Dual-frequency MEMS resonator with independent transduction mechanism and manufacturing method thereof

Abstract

The present disclosure relates to MEMS-based resonators and oscillators, the resonator including a resonator having a unitary resonating element having a first sub-region, a second sub-region, and a decoupler located between the first sub-region and the second sub-region such that the decoupler geometrically isolates the first sub-region and the second sub-region. 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 a mechanical energy coupling between the first sub-region and the second sub-region such that the sub-regions are substantially vibrationally isolated from each other. In some embodiments, the first sub-region supports an in-plane eigenmode and may be piezoelectrically actuated and sensed, while the second sub-region supports an out-of-plane eigenmode and may be capacitively actuated and sensed.

Description

Technical Field

[0001] This disclosure relates to microelectromechanical (MEMS) resonators and methods for manufacturing the same. Background Technology

[0002] The rise of the Internet of Things (IoT) has spurred the development of numerous sensor-based devices used in wearables, smartphones, and remote sensing for industrial and consumer applications. These devices commonly employ timing references for tracking time, synchronizing events in digital integrated circuits (ICs), and processing signals. For such applications, high-accuracy MEMS resonators are likely desirable. Summary of the Invention

[0003] This disclosure relates to a dual-frequency output MEMS oscillator and MEMS resonator operable to provide a reference signal with high-temperature stability and low phase noise. According to embodiments of this disclosure, a first reference signal can be provided via piezoelectric transduction and a second reference signal can be provided via capacitive transduction, both serving as their own temperature references. The first reference signal exhibits low frequency drift and low phase noise with varying temperature, while the second reference signal exhibits high output current and a high quality factor (Q factor). Embodiments of this disclosure provide a highly accurate and stable frequency reference with high accuracy, high output current, low power consumption, and low temperature drift.

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

[0005] In stark contrast to existing technologies, the resonator according to this disclosure has independent in-plane and out-of-plane eigenmodes, which are supported in different, geometrically isolated, and vibrationally decoupled sub-regions within the same resonator structure. Furthermore, one eigenmode is actuated and sensed via a first transduction mechanism, while the other eigenmode is actuated and sensed via a different second transduction mechanism. Therefore, embodiments according to this disclosure enable simpler device designs, improved performance with lower phase noise, and lower costs compared to those achievable in the prior art.

[0006] An exemplary embodiment is a timing reference including a dual-frequency resonator comprising an integral resonant element held above an underlying substrate, such that the resonant element and / or portions thereof are movable relative to the substrate. The resonant element includes a first sub-region and a second sub-region, and a decoupler disposed between the first and second sub-regions. The first sub-region supports in-plane eigenmodes actuated and sensed via piezoelectric transduction, and the second sub-region supports out-of-plane eigenmodes actuated and sensed via capacitive transduction. The first and second sub-regions are geometrically isolated from each other by the decoupler, which suppresses mechanical coupling between the two sub-regions. Thus, the first and second sub-regions are substantially decoupled in an oscillatory manner.

[0007] In one exemplary embodiment, the first sub-region includes four piezoelectric members arranged around a decoupler. Each piezoelectric member includes a rod of structural material operatively coupled to a piezoelectric transducer to excite and sense in-plane vibration modes in its respective rod, such that all piezoelectric members vibrate at the same frequency. Each rod is held in a clamp-and-hold arrangement between a central plate and an anchor immovably disposed on an underlying substrate, such that its respective piezoelectric member resonates at 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 with different in-plane vibration modes such as width-extension modes, bulk acoustic modes, surface acoustic modes, etc.

[0008] In one exemplary embodiment, the second sub-region includes four capacitive members arranged around a central plate. Each capacitive member includes a block of structural material that is part of a capacitive transducer for exciting and sensing out-of-plane vibration modes within that block. Each block is held in a cantilever arrangement extending from the central plate such that its corresponding capacitive member resonates in a flexural mode at a second frequency significantly lower than the first frequency. In some embodiments, the second sub-region includes a different number of capacitive members. In some embodiments, the capacitive members of the second sub-region resonate together with different out-of-plane vibration modes such as a thickness extension mode, a saddle mode, a torsional mode, etc.

[0009] The first sub-region is actuated and sensed via piezoelectric transduction and provides a first frequency signal, characterized by a first frequency, to the measurement circuit. The second sub-region is actuated and sensed via capacitive transduction and provides a second frequency signal, characterized by a second frequency, to the measurement circuit.

[0010] 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 implementations, the first sub-region includes a compensation element to control the frequency temperature coefficient of its piezoelectric component.

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

[0013] According to one embodiment of the present disclosure, a microelectromechanical system (MEMS) device includes a resonator disposed on a substrate, the resonator having an integral resonant element comprising: a first sub-region supporting a first eigenmode having a first frequency; a second sub-region supporting a second eigenmode having a second frequency different from the first frequency; and a decoupler located between the first sub-region and the second sub-region, wherein the decoupler geometrically isolates the first sub-region and the second sub-region to reduce mechanical energy coupling between the first sub-region and the second sub-region, thereby decoupling the two sub-regions substantially in an oscillatory manner.

[0014] According to another embodiment of this disclosure, a method for providing two frequency signals from a MEMS device is provided, the method comprising: exciting a first eigenmode in a first sub-region of a resonator disposed on a substrate, the resonator having an integral resonant element comprising: (i) a first sub-region supporting the first eigenmode such that the first eigenmode has a first frequency; (ii) a second sub-region supporting a second eigenmode having a second frequency different from the first frequency; and (iii) a decoupler geometrically isolating the first sub-region and the second sub-region such that mechanical energy coupling between the first sub-region and the second sub-region is reduced; 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 different from 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] According to another embodiment of the present disclosure, a method for forming a MEMS device for providing a timing reference is disclosed, the method comprising: forming a first cavity in a first substrate; bonding 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 monolithic resonant element including a first sub-region, a second sub-region, a decoupler geometrically isolating the first and second sub-regions, and at least one anchor mechanically coupling 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; bonding the third substrate and the device layer such that the resonant element is encapsulated in a chamber at least partially defined by the first and second cavities; thinning the third substrate such that the isolation trenches collectively define a plurality of electrically disconnected conductive regions, wherein a first conductive region in the plurality of conductive regions is electrically connected to the piezoelectric transducer, and wherein a second conductive region in the plurality of conductive regions defines an electrode of a capacitive transducer including a second sub-region; and forming a plurality of contact pads, each contact pad being electrically connected to a different conductive region in the plurality of conductive regions. Attached Figure Description

[0016] Figure 1 A block diagram of a system for providing timing reference according to this disclosure is depicted.

[0017] Figure 2 Operation of an exemplary method for providing a timing reference according to this disclosure is described.

[0018] Figure 3 A schematic diagram depicting a perspective view of a first exemplary resonator according to this disclosure is shown.

[0019] Figures 4A to 4B The diagrams depict the displacements caused in subregions SR1 and SR2, respectively.

[0020] Figure 5 The temperature drift of resonator 102 was depicted as predicted by simulation using the finite element method (FEM).

[0021] Figure 6 A schematic perspective view depicting a second example of a resonator suitable for use in system 100.

[0022] Figures 7A to 7B The diagrams depict the displacements induced in sub-regions SR1 and SR2 of the resonator 600, respectively.

[0023] Figure 8 The temperature drift of resonator 600 was depicted as predicted by simulation using the finite element method (FEM).

[0024] Figure 9A graph depicting the response of yet another resonator configuration according to this disclosure is shown.

[0025] Figure 10 The operation of a method suitable for manufacturing a resonator according to this disclosure is described.

[0026] Figure 11A to Figure 11F A schematic diagram depicts cross-sectional views of the resonator according to this disclosure at different manufacturing stages. Detailed Implementation

[0027] The following description merely illustrates the principles of this disclosure. Therefore, it should be understood that those skilled in the art will be able to conceive of various arrangements that, although not expressly described or shown herein, embody the principles of this disclosure and are included within its spirit and scope.

[0028] Furthermore, all examples and conditional language described herein are explicitly intended for illustrative purposes only to help the reader understand the principles of this disclosure and the concepts proposed by the inventors to advance the art, and should be regarded as examples and conditions not limited to such specific descriptions.

[0029] Furthermore, all statements herein describing the principles, aspects, and embodiments of this disclosure, and specific examples thereof, are intended to cover their structural and functional equivalents. Additionally, such equivalents are intended to include both currently known equivalents and those developed in the future, i.e., any element developed that performs the same function, regardless of its structure.

[0030] Therefore, for example, those skilled in the art will understand that any block diagram herein represents a conceptual view of an exemplary circuit embodying the principles of this disclosure. Similarly, it should be understood that any flowchart, diagram, state transition diagram, pseudocode, etc., represents various processes that can be substantially represented in a computer-readable medium and thus executed by a computer or processor (whether or not such computer or processor is explicitly shown).

[0031] The functionality of the various elements shown in the diagram (including any functional blocks that may be labeled "processor") can be provided using dedicated hardware and hardware capable of executing software in association with appropriate software. When provided by a processor, the functionality can be provided by a single dedicated processor, a single shared processor, or multiple separate processors (some of which may be shared). Furthermore, the explicit use of the terms "processor" or "controller" should not be construed as specifically referring to hardware capable of executing software, and may implicitly include, but is not limited to, digital signal processor (DSP) hardware, network processors, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs) for storing software, read-only memory (ROM), random access memory (RAM), and non-volatile storage devices. Other conventional and / or custom hardware may also be included.

[0032] A software module, or a simple module implied as software, may be represented herein as a flowchart element or any combination of other elements indicating the execution of process steps and / or a textual description. Such modules may be executed by hardware, whether explicitly or implicitly shown.

[0033] Unless otherwise expressly stated herein, the accompanying drawings, including the graphic representations, are not drawn to scale.

[0034] The following terms are defined for use in this specification (including the appended claims): • A resonant element is defined as an integral structural element capable of resonating in at least two independent eigenmodes; • A node is defined as a point within the shape of an oscillation mode where the average oscillation amplitude is less than 20% of the maximum amplitude of the oscillation mode shape. The nodes of a dual-output MEMS device resonating in out-of-plane and in-plane modes can be different or the same. • Distributed cross-sectional modes are defined as eigenmodes that are actuated in the cross-section of a device and comprise a propagation series (at least two) of substantially identical modes. Lamé (or quasi-Lamé) and shear (or quasi-shear) modes are examples of eigenmodes that can resonate in distributed cross-sectional modes; • An in-plane resonant mode is defined as a resonant mode that causes displacement along directions substantially parallel or collinear with the x and y axes of the resonator plane. Examples of in-plane resonant modes include in-plane volume acoustic (BAW) modes (such as longitudinal waves, transverse (shear) waves, and distributed cross-section modes), surface acoustic (SAW) modes (such as Rayleigh waves, Lamb waves, and Love waves), etc. • Out-of-plane resonant modes are defined as resonant modes that cause significant displacement along the xy-axis perpendicular to the device or along the z-axis relative to the plane of the resonant element. Examples of out-of-plane resonant modes include out-of-plane BAW modes (such as flexural modes, thickness extension modes, saddle modes, torsional modes, etc.); • Mechanically active regions are defined as regions of structured material that are attached to the substrate but can move relative to the substrate.

[0035] Crucially, a high-quality timing reference provides a highly accurate reference frequency signal that (1) is stable over a wide temperature range and (2) exhibits low phase noise. Previously, prior art timing references were based on quartz crystal resonators; however, silicon-based MEMS resonators have recently been introduced. Unfortunately, conventional silicon-based MEMS resonators suffer from poor temperature stability, poor phase noise performance, or both.

[0036] Temperature stability Compared to quartz crystal resonators, existing silicon-based MEMS resonators lack temperature stability, which hinders their widespread adoption. Silicon-based MEMS resonators exhibit an inherent first-order temperature-induced frequency drift of approximately -30 ppm / °C, resulting in a temperature stability of approximately 3,750 ppm over a typical industrial temperature range of -40°C to 85°C. In contrast, AT-cut quartz resonators exhibit a temperature stability of approximately 20 ppm over the industrial operating temperature range.

[0037] The frequency change of a MEMS resonator with respect to temperature is given by the equation f ( T ) = f 0[ TCF 1 ( T ) + TCF 2 ( T ) 2 The expression +… is given, where f0 is the resonant frequency of the resonator at the reference temperature, ΔT is the deviation from the reference temperature, TCF1 is the first-order temperature coefficient of frequency (TCF), and TCF2 is the second-order temperature coefficient of frequency. For monocrystalline silicon, the value of TCF2 is typically between -25 and -80 ppb / ℃. 2 Within a certain range, depending on the type and concentration of dopant, this can result in a temperature-induced frequency drift of approximately 200 ppm to 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 (approximately 3,750 ppm based on -30 ppm / °C), it is still significantly worse than the typical temperature-induced frequency drift available from AT-cut quartz crystals. Therefore, further reductions in the temperature-induced frequency drift of silicon-based MEMS resonators are desired to enable their widespread adoption in the timing market.

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

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

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

[0041] Unfortunately, many methods for actuating and sensing two independent eigenmodes in a MEMS resonator to implement dual-mode temperature sensing schemes utilize a single transducer mechanism to actuate and sense both in-plane and out-of-plane eigenmodes in the same (or substantially overlapping) geometry of the MEMS resonator. However, for certain timing applications, such as those requiring low phase noise, utilizing a single transducer mechanism to actuate and sense multiple eigenmodes in the same geometry may limit performance.

[0042] Phase noise performance Those skilled in the art will understand that phase noise in different segments of the spectrum generated by an actuated and sensed MEMS resonator is governed by different parameters. Near-carrier phase noise (<500Hz) is governed by the resonator's Q factor, but far-carrier noise depends primarily on the output current; see, for example, D. Agrawal and A. Seshia, "An analytical formula for phase noise in MEMS oscillator". IEEE Trans. Ultrasonic Ferroelectric Freq. Cont Volume 61, Issue 12, pp. 1938-1952 (2014).

[0043] As the excitation signal increases, the resonator's output current typically increases due to the increased resonator displacement. While this improves far-carrier noise, the frequency peak becomes highly nonlinear, resulting in a lower Q factor, which reduces near-carrier phase noise.

[0044] Many existing MEMS resonators are based on capacitively induced and sensed out-of-plane resonance. Unfortunately, for capacitively transduced MEMS resonators, the maximum achievable displacement is limited to about one-third of the size of a fixed gap, after which the moving element rapidly moves to contact the opposite side of the gap (a process known as "pulling in"). Furthermore, capacitive transduction is inherently a quadratic response, and electrical nonlinearity begins to appear at approximately 1 / 10 to 1 / 7 of the gap, depending on the eigenmode and gap width. Therefore, even though the motion resistance of a capacitively transduced MEMS resonator can be reduced by decreasing the gap size, this also reduces the output current due to the eventual decrease in displacement amplitude.

[0045] In contrast, quartz crystal resonators are piezoelectric transducers and their displacement is not limited by pull-in, but only by the mechanical nonlinearity of their intrinsic modes. Therefore, piezoelectric transduction is highly desirable because it generates high output current for MEMS resonators designed for low-noise applications.

[0046] However, in dual-frequency MEMS resonators, the most common configuration is the presence of both in-plane and out-of-plane eigenmodes. Unfortunately, piezoelectric transduction of out-of-plane eigenmodes has inherent and significant performance drawbacks. For example, achieving large output currents is difficult due to the relatively small stress that may be induced in the out-of-plane direction. Furthermore, the electrodes of the piezoelectric actuators typically must be wired via anchors that connect the MEMS resonator to the rest of the MEMS die, increasing anchor losses and reducing the overall Q of the MEMS resonator. Increasing the number of anchors can also amplify the stress gradient across the MEMS resonator due to wafer-level and chip-level packaging processes. Finally, using only eigenmodes with nodes suitable for side anchoring severely limits design space.

[0047] To mitigate at least some of the drawbacks associated with a single transducer mechanism, methods for actuating and sensing independent eigenmodes via independent transducer approaches have been explored.

[0048] WO 2019 / 048736 discloses an example of a frequency reference oscillator including a first oscillator and a second oscillator. The first oscillator includes an electrostatically actuated first resonator, and the second oscillator includes a piezoelectrically actuated second resonator. The first resonator is selected to have high long-term stability, and a stability control circuit using 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 and second oscillators are thermally insulated from each other, and a thermostat independently regulates the temperature of the first and second resonators. However, the need for temperature control of the oscillators significantly increases the power consumption. Furthermore, the resonators must be physically and thermally isolated, thus increasing the overall device footprint, which is undesirable for many applications such as IoT, wearable devices, etc.

[0049] Similarly, WO 2020 / 003246 discloses a dual-frequency output MEMS resonator and MEMS oscillator that can selectively and simultaneously operate in both in-plane and out-of-plane vibration modes, thereby providing two different frequencies. A system and method for determining the temperature of the dual-frequency output MEMS resonator are provided by mixing the two frequency signals together. However, in the disclosed device, the sub-regions that excite the in-plane vibration mode and the sub-regions that excite the out-of-plane vibration mode are not geometrically isolated. Therefore, mechanical energy (e.g., vibration, etc.) can easily couple between the sub-regions, resulting in undesirable stray signals when one or both vibration modes are excited.

[0050] Furthermore, the in-plane and out-of-plane vibration modes must be sufficiently far apart in frequency so that modal interference does not affect phase noise performance, thereby constraining the possible operating frequencies. In addition, using the same transduction mechanism to actuate and sense the resonator further increases the likelihood that modal coupling will reduce the Q-factor of the intrinsic modes when operating both in-plane and out-of-plane vibration modes simultaneously.

[0051] Therefore, for existing MEMS-based timing references, it is difficult (if not impossible) to provide a frequency reference with low phase noise, high accuracy, high output current, low temperature drift, low power consumption, and time stability in a small footprint.

[0052] One aspect of this disclosure is that by employing a dual-frequency MEMS oscillator and resonator that actuates and senses two independent eigenmodes via different transduction methods, many (if not all) of the limitations of the prior art described above can be overcome.

[0053] Figure 1 A block diagram of a system for providing a timing reference according to the present disclosure is depicted. System 100 includes a resonator 102, oscillators OSC1 and OSC2, and measurement circuitry 104.

[0054] Figure 2 Operation of an exemplary method for providing a timing reference according to this disclosure is depicted. Method 200 begins with operation 201, in which a resonator 102 is provided. Continuing to refer to... Figure 1 And reference Figures 3 to 5 Let's describe method 200.

[0055] The resonator 102 is a silicon-based dual-frequency MEMS device configured to actuate and sense two independent eigenmodes using different transduction mechanisms, each of which appears in a different sub-region of the device.

[0056] One aspect of this disclosure is that a resonator having an integral resonant element comprising a geometrically isolated first sub-region and a second sub-region provides a significant advantage over the prior art, wherein a first eigenmode is realized in the first sub-region and a second eigenmode is realized in the second sub-region.

[0057] It will be apparent to those skilled in the art that if there exists a common subregion of the same resonator with two vibrational modes that are strongly excited during modal vibration, mechanical energy can couple between the two modes (i.e., leakage) even at different frequencies during simultaneous operation. For example, in the case of independent in-plane and out-of-plane modes, some undesirable stray electrical signals may appear in the out-of-plane mode if the in-plane mode causes small out-of-plane excitation (due to mode shape defects), or vice versa.

[0058] However, in embodiments according to this disclosure, the sub-regions of the resonator are separated by decouplers that suppress vibrational coupling between the sub-regions. Therefore, mechanical energy leakage from one mode to another is reduced, and leakage signals (spurious signals) are decreased. Furthermore, undesirable spurious modes can also cause a decrease in the Q-factor in the actuated mode. Therefore, the MEMS resonator according to this disclosure is configured to have in-plane and out-of-plane eigenmodes in geometrically isolated sub-regions, wherein the eigenmodes are actuated and sensed using independent transduction mechanisms. Such resonators are particularly desirable in some applications, such as those requiring low phase noise.

[0059] like Figure 1 As depicted, resonator 102 is an integral structure comprising sub-regions SR1 and SR2 and a decoupler 106 disposed between the sub-regions. Resonator 102 is configured such that each of the sub-regions SR1 and SR2 supports the formation of different eigenmodes, and decoupler 106 substantially suppresses vibrational coupling between the two sub-regions. In other words, although sub-regions SR1 and SR2 and decoupler 106 are adjacent portions of the same resonant element, decoupler 106 geometrically isolates sub-regions SR1 and SR2.

[0060] Figure 3 A schematic perspective view of a first exemplary resonator according to the present disclosure is depicted. The resonator 102 includes a resonant element 302, an anchor 304, a portion of a piezoelectric transducer 306 and a capacitive transducer 308, all disposed on a substrate 310.

[0061] The resonant element 302 is an integral component of the structural material M1. The resonant element 302 includes beams 312A, 312B, 312C, and 312D (collectively referred to as beam 312), blocks 308A, 308B, 308C, and 308D, a central member 314, and a fastener 316.

[0062] Each of the beams 312 is held between the anchor 304 and the central member 314 by a clamp-on arrangement. The beams 312 collectively define a subregion SR1 configured to support a desired in-plane eigenmode having a frequency F1 and a first frequency temperature coefficient TCF. A In the depicted example, subregion SR1 is configured to resonate in a quasi-width extension (WE) mode. In some embodiments, subregion SR1 is configured to resonate in different in-plane modes such as Lamé mode, quasi-Lamé mode, shear mode, quasi-shear mode, etc.

[0063] It should be noted that while the described examples include resonators directly attached to rigid anchors, many alternatives to this configuration are within the scope of this disclosure. For example, the resonator can: i. Attached to an anchor post formed by the substrate 310; or ii. An anchor post attached to a capping substrate included in the resonator structure; or iii. Anchor posts attached to a device layer included in the resonator structure; or iv. Anchor posts attached to one or more non-edge nodes of the resonator; or v. To attach to an anchor, including an anchoring spring configured to reduce anchor wear; or vi. Electrically grounded via at least one 304 anchor; or vii. Any combination of i, ii, iii, iv, v, and vi.

[0064] Each of blocks 308A to 308D is connected to the central member 314 by a tether 316, such that the blocks are held in a cantilevered arrangement that enables their out-of-plane motion. Blocks 308A to 308D collectively define a subregion SR2, which is configured to support a desired out-of-plane eigenmode having a frequency F2 and a second frequency temperature coefficient TCF. B Preferably, TCFB The absolute value of the first-order component, which is not equal to 0 ppm / ℃, is |TCF B,1 |and as close to 0 ppb / ℃ as possible 2 absolute value of second-order component | TCF B,2 |

[0065] The central member 314 and the tethering member 316 together define the decoupler 106, which is configured to geometrically isolate sub-regions SR1 and SR2, thereby suppressing vibration coupling between the two sub-regions.

[0066] Anchor 304 is a pillar of structural material M1 configured to hold resonant element 302 above substrate 310, thereby enabling beam 312 and blocks 308A to 308D to move relative to the substrate, thus making the beams and blocks mechanically active. In the depicted example, substrate 310 is a conventional single-crystal silicon wafer; however, any substrate suitable for MEMS fabrication may be used without departing from the scope of this disclosure.

[0067] In the depicted example, at least one anchor 304 is connected to a node of sub-region SR1 to reduce anchor wear. In some embodiments, at least one anchor 304 is connected to its corresponding beam 312 to reduce anchor wear, wherein the anchoring spring is configured to reduce anchor wear even when connected to a non-node.

[0068] In the example depicted, the structural material M1 is monocrystalline silicon; however, those skilled in the art will recognize upon reading this specification that many other structural materials may be used in the resonant element 302 and / or the anchor 304 without departing from the scope of this disclosure.

[0069] Furthermore, preferably, the structural material M1 is uniformly doped with a dopant having a concentration that reduces the absolute value of the second-order frequency temperature coefficient |TCF2| of the in-plane vibration modes of beam 312. Preferably, within the desired operating temperature range of system 100, |TCF2| is reduced to be as close as possible to 0 ppb / ℃. 2 In the depicted example, the desired operating temperature range is -40°C to 85°C; however, other operating temperature ranges are also within the scope of this disclosure. In the depicted example, the structural material M1 has a concentration of about 1.0 × 10⁻⁶. 20 cm -3 and 2.4×10 20 cm -3 The highly n-type doped single-crystal silicon between these layers results in |TCF2| being less than approximately 1 ppb / ℃. 2 In some implementations, the structural material M1 is doped such that |TCF2| is less than about 0.01 ppb / ℃. 2 .

[0070] Furthermore, in the depicted example, at least one sub-region of the resonant element 302 is geometrically modified to reduce the absolute value of the first-order frequency temperature coefficient |TCF1| of the in-plane vibration mode of beam 312 to as close as possible to zero within the desired operating temperature range of system 100. For the purposes of this specification (including the appended claims), the term "geometric modification" is defined as altering the structural material of sub-region SR1 such that its |TCF1| is lower than the nominal |TCF1| it would have without such alteration. Examples of geometric modifications according to this disclosure include: i. A change in the shape of at least a portion of subregion SR1 (e.g., beam 312, etc.); or ii. An angular offset between the principal crystal axis of the monocrystalline silicon and the longitudinal axis of at least one beam 312, wherein the longitudinal axis is the axis that exhibits the dominant motion during resonant oscillation; or iii. Combinations of i and ii.

[0071] In the depicted example, by aligning the longitudinal axis of at least one of the beams 312, it is made possible from the monocrystalline silicon... <110> The crystal axis is rotated at an angle of approximately 34°, thereby geometrically modifying the resonant element 302. In the depicted example, this geometric modification produces a |TCF1| value of less than approximately 1 ppm / °C. In some embodiments, the |TCF1| value is reduced to less than approximately 0.01 ppm / °C.

[0072] It should be noted that the absolute value of |TCF2| of the in-plane resonant mode of a uniformly doped resonant element over the operating temperature range can be achieved by doping the element with n-type dopant, p-type dopant, or a combination of n-type and p-type dopant. In some embodiments, the resonant element is doped with n-type dopant at a concentration between approximately 1.0 × 10⁻⁶. 20 cm -3 and 2.4×10 20 cm -3 In some implementations, the resonant element is doped with a p-type dopant at a concentration between 2.0 × 10⁻⁶. 20 cm -3 and 2.4×10 20 cm -3 Between, so as to reduce |TCF2| to about 0 ppb / ℃ 2 It should also be noted that the materials, dopants, and doping levels provided herein are merely exemplary, and many alternatives may be used without departing from the scope of this disclosure.

[0073] The piezoelectric transducer 306 includes piezoelectric elements 306A, 306B, 306C, and 306D, which are operatively coupled to beams 312A through 312D, respectively. Each of the piezoelectric elements 306A through 306D includes a layer stack disposed on its respective beam 312, wherein the layer stack includes a layer of piezoelectric material disposed between a pair of electrical contacts. The piezoelectric transducer 306 is configured as an actuation and sensing sub-region SR1. It should be noted that, although not in Figure 3 As shown, the conductive traces used to provide electrical connections to the electrodes of the piezoelectric elements 306A to 306D are wired via anchor 304.

[0074] The capacitor transducer 308 comprises blocks 308A to 308D, each block acting as one plate of a parallel-plate capacitor. Although not explicitly stated... Figure 3 As shown, each capacitor includes a second plate disposed above one of blocks 308A to 308D. The capacitive transducer 308 is configured to actuate and sense the sub-region SR2.

[0075] As described above, the decoupler 106 is configured to geometrically isolate sub-regions SR1 and SR2, thereby suppressing vibrational coupling between the two sub-regions.

[0076] Figures 4A to 4B The diagrams depict the displacements induced in subregions SR1 and SR2, respectively. It should be noted that in Figures 400 and 402, no displacement is indicated by a light shade and the maximum displacement is indicated by the darkest shade.

[0077] As shown in Figure 400, the displacement caused by the in-plane eigenmode of the resonator 102 is essentially isolated from subregion SR1, and produces little or no displacement in subregion SR2.

[0078] In a similar manner, Figure 402 shows that the displacement caused therein by the out-of-plane eigenmodes of the resonator 102 is substantially isolated from subregion SR2, while producing little or no displacement in subregion SR1.

[0079] As is evident from Figures 400 and 402, including decoupler 106 substantially suppresses the mechanical energy coupling between subregions SR1 and SR2.

[0080] Now back Figure 1Oscillator OSC1 is electrically connected to resonator 102, enabling it to operate for actuating and sensing desired in-plane eigenmodes in sub-region SR1. Similarly, oscillator OSC2 is electrically connected to resonator 102, enabling it to operate for actuating and sensing desired out-of-plane eigenmodes in sub-region SR2. It should be noted that, although not shown here, system 100 typically also includes power supply components to provide alternating current (AC) and / or direct current (DC) electrical signals to actuate and sense sub-regions of resonator 102.

[0081] At operation 202, the oscillator OSC1 actuates and senses the in-plane eigenmode in the sub-region SR1.

[0082] Oscillator OSC1 provides an electrical signal 108A, characterized by a first frequency F1 (the frequency of the excited in-plane resonant mode) and a first characteristic phase noise N1. In the depicted example, oscillator OSC1 includes a transimpedance amplifier (TIA) connected to automatic gain control (AGC). The TIA converts the current from at least one sub-region configured for piezoelectric transduction into the electrical signal 108A, while the AGC modulates the oscillation amplitude and reduces mechanical nonlinear effects.

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

[0084] In the depicted example, the oscillator OSC2 is configured to actuate and sense the out-of-plane vibration modes of the sub-region SR2 using capacitive transduction. Typically, the oscillator OSC2 excites the fundamental out-of-plane resonant modes in the sub-region SR2.

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

[0086] The resonator 102 is configured such that the frequency F1 is greater than the frequency F2 and the phase noise N1 is less than the phase noise N2. One or both of the first oscillator and the second oscillator can be configured to operate selectively, operate at specific time intervals, or operate continuously.

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

[0088] Circuit 104 includes a complementary metal-oxide-semiconductor (CMOS) circuit configured to mix frequency signals 108A and 108B and provide a corresponding output signal 110, as well as various other functions. In the depicted example, circuit 104 is a nonlinear circuit configured to generate a temperature signal based on frequency signals 108A and 108B using various specific implementations and topologies known in the art. In the depicted example, the output signal 110 is characterized by a third frequency F3 proportional to the temperature of resonator 102.

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

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

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

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

[0093] Figure 5 The temperature drift of resonator 102 was depicted as predicted by simulation using the finite element method (FEM).

[0094] It should be noted that the configuration of the system 100 described above is merely one specific embodiment of this disclosure. For example, in some embodiments, sub-region SR1 is configured to operate in out-of-plane vibration mode, while sub-region SR2 is configured to operate in out-of-plane vibration mode. Upon reading this specification, it will be apparent to those skilled in the art that other combinations of intrinsic modes can be conceived without departing from the scope of this disclosure.

[0095] It should also be noted that the resonator 102 is merely an example of a resonator configuration with two geometrically isolated sub-regions, each supporting a different independent eigenmode, and each eigenmode can be actuated and sensed by different transduction methods according to this disclosure.

[0096] Figure 6A schematic perspective view depicting a second example of a resonator suitable for use in system 100 is shown. The resonator 600 includes a resonant element 602, an anchor 304, a piezoelectric transducer 606, and a capacitive transducer 608, all disposed on a substrate 310.

[0097] The resonant element 602 includes beams 612A, 612B, 612C, and 612D (collectively referred to as beam 612), blocks 608A, 608B, 608C, and 608D, member 614, and fastener 616, which are respectively similar to beam 312, blocks 308A to 308D, central member 314, and fastener 316.

[0098] The piezoelectric transducer 606 includes piezoelectric elements 606A, 606B, 606C, and 606D, which are operatively coupled to beams 612A to 612D, respectively.

[0099] The capacitor transducer 608 includes blocks 608A to 608D, each of which acts as one plate of a parallel-plate capacitor.

[0100] Piezoelectric elements 606A to 606D and beams 612A to 612D together define sub-region SR1, while blocks 608A to 608D together define sub-region SR2.

[0101] The piezoelectric transducer 606 and the capacitor transducer 608 are similar to those described above and regarding Figure 3 The piezoelectric transducer 606 and the capacitive transducer 608 are described. The piezoelectric transducer 606 is configured to actuate and sense a desired in-plane eigenmode in the actuation and sensing sub-region SR1, while the capacitive transducer 608 is configured to actuate and sense a desired out-of-plane eigenmode in the actuation and sensing sub-region SR2.

[0102] Component 614 and tether 616 together define a decoupler 604 similar to decoupler 106. Decoupler 604 is configured to geometrically isolate subregions SR1 and SR2, thereby decoupling the two subregions substantially in a vibratory manner.

[0103] Therefore, similar to the resonator 102 described above, the resonator 600 is configured with an arrangement of beams, anchors, blocks, tethers, decouplers, and transducers, which together define a monolithic element of structural material M1. This monolithic element has a first sub-region configured to support in-plane eigenmodes and a second sub-region configured to support out-of-plane eigenmodes, wherein the first and second sub-regions are geometrically isolated by decouplers. Although some or all of the elements of the resonator 600 are configured and / or arranged differently from those of the resonator 102, the resonator 600 is operationally similar to the resonator 102.

[0104] It should be noted that when beams 612A to 612D are made of a single material (monocrystalline silicon in the depicted example), the subregion SR1 is characterized by the first absolute value of the temperature coefficient of the first frequency of its in-plane resonant mode, |TCF1|1.

[0105] However, in the depicted example, each of the beams 612 includes a plurality of compensation features 618 in each of the monocrystalline silicon beams, which modify the beam such that the absolute value of the first-order frequency temperature coefficient of its in-plane resonant mode is reduced to below the value |TCF1|1|2. Preferably, |TCF1|2 is reduced to the lowest possible value (e.g., about 0 ppm / °C). For the purposes of this specification (including the appended claims), "compensation material" is defined as a material having material properties different from those of the structural material forming the body of its respective resonant element. For example, for a beam where the structural material M1 is monocrystalline silicon, suitable compensation materials include, but are not limited to, silicon oxide, undoped silicon, silicon nitride, polycrystalline silicon, diamond, silicon carbide, and metals. Other suitable structures and compensation materials will become apparent to those skilled in the art upon reading this disclosure. In some embodiments, the compensation material has a first-order frequency temperature coefficient and / or a second-order frequency temperature coefficient with the opposite sign to the frequency temperature coefficient of the structural material M1.

[0106] In the depicted example, each compensating feature 618 is a region with compensating material, the width of which is less than the width of its corresponding beam 612. Each compensating feature 618 is formed within its corresponding beam such that its compensating material extends through the entire thickness of the beam. In some embodiments, the compensating feature 618 extends only partially into the thickness of its corresponding beam, resides on one or more surfaces of its corresponding beam, or is any combination thereof.

[0107] Figures 7A to 7B The diagrams depict the induced displacements in sub-regions SR1 and SR2 of resonator 600, respectively. It should be noted that in Figures 700 and 702, no displacement is indicated by a light shade and the maximum displacement is indicated by the darkest shade.

[0108] As shown in Figure 700, the displacement caused by the in-plane eigenmode of the resonator 600 is essentially isolated from subregion SR1, and produces little or no displacement in subregion SR2.

[0109] In a similar manner, Figure 702 shows that the displacement caused therein by the out-of-plane eigenmodes of the resonator 600 is substantially isolated from subregion SR2, while producing little or no displacement in subregion SR1.

[0110] As is evident from Figures 700 and 702, including decoupler 604 substantially suppresses the mechanical energy coupling between subregions SR1 and SR2.

[0111] Figure 8 The temperature drift of resonator 600 was depicted as predicted by simulation using the finite element method (FEM).

[0112] It should be noted that resonators 102 and 600 are merely two examples of the many resonator configurations according to this disclosure.

[0113] Figure 9 A graph depicting the response of another resonator configuration according to this disclosure is shown. Modeling results of the mechanical behavior of resonator 900 are provided in Figures 902, 904, 906, and 908. Resonator 900 is similar to resonators 102 and 600 and includes: a first sub-region (i.e., SR1) configured to support in-plane resonant modes; a second sub-region (i.e., SR2) configured to support out-of-plane resonant modes; and a decoupler that geometrically isolates the two sub-regions as discussed above. In a manner similar to resonators 102 and 600, sub-region SR1 is configured for piezoelectric transduction and sub-region SR2 is configured for capacitive transduction.

[0114] Figure 902 depicts the displacement pattern of subregion SR1 when resonating in an in-plane mode with piezoelectric transduction, specifically the displacement pattern of the distributed cross-sectional shear mode.

[0115] Figure 904 depicts the volumetric strain pattern that appears in subregion SR1 when resonance occurs in a distributed cross-sectional shear mode.

[0116] Figure 906 depicts the displacement pattern that appears in subregion SR2 when resonating in flexural mode.

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

[0118] Figure 10 The operation of a method suitable for manufacturing a resonator according to this disclosure is described herein. (References provided in this document are not included.) Figure 6 Method 1000 is illustrated in Figures 11A to 11E. However, it should be noted that the manufacturing steps described herein are merely exemplary, and many variations of suitable manufacturing methods will become apparent to those skilled in the art upon reading this disclosure.

[0119] Figure 11A to Figure 11F A schematic diagram depicts cross-sectional views of the resonator according to this disclosure at different manufacturing stages.

[0120] Method 1000 begins with operation 1001, in which a cavity 1102 is formed in the substrate by etching from surface 1104 into the substrate 310 in a conventional manner. The cavity 1102 is formed to a depth sufficient to allow full motion of blocks 608A to 608D when the desired out-of-plane eigenmode is excited in sub-region SR2. In some embodiments, the depth of cavity 1102 is also selected to enable a suitable final vacuum level to be achieved in the cavity once the resonator fabrication is complete. Typically, surface 1104 includes a layer of electrical insulator (as shown), such as silicon dioxide, to facilitate bonding with substrate 1106 and to provide electrical isolation between adjacent elements of resonator 600, as described below.

[0121] At optional operation 1002, compensation features 618 are formed in substrate 1106 such that they partially extend through the thickness of the substrate. In the depicted example, substrate 1106 includes a structural material M1, which is a uniformly doped monocrystalline silicon with a given concentration of dopant that reduces the absolute value of the second-order frequency temperature coefficient |TCF2| of at least one desired intrinsic mode to a very low value within the expected operating temperature of system 100, as described above and with respect to resonator 102. In some embodiments, substrate 310 is a conventional monocrystalline silicon substrate doped in substantially the same manner as substrate 1106; however, other materials and / or doping concentrations may also be used for substrate 310.

[0122] In the depicted example, the compensation feature 618 comprises silicon dioxide and is formed by first creating vertical trenches extending from surface 1108 into substrate 1106 using conventional patterning and etching techniques. Once the trenches are formed, they are filled with a compensation material M2, which is selected based on the material used as structural material M1. In the depicted example, the compensation material M2 is silicon dioxide, and the trenches are completely filled by conventional methods (e.g., oxidation, chemical vapor deposition, spin coating, evaporation, sputtering, electroplating, growth, etc.). In some embodiments, the trenches are only partially filled with compensation material. In some embodiments, the compensation material M2 is not silicon dioxide. Alternative compensation materials suitable for this disclosure include, but are not limited to, silicon nitride, polycrystalline silicon, diamond, silicon carbide, metals, etc. After reading this specification, those skilled in the art should understand how to select suitable materials for use as structural material M1 and compensation material M2.

[0123] It should be noted that, as discussed above, the compensation feature 618 represents only one method of modification for reducing the value of |TCF1|. In some embodiments, for example, geometric modifications are used to reduce the value of |TCF1|. Geometric modifications according to this disclosure include, but are not limited to, aligning the resonant element 302 (or the resonant element 602, etc.) at a non-zero angle relative to the principal crystal axis of its structural material, changing the shape of the sub-region SR1, etc.

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

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

[0126] At operation 1004, the thickness of substrate 1106 is reduced to form the desired thickness of resonant element 602, thereby defining device layer 1110 having top surface 1112. In some embodiments, compensation feature 618 has a different depth than resonant element 602, such that compensation feature does not extend completely through the resulting thickness of device layer 1110. In the depicted example, substrate 1106 is thinned by grinding and polishing; however, any conventional method may be used to thin substrate 1106 without departing from the scope of this disclosure.

[0127] Figure 11B depicts the bonding of substrates 310 and 1106 after the substrate 1106 has been thinned to form device layer 1110.

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

[0129] At operation 1006, a separation trench 1116 is etched through the device layer 1110 via conventional patterning and etching, thereby defining the shape of the resonator 600 (including the resonant element 602 and the anchor 304). In some embodiments, the separation trench 1116 is formed simultaneously with the trench for compensating feature 618 during operation 1002. In some embodiments, the shape of the resonator 600 is defined at different points during the manufacturing process.

[0130] Figure 11C depicts the newly formed resonator 600' after the formation of the piezoelectric transducer 606, contact 1114, and separation trench 1116. For clarity, only the contact 1114 of the piezoelectric transducer 606 is shown in Figure 11C, and the top and bottom electrodes are not shown.

[0131] At operation 1007, one or more isolation trenches 1122 are formed by etching trenches into surface 1120 and backfilling the trenches with a dielectric material in a conventional manner, partially penetrating the thickness of the capping substrate 1118. In the depicted example, the capping substrate 1118 is a monocrystalline silicon substrate, and the isolation trenches 1122 are filled with silicon dioxide in a manner similar to that of the compensation feature 618 discussed above. In some embodiments, the isolation trenches 1122 are filled with a material other than silicon dioxide, such as doped polycrystalline silicon, silicon nitride, or a combination of suitable materials.

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

[0133] In optional operation 1009, getter 1126 is formed by depositing getter material in cavity 1124 in a conventional manner.

[0134] In some implementations, such as those intended for applications where a high vacuum environment is not required for resonator 600, or resonators with a sufficiently high Q factor, optional operations 1008 and 1009 are not necessary.

[0135] At operation 1010, the capping substrate 1118 is bonded to the device layer 1110 in a conventional manner to form the chamber 1128 of the encapsulated resonator 600.

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

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

[0138] It should be noted that after the capping substrate 1118 has been thinned to its appropriate thickness, the isolation trench 1122 defines various other features that can be electrically disconnected from each other, such as the top electrode 1130 of the capacitive transducer 608 (also referred to herein as the capacitive electrode), through-silicon vias (TSVs) 1132 for electrically connecting the contacts 1114 of the piezoelectric elements 606A to 606D, etc. The top electrode 1130 may be located directly above the corresponding sub-region SR2 of the device layer for out-of-plane actuation and resonance of the capacitive transducer.

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

[0140] At operation 1013, the resonator 600 is fabricated by forming electrical contact pads 1136.

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

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

[0143] Although each of substrates 310, 1106, and 1118 is a monocrystalline silicon substrate, other materials may be used for any of these substrates without departing from the scope of this disclosure. Alternative substrate materials include, but are not limited to, silicon carbide, polycrystalline silicon, compound semiconductors, glass, etc.

[0144] In some implementations, the resonator includes additional MEMS devices (e.g., sensors, actuators, accelerometers, etc.) and / or electronic circuitry. For example, the depicted examples are compatible with fabrication in CMOS processing facilities, thereby enabling monolithic integration of CMOS electronics with the resonator according to this disclosure.

[0145] Furthermore, while method 1000 is capable of fabricating a MEMS device comprising a set of capacitive electrodes and a set of piezoelectric electrodes, different configurations of resonators with different electrode arrangements can be realized without departing from the scope of this disclosure.

[0146] For example, one or more separation trenches 1116 may be configured to define one or more independent tuning electrodes capable of introducing complex strain into the resonant structure. Alternatively, fabrication of the resonator according to this disclosure may include fabricating a set of capacitive electrodes in device layer 1110 such that they achieve in-plane capacitive transduction of in-plane intrinsic modes. Furthermore, fabrication of the resonator according to this disclosure may include fabricating a set of capacitive electrodes in substrate 310 such that they are positioned below device layer 1110. Further, device layer 1110 may be doped with a given concentration such that at least a portion of the resonant element is sufficiently conductive to function as an electrode, thereby preventing the deposition of bottom electrodes for piezoelectric elements 606A to 606D.

[0147] It should be understood that this disclosure teaches only one example of an exemplary embodiment, and those skilled in the art can readily conceive of many variations of the embodiments according to this disclosure after reading it, and the scope of the invention is defined by the following claims.

Claims

1. A microelectromechanical system (MEMS) device, the MEMS device comprising a resonator disposed on a substrate, the resonator having an integrated resonant element, the integrated resonant element comprising: A first sub-region, wherein the first sub-region supports a first eigenmode having a first frequency; The second sub-region supports a second eigenmode having a second frequency different from the first frequency; as well as A decoupler located between a first sub-region and a second sub-region, wherein the decoupler geometrically isolates the first sub-region and the second sub-region to reduce mechanical energy coupling between the first sub-region and the second sub-region.

2. The MEMS device according to claim 1, further comprising: A piezoelectric transducer, wherein the piezoelectric transducer is operatively coupled to the first sub-region to operate the first sub-region by piezoelectric transduction; And an electrode, which is operatively coupled to the second sub-region to operate the second sub-region via capacitive transduction.

3. The MEMS device according to claim 1, wherein the first intrinsic mode is an in-plane intrinsic mode.

4. The MEMS device according to claim 3, wherein the first intrinsic mode is an in-plane volume acoustic mode or a surface acoustic mode.

5. The MEMS device according to claim 1, wherein the second intrinsic mode is an out-of-plane intrinsic mode.

6. The MEMS device according to claim 5, wherein the second intrinsic mode is a bulk acoustic mode.

7. The MEMS device according to 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 to the substrate via a first anchor.

9. The MEMS device according to claim 8, wherein the first anchor is located at a node of the first intrinsic mode.

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

11. The MEMS device according to claim 1, wherein the first intrinsic mode is an in-plane intrinsic mode and the second intrinsic mode is an out-of-plane intrinsic mode.

12. The MEMS device of claim 1, wherein the resonator comprises monocrystalline silicon and passes through a density of less than or equal to 1 ppb / ℃. 2 It is characterized by the absolute value of the second-order frequency temperature coefficient (|TCF2|).

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 monocrystalline silicon and passes through a density of less than or equal to 0.01 ppb / ℃. 2 The |TCF2| is used to characterize it.

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 a single-crystal silicon having a first crystal axis, and the first sub-region having a first axis along which the first sub-region exhibits the dominant motion of the first intrinsic mode, and wherein the first crystal 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 (|TCF1|) of a first-order frequency temperature coefficient, wherein if the first crystal axis is aligned with the first axis, the first absolute value is lower than the nominal absolute value of |TCF1|.

17. The MEMS device of claim 1, wherein when the first sub-region comprises a first material and a compensation material, wherein the first material is characterized by a first absolute value (|TCF1|1) of the first-order frequency temperature coefficient of the first intrinsic mode, and wherein the first material and the compensation material are jointly characterized by a second absolute value (|TCF1|2) of the first-order temperature coefficient of the first intrinsic mode that is less than |TCF1|1.

18. The MEMS device of claim 17, wherein the compensation material has a first-order frequency temperature coefficient and / or a second-order frequency temperature coefficient with the opposite sign to the frequency temperature coefficient of the first material.

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

20. The MEMS device of claim 17, wherein the first sub-region includes at least one beam, the at least one beam including at least one compensation feature containing the compensation material.

21. The MEMS device of claim 17, wherein the first material is doped single-crystal silicon, and the compensation material is selected from the group consisting of silicon oxide, undoped single-crystal silicon, silicon nitride, polycrystalline silicon, diamond, silicon carbide, and metals.

22. The MEMS device of claim 1, further comprising a piezoelectric transducer for actuating and sensing the first intrinsic mode.

23. The MEMS device of claim 1, further comprising a capacitive electrode for actuating and sensing the second intrinsic mode.

24. The MEMS device according to claim 1, further comprising: A piezoelectric transducer for actuating and sensing the first intrinsic mode; as well as Capacitive electrodes for actuating and sensing the second intrinsic mode; The first eigenmode is an in-plane eigenmode.

25. The MEMS device according to claim 24, further comprising: A first oscillator, wherein the first oscillator is operatively coupled to the piezoelectric transducer; as well as A second oscillator is operatively coupled to the capacitive electrode.

26. The MEMS device according to claim 1, wherein the MEMS device is a MEMS oscillator.

27. The MEMS device according to claim 1, wherein the MEMS device further comprises 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 comprising: A first eigenmode is excited in a first sub-region of a resonator disposed on a substrate, the resonator having an integral resonant element comprising: (i) A first sub-region, the first sub-region supporting the first intrinsic mode, such that the first intrinsic mode has a first frequency; (ii) a second sub-region, the second sub-region supporting a second eigenmode having a second frequency different from the first frequency; and (iii) A decoupler that geometrically isolates the first sub-region and the second sub-region such that the mechanical energy coupling between the first sub-region and the second sub-region is reduced; Sensing the first eigenmode, wherein the first eigenmode is excited and sensed via a first transduction mechanism; The second intrinsic mode in the second sub-region is excited and sensed via a second transduction mechanism different from the first transduction mechanism; Provide the first sensed eigenmode as a first frequency signal; and The second sensed intrinsic mode is provided as a second frequency signal.

29. The method of claim 28, further comprising providing a first transducer method as a piezoelectric transducer.

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

31. The method of claim 28, further comprising providing the first transducer as a piezoelectric transducer and providing the second transducer as a capacitive transducer.

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

33. The method of claim 32, wherein the first intrinsic mode is a bulk acoustic mode or a surface acoustic mode.

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 intrinsic mode is selected from the group consisting of a free flexure mode, a thickness extension mode, a saddle-shaped mode, and a torsion mode.

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 intrinsic mode in the first sub-region with a first oscillator and exciting the second intrinsic mode in the second sub-region with a second oscillator.

38. The method of claim 37, wherein the first sub-region has a first temperature coefficient of frequency (TCF) and a first characteristic phase noise, and wherein the second sub-region 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 for forming a MEMS device for providing a timing reference, the method comprising: A first cavity is formed in a first substrate; Join the second substrate and the first substrate; Thin the second substrate to define the device layer; A piezoelectric transducer is formed on the first sub-region of the device layer; The device layer is patterned to form a resonator, the resonator including a monolithic resonant element, the monolithic resonant element including a first sub-region supporting a first eigenmode having a first frequency, a second sub-region supporting a second eigenmode having a second frequency, a decoupler geometrically isolating the first sub-region and the second sub-region, and at least one anchor mechanically coupling the first sub-region and the substrate. Multiple isolation trenches are formed that extend through a portion of the third substrate; A second cavity is formed in the third substrate; The third substrate and the device layer are joined such that the resonant element is encapsulated in a chamber at least partially defined by the first cavity and the second cavity; The third substrate is thinned such that the isolation trenches collectively define a plurality of electrically disconnected conductive regions, wherein a first conductive region in the plurality of conductive regions is electrically connected to the piezoelectric transducer, and wherein a second conductive region in the plurality of conductive regions defines an electrode of a capacitive transducer including the second sub-region. as well as Multiple contact pads are formed, and each contact pad is electrically connected to a different conductive region in the multiple conductive regions.

41. The method of claim 40, wherein each of the first substrate, the second substrate, and the third substrate comprises monocrystalline silicon.

42. The method of claim 41, wherein at least one of the first substrate, the second substrate, and the third substrate is single-crystal silicon doped with an n-type dopant, the doping concentration of the n-type dopant being approximately 1.0 × 10⁻⁶. 20 cm -3 From approximately 2.4 × 10 20 cm -3 Within the range.

43. The method of claim 41, wherein at least one of the first substrate, the second substrate, and the third substrate is single-crystal silicon doped with a p-type dopant, the p-type dopant having a doping concentration of about 2.0 × 10⁻⁶. 20 cm -3 From approximately 2.4 × 10 20 cm -3 Within the range.

44. The method of claim 41, further comprising forming at least one compensation feature in the first sub-region, wherein the at least one compensation feature comprises a compensation material selected from the group consisting of silicon oxide, undoped single-crystal silicon, silicon nitride, polycrystalline silicon, diamond, silicon carbide, and metals.

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

46. ​​The method of claim 40, wherein the device layer comprises a first material having a principal crystal axis, and the method further comprises patterning the device layer such that the resonator has a first axis at a non-zero angle relative to the principal crystal axis, such that the first intrinsic mold has a first absolute value of a first frequency temperature coefficient of a first resonant mode, wherein if the first axis is aligned with the principal crystal axis, the first absolute value is less than a second absolute value of the first frequency temperature coefficient.

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

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

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