Abstract:
A method of forming a micromechanical resonator includes forming a resonator body anchored to a substrate by at least a first anchor. This resonator body may include a semiconductor or other first material having a negative temperature coefficient of elasticity (TCE). A two-dimensional array of spaced-apart trenches are provided in the resonator body. These trenches may be filled with an electrically insulating or other second material having a positive TCE. The array of trenches may extend uniformly across the resonator body, including regions in the body that have relatively high and low mechanical stress during resonance. This two-dimensional array (or network) of trenches can be modeled as a network of mass-spring systems with springs in parallel and/or in series with respect to a direction of a traveling acoustic wave within the resonator body during resonance.

Description:
REFERENCE TO PRIORITY APPLICATIONS 
     This application claims priority to U.S. Provisional Application Ser. Nos. 61/218,518, filed Jun. 19, 2009 and 61/314,290, filed Mar. 16, 2010, the disclosures of which are hereby incorporated herein by reference. 
    
    
     REFERENCE TO RELATED APPLICATIONS 
     This application is related to U.S. application Ser. No. 12/535,284, filed Aug. 4, 2009, the disclosure of which is hereby incorporated herein by reference. 
     FIELD OF THE INVENTION 
     The present invention relates to integrated circuit devices and methods of forming same and, more particularly, to micromechanical devices and methods of forming same. 
     BACKGROUND OF THE INVENTION 
     Micro-electromechanical (MEMs) resonators can provide small form factor, ease of integration with conventional semiconductor fabrication techniques and high f·Q products. High frequency and high-Q width-extensional mode silicon bulk acoustic resonators (SiBARs) and film bulk acoustic wave resonators (FBARs) have demonstrated atmospheric Q factors in excess of 10,000 at or above 100 MHz, with moderate motional resistances. Such resonators are disclosed in an article by S. Pourkamali et al., entitled “Low-Impedance VHF and UHF Capacitive Silicon Bulk Acoustic Wave Resonators—Part I: Concept and Fabrication,” IEEE Trans. On Electron Devices, Vol. 54, No. 8, pp. 2017-2023, August (2007), the disclosure of which is hereby incorporated herein by reference. 
     The resonant frequency of silicon micro-electromechanical resonators is dependent on the physical dimensions of the resonating structure. This causes the resonant frequency of those resonators to deviate from a designed target value in response to variations in photolithography, etching and film thickness. For example, as described in an article by G. Casinovi et al., entitled “Analytical Modeling and Numerical Simulation of Capacitive Silicon Bulk Acoustic Resonators,” IEEE Intl. Conf. on Micromechanical Systems (2009), a 2 μm variation in thickness of a 100 MHz width-extensional mode SiBAR can cause a 0.5% variation in its center frequency, while lithographic variations of ±0.1 μm in the width of the resonator can cause an additional 0.5% variation in frequency. 
     Unfortunately, even when efforts to reduce the adverse effects of variations in photolithography, etching and film thickness on resonant frequency are successful, additional changes in resonant frequency may occur in response to changes in operating temperature. These temperature-based changes in resonant frequency can be reduced using modified fabrication processes and active compensation circuits. However, because circuit-based compensation techniques typically increase the complexity and power requirements of resonator devices, passive fabrication-based compensation techniques based on the intrinsic properties of the resonator materials are generally preferable to circuit-based compensation techniques. Conventional passive compensation techniques are disclosed in U.S. Patent Publication Nos. 2010/0032789 to Shoen et al., entitled “Passive Temperature Compensation of Silicon MEMS Devices;” and 2009/0160581 to Hagelin et al., entitled “Temperature Stable MEMS Resonator.” 
     SUMMARY OF THE INVENTION 
     Methods of forming micromechanical resonators operable in a bulk acoustic mode include forming a resonator body anchored to a substrate by at least a first anchor. This resonator body may include a semiconductor or other first material having a negative temperature coefficient of elasticity (TCE). A two-dimensional array of spaced-apart trenches are provided in the resonator body. These trenches may be filled with an electrically insulating or other second material having a positive TCE. The array of trenches may extend uniformly across the resonator body, including regions in the body that have relatively high and low mechanical stress during resonance. This two-dimensional array (or network) of trenches can be modeled as a network of mass-spring systems with springs in parallel and/or in series with respect to a direction of a traveling acoustic wave within the resonator body during resonance. 
     To achieve a high degree of temperature compensation, the array of spaced-apart trenches may have a sufficient density in the resonator body to meet the following relationship:
 
1≦− R   V (TCE I /TCE S )[( E   I   /E   S )+(ρ I /ρ S ) 1/2 ( E   I   /E   S ) −1/2 ]≦3,
 
where R V =(V I /V S ); TCE S , E S , ρ S  and V S  represent the temperature coefficient of elasticity, Young&#39;s modulus, density and volume of the first material in the resonator body, respectively; and TCE I , E I , ρ I  and V I  represent the temperature coefficient of elasticity, Young&#39;s modulus, density and total volume of the second material in the array of spaced-apart trenches, respectively. Thus, in the event the first material is silicon and the second material is silicon dioxide, the ratio R V  may have a value in a range from about 0.14 to about 0.42, where TCE S , E S  and ρ S  for silicon are represented as −52 ppm/° C., 169 GPa and 2.33 grams/cm 3 , respectively, and TCE I , E I  and ρ I  for silicon dioxide are represented as 180 ppm/° C., 73 GPa and 2.63 grams/cm 3 .
 
     According to some embodiments of the invention, the array of spaced-apart trenches may extend partially through the resonator body or may extend entirely through the resonator body as through-body holes. According to additional embodiments of the invention, the spaced-apart trenches in the array may be arranged in a checkerboard pattern. In further embodiments of the invention, the spaced-apart trenches in the array are arranged as a two-dimensional array of spaced-apart trenches having a first plurality of rows of spaced-apart trenches and a second plurality of columns of spaced-apart trenches. According to these embodiments of the invention, each of the first plurality of rows of spaced-apart trenches has an equivalent number of spaced-apart trenches therein and each of the second plurality of columns of spaced-apart trenches has an equivalent number of spaced-apart trenches therein. 
     According to still further embodiments of the invention, a bottom electrode of the resonator may be formed on the resonator body, a piezoelectric layer may be formed on the bottom electrode and at least one top electrode may be formed on the piezoelectric layer. According to additional aspects of these embodiments of the invention, a combination of a number of spaced-apart trenches in the array and the second material is sufficient to fully temperature compensate the micromechanical resonator, which includes the resonator body, bottom electrode, piezoelectric layer and at least one top electrode. To achieve full or at least nearly full temperature compensation, the density of the filled trenches in the upper surface of a resonator body may be set to a value of at least five trenches/square for each square region on an upper surface of the resonator body having an area equal to t 2 , where t is a thickness of the resonator body as measured between upper and lower surfaces thereof and t is greater than about 10 microns. Alternatively, the density of the filled trenches in the upper surface of the resonator body may be set to a value of at least one trench/square for each square region on an upper surface of the resonator body having an area equal to t 2 , for cases where t is in a range from about 2 microns to about 10 microns. 
     According to additional embodiments of the invention, a method of forming a micromechanical resonator includes forming a resonator body having upper and lower surfaces thereon. This resonator body includes a first material having a negative temperature coefficient of elasticity (TCE) and a two-dimensional array of spaced-apart through-body holes filled with a second material having a positive TCE. The through-body holes may have minimum and maximum lateral dimensions in a range from about 0.1 T to about 0.2 T, where T is a thickness of the resonator body and T is greater than about 10 microns. 
     The step of forming a resonator body may include etching a two-dimensional array of spaced-apart trenches in the resonator body and then depositing the electrically insulating material onto a surface of the resonator body and into the two-dimensional array of spaced-apart trenches using, for example, a low pressure chemical vapor deposition technique. The step of etching a two-dimensional array of spaced-apart trenches in the resonator body may include using an etching process that alternates repeatedly between an isotropic plasma etching of the resonator body and a deposition of a chemically inert passivation layer on the resonator body. 
     A dry etching step may then be performed. This dry etching step may include dry etching the electrically insulating material to thereby remove portions of the electrically insulating material from the surface of the resonator body and from within the two-dimensional array of spaced-apart trenches. The depositing and dry etching steps may be repeatedly performed in sequence at least once until the two-dimensional array of spaced-apart through-body holes is formed and completely filled with the electrically insulating material. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a plan view of a suspended resonator body having a two-dimensional array of spaced-apart trenches therein filled with a material having a positive TCE, according to embodiments of the invention. 
         FIG. 1B  is a perspective view of a micromechanical resonator operable in a bulk acoustic mode, according to embodiments of the present invention. 
         FIG. 1C  is a plan view of a suspended resonator body having a checkerboard pattern of spaced-apart trenches therein filled with a material having a positive TCE, according to additional embodiments of the invention. 
     
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
     The present invention now will be described more fully with reference to the accompanying drawings, in which preferred embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Like reference numerals refer to like elements throughout. 
     It will be understood that when an element or layer is referred to as being “on,” “connected to” or “coupled to” another element or layer (and variants thereof), it can be directly on, connected or coupled to the other element or layer or intervening elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly connected to” or “directly coupled to” another element or layer (and variants thereof), there are no intervening elements or layers present. Like reference numerals refer to like elements throughout. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items and may be abbreviated as “/”. 
     It will be understood that, although the terms first, second, third etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer or section from another region, layer or section. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the present invention. 
     Spatially relative terms, such as “beneath,” “below,” “lower,” “above,” “upper” and the like, may be used herein for ease of description to describe one element or feature&#39;s relationship to another element(s) or feature(s) as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the term “below” can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the present invention. As used herein, the singular forms “a,” “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprising”, “including”, having” and variants thereof, when used in this specification, specify the presence of stated features, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and/or groups thereof. In contrast, the term “consisting” of when used in this specification, specifies the stated features, steps, operations, elements, and/or components, and precludes additional features, steps, operations, elements and/or components. 
     Embodiments of the present invention are described herein with reference to cross-section and perspective illustrations that are schematic illustrations of idealized embodiments (and intermediate structures) of the present invention. As such, variations from the shapes of the illustrations as a result, for example, of manufacturing techniques and/or tolerances, are to be expected. Thus, embodiments of the present invention should not be construed as limited to the particular shapes of regions illustrated herein but are to include deviations in shapes that result, for example, from manufacturing. For example, a sharp angle may be somewhat rounded due to manufacturing techniques/tolerances. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
       FIG. 1A  illustrates a plan view of a suspended resonator body  12  of a micromechanical resonator. This resonator body  12  is suspended on opposite sides by a pair of anchors  12   a ,  12   b , which are attached to a surrounding substrate  10  and aligned to a longitudinal axis of the resonator body  12 . As highlighted by the aforementioned U.S. application Ser. No. 12/535,284, filed Aug. 4, 2009, which is hereby incorporated herein by reference, the resonator body  12  may be suspended opposite a recess in the substrate  10 . 
     The resonator body  12  of  FIG. 1A  is illustrated as having a two-dimensional array of spaced-apart square trenches  14  therein, which are filled with an electrically insulating material  16   a  or another material having a positive temperature coefficient of elasticity (TCE). These trenches  14  may extend partially or, more preferably, completely through the resonator body  12  as through-body holes. According to some embodiments of the invention, the resonator body  12  may be configured as a semiconductor body, such as a silicon body, or another material having a negative TCE and the electrically insulating material  16   a  may be silicon dioxide. Similarly, the resonator body  12 ′ of  FIG. 1C  is illustrated as having a checkerboard pattern of spaced-apart trenches  14  therein. Because the checkerboard pattern of spaced-apart trenches  14  may be treated as including a two-dimensional array of trenches in the spaces or gaps between the trenches of another two-dimensional array, greater temperature compensation may be provided by the embodiment of  FIG. 1C  relative to the embodiment of  FIG. 1A . 
       FIG. 1B  is a perspective view of a micromechanical resonator  100  operable in a bulk acoustic mode. This resonator  100  includes a semiconductor resonator body  12  having a two-dimensional array of spaced-apart trenches  14  therein. In particular, the resonator  100  of  FIGS. 1A-1B  includes a resonator body  12  anchored to a surrounding substrate  10  by a pair of anchors  12   a ,  12   b . The resonator body  12  includes a semiconductor material (e.g., silicon) and a two-dimensional array of spaced-apart square through-body holes  14 , which are completely filled with an electrically insulating material  16   a  having a positive TCE. To achieve a high degree of temperature compensation, the density of the array of spaced-apart trenches should be sufficient to meet the following relationship:
 
0.5 ≦−R   V (TCE I /TCE S )[( E   I   /E   S )+(ρ I /ρ S ) 1/2 ( E   I   /E   S ) −1/2 ],  (1)
 
where R V =(V I /V S ); TCE S , E S , ρ S  and V S  represent the temperature coefficient of elasticity, Young&#39;s modulus, density and volume of the first material in the resonator body, respectively; and TCE I , E I , ρ I  and V I  represent the temperature coefficient of elasticity, Young&#39;s modulus, density and total volume of the second material in the array of spaced-apart trenches, respectively. More preferably, the density of the array of spaced-apart trenches should be sufficient to meet the following relationship:
 
1≦− R   V (TCE I /TCE S )[( E   I   /E   S )+(ρ I /ρ S ) 1/2 ( E   I   /E   S ) −1/2 ]≦3.  (2)
 
Thus, in the event the first material is silicon and the second material is silicon dioxide, the ratio R V  may have a value in a range from about 0.14 to about 0.42, where TCE S , E S  and ρ S  for silicon are represented as −52 ppm/° C., 169 GPa and 2.33 grams/cm 3 , respectively, and TCE I , E I  and ρ I  for silicon dioxide are represented as 180 ppm/° C., 73 GPa and 2.63 grams/cm 3 .
 
     In addition to the insulator-filled array of through-body holes  14 , some additional degree of temperature compensation may be provided by a thin electrically insulating layer  16   b  (e.g., SiO 2 ), which is formed directly on an upper surface of the resonator body  12 . This electrically insulating layer  16   b , which may remain on the resonator body  12  after the through-body holes  14  are filled, may have a planarized upper surface. Conventional techniques may then be performed to deposit a bottom resonator electrode  18  (e.g., molybdenum (Mo) electrode) on the planarized upper surface, a piezoelectric layer  20  (e.g., aluminum nitride (AlN)) on the bottom electrode  18  and a pair of electrodes  22   a ,  22   b  (e.g., input and output electrodes) on the piezoelectric layer  20 . 
     In addition, because the semiconductor resonator body  12  is typically relatively thick, some additional constraints on the dimensions of the holes may apply. For fabrication reasons, it may be preferable that the lateral dimensions of the holes be no smaller than approximately 10% of the thickness of the resonator body. Thus, for a silicon resonator body  12  having a thickness of about 20 um, the lateral dimensions of the holes  14  should be no smaller than about 2 um. Moreover, in order to evenly distribute the holes  14  over the entire surface of the resonator body  12 , the hole dimensions should be maintained close to the minimum value. This conclusion supports a requirement in some embodiments of the invention that a lateral dimension of the through-body holes be set at a range from about 0.1 T to about 0.2 T, where T is a thickness of the resonator body and T is greater than about 10 microns. Accordingly, for a silicon resonator body  12  having dimensions of 250 um wide, 143 um long and 20 um thick, a hole pattern consisting of a 24×42 matrix of equally spaced 3.1 um×3.1 um square holes satisfies a volume ratio of about 0.37. 
     According to still further embodiments of the invention, a bottom electrode of the resonator may be formed on the resonator body, a piezoelectric layer may be formed on the bottom electrode and at least one top electrode may be formed on the piezoelectric layer. According to additional aspects of these embodiments of the invention, a combination of a number of spaced-apart trenches in the array and the second material is sufficient to fully temperature compensate the micromechanical resonator, which includes the resonator body, bottom electrode, piezoelectric layer and at least one top electrode. To achieve full or at least nearly full temperature compensation, the density of the filled trenches in the upper surface of a resonator body may be set to a value of at least five trenches/square for each square region on an upper surface of the resonator body having an area equal to t 2 , where t is a thickness of the resonator body as measured between upper and lower surfaces thereof and t is greater than about 10 microns. Alternatively, the density of the filled trenches in the upper surface of the resonator body may be set to a value of at least one trench/square for each square region on an upper surface of the resonator body having an area equal to t 2 , for cases where t is in a range from about 2 microns to about 10 microns. 
     In order to inhibit the formation of voids within the deep insulator-filled holes  14 , which have relatively large aspect ratios, steps may be taken to form trenches having sufficiently tapered sidewalls and sufficiently wide top-surface openings that are less likely to be occluded with insulating material during filling of the holes  14 . In particular, steps may be taken to etch a two-dimensional array of spaced-apart trenches that extend partially through the resonator body, prior to depositing the electrically insulating material onto a surface of the resonator body  12  and into the two-dimensional array of uniformly spaced-apart trenches using a technique such as low pressure chemical vapor deposition (LPCVD). Thereafter, the electrically insulating material is dry etched to remove portions of the electrically insulating material from the surface of the resonator body and from within the two-dimensional array of uniformly spaced-apart trenches. This dry etching step may include blanket dry etching the electrically insulating material across the surface of the resonator body. More specifically, the dry etching process may alternate repeatedly between an isotropic plasma etching of the resonator body and a deposition of a chemically inert passivation layer on the resonator body. The depositing and dry etching steps are then repeatedly performed in sequence until the two-dimensional array of uniformly spaced-apart holes is formed and completely filled with the electrically insulating material. Thereafter, a sequence of steps is performed to form a bottom electrode on the resonator body, a piezoelectric layer on the bottom electrode and at least one top electrode on the piezoelectric layer. In addition, a selective etching step may be performed to etch through the resonator body material and release the resonator body opposite a recess in the substrate (e.g., by removing an underlying sacrificial material in the recess). 
     In the drawings and specification, there have been disclosed typical preferred embodiments of the invention and, although specific terms are employed, they are used in a generic and descriptive sense only and not for purposes of limitation, the scope of the invention being set forth in the following claims.