Dual-frequency MEMS resonators having independent transduction mechanisms and methods of fabrication

Abstract

The present disclosure is directed toward MEMS-based resonators and oscillators including a resonator having a unitary resonating element having a first sub-region, a second sub-region, and a decoupler located between them such that it geometrically isolates the first and second sub-regions. The first sub-region supports a first eigenmode that is actuated and sensed via a first transduction mechanism. The second sub-region supports a second, independent eigenmode that is actuated and sensed via a second, different, transduction mechanism. The decoupler mitigates coupling of mechanical energy between the first and second sub-regions such that the sub-regions are substantially vibrationally isolated from one another. In some embodiments, the first sub-region supports an in-plane eigenmode and can be actuated and sensed piezoelectrically, while the second sub-region supports an out-of-plane eigenmode and can be actuated and sensed capacitively.

Description

DUAL-FREQUENCY MEMS RESONATORS HAVING INDEPENDENT TRANSDUCTION MECHANISMS AND METHODS OF FABRICATIONTechnical Field[oooi] The present disclosure relates to microelectromechanical (MEMS) resonators and methods for their fabrication.Background

[0002] The advent of Internet of Things (loT) has given rise to a myriad of sensor-based devices used in wearables, smartphones, and remote sensing for industrial and consumer applications. Ubiquitous in these devices are timing references for keeping track of time, synchronizing events in digital integrated circuits (ICs), and processing signals. High-accuracy MEMS resonators may be desirable for such applications.Summary

[0003] The present disclosure is directed to dual-frequency-output MEMS oscillators and MEMS resonators operative for providing a reference signal having high temperature stability and low phase noise. Embodiments in accordance with the present disclosure can serve as their own temperature reference by providing a first reference signal via piezoelectric transduction and a second reference signal via capacitive transduction. The first reference signal exhibits low frequency drift with changing temperature and low phase noise, which the second reference signal exhibits high output current and a high quality-factor (Q-factor). Embodiments in accordance with the present disclosure are capable of providing highly accurate, stable frequency references with high accuracy, high output current, low power consumption, and low temperature drift.

[0004] Like oscillators and resonators known in the prior art, embodiments in accordance with the present disclosure include a MEMS resonator having in-plane and out-of-plane eigenmodes that are characterized by different temperature coefficients of frequency. Unfortunately, prior-art devices have significant drawbacks, such as high phase noise due to modal coupling, which is exacerbated by exciting both eigenmodes in substantially the same geometric region, as well as using the same transduction mechanism to excite and sense both eigenmodes.

[0005] In sharp contrast to the prior art, a resonator in accordance with the present disclosure has independent in-plane and out-of-plane eigenmodes that aresupported in different, geometrically isolated, vibrationally decoupled sub-regions of the same resonator structure. In addition, one eigenmode is actuated and sensed via a first transduction mechanism, while the other eigenmode is actuated and sensed via a second, different transduction mechanism. As a result, embodiments in accordance with the present disclosure enable simpler device design, improved performance with lower phase noise, and lower cost than can be realized in the prior art.

[0006] An illustrative embodiment is a timing reference including a dualfrequency resonator including a unitary resonating element that is held above an underlying substrate such that the resonating element, and / or portions thereof, can move relative to the substrate. The resonating element includes first and second subregions and a decoupler that is disposed between them. The first sub-region supports an in-plane eigenmode that is actuated and sensed via piezoelectric transduction and a second sub-region supports an out-of-plane eigenmode that is actuated and sensed via capacitive transduction. The first and second sub-regions are geometrically isolated from one another by the decoupler, which can inhibit coupling of mechanical energy between the two sub-regions. As a result, the first and second sub-regions are substantially vibrationally decoupled.

[0007] In an illustrative embodiment the first sub-region includes four piezoelectric members arranged about the decoupler. Each piezoelectric member includes a bar of structural material that is operatively coupled with a piezoelectric transducer to excite and sense an in-plane vibrational mode in its respective bar such that all of the piezoelectric members vibrate at the same frequency. Each bar is held in a clamped-clamped arrangement between the central plate and an anchor that is immovably disposed on an underlying substrate such that its respective piezoelectric member resonates in a quasi-width-extension vibration mode at a first frequency. In some embodiments, the first sub-region includes a different number of piezoelectric members. In some embodiments, the piezoelectric members of the first sub-region resonate in a different in-plane vibrational mode, such as a width-existential mode, a bulk acoustic-wave mode, a surface acoustic-wave mode, and the like.

[0008] In an illustrative embodiment the second sub-region includes four capacitive members arranged about the central plate. Each capacitive member includes a slab of structural material that is part of a capacitive transducer to excite and sense an out-of-plane vibrational mode in the slabs. Each slab is held in a cantilever arrangement that extends from the central plate such that its respective capacitive member resonates in a flexural mode at a second frequency that is significantly lower than the first frequency. In some embodiments, the second sub-region includes a different number ofcapacitive members. In some embodiments, the capacitive members of the second subregion resonate together in a different out-of-plane vibrational mode, such as a thickness extensional mode, a saddle mode, a torsional mode, and the like.

[0009] The first sub-region is both actuated and sensed via piezoelectric transduction and provides a first frequency signal characterized by the first frequency to a measurement circuit. The second sub-region is both actuated and sensed via capacitive transduction and provides a second frequency signal characterized by the second frequency to the measurement circuit.[ooio] The measurement circuit mixes the first and second frequency signals to generate a third frequency signal that is substantially proportional to the temperature of the resonator. In some embodiments, the measurement circuit applies a compensation factor to the first frequency signal and generates a temperature-compensated output frequency signal.

[0011] In some embodiments, the first sub-region includes compensating elements to control the temperature coefficient of frequency of its piezoelectric members.

[0012] In some embodiments, the first sub-region and second sub-region are separated by one or more additional resonator sub-regions that geometrically isolate the first and second sub-regions and mitigate coupling of mechanical energy between them.

[0013] An embodiment in accordance with the present disclosure is a microelectromechanical system (MEMS) device including a resonator disposed on a substrate, the resonator having a unitary resonating element that includes: a first subregion that supports a first eigenmode having a first frequency; a second sub-region that supports a second eigenmode having a second frequency that is different than the first frequency; and a decoupler that is located between the first and second sub-regions, wherein the decoupler geometrically isolates the first and second sub-regions to mitigate coupling of mechanical energy between them, thereby substantially vibrationally decoupling the two sub-regions.

[0014] Another embodiment in accordance with the present disclosure is a method for providing two frequency signals from a MEMS device, the method including : exciting a first eigenmode in a first sub-region of a resonator disposed on a substrate, the resonator having a unitary resonating element that includes: (i) the first sub-region, the first sub-region supporting the first eigenmode such that it has a first frequency; (ii) a second sub-region supporting a second eigenmode having a second frequency that is different than the first frequency; and (iii) a decoupler that geometrically isolates thefirst and second sub-regions such that the coupling of mechanical energy between them is mitigated; sensing the first eigenmode, wherein the first eigenmode is excited and sensed via a first transduction mechanism; exciting and sensing the second eigenmode in the second sub-region via a second transduction mechanism that is different than the first transduction mechanism; providing the first sensed eigenmode as a first frequency signal; and providing the second sensed eigenmode as a second frequency signal.

[0015] Yet another embodiment in accordance with the present disclosure is a method of forming a MEMS device for providing a timing reference, the method including : forming a first cavity in a first substrate; joining a second substrate and the first substrate; thinning the second substrate to define a device layer; forming a piezoelectric transducer on a first sub-region of the device layer; patterning the device layer to form a unitary resonating element that includes the first sub-region, a second sub-region, a decoupler that geometrically isolates the first and second sub-regions, and at least one anchor that mechanically couples the first sub-region and the substrate; forming a plurality of isolation trenches through a portion of a third substrate; forming a second cavity in the third substrate; joining the third substrate and the device layer such that the resonating element is enclosed in a chamber at least partially defined by the first cavity and the second cavity; thinning the third substrate such that the isolation trenches collectively define a plurality of electrically conductive regions that are electrically disconnected from each other, wherein a first electrically conductive region of the plurality thereof is electrically connected to the piezoelectric transducer, and wherein a second electrically conductive region of the plurality thereof defines an electrode of a capacitive transducer that includes the second sub-region; and forming a plurality of contact pads, each contact pad being electrically connected with a different electrically conductive region of the plurality thereof.Brief Description of the Drawings

[0016] FIG. 1 depicts a block diagram of a system for providing a timing reference in accordance with the present disclosure.

[0017] FIG. 2 depicts operations of an exemplary method for providing a timing reference in accordance with the present disclosure.

[0018] FIG. 3 depicts a schematic drawing of a perspective view of a first exemplary resonator in accordance with the present disclosure.

[0019] FIGS. 4A-B depict plots of the induced displacement in sub-regions SRI and SR2, respectively.

[0020] FIG. 5 depicts the temperature drift of resonator 102, as predicted by a finite element method (FEM) simulation.

[0021] FIG. 6 depicts a schematic diagram of a perspective view of a second example of a resonator suitable for use in system 100.

[0022] FIGS. 7A-B depict plots of the induced displacement in sub-regions SRI and SR2 of resonator 600, respectively.

[0023] FIG. 8 depicts the temperature drift of resonator 600, as predicted by a finite element method (FEM) simulation.

[0024] FIG. 9 depicts plot of the response of yet another resonator configuration in accordance with the present disclosure.

[0025] FIG. 10 depicts operations of a method suitable for fabricating a resonator in accordance with the present disclosure.

[0026] FIGS. 11A-F depicts schematic drawings of cross-sectional views of a resonator in accordance with the present disclosure at different stages of fabrication.Detailed Description

[0027] The following merely illustrates the principles of the disclosure. It will thus be appreciated that those skilled in the art will be able to devise various arrangements which, although not explicitly described or shown herein, embody the principles of the disclosure and are included within its spirit and scope.

[0028] Furthermore, all examples and conditional language recited herein are principally intended expressly to be only for pedagogical purposes to aid the reader in understanding the principles of the disclosure and the concepts contributed by the inventor(s) to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions.

[0029] Moreover, all statements herein reciting principles, aspects, and embodiments of the disclosure, as well as specific examples thereof, are intended to encompass both structural and functional equivalents thereof. Additionally, it is intended that such equivalents include both currently known equivalents as well as equivalents developed in the future, i.e., any elements developed that perform the same function, regardless of structure.

[0030] Thus, for example, it will be appreciated by those skilled in the art that any block diagrams herein represent conceptual views of illustrative circuitry embodying the principles of the disclosure. Similarly, it will be appreciated that any flow charts, flowdiagrams, state transition diagrams, pseudo code, and the like represent various processes which may be substantially represented in computer readable medium and so executed by a computer or processor, whether or not such computer or processor is explicitly shown.

[0031] The functions of the various elements shown in the Drawing, including any functional blocks that may be labeled as "processors", may be provided through the use of dedicated hardware as well as hardware capable of executing software in association with appropriate software. When provided by a processor, the functions may be provided by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared. Moreover, explicit use of the term "processor" or "controller" should not be construed to refer exclusively to hardware capable of executing software, and may implicitly include, without limitation, digital signal processor (DSP) hardware, network processor, application specific integrated circuit (ASIC) field programmable gate array (FPGA) read-only memory (ROM) for storing software, random access memory (RAM), and non-volatile storage. Other hardware, conventional and / or custom, may also be included.

[0032] Software modules, or simply modules which are implied to be software, may be represented herein as any combination of flowchart elements or other elements indicating performance of process steps and / or textual description. Such modules may be executed by hardware that is expressly or implicitly shown.

[0033] Unless otherwise explicitly specified herein, the figures including the drawing are not drawn to scale.

[0034] The following terms are defined for use in this Specification, including the appended claims:• resonating element is defined as a unitary structural element that is capable of resonating in at least two independent eigenmodes;• nodal point is defined as a point in an oscillation mode shape that has average amplitude of oscillation that is less than 20% of the maximum amplitude of the oscillation mode shape. The nodal points of a dual-output MEMS device resonating in an out-of-plane mode and an in-plane mode may be different or may be the same;• distributed cross-sectional mode is defined as an eigenmode that is actuated in the cross-section of the device and that contains a propagating series (at least two) of essentially identical modes. Lame (or quasi-Lame), shear (or quasi-shear) modes are examples of eigenmodes which may resonate in distributed cross-sectional modes;• In-plane resonance mode is defined as a resonance mode that gives rise to displacement along directions substantially parallel to or colinear with the x-y axis of a resonator plane. Examples of in-plane resonance modes include in-plane bulk acoustic wave (BAW) modes (such as longitudinal waves, transverse (shear) waves, distributed cross-sectional modes), surface acoustic wave (SAW) modes (such as Rayleigh waves, lamb waves, love waves), and the like;• Out-of-plane resonance mode is defined as a resonance mode that gives rise to significant displacement along directions that are normal to the x-y axis of a device or along the z axis with respect to the resonating element plane. Examples of out-of-plane resonance modes include out-of- plane BAW modes (such as flexural modes, thickness extensional modes, saddle modes, torsional modes), and the like;• mechanically active region is defined as a region of structural material that is attached to a substrate but capable of movement relative to the substrate.

[0035] It is of critical importance that a high-quality timing reference provide a highly accurate reference frequency signal that is (1) stable over a wide temperature range, and (2) exhibits low phase noise. Historically, prior-art timing references have been based on quartz-crystal resonators; however, more recently, silicon-based MEMS resonators have been introduced. Unfortunately, conventional silicon-based MEMS resonators have poor temperature stability, poor phase-noise performance, or both.Temperature Stability

[0036] As compared to quartz-crystal resonators, prior-art silicon-based MEMS resonators lack temperature stability, which has curbed their widespread adoption. Silicon-based MEMS resonators have an inherent first order temperature-induced frequency drift of approximately -30 ppm / °C, resulting in a temperature stability of approximately 3,750 ppm over the typical industrial temperature range of -40°C to 85°C. In comparison, AT-cut quartz resonators have a temperature stability of approximately 20 ppm over the industrial temperature range of operation.

[0037] The change in frequency with respect to temperature of a MEMS resonator is given by the equation f(T) = fo[TCFi*( T) + TCF2*(A792+ ...] where fo is the resonance frequency of the resonator at a reference temperature, AT is the deviation from the reference temperature, TCFi is the first order temperature coefficient of frequency (TCF), and TCF2 is the second order temperature coefficient of frequency. For single-crystal silicon the value of TCF2 is typically within the range of -25 to -80 ppb / °C2depending on the dopant type and concentration, which can result in a temperature- induced frequency drift of approximately 200-400 ppm over the industrial temperature range. While this second order temperature-induced frequency drift is relatively small compared to the uncompensated temperature-induced frequency drift of single-crystal silicon (~3,750 ppm based on -30 ppm / °C), it is still significantly worse than the typical temperature-induced frequency drift that AT-cut quartz crystals can provide. As such, it is desirable to further reduce the temperature-induced frequency drift of silicon-based MEMS resonators in order enable their wide adoption in the timing market.

[0038] A reduction in the temperature-induced frequency drift in silicon-based MEMS resonators has been demonstrated by employing temperature compensation approaches, which can be performed actively, passively, or via a combination of active and passive techniques.

[0039] Examples of active compensation include the use of an external temperature reference, such as a bipolar junction transistor (BJT), which is integrated into the circuitry associated with the resonator. Alternatively, a reference element (e.g., a polysilicon resistor, a silicon-based resistor, a MEMS device having a known TCF, etc.) can be fabricated on the MEMS die itself. Unfortunately, incorporating a reference element on a MEMS die increases its overall size and can become a limiting factor in achieving smaller package footprints. Furthermore, there is some uncertainty when estimating the true temperature of the MEMS resonator based on another element, dueto thermal gradients and stress effects in the reference element caused by the physical separation between it and the MEMS resonator.

[0040] To overcome this uncertainty, it has been proposed to use the MEMS resonator, itself, as a reference element by configuring it such that two independent eigenmodes with different TCFs can be actuated and sensed. The eigenmode that is used as the temperature reference has a known TCF that is preferably linear. This approach is known as a "dual-mode temperature-sensing scheme."

[0041] Unfortunately, many approaches for actuating and sensing two independent eigenmodes in a MEMS resonator for the purposes of executing a dualmode temperature-sensing scheme utilize a single transduction mechanism to actuate and sense both an in-plane eigenmode and an out-of-plane eigenmode in the same (or substantially overlapping) geometrical portion of the MEMS resonator. However, for certain timing applications, such as applications which require low phase noise, utilizing a single transduction mechanism that actuates and senses multiple eigenmodes in the same geometrical portion can limit performance.Phase-Noise Performance

[0042] As will be appreciated by one skilled in the art, phase noise in different sections of the frequency spectrum produced by an actuated and sensed MEMS resonator are dominated by different parameters. Close-to-carrier phase noise (<500Hz) is dominated by the Q-factor of the resonator, but far-from-carrier noise is mostly dependent on the output current, see for example D. Agrawal and A. Seshia, "An analytical formulation for phase noise in MEMS oscillators," IEEE Trans. Ultrasonic Ferroelectric Freq. Cont., Vol. 61, No. 12, pp. 1938-1952 (2014).

[0043] When an excitation signal increases, the output current of a resonator typically increases due to increased resonator displacement. While this improves far- from-carrier noise, the frequency peak becomes highly nonlinear resulting in lower Cofactor, which lowers the close-to-carrier phase noise.

[0044] Many prior-art MEMS resonators are based on capacitively induced and sensed out-of-plane resonance. Unfortunately, for capacitively transduced MEMS resonators, the maximum obtainable displacement is limited to approximately one-third of the size of a fixed gap, after which the moving element rapidly moves into contact with the opposite side of the gap (referred to as "pull-in"). Furthermore, the capacitive transduction itself is a quadratic response by nature, and electrical nonlinearities begin to arise around l / 10thto l / 7thof the gap depending on the eigenmode and gap width. Hence, even though the motional resistance of a capacitively transduced MEMS resonatorcan be reduced by going to smaller gap sizes, this also reduces the output current due to resultant reduction in displacement amplitude.

[0045] In contrast, quartz-crystal resonators are piezoelectrically transduced and the displacement is not limited by pull-in but, rather, only by the mechanical nonlinearity of the eigenmode. As a result, piezoelectric transduction is highly desirable since it gives rise to high output currents for MEMS resonators intended for low-noise applications.

[0046] However, in dual-frequency MEMS resonators it is most common to have an in-plane eigenmode and an out-of-plane eigenmode. Unfortunately, there are significant performance disadvantages inherent to piezoelectrically transducing an out- of-plane eigenmode. For example, it is difficult to realize a large output current due to the relatively small stress that can be induced in the out-of-plane direction. In addition, the electrodes of the piezoelectric actuator would typically have to be routed via an anchor connecting the MEMS resonator to the rest of the MEMS die, thereby increasing anchor loss and reducing overall Q of the MEMS resonator. Increasing the number of anchors can also increase the stress gradient across the MEMS resonator as a result of wafer-level-packaging and chip-scale packaging processes. Finally, using only eigenmodes with nodal points suitable for side anchoring would severely restrict the design space.

[0047] To mitigate at least some of the disadvantages associated with single transduction mechanisms, approaches in which independent eigenmodes are actuated and sensed via independent transduction methods have been explored.

[0048] Examples of frequency-reference oscillators including a first oscillator containing a first resonator that is electrostatically actuated and a second oscillator containing a second resonator that is piezoelectrically actuated are disclosed in WO 2019 / 048736. The first resonator is chosen to have high long-term stability, while a stability-control circuit utilizing the output signal of the first resonator tunes the frequency obtained from the second resonator. The second resonator is piezoelectrically actuated to obtain a low phase noise output. The first oscillator and the second oscillator are thermally insulated from each other and a thermostatic controller independently adjusts the temperature of the first resonator and the second resonator. The need for temperature controlling the oscillators significantly adds to the power consumed, however. In addition, the resonators must be physically and thermally isolated, which increases the overall device footprint which is undesirable for many applications, such as IOT, wearables, and the like.

[0049] In similar fashion, WO 2020 / 003246 discloses a dual-frequency output MEMS resonator and MEMS oscillator, which can be operated selectively and concurrently in an in-plane mode of vibration and an out-of-plane mode of vibration, thereby providing two different frequencies. Systems and methods for determining a temperature of the dual-frequency output MEMS resonator are provided by mixing the two frequency signals together. However, in the disclosed devices, the sub-regions in which an in-plane mode of vibration is excited and the sub-regions in which an out-of- plane mode of vibration is excited are not geometrically isolated. As a result, mechanical energy (e.g., vibrations, etc.) can readily couple between the sub-regions, giving rise to undesirable spurious signals when one or both modes of vibration are excited.

[0050] In addition, the in-plane mode of vibration and the out-of-plane mode of vibration must be sufficiently far apart in frequency such that modal interference does not affect phase-noise performance, thereby putting constraints on the possible frequencies of operation. Furthermore, the resonators are actuated and sensed using the same transduction mechanism, which further increases the likelihood that modal coupling will reduce the Q-factor of an eigenmode when the in-plane mode of vibration and the out-of-plane mode of vibration are operated simultaneously.

[0051] As a result, it has been difficult, if not impossible, for prior-art MEMS- based timing references to provide a low phase noise, high-accuracy, high output current, low temperature drift, low power consumption and temporally stable frequency reference on a small footprint.

[0052] It is an aspect of the present disclosure that many, if not all, of the limitations of the prior art described above can be overcome by employing dualfrequency MEMS oscillators and resonators that actuate and sense two independent eigenmodes via different transduction methods.

[0053] FIG. 1 depicts a block diagram of a system for providing a timing reference in accordance with the present disclosure. System 100 includes resonator 102, oscillators OSC1 and OSC2, and measurement circuit 104.

[0054] FIG. 2 depicts operations of an exemplary method for providing a timing reference in accordance with the present disclosure. Method 200 begins with operation 201, wherein resonator 102 is provided. Method 200 is described with continuing reference to FIG. 1, as well as reference to FIGS. 3-5.

[0055] Resonator 102 is a dual-frequency silicon-based MEMS device configured to actuate and sense two independent eigenmodes using different transduction mechanisms, where each eigenmode arises in a different sub-region of device.

[0056] It is an aspect of the present disclosure that resonator having a unitary resonating element including first and second sub-regions that are geometrically isolated from one another, where a first eigenmode is realized in the first sub-region and a second eigenmode is realized in the second sub-region, affords significant advantage over the prior art.

[0057] As will be apparent to one skilled in the art, if there are common subregions of the same resonator having two vibrational modes that are strongly excited during modal vibration, even at different frequencies, mechanical energy can couple ( / '.e., leak) between the two modes during simultaneous operation. For example, in the case of independent in-plane and out-of-plane modes, if the in-plane mode causes a small out-of-plane excitation (due to mode shape imperfections), or vice-versa, some unwanted spurious electrical signal in the out-of-plane mode can emerge.

[0058] In embodiments in accordance with the present disclosure, however, subregions of a resonator are separated by a decoupler that inhibits vibrational coupling between the sub-regions. As a result, leakage of mechanical energy from one mode into the other is mitigated and the leakage signal (spurious signal) is reduced. Furthermore, unwanted spurious modes can also lead to a drop in Q-factor in the actuated mode. As a result, MEMS resonators in accordance with the present disclosure are configured to have an in-plane eigenmode and an out-of-plane eigenmode in geometrically isolated sub-regions, where the eigenmodes are actuated and sensed with independent transduction mechanisms. Such resonators are particularly desirable in some applications, such as those requiring low phase noise, and the like.

[0059] As depicted in FIG. 1, resonator 102 is a unitary structure that includes sub-regions SRI and SR2 and decoupler 106, which is disposed between the subregions. Resonator 102 is configured such that each of sub-regions SRI and SR2 supports the development of a different eigenmode and decoupler 106 substantially inhibits vibrational coupling between the two sub-regions. In other words, although subregions SRI and SR2 and decoupler 106 are contiguous portions of the same resonating element, decoupler 106 geometrically isolates sub-regions SRI and SR2.

[0060] FIG. 3 depicts a schematic drawing of a perspective view of a first exemplary resonator in accordance with the present disclosure. Resonator 102 includes resonating element 302, anchors 304, piezoelectric transducer 306, and a portion of capacitive transducer 308, all of which are disposed on substrate 310.

[0061] Resonating element 302 is a unitary element of structural material Ml. Resonating element 302 includes beams 312A, 312B, 312C, 312D (referred to,collectively, as beams 312), slabs 308A, 308B, 308C, 308D, central member 314, and tethers 316.

[0062] Each of beams 312 is held in a clamped-clamped arrangement between an anchor 304 and central member 314. Beams 312 collectively define sub-region SRI, which is configured to support a desired in-plane eigenmode having frequency Fl and have a first temperature coefficient of frequency TCFA. In the depicted example, sub-region SRI is configured to resonate in a quasi-width-extensional (WE) mode. In some embodiments, sub-region SRI is configured to resonate in a different in-plane mode, such as a Lame mode, a quasi-Lame mode, shear modes, quasi-shear modes, and the like.

[0063] It should be noted that, while the depicted example includes a resonator that is directly attached to rigid anchors, many alternatives to such a configuration are within the scope of the present disclosure. For example, a resonator can: i. be attached to anchoring posts formed from substrate 310; orII. be attached to anchoring posts formed from a capping substrate included in the resonator structure; or ill. be attached to anchoring posts formed from a device layer included in the resonator structure; or iv. be attached to anchoring posts located at one or more non-edge nodal points of the resonator; or v. be attached to an anchor that includes an anchoring spring configured that reduces anchoring loss; or vi. be electrically grounded via at least one anchor 304; or vii. any combination of i, ii, ill, iv, v, and vi.

[0064] Each of slabs 308A through 308D is connected to central member 314 by a tether 316 such that the slab is held in a cantilever arrangement that enables its out- of-plane motion. Slabs 308A through 308D collectively define sub-region SR2, which is configured to support a desired out-of-plane eigenmode having frequency F2 and have a second temperature coefficient of frequency TCFB. Preferably, TCFB has an absolute value of the first order component |TCFB,I | that is not equal to 0 ppm / °C and an absolute value of the second order component | TCFB,2 | that is as close to 0 ppb / °C2as possible.

[0065] Central member 314 and tethers 316 collectively define decoupler 106, which is configured to geometrically isolate sub-regions SRI and SR2, thereby suppressing vibrational coupling between the two sub-regions.

[0066] Anchors 304 are posts of structural material Ml that are configured to hold resonating element 302 above substrate 310, thereby enabling motion of beams 312 and slabs 308A through 308D relative to the substrate, rendering the beams and slabs mechanically active. In the depicted example, substrate 310 is a conventional single-crystal silicon wafer; however, any substrate suitable for MEMS fabrication can be used without departing from the scope of the present disclosure.

[0067] In the depicted example, at least one anchor 304 is connected to a nodal point of sub-region SRI in order to reduce anchor loss. In some embodiments, at least one anchor 304 is connected to its respective beam 312 to reduce anchor loss, where the anchoring spring is configured to reduce anchor loss even when connected to a non- nodal point.

[0068] In the depicted example, structural material M l is single-crystal silicon; however, one skilled in the art will recognize, after reading this Specification, that many other structural materials can be used in resonating element 302 and / or anchors 304 without departing from the scope of the present disclosure.

[0069] Furthermore, preferably, structural material M l is homogenously doped with a dopant having a concentration that reduces the absolute value of the second order temperature coefficient of frequency, ITCF2I , of the in-plane mode of vibration of beams 312. Preferably, ITCF21 is reduced to as close to 0 ppb / °C2as possible within the desired operating temperature range of system 100. In the depicted example, the desired operating temperature range is -40°C to 85°C; however, other operating temperature ranges are within the scope of the present disclosure. In the depicted example, structural material M l is highly n-doped single-crystal silicon having a concentration of between approximately l.OxlO20cm'3and 2.4xlO20cm-3, such that ITCF2I is less than approximately 1 ppb / °C2. In some embodiments, structural material Ml is doped such that ITCF2I is less than approximately 0.01 ppb / °C2.

[0070] In addition, in the depicted example, at least one sub-region of resonating element 302 is geometrically modified to reduce the absolute value of the first order temperature coefficient of frequency |TCFi| of the in-plane mode of vibration of beams 312 to as close to zero as possible within the desired operating temperature range of system 100. For the purposes of this Specification, including the appended claims, the term "geometrically modified" is defined as an alteration of the structural material ofsub-region SRI such that its |TCFi| is lower than the nominal |TCFi| it would have without such alteration. Examples of geometric modification in accordance with the present disclosure include: i. a change in the shape of the at least one portion (e.g., a beam 312, etc.) of sub-region SRI; orII. an angular offset between a dominant crystallographic axis of single- crystal-silicon and the longitudinal axis of at least one beam 312, where the longitudinal axis is the axis in which predominant motion is exhibited during resonant oscillation; or ill. a combination of i and II.

[0071] In the depicted example, resonating element 302 is geometrically modified by aligning the longitudinal axis of at least one of beams 312 such that it is rotated at an angle of approximately 34° from the <110> crystal axis of single-crystal silicon. In the depicted example, this geometric modification gives rise to a value for |TCFi | that is less than approximately 1 ppm / °C. In some embodiments, the value for |TCFi | is reduced to less than approximately 0.01 ppm / °C.

[0072] It should be noted that the absolute value of the ITCF2I of the in-plane resonance mode of a homogenously doped resonating element within an operating temperature range can be accomplished by doping the element with n-type dopants, p- type dopants, or a combination of n- and p-type dopants. In some embodiments, a resonating element is doped with n-type dopant to a concentration of between approximately l.OxlO20cm'3and 2.4xlO20cm'3. In some embodiments, a resonating element is doped with a p-type dopant to a concentration of 2.0xl020cm'3and 2.4xl020cm'3in order to reduce ITCF21 to be approximately 0 ppb / °C2. It should be further noted that the materials, dopants, and doping levels provided here are merely exemplary and that many alternatives can be used without departing from the scope of the present disclosure.

[0073] Piezoelectric transducer 306 includes piezoelectric elements 306A, 306B, 306C, 306D, which are operatively coupled with beams 312A through 312D, respectively. Each of piezoelectric elements 306A through 306D includes layer stack disposed on its respective beam 312, where the layer stack includes a layer of piezoelectric material disposed between a pair of electrical contacts. Piezoelectric transducer 306 is configured to actuate and sense sub-region SRI. It should be noted that, although not shown in FIG. 3, conductive traces for providing electrical connectionto the electrodes of piezoelectric elements 306A through 306D are routed via anchors 304.

[0074] Capacitive transducer 308 includes slabs 308A through 308D, each of which acts as one plate of a parallel plate capacitor. Although not shown in FIG. 3, each capacitor includes a second plate that is disposed above one of slabs 308A through 308D. Capacitive transducer 308 is configured to actuate and sense sub-region SR2.

[0075] As noted above, decoupler 106 is configured to geometrically isolate subregions SRI and SR2, thereby suppressing vibrational coupling between the two subregions.

[0076] FIGS. 4A-B depict plots of the induced displacement in sub-regions SRI and SR2, respectively. It should be noted that, in plots 400 and 402, no displacement is indicated as light shading and maximum displacement is indicated by darkest shading.

[0077] As evinced by plot 400, the displacement induced in resonator 102 due to its in-plane eigenmode is substantially isolated to sub-region SRI with little or no displacement developing in sub-region SR2.

[0078] In similar fashion, plot 402 shows that the displacement induced in resonator 102 due to its out-of-plane eigenmode is substantially isolated to sub-region SR2 with little or no displacement developing in sub-region SRI.

[0079] As is readily apparent from plots 400 and 402, the inclusion of decoupler 106 substantially suppresses coupling of mechanical energy between sub-regions SRI and SR2.

[0080] Returning now to FIG. 1, oscillator OSC1 is electrically connected to resonator 102 such that it is operative for actuating and sensing the desired in-plane eigenmode in sub-region SRI. In similar fashion, oscillator OSC2 is electrically connected to resonator 102 such that it is operative for actuating and sensing the desired out-of-plane eigenmode in sub-region SR2. It should be noted that, although not shown here, system 100 also typically includes power supply components to provide alternating current (AC) and / or direct current (DC) electrical signals for actuation and sensing of the sub-regions of resonator 102.

[0081] At operation 202, oscillator OSC1 actuates and senses an in-plane eigenmode in sub-region SRI.

[0082] Oscillator OSC1 provides electrical signal 108A, which is characterized by first frequency Fl (the frequency of the excited the in-plane resonance mode) and by first characteristic phase noise, Nl. In the depicted example, oscillator OSC1 includes atransimpedance amplifier (TIA) connected to an automatic gain control (AGC). The TIA converts the current from the at least one sub-region configured for piezoelectric transduction to electrical signal 108A, while the AGC regulates oscillation amplitude and reduces mechanical non-linear effects.

[0083] At operation 203, oscillator OSC2 actuates and senses an out-of-plane eigenmode in sub-region SR2.

[0084] In the depicted example, oscillator OSC2 is configured for actuating and sensing, using capacitive transduction, an out-of-plane vibration mode of sub-region SR2. Typically, oscillator OSC2 excites the fundamental out-of-plane resonance mode in sub-region SR2.

[0085] Oscillator OSC2 provides electrical signal 108B, which is characterized by second frequency, F2, and second characteristic phase noise, N2. In the depicted example, oscillator OSC2 includes a TIA connected to an AGC. The TIA converts the current from sub-region SR2 to electrical signal 108B, while the AGC regulates oscillation amplitude and reduces mechanical non-linear effects.

[0086] Resonator 102 is configured such that frequency Fl is greater than the frequency F2 and phase noise N1 is less than phase noise N2. One or both of the first oscillator and the second oscillator may be configured to be operated selectively, operated at specific time intervals or operated continuously.

[0087] At operation 204, circuit 104 generates output signal 110 based on electrical signals 108A and 108B.

[0088] Circuit 104 includes Complementary Metal-Oxide-Semiconductor (CMOS) circuitry configured to mix frequency signals 108A and 108B and provide commensurate output signal 110, among various other functions. In the depicted example, circuit 104 is a nonlinear electrical circuit that is configured to generate a temperature signal based on frequency signals 108A and 108B using various implementations and topologies known in the art. In the depicted example, output signal 110 is characterized by a third frequency F3 that is proportional to a temperature of resonator 102.

[0089] It should be noted that several approaches for mixing frequency signals 108A and 108B to provide output signal 110 such that its frequency is proportional to a temperature of resonator 102 are known in the prior art, such as those described by G. Xereas, et a / ., in US Patent No. 11,305,981, which is incorporated herein by reference.

[0090] At optional operation 205, circuit 104 employs a temperature compensation algorithm to improving the temperature stability of output signal 110, preferably to sub-ppm levels, which can be used as a temperature-compensated timing reference.

[0091] At optional operation 206, a temperature of resonator 102 is determined based on frequency F3 of output signal 110. In the depicted example, the temperature is determined by circuitry included in circuit 104. In some embodiments, the temperature is determined by a processor, controller, and the like, which is in communication with circuit 104.

[0092] At optional operation 207, circuit 104 provides the determined temperature as output signal 112.

[0093] FIG. 5 depicts the temperature drift of resonator 102, as predicted by a finite element method (FEM) simulation.

[0094] It should be noted that the configuration of system 100 described above is merely one implementation in accordance with the present disclosure. For example, in some embodiments, sub-region SRI is configured to operate in an out-of-plane mode of vibration, while sub-region SR2 is configured to operate in an out-of-plane mode of vibration. As will be apparent to one skilled in the art, after reading this Specification, other combinations of eigenmodes can be contemplated without departing from the scope of the present disclosure.

[0095] It should be further noted that resonator 102 is merely one example of a resonator configuration having two geometrically isolated sub-regions, each of which supports a different independent eigenmode, and where each eigenmode can be actuated and sensed by a different transduction method in accordance with the present disclosure.

[0096] FIG. 6 depicts a schematic diagram of a perspective view of a second example of a resonator suitable for use in system 100. Resonator 600 includes resonating element 602, anchors 304, piezoelectric transducer 606, and capacitive transducer 608, all of which are disposed on substrate 310.

[0097] Resonating element 602 includes beams 612A, 612B, 612C, 612D (referred to, collectively, as beams 612), slabs 608A, 608B, 608C, 608D, member 614, and tethers 616, which are analogous to beams 312, slabs 308A through 308D, central member 314, and tethers 316, respectively.

[0098] Piezoelectric transducer 606 includes piezoelectric elements 606A, 606B, 606C, 606D, which are operatively coupled with beams 612A through 612D, respectively.

[0099] Capacitive transducer 608 includes slabs 608A through 608D, each of which acts as one plate of a parallel plate capacitor.[ooioo] Piezoelectric elements 606A through 606D and beams 612A through 612D collectively define sub-region SRI, while slabs 608A through 608D collectively define sub-region SR2.[ooioi] Piezoelectric transducer 606 and capacitive transducer 608 are analogous to piezoelectric transducer 306 and capacitive transducer 308, respectively, which are described above and with respect to FIG. 3. Piezoelectric transducer 606 is configured to actuate and sense the desired in-plane eigenmode in sub-region SRI, while capacitive transducer 608 is configured to actuate and sense the desired out-of- plane eigenmode in sub-region SR2.

[0102] Member 614 and tethers 616 collectively define decoupler 604, which is analogous to decoupler 106. Decoupler 604 is configured to geometrically isolate sub-regions SRI and SR2, thereby substantially vibrationally decoupling the two sub-regions.

[0103] As a result, like resonator 102 described above, resonator 600 is configured with an arrangement of beams, anchors, slabs, tethers, decoupler, and transducers that collectively defines a unitary element of structural material Ml having a first sub-region configured to support an in-plane eigenmode and a second sub-region configured to support an out-of-plane eigenmode, wherein the first and second subregions are geometrically isolated by a decoupler. While some or all of the elements of resonator 600 are configured and / or arranged differently than those of resonator 102, operationally, resonator 600 is analogous to resonator 102.

[0104] It should be noted that, when beams 612A through 612D consist of a single material (single-crystal silicon, in the depicted example), sub-region SRI is characterized by a first absolute value, |TCFi| i, of the first order temperature coefficient of frequency of its in-plane resonance mode.

[0105] However, in the depicted example, each of beams 612 includes a plurality of compensating features 618 in each of the single-crystal silicon beams, the inclusion of which modifies the beam such that the absolute value of the first order temperature coefficient of frequency of its in-plane resonance mode is reduced to avalue, |TCFi 12 that is lower than |TCFi| i. Preferably, |TCFi 12 is reduced to a value as low as possible (e.g., approximately 0 ppm / °C). For the purposes of this Specification, including the appended claims, a "compensating material" is defined as a material that has material properties different then the structural material from which the bulk of its respective resonating element is formed. For example, for beams whose structural material Ml is single-crystal silicon, suitable compensating materials include, without limitation, silicon oxides, undoped silicon, silicon nitride, polysilicon, diamond, silicon carbide and metal. Other suitable structural and compensating materials will be apparent to one skilled in the art after reading this disclosure. In some embodiments, a compensating material has a first order temperature coefficient of frequency and / or a second order temperature coefficient of frequency that is of the opposite sign to that of structural material Ml.

[0106] In the depicted example, each compensating feature 618 is a region of compensating material having a width that is less than that of its respective beam 612. Each compensating feature 618 is formed within its respective beam such that its compensating material extends through the entire thickness of the beam. In some embodiments, compensating features 618 extend only partly into the thickness of their respective beams, reside on one or more surfaces of their respective beams, or any combination thereof.

[0107] FIGS. 7A-B depict plots of the induced displacement in sub-regions SRI and SR2 of resonator 600, respectively. It should be noted that, in plots 700 and 702, no displacement is indicated as light shading and maximum displacement is indicated by darkest shading.

[0108] As evinced by plot 700, the displacement induced in resonator 600 due to its in-plane eigenmode is substantially isolated to sub-region SRI with little or no displacement developing in sub-region SR2.

[0109] In similar fashion, plot 702 shows that the displacement induced in resonator 600 due to its out-of-plane eigenmode is substantially isolated to sub-region SR2 with little or no displacement developing in sub-region SRI.

[0110] As is readily apparent from plots 700 and 702, the inclusion of decoupler 604 substantially suppresses coupling of mechanical energy between subregions SRI and SR2.

[0111] FIG. 8 depicts the temperature drift of resonator 600, as predicted by a finite element method (FEM) simulation.

[0112] It should be noted that resonators 102 and 600 are merely two examples of myriad resonator configurations in accordance with the present disclosure.

[0113] FIG. 9 depicts plot of the response of yet another resonator configuration in accordance with the present disclosure. Modeling results for the mechanical behavior of resonator 900 are provided in plots 902, 904, 906, and 908. Resonator 900 is analogous to resonator 102 and 600 and includes: a first sub-region ( / .e., SRI) that is configured to support an in-plane resonance mode; a second subregion ( / .e, SR2) that is configured to support an out-of-plane resonance mode; and a decoupler that geometrically isolates the two sub-regions, as discussed above. In analogous fashion to resonators 102 and 600, sub-region SRI is configured for piezoelectric transduction and sub-region SR2 is configured for capacitive transduction.

[0114] Plot 902 depicts the displacement pattern of sub-region SRI of when resonating in a piezoelectrically transduced in-plane mode - specifically, that of a distributed cross-sectional shear mode.

[0115] Plot 904 depicts the volumetric strain pattern that arises in subregion SRI while resonating in a distributed cross-sectional shear mode.

[0116] Plot 906 depicts the displacement pattern that arises in sub-region SR2 while resonating in a flexural mode.

[0117] Plot 908 depicts a cross-sectional view of resonator 900.

[0118] FIG. 10 depicts operations of a method suitable for fabricating a resonator in accordance with the present disclosure. Method 1000 is described herein with reference to FIGS. 6 and FIGS. 11A-E. It should be noted, however, that the fabrication steps described here are merely exemplary and that many variations of suitable fabrication methods will be apparent to one skilled in the art after reading this disclosure.

[0119] FIGS. 11A-F depicts schematic drawings of cross-sectional views of a resonator in accordance with the present disclosure at different stages of fabrication.

[0120] Method 1000 begins with operation 1001, wherein cavity 1102 is formed in substrate 310 by etching into the substrate from surface 1104 in conventional fashion. Cavity 1102 is formed with a depth sufficient to enable full motion of slabs 608A through 608D when the desired out-of-plane eigenmode is excited in subregion SR2. In some embodiment, the depth of cavity 1102 is also selected to enable a suitable final vacuum level in the cavity once fabrication of the resonator is complete.Typically, surface 1104 includes a layer of electrical insulator (as shown), such as silicon dioxide, for facilitating bonding with substrate 1106 and enabling electrical isolation between adjacent elements of resonator 600, as described below.

[0121] At optional operation 1002, compensating features 618 are formed in substrate 1106 such that they extend partially through its thickness. In the depicted example, substrate 1106 includes structural material Ml, which is homogenously doped single-crystal-silicon with a dopant having a given concentration that reduces the absolute value of the second order temperature coefficient of frequency | TCF21 of at least one desired eigenmode to a very low value over the expected operating temperature of system 100, as described above and with respect to resonator 102. In some embodiments, substrate 310 is a conventional single-crystal silicon substrate that is doped in substantially the same manner as substrate 1106; however, other materials and / or doping concentrations can be used for substrate 310.

[0122] In the depicted example, compensating features 618 include silicon dioxide and are formed by first forming vertical trenches that extend into substrate 1106 from surface 1108 using conventional patterning and etching techniques. Once the trenches have been formed, they are filled with compensating material M2, which is selected based on the material used as structural material Ml. In the depicted example, compensating material M2 is silicon dioxide and the trenches are completely filled via conventional methods (e.g., oxidation, chemical vapor deposition, spin-on processing, evaporation, sputtering, electroplating, growth, etc.). In some embodiments, the trenches are only partially filled with compensating material. In some embodiments, compensating material M2 is other than silicon dioxide. Alternate compensating materials suitable for use in accordance with the present disclosure include, without limitation, silicon nitride, polysilicon, diamond, silicon carbide, metals, and the like. It will be clear to one skilled in the art, after reading this Specification, how to select materials appropriate for use as structural material Ml and compensating material M2.

[0123] It should be noted that, as discussed above, compensating features 618 represent merely one modification approach for reducing the value of |TCFi| . In some embodiments, for example, a geometric modification is used to reduce value of |TCFi| . Geometric modifications in accordance with the present disclosure include, without limitation, orienting resonating element 302 (or resonating element 602, etc.) at a non-zero angle relative to a dominant crystallographic axis of its structural material, changing the shape of sub-region SRI, and the like.

[0124] FIG. 11A depicts substrates 310 and 1106 after operations 1001 and 1002.

[0125] At operation 1003, substrates 310 and 1106 are joined at surfaces 1104 and 1108. In the depicted example, substrates 310 and 1106 are joined via fusion bonding; however, many alternate methods for joining the substrates (e.g., oxygen-assisted plasma bonding, thermo-anodic bonding, eutectic bonding, etc.) can be used without departing from the scope of the present disclosure.

[0126] At operation 1004, the thickness of substrate 1106 is reduced to establish the desired thickness of resonating element 602, thereby defining device layer 1110 having top surface 1112. In some embodiments, compensating features 618 have a different depth than resonating element 602 such that the compensating features do not extend completely through the resultant thickness of device layer 1110. In the depicted example, substrate 1106 is thinned via lapping and grinding; however, any conventional method can be used to thin substrate 1106 without departing from the scope of the present disclosure.

[0127] FIG. 11B depicts bonded substrates 310 and 1106 after the thinning of substrate 1106 to form device layer 1110.

[0128] At operation 1005, piezoelectric elements 606A through 606D are formed in conventional fashion, thereby defining nascent piezoelectric transducer 606. In the depicted example, each piezoelectric element includes a layer of piezoelectric material disposed between a pair of electrodes, each including a contact 1114. In the depicted example, the piezoelectric material is aluminum nitride and the electrodes include molybdenum (MO) and gold. It should be noted, however, that many alternative materials can be used for the piezoelectric material (e.g., scandium aluminum nitride, zinc oxide, lead zirconate titanate, etc.), as well as for one or both of the electrodes of the piezoelectric elements (e.g., platinum, aluminum, etc.). It should be noted that, after operation 1006, no metal remains on slabs 608A through 608D. In addition, in some embodiments, a via is formed through the piezoelectric material to enable electrical contact with the bottom electrodes of piezoelectric elements 606A through 606D. In some embodiments, the piezoelectric material is patterned to expose a portion of each bottom electrode of the piezoelectric elements.

[0129] At operation 1006, separation trenches 1116 are etched completely through device layer 1110 via conventional patterning and etching, thereby defining the shape of resonator 600, including resonating element 602 and anchors 304. In some embodiments, separation trenches 1116 are formed at the same time asthe trenches for compensation features 618 are formed during operation 1002. In some embodiments, the shape of resonator 600 is defined at a different point in the fabrication process.

[0130] FIG. 11C depicts nascent resonator 600' after the formation of piezoelectric transducer 606, contacts 1114, and separation trenches 1116. For clarity, only contacts 1114 of piezoelectric transducer 606 are shown in FIG. 11C and the top and bottom electrodes are not shown.

[0131] At operation 1007, one or more isolation trenches 1122 are formed partially through the thickness of capping substrate 1118 by etching trenches into surface 1120 and backfilling the trenches with dielectric material in conventional fashion. In the depicted example, capping substrate 1118 is a single-crystal silicon substrate and isolation trenches 1122 are filled with silicon dioxide, in analogous fashion to compensating features 618, as discussed above. In some embodiments, isolation trenches 1122 are filled with a material other than silicon dioxide, such as doped polysilicon, silicon nitride, a combination of suitable materials, and the like.

[0132] At optional operation 1008, cavity 1124 is formed by etching into surface 1120 of capping substrate 1118.

[0133] At optional operation 1009, getter 1126 is formed by depositing getter material in cavity 1124 in conventional fashion.

[0134] In some embodiments, such as those intended for applications not requiring a high-vacuum environment for resonator 600, for resonators having a sufficiently high Q-factor, and the like, optional operations 1008 and 1009 are not required.

[0135] At operation 1010, capping substrate 1118 is bonded to device layer 1110 in conventional fashion, thereby forming chamber 1128, which encloses resonator 600.

[0136] In the depicted example, operation 1010 is performed while nascent resonator 600' is held in a vacuum chamber whose environment is controlled to establish the desired vacuum level within chamber 1128.

[0137] At operation 1011, the thickness of capping substrate 1118 is reduced to its desired final thickness in conventional fashion, such as by grinding, lapping, etching, polishing, and the like. Operation 1011 also forms top surface 1133.

[0138] It should be noted that, after capping substrate 1118 has been thinned to its proper thickness, isolation trenches 1122 define various other featuresthat many be electrically disconnected from each other, such as top electrodes 1130 (also referred to herein as capacitive electrodes) of capacitive transducer 608, through- silicon vias (TSV) 1132 for electrically connecting contacts 1114 of piezoelectric elements 606A through 606D, and the like. The top electrodes 1130 may be directly over corresponding sub-regions SR2 of the device layer for out-of-plane actuation and resonance of the capacitive transducers.

[0139] At operation 1012, passivation layer 1134 is formed on top surface 1133 of the thinned capping substrate 1118 and patterned to define vias for enabling electrical contact to top electrodes 1130 and TSV 1132.

[0140] At operation 1013, the fabrication of resonator 600 is completed by the formation of electrical contact pads 1136.

[0141] In some embodiments, method 1000 includes operations for adding circuitry for oscillators OSC1 and OSC2 to resonator 102, thereby completing resonator 102.

[0142] In some embodiments, method 1000 includes operations for adding circuit 104 to oscillators OSC1 and OSC2 and resonator 102, thereby realizing a monolithically integrated system 100.

[0143] Although each of substrates 310, 1106, and 1118 is a singlecrystal silicon substrate, other materials can be used for any of these substrates without departing from the scope of the present disclosure. Alternative substrate materials include, without limitation, silicon carbide, polycrystalline silicon, compound semiconductors, glasses, and the like.

[0144] In some embodiments, additional MEMS devices (e.g., sensors, actuators, accelerometers, etc.) and / or electronic circuitry are included in a resonator. For example, the depicted examples are compatible with fabrication in a CMOS processing facility, thereby enabling monolithic integration of CMOS electronics with a resonator in accordance with the present disclosure.

[0145] Furthermore, while method 1000 enables fabrication of a MEMS device including a set of capacitive electrodes and a set of piezoelectric electrodes, different configurations of resonators having different electrode arrangements may be implemented without departing from the scope of the present disclosure.

[0146] For example, one or more separation trenches 1116 can be configured to define one or more independent tuning electrodes that enable the introduction of complex strains on the resonant structure. Alternatively, fabrication of aresonator in accordance with the present disclosure can include fabrication of a set of capacitive electrodes in device layer 1110 such that they enable in-plane capacitive transduction of an in-plane eigenmode. Furthermore, fabrication of a resonator in accordance with the present disclosure can include fabrication of a set of capacitive electrodes in substrate 310, such that they are positioned below device layer 1110. Still further, device layer 1110 can be doped with a given concentration that renders at least a portion of a resonating element sufficiently conductive to serve as an electrode, thereby obviating deposition of the bottom electrode of piezoelectric elements 606A through 606D.

[0147] It is to be understood that the disclosure teaches just one example of the illustrative embodiment and that many variations of embodiments in accordance with the present disclosure can easily be devised by those skilled in the art after reading this disclosure and that the scope of the present invention is to be determined by the following claims.

Claims

What is claimed is:

1. A microelectromechanical system (MEMS) device comprising a resonator disposed on a substrate, the resonator having a unitary resonating element that includes: a first sub-region that supports a first eigenmode having a first frequency; a second sub-region that supports a second eigenmode having a second frequency that is different than the first frequency; and a decoupler that is located between the first and second sub-regions, wherein the decoupler geometrically isolates the first and second sub-regions to mitigate coupling of mechanical energy between them.

2. The MEMS device of claim 1 further comprising a piezoelectric transducer operably coupled with the first sub-region to operate the first sub-region by piezoelectric transduction and an electrode operably coupled with the second sub-region to operate the second sub-region by capacitive transduction.

3. The MEMS device of claim 1 wherein the first eigenmode is an in-plane eigenmode.

4. The MEMS device of claim 3 wherein the first eigenmode is an in-plane bulk acoustic wave mode or a surface acoustic wave mode.

5. The MEMS device of claim 1 wherein the second eigenmode is an out-of-plane eigenmode.

6. The MEMS device of claim 5 wherein the second eigenmode is a bulk acoustic wave mode.

7. The MEMS device of claim 1 wherein the second frequency is lower than the first frequency.

8. The MEMS device of claim 1 wherein the first sub-region is mechanically coupled with the substrate via a first anchor.

9. The MEMS device of claim 8 wherein the first anchor is located at a nodal point of the first eigenmode.

10. The MEMS device of claim 8 wherein the first sub-region is mechanically coupled with the first anchor via an anchor.

11. The MEMS device of claim 1 wherein the first eigenmode is an in-plane eigenmode and the second eigenmode is an out-of-plane eigenmode.

12. The MEMS device of claim 1 wherein the resonator comprises single-crystal silicon and is characterized by an absolute value of a second order temperature coefficient of frequency ( ITCF21 ) that is less than or equal to 1 ppb / °C2.

13. The MEMS device of claim 12 wherein the single-crystal silicon is doped to a first concentration.

14. The MEMS device of claim 1 wherein the resonator comprises single-crystal silicon and is characterized by a ITCF21 that is less than or equal to 0.01 ppb / °C2.

15. The MEMS device of claim 14 wherein the single-crystal silicon is doped to a first concentration.

16. The MEMS device of claim 1 wherein the resonator comprises single-crystal silicon having a first crystallographic axis and the first sub-region has a first axis along which the first sub-region exhibits a predominant motion of the first eigenmode, and wherein the first crystallographic axis has an angular offset from the first axis of the first sub-region such that the first sub-region is characterized by a first absolute value of a first order temperature coefficient of frequency (|TCFi| ) that is lower than a nominal absolute value of the |TCFi| if the first crystallographic axis were aligned with the first axis.

17. The MEMS device of claim 1 wherein, when the first sub-region comprises a first material and a compensating material, wherein the first material is characterized by a first absolute value of a first order temperature coefficient of frequency of the first eigenmode ( |TCFi 11), and wherein the first material and the compensating material that are collectively characterized by a second absolute value of the first order temperature coefficient of the first eigenmode ( |TCFi 12) that is less than |TCFi 11.

18. The MEMS device of claim 17 wherein the compensating material has a first order temperature coefficient of frequency and / or a second order temperature coefficient of frequency that is of an opposite sign to that of first material.

19. The MEMS device of claim 17 wherein the compensating material is disposed on a surface of the first sub-region.

20. The MEMS device of claim 17 wherein the first sub-region includes at least one beam that includes at least one compensating feature that comprises the compensating material.

21. The MEMS device of claim 17 wherein the first material is a doped singlecrystal silicon and the compensating material is selected from the group consisting of asilicon oxide, undoped single-crystal silicon, silicon nitride, polysilicon, diamond, silicon carbide, and a metal.

22. The MEMS device of claim 1 further comprising a piezoelectric transducer to actuate and sense the first eigenmode.

23. The MEMS device of claim 1 further comprising a capacitive electrode to actuate and sense the second eigenmode.

24. The MEMS device of claim 1 further comprising : a piezoelectric transducer to actuate and sense the first eigenmode; and a capacitive electrode to actuate and sense the second eigenmode; wherein the first eigenmode is an in-plane eigenmode.

25. The MEMS device of claim 24 further comprising : a first oscillator that is operatively coupled with the piezoelectric transducer; and a second oscillator that is operatively coupled with the capacitive electrode.

26. The MEMS device of claim 1 wherein the MEMS device is a MEMS oscillator.

27. The MEMS device of claim 1 further comprising electronic circuitry, wherein the resonator and the electronic circuitry are monolithically integrated on the substrate.

28. A method for providing two frequency signals from a MEMS device, the method including : exciting a first eigenmode in a first sub-region of a resonator disposed on a substrate, the resonator having a unitary resonating element that comprises:(i) the first sub-region, the first sub-region supporting the first eigenmode such that it has a first frequency;(ii) a second sub-region supporting a second eigenmode having a second frequency that is different than the first frequency; and(iii) a decoupler that geometrically isolates the first and second subregions such that coupling of mechanical energy between them is mitigated; sensing the first eigenmode, wherein the first eigenmode is excited and sensed via a first transduction mechanism; exciting and sensing the second eigenmode in the second sub-region via a second transduction mechanism that is different than the first transduction mechanism; providing the first sensed eigenmode as a first frequency signal; and providing the second sensed eigenmode as a second frequency signal.

29. The method of claim 28 further comprising providing the first transduction method as piezoelectric transduction.

30. The method of claim 28 further comprising providing the second transduction method as capacitive transduction.

31. The method of claim 28 further comprising providing the first transduction method as piezoelectric transduction and the second transduction mechanism as capacitive transduction.

32. The method of claim 28 wherein the first eigenmode is an in-plane eigenmode.

33. The method of claim 32 wherein the first eigenmode is a bulk acoustic wave mode or a surface acoustic wave modes.

34. The method of claim 28 wherein the second eigenmode is an out-of-plane eigenmode.

35. The method of claim 34 wherein the second eigenmode is selected from the group consisting of flexural modes, thickness extensional modes, saddle modes, and torsional modes.

36. The method of claim 28 wherein the second frequency is lower than the first frequency.

37. The method of claim 28 further comprising exciting the first eigenmode in the first sub-region with a first oscillator and exciting the second eigenmode in the second sub-region with a second oscillator.

38. The method of claim 37 wherein the first sub-region and has a first temperature coefficient of frequency (TCF) and a first characteristic phase noise, and wherein the second sub-region and has a second TCF and a second characteristic phase noise, and further wherein the first characteristic phase noise is less than the second characteristic phase noise.

39. The method of claim 38 further comprising selectively operating the first oscillator.

40. A method of forming a MEMS device for providing a timing reference, the method including : forming a first cavity in a first substrate; joining a second substrate and the first substrate; thinning the second substrate to define a device layer;forming a piezoelectric transducer on a first sub-region of the device layer; patterning the device layer to form a resonator comprising a unitary resonating element that includes the first sub-region that supports a first eigenmode having a first frequency, a second sub-region that supports a second eigenmode having a second frequency, a decoupler that geometrically isolates the first and second sub-regions, and at least one anchor that mechanically couples the first sub-region and the substrate; forming a plurality of isolation trenches through a portion of a third substrate; forming a second cavity in the third substrate; joining the third substrate and the device layer such that the resonating element is enclosed in a chamber at least partially defined by the first cavity and the second cavity; thinning the third substrate such that the isolation trenches collectively define a plurality of electrically conductive regions that are electrically disconnected from each other, wherein a first electrically conductive region of the plurality thereof is electrically connected to the piezoelectric transducer, and wherein a second electrically conductive region of the plurality thereof defines an electrode of a capacitive transducer that includes the second sub-region; and forming a plurality of contact pads, each contact pad being electrically connected with a different electrically conductive region of the plurality thereof.

41. The method of claim 40 wherein each of the first, second, and third substrates comprises single-crystal silicon.

42. The method of claim 41 wherein at least one of the first, second, and third substrates is single-crystal silicon doped with a n-type dopant at a doping concentration that is within a range of approximately l.OxlO20cm-3to approximately 2.4xl020cm'3.

43. The method of claim 41 wherein at least one of the first, second, and third substrates is single-crystal silicon doped with a p-type dopant at a doping concentration that is within a range of approximately 2.0xl020cm-3to approximately 2.4xl020cm'3.

44. The method of claim 41 further comprising forming at least one compensating feature in the first sub-region, wherein the at least one compensating feature includes a compensating material that is selected from the group consisting of a silicon oxide, undoped single-crystal silicon, silicon nitride, polysilicon, diamond, silicon carbide, and a metal.

45. The method of claim 40 further comprising patterning the device layer to include a geometric modification that reduces an absolute value of a first order temperature coefficient of frequency of the first eigenmode.

46. The method of claim 40 wherein the device layer comprises a first material that has a dominant crystallographic axis, and further comprising patterning the device layer such that the resonator has a first axis that is at a non-zero angle relative to the dominant crystallographic axis such that the first eigenmode has a first absolute value of a first order temperature coefficient of frequency of a first resonant mode that is less than a second absolute value of the first order temperature coefficient of frequency if the first axis were aligned with the dominant crystallographic axis.

47. The method of claim 40 further comprising electrically connecting the MEMS device with electronic circuitry.

48. The method of claim 47 further comprising forming the electronic circuitry such that the electronic circuitry and the resonator are monolithically integrated on the substrate.

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