11 , sectioned along dotted lines A–A′. 
   

   DETAILED DESCRIPTION 
   There are many inventions described and illustrated herein. These inventions are directed to a method of fabricating a microelectromechanical resonator having an output frequency that may be adjusted, tuned, set, defined and/or selected whether before and/or after final packaging. In a first aspect, the method of the present invention adjusts, tunes, sets, defines and/or selects the frequency of the microelectromechanical resonator by changing and/or removing material from the mechanical structure of the resonator by resistively heating one or more elements and/or beams of the mechanical structure (for example, the moveable or expandable electrodes). 
   In this aspect of the present invention, an electrical current is applied to the moveable electrodes to resistively heat the electrode to a sufficient temperature so as to change and/or remove material from one or more moveable electrodes of the mechanical structure. In one embodiment, the material may be changed and/or removed from selected portions of the moveable electrode(s) (for example, the areas of high stress or tension). In another embodiment, material is changed and/or removed from all or substantially all of the active areas of the moveable electrodes (for example, those areas that oppose the fixed electrodes). In this way, the spring constant changes and/or the mass of the beam changes, which, in turn, causes a change in the frequency of the output of the resonator. 
   For example, with reference to  FIG. 1 , in a first embodiment of this aspect of the present invention, MEMS resonator  10  includes mechanical structure  12  having moveable beams  14   a  and  14   b  disposed between anchors  16   a  and  16   b . In this embodiment, moveable beams  14   a  and  14   b  are comprised of a material that includes a resistance in the presence of an electrical current, such as a conducting material (for example, a metal material) or semi-conducting material (for example, silicon and/or germanium). 
   The MEMS resonator  10  further includes fixed electrodes  18   a  and  18   b  and electrical contacts  20   a  and  20   b . The electrical contacts  20   a  and  20   b , in this embodiment, are connected to an electrical source (not illustrated) that provides an electrical current. For example, in one embodiment, electrical contact  20   a  is connected to the electrical source and electrical contact  20   b  is connected to a common and/or ground potential. In another embodiment, electrical contacts  20   a  and  20   b  are connected between terminals and/or contacts of the electrical source. 
   Notably, fixed electrodes  18   a  and  18   b  and electrical contacts  20   a  and  20   b  may be comprised of a conducting material (for example, a metal material such as aluminum) or semi-conducting material (for example, silicon, germanium, and/or impurity doped versions thereof). It may be advantageous to employ a material that has a relatively low resistivity and is suitable for, or compatible with, additional processing, for example, CMOS integration. 
   The electrical source (not illustrated) provides an electrical current that flows through moveable beams  14   a  and  14   b  and between electrical contacts  20   a  and  20   b . In operation, an electrical current flows through moveable beams  14   a  and  14   b , which are resistively heated. For example, where a higher voltage is applied to electrical contact  20   a  and a lower voltage is applied to (or exists at) electrical contact  20   b , the electrical current (as conventionally designated) flows from electrical contact  20   a  to electrical contact  20   b , as illustrated in  FIG. 1 . 
   Briefly, by way of background, an element having an electrical resistance (R) will convert electrical energy to thermal energy when an electrical current (I) is passed through the resistive element. In the context of the present invention, the power (P) dissipated in the form of heat by means of the resistive heating arising from application of a heating current (I) to the electrical resistance inherent in the beam structure may be characterized by the following equation:
 
 P   heat   =I   2   ·R   beam   EQUATION 3
 
   As such, heating current (I) flowing between electrical contacts  20   a  and  20   b  generates resistive heating in moveable beam  14 . This resistive heating process may be accurately controlled, as described in detail below, to remove a predetermined amount of material from moveable beam(s)  14  to adjust, tune, set, define and/or select the frequency of the microelectromechanical resonator. Thereafter, MEMS resonator  10  provides a predetermined, selected and/or defined output frequency. 
   In those instances where moveable beams  14   a  and  14   b  are comprised of a polycrystalline silicon, resistively heating moveable beams  14   a  and  14   b  to, for example, temperatures in the range of approximately 300° C. to approximately 900° C. may anneal moveable beams  14   a  and  14   b . In this way, the consistence and therefore the characteristics of moveable beams  14   a  and  14   b  may change. For example, larger grains may form, stress within the beams is released, which leads to a change in the Young&#39;s Modulus. 
   In addition, where moveable beams  14   a  and  14   b  are resistively heated to temperatures in the range of approximately 900° C. to approximately 1200° C., the monocrystalline and/or polycrystalline silicon surfaces of moveable beams  14   a  and  14   b  may begin to melt due, for example, to the lower binding energy of the surface atoms. Notably, this effect may depend on the surface passivation of the material of moveable beams  14   a  and  14   b . For example, where the moveable electrodes are released using well known wet etching techniques and buffered HF mixtures (i.e., a buffered oxide etch) or well known vapor etching techniques using vapor HF, and later encapsulated using thin film encapsulation techniques, the chamber containing mechanical structures  12  of MEMS resonator  10  is sealed in a reactive H 2  environment thereby leaving chlorine and hydrogen terminated high reactive silicon surfaces. Notably, melting surfaces may reform to a lower surface energy state, which will likely change the geometry of moveable beams  14   a  and  14   b , and therefore their stiffness. 
   Where moveable beams  14   a  and  14   b  are resistively heated to temperatures greater than approximately 1000° C. to 1200° C., the monocrystalline and/or polycrystalline silicon surfaces atoms of moveable beams  14   a  and  14   b  may begin to evaporate and migrate from the surface of moveable beams  14   a  and  14   b  to surrounding cold surfaces (for example, fixed electrodes  18   a  and  18   b ). In this way, moveable beams  14   a  and  14   b  thin, thereby changing the mass. In addition, the spring constant(s) of moveable beams  14   a  and/or  14   b  is/are also reduced. 
   For example, removal of several atomic layers (i.e., in the range of 1 nm) from the surface of moveable beams  14   a  and  14   b  may be sufficient to change the frequency of a 2 MHz continuous clamp-clamp two beam resonator (see  FIG. 2B ) by 114 ppm (where moveable beams  14   a  and  14   b  are in the range of 185 μm in length and 9 μm in width). EQUATIONS 1 and 2 provide a relationship between the stiffness and the width of a beam. 
   Notably, the present invention may employ any configuration, design and/or control of mechanical structure  12  of MEMS resonator  10 . Indeed, all configurations, designs and/or control of mechanical structure  12 , whether now known or later developed, are intended to fall within the scope of the present invention. For example, mechanical structure  12  may include (1) one or more moveable beams  14  disposed between one or more anchors  16 , (2) bulk-type configurations (see, for example,  FIGS. 11 and 12 ), and (3) structures oscillating in any and all directions, for example, in-plane and out-of-plane. 
   Moreover, there are many methods and techniques for fabricating MEMS resonator  10 , including moveable beam(s)  14  and fixed electrodes  18 . For example, the materials and/or layers of moveable beam(s)  14  may be deposited and thereafter, using well known lithographic, etching and/or doping techniques, moveable beam(s)  14  may be formed from such materials and/or layers. All methods of fabricating MEMS resonator  10 , including moveable beam(s)  14 , whether now known or later developed, are intended to be within the scope of the present invention. 
   In addition, in one embodiment, mechanical structure  12  is encapsulated, using a thin film or wafer level encapsulation techniques, in a chamber. In this regard, MEMS resonator  10  may be sealed or encapsulated using conventional thin film encapsulation techniques and structures. (See, for example, WO 01/77008 A1 and WO 01/77009 A1). Other thin film encapsulation techniques are suitable. Indeed, all thin film encapsulation techniques, whether now known or later developed, are intended to be within the scope of the present invention. 
   For example, the encapsulation techniques described and illustrated in non-provisional patent application “Microelectromechanical Systems Having Trench Isolated Contacts, and Methods of Fabricating Same”, which was filed on Jun. 4, 2003 and assigned Ser. No. 10/455,555 (hereinafter “Microelectromechanical Systems Having Trench Isolated Contacts Patent Application”) may be employed. All of the inventions/embodiments (including, for example, the mechanical structure fabrication, the encapsulation and the electrical isolation techniques) described and illustrated in the Microelectromechanical Systems Having Trench Isolated Contacts Patent Application may be implemented in conjunction with the temperature compensation techniques described and illustrated herein. For the sake of brevity, the embodiments described and illustrated in the Microelectromechanical Systems Having Trench Isolated Contacts Patent Application, implemented in conjunction with the temperature compensation techniques described and illustrated herein, will not be repeated in detail but will only be summarized. It is expressly noted, however, that the entire contents of the Microelectromechanical Systems Having Trench Isolated Contacts Patent Application, including, for example, the features, attributes, alternatives, materials, techniques and advantages of all of the inventions, are incorporated by reference herein. 
   In one embodiment, the resistive heating of moveable beams  14   a  and/or  14   b  is focused, concentrated and/or localized to provide selective and/or predetermined changes in, and/or removal of material from mechanical structure  12  of MEMS resonator  10 . For example, with reference to  FIG. 2A , in one embodiment, moveable beams  14   a  and/or  14   b  are designed and/or manufactured to provide focused, concentrated and/or localized heating of high tension areas  22  of moveable beams  14   a  and  14   b . Notably, changing and/or removing material from high tension areas  22  may have a greater impact or effect on the frequency of MEMS resonator  10  (relative to other areas of moveable beams  14   a  and  14   b ) because of the change in mechanical stiffness of moveable beams  14   a  and  14   b  (see, for example, EQUATIONS 1 and 2). 
   The high tension areas  22  may be heated differently from other areas by providing a vertical and/or horizontal impurity doping profiles (for example, n-type impurities such as phosphorous) in or on moveable beams  14   a  and/or  14   b . A doping profile provides higher or lower resistances at selective locations along moveable beams  14   a  and/or  14   b . In this way, selective resistive heating is provided in moveable beam  14   a  and/or  14   b  as electrical current (I) is applied through electrical contacts  20   a  and  20   b.    
   For example, high tension areas  22  may be more lightly doped (for example, undoped) with impurities than the other areas of moveable beams  14   a  and/or  14   b . This provides high tension areas  22  with greater resistances to electrical current flow relative to other areas of moveable beams  14   a  and/or  14   b . In this way, high tension areas  22  are heated to higher temperatures than other areas of moveable beams  14   a  and/or  14   b.    
   In one embodiment, where moveable beams  14   a  and  14   b  are comprised of monocrystalline and/or polycrystalline silicon, resistively heating high tension areas  22  to temperatures greater than approximately 1000° C. to 1200° C., may cause the surfaces atoms of high tension areas  22  to evaporate and migrate from the surface of high tension areas  22  to surrounding colder surfaces. As mentioned above, in this embodiment, high tension areas  22  may attain higher temperatures for a given electrical current (I) than the other areas of moveable beams  14   a  and  14   b . In this way, high tension areas  22  of moveable beams  14   a  and  14   b  may thin before other areas of moveable beams  14   a  and  14   b . (See,  FIG. 2B ). The “thinning” of high tension areas  22  creates a selective change in mass of moveable beams  14   a  and  14   b , which may selectively reduce the spring constant(s) of moveable beams  14   a  and/or  14   b  in the region pertaining to high tension areas  22 . 
   Notably, all methods and techniques for fabricating moveable beams  14 , including high tension areas  22 , of  FIG. 2A , whether now known or later developed, are intended to be within the scope of the present invention. For example, the material(s) and/or layer(s) of moveable beam(s)  14  may be deposited and thereafter, using well known doping techniques, high tension areas  22  of moveable beam(s)  14  may be formed from such material(s) and/or layer(s). The heat flow through mechanical structure  12  to the surrounding material (for example, the heat flow through the substrate and anchors  16   a  and  16   b ), and its impact on such materials, should be considered when implementing the selective, concentrated and/or focused resistive heating techniques. 
   As mentioned above, an electrical source provides an electrical current that flows through moveable beams  14   a  and/or  14   b  and between electrical contacts  20   a  and  20   b . In certain embodiments, all or substantially all of the heat is generated in high tension areas  22  as electrical current flows through moveable beams  14   a  and/or  14   b  because of the relative resistivities of the different areas of moveable beams  14   a  and/or  14   b.    
   With reference to  FIG. 3 , in one embodiment of the present invention, control circuitry  24  determines and/or calculates the electrical current (from electrical source  26 ) required to adjust, tune, set, define and/or select the frequency of MEMS resonator  10  by changing and/or removing material from mechanical structure  12  of MEMS resonator  10  via resistively heating one or more elements and/or beams (or portions thereof of mechanical structure  12 . The control circuitry  24  employs the “initial” or current frequency of the output of MEMS resonator  10  to determine and/or calculate an appropriate electrical current for a given design of MEMS resonator  10  at a given operating temperature or range of temperatures. Notably, control circuitry  24  may perform and/or implement the techniques of the present invention during, for example, fabrication, test, and/or calibration, which may be before and/or after final packaging. 
   The control circuitry  24  may employ a number of techniques to determine the appropriate heating required to adjust, tune and/or provide a particular output frequency of MEMS resonator  10 . For example, based on an “initial” and/or current frequency, control circuitry  24  may employ a look-up table and/or a predetermined or mathematical relationship (either or both contained in resident memory, not illustrated) to adjust and/or control the heating of certain beam structures of MEMS resonator  10  to thereby compensate, adjust, and/or tune the frequency of the output of MEMS resonator  10  by changing and/or removing material from mechanical structure  12 . The look-up table and/or a predetermined or mathematical relationship may be derived using empirical data based on the affects of resistively heating (as described above, for example, to a temperature in the range of approximately 300° C. to approximately 900° C. and/or in the range of approximately 900° C. to approximately 1200° C.) mechanical structure  12  on the frequency of the output signal. The resistive heating, which may be expressed as temperature, may be correlated to the electrical current output by electrical source  26 . Notably, all techniques and/or configurations for controlling the resistive heating of certain beam structures of MEMS resonator  10  to compensate, adjust and/or tune the frequency of the output of MEMS resonator  10  (by changing and/or removing material from mechanical structure  12 ), whether now known or later developed, including those discussed above, are intended to be within the scope of the present invention. 
   In certain embodiments of the present invention, the adjustment, compensation and/or tuning of the frequency of MEMS resonator  10  may be an iterative process. That is, the “initial” or current frequency of the output signal of MEMS resonator  10  may be measured, mechanical structure  12  may be subjected to resistive heating (as described above) and after cooling, control circuitry  24  may determine if additional adjustment and/or tuning of the frequency of MEMS resonator  10  is required based on the measured frequency of the output of MEMS resonator  10  (i.e., is the measured resonant frequency the desired, selected and/or predetermined resonant frequency and/or within an desired, acceptable and/or predetermined range of frequencies). If so, then the process is repeated. (See, for example,  FIG. 4 ). 
   The process of adjusting and/or tuning the frequency of the output of MEMS resonator  10  may include any combination and/or permutation of resistive heating temperatures of moveable beam(s)  14  to adjust and/or tune the frequency of the output of MEMS resonator  10 . In this regard, moveable beam  14   a  may first be resistively heated to a temperature of approximately 1200° C. After cooling, control circuitry  24  may determine (after measurement) that additional adjustment and/or tuning of the frequency of MEMS resonator  10  is required. In this second resistive heating process, moveable beam  14   a  may be heated to a temperature in the range of approximately 900° C. to less than approximately 1200° C. to provide a relatively smaller adjustment to the resonant frequency. Notably, the amount of time moveable beam  14   a  is subjected to the heating also has an effect of how much material is moved or removed. Thereafter, control circuitry  24  may determine that the resonant frequency is within a predetermined specification (i.e., range of frequencies such as 20 MHz±1%). As such, the combination of the heating processes provides proper adjustment and/or tuning of the resonant frequency of MEMS resonator  10 . All combination and/or permutation of resistive heating temperatures are intended to fall within the scope of the present invention. 
   Notably, the “initial” and/or current frequency of MEMS resonator  10  may be measured, sampled, sensed before and/or after packaging or integration/incorporation. The MEMS resonator  10  may also be calibrated, adjusted and/or tuned at more than one operating condition (for example, more than one temperature). 
   During the resistive heating process, the temperature of certain structures of mechanical structure  12  (for example, moveable beam(s)  14 ) may be determined and/or measured using many different direct and indirect techniques. All techniques of determining and/or measuring the temperature of mechanical structure  12 , including moveable beam(s)  14 , are intended to fall within the scope of this invention. For example, in one embodiment, the electrical current may be measured and, based thereon, the temperature of moveable beam(s)  14  may be determined using, for example, empirical information or a mathematical relationship. In another embodiment, an optical infrared method of measuring the temperature may be employed. 
   In yet another embodiment, control circuitry  24  employs information/data from temperature sensors  28  (for example, diodes, transistors, resistors or varistors, and/or one or more MEMS temperature transducers which are disposed and/or located on or in the substrate of MEMS resonator  10 ) that are thermally coupled to moveable beam(s)  14  and/or those areas of moveable beam(s)  14  that are resistively heated (for example, high tension areas  22 ) to appropriately control the temporal and other characteristics (for example, amplitude) of the electrical current output by electrical source  26 . The electrical source  26  may (dependently or independently) change and/or modify the electrical current applied through moveable beams  14   a  and/or  14   b  and thereby adjust the temperature of moveable beams  14   a  and/or  14   b.    
   The temperature sensors  28  may be employed on and/or in close proximity to moveable beam(s)  14  and/or anchor  20  to measure, sense and/or sample information of the actual temperature of moveable beams  14   a  and  14   b . It may be advantageous to locate temperature sensors  28  in areas where the material is neither (substantially) changed nor removed. For example, it may be advantageous to locate temperature sensors  28  in areas other than those areas where surfaces atoms evaporate (for example, high tension areas  22  of  FIG. 2B ). 
   The temperature sensors  28  provide information of the temperature of moveable beams  14   a  and  14   b  or region(s) in proximity to moveable beams  14   a  and  14   b  to control circuitry  24 . In this way, control circuitry  24  may determine, calculate and/or estimate the temperature of moveable beams  14   a  and  14   b  and, in response, control and/or instruct electrical source  26  to apply or provide an appropriate current to thereby resistively heat moveable beams  14   a  and  14   b  (or selected portions thereof). In one embodiment, control circuitry  24  may compare the actual operating temperature to the predetermined, selected and/or desired temperature using one of a number of conventional feedback and/or control techniques, as discussed in more detail below. 
   In another aspect, the present invention employs resistive heating of one or more frequency adjustment structures to evaporate material onto the mechanical structure of the MEMS resonator. In one embodiment of this aspect of the invention, the frequency adjustment structure(s) are comprised of a monocrystalline and/or polycrystalline silicon materials and are disposed near (for example, directly proximate and/or opposing) the moveable members of the mechanical structure such that the material that evaporates from the frequency adjustment structures is deposited onto the moveable members. In another embodiment, the frequency adjustment structure(s) are comprised of a monocrystalline and/or polycrystalline silicon material and are located, relative to the mechanical structure so that the deposition of material from the frequency adjustment structure(s) is focused, concentrated and/or localized to provide selective and/or predetermined changes (i.e., thickening) of selective beams/members of the mechanical structure (for example, the high tension areas). 
   With reference to  FIG. 5 , in one embodiment, one or more frequency adjustment structures  30  (in the illustrative example, four frequency adjustment structures) are spatially located, relative to mechanical structure  12 , such that when frequency adjustment structures  30  are resistively heated, via an electrical current, to a temperature that causes atoms on the surface of frequency adjustment structures  30  to evaporate and migrate to the cooler surfaces of moveable beams  14   a  and  14   b . In this way, the thickness of moveable beams  14   a  and  14   b  is increased (see  FIG. 6 ) and, as such, the frequency of the output of MEMS resonator  10  is increased. For example, adding several atomic layers (i.e., in the range of 1 nm) onto the surface of moveable beams  14   a  and  14   b  may be sufficient to change the frequency of a 2 MHz continuous clamp-clamp two beam resonator (resonator  10  as illustrated in  FIG. 5 ) by 114 ppm (where moveable beams  14   a  and  14   b  are in the range of 185 μm in length and 9 μm in width). EQUATIONS 1 and 2 provide a relationship between the stiffness and the width of a beam of a resonator. 
   With reference to  FIG. 6 , where frequency adjustment structures  30  are comprised of a monocrystalline and/or polycrystalline silicon, the monocrystalline and/or polycrystalline silicon surfaces are resistively heated to temperatures greater than approximately 1200° C. and surface atoms of frequency adjustment structures  30  may begin to evaporate and migrate to surrounding colder surfaces (for example, moveable beams  14   a  and  14   b ). In this way, moveable beams  14   a  and  14   b  are thickened by the addition of evaporated material  32 . In addition, the spring constant(s) of moveable beams  14   a  and/or  14   b  may also be increased. 
   In one embodiment of this aspect of the invention, mechanical structure  12  is encapsulated, using a thin film or wafer level encapsulation techniques, in a chamber. In this regard, with continued reference to  FIG. 6 , MEMS resonator  10  includes encapsulation structure  34 , including one or more encapsulation layers (here,  36   a  and  36   b ), to seal chamber  38 . In the illustrative embodiment, encapsulation structure  34  includes first encapsulation layer  36   a  and second encapsulation layer  36   b . As described in detail in the Microelectromechanical Systems Having Trench Isolated Contacts Patent Application, in one embodiment, first encapsulation layer  36   a  is deposited on a sacrificial layer, for example, silicon dioxide or silicon nitride, to secure, space and/or protect mechanical structure  12 , including moveable beams  14   a  and  14   b . Thereafter, passages or vents (not illustrated in this cross-section) are formed and/or etched in encapsulation layer  36   a  to permit or facilitate etching and/or removal of at least selected portions of the sacrificial layer and sacrificial/insulator layer  40  (which is disposed on substrate  42 ). 
   After etching and/or removal of at least selected portions of the sacrificial layer and sacrificial/insulator layer  40  and releasing of, for example, moveable beams  14   a  and  14   b , second encapsulation layer  36   b  is deposited on first encapsulation layer  36   a  and in and/or on the vents or passages within first encapsulation layer  36   a  thereby “sealing” chamber  38 . 
   Notably, other thin film encapsulation techniques are suitable. Indeed, as mentioned above, all thin film encapsulation techniques, whether now known or later developed, are intended to be within the scope of the present invention. 
   In those instances where small changes in frequency of MEMS resonator  10  are desired, it may be advantageous to design and locate frequency adjustment structures  30  such that areas of moveable beams  14   a  and  14   b  other than high tension areas  22  are selectively thickened. With reference to  FIG. 7 , in one embodiment, frequency adjustment structures  30  are located opposite moveable beams  14   a  and  14   b . In this embodiment, however, frequency adjustment structures  30  do not oppose high tension areas  22  of moveable beams  14   a  and  14   b . In this way, the majority of the surface atoms of frequency adjustment structures  30  that evaporate, in response to the resistive heating, migrate to areas of moveable beams  14   a  and  14   b  other than high tension areas  22 . Thus, moveable beams  14   a  and  14   b  are thickened by the addition of evaporated material  32  but the impact or effect on the frequency of MEMS resonator  10  is not as large as when high tension areas  22  are thickened. 
   In contrast, with reference to  FIGS. 8A and 8B , essentially only high tension areas  22  of moveable beams  14   a  and  14   b  may be selectively thickened by appropriately locating frequency adjustment structures  30  opposite and/or proximate only high tension areas  22 . In this embodiment, larger changes in frequency may be readily obtained. 
   Notably, frequency adjustment structures  30  of  FIGS. 5 and 7  are integrated with or into fixed electrode(s)  18 . In contrast, frequency adjustment structures  30  of  FIG. 8A  are separate structures and, as such, not integrated with or into fixed electrode(s)  18 . All permutations and combinations of integrated and non-integrated frequency adjustment structures  30  are intended to fall within the present invention. (See, for example,  FIG. 8B  wherein both integrated and non-integrated frequency adjustment structures  30  are illustrated). 
   With reference to  FIG. 9A , control circuitry  24  determines and/or calculates the electrical current (from electrical source  26 ) required to adjust, tune, set, define and/or select the frequency of MEMS resonator  10  by adding material to mechanical structure  12  (for example, to portions of moveable beams  14   a  and  14   b ) via resistive heating of one or more frequency adjustment structures  30 . The control circuitry  24  may operate in the same or similar manner as described with reference to  FIGS. 1 and 4 . For the sake of brevity, that discussion will not be repeated. 
   In a third aspect, the present invention is directed to a method of adjusting, tuning, setting, defining and/or selecting the frequency of the output of MEMS resonator  10  (before and/or after final packaging) using the output of a light source (for example, a laser) to heat frequency adjustment structures  30 . The MEMS resonator  10  of this aspect of the invention is encapsulated in a chamber using the thin film or wafer level encapsulation techniques described above. The frequency of MEMS resonator  10  is adjusted, tuned and/or set by adding material (via evaporation from frequency adjustment structures  30 ) to mechanical structures  12  (for example, the moveable or expandable electrodes). In one embodiment, the material may be added to selected portions of the moveable electrode(s) (for example, the areas of high stress or tension). In another embodiment, material is changed and/or removed from all or substantially all of the active areas of the moveable electrodes (for example, those areas that oppose the fixed electrodes). 
   With reference to  FIG. 10 , in one embodiment of this aspect of the present invention, light source  44  (for example, one or more lasers, lamps, light emitting diode (LED), electrical element or other mechanism for producing high energy radiation) outputs light  46  at a predetermined wavelength. The light  46  is focused and incident on frequency adjustment structures  30  and, responsively heats frequency adjustment structures  30 . In those instances where frequency adjustment structures  30  are comprised of monocrystalline and/or polycrystalline silicon, the surfaces may be heated to temperatures greater than approximately 1000° C. to 1200° C. Accordingly, the monocrystalline and/or polycrystalline silicon surface atoms of frequency adjustment structures  30  may begin to evaporate and migrate to surrounding colder surfaces of opposing moveable beams  14   a  and  14   b . In this way, moveable beams  14   a  and  14   b  are thickened by evaporated material  32 . In addition, the spring constant(s) of moveable beams  14   a  and/or  14   b  may also be reduced. 
   In those instances where mechanical structure  12  is encapsulated, using a thin film or wafer level encapsulation techniques, in a chamber prior to final packaging, it may be advantageous to employ light source  44  and light  46  having optical properties (for example, a wavelength and focus) that are not absorbed by or in the encapsulation material(s) (i.e., the encapsulation structure is transparent to light source  44  and light  46 ). With continued reference to  FIG. 10 , MEMS resonator  10  may include encapsulation structure  34 , including first and encapsulation layers  36   a  and  36   b , to seal chamber  38 . As described in detail in the Microelectromechanical Systems Having Trench Isolated Contacts Patent Application, in one embodiment, encapsulation structure  34  may be comprised of polycrystalline silicon or amorphous silicon materials. That is, first encapsulation layer  36   a  may be, for example, a polycrystalline silicon or amorphous silicon and second encapsulation layer  36   b , which is deposited over or in vent in first encapsulation layer  36   a  to seal the chamber, may also be comprised of polycrystalline silicon or amorphous silicon. 
   In this embodiment, light  46  that includes a wavelength of about 700 nm to about 1900 nm and which is focused on frequency adjustment structures  30 . Under these conditions, encapsulation structure  34  is sufficiently “transparent” to light  46  and the energy therein is applied and/or focused to frequency adjustment structures  30  (see focus areas  48 ). The monocrystalline and/or polycrystalline silicon surface atoms of frequency adjustment structures  30  may migrate to surrounding colder surfaces of opposing moveable beams  14   a  and  14   b . In this way, moveable beams  14   a  and  14   b  are thickened by evaporated material  32 . 
   Notably, in this embodiment, the heating and frequency adjustment of MEMS resonator  10  may be performed before final packaging but after encapsulation. Moreover, the heating and frequency adjustment may be performed after final packaging provided the package is sufficiently transparent to light  46  (and its wavelength). 
   The vertical local heating may be achieved via a wide laser beam, which is focused to a spot only in one horizontal plane. Although encapsulation structure  34 , which is comprised of a polycrystalline silicon or amorphous silicon is sufficiently transparent to light  46 , absorption of light  46  by the underlying frequency adjustment structures  30 , and heating thereof, is necessary to evaporate polycrystalline silicon surface atoms of frequency adjustment structures  30  to thereby deposit evaporated material  32  on moveable beams  14   a  and  14   b . Notably, the vertical focus is optimized to reduce the heating in encapsulation structure  34  and in substrate  42  and to create a hot spot (a three dimensional area) in the desired and/or predetermined location on or in mechanical structure  12 . 
   There are many inventions described and illustrated herein. While certain embodiments, features, materials, configurations, attributes and advantages of the inventions have been described and illustrated, it should be understood that many other, as well as different and/or similar embodiments, features, materials, configurations, attributes, structures and advantages of the present inventions that are apparent from the description, illustration and claims. As such, the embodiments, features, materials, configurations, attributes, structures and advantages of the inventions described and illustrated herein are not exhaustive, and it should be understood that other, similar, as well as different, embodiments, features, materials, configurations, attributes, structures and advantages are within the scope of the present invention. 
   For example, as mentioned above, many (direct and indirect) temperature sensing and feedback techniques and/or configurations may be employed in the present invention. All temperature sensing and feedback techniques and/or configurations, whether now known or later developed, including those discussed above, are intended to be within the scope of the present invention. 
   Further, the electrical source that provides current to the heating elements may include one or more independent sources to enhance the flexibility of the resistive heating of the moveable beam and/or the frequency adjustment structures. (See, for example,  FIGS. 9B–9D ). For example, one of a plurality of electrical sources may be “dedicated” to one or more frequency adjustment structures (see,  FIGS. 9A and 9D ) and/or one electrical source may be “dedicated” to one or more moveable beams (see, for example,  FIGS. 9B ,  9 C and  9 D). In this regard, the heating of the frequency adjustment structures and/or the moveable beams may be independently controlled via one or more electrical sources. All permutations and configurations of independently or dependently controlling the frequency adjustment structure(s) and/or the moveable beam(s) are intended to come within the present invention. Notably, control circuitry  24  may operate and/or control electrical source(s)  26  in the same or similar manner as described with reference to  FIGS. 1 and 4 . For the sake of brevity, that discussion will not be repeated. 
   Further, the present inventions may employ any temperature sensor or sensing technique, whether now known or later developed. For example, the present inventions may employ a temperature sensing technique using the moveable beam itself as a first temperature sensor and at least a second temperature sensor, disposed in the resonator, which measures, for example, the temperature of the substrate distant from the heating element(s) or sufficiently disposed therefrom such that the heating element(s) do not prevent the sensor from detecting, sampling and/or measuring the temperature of the substrate. In this embodiment, the non-conformal temperature of the moveable beam may depend on the temperature difference between the desired beam temperature and the temperature of the substrate. Thus, by calculating and/or determining this difference, the actual temperature of the moveable beam may be approximated and/or extrapolated using, for example, a look-up table that correlates the aforementioned difference and the actual temperature. 
   Alternatively, the control circuitry may employ a predetermined or mathematical relationship to estimate the temperature of the moveable beam wherein that relationship uses temperature difference between the desired beam temperature and the temperature of the substrate. Such temperature sensing techniques may significantly improve the temperature estimate of the moveable beam, which in turn, may result in an enhanced accuracy of the frequency of the output signal of the MEMS resonator. 
   The present invention may be implemented on unpackaged resonators which may be heated at a wafer level on a probe station at, for example, final wafer probing. An open plastic package (i.e., a pre-molded package) may also be employed. Alternatively, the present invention may be implemented on packaged resonators, before the lid is attached and/or secured. 
   Notably, although anchors  16  are illustrated as free-standing and square-shaped, any anchor structure may be employed which secures mechanical structure  12  to, for example, the substrate. That is, anchors  16  may be directly attached to the substrate or fixed in relation to a substrate through intervening/overlaying layer(s) or structure(s). Indeed, anchors  16  may employ any form of anchoring techniques, whether now known or later developed. For example, the present invention may employ the anchoring techniques described and illustrated in non-provisional patent application entitled “Anchors for Microelectromechanical Systems Having an SOI Substrate, and Method for Fabricating Same”, which was filed on Jul. 25, 2003 and assigned Ser. No. 10/627,237 (hereinafter “Anchors for Microelectromechanical Systems Patent Application”). In this regard, any and all of the embodiments of MEMS resonator  10  according to the present inventions may be anchored, for example, to a substrate, using the anchors (and anchoring techniques) as described and illustrated in Anchors for Microelectromechanical Systems Patent Application. For the sake of brevity, the anchoring techniques of Anchors for Microelectromechanical Systems Patent Application, implemented in conjunction with the inventions described and illustrated herein, will not be repeated in detail. It is expressly noted, however, that the entire contents of the Anchors for Microelectromechanical Systems Patent Application, including, for example, the features, attributes, alternatives, materials, techniques and advantages of all of the embodiments and/or inventions, are incorporated by reference herein. 
   Moreover, MEMS resonator  10 , as mentioned above, may be encapsulated using any thin film encapsulation techniques, whether now known or later developed. For example, the present invention may employ the encapsulation techniques described and illustrated in non-provisional patent application entitled “Microelectromechanical Systems, and Method of Encapsulating and Fabricating Same”, which was filed on Jun. 4, 2003 and assigned Ser. No. 10/454,867 (hereinafter “Microelectromechanical Systems and Method of Encapsulating Patent Application”). In this regard, any and all of the embodiments of MEMS resonator  10  according to the present invention may be encapsulated using the techniques described and illustrated in Microelectromechanical Systems and Method of Encapsulating Patent Application. Moreover, MEMS resonator  10  according to the present invention may also include or employ the techniques of fabricating the mechanical structure and electrically isolating contact areas and/or field areas from other electrically conductive materials, as described and illustrated in Microelectromechanical Systems and Method of Encapsulating Patent Application. For the sake of brevity, the encapsulation and isolation techniques of Microelectromechanical Systems and Method of Encapsulating Patent Application, implemented in conjunction with the inventions described and illustrated herein, will not be repeated. It is expressly noted, however, that the entire contents of the Microelectromechanical Systems and Method of Encapsulating Patent Application, including, for example, the features, attributes, alternatives, materials, techniques and advantages of all of the embodiments and/or inventions, are incorporated by reference herein. 
   Further, while the exemplary embodiments of the present inventions have been described in the context of microelectromechanical systems including micromechanical structures or elements, the present inventions are not limited in this regard. Rather, the inventions described herein are applicable to other electromechanical systems including, for example, nanoelectromechanical resonators. Thus, the present inventions may be pertinent to electromechanical systems, for example, resonators, made in accordance with fabrication techniques, such as lithographic and other precision fabrication techniques, which reduce mechanical components to a scale that is generally comparable to microelectronics. 
   As mentioned above, MEMS resonator  10  may employ any type of MEMS design and/or control, whether now known or later developed, including those discussed in detail above. For example, bulk-type resonators (see, for example,  FIGS. 11 and 12 ) as well as resonators oscillating in all directions, in-plane and out-of-plane, are applicable. The resonator configurations of the illustrative examples are not to be construed or interpreted in a limiting sense. 
   In the context of bulk-type resonators, the frequency is proportional to the geometry and material of the resonator. The frequency is directly proportional to the width in the direction of oscillation. As such, material deposition (from opposing frequency adjustment structures  30  which is integrated with fixed electrodes  18   a  and  18   b ) may increase the length of expanding and contracting electrode  50  of bulk resonators. (See, for example,  FIGS. 11 and 12 ). In this way, the frequency of MEMS resonator  10  may be lowered. 
   Alternatively, moveable beam(s)  14  of the bulk-type resonator may be heated (using electrical source  26  and/or light source  44 ) as described in the first aspect of the present invention. That is, initially the material of moveable beam(s)  14  may be annealed and thereafter the change in frequency of MEMS resonator  10  may be measured, detected, sampled and/or determined by control circuitry  24 . The surface material of moveable beam(s)  14  may also be changed by melting and/or evaporation, via application of a higher electrical current (I) or higher intensity of light  46 , and thereafter the change in frequency of MEMS resonator  10  may be measured, detected, sampled and/or determined by control circuitry  24 . 
   Although the exemplary embodiments of the present invention have illustrated frequency adjustment structures that are laterally displaced from moveable beams  14   a  and  14   b , frequency adjustment structures may be disposed vertically in addition or in lieu thereof. Thus, by incorporating frequency adjustment structures above and/or below mechanical structures  12 , material deposition may be accomplished in the vertical plane. This technique may be advantageous for resonators  10  oscillating in all directions, in plan and out of plane. 
   The terms “resonator”, “MEMS resonator” or “micromechanical resonator” as used throughout this description cover a broad class of micro-machined structures and useful combinations of these structures. Such combinations typically include electronic circuitry, such as circuitry used to drive, power, monitor, and control the resonator. Micro-machined structures, such as holes, channels, cantilevers, bending beams, springs, tuning forks, membranes, substrate anchors, electrical contacts, etc., are building blocks for more complex devices, such as transducers. A transducer is generally any device capable of converting one form of energy into another. Transducers, including sensors and actuators, are an example of the type of devices susceptible to the benefits of the present invention. 
   Contemporary resonators often include at least one micro-machined structure generally referred to hereafter as a “beam structure.” The term is broadly construed to cover any transducer designed to mechanically move when acted upon by an external force (for example, electrical, magnetic, and/or physical). Single bending beams, multiple beam tuning forks are examples of beam structures. Both continuous and discrete structures are encompassed by the term beam structure. 
   It should be further noted that while the present inventions have been described in connection with SOI, other substrates are suitable. For example, the first semiconductor layer may be materials in column IV of the periodic table, for example, silicon, germanium, carbon; also combinations of these, for example, silicon germanium, or silicon carbide; also of III-V compounds, for example, gallium phosphide, aluminum gallium phosphide, or other III-V combinations; also combinations of III, IV, V, or VI materials, for example, silicon nitride, silicon oxide, aluminum carbide, or aluminum oxide; also metallic silicides, germanides, and carbides, for example, nickel silicide, cobalt silicide, tungsten carbide, or platinum germanium silicide; also doped variations including phosphorus, arsenic, antimony, boron, or aluminum doped silicon or germanium, carbon, or combinations like silicon germanium; also these materials with various crystal structures, including single crystalline, polycrystalline, nanocrystalline, or amorphous; also with combinations of crystal structures, for instance with regions of single crystalline and polycrystalline structure (whether doped or undoped). Indeed, the first semiconductor layer may also be a metal or metal type material (in which case it would be a first conductor layer disposed on the first substrate layer). Notably, the mechanical structure (for example, moveable beam  14 ) may be comprised of the same materials as described above with respect to the first semiconductor layer. 
   It should be further noted that the term “circuit” may mean, among other things, a single component or a multiplicity of components (whether in integrated circuit form or otherwise), which are active and/or passive, and which are coupled together to provide or perform a desired function. The term “circuitry” may mean, among other things, a circuit (whether integrated or otherwise), a group of such circuits, a processor(s), a state machine, a group of state machines, software, a processor(s) implementing software, or a combination of a circuit (whether integrated or otherwise), a group of such circuits, a state machine, group of state machines, software, a processor(s) and/or a processor(s) implementing software, processor(s) and circuit(s), and/or processor(s) and circuit(s) implementing software. 
   Finally, the term “data” may mean, among other things, a current or voltage signal(s) whether in an analog or a digital form. The term “measure” means, among other things, sample, sense, inspect, detect, monitor and/or capture. The phrase “to measure” or similar, means, for example, to sample, to sense, to inspect, to detect, to monitor and/or to capture.