Abstract:
One embodiment of the present inventions sets forth a method for decreasing a temperature coefficient of frequency (TCF) of a MEMS resonator. The method comprises lithographically defining slots in the MEMS resonator beams and filling the slots with a compensating material (for example, an oxide) wherein the temperature coefficient of Young&#39;s Modulus (TCE) of the compensating material has a sign opposite to a TCE of the material of the resonating element.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional of application Ser. No. 11/963,709, filed Dec. 21, 2007 (now U.S. Pat. No. 8,234,774), which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     Embodiments of the present invention relate generally to temperature compensated microelectromechanical systems (MEMS) oscillators and, more specifically, to a temperature stable MEMS resonator. 
     2. Description of the Related Art 
     Many electronic devices include a real-time clock that runs continuously so that accurate time and date information, among other things, may always be maintained. Oscillators are commonly used in the timing circuitry of hand-held and portable electronic devices, such as wrist watches and cell phones. A typical oscillator circuit includes a resonator and an associated drive circuit to drive the resonator. Quartz is often used for the resonator. However, with the continuous push to decrease the size of electronic circuits, MEMS resonators fabricated from silicon are expected to replace quartz resonators in various oscillator circuit designs. 
     A major obstacle, though, to implementing MEMS resonators is that the mechanical properties of some MEMS resonator materials are dependent on temperature. Material stiffness is one example of a mechanical property that is dependent on the temperature. The temperature dependence of the material stiffness may be described with the temperature coefficient of stiffness, also known as temperature coefficient of Young&#39;s Modulus (TCE). As a result of the temperature dependence of the mechanical properties of MEMS resonator materials, properties of MEMS resonators (e.g., resonant frequency) may also exhibit temperature dependence. For example, a thermal coefficient of frequency (TCF) of a MEMS resonator, derived from the design of the resonator and the material properties of the one or more materials that make up the resonator, may be 30 ppm/° C., which means that if the MEMS resonator normally oscillates at a frequency of 1 MHz, then a 1° C. change in temperature results in a 30 Hz frequency shift. For some applications, the TCF of the resonator should be less than 1 ppm/° C. Consequently, many MEMS oscillator circuits require some form of temperature compensation to maintain the frequency of the signal produced by the MEMS resonator (referred to herein as the “output signal”) at a target value defined by a particular application. 
     One way to address the temperature dependence of MEMS resonator materials is to employ additional electronic circuits that periodically adjust the frequency of the output signal to maintain the frequency at the target value despite temperature fluctuations within the system. However, temperature-compensation electronic circuits are complicated to design and implement, take up valuable chip area, add to the overall chip cost, increase total test time, and consume significant amounts of power. 
     Another way to address the temperature dependence of MEMS resonator materials is to decrease the magnitude of the TCF of the MEMS resonator by oxidizing the surface of the MEMS resonator beams. As is well-known, some oxides become stiffer at higher temperatures, thereby counteracting the behavior of the MEMS resonator material over temperature. The addition of oxide may reduce the magnitude of the TCF of the MEMS resonator to nearly 0 ppm/° C. This approach, however, has several major drawbacks. 
     One drawback is related to process control. The TCF of a MEMS resonator coated with oxide is dependent on the thickness of the oxide on its surface. However, in a manufacturing environment, controlling oxide growth to better than 10% may be challenging, making TCF control via oxide coating difficult as well. Another drawback is that the oxide layer may accumulate electrical charge on the surface. Charge build-up on the surface of a MEMS resonator may cause the frequency of the resonator to drift over time. Yet another drawback arises from design limitations inherent in MEMS resonator systems. In order to counteract the behavior of MEMS resonator materials, a sufficient amount of oxide should be grown on the MEMS resonator beams. However, a thick layer of oxide requires a longer deposition time and increases the risk of stress-induced cracking, especially during or after an annealing step. In addition, large amounts of oxide may cause the stress in the MEMS resonator beams to become poorly controlled, adding uncertainty to its desired resonant frequency. Finally, a thick oxide layer may bridge or nearly bridge the gap between the MEMS resonator beams and their corresponding electrodes, leading to device failure. For example, if a MEMS resonator beam is 20 μm wide, and there is a gap of 0.7 μm between the beam and the electrodes, growing the 1.5-2 um of oxide necessary to reduce the TCF of the MEMS resonator is not possible. 
     As the foregoing illustrates, what is needed in the art is a better way to decrease the TCF of a MEMS resonator. 
     SUMMARY OF THE INVENTION 
     One embodiment of the present invention sets forth a method for fabricating a microelectromechanical system (MEMS) resonator having a reduced thermal coefficient of frequency (TCF). The method includes the steps of defining one or more slots within the MEMS resonator, fabricating the one or more slots, and filling the one or more slots with oxide. 
     One advantage of the disclosed method is that by growing or depositing oxide within the slots, the amount of oxide growth or deposition on the outside surfaces of the MEMS resonator may be reduced. As a result, the TCF of the MEMS resonator may be changed in a manner that is beneficial relative to prior art approaches. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       So that the manner in which the above recited features of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only typical embodiments of this invention and are therefore not to be considered limiting of its scope, for the invention may admit to other equally effective embodiments. 
         FIG. 1A  is a conceptual diagram of a MEMS resonator, according to one embodiment of the present invention; 
         FIG. 1B  illustrates a cross-section of the MEMS resonator beam of  FIG. 1A , according to one embodiment of the present invention; 
         FIG. 2  is a conceptual diagram of a MEMS resonator, according to another embodiment of the present invention; 
         FIGS. 3A through 3D  illustrate the process of filling slots within a MEMS resonator with oxide, according to one embodiment of the present invention; 
         FIG. 4A  illustrates the effects of placing slots filled with oxide in areas of high strain concentration on the TCF of a MEMS resonator, according to one embodiment of the present invention; 
         FIG. 4B  is a magnified view of the area of  FIG. 4A  where the TCF of a MEMS resonator with slots is within 1 ppm/° C.; 
         FIG. 5  sets forth a flow diagram of method steps for filling slots within a MEMS resonator with oxide, according to another embodiment of the present invention; 
         FIGS. 6A through 6E  illustrate the process of completely filling the slots within the MEMS resonator of  FIG. 2  with oxide, according to the method steps of  FIG. 5 ; 
         FIGS. 7A through 7E  illustrate the process of partially filling the slots within the MEMS resonator of  FIG. 2  with oxide, according to the method steps of  FIG. 5 ; 
         FIG. 8  is a conceptual diagram of an extensional resonator, according to one embodiment of the present invention; 
         FIG. 9  is a conceptual diagram of an electronic device configured to implement one or more aspects of the present invention; and 
         FIGS. 10A through 10E  illustrate different ways to position a MEMS resonator, a drive circuit, and application circuitry on one or more substrates. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1A  is a conceptual diagram of a MEMS resonator  100 , according to one embodiment of the present invention. As shown, the MEMS resonator  100  includes a MEMS resonator anchor  116  that fixes a base  118  of the MEMS resonator  100  to an underlying handle wafer (not shown). The MEMS resonator  100  further includes MEMS resonator beams  112  and  114  of length L that are mechanically coupled to the base  118 . By applying a time-varying signal to drive electrodes (not shown) at a given frequency and, optionally, a DC voltage between the MEMS resonator  100  and the drive electrodes, electrostatic forces are generated that cause the MEMS resonator beams  112  and  114  to oscillate in a tuning fork fashion, as indicated by arrows  122  and  124 , respectively. In response to the motion of the MEMS resonator beams  112  and  114 , the average capacitance between a sense electrode (not shown) and the MEMS resonator beams  112  and  114  changes at a substantially constant frequency at a constant temperature. The capacitance can be measured, and the resulting signal can then be used to generate a timing signal. 
     As also shown, the MEMS resonator  100  includes slots  130  positioned in different locations within the MEMS resonator beams  112  and  114  and the base  118 . The slots  130  are filled with a compensating material (e.g., oxide) that has a TCE with an opposite sign relative to the MEMS resonator material. As previously described herein, at higher temperatures, oxide typically becomes stiffer, while the MEMS resonator material (e.g., silicon) typically becomes less stiff. Thus, filling the slots  130  with oxide counters the changing properties of the MEMS resonator material over temperature. More specifically, the overall TCF of the MEMS resonator  100  is proportional to a weighted average of the TCE of the MEMS resonator material and the TCE of the oxide, based on the placement of the oxide in the strain field of the MEMS resonator  100 . 
     Placing oxide in slots within the MEMS resonator itself offers several advantages over growing oxide on the outside surfaces of the MEMS resonator, as is done in prior art approaches. One advantage is increased control over the oxide growth process. Oxide growth in the slots may be self-limiting because the amount of oxide cannot exceed the size of the slots. Another advantage is that if oxide is also desired on the outside surfaces of the MEMS resonator adding oxide within the slots allows the amount of oxide on the outside surfaces of the MEMS resonator to be reduced. A thinner oxide layer on the outside surfaces enables oxide to be grown in a larger number of MEMS resonator systems without conflicting with the geometric and spatial constraints of those systems. In addition, better frequency control of the MEMS resonator may be achieved because the characteristics of the MEMS resonator elements become more predictable with thinner layers of oxide on the outside surfaces of the resonator elements. Furthermore, reducing the thickness of the oxide layers grown on the MEMS resonator decreases the stresses within the MEMS resonator material resulting from a lattice mismatch between the oxide and the MEMS resonator material, thereby reducing the risk of stress-induced cracking. Finally, reducing the amount of oxide may result in improved transduction within the MEMS resonator. 
     Persons skilled in the art will recognize that oxide may be placed in/on the MEMS resonator using growth, deposition, or a combination of both growth and deposition. Therefore, one should understand that anywhere an oxide growth is discussed in the present application, oxide deposition or a combination thereof could be used as well. 
     Furthermore, in lieu of to filling the slots with oxide, the slots described in the present application may be filled with any suitable compensating material that has a TCE with an opposite sign to the TCE of the MEMS resonator material. For example, in one embodiment, a MEMS resonator may be formed from silicon oxide (SiO 2 ), slots may be filled with Si, sacrificial material may be Si, and cap/liner material may be silicon nitride (SiN). 
       FIG. 1B  illustrates a cross-section of the MEMS resonator beam  112  along line  140  of  FIG. 1A . The cross-sectional view further illustrates the arrangement of the slots  130  within the MEMS resonator  100 , according to one embodiment of the present invention. As shown, H indicates the height of the MEMS resonator beam  112 , and W indicates the width of the MEMS resonator beam  112 . The slots  130  may be lithographically defined from the top face  144 , in the pattern illustrated in  FIG. 1A , and extended all the way to the bottom face  142 , as illustrated in  FIG. 1B , in the form of narrow trenches. The oxide can be introduced within the slots  130  through the processes of growth, deposition, or a combination thereof. The pattern and number of slots may also be varied to meet design goals. 
     Referring back now to  FIG. 1A , when oscillating, as indicated by the arrows  122  and  124 , the MEMS resonator beams  112  and  114  are the resonating elements of the MEMS resonator  100 , and are subject to flexural stresses. Along the length L of the MEMS resonator beam  112 , the flexural stress is larger on outside sidewalls  141  and  143  and decreases towards the center of the MEMS resonator beam  112 . Similarly, along the length L of the MEMS resonator beam  114 , the flexural stress is larger on outside sidewalls  145  and  147  and decreases towards the center of the MEMS resonator beam  114 . In addition, for both the MEMS resonator beams  112  and  114 , the flexural stresses are relatively large near the base  118  and decrease towards the opposite end of each beam, away from the base  118 . Thus, areas  161 ,  163 ,  165 , and  167  near the base  118  indicate the regions of the MEMS resonator beams  112  and  114  that are subject to the largest flexural stresses. As described in greater detail in  FIG. 2 , the greater the flexural stresses in a given area, the greater the dependence of the overall TCF of a MEMS resonator on the individual TCEs of the materials comprising that area. Therefore, placing the slots filled with oxide in the areas that experience large flexural stresses increases the effective contribution of the TCE of the oxide to the overall TCF of the MEMS resonator, which facilitates lowering the overall TCF of the MEMS resonator. 
       FIG. 2  is a conceptual diagram of a MEMS resonator  200 , according to another embodiment of the present invention. Similar to the MEMS resonator  100 , the MEMS resonator  200  includes MEMS resonator beams  212  and  214 , slots  230  filled with a compensating material (e.g., oxide) that has a TCE with an opposite sign relative to the MEMS resonator material, and a MEMS resonator anchor  216  that fixes a base  218  of the MEMS resonator  200  to an underlying handle wafer (not shown). Again, the MEMS resonator beams  212  and  214  of length L are mechanically coupled and oscillate in a tuning fork fashion, as indicated by arrows  222  and  224 , respectively, leading to the generation of a reference signal. 
     As shown, the MEMS resonator  200  differs from the MEMS resonator  100  in that outside sidewalls  241 ,  243 ,  245 , and  247  of the MEMS resonator beams  212  and  214  have serrated surface with a plurality of teeth. Cutting serrations into the outside edge of the resonator can shift the maximum strain field inward, along the base of the serrations near lines  251 ,  253 ,  255 , and  257 . For example, for the MEMS resonator beam  212 , the flexural stresses are largest along the lines  251  and  253  that extend along the base of the teeth and decreases towards the outside sidewalls  241  and  243  and towards the center of the MEMS resonator beam  212 . Similarly, for the MEMS resonator beam  214 , the flexural stresses are largest along the lines  255  and  257  that extend along the base of the teeth and decreases towards the outside sidewalls  245  and  247  and towards the center of the MEMS resonator beam  214 . Furthermore, for both the MEMS resonator beams  212  and  214 , the flexural stress is relatively large near the base  218 , and decreases to the tip of each beam. Thus, areas  261 ,  263 ,  265 , and  267  near the base  218  indicate the regions of the MEMS resonator beams  212  and  214  that are subject to the largest flexural stress, while the serrated teeth of the outside sidewalls  241 ,  243 ,  245 , and  247  experience minimal stress when the MEMS resonator beams  212  and  214  oscillate during operation. 
     In various embodiments, the serrations may be of any suitable profile. Therefore, one should understand that anywhere serrated teeth are discussed in the present application, other irregular profiles could be used as well. For example, instead of having the serrated teeth on the outside sidewalls, the MEMS resonator beams may include outside sidewalls with rounded teeth profile, a sinusoidal profile, an “arc-to-point” profile, a “skewed teeth” profile, an interlocked profile, or a combination thereof. 
     Enhancing the stiffness of the MEMS resonator beams  212  and  214  in regions that experience large stresses has a greater marginal impact on the overall stiffness of the MEMS resonator  200  than enhancing the stiffness in regions that experience lesser stresses. Thus, whenever possible, by placing slots filled with a compensating material in the regions of the largest stress, as shown with the slots  230  within the areas  261 ,  263 ,  265 , and  267 , the contribution of the compensating material in the slots  230  to the overall stiffness of the MEMS resonator  200  is increased. Whenever placing slots filled with the compensating material in the regions of the largest stress is not technically feasible, placing slots filled with the compensating material in the regions subject to larger stresses relative to other regions, the contribution of the compensating material in the slots to the overall stiffness of the MEMS resonator is still increased. Consequently, the contribution of the TCE of the compensating material to the overall TCF of the MEMS resonator, proportional to a weighted average of the TCE of the MEMS resonator material and the TCE of the compensating material, is also increased. As a result, the total amount of compensating material necessary to counteract the behavior of the MEMS resonator material and achieve a particular desired overall TCF value may further be reduced relative to prior art techniques. All of the advantages of further reducing the thickness of compensating material layers (e.g., oxide layers), discussed above, apply with equal force to the MEMS resonator  200 . 
     In addition, since serrating the outside sidewalls  241 ,  243 ,  245 , and  247  effectively shifts the regions of the largest flexural stresses within the MEMS resonator beams  212  and  214  further inward, the overall TCF of the MEMS resonator  200  is less sensitive to variations in the thickness of oxide grown on the outside sidewalls  241 ,  243 ,  245 , and  245 . Therefore, serrating the outside sidewalls  241 ,  243 ,  245 , and  245  provides the benefit of increased tolerance in oxide growth variations during fabrication of the MEMS resonator  200 . 
       FIGS. 3A through 3D  illustrate the process of filling the slots  230  within the MEMS resonator  200  with oxide, according to one embodiment of the present invention. While the process is described with relation to the MEMS resonator  200 , the same process applies to filling with oxide the slots  130  within the MEMS resonator  100 . 
       FIG. 3A  illustrates a cross-sectional view of the slot  230  etched in the MEMS resonator beam  212  before the oxidation process starts. The original boundaries of the bottom and top faces of the MEMS resonator beam  212  are shown as top face  342  and bottom face  344 , respectively. The original boundaries of the surfaces created by etching the slot  230  are shown as a left slot sidewall  313  and a right slot sidewall  315 .  FIG. 3B  illustrates the slot  230  after the oxidation process has started. The oxide grows substantially equally on the top face  342 , the bottom face  344 , the left slot sidewall  313 , and the right slot sidewall  315 , as indicated with the cross-hatched areas. As a result of oxide growth, the boundaries of the top and bottom faces  342 ,  344  expand, as shown with oxide boundaries  352  and  354 . Similarly, the boundaries of the left and right slot sidewalls  313 ,  315  expand as well, as shown with oxide boundaries  323  and  325 . During the oxidation process, the oxide may grow both outward the original boundaries (about 60% of the growth) and inward the original boundaries of the material (about 40% of the growth). Thus, the boundaries of the MEMS resonator material shift inwards, as shown with oxide boundaries  333  and  335 . 
     As the oxide continues to grow, the oxide boundaries  352 ,  354 ,  323 ,  325 ,  333 , and  335  expand further in their respective directions. Eventually, the lines  323  and  325  come so closer together that the slot  230  is plugged shut, as shown in  FIG. 3C , leaving a small gap  330 . Since free oxygen molecules cannot easily reach the gap  330 , the oxide growth in the slot  230  stops. The moment in the oxidation process when the slot  230  is plugged shut is referred to herein as “pinch-off.” After pinch-off, the oxide continues to grow only on the top and bottom faces  342 ,  344 , as illustrated in  FIG. 3D , where the oxide boundaries  352  and  354  are expanded even further. 
     In different implementations, the slots  230  may be filled completely, by allowing the oxidation or deposition process to continue past pinch-off (as illustrated in  FIG. 3D ), or partially, by stopping the oxidation or deposition process before pinch-off (as illustrated in  FIG. 3B ). Completely filling the slot  230  with oxide increases the range of allowable oxide thickness and is attractive for manufacturing control because of the pinch-off. However, when the oxide boundaries  323  and  325  come into contact with each other, excessive in-plane stress and stress gradients may arise, which may be detrimental to the characteristics of the MEMS resonator  200 . For this reason, partial filling of the slots  230  may be preferred since the oxide boundaries  323  and  325  do not come into contact with one another. After the slots  230  are partially filled with oxide, the remaining gap in the slot  230  may be filled with a low-stress cap layer, such as silicon. 
       FIG. 4A  illustrates the effects of placing slots filled with oxide in areas of high strain concentration on the TCF of a MEMS resonator, according to one embodiment of the present invention. As shown, a line  402  is a reference line, indicating a TCF of 0 ppm/° C. A line  404  represents the TCF of a conventional single ended cantilever beam MEMS resonator with a serrated 4 μm-wide beam for different oxide thicknesses on the outside sidewalls of the MEMS resonator beam. A line  406  represents the TCF of a conventional single ended cantilever beam MEMS resonator with a serrated 8 μm-wide beam for different oxide thicknesses on the outside sidewalls of the MEMS resonator beam. The term “conventional” implies that the MEMS resonator is uniformly oxidized on the surface and does not include slots with oxide within the MEMS resonator beam. When the conventional MEMS resonators do not contain any oxide on their surfaces (point  412  in  FIG. 4A ), the TCF of those resonators is −30 ppm/° C. As shown, the slope of the line  406  is smaller than the slope of the line  404 , indicating that more oxide must be grown on the surface of the MEMS resonator with a 8 μm-wide beam compared to the MEMS resonator with a 4 μm-wide beam to reduce the TCF to a particular target value. 
     As also shown in  FIG. 4A , line  408  represents the TCF of a single ended cantilever beam MEMS resonator with a serrated 19 μm-wide beam containing slots filled with oxide for different oxide thicknesses on the top and bottom faces of the MEMS resonator beam. Referring back now to  FIGS. 3A through 3D , the point  412  on the line  408  corresponds to  FIG. 3A , where the process to fill the slots with oxide has not yet started. Point  414  on the line  408  corresponds to  FIG. 3B , where the slots are partially filled with the oxide. Point  416  on the line  408  corresponds to  FIG. 3C , where, at pinch-off, the oxide plugs the slot shut. Between the points  412  and  416 , the slope of the line  408  is greater than the slope of the line  406 . Again, a greater slope indicates that a thinner layer of oxide is needed on the surface of the MEMS resonator with slots and a 19 μm-wide beam compared to the conventional MEMS resonator with a 8 μm-wide beam to reduce the TCF to a particular target value. The line  408  has a greater slope between the points  412  and  416  than the line  406  because, between the points  412  and  416 , the overall TCF of the MEMS resonator with slots is dominated by the oxide growth in the slots. As previously described, positioning the slots in the regions of the MEMS resonator beam that are subject to the largest flexural stresses increases the contribution of the oxide in the slots to the overall TCF of the MEMS resonator. As a result, the total amount of oxide on the surfaces of the MEMS resonator beam needed to decrease the magnitude of TCF of the MEMS resonator from −30 ppm/° C. to a particular target value is reduced. For example, as indicated with a line  430 , in order to reduce the TCF to −5 ppm/° C., 0.6 μm of oxide is required to be grown on the surfaces of the conventional MEMS resonator with a 8 μm-wide beam. However, only about 0.33 μm of oxide is required to be grown on the surfaces of the MEMS resonator with slots and a 19 μm-wide beam to achieve the same TCF. 
     Point  416  on the line  408  corresponds to  FIG. 3D , where, after pinch-off, the oxide continues to grow on the bottom and top faces of the MEMS resonator beam. After the point  416 , the slope of the line  408  is less than the slope of the line  406 . The slope of the line  408  decreases after the point  418  because, after the oxide plugs the slots shut, the overall TCF of the MEMS resonator with slots is dominated by the oxide growth on the bottom and top faces of the MEMS resonator beam. As a result, after the point  416 , the overall TCF of the MEMS resonator with slots is not determined by oxide growth (deposition) on its sidewalls  241 ,  243 ,  245 ,  247  because the serration of the surface routes the strain field away from oxide grown or deposited on these surfaces. On a MEMS resonator with slots but without the serration, the slope of the line  408  after the point  416  would be greater. 
     Persons skilled in the art will recognize that, in order to improve manufacturability, the slope of the TCF curve for a MEMS resonator, as the curve crosses through TCF=0, should be minimized. By doing so, the TCF of the MEMS resonator may remain within a desired range for a larger range of oxide thicknesses. For example,  FIG. 4B  is a magnified view of an area  420  where the TCF of the MEMS resonator with slots is within 1 ppm/° C. As shown, the value of oxide thickness for which the TCF of the MEMS resonator with slots is 0 ppm/° C. is 0.5 μm and the range of the oxide thickness for which the TCF of the MEMS resonator with slots is within ±1 ppm/° C. is 0.1 μm. Thus, the design of the MEMS resonator with slots achieves the desired overall TCF value with a thinner layer of oxide, while allowing variations in oxide thickness to be as large as ±10%. In addition, it allows for increased tolerance range in dimensions of resonator prior to oxide growth or deposition. 
       FIG. 5  sets forth a flow diagram of method steps for filling slots within the MEMS resonator  200  with oxide, according to another embodiment of the present invention. Again, while the process is described with relation to the MEMS resonator  200 , the same process applies with equal force to filling the slots  130  within the MEMS resonator  100  with oxide. 
     The method begins in step  502 , where the slots  230  are lithographically defined and fabricated. In step  504 , the slots  230  are lined with a liner material such as silicon, resistant to the release etchant, commonly hydrofluoric (HF) acid. In step  506 , oxide is added to the slots  230  through oxide growth, deposition, or a combination thereof. Depending on the particular application, the slots  230  may be filled with oxide completely or partially, as described above. In step  508 , the excess oxide is removed from the MEMS resonator  200  so that the oxide remains only within the slots  230 . Finally, in step  510 , the slots  230  are capped with a capping material resistant to the release etchant. Again, silicon may be used as a capping material. 
       FIGS. 6A through 6E  illustrate the process of completely filling the slots  230  within the MEMS resonator  200  with oxide, according to the method steps of  FIG. 5 .  FIG. 6A  illustrates the slot  230  etched in the MEMS resonator beam  212  (step  502 ). As shown, the MEMS resonator beam  212  is fabricated on top of a buried oxide layer  610 , which is fabricated on top of a handle wafer  615 .  FIG. 6B  illustrates the slot  230  lined with a liner material  620  resistant to the release etch process (step  504 ).  FIG. 6C  illustrates the slot  230  filled completely with oxide  630  (step  506 ).  FIG. 6D  illustrates the excess oxide  630  removed from the surfaces of the MEMS resonator beam  212  such that the oxide  630  remains only within the slot  230  (step  508 ).  FIG. 6E  illustrates the slot  230  capped with a capping material  640  (step  510 ). 
       FIGS. 7A through 7E  illustrate the process of partially filling the slots  230  within the MEMS resonator  200  with oxide, according to the method steps of  FIG. 5 .  FIG. 7A  illustrates the slot  230  etched in the MEMS resonator beam  212  (step  502 ). As shown, the MEMS resonator beam  212  is fabricated on top of the buried oxide layer  610 , which is fabricated on top of the handle wafer  615 .  FIG. 7B  illustrates the slot  230  lined with the liner material  620  resistant to the release etch process (step  504 ).  FIG. 7C  illustrates slot  230  partially filled with the oxide  630  (step  506 ).  FIG. 7D  illustrates the excess oxide  630  removed from the surfaces of the MEMS resonator beam  212  such that the oxide  630  remains only within the partially filled slot  230  (step  508 ). Finally,  FIG. 7E  illustrates the partially filled slot  230  capped with the capping material  640 . 
     The particular process that may be implemented to fill the slots  230  with oxide depends on when the oxidation process takes place in relation to the HF vapor etching step during the fabrication of the MEMS resonator  200 . Persons skilled in the art will recognize that the step of HF vapor etching is intended to etch the buried oxide layer  610  and release the MEMS resonator  200 . If the process of filling the slots  230  with oxide is carried out after the release etching step, then the process described in FIGS.  3 A through  3 D, above, may be implemented. If, however, the process of filling the slots  230  with oxide is carried out before the HF vapor etching step, then the HF vapor may etch not only the buried oxide layer  610 , but also the oxide within the slots  230 . In some devices, some etching of the oxide within the slots may be acceptable and a liner and cap are not required. Additionally, if compensating material is not substantially affected by release etchant, a cap/liner may not be needed. The additional steps of lining and capping the slots  230  with silicon, as described in  FIGS. 5 ,  6 A through  6 E, and  7 A through  7 E above, are included to prevent the HF vapor from etching the oxide in the slots  230  when the buried oxide layer  610  is etched. In this manner, when the MEMS resonator  200  is released after the buried oxide layer  610  is etched with the HF vapor, the oxide remains embedded within the slots  230 . 
     In addition to the foregoing, the capping material  640  ensures that the surface of the MEMS resonator  200  remains conductive which prevents charge from accumulating on the surface of the oxide  630 . As a result, the electrostatic problems previously described herein may be eliminated. The liner material may also be made conductive for similar reasons. 
     The foregoing description applies to MEMS resonators that are comprised of resonating elements that exhibit flexural (bending) mechanical modes of resonance. Some resonator devices may include resonating elements that exhibit extensional (stretching) modes of resonance. Extensional resonators may also be temperature compensated using structures that include slots filled with a compensating material.  FIG. 8  is a conceptual diagram of an extensional resonator  800 , according to one embodiment of the present invention. The extensional resonator  800  includes an extensional resonator beam  812  configured as a straight bar and anchored near its center with an anchor  816 . In other embodiments, extensional mode resonators may include plates, rings, or other shapes and structures. 
     The extensional resonator beam  812  oscillates in a stretching fashion, as indicated by arrows  822  and  824 , leading to the generation of a reference signal. The extensional resonator  800  also includes slots  830  filled with a compensating material (e.g., oxide) that has a TCE with an opposite sign relative to the MEMS resonator material. 
     In an extensional mode resonator, strain fields may be more uniformly distributed through the thickness and width of the resonator. For example, for the extensional resonator  800 , the lowest order extensional resonant mode will have its highest strain field in an area  865  (i.e., the area  865  is a region subject to the largest extensional stress). The maximum stress regions in an extensional mode resonator may not be situated near the edges of the resonator beam. 
     Similarly to the MEMS resonator  200 , enhancing the stiffness of the MEMS resonator beam  812  in regions that experience large stresses has a greater marginal impact on the overall stiffness of the MEMS resonator  800  than enhancing the stiffness in regions that experience lesser stresses. Thus, whenever possible, by placing slots filled with a compensating material in the regions of the largest extensional stress, as shown with the slots  830  within the area  865 , the contribution of the compensating material in the slots  830  to the overall stiffness of the MEMS resonator  800  is increased. Whenever placing slots filled with compensating material in the regions of the largest extensional stress is not technically feasible, placing slots filled with compensating material in the regions of larger stress rather than placing the slots with compensating material in the regions of lesser stress, the contribution of the compensating material in the slots to the overall stiffness of the MEMS resonator is still increased. Consequently, the contribution of the TCE of the compensating material to the overall TCF of the MEMS resonator, proportional to a weighted average of the TCE of the MEMS resonator material and the TCE of the compensating material, is also increased. 
     More specifically, for extensional mode resonating elements, experimentation has shown that a ratio of about 40% compensating material (e.g., oxide) to MEMS resonator material (e.g., silicon) effectively balances the TCF of the MEMS resonator. The ratio applies to the thickness of the MEMS resonating element in a plane perpendicular to the stretching movement of the MEMS resonating element. 
       FIG. 9  is a conceptual diagram of an electronic device  900  configured to implement one or more aspects of the present invention. As shown, electronic device  900  includes, without limitation, a timing signal generator  920  configured to provide a timing signal to application circuitry  910 . The timing signal generator  920  includes a MEMS oscillator sustaining circuit  930 . In one embodiment, the MEMS oscillator sustaining circuit  930  includes the MEMS resonator  200 , where the serrated MEMS resonator beams  212  and  214  are fabricated as shown in  FIG. 2 . In another embodiment, the MEMS oscillator sustaining circuit  930  may include the MEMS resonator  100 , where the MEMS resonator beams  112  and  114  are fabricated as shown in  FIG. 1 . In yet another embodiment, the MEMS oscillator sustaining circuit  930  may include the extensional resonator  800 , where the extensional resonator beam  812  is fabricated as shown in  FIG. 8 , or any other suitable MEMS resonator according to the present invention. Furthermore, the MEMS oscillator sustaining circuit  930  includes a drive circuit (not shown) that drives the MEMS resonator  200 . Electronic device  900  may be any type of electronic device that includes application circuitry requiring a timing signal. Some examples of electronic device  900  include, without limitation, an electronic wrist watch, a personal digital assistant, or a cellular phone. 
     Using  FIG. 9  as an example, in alternate embodiments, the MEMS resonator  200  may be disposed on/in the same substrate or on/in different substrates than the drive circuit. Moreover, the application circuitry  910  may be disposed on/in the same substrates as the MEMS resonator  200  and/or the drive circuit.  FIGS. 10A through 10E  illustrate different ways to position the MEMS resonator  200 , a drive circuit  1090 , and the application circuitry  910  on one or more substrates. In particular, the MEMS resonator  200  and/or the drive circuit  1090  and/or the application circuitry  910  may be integrated on/in the same substrate  1000 , as shown on  FIG. 10A , on/in different substrates  1000   a ,  1000   b  and  1000   c , as shown on  FIG. 10B , or on/in different substrates  1000   d ,  1000   e ,  1000   f ,  1000   g ,  1000   h  and  1000   i , as shown on  FIGS. 10C ,  10 D, and  10 E. All permutations and combinations thereof are intended to fall within the scope of the present invention. 
     While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.