Abstract:
An acoustic resonator comprises (a) a substrate having atop surface and a bottom surface, a first end portion and an opposite, second end portion, and a body portion defined therebetween; (b) an acoustic mirror having a top surface and a bottom surface, a first end portion and an opposite, second end portion, and a body portion defined therebetween, wherein the bottom surface is formed on the top surface of the substrate; (c) a first electrode having a top surface and a bottom surface, a first end portion and an opposite, second end portion, and a body portion defined therebetween, wherein the bottom surface is formed on the top surface of the acoustic mirror; (d) a piezoelectric layer having a top surface and a bottom surface, a first end portion and an opposite, second end portion, and a body portion defined therebetween, wherein the bottom surface is formed on the top surface of the first electrode; and (e) a second electrode having a top surface and a bottom surface, a first end portion and an opposite, second end portion, and a body portion defined therebetween. The bottom surface is formed on the top surface of the piezoelectric layer, wherein the overlapped area of body portions of the substrate, the acoustic mirror, the first electrode, the piezoelectric layer and the second electrode is defined as an active area A.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present application is a continuation application under 37 C.F.R. §1.53(b) of U.S. patent application Ser. No. 12/626,035 filed on Nov. 25, 2009, naming John Choy, et al. as inventors. Priority under 35 U.S.C. §120 is claimed from U.S. patent application Ser. No. 12/626,035, and the entire disclosure of U.S. patent application Ser. No. 12/626,035 is specifically incorporated herein by reference. 
         [0002]    The present application is also a continuation-in-part of and claims priority under 35 U.S.C. §120 from U.S. patent application Ser. No. 12/490,525 entitled “ACOUSTIC RESONATOR STRUCTURE COMPRISING A BRIDGE” to John Choy, et al. and filed on Jun. 24, 2009. The disclosure of this application is specifically incorporated herein by reference. 
     
    
     BACKGROUND 
       [0003]    In many electronic applications, electrical resonators are used. For example, in many wireless communications devices, radio frequency (rf) and microwave frequency resonators are used as filters to improve reception and transmission of signals. Filters typically include inductors and capacitors, and more recently resonators. 
         [0004]    As will be appreciated, it is desirable to reduce the size of components of electronic devices. Many known filter technologies present a barrier to overall system miniaturization. With the need to reduce component size, a class of resonators based on the piezoelectric effect has emerged. In piezoelectric-based resonators, acoustic resonant modes are generated in the piezoelectric material. These acoustic waves are converted into electrical waves for use in electrical applications. 
         [0005]    One type of piezoelectric resonator is a Film Bulk Acoustic Resonator (FBAR). The FBAR has the advantage of small size and lends itself to Integrated Circuit (IC) manufacturing tools and techniques. The FBAR includes an acoustic stack comprising, inter alia, a layer of piezoelectric material disposed between two electrodes. Acoustic waves achieve resonance across the acoustic stack, with the resonant frequency of the waves being determined by the materials in the acoustic stack. 
         [0006]    FBARs are similar in principle to bulk acoustic resonators such as quartz, but are scaled down to resonate at GHz frequencies. Because the FBARs have thicknesses on the order of microns and length and width dimensions of hundreds of microns, FBARs beneficially provide a comparatively compact alternative to known resonators. 
         [0007]    Desirably, the bulk acoustic resonator excites only thickness-extensional (TE) modes, which are longitudinal mechanical waves having propagation (k) vectors in the direction of propagation. The TE modes desirably travel in the direction of the thickness (e.g., z-direction) of the piezoelectric layer. 
         [0008]    Unfortunately, in addition to the desired TE modes there are lateral modes, known as Rayleigh-Lamb modes, generated in the acoustic stack as well. The Rayleigh-Lamb modes are mechanical waves having k-vectors that are perpendicular to the direction of TE modes, the desired modes of operation. These lateral modes travel in the areal dimensions (x, y directions of the present example) of the piezoelectric material. Among other adverse effects, lateral modes deleteriously impact the quality (Q) factor of an FBAR device. In particular, the energy of Rayleigh-Lamb modes is lost at the interfaces of the FBAR device. As will be appreciated, this loss of energy to spurious modes is a loss in energy of desired longitudinal modes, and ultimately a degradation of the Q-factor. 
         [0009]    What is needed, therefore, is an acoustic resonator that overcomes at least the known shortcomings described above. 
       SUMMARY 
       [0010]    In accordance with a representative embodiment, a piezoelectric resonator structure, comprises: (a) a substrate having atop surface and a bottom surface, a first end portion and an opposite, second end portion, and a body portion defined therebetween; (b) an acoustic minor having a top surface and a bottom surface, a first end portion and an opposite, second end portion, and a body portion defined therebetween, wherein the bottom surface is formed on the top surface of the substrate; (c) a first electrode having a top surface and a bottom surface, a first end portion and an opposite, second end portion, and a body portion defined therebetween, wherein the bottom surface is formed on the top surface of the acoustic mirror; (d) a piezoelectric layer having a top surface and a bottom surface, a first end portion and an opposite, second end portion, and a body portion defined therebetween, wherein the bottom surface is formed on the top surface of the first electrode; and (e) a second electrode having a top surface and a bottom surface, a first end portion and an opposite, second end portion, and a body portion defined therebetween. The bottom surface is formed on the top surface of the piezoelectric layer, wherein the overlapped area of body portions of the substrate, the acoustic mirror, the first electrode, the piezoelectric layer and the second electrode is defined as an active area A. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]    The illustrative embodiments are best understood from the following detailed description when read with the accompanying drawing figures. It is emphasized that the various features are not necessarily drawn to scale. In fact, the dimensions may be arbitrarily increased or decreased for clarity of discussion. Wherever applicable and practical, like reference numerals refer to like elements. 
           [0012]      FIG. 1A  shows a cross-sectional view of an acoustic resonator in accordance with a representative embodiment. 
           [0013]      FIG. 1B  shows atop view of an acoustic resonator in accordance with a representative embodiment. 
           [0014]      FIG. 2A  shows a graph of the Q-factor at parallel resonance (Q p ) versus width of the cantilevered portion(s) of an acoustic resonator in accordance with a representative embodiment. 
           [0015]      FIG. 2B  shows a graph of the Q-factor at series resonance (Q s ) versus width of the cantilevered portion(s) of an acoustic resonator in accordance with a representative embodiment. 
           [0016]      FIG. 3  shows a cross-sectional view of an acoustic resonator in accordance with a representative embodiment. 
           [0017]      FIG. 4A  shows a graph of the Q-factor at parallel resonance (Q p ) versus width of the cantilevered portion(s) of an acoustic resonator in accordance with a representative embodiment. 
           [0018]      FIG. 4B  shows a graph of the Q-factor at series resonance (Q s ) versus width of the cantilevered portion(s) of an acoustic resonator in accordance with a representative embodiment. 
           [0019]      FIG. 4C  shows a graph of the Q-factor at parallel resonance (Q p ) versus width of the cantilevered portion(s) of an acoustic resonator in accordance with a representative embodiment. 
           [0020]      FIG. 5A  shows a cross-sectional view of an acoustic resonator in accordance with a representative embodiment taken along line  5 A- 5 A in  FIG. 5B . 
           [0021]      FIG. 5B  shows a top view of an acoustic resonator in accordance with a representative embodiment. 
           [0022]      FIG. 6  shows a cross-sectional view of an acoustic resonator in accordance with a representative embodiment. 
           [0023]      FIG. 7  shows a simplified schematic diagram of an electrical filter in accordance with a representative embodiment. 
       
    
    
     DEFINED TERMINOLOGY 
       [0024]    It is to be understood that the terminology used herein is for purposes of describing particular embodiments only, and is not intended to be limiting. The defined terms are in addition to the technical and scientific meanings of the defined terms as commonly understood and accepted in the technical field of the present teachings. 
         [0025]    As used in the specification and appended claims, the terms ‘a’, ‘an’ and ‘the’ include both singular and plural referents, unless the context clearly dictates otherwise. Thus, for example, ‘a device’ includes one device and plural devices. 
         [0026]    As used in the specification and appended claims, and in addition to their ordinary meanings, the terms ‘substantial’ or ‘substantially’ mean to with acceptable limits or degree. For example, ‘substantially cancelled’ means that one skilled in the art would consider the cancellation to be acceptable. 
         [0027]    As used in the specification and the appended claims and in addition to its ordinary meaning, the term ‘approximately’ means to within an acceptable limit or amount to one having ordinary skill in the art. For example, ‘approximately the same’ means that one of ordinary skill in the art would consider the items being compared to be the same. 
       DETAILED DESCRIPTION 
       [0028]    In the following detailed description, for purposes of explanation and not limitation, specific details are set forth in order to provide a thorough understanding of illustrative embodiments according to the present teachings. However, it will be apparent to one having ordinary skill in the art having had the benefit of the present disclosure that other embodiments according to the present teachings that depart from the specific details disclosed herein remain within the scope of the appended claims. Moreover, descriptions of well-known apparati and methods may be omitted so as to not obscure the description of the illustrative embodiments. Such methods and apparati are clearly within the scope of the present teachings. 
         [0029]    Generally, it is understood that the drawings and the various elements depicted therein are not drawn to scale. Further, relative terms, such as “above,” “below,” “top,” “bottom,” “upper” and “lower” are used to describe the various elements&#39; relationships to one another, as illustrated in the accompanying drawings. It is understood that these relative terms are intended to encompass different orientations of the device and/or elements in addition to the orientation depicted in the drawings. For example, if the device were inverted with respect to the view in the drawings, an element described as “above” another element, for example, would now be below that element. 
         [0030]      FIG. 1A  is a cross-sectional view along the line  1 B- 1 B of an acoustic resonator  100  in accordance with a representative embodiment. Illustratively, the acoustic resonator  100  comprises an FBAR. The acoustic resonator  100  comprises a substrate  101 , a first electrode  102  disposed beneath a piezoelectric layer  103 , which comprises a first surface in contact with a first electrode  102  and a second surface in contact with a second electrode  104 . An optional passivation layer  105  is provided over the second electrode  104 . A cantilevered portion  106  of the second electrode  104  is provided on at least one side of the second electrode  104 . The cantilevered portion  106  may also be referred to as a ‘wing.’ 
         [0031]    The acoustic resonator  100  may be fabricated according to known semiconductor processing methods and using known materials. Illustratively, the acoustic resonator  100  may be fabricated according to the teachings of commonly owned U.S. Pat. Nos. 5,587,620; 5,873,153; 6,384,697; 6,507,983; and 7,275,292 to Ruby, et al.; and 6,828,713 to Bradley, et al. The disclosures of these patents are specifically incorporated herein by reference. It is emphasized that the methods and materials described in these patents are representative and other methods of fabrication and materials within the purview of one of ordinary skill in the art are contemplated. 
         [0032]    When connected in a selected topology, a plurality of acoustic resonators  100  can act as an electrical filter. For example, the acoustic resonators  100  may be arranged in a ladder-filter arrangement, such as described in U.S. Pat. No. 5,910,756 to Ella, and U.S. Pat. No. 6,262,637 to Bradley, et al., the disclosures of which are specifically incorporated herein by reference. The electrical filters may be used in a number of applications, such as in duplexers. 
         [0033]    The first and second electrodes  102 ,  104  each comprise an electrically conductive material (e.g., molybdenum (Mo)) and provide an oscillating electric field in the y-direction of the coordinate system shown (i.e., the direction of the thickness of the piezoelectric layer  103 ). In the illustrative embodiment described presently, the y-axis is the axis for the TE (longitudinal) mode(s) for the resonator. In a representative embodiment, the piezoelectric layer  103  and first and second electrodes  102 , 104  are suspended over a cavity  107  formed by selective etching of the substrate  101 . The cavity  107  may be formed by a number of known methods, for example as described in referenced commonly owned U.S. Pat. No. 6,384,697 to Ruby, et al. Accordingly, the acoustic resonator  100  is a mechanical resonator, which can be electrically coupled via the piezoelectric layer  103 . Other configurations that foster mechanical resonance by FBARs are contemplated. For example, the acoustic resonator  100  can be located over an acoustic mirror, such as a mismatched acoustic Bragg reflector (not shown) formed in or on the substrate  101 . FBARs provided over an acoustic mirror are sometimes referred to as solid mount resonators (SMRs) and, for example, may be as described in U.S. Pat. No. 6,107,721 to Lakin, the disclosure of which is specifically incorporated into this disclosure by reference in its entirety. 
         [0034]    The cantilevered portion  106  of the second electrode  104  extends over a gap  108 , which illustratively comprises air. In a representative embodiment, a sacrificial layer (not shown) is deposited by known technique over the first electrode  102  and a portion of the piezoelectric layer  103 . The second electrode  104  and passivation layer  105  are provided over the sacrificial layer. Illustratively, the sacrificial material comprises phosphosilicate glass (PSG), which illustratively comprises 8% phosphorous and 92% silicon dioxide. After the formation of the second electrode  104  and passivation layer  105 , the sacrificial layer is etched away illustratively with hydrofluoric acid leaving the cantilevered portion  106 . In a representative embodiment, the sacrificial layer provided to form the cantilevered portion  106  and the sacrificial layer provided to form the cavity  107  are removed in the same process step. 
         [0035]    Notably, rather than air, the gap  108  may comprise other materials including tow acoustic impedance materials, such as carbon (C) doped SiO 2 , which is also referred as Black-diamond; or dielectric resin commercially known as SiLK; or benzocyclobutene (BCB). Such low acoustic impedance materials may be provided in the gap  108  by known methods. The low acoustic impedance material may be provided after removal of sacrificial material used to form the gap  108 , or may be used instead of the sacrificial material in the gap  108 , and not removed. 
         [0036]    The region of contacting overlap of the first and second electrodes  102 ,  104 , the piezoelectric layer  103  and the cavity  107 , or other reflector (e.g., Bragg reflector (not shown)) is referred to as an active area  110  of the acoustic resonator  100 . By contrast, an inactive area of the acoustic resonator  100  comprises a region of overlap between first electrode  102  or second electrode  104 , or both, and the piezoelectric layer  103  not disposed aver the cavity  107 , or other suspension structure, or acoustic mirror. As described more fully in the parent application, it is beneficial to the performance of the acoustic resonator  100  to reduce the area of the inactive region of the acoustic resonator  100  to the extent practical. 
         [0037]    The cantilevered portion  106  extends beyond an edge of the active area  110  by a width  109  as shown. An electrical contact  111  is connected to a signal line (not shown) and electronic components (not shown) selected for the particular application of the acoustic resonator  100 . This portion of the acoustic resonator  100  comprises an interconnection side  112  of the acoustic resonator  100 . As will become clearer as the present description continues, the interconnection side  112  of the second electrode  104  to which the electrical contact  111  is made does not comprise a cantilevered portion. By contrast, one or more non-connecting sides  113  of the acoustic resonator  100  may comprise cantilevered portions  106  that extend beyond the edge of the active area  110 . 
         [0038]      FIG. 1B  shows a top view of the acoustic resonator  100  shown in cross-sectional view in  FIG. 1A  and in accordance with a representative embodiment. The acoustic resonator  100  also comprises the second electrode  104  with the optional passivation layer  105  disposed thereover. The second electrode  104  of the present embodiment is illustratively apodized to reduce acoustic losses. Further details of the use of apodization in acoustic resonators may be found in commonly owned U.S. Pat. No. 6,215,375 to Larson III, et al; or in commonly owned U.S. Patent Application Publication 20070279153 entitled “Piezoelectric Resonator Structures and Electrical Filters” filed May 31, 2006, to Richard C. Ruby. The disclosures of this patent and patent application publication are specifically incorporated herein by reference in their entirety. 
         [0039]    The second electrode  104  comprises non-connecting sides  113  and interconnection side  112 . In a representative embodiment, cantilevered portions  106  are provided along each non-contacting side  113  and have the same width. This is merely illustrative, and it is contemplated that at least one side  113 , but not all comprise a cantilevered portion  106 . Furthermore, it is contemplated that the second electrode  104  comprises more or fewer than four sides as shown. For example, a pentagonal-shaped second electrode is contemplated comprising four sides with cantilevered portions on one or more of the sides, and the fifth side providing the interconnection side. In a representative embodiment, the shape of the first electrode  102  is substantially identical to the shape of the second electrode  104 . Notably, the first electrode  102  may comprise a larger area than the second electrode  104 , and the shape of the first electrode  102  may be different than the shape of the second electrode  104 . 
         [0040]    The fundamental mode of the acoustic resonator  100  is the longitudinal extension mode or “piston” mode. This mode is excited by the application of a time-varying voltage to the two electrodes at the resonant frequency of the acoustic resonator  100 . The piezoelectric material converts energy in the form of electrical energy into mechanical energy. In an ideal FBAR having infinitesimally thin electrodes, resonance occurs when the applied frequency is equal to the velocity of sound of the piezoelectric medium divided by twice the thickness of the piezoelectric medium: f=v ac /(2*T), where T is the thickness of the piezoelectric medium and v ac  is the acoustic phase velocity. For resonators with finite thickness electrodes, this equation is modified by the weighted acoustic velocities and thicknesses of the electrodes. 
         [0041]    A quantitative and qualitative understanding of the Q of a resonator may be obtained by plotting on a Smith Chart the ratio of the reflected energy to applied energy as the frequency is varied for the case in which one electrode is connected to ground and another to signal, for an FBAR resonator with an impedance equal to the system impedance at the resonant frequency. As the frequency of the applied energy is increased, the magnitude/phase of the FBAR resonator sweeps out a circle on the Smith Chart. This is referred to as the Q-circle. Where the Q-circle first crosses the real axes (horizontal axes), this corresponds to the series resonance frequency f s . The real impedance as measured in Ohms) is R s . As the Q-circle continues around the perimeter of the Smith chart, it again crosses the real axes. The second point at which the Q circle crosses the real axis is labeled f p , the parallel or anti-resonant frequency of the FBAR. The real impedance at f p  is R p . 
         [0042]    Often it is desirable to minimize R s  while maximizing R p . Qualitatively, the closer the Q-circle “hugs” the outer rim of the Smith chart, the higher the Q-factor of the device. The Q-circle of an ideal lossless resonator would have a radius of one and would be at the edge of the Smith chart. However, as noted above, there are energy losses that impact the Q-factor of the device. For instance, and in addition to the sources of acoustic losses mentioned above, Rayleigh-Lamb (lateral or spurious) modes are in the x,y dimensions of the piezoelectric layer  103 . These lateral modes are due to interfacial mode conversion of the longitudinal mode traveling in the z-direction; and due to the creation of non-zero propagation vectors, k x  and k y , for both the TE mode and the various lateral modes (e.g., the S 0  (symmetric) mode and the zeroth and (asymmetric) modes, A 0  and A 1 ), which are due to the difference in effective velocities between the regions where electrodes are disposed and the surrounding regions of the resonator where there are no electrodes. At a specific frequency, the acoustic wave length of an acoustic resonator is determined by v/f where v is acoustic velocity and f is frequency. It is believed that periodicity of Qp (i.e., the position of maxima and minima as a function of the width  109  of the cantilevered portion  106 ) is related to the acoustic wave length. At a maxima of Qp, the vibration of the wing  106  is comparatively far from its mechanical resonance; while at a minima mechanical resonance of the cantilevered portion  106  occurs. This phenomenon can be appreciated from a review of  FIG. 2A  below, for example: as frequency decreases, acoustic wave length increases, and the width  109  of the cantilevered portion  106  at a maxima increases accordingly. 
         [0043]    Regardless of their source, the lateral modes are parasitic in many resonator applications. For example, the parasitic lateral modes couple at the perimeter of the resonator and remove energy available for the longitudinal modes and thereby reduce the Q-factor of the resonator device. Notably, as a result of parasitic lateral modes and other acoustic losses sharp reductions in Q can be observed on a Q-circle of the Smith Chart of the parameter. These sharp reductions in Q-factor are known as “rattles” or “loop-de-loops,” which are shown and described below. 
         [0044]    The cantilevered portion(s)  106  of the representative embodiments provide a change in the acoustic impedance at the boundary of the active area  110  of the acoustic resonator  100 . As a result, reflections of lateral modes at the boundary are promoted. In a representative embodiment, the boundary of the active area  110  of the acoustic resonator  100  and the cantilevered portion  106  is solid (first and second electrodes  102 ,  104  and piezoelectric layer  103 ) and air, which presents a comparatively large impedance mismatch and a comparatively high reflection coefficient. As a result, lateral modes are comparatively highly reflected, which improves the Q-factor by two mechanisms. First, because the reflected lateral modes are not transmitted, their energy is not lost. Improving the losses by reducing transmission of lateral modes outside the active area  110  of the acoustic resonator  100  can increase the Q-factor of the acoustic resonator  100 . Second, a portion of the reflected lateral modes is converted into desired longitudinal modes. The greater the wave energy is in longitudinal modes, the higher the Q-factor. As a result, the cantilevered portion(s)  106  of the acoustic resonator  100  enhances the Q-factor of both the parallel and the series resonance (i.e., Q p  and Q s ). 
         [0045]      FIG. 2A  shows a graph  200  of the Q-factor at parallel resonance (Q p ) versus width (e.g., width  109 , also referred to as “wing width”) of the cantilevered portion(s)  106  (“wings”) of an acoustic resonator in accordance with a representative embodiment. The graph  200  provides data of an acoustic resonator comprising three cantilevered portions  106 , such as illustratively shown in  FIGS. 1A and 1B . The Q-factor is dependent on the width of the cantilevered portion  106  for a given parallel resonance frequency. As shown, there are relative maxima in Q p  at points  201 ,  202  and  203 ; and local minima at points  204 ,  205  and  206  as the width  109  increases. Notably, Q p  improves significantly at a certain width  109 , compared with width  109  of the cantilevered portion  106  being zero, which is equivalent to an acoustic resonator having substantially the same structure as acoustic resonator  100  but not comprising the cantilevered portion  106 . 
         [0046]    Improvements in Q p  due to the inclusion of the cantilevered portion  106  results from different boundary conditions at the edge of the active area  110  of the acoustic resonator  100  compared to an acoustic resonator not comprising a cantilevered portion(s). As described above, the cantilevered portion  106  at the edge of active area  110  of the acoustic resonator  100  will reflect certain acoustic modes due to the impedance mismatch at the boundary of the cantilevered portion  106  and the active area  110 , resulting in improved Q. It is believed that the local minima may result from the excitation of a mechanical resonance of the cantilevered portion  106 , which results in losses. The excited resonance conditions at relative minima (points  204 ,  205 ,  206 ), result in energy not reflected back into the active area  110  of the acoustic resonator  100 , losses and reduced Q. Accordingly, when designing acoustic resonator  100 , the width  109  of the cantilevered portion  106  is beneficially selected at a relative maximum (points  201 ,  202 ,  203 ), and not at a relative minimum (points  204 ,  205 ,  206 ). 
         [0047]      FIG. 2B  shows a graph  207  of the Q-factor at series resonance (Q s ) versus width (e.g., width  109  (‘wing width’)) of the cantilevered portion  106  (‘wing’) of an acoustic resonator in accordance with a representative embodiment. The graph  207  provides data of an acoustic resonator comprising three cantilevered portions  106 , such as illustratively shown in  FIGS. 1A and 1B . The Q-factor is dependent on the width  109  of the cantilevered portion  106  for a given series resonance frequency. As shown, there are relative maxima in Q s , at points  208 ,  209  and  210  and local minima at points  211 ,  212  and  213  as the width  109  increases. Notably, Q s  improves significantly at a certain width  109 , compared with width=0 of the cantilevered portion  106 , which is equivalent to an acoustic resonator having substantially the same configuration as acoustic resonator  100  but without cantilevered portions  106 . 
         [0048]    As described above, the cantilevered portion  106  at the edge of active area  110  of the acoustic resonator will reflect certain acoustic modes due to the impedance mismatch at the boundary of the cantilevered portion  106  and the active area  110 , resulting in improved Q. It is believed that the local minima may result from the excitation of a mechanical resonance of the cantilevered portion  106 , which results in losses. The excited resonance conditions at relative minima (points  211 ,  212  and  213 ) result in energy not reflected back into the active area  110  of the acoustic resonator  100 , losses and, therefore, reduced Q. Accordingly, when designing acoustic resonator  100 , the width  109  of the cantilevered portion  106  is beneficially selected at a relative maximum (points  208 , 209  or  210 ), and not at a relative minimum (points  211 ,  212  or  213 ). 
         [0049]    Moreover, because the cantilevered portion  106  does not generate spurious lateral modes, there is no attendant degradation in Q near the series resonance frequency as can occur with the inclusion of known raised frame elements (sometimes referred to as ‘outies’) and known recessed frame elements (sometimes referred to as ‘innies’.) Notably, both raised frame elements and recessed frame elements may be disposed annularly about acoustic resonator and are sometimes referred to as annular recesses and annular frames. The raised frame elements and recessed frame elements may generate spurious modes, but recessed frame elements improve the coupling coefficient (k t   2 ), and raised frame elements may slightly decrease k t   2 . Furthermore the cantilevered portion  106  does not generate spurious modes because its location is not within the active area  110 . The cantilevered portion  106  also does not degrade k t   2  as significantly as the raised and recessed frame elements. As can be appreciated from a review of  FIG. 2A , k t   2  at peak Q corresponds to a width of the cantilevered portion  106  of approximately 4.75 μm is approximately 5.2. This represents an increase in k t   2  of approximately 10% greater than that of a known acoustic resonator with a raised frame element. 
         [0050]      FIG. 3  shows a cross-sectional view of an acoustic resonator  300  in accordance with a representative embodiment. Many of the features of the acoustic resonator  300  are common to those of acoustic resonator  100  described in connection with representative embodiments in  FIGS. 1A-1B . The details of common features, characteristics and benefits thereof are not repeated in order to avoid obscuring the presently described embodiments. 
         [0051]    The acoustic resonator  300  comprises a bridge  301  along the interconnection side  112 . The bridge  301  provides a gap  302 , which may be avoid (e.g., air) or may be filled with a low acoustic impedance material. The bridge  301  is described in the parent application (Ser. No. 12/490,525 entitled “ACOUSTIC RESONATOR STRUCTURE COMPRISING A BRIDGE”), and as such many of the details of the bridge  301  are not repeated in the present application to avoid obscuring the description of the representative embodiments of the acoustic resonator  300 . 
         [0052]    As described above, the cantilevered portion  106  provides an improvement in the Q-factor. Similarly, the bridge  301  also provides an improvement in the Q-factor. Beneficially, the combination of the cantilevered portion  106  and the bridge  301  provides a further improvement in the Q-factor of the acoustic resonator  300 . To this end, inclusion of the bridge  301  with the cantilevered portion  106  in the acoustic resonator  300  results in an improvement in the Q-factor at parallel resonance (Qp) and some impact on the Q-factor at series resonance (Qs). This is somewhat expected since the bridge  301  predominantly impacts Qp, as described in the parent application. 
         [0053]      FIG. 4A  shows a graph  400  of the Q-factor at parallel resonance (Qp) versus width (e.g., width  109 , (‘wing width’)) of the cantilevered portion  106  of an acoustic resonator comprising a bridge (e.g., acoustic resonator  300 ) in accordance with a representative embodiment. The graph  400  provides data of an acoustic resonator comprising three cantilevered portions  106 , such as illustratively shown in  FIGS. 1A and 1B . The Q-factor is dependent on the wing width (e.g., width  109 ) for a given parallel resonance frequency. As shown, there are relative maxima in Q p  at points  401 ,  402  and  403 ; and relative minima at points  404  and  405  as the width  109  increases. Notably, Q p  improves significantly at a certain width  109 , compared with width=0 of the cantilevered portion  106 , which is equivalent to an acoustic resonator having substantially the same configuration shown in  FIG. 3  but without cantilevered portions  106 . 
         [0054]    The synergistic impact of the combination of the bridge  301  and the cantilevered portions  106  on Qp can be appreciated by a comparison of data in  FIGS. 2A and 4A . For example, in an embodiment comprising cantilevered portion  106  having a width (e.g., width  109 ) of approximately 2.5 μm, Qp  FIG. 2A  (near point  201 , for example) is approximately 850. By contrast, in an embodiment comprising bridge  301  and cantilevered portion  106  having a width of approximately 2.5 μm (e.g., near point  406 ) provides Qp of approximately 1500. Similarly, in an embodiment comprising cantilevered portion  106  having a width (e.g., width  109 ) of approximately 3.0 μm, Qp in  FIG. 2A  (near point  202 , for example) is approximately 975. By contrast, in an embodiment comprising bridge  301  and cantilevered portion  106  having a width of approximately 3.0 μm provides Qp approximately 1750 (e.g., point  402  in  FIG. 4A ). 
         [0055]      FIG. 4B  shows a graph  407  of the Q-factor at series resonance (Q s ) versus width (e.g., width  109 ) of the cantilevered portion  106  of an acoustic resonator comprising a bridge (e.g., acoustic resonator  300 ) in accordance with a representative embodiment. The graph  407  provides data of an acoustic resonator comprising three cantilevered portions  106 , such as illustratively shown in  FIGS. 1A and 1B . The Q-factor is dependent on the wing width for a given series resonance frequency. As shown, there are relative maxima in Q p  at points  408 ,  409  and  410 ; and relative minima at points  411 ,  412 ,  413  and  414  as the width  109  increases. Notably, Q s  improves significantly at a certain width  109 , compared with width=0 of the cantilevered portion  106 , which is equivalent to an acoustic resonator having substantially the same configuration shown in  FIG. 3  but without cantilevered portions  106 . As note previously, the impact of the bridge  301  on improved Q s  is less dramatic than its impact on Q p . 
         [0056]      FIG. 4C  shows a graph of the Q-factor at parallel resonance (Q p ) versus width of the cantilevered portion(s) of an acoustic resonator in accordance with a representative embodiment. As the total thickness of the acoustic stack decreases, the resonance frequency increases and, therefore, the acoustic wavelength at the resonance frequency decreases. An optimum width  109  (‘wing width’) of the cantilevered portion  106 , at which the most Q enhancement is achieved, is determined by resonance acoustic quarter-wavelength, therefore smaller optimum wing width is required to achieve optimum Q, Notably,  FIG. 4C  relates to an acoustic resonator having a parallel resonance of 800 MHz. A maximum Q-value (shown at point  415 ) is attained at a wing width of approximately 1.6 μm. 
         [0057]      FIG. 5A  shows a cross-sectional view of an acoustic resonator  500  taken along line  5 B- 5 B in accordance with a representative embodiment.  FIG. 5B  shows atop view of the acoustic resonator  500 . Many of the features of the acoustic resonator  500  are common to those of acoustic resonators  100 ,  300  described in connection with representative embodiments in  FIGS. 1A-1B  and  3 . The details of common features, characteristics and benefits thereof are not repeated in order to avoid obscuring the presently described embodiments. 
         [0058]    The acoustic resonator  500  comprises the bridge  301  along the interconnection side  112 . The bridge  301  provides the gap  302 , which may be a void (e.g., air) or may be filled with a low acoustic impedance material. In addition to the bridge  301 , the acoustic resonator  500  comprises a raised frame element  501  (commonly referred to as an ‘outie’). The raised frame element  501  may be provided over one or more sides of the acoustic resonator  500  and provides an acoustic mismatch at the boundary of the second electrode  104 , thereby improving signal reflections at the boundary and reducing acoustic tosses. Ultimately, reduced losses translate into an improved Q-factor of the device. While the raised frame element  501  are shown disposed over the second electrode  103 , these features may instead be provided over the first electrode  102  and beneath the piezoelectric layer  103 , or selectively on both the first and second electrodes  102 , 104 . Further details of the use, formation and benefits of the raised frame element  501  may be found for example, in commonly owned U.S. Pat. No. 7,280,007 entitled “Thin Film Bulk Acoustic Resonator with a Mass Loaded Perimeter” to Feng, et al.; and commonly owned U.S. Patent Application Publication 20070205850 entitled “Piezoelectric Resonator Structure and Electronic Filters having Frame Elements” to Jamneala, et al. The disclosures of this patent and patent application publication are specifically incorporated herein by reference. 
         [0059]    The raised frame element  501  results in an increase in the parallel impedance (Rp) but generates spurious modes below the series resonance frequency; whereas the cantilevered portion  106  increases Rp without degrading Qs. This is because the area of the raised frame element  501  represents a comparatively small fraction of the active area of the acoustic resonator  500 . It can be shown that this is equivalent to an acoustic resonator connected in parallel to an acoustic resonator comprising a frame element. Since the resonance frequency of an acoustic resonator comprising the raised frame element  501  is lower, spurious modes are generated below f s  of the acoustic resonator without the frame element. The addition of the cantilevered portion  106  to the acoustic resonator  500  comprising the raised frame element  501  further increases Rp without resulting in additional spurious modes below f s  because the wing  106  lies outside of the active area  110  of the acoustic resonator  500 . 
         [0060]      FIG. 6  shows a cross-sectional view of an acoustic resonator  600  in accordance with a representative embodiment. Many of the features of the acoustic resonator  600  are common to those of acoustic resonators  100 ,  300 ,  500  described in connection with representative embodiments in  FIGS. 1A-1B ,  3 ,  5 A and  5 B. The details of common features, characteristics and benefits thereof are not repeated in order to avoid obscuring the presently described embodiments. 
         [0061]    The acoustic resonator  600  comprises the bridge  301  along the interconnection side  112 . The bridge  301  provides the gap  302 , which may be a void (e.g., air) or may be filled with a low acoustic impedance material. In addition to the bridge  301 , the acoustic resonator  600  comprises a recessed frame element  601  (‘innie’). The recessed frame element  601  may be disposed along one or more sides of the acoustic resonator  600  and provides an acoustic mismatch at the perimeter of the second electrode  104 , thereby improving signal reflections and reducing acoustic tosses. Ultimately, reduced losses translate into an improved Q-factor of the device. While the recessed frame element  601  is shown disposed over the second electrode  104 , the recessed frame element  601  may instead be provided over the first electrode  102  and beneath the piezoelectric layer  103 , or selectively on both the first and second electrodes  102 , 104 . Further details of the use, formation and benefits of the recessed frame element  601  may be found for example, in commonly owned U.S. Pat. No. 7,280,007 entitled “Thin Film Bulk Acoustic Resonator with a Mass Loaded Perimeter” to Feng, et al.; and commonly owned U.S. Patent Application Publication 20070205850 entitled “Piezoelectric Resonator Structure and Electronic Filters having Frame Elements” to Jamneala, et al. The disclosures of this patent and patent application publication are specifically incorporated herein by reference. Moreover, the incorporation of both a raised frame element (e.g., raised frame element  501 ) and a recessed frame (e.g., recessed frame element  601 ) in an acoustic resonator  100 ,  300 ,  500 ,  600  is also contemplated by the present teachings. The incorporation of both raised and recessed frame elements in an acoustic resonator is disclosed in the parent application (U.S. patent application Ser. No. 12/490,525). 
         [0062]    When connected in a selected topology, a plurality of acoustic resonators  100 ,  300 ,  500 ,  600  can function as an electrical filter.  FIG. 7  shows a simplified schematic block diagram of an electrical filter  700  in accordance with a representative embodiment. The electrical filter  700  comprises series acoustic resonators  701  and shunt acoustic resonators  702 . The series acoustic resonators  701  and shunt acoustic resonators  702  may comprise the acoustic resonators  100 ,  300 ,  500 ,  600  described in connection with the representative embodiments of  FIGS. 1A ,  1 B,  3 ,  5 A,  5 B and  6 . The electrical filter  700  is commonly referred to as a ladder filter, and may be used for example in duplexer applications. Further details of a ladder-filter arrangement may be as described for example in U.S. Pat. No. 5,910,756 to Ella, and U.S. Pat. No. 6,262,637 to Bradley, et al. The disclosures of these patents are specifically incorporated by reference. It is emphasized that the topology of the electrical filter  700  is merely illustrative and other topologies are contemplated. Moreover, the acoustic resonators of the representative embodiments are contemplated in a variety of applications besides duplexers. 
         [0063]    In accordance with illustrative embodiments, acoustic resonators for various applications such as in electrical filters are described having an electrode comprising a cantilevered portion. Additionally, acoustic resonators for various applications such as in electrical fitters are described having an electrode comprising a cantilevered portion and a bridge. One of ordinary skill in the art appreciates that many variations that are in accordance with the present teachings are possible and remain within the scope of the appended claims. These and other variations would become clear to one of ordinary skill in the art after inspection of the specification, drawings and claims herein. The invention therefore is not to be restricted except within the spirit and scope of the appended claims.