High-performance microelectromechanical systems resonators for timing and frequency reference applications

Abstract

Microelectromechanical systems (MEMS) resonators may potentially replace quartz crystal resonators offering reduced footprint but must meet stringent performance levels. Thin-film piezoelectric on substrate devices have emerged as a viable solution where lower motional resistance has been obtained via a stronger coupling coefficient but the presence of an additional layer results in a lower quality factor (Q). High Q is important to reduce close-to- carrier frequency phase noise in oscillators which is important in timing and frequency reference applications of resonators. The inventors have established designs and methods of improving the Q of low Q MEMS resonator devices through mechanical coupling in tank configuration through optimum mode selection and the appropriate coupling location as well as the extraction of novel modes via acoustic / geometric engineering.

Description

HIGH-PERFORMANCE MICROELECTROMECHANICAL SYSTEMS RESONATORS FOR TIMING AND FREQUENCY REFERENCE APPLICATIONSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This patent application claims the benefit of priority to U.S. Provisional Patent Application 63 / 651,628 filed May 24, 2024.FIELD OF THE INVENTION

[0002] This patent application relates to microelectromechanical systems (MEMS) resonators and more particularly to designs and methods of improving the quality factor ( ) of low Q MEMS resonator devices.BACKGROUND OF THE INVENTION

[0003] Microelectromechanical systems (MEMS) resonators have often been considered the leading candidates to replace legacy quartz crystal resonators to meet the miniaturizing footprint demands of integrated electronics for various applications. However, MEMS resonators must exhibit the stringent performance levels achieved by high-performance crystal resonators. The two main categories of MEMS resonators have their merits as well as shortcomings. Capacitive resonators have already matched quality factors ( ) of piezoelectric quartz crystals yet the high motional resistance (7?m) along with issues of non-linearity pose obstacles. On the flip side, piezoelectric MEMS resonators exhibit low Rmbut cannot compare in Q values. Thin-film piezoelectric on substrate (TPoS) devices have emerged as a viable option to counter the shortcomings of the two transduction mechanisms. However, while a lower Rmhas been obtained via a stronger coupling coefficient (k^ ), the presence of an additional layer has resulted in a lower 0 in comparison to a single-crystal silicon (SCS) resonator, see for example Hung et al. “ 9-boosted AIN array-composite resonator with (?>10,000” (2010 Int. Electron Devices Meeting, IEEE, p. 7.3.1-7.3.4. doi: 10.1109 / IEDM.2010.5703315). A high Q is important to reduce the close-to-carrier frequency phase noise in oscillators. Hence, for timing and frequency reference applications, a high- quality factor becomes indispensable.

[0004] Accordingly, the inventors have established designs and methods of improving the Q of low Q MEMS resonator devices through mechanical coupling in tank configuration through optimum mode selection and the appropriate coupling location.

[0005] Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures.SUMMARY OF THE INVENTION

[0006] It is an object of the present invention to mitigate limitations in the prior art relating to microelectromechanical systems (MEMS) resonators and more particularly to designs and methods of improving the -Q- of low Q MEMS resonator devices.

[0007] In accordance with an embodiment of the invention there is provided a method of providing a resonator comprising: providing a membrane element suspended above a substrate supporting a piezoelectric layer which when electrically driven excites the membrane element to operate as a bulk acoustic wave resonator in a Button-like mode; providing a plurality of acoustic reflectors comprising a number of subsets of the plurality of acoustic reflectors where each subset of the plurality of acoustic reflectors is coupled at a predetermined point around the periphery of the membrane element via a coupling beam; and providing a plurality of anchors where each anchor of the plurality of anchors is coupled at one end to a predetermined point around the periphery of the membrane element and at another distal end to the substrate; wherein each acoustic reflector is suspended above the substrate.

[0008] In accordance with an embodiment of the invention there is provided a resonator comprising: a membrane element suspended above a substrate supporting a piezoelectric layer which when electrically driven excites the membrane element to operate as a bulk acoustic wave resonator in a predetermined Button-like mode; a plurality of acoustic reflectors comprising a number of subsets of the plurality of acoustic reflectors where each subset of the plurality of acoustic reflectors is coupled at a predetermined point around the periphery of the membrane element via a coupling beam; and a plurality of anchors where each anchor of the plurality of anchors is coupled at one end to a predetermined point around the periphery of the membrane element and at another distal end to the substrate; whereineach acoustic reflector is suspended above the substrate.

[0009] Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures.BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Embodiments of the present invention will now be described, by way of example only, with reference to the attached Figures, wherein:

[0011] Figure 1 depicts a three-dimensional representation of the stack of structural layers of a proposed thin-film piezoelectric on substrate (TPoS) resonator according to an embodiment of the invention operating in a 4-port differential transduction scheme;

[0012] Figure 2 differential operating modes of a TPoS resonator according to an embodiment of the invention depicts a strain profile for a higher wineglass (HWG) tank operating mode coupled to 4 breathing modes indicating the acoustic strain energy reflection towards central tank and a strain profile for a Button-like (BL) operating mode coupled to 4 shear modes;

[0013] Figure 3 depicts a process flow for a fabrication process of a tank mode resonator according to an embodiment of the invention using the commercial PiezoMUMPSs process;

[0014] Figure 4 depicts a micrograph of a fabricated resonator according to an embodiment of the invention with critical dimensions and differential polarities labelled;

[0015] Figure 5 depicts measured S21 curves with the electrical parameters extracted through curve fitting, along with the displacement profiles inset for a standalone HWG device and a standalone BL device;

[0016] Figure 6 measured S21 plots with the electrical parameters extracted through curve fitting, along with the displacement profiles for the HWG tank with breathing modes coupled at the zero displacement points, resulting in weak movement for the single crystal silicon (SCS) structures, and the BL tank with the shear modes coupled at high displacement points for optimal energy sharing and higher unloaded quality factor;

[0017] Figure 7 depicts a plot of the variation in unloaded quality factor of a BL Shear coupled mode resonator according to an embodiment of the invention as a function of ambient pressure;

[0018] Figure 8A depicts test structures for inventive Button-like and wine glass mode resonators according to embodiments of the invention with full and partial aluminum nitride (AIN) layers designed to operate in saddle mode for enhanced the frequency tuning of the device;

[0019] Figure 8B depicts a test structure comprising an array of bulk acoustic wave (BAW) resonators to reduce motional resistance according to an embodiment of the invention;

[0020] Figure 8C depicts measured S21 performance for a discrete button-like (BL) mode resonator according to an embodiment of the invention and a BL-mode resonator array according to an embodiment of the invention showing enhanced peak strength for the array relative to the discrete resonator under ambient air conditions;

[0021] Figure 8D depicts measured S21 performance for a BL-mode resonator array according to an embodiment of the invention at various input power levels indicating linear resonator performance and stable quality factor with varying input power;

[0022] Figure 9 depicts test structures for varying coupling of the BAW resonators according to embodiments of the invention for quantifying the quality factor;

[0023] Figure 10 depicts test structures for tuning BAW resonators according to embodiments of the invention to adjust temperature coefficient of frequency;

[0024] Figure 11 depicts designs of BAW resonators according to embodiments of the invention for manufacturing upon the MIDIS Teledyne process flow which provides vacuum packaging at the wafer level;

[0025] Figure 12A depicts designs for BAW resonators according to embodiments of the invention with reduced motional resistance for improved quality factor together with a reference BAW resonator design;

[0026] Figure 12B depicts strain profiles for the BAW resonator designs depicted Figure 12A;

[0027] Figure 13 depicts designs for arrays of BAW resonators according to embodiments of the invention with reduced motional resistance for improved quality factor;

[0028] Figure 14 depicts designs for BAW resonators according to embodiments of the invention with high quality factor for high frequency operation;

[0029] Figure 15 depicts designs for BAW resonators according to embodiments of the invention with rectangular acoustic reflectors;

[0030] Figure 16 depicts a BAW resonator according to an embodiment of the invention wherein enhanced frequency tuning is achieved by disposing the piezoelectric layer upon the coupled resonators rather than the central disk; and\

[0031] Figure 17 depicts a BAW resonator according to an embodiment of the invention wherein geometric engineering of a length-extensional structure provides an acoustically engineered dumbbell resonant mode;

[0032] Figure 18 depicts a BAW resonator employing an array of BAW resonator structures as depicted in Figure 17 according to an embodiment of the invention;

[0033] Figure 19 depicts high frequency resonant mode operation of the BAW resonator structure depicted in Figure 18;

[0034] Figure 20 depicts BAW resonator designs according to embodiments of the invention providing planar actuated pseudo-Lame resonators with varying electrode structures and coupled breathing mode discs;

[0035] Figure 21 depicts a BAW resonator design according to an embodiment of the invention providing a planar actuated pseudo-Lame resonator with piezoelectric excitation;

[0036] Figure 22 depicts tank mode BAW resonators according to embodiments of the invention with holes within the appended discs to the central resonator for temperature coefficient of frequency reduction; and

[0037] Figure 23 depicts a tank mode BAW resonator according to an embodiment of the invention with a hole within the central resonator for temperature coefficient of frequency reduction.DETAILED DESCRIPTION

[0038] The present invention is directed to microelectromechanical systems (MEMS) resonators and more particularly to designs and methods of improving the quality factor ( ) of low Q MEMS resonator devices.

[0039] The ensuing description provides representative embodiment(s) only, and is not intended to limit the scope, applicability or configuration of the disclosure. Rather, the ensuing description of the embodiment(s) will provide those skilled in the art with an enabling description for implementing an embodiment or embodiments of the invention. It would be understood by one of skill in the art that various changes can be made in the function and arrangement of elements without departing from the scope of the invention as set forth in the claims. Accordingly, an embodiment is an example or implementation of the inventions and not the sole implementation. Various appearances of “one embodiment,” “an embodiment” or “some embodiments” do not necessarily all refer to the same embodiments. Although various features of the invention may be described in the context of a single embodiment, the features may also be provided separately or in any suitable combination. Conversely, although the invention may be described herein in the context of separate embodiments for clarity, the invention can also be implemented in a single embodiment or any combination of embodiments.

[0040] Reference in the specification to “one embodiment,” “an embodiment,” “some embodiments” or “other embodiments” means that a particular feature, structure, or characteristic described in connection with the embodiments is included in at least one embodiment, but not necessarily all embodiments, of the invention. The phraseology and terminology employed herein is not to be construed as limiting but is for descriptive purposes only. It is to be understood that where the claims or specification refer to “a” or “an” element, such reference is not to be construed as there being only one of that element. It is to be understood that where the specification states that a component feature, structure, or characteristic “may,” “might,” “can” or “could” be included, that particular component, feature, structure, or characteristic is not required to be included.

[0041] Reference to terms such as “left,” “right,” “top,” “bottom”, “front” and “back” are intended for use in respect to the orientation of the particular feature, structure, or element within the figures depicting embodiments of the invention. It would be evident that such directional terminology with respect to the actual use of a device has no specific meaning as the device can be employed in a multiplicity of orientations by the user or users.

[0042] Reference to terms “including,” “comprising,” “consisting” and grammatical variants thereof do not preclude the addition of one or more components, features, steps, integers or groups thereof and that the terms are not to be construed as specifying components, features, steps or integers. Likewise, the phrase “consisting essentially of,” and grammatical variants thereof, when used herein is not to be construed as excluding additional components, steps, features integers or groups thereof but rather that the additional features, integers, steps, components or groups thereof do not materially alter the basic and novel characteristics of the claimed composition, device or method. If the specification or claims refer to “an additional” element, that does not preclude there being more than one of the additional elements.

[0043] A “piezoelectric” material as used herein may refer to, but is not limited to, aluminum nitride (AIN), zinc oxide (ZnO) or lead zirconate titanate (PZT, Pb[ZrTil-X]O3) for example, is deposited onto one or more surfaces of a free element (i.e. moveable part). Other piezoelectric materials may include, but not be limited to, piezoelectric ceramics (piezoceramics), lead free piezoceramics, Group III-V semiconductors, Group II-VI semiconductors, and polymers such as polyvinylidene fluoride (PVDF) and its copolymers, polyamides, Parylene-C together with non-crystalline polymers such as polyimide and polyvinylidene chloride (PVDC).

[0044] Within the embodiments of the invention a resonant element is described and depicted, e.g. Central Disk 110 in Figure 1 for example, which is formed by a membrane suspendedabove a substrate. Due to the geometric variances of the resonant element whilst this may be described by different names / titles within the following description this element is referred to as a “membrane element” within the claims to encompass the geometric variances described and depicted.

[0045] Microelectromechanical systems (MEMS) resonators have often been considered the leading candidates to replace legacy quartz crystal resonators to meet the miniaturizing footprint demands of integrated electronics for various applications. However, MEMS resonators must exhibit the stringent performance levels achieved by high-performance crystal resonators. The two main categories of MEMS resonators have their merits as well as shortcomings. Capacitive resonators have already matched quality factors ( ) of piezoelectric quartz crystals yet the high motional resistance (7?m) along with issues of non-linearity pose obstacles. On the flip side, piezoelectric MEMS resonators exhibit low Rmbut cannot compare in Q values. Thin-film piezoelectric on substrate (TPoS) MEMS devices have emerged as a viable option to counter the shortcomings of the two transduction mechanisms. However, while a lower Rmhas been obtained via a stronger coupling coefficient (k ), the presence of an additional layer has resulted in a lower 0 in comparison to a single-crystal silicon (SCS) resonator, see Hung et al. “ ^-boosted AIN array-composite resonator with (?>10,000” (2010 Int. Electron Devices Meeting, IEEE, p. 7.3.1-7.3.4. doi: 10.1109 / IEDM.2010.5703315). A high Q is important to reduce the close-to-carrier frequency phase noise in oscillators. Hence, for timing and frequency reference applications, a high-quality factor becomes indispensable.

[0046] Research efforts to enhance the low Q of TPoS resonators include mechanically coupled arrays of TPoS resonators with electrode-less structures to boost the energy storage of the overall resonator. Further, mechanical coupling of traditionally high Q exhibiting Lame modes with a piezoelectrically transduced length extensional (LE) mode achieved significant improvements in quality factors. Similarly, the extension of this concept in 2-D arrays of Lame modes achieved increased frequency -quality factor product f. Q values for TPoS resonators.

[0047] The inventors within the following specification describe an approach for enhanced mechanical coupling to achieve improved Q factor. The device constitutes a piezoelectrically driven silicon resonator mechanically attached to single crystal silicon (SCS) structures in a tank topology. In contrast to the prior art approaches the inventive designs presented herein employ non-conventional modes that are optimized for a tank configuration targeting Q- boosting. Finite element simulations were performed to further explore the technique where two different mode configurations were compared. Low-cost commercial fabricationtechnology has been employed to validate the concepts and experimental results presented below validate the design methodology.

[0048] RESONATOR DESIGN

[0049] A 3 -dimensional rendering of a MEMS resonator design according to an embodiment of the invention is shown in Figure 1 wherein a central TPoS Disk 110 (also referred to as the “tank”) is coupled to 4 small single-crystal silicon (SCS) Disks 140 through narrow mechanical Coupling Beams 120. The central TPoS Disk 110 within an embodiment of the invention comprises a 10-micron silicon Device Layer 150, on top of which a thin 0.5 pm aluminum nitride (AIN) layer has been deposited which is further layered with aluminum acting as the top electrode which is coupled via traces on Anchor Beams 130 to Electrodes 160. The piezoelectric thin film and the metal electrodes are arranged in a fan-like 4-port layout for a fully differential transduction mechanism. Thus, the central TPoS Disk 110 has a differential strain profile which aids in nullifying the feed-through capacitance resulting in a stronger output signal. Within an embodiment of the invention the TPoS Disk 110 is mechanically coupled to 4 SCS Disks 140 along the <100> crystallographic axes.

[0050] In order to test the validity of the / -enhancement methodology as well as to outline critical design aspects the inventors analyzed two different mode pairs as depicted in Figure 2. Eigenfrequency simulations have been performed in COMSOL Multiphysics to obtain the mode shapes which are essential to determine the electrode placements for optimum mode extraction. Mode-I has a higher wineglass (HWG) mode as the tank mode and is attached to four breathing modes as can be seen by the strain profile depicted in first Image 200A in Figure 2. Mode-II is shown by the strain profile in second Image 200B in Figure 2 is where, whereas a “button like” BL mode is evident in the central tank appended to four disks vibrating in the shear mode. Areas of tensile and compressive strains on the respective modes have been indicated along with the nodal points for anchoring. The specific mode shapes have been obtained by appropriate selection of the disk diameters obtained through frequency matching. Figure 2 also visually depicts the quality factor enhancement methodology, in which the 4 SCS disks (SCS Disks 140 in Figure 1) act as acoustic reflecting structures to minimize strain energy dissipation from the central tank. The concept of strain energy dissipation has been demonstrated in the prior art for anchor loss mitigation, see for example Harrington et al. “Inplane acoustic reflectors for reducing effective anchor loss in lateral-extensional MEMS resonators” (J. Micromech. Microeng., vol. 21, no. 8, p. 085021, Jul. 2011, doi: 10.1088 / 0960- 1317 / 21 / 8 / 085021), where cavities in the substrates forced an impedance mismatching to minimize strain transference from the anchoring tethers. However, within embodiments of theinvention, the SCS Disks 140 provide physical vibrating structures which are employed as acoustic reflecting structures to minimize strain energy dissipation from the central TPoS Disk 110.

[0051] This performance improvement technique of exploiting SCS Disks 140 as acoustic reflecting structures to minimize strain energy dissipation from the central TPoS Disk 110 also dictates the mode appropriation for the device. While the central tank resonance mode has been chosen to be differential to improve the electromechanical signal strength which brings down overall motional impedance of the resonator (TPoS Disk 110), the mode shapes of the appended SCS disks (SCS Disks 140) impose another criterion. Contrary to prior resonator research where low anchor loss modes are preferred, the four appended disks (SCS Disks 140) should exhibit higher tether loss so that this energy is transferred back to the central tank (TPoS Disk 110) via the Coupling Beams 120. To quantitatively define this design objective, a ratio T between the strain energy in the coupling beam, Coupling Beam 120, Ucpirto the strain energy of the resonator disk, TPoS Disk 110, Uresis defined by Equation (1).F UCpir / Ures(1)

[0052] Using COMSOL Multiphysics, the strain energies Ucptrand Uresare obtained through the volume integration function. The calculated energy ratios for the breathing and the shear modes are tabulated in Table 1. This predicts that the shear mode reflects higher acoustic energy resulting in a higher Q enhancement potential for the Mode-II.Table 1: Simulated T Values for Breathing and Shear Modes as a Measure of Strain Energy Reflection (A = 1 x 10“4)

[0053] FABRICATION

[0054] In order to demonstrate the benefit of the inventive design methodology the inventors employed a low-cost commercial technology, PiezoMUMPs from Science (see for example Cowen et al. “PiezoMUMPs Design Handbook” MEMSCAP Inc, vol. 1, 2014), to fabricate the devices described in this work. This employs a 5-mask fabrication process starting with a silicon-on-insulator (SOI) wafer of 150 mm as shown in first Image 300A in Figure 3. The top layer is n-doped through phospho-silicate glass (PSG) for enhancing electrical conductivity. Thermally grown oxide is deposited and patterned as shown in second Image 300B in Figure 3 to prevent electrical contacts in areas without aluminum nitride (AIN). The AIN is then RFsputtered followed by deposition, patterning and etching as depicted in third Image 300C in Figure 3. A metal stack of 20 nm chrome and 1 fim aluminum form the top conducting layer. The resulting electrodes are layered through a lift -off process to form electrical pathways and bond pads as shown in fourth Image 300D in Figure 3. Lithographical etching of the silicon is performed in the next step using deep-reactive ion etching (DRIE) to form the structural components of the TPoS and SCS structures as depicted in fifth Image 300E in Figure 3. Thereafter, the frontside of the substrate is covered with a protective coating for the bottom side DRIE release of the structure as depicted in sixth Image 300F in Figure 3. Finally, the protective coatings are dry plasma etched to form the final released structure.

[0055] A micrograph of the proposed design as fabricated through this process is shown in Figure 4 where the TPoS disk (TPoS Disk 110 in Figure 1) has a diameter of 460 fim and the SCS disks (SCS Disks 140 in Figure 1) have a dimeter of 158 / rm. The differential transduction scheme is also depicted to obtain the desired mode while suppressing unwanted motion. Accordingly the Positive and Negative Drive Electrodes 410A and 410B and Positive and Negative Sense Electrodes 420A and 420B together with the Ground Contacts 430 are identified in Figure 4. Critical dimensions include the diameters of the central TPoS tank (TPoS Disk 110 in Figure 1) and the non-transducing SCS disks (SCS Disks 140 in Figure 1). The inset shows the width of the anchors (Anchor Beams 130 in Figure 1) as 16 fim which is the lowest thickness limit for metal-piezoelectric on silicon stack accessible in the PiezoMUMPSs process employed. To determine the efficacy of the Q enhancement, a standalone disk was also fabricated without the non-transducing SCS structures.

[0056] MEASUREMENTS

[0057] A vector network analyzer (VNA) was utilized to obtain frequency domain characterization of the fabricated devices. Devices were actuated in both ambient air and partial vacuum conditions at 90 mTorr. As the VNA employed was a 2-port device, signal splitters were employed for differential transduction. To extract the electrical lumped parameters, a modified equivalent circuit modeling technique was used to curve fit the measured signal with the equations presented by Ah et al. in “Piezoelectric-on-Silicon Square Wine-Glass Mode Resonator for Enhanced Electrical Characterization in Water” (IEEE Trans. Electron Devices, vol. 65, no. 5, pp. 1925-1931, May 2018, doi: 10.1109 / TED.2018.2810700).

[0058] The measured S21 magnitude for the standalone HWG and BL modes is depicted in first and second Images 500A and 500B respectively in Figure 5, along with their displacement profiles plots. The measurements values obtained for the tank mode counterparts have beendepicted in first and second Images 600A and 600B in Figure 6, respectively, along with their displacement profiles. The measured and curve-fitted plots are shown for each device, and the values of interest obtained through the curve fittings are presented in the top-right of each plot. The unloaded quality factor Qulis the mechanical quality factor obtained by removing the influence of electrical loading on the device and is calculated from the loaded quality factor, Qi, the motional resistance, Rm, and the parasitic electrical resistance, Rp, using the following formula given by Equation (2), see Wu et al., “Wafer-Level Vacuum-Packaged High- Performance AlN-on-SOI Piezoelectric Resonator for Sub-100-MHz Oscillator Applications” (IEEE Transactions on Industrial Electronics, vol. 65, no. 4, pp. 3576-3584, Apr. 2018, doi: 10. 1109 / TIE.2017.2748041).

[0059] It should be noted that there is a slight difference in the resonance frequencies between the reference standalone and the tank mode devices, which is due to a slight difference in the central tank radius (200 / rm compared to 230 / rm)., however, as it has been shown in previous work that within the 200-250 fim disk diameter range, the Q remains fairly constant for the HWG and BL modes, see Wu for example, a comparison for Q enhancement remains valid.

[0060] The standalone HWG and BL modes have Quivalues of 2,794 and 4,994 respectively, with the higher strain confinement of the BL mode resulting in less energy dissipation, and consequently less anchor movement thereby resulting in a higher Q. The HWG-Breathing coupled mode has a performance enhancement of 1 ,6X compared to the standalone HWG mode with a Quiof 4,563, whereas the BL-Shear coupled mode has a near 10X improvement in its Qui compared to its standalone counterpart at 46,503. This difference in ^-enhancement was predicted in the design section, where the shear mode due to higher strain energy transference aids in the ?-boosting of the BL mode. However, another major reason can be observed from the displacement plots profiles as the HWG has been coupled at the low displacement points to the breathing modes, resulting in less movement. On the contrary, the BL mode has high displacement coupling with the shear modes, thus improving and increasing energy sharing. This shows that the displacement plot profile along with the strain profile plot are critical for determining the correct coupling point in mechanically coupled devices for achieving Q- enhancement. On the motional resistance front, the HWG-Breathing coupled mode performs better than the BL-Shear coupled mode. The reason for this can be understood from the mode shapes of second Image 200B in Figure 2, where the BL mode has a visibly weaker strain compared to the HWG, resulting in non-optimized mode extraction. This issue can beovercome by tuning the dimension of the central BL tank to improve the strength of the strain. Another possible reason could be that the electrode shapes depicted in Figure 4 are more closely aligned with the HWG strain profde than that of the BL mode. Another reason could be due to the electrode shapes of Figure 4 matching the HWG strain shape more compared to the BL mode.

[0061] The influence of atmospheric pressure on the BL-shear mode was obtained by periodically releasing the pressure within the vacuum chamber, as shown in Figure 7. The resonator mode has high dependence on the ambient pressure, as a Quldrop of 2.5X is observed from 46,503 at 90 mTorr to 19,338 as the pressure is increased to atmospheric pressure. This indicates a higher out of plane motion for the shear mode which results in slide-fdm damping in ambient air conditions. However, this value is still one of the highest reported in ambient air for TPoS resonators.

[0062] The inventors have demonstrated a robust, lithographically defined methodology that significantly enhances the quality factor through a BL-Shear coupled mode resonator, achieving nearly a tenfold Q improvement. As indicated by the comparative performance data presented in Table 2, the BL-Shear coupled mode exhibits one of the highest thickness- normalized unloaded quality factors in ambient air reported. This attribute renders it highly suitable for applications in low-noise oscillators or filters with minimal vacuum packaging requirements thereby simplifying the manufacturing process and providing low cost oscillators. The inventors have also highlighted two major design considerations for enhancing the quality factor through mechanical coupling, namely the choice of mode shape and the location of the couplers. The inventors anticipate that there is potential to further optimize the BL-shear mode for a stronger strain profile, which could lead to a reduction in motional impedance and additional improvements in the quality factorTable 2: Comparison of High-Performance TPoS Resonators according to Embodiment of the Invention with Prior Art TPoS Resonators

[0063] As outlined above silicon MEMS resonators have many advantages in terms of device size, fabrication and vacuum package, however, for piezoelectrically transduced resonators, the short-term frequency stability characterized by the Q of the output signal is still not comparable to quartz or capacitive MEMS resonators. On the other hand, capacitive resonators suffer from insertion loss characterized by a motional resistance which impedes their widespread acceptance for timing and filtering applications. Similarly, the high temperature dependence of resonance frequency is also a major issue for silicon-based MEMS resonators.

[0064] As noted to date the problem of a low-quality factor for piezoelectric resonators has been solved by either increasing the thickness of the silicon device layer, or by reducing dissipation mechanisms such as anchor toss, thermoelastic damping, and air damping. Another way to have a higher-quality factor signal is to use capacitively transduced devices. The high motional resistance of capacitive devices can be overcome by increasing bias voltage, using reduced capacitive gaps and by employing mechanical arrays. Various active and passive methodologies are present for achieving temperature stability such as DC biasing, micro- ovenization, oxide layering or high doping of silicon device layer.

[0065] However, fabrication limitations of commercial technologies limit the maximum thickness for the silicon layer and hence in-house facilities could be required, which is not ideal for high-volume production. Mitigating individual toss mechanisms such as anchor and thermoelastic damping have their limitations in terms of performance enhancement. To reduce air damping, vacuum packaging is employed which can be expensive process thereby increasing the price of the end product. Techniques for reducing motional resistance of capacitive devices are also limited by minimum fabrication tolerances and issues of nonlinearity with increased voltages. Mechanical arrays can be an effective methodology; however, the enhanced degree of freedom can result in spurious peaks in close proximity to the peak of interest. Ovenization for temperature stability could be power expensive, while passive techniques are not either effective for bulk modes at high frequency (in case of oxide layering) or are not available in commercial fabrication facilities (in case of silicon doping technique)

[0066] Accordingly, the inventors have exploited what they refer to as “specialized modes” such as the shear mode mechanically coupled in optimized configurations to improve the performance by energy boosting for quality factor enhancement. For reducing the motional resistance, the mode of transduction has been chosen to be a novel Button-like mode which ishighly strain-confined, resulting in a stronger signal and reduced insertion loss. The Buttonlike mode has also proven to be intrinsically spurious -mode-free, which is highly beneficial for mechanical coupling and arraying in various configurations. Coupling of the Button-like mode with conventional wine-glass modes has also shown remarkable performance values. For temperature compensation, electrostatic tuning is a commercially fabrication-compatible approach. Low bias voltages can be required by using lower stiffness modes such as the proposed saddle mode or by increasing the tuning area by placing the electrodes on top of the resonator.

[0067] Accordingly, the solution described according to embodiments of the invention distinguishes itself in terms of both fabrication facilitation as well as cost reduction. Since the devices according to embodiments of the invention exhibit high-quality factors even in ambient air, there is no expensive vacuum packaging requirement. Secondly, the performance enhancement methodology of MEMS resonators according to embodiments of the invention is lithograph! cally / CAD defined allowing high volume commercial MEMS fabrication facilities to be employed for mass production without requiring any specialized technology or materials. However, the devices are compatible with commercial vacuum-packaging of devices for higher precision requirements whilst temperature stability has been achieved using relatively low voltages.

[0068] Now referring to Figure 8A there are depicted first to third Images 800A to 800C respectively of test structures for inventive Button-like and wine glass mode resonators according to embodiments of the invention with full and partial aluminum nitride (AIN) layers designed to operate in saddle mode for enhanced the frequency tuning of the device together with a test structure comprising an array of bulk acoustic wave (BAW) resonators to reduce motional resistance according to an embodiment of the invention. The test structures by varying full or partial AIN layers vary the Cm / C0ratio of the resonators where Cm is the motional capacitance of the resonator and Co is the nominal capacitance of the transducer. First Image 800A depicts a resonator design with a full AIN layer whilst seconds Image 800B depicts a resonator design with partial AIN layer. The partial AIN design of second Image 800B is depicted in third Image 800C as a test cell with rectangular SCS disks.

[0069] Referring to Figure 8B there is depicted a fourth Image 800D depicts an array of partial AIN layer resonators of unit cell design of second Image 800B in Figure 8A in order to reduce the motional resistance of the resonator. Now referring to Figure 8C there are depicted S21 performance measurement plots for a fabricated discrete button-like (BL) mode resonator according to an embodiment of the invention and a fabricated BL-mode resonator arrayaccording to an embodiment of the invention. From Figure 8C it is event that the array device exhibits an enhanced peak strength and quality factor relative to the discrete resonator. The measurements being performed under ambient air conditions and show a reduced motion impedance Rm of 108 Q for the array versus 822 for the discrete resonator.

[0070] Now referring to Figure 8D there is depicted a plot of measured S21 performance for a BL-mode resonator array according to an embodiment of the invention at various input power levels indicating linear resonator performance and stable quality factor with varying input power. At -10 dBm the peak S21 is -7.02 dB whereas at +10 dBm it is -6.89 dB, a difference of 0.13 dB in measured S21 for a 20 dB input power change. Over this range the quality factor Quireduces from 8,186 at -10 dBm input power to 8,033 at +10 dBm input power, which equates to a 1.9% reduction in quality factor for a 100 times power increase.

[0071] Referring to Figure 9 there are depicted first to third Images 900A to 900C of test structures for varying coupling of the BAW resonators according to embodiments of the invention for quantifying the quality factor. First Image 900A depicts a central TPoS Disk with four SCS Disks such as depicted in Figure 4 with partial AIN layer. Second Image 900B depicts the central TPoS Disk but now each SCS Disk of the four SCS Disks depicted in first Image 900A are replaced with an array of three coupled SCS Disks where the three SCS Disks are coupled to each other and the central SCS Disk of each array is coupled to the central TPoS disk. Within other embodiments of the invention the number of coupled SCS Disks within each array may be 1, 2, 3 or other positive integer. The array of SCS Disks may be coupled to the central TPoS Disk via one beam, such as Coupling Beam 120 depicted in Figure 1 and as depicted in Figure 14, or via multiple beams. Similarly, the SCS Disks within the array may be coupled to a single SCS Disk which is coupled to the central TPoS Disk or they may be coupled to subsets of the array of SCS Disks and then multiple SCS Disks coupled to the central TPoS Disk. Within second Image 900B the array of SCS Disks are disposed within a large common trench of a defined geometry, in this instance rectangular.

[0072] In contrast in third Image 900C depicts a variant of the resonator design depicted in second Image 900B is depicted where, rather than each array of SCS Disks being within a large common trench each SCS Disk is separated from the substrate by only a narrow trench for the larger portion of its periphery except for the region between each pair of SCS Disks.

[0073] Now referring to Figure 10 there are depicted first to third Images 1000A to 1000C of test structures for tuning BAW resonators according to embodiments of the invention to adjust temperature coefficient of frequency. First Image 1000A depicts the central TPoS Disk and four circular SCS Disks wherein tuning is implemented through electrostatic tuning inconjunction with the piezoelectric driving of the resonator. In contrast second and third Images 1000B and 1000C depicts BAW resonators where tuning is implemented through a gap closing technique to adjust the strength of an electrostatic coupling between the gap closing elements and the SCS Disks. The central TPoS disk being piezoelectric driven.

[0074] Within the preceding description MEMS resonators according to embodiments of the invention were described as being designed and fabricated using the PiezoMUMPs process and design rules from Science. However, it would be evident that the designs depicted and presented within this specification of MEMS resonators according to embodiments of the invention may be designed and fabricated using other fabrication process flows and design rules. For example, referring to Figure 11 there are depicted first to third Images 1100A to 1100C of BAW MEMS resonators according to embodiments of the invention designed for manufacturing upon the MEMS Integrated Design for Inertial Sensors (MIDIS™) process flow from Teledyne™ which beneficially provides vacuum packaging at the wafer level. The BAW resonators exploit the best performance BAW resonator designs prototyped according to the designs depicted in Figures 8 to 10 respectively. First Image 1100A depicts a BL-mode central tank resonator with SCS Disks and electrostatic gap closers for tuning. Third Image 1100C depicts a BL-mode central tank resonator with SCS Disks.

[0075] Now referring to Figure 12A there are depicted first to third Images 1200A to 1200C respectively for designs of BAW resonators according to embodiments of the invention with reduced motional resistance for improved quality factor together with a reference BAW resonator design. First Image 1200A depicts a reference BAW resonator design whilst second Image 1200B depicts an acoustically engineered biconvex (AE-BICON) BAW resonator design. Third Image 1200C depicts a Coupled AE-BICON BAW resonator for quality factor enhancement with tuning via the temperature coefficient of frequency (TCF) of the BAW resonator which is given by Equation (3) below where T is the temperature and f is the resonant frequency of the TPoS resonator. The Coupled AE-BICON BAW resonator in third Image 1200C comprising Central Resonator 1210 and a pair of Button-Like Coupled Disk Elements 1220.TCF = l / n / 8f / 8T) (3)

[0076] Referring to Figure 12B there are depicted first to third Images 1200D to 1200F respectively of the strain profiles for the BAW resonator designs depicted Figure 12A. Accordingly, first Image 1200D depicts the strain profile of the reference BAW resonator design depicted in first Image 1200A in Figure 12A showing the conventional width extensionmode of the BAW resonator element. Second Image 1200E depicts the strain profde of the AE- BICON BAW design depicted in second Image 1200B in Figure 12A showing confined strain profile resulting in lower displacement at the ends of the resonator element for reduced anchor losses.

[0077] Third Image 1200F depicts the strain profile of the Coupled AE-BICON BAW design depicted in third Image 1200C in Figure 12A where similarly showing the confined strain profile resulting in lower displacement at the ends of the resonator element for reduced anchor losses. However, the central resonance is now coupled to the pair of Button-Like Coupled Disk Elements 1220 resulting in a high quality factor resonance.

[0078] Referring to Figure 13 there are depicted first to fourth Images 1300A to 1300D for designs of arrays of BAW resonators according to embodiments of the invention with reduced motional resistance for improved quality factor. First Image 1300A depicts an array of 3 coupled BAW resonators with rectangular central TPoS resonators whereas second Image 1300B depicts an array of 3 coupled AE-BICON BAW Resonators with TCF tuning, each AE- BICON BAW resonator being of the design depicted in third Image 1200C in Figure 12A. Third Image 1300C depicts an array of 3 BAW resonators where each BAW resonator comprises a central TPoS disk with four circular disk based acoustic reflector elements. Fourth image 1300D depicts an array of 3 BAW resonators where each BAW resonator comprises a central TPoS disk with four rectangular disk based acoustic reflector elements. In each instance the array of BAW resonators results in devices with high quality factor and low motional resistance.

[0079] Now referring to Figure 14 there are depicted first to fourth Images 1400A to WOOD respectively of BAW resonator designs according to embodiments of the invention with high quality factor for high frequency operation. These being:

[0080] First Image 1400A wherein the BAW resonator comprises a central disk and a four disk acoustic reflector elements disposed equally around the periphery;

[0081] Second Image 1400B wherein the BAW resonator comprises a central disk with four pairs of acoustic reflector elements disposed equally around the periphery where each pair of acoustic reflector elements are disposed linearly away from the central disk;

[0082] Third Image 1400C wherein the BAW resonator comprises a central disk with four triplets of acoustic reflector elements disposed equally around the periphery where each triplet of acoustic reflector elements are disposed linearly orthogonal to an axisdisposed along the central disk through the central acoustic reflector of the triplet of acoustic reflectors; and

[0083] Fourth Image MOOD wherein the BAW resonator comprises a central disk with four sextets of acoustic reflector elements disposed equally around the periphery where each sextet of acoustic reflector elements comprises a first triplet disposed linearly orthogonal to an axis disposed along the central disk through the central acoustic reflector of the triplet of acoustic reflectors and a second triplet parallel to the first triplet further away from the central disk than the first triplet.

[0084] Referring to Figure 15 depicts designs for BAW resonators according to embodiments of the invention with rectangular acoustic reflectors wherein first Image 1500A depicts a design with four acoustic reflectors around the periphery of the central resonator whilst second Image 1500B depicts a design with four triplets of acoustic reflector elements disposed equally around the periphery where each triplet of acoustic reflector elements are disposed linearly orthogonal to an axis disposed along the central disk through the central acoustic reflector of the triplet of acoustic reflectors. Also depicted is third Image 1500C wherein the central disk is coupled to four square acoustic reflectors which now include additional tuning electrodes. The central (tank) resonator employing a piezoelectric layer.

[0085] Now referring to Figure 16 there is depicted a BAW resonator according to an embodiment of the invention wherein enhanced frequency tuning is achieved by disposing the piezoelectric layer upon the coupled resonators rather than the central disk.

[0086] Whilst the acoustic reflector elements depicted within embodiments of the invention presented within Figures 1 to 16 have been circular, rectangular or square it would be evident that other geometries may be employed without departing from the scope of the invention including elliptical geometries, hexagonal geometries, other axially symmetric geometries symmetric along an axis central to the resonator element to the centre of the central disk, etc.

[0087] Referring to Figure 17 there are depicted first and second Images 1700A and 1700B respectively depicting strain and displacement profiles for a BAW resonator according to an embodiment of the invention wherein geometric engineering of a length-extensional structure provides an acoustically engineered dumbbell resonant mode together with a Layout 1700C of the BAW resonator with DC tuning electrodes. The physical layout, Layout 1700C, of an embodiment of the BAW resonator is depicted comprising the Central Resonator 1710, AC excitation metal Electrodes 1720 and Electrostatic Tuning Elements 1730. Geometric engineering of a length-extensional rectangular structure results in a dumbbell-like structure which resonates in a novel shear-length extension coupled mode. The geometrically engineeredresonator provides a higher quality factor by reducing thermoelastic damping through the shear wave characteristic motion in the resonator. The metal Electrodes 1720 provide for piezoelectric excitation whilst the Electrostatic Tuning Elements 1730 provide for temperature compensation and may be replaced with clamping structures within other embodiments of the invention.

[0088] Now referring to Figure 18 there are depicted first and second Images 1800A and 1800B respectively depicting strain and displacement profiles for a BAW resonator according to an embodiment of the invention together with a Layout 1800C of the BAW resonator with DC tuning electrodes. The BAW resonator employs a stacked array of first to third “Dumbbell” Resonator Structures 1810 to 1830 wherein the second “Dumbbell” Resonator Structure 1820 comprises piezoelectric material and metal electrode as depicted by AC excitation metal Electrodes 1720 in Figure 17 and is mechanically coupled by first and second Beams 1840 and 1850 respectively to the first and third “Dumbbell” Resonator Structures 1810 and 1830 where the Beams are at the mid-point of each of the first to third “Dumbbell” Resonator Structures 1810 to 1830.

[0089] The first and second Beams 1840 and 1850 through the central nodal points act to decouple the centrally actuated structure, second “Dumbbell” Resonator Structure 1820, from the substrate. The shear-length extensional mode is transduced within the central region of the second “Dumbbell” Resonator Structure 1820. The piezoelectric excitation metal electrodes may be placed on the whole structure or they may be disposed upon only the central length extensional region for higher overall quality factor. The first and third “Dumbbell” Resonator Structures 1810 and 1830 move in opposite phase to the central second “Dumbbell” Resonator Structure 1820 and act to cancel anchor movements of the central second “Dumbbell” Resonator Structure 1820. These attached structures, first and third “Dumbbell” Resonator Structures 1810 and 1830 are weakly actuated through nA / 2 coupling to reduce thermoelastic damping by reduction in strain strength.

[0090] Whilst an array of 3 “Dumbbell” Resonator Structures is depicted in Figure 18 it would be evident that N “Dumbbell” Resonator Structures may be employed where N is a positive odd integer. The outer “Dumbbell” Resonator Structures may be replaced with other resonator structures to decouple the central “Dumbbell” Resonator Structure from the anchors or act to cancel anchor movements provided that they resonate at the required frequency and opposite phase to the central “Dumbbell” Resonator Structure.

[0091] As depicted in Layout 1800C Electrostatic Tuning Elements 1860 also provided for tuning and may be replaced with clamping structures within other embodiments of theinvention. These Electrostatic Tuning Elements 1860 and AC excitation metal electrodes 1870 provide for tuning both to compensate for the temperature dependent frequency shift of the BAW resonator and fabrication variations. The simulations and measurements performed by the inventors have shown that these resonators provide clean spectra with minimal spurious modes making them suitable for oscillator applications.

[0092] Referring to Figure 19 there is depicted high frequency resonant mode operation of the BAW resonator structure depicted in Figure 18. First and second Images 1900A and 1900B respectively depict strain and displacement profiles for a high frequency mode of oscillation of the BAW resonator depicted in Figure 18. The high-frequency mode has a high quality factor thereby providing a MEMS resonator with high f * Q product, a crucial figure of merit for resonators.

[0093] Now referring to Figure 20 there are depicted BAW resonator designs according to embodiments of the invention providing planar actuated pseudo-Lame resonators with varying electrode structures and coupled breathing mode discs. First Image 2000A depicts a layout of a side anchored rectangular plate resonator with rectangular electrodes whilst second Image 2000B depicts the shear mode displacement profile of the resonator showing higher displacement within the central region with rectangular electrodes. Third and fourth Images 2000C and 2000D depicts another side anchored rectangular plate resonator with rectangular electrodes but with elliptical electrodes. Accordingly, the designs depicted in first and third Images 2000A and 2000C with rectangular and elliptical electrodes depict high shear with low thermoelastic damping. In each instance higher motion occurs within the central portion of the rectangular resonator away from the anchors resulting in reduced anchor loss. The different electrode geometries depicting that anchor loss optimization can be established by appropriate design of the electrodes.

[0094] Fifth Image 2000E depicts a layout of a coupled differential mode BAW resonator wherein four breathing mode discs are disposed in pairs on either side of the rectangular resonator. The resulting shear mode strain profile being depicted in sixth Image 2000F where it is evident that there is high coupling between the higher order pseudo-shear mode of the central rectangular resonator and the coupled breathing mode discs. Whilst an array of 4 coupled breathing mode discs is depicted in Figure 20 it would be evident that N coupled breathing mode discs may be employed where N is a positive even integer.

[0095] Referring to Figure 21 there is depicted a BAW resonator design according to an embodiment of the invention providing a planar actuated pseudo-Lame resonator with piezoelectric excitation. First and second Images 2100A and 2100B depicting the displacementprofile and strain profile respectively for the ladder configuration comprising first to third Resonator Elements 2110 to 2130 respectively where the central second Resonator Element 2120 is coupled to the first and third Resonator Elements 2110 and 2130 via first and second Beams 2140 and 2150 respectively. The first and third Resonator Elements 2110 and 2130 being coupled to the substrate via beams at either end of the first and third Resonator Elements 2110 and 2130. The central Resonator Element 2120 employing three Electrodes 2160(A) to 2160(C) which are disposed along its length as evident in third Image 2100C which depicts a layout of the BAW resonator.

[0096] The BAW resonator depicted in first and second Images 2100A and 2100B resonates in planar Lame modes which are piezoelectrically excited in the non-square geometric structure to yield the low thermoelastic damping resonance associated with the traditional Lame mode. It is known in the prior art that traditional Lame modes are not excitable piezoelectrically in square structures due to strain cancelling, therefore, a net strain is obtained for the Lame mode by the inventors by increasing the aspect ratio of the resonator element and transducing a train of Lame modes. The inventors have established from simulations that improved strain profiles are established when the resonator is anchored at high displacement points allowing Lame modes to piezoelectrically excited and accordingly the main resonator body, second Resonator Element 2120, is coupled with the first and third Resonator Elements 2110 and 2130 to decouple the second Resonator Element 2120 from the substrate, improve strain and reduce anchor losses. Whilst an array of 3 electrodes and excitation regions are depicted in Figure 21 it would be evident that N electrodes may be employed where N is a positive odd integer and preferably N is equal to or greater than 3.

[0097] Now referring to Figure 22 there are depicted first to fifth Images 2200A to 2200E of tank mode BAW resonators according to embodiments of the invention employing holes / openings within coupled resonator elements. In first to third Images 2200A to 2200C the layout, and displacement profiles of two resonating modes, BL-4Shear Mode I and BL-4WG Mode II. The layout in first Image 2200A comprising Central Resonator Element 2210 and four Coupled Resonator Elements 2220 disposed around the periphery of the Central Resonator Element 2210. Disposed within each Coupled Resonator Element 2220 is Circular Opening 2230.

[0098] In contrast fourth and fifth Images 2200D and 2200E depict a layout and BL-4Shear Mode displacement profile of an alternate design embodiment comprising Central Resonator Element 2210 and the four Coupled Resonator Elements 2220 disposed around the periphery of the Central Resonator Element 2210 but now with Square Openings 2240 within eachCoupled Resonator Element 2220. The Square Openings 2240 being rotated such a diagonal of each Square Opening 2240 being aligned radially with the Central Resonator Element 2220.

[0099] The inventors have established that the holes / openings within the Coupled Resonator Elements at different locations on the tank mode provide for reduction of the temperature coefficient of frequency (TCF) of the BAW resonator. As the Central Resonator Element 2220 employs a piezoelectric layer for exciting the resonant mode the holes / openings to modify the TCF are added by the inventors to the appended Coupled Resonator Elements disposed around the Central Resonator Element. As evident within first and fourth Images 2200A and 2200D the mode of resonance can be adjusted by use of a different perforation geometry.

[0100] Referring to Figure 23 there are depicted first and second Images 2300A and 2300B of a tank mode BAW resonator according to an embodiment of the invention with a hole within the central resonator for temperature coefficient of frequency reduction. The BAW resonator in common with the tank mode BAW resonators depicted in Figure 22 comprising a Central Resonator Element 2310 and four Coupled Resonator Elements 2320 disposed around the periphery of the Central Resonator Element 2310. However, in this BAW resonator the tank mode excitation is via piezoelectric layers disposed on each Coupled Resonator Element 2320 and accordingly the TCF reduction is implemented by adding Circular Opening 2330 to the Central Resonator Element such that the piezoelectric transduction is not impacted. First Image 2300A depicts the layout whilst second Image 2300B depicts the displacement profile of a higher order wine glass mode of the Central Resonator Element 2310 coupled to four Breathing Modes within the Coupled Resonator Elements 2320.

[0101] Specific details are given in the above description to provide a thorough understanding of the embodiments. However, it is understood that the embodiments may be practiced without these specific details. For example, circuits may be shown in block diagrams in order not to obscure the embodiments in unnecessary detail. In other instances, well-known circuits, processes, algorithms, structures, and techniques may be shown without unnecessary detail in order to avoid obscuring the embodiments.

[0102] The foregoing disclosure of the exemplary embodiments of the present invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many variations and modifications of the embodiments described herein will be apparent to one of ordinary skill in the art in light of the above disclosure. The scope of the invention is to be defined only by the claims appended hereto, and by their equivalents.

[0103] Further, in describing representative embodiments of the present invention, the specification may have presented the method and / or process of the present invention as a particular sequence of steps. However, to the extent that the method or process does not rely on the particular order of steps set forth herein, the method or process should not be limited to the particular sequence of steps described. As one of ordinary skill in the art would appreciate, other sequences of steps may be possible. Therefore, the particular order of the steps set forth in the specification should not be construed as limitations on the claims. In addition, the claims directed to the method and / or process of the present invention should not be limited to the performance of their steps in the order written, and one skilled in the art can readily appreciate that the sequences may be varied and still remain within the spirit and scope of the present invention.

Claims

CLAIMSWhat is claimed is:

1. A method of providing a resonator comprising: providing a membrane element suspended above a substrate supporting a piezoelectric layer which when electrically driven excites the membrane element to operate as a bulk acoustic wave resonator in a Button-like mode; providing a plurality of acoustic reflectors comprising a number of subsets of the plurality of acoustic reflectors where each subset of the plurality of acoustic reflectors is coupled at a predetermined point around the periphery of the membrane element via a coupling beam; and providing a plurality of anchors where each anchor of the plurality of anchors is coupled at one end to a predetermined point around the periphery of the membrane element and at another distal end to the substrate; wherein each acoustic reflector is suspended above the substrate; and the membrane element has a defined geometry.

2. The method according to claim 1, wherein each subset of the plurality of acoustic reflectors comprises N acoustic reflectors; the subset of the plurality of acoustic reflectors are disposed in sets of M acoustic reflectors where each set of M acoustic reflectors is disposed at a predetermined position away from the centre of the membrane element;N is an integer greater than or equal to 1; andM is an integer greater than or equal to 1.

3. The method according to claim 2, whereinN = 3 and M = 1; each set of M acoustic reflectors is disposed along an axis orthogonal to another axis between a central acoustic reflector of the set of M acoustic reflectors and the center of the membrane element; each outer acoustic reflector of the set of M acoustic reflectors is mechanically coupled to the central acoustic reflector of the set of M acoustic reflectors; and the central beam is coupled to the central coupling beam of the set of M acoustic reflectors.

4. The method according to claim 2, whereinN = 6 and M = 2; each set of M acoustic reflectors is disposed along an axis orthogonal to another axis between a central acoustic reflector of the set of M acoustic reflectors and the center of the membrane element; each outer acoustic reflector of the set of M acoustic reflectors is mechanically coupled to the central acoustic reflector of the set of M acoustic reflectors; and the central beam is coupled to the central coupling beam of each set of M acoustic reflectors.

5. The method according to claim 1, wherein at least one of: each acoustic reflector of the plurality of acoustic reflectors is a single crystal silicon disk of predetermined geometry; and the predetermined geometry of the membrane element is one of circular, elliptical, biconvex, square and rectangular.

6. The method according to claim 1, wherein each acoustic reflector of the plurality of acoustic reflectors is a disk of predetermined geometry; and the predetermined geometry is one of circular, elliptical, biconvex, square and rectangular.

7. The method according to claim 1, further comprising tuning a frequency of operation of the resonator by tuning each another subset of the plurality of acoustic reflectors where the tuning is by one of electrostatic tuning and a gap closer disposed adjacent to each acoustic reflector of the another subset of the plurality of acoustic reflectors.

8. The method according to claim 1, wherein the membrane element resonates in either a higher wineglass (HWG) tank operating mode or a Button-like (BL) operating mode.

9. The method according to claim 1, wherein the resonator is one of an array of resonators;the membrane element of each end resonator of the array of resonators is mechanically coupled to an adjacent resonator of the array of resonators; and the membrane element of each resonator of the array of resonators other than each end resonator of the array of resonators is coupled to one side to another adjacent resonator of the array of resonators and on a second distal side to a further adjacent resonator of the array of resonators.

10. A resonator comprising: a membrane element suspended above a substrate supporting a piezoelectric layer which when electrically driven excites the membrane element to operate as a bulk acoustic wave resonator in a Button-like mode; a plurality of acoustic reflectors comprising a number of subsets of the plurality of acoustic reflectors where each subset of the plurality of acoustic reflectors is coupled at a predetermined point around the periphery of the membrane element via a coupling beam; and a plurality of anchors where each anchor of the plurality of anchors is coupled at one end to a predetermined point around the periphery of the membrane element and at another distal end to the substrate; wherein each acoustic reflector is suspended above the substrate; and the membrane element has a defined geometry.

11. The resonator according to claim 10, wherein each subset of the plurality of acoustic reflectors comprises N acoustic reflectors; the subsets of the plurality of acoustic reflectors are disposed in sets of M acoustic reflectors where each set of M acoustic reflectors is disposed at a predetermined position away from the centre of the membrane element;N is an integer greater than or equal to 1; andM is an integer greater than or equal to 1.

12. The resonator according to claim 11, whereinN = 3 and M = 1; each set of M acoustic reflectors is disposed along an axis orthogonal to another axis between a central acoustic reflector of the set of M acoustic reflectors and the center of the membrane element;each outer acoustic reflector of the set of M acoustic reflectors is mechanically coupled to the central acoustic reflector of the set of M acoustic reflectors; and the central beam is coupled to the central coupling beam of the set of M acoustic reflectors.

13. The resonator according to claim 11, whereinN = 6 and M = 2; each set of M acoustic reflectors is disposed along an axis orthogonal to another axis between a central acoustic reflector of the set of M acoustic reflectors and the center of the membrane element; each outer acoustic reflector of the set of M acoustic reflectors is mechanically coupled to the central acoustic reflector of the set of M acoustic reflectors; and the central beam is coupled to the central coupling beam of each set of M acoustic reflectors.

14. The resonator according to claim 10, wherein at least one of: each acoustic reflector of the plurality of acoustic reflectors is a single crystal silicon disk of predetermined geometry; and the predetermined geometry of the membrane element is one of circular, elliptical, biconvex, square and rectangular.

15. The method according to claim 10, wherein each acoustic reflector of the plurality of acoustic reflectors is a disk of predetermined geometry; and the predetermined geometry is one of circular, elliptical, biconvex, square and rectangular.

16. The resonator according to claim 10, further comprising tuning a frequency of operation of the resonator by tuning each another subset of the plurality of acoustic reflectors where the tuning is by one of electrostatic tuning and a gap closer disposed adjacent to each acoustic reflector of the another subset of the plurality of acoustic reflectors.

17. The resonator according to claim 10, whereinthe membrane element resonates in either a higher wineglass (HWG) tank operating mode or a Button-like (BL) operating mode.

18. The resonator according to claim 10, wherein the resonator is one of an array of resonators; the membrane element of each end resonator of the array of resonators is mechanically coupled to an adjacent resonator of the array of resonators; and the membrane element of each resonator of the array of resonators other than each end resonator of the array of resonators is coupled to one side to another adjacent resonator of the array of resonators and on a second distal side to a further adjacent resonator of the array of resonators.

19. The method according to claim 10, wherein each subset of the plurality of acoustic reflectors comprises a single acoustic reflector; the subsets of the plurality of acoustic reflectors are disposed in a set of four acoustic reflectors where each set of the four acoustic reflectors is disposed at a predetermined position around the periphery of the membrane element; each acoustic reflector comprises a disk with a central opening disposed through the opening of a predetermined profde; and the central opening is one of circular and square where a diagonal of the square is radially aligned with the membrane element.

20. The method according to claim 10, wherein each subset of the plurality of acoustic reflectors comprises a single acoustic reflector; the subsets of the plurality of acoustic reflectors are disposed in a set of four acoustic reflectors where each set of the four acoustic reflectors is disposed at a predetermined position around the periphery of the membrane element; and the membrane element comprises a central circular opening disposed through it.CLAIMSWhat is claimed is:

1. A method of providing a resonator comprising: providing a central disk suspended above a substrate supporting a piezoelectric layer which when electrically driven excites the central disk to operate as a bulk acoustic wave resonator in a Button-like mode; providing a plurality of acoustic reflectors comprising a number of subsets of the plurality of acoustic reflectors where each subset of the plurality of acoustic reflectors is coupled at a predetermined point around the periphery of the central disk via a coupling beam; and providing a plurality of anchors where each anchor of the plurality of anchors is coupled at one end to a predetermined point around the periphery of the central disk and at another distal end to the substrate; wherein each acoustic reflector is suspended above the substrate.

2. The method according to claim 1 , wherein each subset of the plurality of acoustic reflectors comprises N acoustic reflectors; the subset of the plurality of acoustic reflectors are disposed in sets of M acoustic reflectors where each set of M acoustic reflectors is disposed at a predetermined position away from the centre of the central disk;N is an integer greater than or equal to 1; andM is an integer greater than or equal to 1.

3. The method according to claim 2, whereinN = 3 and M = 1; each set of M acoustic reflectors is disposed along an axis orthogonal to another axis between a central acoustic reflector of the set of M acoustic reflectors and the center of the central disk; each outer acoustic reflector of the set of M acoustic reflectors is mechanically coupled to the central acoustic reflector of the set of M acoustic reflectors; and the central beam is coupled to the central coupling beam of the set of M acoustic reflectors.- 24 -4. The method according to claim 2, whereinN = 6 and M = 2; each set of M acoustic reflectors is disposed along an axis orthogonal to another axis between a central acoustic reflector of the set of M acoustic reflectors and the center of the central disk; each outer acoustic reflector of the set of M acoustic reflectors is mechanically coupled to the central acoustic reflector of the set of M acoustic reflectors; and the central beam is coupled to the central coupling beam of each set of M acoustic reflectors.

5. The method according to claim 1, wherein each acoustic reflector of the plurality of acoustic reflectors is a single crystal silicon disk of predetermined geometry.

6. The method according to claim 1 , wherein each acoustic reflector of the plurality of acoustic reflectors is a disk of predetermined geometry; and the predetermined geometry is one of circular, elliptical, biconvex, square and rectangular.

7. The method according to claim 1, further comprising tuning a frequency of operation of the resonator by tuning each another subset of the plurality of acoustic reflectors where the tuning is by one of electrostatic tuning and a gap closer disposed adjacent to each acoustic reflector of the another subset of the plurality of acoustic reflectors.

8. The method according to claim 1, wherein the central disk resonates in either a higher wineglass (HWG) tank operating mode or a Buttonlike (BL) operating mode.

9. The method according to claim 1 , wherein the resonator is one of an array of resonators; the central disk of each end resonator of the array of resonators is mechanically coupled to an adjacent resonator of the array of resonators; and the central disk of each resonator of the array of resonators other than each end resonator of the array of resonators is coupled to one side to another adjacent resonator of the array- 25 -of resonators and on a second distal side to a further adjacent resonator of the array of resonators.

10. A resonator comprising: a central disk suspended above a substrate supporting a piezoelectric layer which when electrically driven excites the central disk to operate as a bulk acoustic wave resonator in a Button-like mode; a plurality of acoustic reflectors comprising a number of subsets of the plurality of acoustic reflectors where each subset of the plurality of acoustic reflectors is coupled at a predetermined point around the periphery of the central disk via a coupling beam; and a plurality of anchors where each anchor of the plurality of anchors is coupled at one end to a predetermined point around the periphery of the central disk and at another distal end to the substrate; wherein each acoustic reflector is suspended above the substrate.

11. The resonator according to claim 10, wherein each subset of the plurality of acoustic reflectors comprises N acoustic reflectors; the subsets of the plurality of acoustic reflectors are disposed in sets of M acoustic reflectors where each set of M acoustic reflectors is disposed at a predetermined position away from the centre of the central disk;N is an integer greater than or equal to 1; andM is an integer greater than or equal to 1.

12. The resonator according to claim 11, whereinN = 3 and M = 1; each set of M acoustic reflectors is disposed along an axis orthogonal to another axis between a central acoustic reflector of the set of M acoustic reflectors and the center of the central disk; each outer acoustic reflector of the set of M acoustic reflectors is mechanically coupled to the central acoustic reflector of the set of M acoustic reflectors; and the central beam is coupled to the central coupling beam of the set of M acoustic reflectors.- 26 -13. The resonator according to claim 11, whereinN = 6 and M = 2; each set of M acoustic reflectors is disposed along an axis orthogonal to another axis between a central acoustic reflector of the set of M acoustic reflectors and the center of the central disk; each outer acoustic reflector of the set of M acoustic reflectors is mechanically coupled to the central acoustic reflector of the set of M acoustic reflectors; and the central beam is coupled to the central coupling beam of each set of M acoustic reflectors.

14. The resonator according to claim 10, wherein each acoustic reflector of the plurality of acoustic reflectors is a single crystal silicon disk of predetermined geometry.

15. The method according to claim 10, wherein each acoustic reflector of the plurality of acoustic reflectors is a disk of predetermined geometry; and the predetermined geometry is one of circular, elliptical, biconvex, square and rectangular.

16. The resonator according to claim 10, further comprising tuning a frequency of operation of the resonator by tuning each another subset of the plurality of acoustic reflectors where the tuning is by one of electrostatic tuning and a gap closer disposed adjacent to each acoustic reflector of the another subset of the plurality of acoustic reflectors.

17. The resonator according to claim 10, wherein the central disk resonates in either a higher wineglass (HWG) tank operating mode or a Buttonlike (BL) operating mode.

18. The resonator according to claim 10, wherein the resonator is one of an array of resonators; the central disk of each end resonator of the array of resonators is mechanically coupled to an adjacent resonator of the array of resonators; and the central disk of each resonator of the array of resonators other than each end resonator of the array of resonators is coupled to one side to another adjacent resonator of the array- 27 -of resonators and on a second distal side to a further adjacent resonator of the array of resonators.

19. The method according to claim 10, wherein each subset of the plurality of acoustic reflectors comprises a single acoustic reflector; the subsets of the plurality of acoustic reflectors are disposed in a set of four acoustic reflectors where each set of the four acoustic reflectors is disposed at a predetermined position around the periphery of the central disk; each acoustic reflector comprises a disk with a central opening disposed through the opening of a predetermined profile; and the central opening is one of circular and square where a diagonal of the square is radially aligned with the central disk.

20. The method according to claim 10, wherein each subset of the plurality of acoustic reflectors comprises a single acoustic reflector; the subsets of the plurality of acoustic reflectors are disposed in a set of four acoustic reflectors where each set of the four acoustic reflectors is disposed at a predetermined position around the periphery of the central disk; and the central disk comprises a central circular opening disposed through it.- 28 -

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