Patent Publication Number: US-8981624-B2

Title: Temperature control of micromachined transducers

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a divisional application of and claims the benefit under 35 U.S.C. Section 120 from U.S. patent application Ser. No. 12/570,298, entitled “Temperature Control of Micromachined Transducers” by David Martin, et al. filed on Sep. 30, 2009, which is a continuation-in-part under 37 C.F.R. § 1.53(b) of commonly owned U.S. patent application Ser. No. 12/495,443, entitled “Piezoelectric Micromachined Transducers” to David Martin, et al., and filed on Jun. 30, 2009. Priority to the cross-referenced parent applications is claimed in accordance with 35 U.S.C. §120, and the entire disclosures of U.S. patent application Ser. No. 12/495,443 and U.S. patent application Ser. No. 12/570,298 are specifically incorporated herein by reference. 
    
    
     BACKGROUND 
     Transducers such as ultrasonic transducers are provided in a wide variety of electronic applications. As the need to reduce the size of many components continues, the demand for reduced-size transducers continues to increase as well. This has lead to comparatively small transducers, which may be micromachined according to technologies such as micro-electromechanical systems (MEMS) technology. One type of transducer is a piezoelectric micromachined transducer (PMT). The PMT includes a layer of piezoelectric material between two conductive plates (electrodes) thereby forming a membrane. When functioning as a receiver, an acoustic wave incident on the membrane results in the application of a time varying force to the piezoelectric material. Application of the time-varying force to a piezoelectric material results in induced stresses in the piezoelectric material, which in-turn creates a time-varying voltage signal across the material. This lime-varying voltage signal may be measured by sensor circuits to determine the characteristics of the incident acoustic wave. Alternatively, this time-varying voltage signal may produce a time-varying charge that is provided to sensor circuits that process the signal and determine the characteristics of the incident acoustic wave. When functioning as a transmitter, a voltage excitation produces vibration of the diaphragm. This in turn radiates acoustic energy into the air (or any gaseous medium). 
     Ultrasonic devices, such as ultrasonic transducers, typically operate at a resonance condition to improve sensitivity in both receive mode and transmit mode. Accordingly, it is useful for the transducer to function at a comparatively accurate resonant frequency, and for multiple transducers designed for use at the selected resonant frequency to be fabricated with such accuracy with repeatability. One drawback to many known PMT structures relates to a lack of repeatability of the resonance frequency from PMT to PMT. To this end, PMTs for certain applications, such as mics rely on the flexure mode of the membrane rather than longitudinal modes. While the resonant frequency of longitudinal modes is not significantly affected by film stress, the resonant frequency of flexural modes is highly dependent on film stress. Thus, variation in film stress can impact the operational characteristics of transducers designed for flexural mode operation. 
     Another source of stress in PMTs is temperature. As is known, every material has a coefficient of thermal expansion (T CE ). Thus a material expands or contracts in proportion to this coefficient. The expansion or contraction of a material induces stress in the material, and mismatches in T CE  between different materials comprising the PMT will result in stress in the membrane layer. The stress in the membrane layer can impact the resonance frequency and the sensitivity of the membrane and thereby the PMT. 
     There is a need, therefore, for a transducer structure that addresses at least the shortcomings described above. 
     SUMMARY 
     In accordance with an illustrative embodiment, a micromachined structure, 
     comprises a substrate having a first coefficient of thermal expansion. The micromachined structure comprises a cavity in the substrate and a membrane layer having a second coefficient of thermal expansion and disposed over the substrate and spanning the cavity, wherein the first coefficient of thermal expansion is substantially identical to the second coefficient of thermal expansion. The micromachined structure comprises an annular resonator disposed over the membrane and comprising a first electrode, a second electrode and a piezoelectric layer between the first and second electrodes. 
     In accordance with another illustrative embodiment, a method of fabricating a piezoelectric micromachined transducer (PMT) comprises: providing a substrate comprising a surface and an opposing surface; forming a cavity in the substrate; forming a membrane layer over the surface and substantially spanning the cavity; and forming an annular transducer over the membrane layer, the annular transducer comprising a first electrode, a second electrode and a piezoelectric layer between the first electrode and the second electrode. 
     In accordance with another illustrative embodiment, a piezoelectric micromachined transducer (PMT) array comprises a substrate and a plurality of PMTs arranged over the substrate. Each of the PMTs comprises a cavity in the substrate; a membrane layer disposed over the substrate and spanning the cavity; and an annular resonator disposed over the membrane. The annular resonator comprises a first electrode, a second electrode and a piezoelectric layer between the first and second electrodes. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The representative 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. 
         FIG. 1  shows a cross-sectional view of a PMT in accordance with a representative embodiment. 
         FIGS. 2A-2F  shows cross-sectional views of a fabrication sequence in accordance with a representative embodiment. 
         FIG. 3  shows a cross-sectional view of a PMT in accordance with a representative embodiment. 
         FIGS. 4A-4C  show a fabrication sequence of a PMT in cross-section and top view in accordance with a representative embodiment. 
         FIG. 5  shows a cross-sectional view of a PMT in accordance with a representative embodiment. 
     
    
    
     DEFINED TERMINOLOGY 
     The terms ‘a’ or ‘an’, as used herein are defined as one or more than one. 
     The term ‘plurality’ as used herein is defined as two or more than two. 
     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. 
     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 
     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 example 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 materials and methods may be omitted so as to avoid obscuring the description of the illustrative embodiments. Nonetheless, such materials and methods that are within the purview of one of ordinary skill in the art may be used in accordance with the illustrative embodiments. Such materials and methods are clearly within the scope of the present teachings. The piezoelectric transducers of the representative embodiments are contemplated for use in a variety of electronic devices. 
     A representative electronic device may be a portable device such as a mobile phone, a camera, a video camera, a personal digital assistant (PDA), a sound recording device, a laptop computer, a tablet computer, a handheld computer, a handheld remote, or an electronic device that comprises the functionality of one or more of these devices. Moreover, the piezoelectric transducers of the representative embodiments are contemplated for use in disparate applications such as industrial automation, (e.g., liquid level sensing), detecting the presence of an object, and measuring gas flow. Additionally, the piezoelectric transducers of the representative embodiments can be used to detect mis-feed in automatic paper feeders in printers and scanners. 
     It is emphasized that the noted devices are merely illustrative and that other devices are contemplated. In some representative embodiments, the electronic device is a device that benefits from a microphone structure having a plurality of microphones, with at least one microphone optionally being adapted to function in more than one mode. 
     In many representative embodiments, the electronic devices are portable. However, this is not essential. In particular, the microphone structures of the present teachings are also contemplated for use in devices/apparatuses that are stationary; and devices/apparatuses that are mobile, but are not ordinarily small enough to be considered portable. For example, the microphone structures of representative embodiments may be used in industrial machinery applications, motor vehicle applications, aircraft applications, and watercraft applications, to name only a few. 
     Additionally, while the present description is drawn primarily to microphones, the present teachings contemplate applications to transducers in general. For example, as one of ordinary skill in the art will readily appreciate, the present teachings may be applied to piezoelectric speakers. 
       FIG. 1  is a cross-sectional view of a PMT  100  in accordance with an illustrative embodiment. The PMT  100  comprises a substrate  101 , a membrane layer  102  and an annular resonator  103 . The annular resonator  103  comprises a first electrode  104  disposed over the membrane layer  102 , a piezoelectric layer  105  and a second electrode  105 . The PMT  100  also comprises a cavity  107  formed in the substrate  101 . Application of a time-dependent voltage to the annular resonator  103  causes a mechanical wave to be launched through the annular resonator  103  and the membrane layer  102 . As the piezoelectric layer  105  oscillates in response to a mechanical perturbation (e.g., a sound wave), the forces generated by the perturbation induce stresses in the piezoelectric layer resulting in generation of a voltage difference across the electrodes  104 ,  106 . Assuming the layer  105  of piezoelectric material (e.g., AlN, ZnO or lead zirconium titanate (PZT)) has a c-axis substantially orthogonal to the membrane surface (parallel to x in the coordinate system shown), the voltage sensitivity is proportional to the lateral stress, σ y , and the ratio of the piezoelectric strain matrix coefficient (d 31 ) and the electric permittivity coefficient (ε 33 ). In certain embodiments the mechanical wave creates a flexure mode to be launched in the membrane layer  102 . 
     The membrane layer  102  illustratively comprises a material having a thermal expansion coefficient (T CE ) that substantially matches the thermal expansion coefficient (T CE ) of the substrate  101 . The membrane layer  102  has a thickness equal to or greater than the thickness of the combined thickness of the layers of the annular resonator  103 . Notably, substrate  101  and the membrane layer  102  dominate the temperature characteristics of the PMT  100 . Moreover, the areal dimension of the annular resonator  103  comprising the first electrode  104 , the piezoelectric layer  105  and the second electrode  105  is beneficially less than the areal dimension of the membrane layer  102 , so that the impact of the resonator  103  on the thermal properties of the PMT  100  is comparatively small, if not negligible. 
     In accordance with a representative embodiment, the annular resonator  103  has a circular shape. This is merely illustratively, and other shapes are clearly contemplated. For example, the annular resonator  103  may be elliptical, square or generally polygonal, such as pentagonal. In accordance with a representative embodiment, the substrate  101  is monocrystalline silicon, and the membrane layer  102  comprises monocrystalline silicon; or polycrystalline silicon (polysilicon) formed by low pressure chemical vapor deposition (LPCVD) or by plasma enhanced chemical vapor deposition (PECVD); or silicon carbide (SiC); or silicon nitride Si 3 N 4 . In other embodiments, the substrate  101  is monocrystalline silicon and the membrane layer  103  comprises boron-doped silicon glass (borosilicate glass) with a boron concentration by weight of approximately 3.0% to approximately 6.0%. In other embodiments, the substrate  101  may comprise silicon-on-insulator (SOI), or may comprise a first silicon wafer bonded to a second silicon wafer, which is thinned by a known thinning process to provide a desired thickness of the substrate  101 . 
     Selection of the material for the membrane layer  102  and its thickness allows for the selection of the resonance frequency and sensitivity of the membrane over a selected temperature range. Notably, a change in temperature will result in a change in the stress in the membrane layer  102 . In turn, a change in the stress in the material will result in a change in the resonance frequency and the sensitivity of the membrane layer  102 . Selection of a material that substantially matches the thermal expansion coefficient (T CE ) of the substrate  101  will ensure that thermally induced stress in the material used for the membrane  102  will be predictable over a temperature range of interest. Specifically, because the material selected for the membrane layer  102  has a thermal expansion coefficient (T CE ) that substantially matches the thermal expansion coefficient (T CE ) of the substrate  101 , the substrate  101  and the membrane layer  102  expand and contract at substantially the same rate versus temperature. As a result, the stress in the membrane layer remains substantially constant with changes in temperature. Accordingly, because the change in stress in the membrane layer  102  due to a change in temperature will alter the resonant frequency of the membrane layer  102  by a predictable amount. Likewise, a change in temperature will alter the sensitivity of the membrane layer  102  to a predictable amount, the sensitivity will change by a predictable amount For purposes of illustration and not limitation, the operating temperature range of the PMT  100  is approximately −40° C. to approximately +60° C. In representative embodiments, this results in a change in the resonant frequency of the membrane layer  102  of approximately −3% to approximately +3%. 
     In accordance with a representative embodiment, selection of the materials for the substrate  101  and the membrane layer  102  results in a substantially constant resonant frequency and sensitivity of the membrane layer  102 . In certain embodiments, the thermal coefficient of expansion (T CE ) of the membrane layer  102  is greater than the thermal expansion coefficient (T CE ) of the substrate  101 . In such embodiments, as the temperature increases, the stress in the membrane layer  102  becomes more compressive; and when the temperature decreases, the stress in the membrane layer  102  becomes more tensile. In other embodiments, the thermal coefficient of expansion (T CE ) of the membrane layer  102  is less than the thermal expansion coefficient (T CE ) of the substrate  101 . In such embodiments, as the temperature increases, the stress in the membrane layer  102  becomes more tensile; and when the temperature decreases, the stress in the membrane layer  102  becomes more compressive. 
     Mechanical waves launched from or incident on the membrane layer  103  travel through a cavity  107  and an opening  108 . In a representative embodiment, a micromachined structure comprises the substrate  101  and the membrane layer  102  spanning the cavity  107 . Notably, the annular resonator  103  disposed over the membrane layer  102  is merely illustrative, and use of other resonator structures disposed over the membrane layer  102  of the micromachined structure are contemplated. 
     In another representative embodiment, the opening  108  is foregone. In this embodiment, the annular resonator  103  is provided over the cavity  107 . In this case the acoustic waves are incident on and radiated away from the front surface of the membrane layer  102 . 
     The cavity  107  spans a distance d 1  as shown in  FIG. 1 . This distance creates the boundary conditions for the equations of motion of the membrane layer  102 ; with the ends of the cavity  107  defined by the distance d 1  and thereby the active region of the membrane  102 . As should be appreciated by one of ordinary skill in the art. the fundamental flexure mode is determined in part by the distance d 1 . Accordingly, the present teachings beneficially contemplate forming the dimension d 1  and the dimensions of the cavity  107  generally with precision to provide a particular fundamental flexure mode in the membrane, and thereby a desired fundamental frequency of operation. 
     In a representative embodiment, the areal shape of the cavity  107  and thus the membrane is circular, and thus the dimension d 1  is a diameter. This is merely illustrative, and the membrane may be of other areal shapes including a square, or an ellipse. Notably, the areal shape of the annular resonator  103  may be substantially the same as that of the cavity  107 , or of a different annular shape than that of the cavity  107 . In either case, the annular resonator  103  is disposed over the membrane layer  102  and the cavity  107 . The opening  108  spans a distance d 2 , and comprises an areal shape that may be substantially same as to that of the cavity  107  or may be different than the areal shape of the cavity  107 . The distance d 2  is less than or equal to the distance d 1 , as the areal dimensions of the opening  108  cannot be greater than the areal dimensions of the cavity. To this end, as described below fabrication of the cavity  107  is comparatively precise and reproducible so that a membrane of a desired fundamental flexure mode can be realized in a repeatable manner. By contrast, the opening  108  is fabricated by less precise methods and, as such, if the areal dimension of opening  108  is greater than that of the cavity  107 , the precision of the membrane is controlled by the fabrication of the opening  108  and not the cavity. As such, the precision and reproducibility of the membrane is compromised. Notably, a known etching technique, the Bosch etching method, may be used to etch the opening  108 . If cavity  107  were not present, cavity  108  then would define d 1 . Using the Bosch method alone to form the opening  108  without the cavity  107 , there would be comparatively high uncertainty in the dimension d 1 . For a typical process, this would be greater than 10 μm. However, by etching the cavity  107  as described above, and then etching the opening  108 , d 1  can be fabricated with a precision of 1 μm or less, or approximately ten times more precisely than use of the Bosch method alone. 
     The annular resonator  103  disposed over the cavity  107  includes characteristics of a film bulk acoustic resonator (FBAR), such as described in patents and patent publications referenced below. While one resonator stack (i.e., first electrode  104 , the piezoelectric layer  105  and the second electrode  106 ) is shown, more than one resonator stack is contemplated. For example, another resonator stack comprising the first and second electrodes  104 ,  106  and the piezoelectric layer  103  may be provided over the resonator stack shown in  FIG. 1 . This structure has similar characteristics as a stack bulk acoustic resonator (SBAR). The SBAR is fabricated by repeating the fabrication sequence of the resonator stack after forming the resonator stack shown in  FIG. 1 , and before removing sacrificial material as discussed below. 
       FIGS. 2A-2F  shows cross-sectional views of a fabrication sequence in accordance with a representative embodiment. Methods, materials and structures of the PMT  100  may be as described in commonly owned U.S. Patent Application Publications: 20080122320 and 20080122317 to Fazzio, et al.; 20070205850 to Jamneala, et al.; 20080258842 to Ruby, et al.; and 20060103492 to Feng, et al.; and may be as described in 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.; 6,828,713 to Bradley, et. al. The disclosures of these patents and patent application publications are specifically incorporated herein by reference. Notably, the teachings of these patents and patent publications is intended to be illustrative of methods, materials and structures useful to the present teachings, but in no way limiting to the present teachings. 
       FIG. 2A  shows the substrate  101  having the cavity  107  formed therein by a known method. In a representative embodiment, the substrate  101  comprises silicon, and the cavity  107  is formed by a known wet etching or dry etching techniques. Additional details of the method of fabricating the cavity  107  are described in the incorporated patents and patent publications. Regardless of the method selected for fabricating the cavity  107 , the degree of precision in the dimensions of the cavity  107  and its reproducibility in large scale allows the setting of and consistency of the resonant frequency of the PMT  100 . 
       FIG. 2B  shows the substrate  101 , having the cavity  107  substantially filled with a sacrificial material  201 . As described in the incorporated patents and patent publications, the sacrificial material is illustratively silicon dioxide (SiO 2 ) or phosphosilicate glass (PSG) formed using a known deposition or growth method. After the sacrificial layer  201  is provided in the cavity  107 , a polishing step, such as chemical mechanical polishing (CMP) is performed so that a surface  202  of the sacrificial layer  201  is substantially flush with a surface  203  of the substrate  101 .  FIG. 2C  shows the substrate  101  after the forming of the membrane layer  102 . In accordance with a representative embodiment, the membrane layer  102  comprises boron doped SiO 2  commonly referred to as borosilicate glass (BSG). In other representative embodiments, the membrane layer  102  comprises one of polysilicon (poly-Si), or silicon nitride (Si 3 N 4 ) or silicon carbide (SiC). These materials are merely illustrative, and other materials are contemplated for use as the membrane layer  102 . Notably, the material selected for the membrane  102  should be reproducibly fabricated with consistent desired material properties such as film stress and thickness in an array of PMTs  100  or across a wafer in large-scale fabrication). Accordingly, to realize sufficient accuracy in the resonant frequency, and reproducibility from one transducer (PMT) to the next in fabrication, it is important to control the thickness of the membrane layer  102  and the film stress of the membrane layer  102 . In choosing the material, other parameters of interest are stiffness. robustness, environmental compatibility. Illustratively, a layer of BSG having a thickness in the range of approximately 0.1 μm to approximately 20.0 μm may be used for the membrane layer  102 . 
     Regardless of the material selected for the membrane layer  102 , formation of this layer is effected by a known method and with considerations for other processes used in the fabrication of the PMT  100 . 
       FIG. 2D  shows the substrate  101  after the forming of a first conductive layer  204 , a piezoelectric layer  205  and a second conductive layer  206  are provided over the membrane layer  102 . These layers are formed using known methods and materials, such as described in one or more the incorporated U.S. patents and Patent Publications, and are not repeated so as to avoid obscuring the description of the present embodiments. 
       FIG. 2F  shows the substrate  101  after the patterning and etching of the first conductive layer  204 , the piezoelectric layer  205  and the second conductive layer  206  to provide the annular resonator  103  comprising the first electrode  104 , the piezoelectric layer  105  and the second electrode  106  over the membrane layer  102 . As described in connection with the embodiment of  FIG. 1 , the annular resonator  103  may be circular in areal shape, or may be square in areal shape, or may be other than circular or square in areal shape. Regardless of the areal shape of the annular resonator  103 , the fabrication of the first electrode  104 , the second electrode  106  and the piezoelectric layer  105  illustratively may be effected according to the teachings of U.S. Patent Application Publications: 20080122320 and 20080122317 to Fazzio, et al. 
       FIG. 2F  shows the substrate  101  after etching to form the opening  108 . The etching of the substrate to form the opening  108  is illustratively effected by deep reactive ion etching (DRIE), or the so-called Bosch Method. Alternatively a wet etch commensurate for use with the remaining materials shown in  FIG. 2E  may be used to provide the opening  108 . After completion of the formation of the opening  108 . the sacrificial layer  201  is removed according to a known method, for example as described in one or more of the incorporated above. After the removal of the sacrificial layer, the PMT  100  shown in  FIG. 1  is realized. 
       FIG. 3  shows a PMT  300  in cross-section in accordance with a representative. Many of the features, materials and methods of fabricating the PMT  300  are common to those above provided in connection with the embodiments of  FIGS. 1-2F . Generally, common details are not repeated to avoid obscuring the description of the presently described embodiments. 
     The PMT  300  comprises the substrate  101  substrate  101 , the membrane layer  102  and the annular resonator  103 . The annular resonator  103  comprises the first electrode  104  disposed over the membrane layer  102 , the piezoelectric layer  105  and the second electrode  105 . 
     The PMT  300  also comprises the cavity  107  formed in the substrate  101 . The PMT  300  does not comprise the opening  108 . Notably, the PMT  300  is designed so that mechanical waves are transmitted to or received from a side  301 , which is the side of the PMT  300  opposing a backside surface  302  of the substrate  101 . In order to facilitate a flexure mode of a suitable amplitude in the membrane layer  102 , a vent  303  is provided to foster pressure equalization between the pressures on each side of the membrane layer  102 . Thus, the vent  303  promotes equal pressure in the cavity  107  as in the ambient region of the PMT  300 . 
     Application of a time-dependent voltage to the annular resonator  103  causes a mechanical wave to be launched through the annular resonator  103  and the membrane layer  102 . As the piezoelectric layer  105  oscillates in response to a mechanical perturbation (e.g., a sound wave), the forces generated by the perturbation induce stresses in the piezoelectric layer resulting in generation of a voltage difference across the electrodes  104 ,  106 . Assuming the layer  105  of piezoelectric material (e.g., AlN, ZnO or lead zirconium titanate (PZT)) has a c-axis substantially orthogonal to the membrane surface (parallel to x in the coordinate system shown), the voltage sensitivity is proportional to the lateral stress, σ y , and the ratio of the piezoelectric strain matrix coefficient (d 31 ) and the electric permittivity coefficient (ε 33 ). Beneficially, the mechanical wave creates a flexure mode to be launched in the membrane layer  102 . Mechanical waves launched from or incident on the membrane layer travel from side  301 . The cavity  107  spans a distance d 1  as shown in  FIG. 3 , and comprises the active area of the membrane of the PMT  300 . Similarly, in a receiving mode, mechanical waves incident on an annular resonator are converted into flexural modes in the layer  105  and to time-dependent voltages due to the piezoelectric affect. Receiver electronics (not shown) then process the voltage signals. 
       FIG. 4A  shows in cross-section the substrate  101  comprising the cavity  107  filled with the sacrificial layer  201 . The CMP step described above has been completed, and the membrane layer  102  has been provided over the substrate  101  and sacrificial layer  201 .  FIG. 4B  shows in cross-section the substrate  101  comprising the cavity  107  filled with the sacrificial layer  201 , after forming of the vent  303 . The vent  303  is formed by a known patterning and etching method, and may be fabricated for example as described in U.S. Pat. No. 6,384,697. The vent  303  serves several functions in the PMTs of the representative embodiments. Beneficially, the vent  303  serves to equalize pressure on both sides of the membrane layer  1032 . In the case where opening  107  is sealed during product assembly, the vent  303  provides and controls the low-frequency behavior of the transducer frequency response. The dimensions and placement of the vent  303  are selected to achieve these and other benefits. 
       FIG. 4C  shows a lop view of the substrate  101  comprising the cavity  107  filled with the sacrificial layer  201 , after forming of the vent  303 . where the section line  4 B- 4 B denotes the perspective of  FIG. 4B . Notably,  FIG. 4C  shows the structure before forming of the annular resonator  103 . Also, as shown, the areal dimension of the cavity  107  is substantially square, although this is merely illustrative, and other areal shapes are contemplated. As noted above, the areal shape of the annual resonator  103  may be of the same areal shape or of a different areal shape that the cavity  107 . 
       FIG. 5  shows a cross-sectional view of a PMT  500  in accordance with a representative embodiment. The PMT  500  comprises components and materials common to the representative embodiments described in connection with  FIGS. 1-4C ; and is fabricated by methods described above in connection with these embodiments. Because many of the details of the components, materials and manufacturing methods are common to those described previously, such details are not repeated in order to avoid obscuring the presently described embodiments. 
     The PMT  500  comprises a passivation layer  501 . The passivation layer  501  is provided over a surface of the PMT  100  as shown. Notably, in the representative embodiment, the passivation layer  501  is provided over the membrane  102  and the annular resonator  103 , and about the layers thereof. 
     In representative embodiments, the passivation layer  501  may be SiC or Si 3 N 4  or BSG, and is deposited by a selected known method. Illustratively, the passivation layer  501  has a thickness of approximately 1000 Angstroms to approximately 5000 Angstroms. In accordance with certain representative embodiments, the passivation layer  501  is selected to have a thermal expansion coefficient (T CE ) that substantially matches the thermal expansion coefficient (T CE ) of the membrane layer  102  and the substrate  101 . In certain embodiments, the material selected for the passivation layer  501  is substantially identical to that of the membrane layer  102 . 
     As will be appreciated by one of ordinary skill in the art, 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.