Patent Publication Number: US-9422157-B2

Title: Method for temperature compensation in MEMS resonators with isolated regions of distinct material

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This patent application is a divisional application of U.S. Application Ser. No. 12/638,919, now U.S. Pat. No. 8,464,418, filed Dec. 15, 2009, which is a divisional application of U.S. Application Ser. No. 11/716,115, filed Mar. 9, 2007, now U.S. Pat. No. 7,639,104, the entire contents and disclosure of each of the foregoing being incorporated herein by reference in its entirety for all purposes. 
    
    
     BACKGROUND 
     1. Field 
     The present invention relates to the field of microelectromechanical systems (MEMS), and more particularly to temperature compensated MEMS resonators. 
     2. Discussion of Related Art 
     “MEMS” generally refers to apparatus incorporating some mechanical structure having a dimensional scale that is comparable to microelectronic devices. For example, less than approximately 250 um. This mechanical structure is typically capable of some form of mechanical motion and is formed at the micro-scale using fabrication techniques similar to those utilized in the microelectronic industry such as thin film deposition, and thin film patterning by photolithography and reactive ion etching (RIE). The micromechanical structure in a MEMS distinguishes a MEMS from a microelectronic device. 
     Certain MEMS include a resonator. MEMS resonators are of particular interest in timing devices for an integrated circuit (IC). The resonator may have a variety of physical shapes, such as, but not limited to, beams and plates. Beams may be anchored on two ends or just one. A beam anchored at only one end is frequently referred to as a cantilevered beam. MEMS  100 , employing a conventional beam resonator, is shown in  FIG. 1A . MEMS  100  includes over substrate  101 , drive/sense electrodes  150  and a beam resonator  105 . A cross-sectional view along the line a-a′ of beam resonator  105  depicted in  Figure 1A  is shown in  FIG. 1B . As the cross-section view shows, beam resonator  105  comprises a single material  130 . 
     A resonator has resonant modes (e.g. flexural, bulk, etc.) of particular frequencies that depend at least upon the physical shape, size and stiffness of the material employed for the resonator. The stiffness of a material, characterized as Young&#39;s modulus, is generally temperature dependent. 
     For a MEMS resonator, such as beam resonator  105 , comprising a single material and therefore having uniform density and mechanical properties, the frequency of all modes and shapes can be derived to be a function of the material Young&#39;s modulus, E , the density, ρ, and a dimensionless constant , κ, or: 
     
       
         
           
             
               
                 
                   f 
                   = 
                   
                     
                       κ 
                       
                         Λ 
                         ⁡ 
                         
                           ( 
                           
                             d 
                             i 
                           
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
                         E 
                         ρ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
     In Equation 1, Λ(d i ) is a function of the geometric dimensions d i of the resonator and has units of length. 
     The temperature dependence of the resonator frequency is independent of the form of Λ(d i ) assuming a linear temperature dependence for these quantities of the form:
 
 E ( T )= E   0 (1+γ( T−T   0 )  (Equation 2)
 
 d   i ( T )= d   i   0 (1+α( T−T   0 ))  (Equation 3)
 
ρ( T )=ρ 0 (1−3α( T−T   0 ))  (Equation 4)
 
so that:
 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           1 
                           E 
                         
                         ⁢ 
                         
                           
                             ∂ 
                             E 
                           
                           
                             ∂ 
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                           = 
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                     = 
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                   , 
                   
                     
                       
                         
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                               d 
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                     α 
                   
                   , 
                   
                     
                       
                         
                           1 
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                             ρ 
                           
                           
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                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ) 
                 
               
             
           
         
       
     
     The temperature dependence of resonator frequency may then be expressed in terms of the linear coefficient of thermal expansion (CTE), α, and the Young&#39;s modulus temperature coefficient, γ: 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁡ 
                     
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                       T 
                       ) 
                     
                   
                   = 
                   
                     
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                       0 
                     
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                         1 
                         + 
                         
                           
                             1 
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                           ⁢ 
                           
                             ( 
                             
                               γ 
                               + 
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                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               T 
                               - 
                               
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                             ) 
                           
                         
                       
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                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ) 
                 
               
             
           
         
       
     
     Typical resonators, comprising semiconductor materials, such as single crystalline or polycrystalline silicon, have a Young&#39;s modulus that decreases with temperature. Thus, resonators comprising such a resonator will generally have a resonant frequency that decreases with increasing temperature. For an exemplary polycrystalline silicon-germanium (SiGe) resonator, the experimentally determined values are γ=−1.075×10 −4 /° C. and α=4.52×10 −6 /° C. Because the magnitude of γ is approximately 20 times larger than that of α, the temperature coefficient of frequency (TCF) is negative for a homogeneous SiGe resonator of any shape and in any mode. Using the values above, the TCF is approximately −51.49×10 −6 /° C. or −51.49 ppm/° C. 
     Due in part to the temperature dependence of the Young&#39;s modulus, fabricating MEMS resonators having temperature sensitivities on the same order of magnitude as existing quartz resonators is therefore challenging. For example, quartz, being relatively temperature stable, has a frequency drift of approximately 0.5 parts per million (ppm) per degree Celsius (° C.), while conventional MEMS resonators consisting of homogeneous materials of uniform density and mechanical properties have drifts on the order of 100 times higher, or 50 ppm/° C. Thus, widespread adoption of MEMS resonators in IC timing devices may require compensating temperature induced frequency variation. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a plan view of a MEMS utilizing a conventional uncompensated resonator. 
         FIG. 1B  is a cross-sectional view of the conventional uncompensated resonator depicted in  FIG. 1A . 
         FIG. 2A  is a plan view of a compensated MEMS cantilevered beam resonator in accordance with an embodiment of the present invention. 
         FIG. 2B  is a cross sectional view of the compensated MEMS cantilevered beam resonator depicted in  FIG. 2A . 
         FIG. 2C  is a plan view of a compensated MEMS cantilevered beam resonator in accordance with an embodiment of the present invention. 
         FIG. 3A  is a plan view of a compensated MEMS cantilevered beam resonator in accordance with an embodiment of the present invention. 
         FIG. 3B  is a graphical result of a mathematical simulation of the frequency variation over a temperature range for a MEMS cantilevered beam resonator depicted in  FIG. 3A . 
         FIGS. 4A-4B  provide a plan view and a cross-sectional view, respectively, of a MEMS plate resonator in accordance with an embodiment of the present invention. 
         FIG. 4C  is a graphical result of a mathematical simulation of frequency variation over a temperature range for a MEMS plate resonator in accordance with an embodiment of the present invention. 
         FIG. 5  is a plan view of a MEMS plate resonator in accordance with an embodiment of the present invention. 
         FIGS. 6A-6E  are prospective views of a method of fabricating resonators in accordance with an embodiment of the present invention. 
         FIGS. 7A-7E  are prospective views of a method of fabricating resonators in accordance with an embodiment of the present invention. 
         FIGS. 8A-8F  are prospective views of a method of fabricating a cantilevered beam resonator in accordance with an embodiment of the present invention. 
         FIGS. 9A-9C  are prospective views of a method of fabricating a cantilevered beam resonator in accordance with an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PRESENT INVENTION 
     In various embodiments, MEMS resonators are described herein with reference to FIGS. However, certain embodiments may be practiced without one or more of these specific details, or in combination with other known methods and materials. In the following description, numerous specific details are set forth, such as specific materials, dimensions and processes, etc., in order to provide a thorough understanding of the present invention. In other instances, well-known manufacturing processes and techniques have not been described in particular detail in order to not unnecessarily obscure the present invention. Reference throughout this specification to “an embodiment” means that a particular feature, structure, material, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Thus, the appearances of the phrase “in an embodiment” in various places throughout this specification are not necessarily referring to the same embodiment of the invention. Furthermore, the particular features, structures, materials, or characteristics may be combined in any suitable manner in one or more embodiments. 
     Described herein are MEMS resonators containing a first material and a second material to tailor the resonator&#39;s temperature coefficient of frequency (TCF). In one embodiment, the two materials have different Young&#39;s modulus temperature coefficients. In one such embodiment, the first material has a negative Young&#39;s modulus temperature coefficient and the second material has a positive Young&#39;s modulus temperature coefficient. In a further embodiment, the first material is a semiconductor and the second material is a dielectric. In an embodiment, the dimensions and location of the second material in the resonator is tailored to meet the resonator TCF specifications for a particular application. In another embodiment, the second material is isolated to a region(s) of the resonator proximate to a point(s) of maximum stress of the resonator. In a particular embodiment, the resonator includes a first material with a trench containing a second material. In another embodiment the resonator includes a second material adjacent to a sidewall of a first material to form a sidewall of a beam resonator on only a portion of the beam. In a specific embodiment, the shape, dimensions, location and arrangement of a second material comprising silicon dioxide is tailored so that the resonator comprising a first material of SiGe will have a TCF of a much lower magnitude than that of either a homogeneous SiGe or homogeneous silicon dioxide resonator. 
     Embodiments of the present invention include resonators of any commonly known design such as a cantilevered beam, a beam anchored at two ends, a dual beam tuning fork, as well as a plate resonator and a ring resonator. The resonator may operate in any resonant mode, such as, but not limited to, flexural, bulk, or lame. As two general examples, a flexural mode embodiment employing a beam resonator and a bulk mode embodiment employing a plate resonator are described in detail below. 
     In one embodiment of the present invention shown in  FIG. 2A , MEMS  200  employs a beam resonator  205 . MEMS  200  has the beam resonator  205  positioned between drive/sense electrodes  250  and connected to substrate  201  by anchor  240 . During operation the resonator  205  flexes in-plane with drive/sense electrodes  250  (i.e. in a plane parallel to substrate  201  over which the resonator extends). As shown, the resonator  205  includes a first material  230  and a second material  225 . 
     Hereinafter, references made to “top surface,” “bottom surface” and “sidewall” are made relative to a generally planar and horizontally oriented substrate to which the resonator is anchored. Thus, referring to  FIG. 2B , “top surface” therefore refers to that surface of the resonator  205  which is opposite substrate  201 , while “bottom surface” refers to the surface of the resonator  205  which faces substrate  201 . References to “sidewall” refer to surfaces generally perpendicular to substrate  201  (i.e. vertical when substrate is in a typical horizontal orientation). 
     Embodiments of the present invention employ second material  225  to form the resonator  205 . In a particular embodiment, second material  225  has a different Young&#39;s modulus temperature coefficient than first material  230 . The Young&#39;s modulus temperature coefficient of second material  225  need only be different than first material  230  over the operational range of the MEMS. Any material having a different Young&#39;s modulus temperature coefficient than first material  230  over the typical operating range of approximately −30° C. to 90° C. may be employed as second material  225 . In an embodiment, first material  230  has a negative Young&#39;s modulus temperature coefficient, while second material  225  has a positive Young&#39;s modulus temperature coefficient. In a further embodiment, first material  230  is a semiconductor such as, but not limited to, silicon (Si), germanium (Ge), and SiGe alloys and second material  225  is amorphous silica (silicon dioxide, SiO 2 ). In one such SiGe embodiment, first material  230  is an alloy composition of approximately 35% silicon and 65% germanium with a boron doping while second material  225  is silicon dioxide. Silicon dioxide has the unusual property of becoming stiffer as temperature increases. For example, an experimentally determined value of γ for silicon dioxide is γ oxide =1.73×10 −4 /° C. Hence, a resonator made of only oxide would have a positive TCF of approximately 86.5 ppm /° C. In an alternate embodiment, second material  225  is diamond. 
     Generally, embodiments of the present invention have a resonator structure primarily formed of first material  230  with second material  225  selectively located to specific regions of the resonator  205  and dimensioned to modify the temperature response of the resonator  205  independent of other properties of the resonator. Thus, second material  225  is selectively located to provide temperature compensation to the resonator  205  in a non-global manner (i.e. second material  225  need not be formed along the entire length of the resonator in any dimension). In this manner, the mode temperature behavior of the resonator can be tailored. These embodiments enable tailoring of the resonator TCF without detrimentally affecting the Q of the resonator. For example, second material  225  may be isolated to specific areas of the resonator  205  to reduce changes to the resonator&#39;s mode shape by reducing the effects of sound velocity mismatch between second material  225  and first material  230 . Selectively locating second material  225  only to isolated regions decouples the effect of the second material&#39;s TCF from the effect of other temperature dependent properties of the second material. For example, where second material  225  has a significantly different temperature coefficient of expansion (TCE) than first material  230 , isolation of second material  225  to specific regions reduces the effect on the TCF of the resonator that strain from the TCE mismatch between the materials has. 
     In one embodiment, second material  225  is located in a region(s) of the resonator  205  proximate to a point(s) of maximum stress within the resonator during operation of the resonator. 
     In a further embodiment, second material  225  is located in a region(s) of the resonator  205  proximate to a point(s) of maximum stress and minimum displacement within the resonator during operation of the resonator. Multiple points of maximum stress may exist where symmetrical points of the resonator experience equivalent stresses. The point(s) of maximum stress and/or minimum displacement is dependent on the design of the resonator and may be approximated for a particular resonator design through mathematical modeling. Such modeling can be accomplished by various known computational techniques, such as finite element analysis (FEA). An optimization may then be performed to both locate and dimension second material  225  proximate to the point(s) where stress is greatest and/or where displacement is at a minimum. In the embodiments shown in  FIGS. 2A-2C and 3A , second material  225  is isolated to opposite sidewalls of the beam resonator  205  in a region of the beam proximate to anchor  240 . As a further illustration, in an alternate embodiment (not shown), a resonator designed to operate in a vertically oriented flexural mode (where flex of the beam is away from and toward the general plane of the substrate to which the resonator is anchored), second material  225  is located on at least the top surface of the resonator (i.e. parallel to the substrate  201  and perpendicular to the sidewalls of the beam resonator) to enhance the longitudinal stiffness of the resonator in the dimension where flexural stress is greatest. 
     In the embodiment shown in  FIG. 2A , the extent of the longitudinal stiffness provided by second material  225  is tailored by dimensioning the length, in the direction X, and thickness, in the direction W, of material  225 . As shown in  FIG. 2B , second material  225  is adjacent to sidewalls of first material  230  to form sidewalls of the resonator  205  extending along the height, H. In this embodiment, opposite sidewalls of the resonator comprising second material  225  enhance the longitudinal stiffness of the resonator along a portion of the beam length along X, shown in  FIG. 2A , influencing the resonant frequency as a function of temperature. The thickness of second material  225 , in the direction W, is selected to provide the longitudinal stiffness in second material  225  required for the desired modification of resonator TCF. 
     In an embodiment, the second material is at least partially contained within a trench in the first material. Embodiments at least partially embedding second material  225  in a trench in first material  330  increases the ability counter the Young&#39;s modulus temperature coefficient of first material  230  because stress loading on second material  225  during resonator operation becomes more normal or less shear. Herein, the meaning of a trench is a lithographically defined depression in first material  230  extending through at least a portion of first material  230 . In particular embodiments, the trench extends entirely through first material  230 . Embedding second material  225  in the trench essentially forms a plug of second material  225  extending between the top surface and bottom surface of first material  230 . Alternatively, embedding second material  225  in the trench fills a well having a bottom floor comprising first material  230 . A trench may be of any general shape, such as, round square or annular (i.e. a ring). 
     As shown in  FIG. 2A , second material  225  is embedded into first material  230  to form a beam resonator where the cross section of first material  230  varies along length of the beam, L. In one such embodiment, the beam resonator has constant cross-sectional area, W*H, as shown in  FIGS. 2B and 2C , along a length of the beam, X.  FIG. 2B  depicts a cross-section of the beam along the a-a′ line shown in  FIG. 2A  while  FIG. 2C  depicts a cross-section of the beam along the b-b′ line shown in  FIG. 2B . Thus, the cross-sectional area, W*H, of the beam is the same in both in a region of the beam having the second material  225  and a region of the beam having only first material  230 . In an alternate embodiment (not shown), second material  225  is embedded into first material  230  to form a beam resonator where both the cross sectional area of first material  230  and cross-sectional area, W*H, of the resonator varies along the beam length direction X. Here, the cross-sectional area, W*H, of the resonator may increase to the extent the thickness of second material  225  exceeds the amount the trench in first material  230  reduces the W dimension of first material  230 . Such an embodiment is advantageous when the W dimension of the resonator is not sufficient to completely incorporate the thickness of second material  225  necessary to provide first material  230  with the longitudinal stiffness required for the desired modification of resonator TCF. 
     Although not explicitly depicted, it should also be appreciated that selectively locating second material  225  adjacent to first material  230  without embedding second material  225  in first material  230  is also within the scope of the present invention. In such an embodiment, the resonator includes a second material adjacent to a sidewall of a first material to form a sidewall of a beam resonator on only a portion of the beam along the length direction X. For example, relative to the MEMS  205  shown in  FIG. 2A , first material  230  would have a constant cross sectional area between a-a′ and b-b′. Thus, at a-a′, second material  225  would increase the W dimension of the beam by the thickness of second material  225 . 
     Just as second material  225  may extend outward in the W direction beyond the sidewall of first material  230  (referring to  FIG. 2B ), second material  225  may also have a greater or lesser height (i.e. depth) in the H direction such that the top surface of second material  225  is not planar with the top surface of first material  230 . In the particular embodiments shown, however, the top surfaces of first material  230  and second material  225  are planar with each other. 
     In an exemplary embodiment depicted in  FIGS. 3A and 3B , the TCF of MEMS  300  employing a SiGe beam resonator is tailored by selectively positioning on the beam a silicon dioxide region with a specific length and width. As shown in  FIG. 3A , a SiGe beam resonator  305  is connected to anchor  340 . The SiGe beam resonator  305  has a beam length, X B , of 147.8 um, a width, W, of 1.5 um and a height (in the H direction of  FIG. 2B ) of 2 um. At a 5 um distance D from the anchor, silicon dioxide  325  is incorporated into the resonator  305  for temperature compensation of the resonant frequency. Silicon dioxide  325  is embedded in trenches or notches formed in SiGe  330 . Silicon dioxide  325  has a nominal length, L O , of 31.4 um, a thickness in the W direction of 0.6 um and a height of 2 um. 
     Attached to silicon dioxide  325  to form an annular structure attached to each side of the resonator  305  is artifact  326 . Artifact  326  is residual silicon dioxide resulting from a particular manufacturing method described in further detail below. Artifact  326  has been dimensioned and shaped to serve as a low compliance spring  328  which allows the portion of the annulus of silicon dioxide  325  not in direct contact with SiGe  330  (artifact  326 ) to bend. In the particular embodiment shown, the length of spring  328 , L S , is 10 um and spring width, W S , of 2 um. However the length and placement of spring  328  are not important to the temperature compensation of the resonator  305 , as long as the stiffness of spring  328  is negligible compared to the longitudinal stiffness of silicon dioxide  325  in contact with SiGe  330 . Furthermore, it should be appreciated the silicon dioxide  325 , as an electrical insulator, may be additionally employed to electrically isolate two regions of the resonator  305 , 
     The graph of  FIG. 3B  depicts finite element simulations for the resonator described in  FIG. 3A . In  FIG. 3B , resonant frequency of the resonator as a function of temperature is graphed for various lengths, L O , of silicon dioxide  325 . The curve marked with open circles shows the temperature dependence for the nominal length of L O =31.4 um. As can be seen, the variation of frequency with temperature is much smaller than the 5000 ppm of a resonator comprising only SiGe over the same 120° C. temperature range. Increasing the length L O  by one micron (curve marked by “+1” in  FIG. 3 ) makes the temperature coefficient slightly positive (approximately 2 ppm/° C.), while decreasing the length has the opposite effect. 
       FIG. 4A  depicts MEMS bulk mode resonator  400  employing a plate  405  with an anchor  440  to substrate  401  surrounded by drive/sense electrodes  450 . The mode of the resonator depends on the voltage phase of electrodes  450 . The dashed lines depict a resonant mode whereby all sides compress and extend in unison. In the embodiment shown, the plate resonator  405  comprises second material  425  contained in trenches in first material  430  to form an isolated block or a plurality of isolated blocks. Generally, the composition, size and shape of the blocks, as well as the arrangement of a plurality of blocks has an influence on the temperature behavior of the structure, and can alter the mode shape that the structure would have. As one of ordinary skill in the art will appreciate, the benefits of selectively locating and dimensioning second material  425  are in many ways analogous to those previously described in the context of a beam resonator. Of course, other bulk mode resonators such as rings, disks or any other shape may employ second material  425 . 
     Similar to the beam resonator embodiments previously discussed, in one plate resonator embodiment, first material  430  has a negative Young&#39;s modulus temperature coefficient, while second material  425  has a positive Young&#39;s modulus temperature coefficient. In one such embodiment, first material  430  is a semiconductor such as, but not limited to, Si, Ge, and SiGe alloys, while second material  425  is amorphous silica (silicon dioxide). 
     In one embodiment, second material  425  is arranged into a radial array to modify the temperature behavior of the resonator with minimal impact to the mode shape of the resonator. in alternate embodiments, the mode shape of the resonator is deliberately altered through arrangement of the blocks of second material  425 . As shown in  FIG. 4A , second material  425  is selectively located in a trench in first material  430  to form a plurality of isolated regions, or blocks, of second material  425  arranged in a radial array  426  about anchor  440 . As shown, the radial arrays are configured to bisect each side of the plate resonator  405 . Such a configuration of second material  425  is dependent on the mode of the resonator, which in this embodiment is represented by the dashed lines. In one such embodiment, first material  430  forms a 60 um square plate, 2 um thick and with a central anchor  440  of 12 um on a side. The plate resonator  405  includes a set of 1 um square blocks of second material  425  arranged in four radial arrays of 4 by 21 blocks embedded in trenches within first material  430 . 
     As depicted in  FIG. 4B , second material  425  fills a trench in first material  430 . In other embodiments, second material  425  may merely form an annular spacer structure along the inner edge of the trench. Furthermore, the trench itself may be of any general shape, such as, round square, annular, etc. In still other embodiments, second material  425  may further comprise a composite of two or more material layers. In one embodiment, the top surface of second material  425  is planar with first material  430 . In an alternate embodiment, the top surface of second material  425  extends above or below the top surface of first material  430 . As shown, the trench in first material  430  extends through first material  430  such that second material  425  forms a block extending between the top surface and bottom surface of first material  430 . However, in other embodiments, the trench containing second material  425  only extends through a portion of first material  430  such that second material  425  fills a well or depression having a bottom floor comprising first material  430 . 
     In a further embodiment, the arrangement of the individual blocks of second material  425  forming an array  426  in first material  430  is predetermined to provide the desired modification to the TCF of the resonator. The array  426  of second material  425  is arranged to have a number of rows of with a particular spacing or density. Shown in  FIG. 4C , finite element simulations of a 60 um square plate of 2 um thick SiGe show the frequency of a resonant mode as a function of temperature for various arrays of silicon dioxide blocks. As the number of rows of blocks is increased from two to eight, the slope of the frequency vs. temperature curve changes from negative to positive. In the embodiment with six rows of blocks is approximately 1 ppm/° C., or about 50 times smaller than for a plate of exclusively SiGe. 
     In particular embodiment, the second material is selectively located and dimensioned based on the desired resonant mode. For example, another bulk mode resonator design is depicted in  FIG. 5 . The resonator employs a plate  500  with an anchor  540 . Here, the resonator is operated in a mode wherein some sides of the plate extend while others compress, as depicted by the dashed lines. Resonator plate  500  is comprised primarily of first material  530  with second material  525  embedded into trenches in first material  530 . In this embodiment, the regions of second material  525  are arranged into radial arrays oriented on the diagonal of plate  500 . Thus, as depicted in  FIGS. 4A and 5 , the specific locations of regions of second material  525  is predetermined based on the resonant mode shape. Furthermore, each isolated region of second material may be individually positioned relative to other isolated regions of second material to tune the temperature coefficient of frequency of the resonator comprised of both first and second material. In this manner additional degrees of design freedom are provided. 
       FIGS. 6A-6E, 7A-7E, 8A-8F and 9A-9C  are prospective views of methods for fabricating resonators in accordance with an embodiment of the present invention.  FIGS. 6A-6E  depict a first method to selectively fabricate a second material in a first material to form a compensated resonator. 
     As shown in  FIG. 6A , on substrate  601 , barrier layer  605  is deposited. Substrate  601  may be any commonly known semiconductor substrate, such as, but not limited to, single crystalline silicon, germanium or a silicon/germanium layer. Substrate  601  may alternatively be comprised of a III-V material such as but not limited to gallium nitride, gallium phosphide, gallium arsenide, indium phosphide or indium antimonide. Moreover, substrate  601  may comprise an insulating layer such as silicon dioxide or silicon nitride embedded below a monocrystalline semiconductor layer to form, for example, a silicon on insulator or germanium on insulator substrate. Substrate  601  may further be an insulator such as glass, sapphire, or quartz. 
     Barrier layer  605  may be an etch stop layer or sacrificial layer to be subsequently removed to release the resonator. Barrier layer  605  may have any commonly known composition, such as, but not limited to, silicon dioxide, silicon oxy nitride, silicon nitride, germanium, silicon, and silicon germanium alloys. Barrier layer  605  may be formed by any commonly known technique, such as, but not limited to, chemical vapor deposition (CVD), low pressure CVD (LPCVD), plasma enhanced (PE) CVD, physical vapor deposition (PVD), evaporation, and electrochemical deposition. In a particular embodiment, barrier layer  605  is of a material which can be formed at a relatively low temperature, below approximately 500° C., to be compatible with common BEOL processes. In one such embodiment, barrier layer  605  is greater than 98% germanium atoms and boron dopant impurity atoms having a total atomic concentration in the range of 5×10 19 -5×10 20  atoms/cm 3  deposited at a temperature of approximately 350° C. using a LPCVD process. 
     Upon barrier layer  605 , first material layer  610  is formed as a structural layer of the resonator. First material layer  610  must also endow a resonant Member with good performance metrics, such as, but not limited to, a sufficiently high Q. In certain embodiments, first material layer  610  is deposited at a temperature below 500° C. to be compatible with typical back end of line (BEOL) microelectronics processing. In one embodiment, silicon and/or germanium is deposited by a LPCVD process. In a particular embodiment employing a germanium barrier layer  605 , first material layer  610  is polycrystalline alloy of silicon and germanium deposited at a temperature of approximately 425° C. using an LPCVD process. 
     Next, as shown in  FIG. 6B , trench  615  is patterned into first material layer  610 . Trench  615  may be etched either partially through first material layer  610  or completely to expose barrier layer  605 . Patterning of trench  615  may be by any commonly known technique, such as lithographic definition of a masking layers and anisotropic etching by plasma-based etch systems. The dimensions of trench  615  are exactly the dimension needed for the slit pattern to compensate or influence the temperature coefficient of the structure properties according to specifications. 
     Then, as shown in  FIG. 6C , second material layer  620  is deposited conformally or superconformally (bottom-up) to fill substantially void-free the defined trench  615 . Second material may be deposited by any conventional means, such as, but not limited to, PVD, PECVD, LPCVD, and electrochemical deposition to fill completely and void-free the defined trench. This can be done as one step, or as sequence of thin deposition and anisotropic etch back steps until the trench is filled. Alternatively, second material  620  may merely be formed by oxidizing first material  610  to form second material  620  on the sidewalls of trench  615 . In certain embodiments, second material layer  620  is deposited at a temperature below 500° C. to be compatible with typical back end of line (BEOL) microelectronics processing. In a particular embodiment employing a first material layer  610  of SiGe, silicon dioxide is deposited using a PECVD process at a temperature between 350° C. and 400° C. In still other embodiments, a composite second material  620  comprising a layer silicon dioxide and a layer of another material, such as silicon nitride or a metal, are deposited. 
     Next, shown in  FIG. 6D , second material layer  620  is etched-back or polished away from the top of first material layer  610  using commonly known methods such as chemical-mechanical polishing (CMP) to for the properly dimensioned second material  625 . In an alternate embodiment, the top surface of second material layer  620  can also be kept to serve as a hard mask for the subsequent steps. 
     Then, as shown in  FIG. 6E , first material layer  610  is patterned to form first material  630  properly dimensioned for the resonator using conventional techniques such as lithographically pattering a masking layer and etching first material layer  610 . In a particular embodiment employing SiGe as first material layer  610  and silicon dioxide as second material  625 , an anisotropic plasma etch chemistry containing at least one gas selected from the group consisting of xenon difluoride (XeF 2 ), silicon tetrachloride (SiCl 4 ), and chlorine (Cl 2 ) is employed. Additional layers above and below first material  630  can be used to encapsulate second material  625 . In the embodiment shown, second material  625  is encapsulated inside first material  630  to avoid exposure of the second material  625  to the environment and avoid stability issues, or simply prevent etching of the secondary material during subsequent steps like release. In an alternate embodiment, second material  625  is not encapsulated in first material  630  and etching of first material layer  610  is performed with a process that is selective to first material layer  610  over second material  625 . 
       FIGS. 7A-7E  depict a second method to selectively fabricate a second material in a first material to form a compensated resonator. This second method has the benefit of not requiring the second material to fill a potentially high aspect ratio trench within the first material. To avoid high aspect trenches that can be difficult to fill without voids, this embodiment forms the second material, having smaller dimensions than first material, prior to forming the second material. 
     As shown in  FIG. 7A , second material  720  is deposited on barrier layer  705  over substrate  701 . Barrier layer  705  can be a sacrificial layer or an etch stop layer. Substrate  701  and barrier layer  705  may be of any material commonly employed in the art, such as, but not limited to, those described in reference to  FIG. 6A . Second material may be deposited by any conventional means, such as, but not limited to, PVD, PECVD, LPCVD, and electrochemical deposition. In a particular embodiment, silicon dioxide is deposited using PECVD process at a temperature between 350° C. and 400° C. In still other embodiments, a composite second material  720  comprising a layer silicon dioxide and a layer of another material, such as silicon nitride or a metal, are deposited. 
     Next, shown in  FIG. 7B , second material layer defined and etched into the second material  725  having the exact dimensions needed to compensate or influence the temperature coefficient of the resonator according to specifications. Patterning of second material  725  may be by any commonly known technique, such as lithographic definition of a masking layers and anisotropic etching by plasma-based etch systems. In a particular embodiment, a fluorine-based plasma etch process is employed to etch a silicon dioxide second material  725 . 
     Then, as shown in  FIG. 7C , first material layer  710  is deposited in a conformal manner over second material  725 . First material layer  710  may be deposited by any commonly known means, such as, but not limited to, those previously described in referenced to  FIG. 6B . Next, as depicted in  FIG. 7D , first material layer  710  is polished by CMP down to the top surface of second material  725  using commonly known techniques and parameters. Finally, first material layer  710  is patterned using commonly known techniques and methods into first material  730  to form the resonator. The resonator may then be released by removing barrier layer  705  (not shown), as is commonly known in the art. 
       FIGS. 8A-8F  depict a third method to selectively fabricate a second material in a first material to form a compensated resonator. This method relies on a spacer based process so that the thickness of the second material advantageously relies only on the deposition thickness of the second material rather than lithography. Nonetheless, to selectively compensate the resonator in accordance with present invention, the shape, length and location of the second material are still controlled by lithography. 
     First, as shown in  FIG. 8A , first material layer  810  is deposited on barrier layer  805  over substrate  801 , just as described in reference to  FIG. 7A . Next,  FIG. 8B  depicts trench  815  lithographically defined and etched into first material layer  810 . At least one dimension of the trench is significantly larger than the targeted width of the second material necessary for temperature compensation or temperature coefficient tuning. In one embodiment, the length of one side of trench  815  is the exact length dimension desired for the second material, while the width is much greater than the width dimension desired for the second material. 
     Next, as shown in  FIG. 8C , second material layer  820  is deposited in a conformal manner by PVD, PECVD, LPCVD or electrochemical deposition. The thickness of the deposition on the sidewall of the trench determines the width of the second material targeted for temperature compensation or temperature coefficient tuning. This deposition can be done as one step, or as sequence of thin deposition and anisotropic etch back steps until the targeted width is achieved. In still other embodiments, a composite second material  820  comprising a layer silicon dioxide and a layer of another material, such as silicon nitride or a metal, are deposited. 
     As shown in  FIG. 8D , second material layer  820  is removed from the bottom of the trench to avoid strong mechanical coupling between the opposite sidewall of the trench. The top surface of second material layer  820  is also etched-back or polished by CMP to remove the secondary material from the top of the primary structural material, thereby forming second material  825  as a spacer along the edge of the trench. In a particular embodiment, employing a silicon dioxide second material layer  820 , a commonly known fluorine-based anisotropic plasma etch forms second material  825  in a manner similar to a spacer etch process common in microelectronics. 
     As shown in  FIG. 8E , first material layer  810  is patterned into first material  830  having proper dimensions to form the resonator using commonly known lithographic and etch techniques. As shown, remaining attached to first material  830  is second material  825  of the appropriate size to compensate the temperature response of the resonator. Attached to second material  825  is artifact  826  forming an annulus with second material  825 . In the embodiment shown, trench  815  of  FIG. 8B  was patterned in a manner to ensure artifact  826  has a shape and dimensions sufficient to act as a low compliance spring. In this manner, only second material  825  provides compensation to the resonator. 
     Finally, in  FIG. 8F , barrier layer  805  is a sacrificial layer removed to release from substrate  801  the first material  830 , second material  825  and artifact  826  as the resonator structure. Commonly known wet etch or dry etch techniques may be used to remove barrier layer  805 . In a particular embodiment employing a germanium barrier layer  805 , a wet etch comprising an aqueous solution of H 2 O 2  with a concentration in the range of 25-35% by volume at a temperature in the range of 80° C.-95° C. is employed. 
     Although artifact  826  can be designed to have minimal impact on the resonator performance, it can be eliminated with a few additional commonly known operations. One such embodiment is shown in  FIGS. 9A-9C . First, spacer  927  is formed in trench  815  of  FIG. 8B  after the formation of second material  825  of  FIG. 8D  to cover the sidewall of second material  925 . Spacer  927  is of a material which provides selectivity to processes capable of etching second material  925 . In a particular embodiment employing a silicon dioxide second material  925 , spacer  927  is a silicon nitride material is deposited by CVD and is anisotropically etched selectively to second material  925 , as is commonly known in the art. Following definition of first material  930  in the same manner described in reference to  FIG. 8F , the structure depicted in  FIG. 9A  remains. As shown, artifact  926  is protected only on one sidewall by spacer  927  while second material  925  is protected on one sidewall by first material  930  and on another sidewall by spacer  927 , enabling artifact  926  to be removed selectively to second material  925 . 
     As shown in  FIG. 9B , artifact  926  is etched isotropically through the as-deposited thickness using commonly known techniques. In one embodiment employing a silicon dioxide second material  925 , a buffered oxide etch (BOE) or other hydrofluoric (HF) based wet chemistry is employed to remove artifact  926  without significantly recessing second material  925 . Following removal of artifact  926 , spacer  927  is selectively removed using commonly known techniques to leave only second material  925  and first material  930 , as shown in  FIG. 9C . In a particular embodiment, spacer  927  is isotropically etched in a wet etchant containing phosphoric acid (H 3 PO 4 ). 
     Although the present invention has been described in language specific to structural features and/or methodological acts, it is to be understood that the invention defined in the appended claims is not necessarily limited to the specific features or acts described. For example, many applications may benefit from embodiments in accordance with the present invention and one of ordinary skill in the art would recognize the temperature compensated resonators described as particularly graceful implementations of the claimed invention useful for Illustrating the present invention.