Patent Application
20190140612
This invention relates to microelectromechanical resonator devices and their associated oscillator control circuits, and more particularly to methods and designs allowing for improved manufacturability and performance including:
Reference oscillators are of great interest because of their ubiquitous use in timing applications generally, and in modern wireless communication devices particularly. They are indispensable to ensure proper synchronization in almost any system. Microelectromechanical system (MEMS) resonators are receiving continuously increasing interest due to their small size as well as their potential for integration with other MEMS devices and electrical circuits on the same chip which makes them excellent candidates for replacing crystal-based resonators in many timing applications. This is especially important for handheld and wearable electronic devices addressing high volume consumer orientated applications where weight, size, and cost are critical parameters.
Accordingly, it is important that the MEMS resonators be manufacturable using semiconductor processing techniques that are either common to those used in low cost electronics such as complementary metal-oxide-semiconductor (CMOS) based electronics for direct monolithic integration or compatible with MEMS formation post-electronics formation with high yield. Accordingly, within the prior art, MEMS resonator performance parameters such as quality factor (Q) and motional resistance are commonly optimized for different resonator designs through aspects such as DC bias, narrow suspension beams and narrow transduction gaps. However, such aspects are typically contrary to the desire for high manufacturing yields and exploitation of lower cost micron resolution semiconductor process lines rather than state-of-the-art sub-micron resolution semiconductor processing lines.
Equally, reduced resonator performance can set severe requirements for the oscillation sustaining circuitry, for example gain and power consumption, in order to reach good overall performance for the MEMS resonator based oscillator. Such control sustaining circuitry typically employ single-ended transimpedance amplifiers (TIAs), due to their lower power consumption than fully differential TIAs, with gain-bandwidth enhancement techniques to improve input-referred noise, as single sided TIA noise performance is worse than differential TIAs, and power consumption.
Accordingly, it would be beneficial to provide MEMS designers with MEMS resonator designs and manufacturing processes that whilst supporting the use of low cost low resolution semiconductor processing yield improved resonator performance thereby reducing the requirements of the oscillator circuitry. It would be further beneficial for the oscillator circuitry to be able to leverage the improved noise performance of differential TIAs without sacrificing power consumption.
Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures.
It is an object of the present invention to mitigate limitations in the prior art relating to microelectromechanical resonator devices and their associated oscillator control circuits, and more particularly to methods and designs allowing for improved manufacturability and performance including:
In accordance with an embodiment of the invention there is provided a method for providing a MEMS device comprising:
In accordance with an embodiment of the invention there is provided a method of forming a MEMS resonator comprising:
In accordance with an embodiment of the invention there is provided a MEMS resonator device comprising:
A method of providing a MEMS resonator device comprising: providing a MEMS resonator comprising:
In accordance with an embodiment of the invention there is provided a MEMS oscillator comprising
In accordance with an embodiment of the invention there is provided MEMS oscillator comprising
In accordance with an embodiment of the invention there is provided a method of providing a MEMS resonator device comprising: providing a MEMS resonator comprising:
In accordance with an embodiment of the invention there is provided a method comprising:
In accordance with an embodiment of the invention there is provided a MEMS device comprising:
Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures.
Embodiments of the present invention will now be described, by way of example only, with reference to the attached Figures, wherein:
The present invention is directed to microelectromechanical resonator devices and their associated oscillator control circuits, and more particularly to methods and designs allowing for improved manufacturability and performance including:
The ensuing description provides exemplary embodiment(s) only, and is not intended to limit the scope, applicability or configuration of the disclosure. Rather, the ensuing description of the exemplary embodiment(s) will provide those skilled in the art with an enabling description for implementing an exemplary embodiment. It being understood that various changes may be made in the function and arrangement of elements without departing from the spirit and scope as set forth in the appended claims.
A: Piezoelectric Bulk Mode Disk Resonator with Post-Processing
A1. Introduction
MEMS resonators are operated typically through two actuation mechanisms: piezoelectric or capacitive. Piezoelectric actuation generally provides high electromechanical transduction efficiencies and low signal transmission losses, resulting in low motional resistances, which is very advantageous as it simplifies the design constraints of the associated electronic circuitry and results in lower power consumption. Also, piezoelectric devices do not require any DC voltage for operation. However, piezoelectric devices generally suffer from lower quality factors.
MEMS resonators can also be classified based on their vibration modes as either flexural or bulk mode devices. Bulk mode devices typically exhibit high stiffness, and are consequently less prone to thermoelastic damping and consequently achieve large quality factors, even at atmospheric pressure.
Combining piezoelectric actuation and bulk-mode operation has been receiving increasing interest for MEMS resonators in order to combine the advantages of both regimes. Amongst piezoelectric materials is aluminum nitride which is a piezoelectric semiconductor material compatible with semiconductor processing techniques which is typically deposited by sputtering. Within the prior art the actuation and sensing of a bulk-mode disk resonator made of aluminum nitride (AlN) is performed by a combination of piezoelectric and capacitive methods. The device resonated at 51 MHz with quality factor of ˜13,000 and an insertion loss of ˜−34 dB. Alternatively, a radial mode AlN resonator has been reported employing a capacitive-piezoelectric actuation scheme using metal electrodes above and beneath the disk structure. The electrostatic electrodes beneath the disk structure were also used to pull it down to the substrate and consequently power the resonator off upon the application of a switching DC voltage. Notably, these prior art designs require complex fabrication process steps to realize submicron gaps in order to avoid excessive motional resistances. Also, within the prior art, Lamé mode resonators utilizing piezoelectric actuation are presented with a resonance frequency of 36.23 MHz, a quality factor of 30,700, and an insertion loss of −66 dB whilst within another design transverse piezoelectric actuation was utilized to achieve bulk mode in-plane resonance in the wine-glass mode. However, the quality factor of the devices presented was degraded by anchor losses in the wide supports whose width was limited by the constraints of the fabrication technology.
Accordingly, the embodiments of the invention described and depicted below in Section A and with respect to
A2. Design
Referring to
The support length is designed, as detailed in Section A3, in order to reduce anchor losses. The supports have a 90° angular spacing, so as to correspond with the nodal points of the wine-glass resonance mode. The support beams are anchored to the substrate at their ends and mechanically connected to the electrical pads. Each of these supports is associated with a pair of pads, one for the signal (S) routed above the piezoelectric layer, and the other for the ground (G), routed through the underlying silicon structural layer. For this purpose, an aluminum layer, Al 120, above the disk structure is patterned into four distinct quadrants, in order to match the strain distribution. Each electrode is electrically connected to a distinct signal pad by an aluminum track routed above its respective suspension beam. The conductive structural silicon layer itself acts as the ground plane of the device, and connects with each ground pad while remaining electrically insulated from the top signal interconnect by a layer of silicon dioxide (SiO2 110). Aluminum nitride is not present on the supports to avoid any unintended transduction which would alter the resonance mode and possibly lead to undesirable spurious modes of vibration.
The dies received from the MEMS foundry were post-processed by successive dry etching of the silicon dioxide on the supports and the device silicon layer using the aluminum nitride and aluminum as hard masks, in order to narrow down the supports from 10 μm to 4 μm (the aluminum interconnect width), as shown in
Finite-element simulations projects a resonance frequency of the post-processed disk in the wine-glass mode to be of approximately 22.9 MHz.
A3. Support Optimization
As mentioned supra, the dies received from the MEMS foundry were post-processed in order to narrow down the supports, reduce the anchor losses and consequently improve the device quality factor. The length of the beams (L3) was estimated theoretically according to Equation (A1) below wherein wS is the support width, f0 is the resonance frequency, E and ρ are the Young's modulus and density of the single-crystalline structural material used, respectively, and λi can be approximated by Equation (A2).
This being 30 μm (i=1) or 54 μm (i=2), so that the support beams resonate at the same frequency as the main suspended structure for a disk diameter of 190 μm and support width of 4 μm, i.e., the dimensions after post-processing. This allows for the resonator to vibrate unimpeded and consequently minimizes the associated anchor losses and maximizes the quality factor. In order to validate the calculated anchor beam length, the structure is simulated using a method wherein a perfectly matched layer (PML) is added at the substrate interface to avoid the reflection of acoustic waves.
This yields λi=36 μm (i=1) or 60 μm (i=2) for a disk diameter of 190 μm and support width of 4 μm (i.e., dimensions after post-processing). Table A3 summarizes the support length values calculated theoretically and predicted by simulation for maximum and minimum quality factors showing very good agreement.
This requires a layout of 42 μm-long supports, as the supports lengthen after post-processing. FEM simulation projects an increase in the quality factor due to anchor losses from ˜9,800 at disk diameter of 200 μm, support width of 10 μm, and support length of 42 μm (i.e., dimensions before post-processing) to ˜30,000 at disk diameter of 190 μm, support width of 4 μm, and support length of 48 μm (i.e., dimensions after post-processing). This corresponds to a factor of −3× improvement. Also, simulation projects an additional quality factor improvement if the support length is modified to match the first maximum in the quality factor curve, which corresponds to a quality factor of ˜43,000.
The simulation results of the 2D model presented here are in very good agreement with the measurements detailed in Section A5 suggesting that the losses due to out-of-plane motion are not significant for this type of resonator. Other methods of anchor loss reduction have been reported in the literature which could possibly be combined with the method according to the embodiment of the invention presented here to further reduce the losses.
A4. Fabrication Process
The resonators presented herein within Section A were fabricated using the PiezoMUMPs technology from MEMSCAP™, followed by an in-house post-processing sequence aimed at reducing the width of the supports, and at overcoming the design rule limitations of the technology. This allows the reduction of the anchor losses and subsequently an increase in the resonator's quality factor. Post-processing of released MEMS devices fabricated in commercial fabrication runs has been reported within the prior art wherein spray coated photoresist mask was used for silicon dry etching the released MEMS dies. In contrast, the resonators according to the embodiment of the invention presented here are self-masked using patterns of materials already present on the dies from the MEMS processing at the commercial foundry. These self-masks being used as etch masks, as explained later in detail.
The fabrication process sequence (see MEMSCAP™ PiezoPUMPs Design Handbook Rev 1.3, MEMSCAP, 2014) followed by the post-processing steps, is illustrated in
The process begins, for example, with 150 mm n-type double-side polished silicon on insulator (SOI) wafers, as shown in
A metal stack composed of 20 nm of chromium (Cr) and 1 μm of aluminum is subsequently deposited and patterned through a lift-off process to form the electrical interconnects and pads, as illustrated in
The MEMS resonator die were then post-processed in-house in order to reduce the width of the support beams and decrease the associated anchor loss. The exposed silicon dioxide was first dry etched using RIE in a mixture of fluoroform (CHF3), carbon tetrafluoride (CF4), and argon (Ar) gases, masked by the aluminum on the supports and the aluminum nitride elsewhere, as shown in
Now referring to
It is evident from
A5. Measurement Results
The structure was intentionally designed with four independent signal electrodes to enable its use within both single-ended and differential electrical configurations, making it possible to directly connect to different amplifier types without the need for extra components or converters such as baluns. It is worth mentioning that operation in differential configuration increases the signal transmission by ˜10 dB due to the added actuation, and does not affect the quality factor, compared to single-ended operation. The device could have been built with only two opposite electrodes and consequently two support beams (i.e., targeted for single-ended operation) in order to achieve higher quality factor due to the lower anchor loss at the expense of potentially higher motional resistance due to the asymmetry in the mode resulting from the geometrical asymmetry.
The dies of the tested devices were directly wire bonded onto a gold-plated PCB. This direct bonding approach was preferred to packaging in order to avoid added parasitics. The resonance characteristics of the devices were measured using the differential test setup shown in
Accordingly, before post-processing the MEMS resonator exhibits a resonance frequency, f0, of ˜20.89 MHz and quality factor, Q, of ˜6,830 and ˜10,320 under atmospheric and 1 mTorr vacuum levels, respectively. After post-processing the resonance frequency is increased to ˜23.27 MHz, which is in good agreement with the FEM simulation results, and the quality factor is now increased to ˜12,850 and ˜31,340 under atmospheric and 1 mTorr vacuum levels, respectively. This illustrates a factor of ˜3× increase in the quality factor as a result of the post-process support narrowing, which is in good agreement with the simulation results presented in Section A3.
The quality factor was extracted directly from the 3-dB bandwidth in the device transmission curves. It is worth mentioning that the frequency is increased after post-processing due to the 10 μm reduction of the disk diameter as a result of the masking aluminum nitride inclusion within the silicon disk structure required by the design rules of the technology. The post-processed resonator exhibits a transmission of ˜46.5 dB (i.e., an insertion loss of 46.5 dB) at atmospheric pressure, which corresponds to a motional resistance of ˜21 kΩ, while it exhibits a transmission of −39 dB (i.e., an insertion loss of 39 dB) under a 1 mTorr vacuum level, which corresponds to a motional resistance of ˜8.8 kΩ.
The post-process narrowing of the supports results in more than a factor of three improvement compared to original devices without post-processing. Because of the bulk-mode nature of the resonator, air damping has relatively little impact on the device performance, as the quality factor varies only by a factor of ˜2.4 over the full range of the studied pressures.
The quality factor approaches its maximum (within 5%) at pressures below 10 Torr. It is to be noted that the reduction of anchor losses is apparent through the stronger dependence of the quality factor of the post-processed devices on ambient pressure (2.4× increase vs 1.5× increase), indicating that air damping is a more significant loss mechanism in the post-processed structures, as a result of the mitigated anchor losses.
Referring to Table A4 there are compared devices according to an embodiment of the invention implemented via post-processing a low-cost commercial MEMS foundry processed device to other state-of-the-art resonators combining bulk-mode resonance and piezoelectric actuation. A few prior art piezoelectric and capacitive bulk-mode devices are also included with Table A4 to highlight the advantages of the design according to embodiments of the invention. The inventive resonator devices achieve the highest quality factor among comparable bulk-mode devices with piezoelectric actuation, which is very close to the quality factor achieved with capacitive devices, and achieve a relatively low motional resistance as well. Importantly, the resonators according to embodiments of the invention no DC voltage for operation which is a key advantage over electrostatic devices. The motional resistances of piezoelectric devices are lower than their capacitive counterparts due to the higher transduction efficiency of piezoelectric transduction.
This work demonstrates inventive resonators exploiting a wine-glass bulk mode disk resonator utilizing a transverse piezoelectric actuation technique to drive the single crystalline silicon disk structure in bulk mode resonance in order to offer a desirable combination of high quality factor, frequency, and low motional resistance without requiring any DC voltage for operation. The length of the resonator supports was optimized to reduce anchor losses and increase the quality factor. Devices were fabricated in a commercial MEMS technology and post-processed in-house to narrow down the anchor beam supports and consequently reduce the anchor losses, allowing for a better quality factor and lower resulting motional resistance. This post-processing methodology allows for overcoming some of the limitations imposed by the fabrication technology and results in a factor of ˜3 increase in the quality factor and same order decrease in the motional resistance. Post-processed resonators were measured to have resonance frequencies of ˜23 MHz and quality factors of ˜13,000 in atmospheric pressure, increasing to ˜31,000 in 1 mTorr vacuum. The devices also demonstrate motional resistances of ˜21 kΩ in atmospheric pressure, reducing to ˜8.8 kΩ in 1 mTorr vacuum. This post-processing technique hence allows for higher performance resonators, and can ultimately result in MEMS-based oscillators that do not require any high voltage biasing circuit, can operate with lower gain sustaining amplifiers, and yield better close-in phase noise performance, because of the increased quality factor and reduced motional resistance of the resonator.
B: Silicon Lamé Mode Resonators with Dual Wafer SOI Technology
A1. Introduction
Interest in MEMS resonators for timing applications is increasing, as their phase noise performance is improving due to the higher performance of the MEMS resonator and the sustaining circuitry. Moreover, the power consumption of the MEMS resonator-based oscillators is decreasing to compete with quartz oscillators, ranging from the mW range down to the μW range, depending on the oscillator's frequency and sustaining circuit design. Bulk-mode devices typically exhibit high stiffness, and are consequently less prone to thermoelastic damping, compared to flexural devices, allowing them to achieve large quality factors (>10,000), even under atmospheric pressure. Within the prior art surface micromachined capacitive bulk-mode resonators exhibiting quality factors of 2,000-150,000 and frequencies as high as 1.52 GHz have been reported. Further, actuation and sensing of a surface micromachined bulk-mode disk resonator made of AlN exploiting a combination of piezoelectric and capacitive methods has also been reported where the device resonates at 51 MHz with quality factor of ˜13,000. Also, within the prior art a radial mode AlN resonator operating at 300 MHz with quality factor of 8,800 has been presented employing a capacitive-piezoelectric actuation scheme using metal electrodes above and beneath the disk structure. The electrostatic electrodes beneath the disk structure are also used to pull it down to the substrate and consequently power the resonator off upon the application of a switching DC voltage. Alternatively, a wine glass bulk mode disk resonator with piezoelectric actuation fabricated in a commercial SOI technology has been reported operating at a frequency of ˜15 MHz and a quality factor as high as ˜5,000 as have piezoelectric actuated Lamé mode resonators utilizing oxide refilled trenches for temperature compensation are presented. Resonance frequencies of ˜36 MHz and quality factors of ˜30,700 are reported. All the previously mentioned resonators utilize mainly two different anchoring schemes for the released movable structures. The first is support beams attached to the nodal points of the structure mode shape and the second is a central anchor in the center nodal point. Both schemes achieve quality factors in the same range. However, the support beam approach is not suitable for creating bulk mode gyroscopes because this type of device utilizes two resonance modes, where the nodes of one mode coincide with the antinodes of the other. Therefore, the circumference of the structure needs to be free, without any anchoring points, so as to allow for free motion in both modes. Piezoelectric cross-sectional Lamé mode resonators with frequencies as high as 1.02 GHz and quality factors of ˜600 have been reported. It is worth mentioning that the quality factor in these prior art structures is mostly limited by several factors including structure thickness, anchor loss, and damping losses resulting from materials added to the main structural materials. Within the prior art, bulk mode resonators including Lamé mode and wine glass mode devices with quality factors in the 106 range have been presented. Such high quality factors are achievable as a result of superior structural material, single crystalline silicon, which is formed into a pure bulk resonating structure, without the need for release holes, and also due to the reduced anchor losses resulting from the narrow anchoring beams. Also, within the prior art are a wine-glass disk resonator with movable electrodes to reduce the transduction gap whilst microfluidic channels have also been combined with a Lamé mode resonator for real-time mass sensing in liquids.
According to the embodiments of the invention Lamé bulk mode square resonators have been fabricated using a novel silicon-on-insulator technology, MicraGEM-Si™ from Micralyne™. These structures are implemented by patterning two wafers with different etched depths and wafer bonding them to create the released movable structures. Within embodiments of the invention two anchoring architectures have been evaluated, one with suspension beams at the nodal corner points, and the other with a central anchoring support. Devices with different support dimensions are fabricated and characterized to evaluate the impact of support size on device performance. The center support architecture presented is also highly suitable for realizing high performance gyroscopes, without the need for release holes or wide center supports, which are probably creating limitations on their quality factors. It would be evident that for this application, the resonating geometry will have to be tailored to support the desired modes for gyroscope operation.
B2. Design
Referring to
Embodiments of the invention are realized through the processing and wafer bonding of two SOI wafers (i.e., the top wafer and the bottom wafer). The top wafer has its handling layer removed after bonding to the bottom wafer such that the resonator is mainly composed of a single-crystalline silicon central square suspended structure acting as the Lamé bulk mode resonator. Within the prototypes manufactured this suspended square is 30 μm thick, has a 230 μm side length, and is formed in the device layer of the top SOI wafer. The Lamé mode resonance frequency can be calculated to be 17.9 MHz from [Equation (B1) below where L is the resonator side length, G and p are the equivalent shear modulus and density of the material, respectively. Two anchoring designs are proposed, wherein one design features comer suspension beams, placed at the nodal points of the resonance mode, as shown in
Pads for electrical connection to the central square are present in the end of each suspension beam. This allows for connecting the DC polarization voltage required for the electrostatic actuation of the device. These support beams are patterned in the device layer of the top SOI wafer. The second design utilizes a central square support to anchor the square resonator structure to the substrate. In this case, electrical connection to the resonating structure is routed through an underlying silicon interconnect formed in the device layer of the bottom SOI wafer, as illustrated in
In both designs, the central structure is surrounded by four electrodes utilized for capacitive actuation and sensing of the structure. The electrodes are formed in the device layer of the top Sol wafer and are separated from the central square by a 2 μm capacitive transduction gap, which is the minimum spacing allowed by the technology. The device layer of the bottom SOI wafer is patterned to form the electrode anchors, the anchors at the end of the suspension beams in the case of corner supported resonators, as well as the central support and interconnect in the case of the centrally supported resonators. Table B1 summarizes the design parameters and targeted resonant frequency of the resonator devices fabricated to demonstrate embodiments of t the invention.
Finite-element-methods (FEM) simulation illustrating the mode-shape of the resonator in the Lamé mode is depicted in
B3. Fabrication Process
The resonators in this work were fabricated in the MicraGEM-Si™ technology from Micralyne™. The fabrication process sequence is depicted schematically in
The buried oxide for both wafers is 1 μm thick. The device layer of the bottom wafer is patterned and etched using deep reactive ion etching (DRIE) stopping on the buried oxide layer isolating the electrical interconnects and forming the anchors for the resonator structure as well as the electrode anchors, as shown in
B4. Measurement Results
The structure was intentionally designed with four independent signal electrodes to enable its use within both single-ended and differential configurations, making it possible to directly connect to different amplifier types without the need for extra components or converters such as baluns. The dies of the tested devices were wire bonded directly onto a gold-plated PCB. This direct bonding approach was preferred to packaging in order to avoid added parasitics. The resonance characteristics of the devices were measured using the differential test setup shown in
The motional resistance, Rx, of a resonator is given by Equation (B4) where Tmax is the signal transmission of the resonator (on a linear scale) at resonance and Z0 is the characteristic impedance (50Ω in the case presented here). The effect of the applied DC polarization voltage, VP, on the motional resistance for both resonator types is illustrated in
The devices exhibit a motional resistance of ˜850 kΩ at 30 V, and of ˜75 kΩ at 100 V. Resonators with different support dimensions were fabricated as discussed supra. Table B2 illustrates the effect of the support design on the resonance quality factor in vacuum. Devices with corner supports of 2 and 3 μm width, and devices with center supports of 5, 6, and 7 μm width were fabricated. It is worth mentioning that the 5 μm support devices did not survive the fabrication process, which can indicate that this dimension was too small to achieve effective wafer bonding between the bottom and top wafers. The 6 μm support devices exhibited a higher yield and the 7 μm devices survived in all the fabricated dies. Center support devices exhibit quality factors ˜15% lower than corner support ones. All characterized devices with corner supports achieve quality factor within the same range suggesting that the performance of this type of devices is not limited by anchor loss. However, center support devices with 6 μm supports exhibit slightly higher quality factor than the 7 μm ones illustrating room for improvement with smaller supports.
Table B3 compares the device proposed here to other state-of-the-art bulk-mode resonators. The proposed resonator achieves superior quality factor in atmospheric pressure, reducing the need for vacuum packaging in some applications. It also exhibits relatively high resonance frequency, and has one of the highest f. Q products. The center support architecture presented is also highly suitable for realizing high performance gyroscopes, without the need for release holes, or for wide center supports, which could improve the achieved quality factors in such designs.
Accordingly, the Lamé bulk mode square resonators fabricated in a novel silicon-on-insulator technology, where structures are formed by patterning two SOI wafers with several etched depths and wafer bonding them to create the released movable resonator structures. Two distinct anchoring architectures, one with suspension beams at the nodal corner points, and the other with a central anchoring support have been demonstrated. The latter is also suitable for creating high performance bulk mode gyroscopes, without the need for release holes, or for wide center supports, both of which can limit the achieved quality factors. The effect of the support size on the resonance quality factor was studied experimentally. Fabricated devices were measured to operate at a resonance frequency of ˜18 MHz and quality factors as high as ˜42,000 in atmospheric pressure, which to the inventors' knowledge is the highest reported to date in such pressure, and ˜871,000 in 100 mTorr vacuum. The resonators also exhibit a f Q product of 1.56×1013 in vacuum, which is one of the highest reported in the literature. Accordingly, the presented devices are well-suited to a wide-range of MEMS resonator applications such as timing, and can provide relatively high performance even in air, reducing the packaging costs. Moreover, the motional resistance can be substantially decreased if the fabrication technology minimal spacing can be further reduced or an alternative solution is established to reduce the capacitive gap size as the motional resistance is proportional to the fourth power of the gap.
C: Capacitive Lamé Resonator with Gap Closing Mechanism for Motional Resistance Reduction
C1. Introduction
As noted supra the motional resistance, R, is proportional to the fourth power of the gap, i.e. R∝g4. Within the prior art this has led to devices exploiting complex manufacturing sequences and/or high resolution lithography in order to achieve the desired features. However, within the prior art gap closing structures have been introduced as an alternative method for transduction gap reduction to overcome the fabrication technology limitations. These include a relatively complex gap closing and locking structure for which no experimental results were reported together with gap closing structures were employed in width extensional and wine-glass disk resonators. However, the gap closing structures suffered from break points which led to electrical contact between the electrodes and the resonator structure resulting in permanent failure.
In order to overcome these limitations, the inventors have established a novel gap closing methodology which is demonstrated in conjunction with a Lamé mode resonator. The gap closing mechanism relies upon the one effect MEMS designers normally seek to mitigate, namely the electrostatic pull-in between the resonator structure and the electrodes. Electrostatic MEMS based actuators form the basis of a wide variety of devices, including micromotors, microswitches, microrelays, microresonators, micromirrors, micropumps, microvalves, and microfilters. However, the electrostatic coupling as voltages increase and/or gaps reduce results in highly nonlinear dynamics, leading to a saddle-node bifurcation, called “pull-in”. Pull-in instability is a crucial effect in electrostatically actuated MEMS and limits their travel ranges, for example. The instability has at its root the domain where the electrostatic force increases more rapidly than the spring force such that the “spring” is overcome, and a sprung portion of a MEMS device is drawn into contact with another portion of the MEMS and electrostatically “fixed” together.
However, in the embodiments of the invention the inventors exploit “pull-in” specifically to overcome the spring force but by exploiting stopper structures, which are added to the MEMS elements in order to avoid electrical contact between the electrodes (spring portion of MEMS device) and resonator structure (other portion of MEMS), and consequently ensure reliable operation. The minimum gap achievable using the novel structure is only limited by the mask grid size thereby allowing for realization of resonators with high quality factor and low loss bulk mode resonators without requiring excessive voltages or complex fabrication steps.
C2. Resonator Design
The resonator's employed within the prototype devices according to an embodiment of the invention are composed of a central square structure which is the main resonator structure. This square is anchored to the substrate through four support beams located at the comer nodal points. The resonator is surrounded by four electrodes as shown schematically in
Alternatively, welding may be used to realise permanent pull-in by locally fusing the silicon together as a result of the localized heating induced by current flowing through small contact regions. Optionally, both stiction and welding may be employed. Stiction (a contraction of static friction) within MEMS refers to where two surfaces with areas below the micrometer range come into close proximity, they may adhere together. At this scale, electrostatic and/or Van der Waals and hydrogen bonding forces become significant. Dimensions of the gap closing folded suspensions were optimized by simulation to ensure a reasonable gap closing voltage.
g
F
=g
I
−g
S (C1)
Referring to
Prototypes were fabricated in two commercial SOI technologies, namely PiezoMUMPs™ from MEMSCAP and MicraGem-Si™ from Micralyne™, highlighting the flexibility of the design. The latter technology provides finer mask grid size (i.e., 100 nm for MicraGem-Si™ versus 250 nm for PiezoMUMPs™). It also allows for smaller device footprint as it avoids deep release trench etching which requires many design rules in PiezoMUMPs™
C3. Measurement Results
A differential setup was used for resonance characterization of the devices, as shown in
As noted supra the prototype resonators according to embodiments of the invention were also fabricated in another commercial technology, MicraGem-Si™, which offers better grid resolution, allowing narrower transducer gaps to be achieved after the electrodes are actuated.
The effect of the bias voltage on the motional resistance is illustrated in
Table C2 lists the performance metrics of a number of published start-of-the art resonators in comparison to those achieved with embodiments of the invention. The inventive design achieves one of the highest frequency Q-factor products (f-Q) while featuring one of the lowest motional resistances, to the inventor's knowledge the lowest reported to date for capacitive resonators, while maintaining relatively low bias voltage. Notably, the design does not require any complex fabrication steps and is fully compatible with commercial silicon-on-insulator microfabrication technologies.
Whilst the embodiments of the invention described and depicted supra in Section C have been square Lamé resonators it would be evident that the electrostatic gap closing mechanism, electrostatic gap closers, and electrostatic pull-in may be applied to other MEMS resonators with other geometries other than square. It would also be evident that the methodology of the electrostatic gap closing mechanism via electrostatic pull-in with electrostatic gap closers and gap stoppers may also be applied to other MEMS resonators such as those exploiting a central support under the resonator beam etc.
3k
Accordingly, Lamé mode resonators exploiting a novel gap closing mechanism have been development employing electrostatic force to reduce the capacitive transduction gaps to sub-micron values overcoming the fabrication technology limitations. Accordingly, this leads to significant resonator loss and motional resistance reduction, and tuning range increase, for the resonators whilst allowing significant cost reductions in the manufacture of the MEMS resonators through use of commercial MEMS production processes.
The inventive mechanism does not have a negative impact on the Q-factor achievable, and the devices maintain a high Q-factor even in air. Prototypes have been fabricated in two commercial silicon-on-insulator processes. Upon the application of a bias voltage of 55 V the capacitive transduction gaps are reduced to sizes as small as 200 nm. A resonance frequency of 18 MHZ with Q-factors as high as ˜870,000 were observed under a 1 mTorr vacuum, with this Q-factor being relatively unaffected at a vacuum level of up to 1 Torr, and reducing to 32,000 at atmospheric pressure. The resonance operation is maintained while reducing the operating bias voltage as low as 20 V. An insertion loss of 33 dB was measured at 55 V, which corresponds to a motional resistance of 4.4 kΩ, more than 60 times lower than that of a similar design without gap closers at the same voltage, which to the inventors' knowledge is the lowest reported to date for capacitive bulk mode resonators. The frequency tuning range is also increased by an order of magnitude, which can be very useful for overcoming ambient conditions and fabrication process variations,
D: Sub-Mw MEMS Oscillator Exploiting Adjustable Bandwidth Fully Differential Transimpedance Amplifier and a Lamé-Mode Resonator
D1. Introduction
Resonators can be classified based on their vibration modes as either flexural or bulk mode devices. Bulk-mode devices typically exhibit high stiffness, and are consequently less prone to thermoelastic damping, compared to flexural devices, allowing them to achieve large quality factors (>10,000), even at atmospheric pressure. Bulk mode resonators including Lamé-mode and wine glass mode devices with quality factors in the 106 range have been reported within the prior art based upon capacitive actuation. Such high quality factors are achievable as a result of superior structural material, single crystalline silicon, which is formed into a pure bulk resonating structure, without the need for release holes, or additional layers on top, which is one of the limitations for the quality factors achieved by piezoelectrically actuated devices
On the other hand, capacitive bulk-mode devices typically exhibit lower transduction efficiencies compared to piezoelectric devices, which translate to higher losses and motional resistances. This can be accounted for by either enhancing the transduction, e.g., sub-micron gaps realized by complex fabrication, high voltages, added combs, or increasing the gain for the transimpedance amplifier (TIA) in order to sustain oscillation. Several transimpedance topologies have been reported in the literature for MEMS-based oscillator purposes. Designs proposed include an automatic gain control circuit to regulate the oscillation amplitude and reduce the resonator mechanical non-linearity effect. Furthermore, the power consumptions of fully differential transimpedance amplifier designs are higher than single-ended TIAs.
Generally, an oscillator is realized by connecting a TIA with the resonator in positive feedback loop to sustain a steady-state oscillation by converting the resonator output current to an output voltage signal and ensure sharp response. The sharpness and quality of the output oscillation is usually determined by the quality factor of the resonator. It is necessary for the TIA to have high transimpedance gain due to the resonator loss caused by its motional resistance. Large bandwidth is also required to ensure that the oscillator phase shift is around 0°, when MEMS-based oscillator operates in series resonance mode. Thus, Barkhausen conditions are fulfilled. Furthermore, low input and output impedances are required to minimize the resonator Q-factor loading. The inventors have established a MEMS based oscillator based upon a Lamé-mode resonator in conjunction with a novel fully differential high gain TIA thereby achieves very competitive performance in terms of power consumption and phase noise relative to the state of the art.
D2. Lamé Mode MEMS Resonator
The Lamé MEMS resonator employed is based upon the inventive design and manufacturing methodology presented in Section B supra. For completeness, a brief description is given in this section wherein
Pads for electrical connection to the central square are present in the end of each suspension beam. This allows for connecting the DC polarization voltage required for the electrostatic actuation of the device. These support beams are patterned in the device layer of the top SOI wafer. The central structure is surrounded by four electrodes utilized for capacitive actuation and sensing of the structure. The electrodes are formed in the device layer of the top SOI wafer and are separated from the central square by a 2 μm capacitive transduction gap, which is the minimum spacing allowed by the technology. The device layer of the bottom SOI wafer is patterned to form the electrode anchors and the anchors at the end of the suspension beams. SEM micrographs of the resonator are shown in
D3. Transimpedance Amplifier Circuit Design
The transimpedance amplifier circuit shown is in
Input Stage 2810 forming part of Input Stage 2720A in
VGA 2820 forming part of VGA 2720B in
Output Stage 2830 forming part of Output Stage 2720C in
Peak Detector 2840 forming part of AGC 2720D; and
Comparator 2850 also forming part of AGC 2720D.
The sustaining amplifier provides low input impedance (RIN) and low output impedance (ROUT) in order to compensate for large parasitic capacitance (CP=4 pF) and push the dominant pole far beyond the oscillation frequency of the MEMS oscillator circuit. This can be translated into high gain-bandwidth (GBW) product for the TIA.
An exemplary embodiment of the invention exploits a MEMS resonator such as an electrostatic Lamé-mode resonator described in Section B2 supra. The gain of the TIA needs to be high enough in order to compensate for the resonator's high motional resistance and sustain the oscillation. Accordingly, a regulated cascode (RGC) topology was chosen as input stage in order to achieve a reasonable trade-off between bandwidth and power consumption. The input impedance of the RGC input stage is given by Equation (D1) where gm1 and gm2 are the transconductance of transistors M1 and M2, respectively. Thus, smaller input impedance can be reached by increasing voltage gain of the local feedback stage given by (1+R3gm1).
The expression of input stage gain is given by Equation (D2) where CIN, C1 and Cgd2 are the total input capacitances of the input stage, the equivalent capacitance between the drain of M1 and the gate of M2, and the gate-drain capacitance of transistors M2, respectively. To achieve a higher gain, R2 should be increased, although it cannot be indeterminately enlarged because of design constraints.
It can be seen from Equation (D2) that the 3-dB bandwidth of the input stage is limited by the dominant pole appearing at the drain of transistor M1 and is given by Equation (D3) where Cgd1, Cgs1, and Cgs2 are the gate-drain capacitance of transistor M1, and the gate-source capacitances of transistors M1, and M2, respectively. The local feedback of the input stage generates a zero at the frequency given by Equation (D4). In order to keep the zero far away from the dominant pole, the gate-drain capacitance of transistor M2 should be decreased by decreasing its width, therefore, RGC input impedance in Equation (D1) will not be dramatically affected since gm2 will not decrease considerably as it is proportional to (WL)2, while its gate capacitance is linearly proportional to (WL)2. This can be compensated by increasing R3 as the input impedance is inversely proportional to (1+R3gm1), as shown in Equation (D1).
The input-referred current noise is an important key performance parameter to be considered when designing the proposed TIA. It can be used to provide a fair comparison between different circuit topologies. Since the noise is mostly contributed by the input stage, then the noise of the other stages can be ignored. Therefore, a noise analysis was derived from
From (5), the noise can be analysed as follows: the thermal noise contribution from R1 is directly assigned to the equivalent input noise, and as the frequency increases, the noise is dominated by terms containing ω2. Therefore, low input equivalent noise can be achieved by increasing resistor R1 and thus for better transimpedance gain performance in terms of noise.
D4. Experimental Results
Two test configuration setups were employed as depicted in
D4.A. Resonator Characterization
The frequency response of the resonator was measured in differential configuration with the VNA under a vacuum level of 100 mTorr for DC polarisation voltage, VP, of 100 V and 200 V, and various input power levels starting from −30 dBm up to 0 dBm.
D4.B. Transimpedance Amplifier Characterization
The fully differential TIA was fabricated using a Taiwan Semiconductor Manufacturing Company (TSMC) 65 nm low-power process and consumes only 0.9 mA from 1-V supply. The total circuit layout area measures 130×225 μm2 as depicted in
D4.C. Oscillator Measurement
D4. C1 Open-Loop Measurements: To confirm that sufficient loop gain was present for the oscillation, the resonator was connected to the TIA in open-loop configuration under vacuum, and the frequency and phase responses were measured using the VNA. As illustrated in
To sustain oscillation in closed-loop, the conditions defined in Equations (D6) and (D7) are required where ϕTOTAL is the total phase shift and ZT, RM, and ROUT are the transimpedance gain, input, and output impedances of TIA, respectively. In this case, both resonator and TIA must have 0° phase shift. It is observed from
ϕTOTAL=0° (D6)
Z
T
≥R
M
+R
IN
+R
OUT (D7)
2) Closed-Loop Measurements:
The resonator and TIA were set in a closed-loop configuration (dashes lines in
The phase noise measurements of the oscillator under vacuum are plotted in
For fair comparison, two figure-of-merits FOM1 and FOM2, are used to evaluate the overall performance in terms of phase noise and power consumption, phase noise floor and motional resistance, respectively. Their expressions are given by Equations (D10) and (D11) respectively where ℑ(fm) is the oscillator phase noise at fm, a specific offset frequency, f0 is the center frequency, PDISS is the DC power consumption of the oscillator circuit (in mW). It can be noticed that the proposed FOM2 is used to evaluate the spent effort on designing low phase noise TIA toward high resonator motional resistance. The calculated FOM1 and FOM2 values for oscillators based on electrostatic resonators are listed in Table D2. As can be seen, the MEMS-based oscillator demonstrated in this work has the best figure-of-merits FOM1 and FOM2 when compared with other oscillators based on electrostatic MEMS resonators illustrating the superior performance achieved here.
Accordingly, the inventors have demonstrated a MEMS oscillator based upon a Lamé-mode capacitive MEMS resonator and a novel fully differential high gain, which when fabricated in a TSMC 65 nm low-power process consumed 0.9 mW. An RGC amplifier was employed to provide the high gain, wide bandwidth and lower input impedance required for an oscillator based upon an electrostatic resonator. The TIA can reach a maximum gain of around 98 dBΩ and adjustable bandwidth with a maximum bandwidth of around 142 MHz and an input-referred current noise below 15 pA/√{square root over (Hz)} in the mid-band. The TIA when integrated with the 18-MHz Lamé-mode MEMS resonator yielded an inventive MEMS oscillator achieving a phase noise of −120 dBc/Hz at 1 kHz offset and phase noise floor of −127 dBc/Hz and offers superior figure-of-merit relative to state-of-the-art devices in respect of power consumption and phase noise.
E: MEMS Oscillator Based on Differential Adjustable-Bandwidth TIA and Piezoelectric Disk Resonator
E1. Introduction
MEMS resonators can be operated through two main widespread actuation mechanisms: piezoelectric or capacitive. Piezoelectric actuation generally provides high electromechanical transduction efficiencies and low signal transmission losses, resulting in low motional resistances, which is advantageous as it simplifies the design constraints of the associated electronic circuitry and results in lower power consumption. Also, piezoelectric devices do not require any DC voltage for operation. However, piezoelectric devices generally suffer from lower quality factors, which can deteriorate the phase noise of the oscillator. Resonators can also be classified based on their vibration modes as either flexural or bulk mode devices. Bulk mode devices typically exhibit high stiffness, and are consequently less prone to thermoelastic damping and consequently achieve large quality factors, even at atmospheric pressure. Within the prior art a disk resonator combining bulk resonance with piezoelectric actuation to achieve a desirable combination of low motional resistance, high frequency and quality factor without requiring any DC voltage for operation. The resonator was realized in a commercial silicon on insulator (SOI) technology.
In order to implement an oscillator with a MEMS resonator, a transimpedance amplifier (TIA) needs to be interfaced with the resonator in a positive feedback loop to sustain a steady-state oscillation by converting the resonator driving current to an output voltage signal [8], [12]. The sharpness and quality of the output oscillation is usually determined by the quality factor of the resonator and the contributed noise of the TIA. To sustain oscillation, it is necessary for the TIA to have high transimpedance gain due to the resonator insertion loss caused by its motional resistance. Large bandwidth is also required to ensure that the oscillator phase shift at the resonance frequency is around 0°, when the MEMS oscillator operates in series resonance mode [13]. Furthermore, low input and output impedances are required to minimize the resonator Q-factor loading. Several transimpedance topologies have been reported in the literature for use in MEMS oscillators with the majority of designs being based on regulated cascode topologies whilst other methodologies include an inverting amplifier topology and a current preamplifier.
Furthermore, most TIAs use a single-ended architecture and gain-bandwidth (GBW) product enhancement techniques so that TIA performance in terms of input-referred noise and power consumption will be improved. However, singled-ended TIAs demonstrate inferior noise performance than that of fully differential TIAs. Differential topologies can benefit of common-mode noise rejection and even harmonics rejection, and therefore, are more desired in applications requiring low noise operation.
The inventors have established a novel MEMS oscillator employing a piezoelectric MEMS resonator which is driven directly and differentially by the TIA forming the closed feedback loop required to provide the MEMS oscillator.
E2. Piezoelectric Disk Resonator
The resonator employed is a disk structure excited through piezoelectric actuation as depicted in
E3. TIA Circuit Design
The transimpedance amplifier circuit (TIA) 3920 according to an embodiment of the invention is depicted in
The complete schematic of the TIA circuit is shown in
E3.A. TIA Input Stage
The input stage should be carefully designed in such a way to satisfy several criteria. Besides the high GBW product criterion, tradeoffs between lower input impedance, power consumption and current noise are also other key performance parameters to be considered when designing the input stage. Three input stage topologies were selected to be compared with the proposed input stage by means of circuit performance simulations using the SpectreRF simulator in a CMOS 65 nm technology. The first design was based on the gm-boosted common-gate (CG) topology, known as regulated cascode (RGC) input stage. The second topology is the common source feedback (CSFB) amplifier which is used to amplify current and which enhances the bandwidth by reducing the size of the load resistance. The third design considered employs a capacitive-feedback current amplifier which drives current into an active load. The input-referred noise of this configuration is expected to be very low because of the absence of noise sources directly at the input.
Each topology was simulated with an additional shunt parasitic capacitance of CP=4 pF, and to make a representative comparison of performance, the transimpedance gain was adjusted to be equal (˜78 dBΩ). A normalized figure-of-merit is used to evaluate the overall performance of the TIA input stage, and is given by Equation (E1). According to Table E1, the capacitive feedback topology exhibits the lowest input-referred current noise, while the CSFB topology exhibits excessive noise. The gain of the RGC input stage is limited by the large load resistor due to the large DC voltage drop across it. The large gain and bandwidth of the CSFB topology can be readily set. However, the limitation of this topology comes from the noise performance. The capacitive feedback topology benefits from current pre-amplification, and the transimpedance gain can be high with a smaller load resistor, unlike resistive feedback topologies. The major drawback of the capacitive feedback topology is that its input impedance is very high at the resonant frequency, which will load a resonator's Q-factor.
In order to benefit from lower input impedance while extending transimpedance gain and bandwidth, the proposed input stage is based on modified versions of the RGC and CSFB topologies by using active feedback, as shown in
1) Input Impedance:
According to the small-signal analysis, the single-ended low-frequency input impedance of the proposed circuit is given by Equation (D2) where RIN,RGC is the input impedance of the RGC circuit and is given by Equation (D3) where gm1, gm2, and gm3 are the transconductance of transistors M1, M2, and M3 respectively. As indicated by Equation (E2) the input impedance of the input stage is (1+R2 gm3) times smaller than an RGC input stage.
2) Transimpedance Gain:
The expression for the input stage transimpedance gain is given by Equation (E4) where CIN and COUT are the total input and the output capacitances of the input stage, respectively, C1 is the equivalent capacitance between the drain of M1 and gate of M2, C2 is the equivalent capacitance between the drain of M2 and gate of M3/M4, and RO,IN is the output impedance of the input stage which is given by RO,IN=rO,4 rO,6 where rO,4 and rO,6 are the output resistances of transistors M4 and M6, respectively. The DC transimpedance gain can then be expressed by Equation (E5) where gm4 is the transconductance of transistor M4.
3) Bandwidth:
It can be seen from Equation (E4) that the 3-dB bandwidth of the input stage is limited by the dominant pole appearing at the drain of transistor M2 and is given by Equation (E6) where Cjd,i={2,3,4} are the gate-drain capacitances of transistors M2, M3 and M4, respectively, and Cgs3 is the gate-source capacitance of transistor M3. The local feedback of the input stage creates a zero at a frequency given by Equation (E7).
To keep the zero far away from the dominant pole the transconductance gm1 of transistor M1 should be increased, i.e. increasing its width. However, increasing the width of M1 will significantly increase capacitance C1, specifically the equivalent capacitance of the drain of M1, and will reduce the zero frequency. Instead, capacitance C1 can be lowered by reducing the width of transistor M2 to decrease the equivalent capacitance at its gate. This will affect the input impedance of the RGC stage as given in Equation (3) since the transconductance gm2 of transistor M2 will be decreased. However, this will not critically affect the input impedance of the RGC stage or the input stage since gm2 is proportional to √{square root over ((W/L)2)}, while its gate capacitance is linearly proportional to (WL)2. On the other hand, decreasing the input impedance amounts to increasing (1+R2 gm3) or (1+R3gm1). The former will affect the TIA DC gain and the input stage bandwidth. Therefore, increasing R3 is selected as the method for input impedance reduction.
4) Noise Analysis:
The input-referred current noise is an important performance parameter to be considered when designing the proposed TIA. It can be used to provide a representative comparison between different circuit topologies (see Table E1). Since the noise is mostly contributed by the input stage, then the noise of the other stages can be neglected to simplify the analysis. Therefore, a noise analysis was carried-out based upon assuming shot noise and flicker noise are ignored and that all noise sources are uncorrelated, the input-referred current noise for the input stage is calculated and its expression is given by Equation (E8) where γ is the noise coefficient, k is Boltzmann's constant, T the absolute temperature and gd0,i={1-6} are the zero-bias drain conductances of transistors M1-M6, respectively.
From Equation (E8), the noise can be analysed as follows: the thermal noise and the channel thermal noise contributions from R1 and M3, respectively, are directly applied to the equivalent input noise. As the frequency increases, the noise is dominated by terms containing ω2. Therefore, to achieve a low noise, resistor R, need to be increased and it is preferable to keep the size of transistor M3 as small as possible to maintain lower input-referred noise as well as higher transimpedance gain and bandwidth performance. However, reducing the size of M3 can increase the input impedance of the TIA, as mentioned earlier, and increasing R3 can compensate the effect of reducing the size of M3, thereby achieving an overall compromise of performance.
E3.B. Variable Gain Amplifier
The variable gain amplifier shown in
E3.C. Output Stage
The output stage shown in
The gain of the SSF is given by Equation (E11) where gm24 and gm26, rO25 and rO26 the transconductances and output resistances of transistors M25 and M26, respectively. As can be seen in Equation (E11), if gm26rO26>>1 and (R7∥rO25) is sufficiently large, the gain of SSF will be close to 1 V/V. The output impedance of the super source follower is given by Equation (E12) where rO24 is the output resistance of transistor M24. The output resistance of the SSF is reduced by a factor of (rO26×gm25) in comparison to the conventional source follower, whose output resistance is ˜1/gm. This enhancement of the output resistance is due to the negative feedback through transistor M25.
E3.D. Automatic Gain Control Circuit
The schematic of the automatic gain control circuit is shown in
E4. Experimental Results
Two test configuration setups, shown in
E4.A. Resonator Characterization
The frequency response of the resonator was measured in differential configuration with the VNA in air as well as under a vacuum level of 100 mTorr. Different input power levels starting from −20 dBm up to +10 dBm were applied to the resonator.
As can be seen in
E4.B. TIA Characterization
The fully differential TIA is fabricated in a TSMC 65 nm CMOS process and consumes 1.4 mA from a 1-V supply. The circuit active area measures 150×220 μm2, and is shown in
E4.C. Oscillator Characterization
1) Open-Loop Measurements:
To confirm that sufficient loop gain was present for the oscillation, the resonator was connected to the TIA in open-loop configuration under vacuum, and the frequency and phase responses were measured using the VNA. As illustrated in
It is observed from
Accordingly, the main advantage of the adjustable bandwidth feature is to set the oscillator total phase shift in open-loop configuration to 0° by setting the TIA's phase shift ϕTIA such that it complements the resonator's phase shift ϕMEMS. This ensures that an oscillation can be sustained in closed-loop, and with a minimal TIA gain, as the 0° phase shift can be set to occur at a frequency near the maximum of the resonator's transmission curve. Note that the loaded Q-factor was measured from the open-loop gain bandwidth to be ˜4000.
2) Closed-Loop Measurements:
The resonator and TIA were connected in a closed-loop configuration (solid lines in
The expression for the oscillator phase noise at a fm offset frequency from the carrier frequency is given by Equation (E16) where ℑ(fm) represents the noise figure of the amplifier, P0 is defined as the oscillation power, f0 represents the carrier frequency, fC is a constant related to 1/f noise corner of the oscillator and QL denotes the loaded Q-factor and is defined as given by Equation (E17) where QUL is the intrinsic Q-factor of the resonator.
The phase noise measurements of the oscillator in air and under vacuum are plotted in
Short-term stability is one of oscillator key performance metrics and is a measure of its frequency stability. The frequency stability of the resonator is illustrated in
In order to obtain a representative comparison, figure-of-merit FOM2 is used to compare the performance of the different oscillators in terms of phase noise and power consumption. It is given by Equation (E18) where PDISS is the DC power consumption of the oscillator circuit in mW. The calculated FOM2 values and summarized specifications for other published MEMS oscillators based on piezoelectric resonators are listed in Table E3.
As can be seen, the MEMS oscillator demonstrated in this work has the best figure-of-merit [FOM2] when compared in air and under vacuum to other oscillators based on piezoelectric MEMS resonators. Notably, the close-to-carrier phase noise is lower under vacuum than the other works while dissipating relatively low-power consumption, thus offering a competitive phase noise at a 10 Hz offset. While the phase noise floor is higher than some prior art, the circuit operates at lower power. The phase noise floor could be improved by further reducing the noise of the TIA at the cost of increased power consumption. Moreover, the resonator could be driven at a higher power level at the cost of degraded close-to-carrier phase noise performance due to noise-folding. Finally, it is important to note that the resonator could be integrated in a system-in-package (SiP) in order to relax the design constraints of the TIA with respect to gain-bandwidth, potentially yielding and enhanced FOM.
According, to an embodiment of the invention a prototype 14-MHz MEMS oscillator based on a piezoelectric disk resonator and on a low-power high gain-bandwidth product fully differential transimpedance amplifier with adjustable bandwidth has been demonstrated. The TIA was fabricated in a TSMC 65 nm CMOS process and consumes 1.4 mW. An input stage topology that is based on the RGC and CSFB topologies and characterized by a high gain, wide bandwidth and low input impedance was proposed. The TIA can reach a maximum gain of ˜80 dBΩ and offers an adjustable bandwidth with a maximum bandwidth of around 214 MHz. The input-referred current noise floor of the TIA was measured to be below 4 pA/√{square root over (Hz)} and achieves a phase noise floor of −130 dBc/Hz whilst offering superior figure-of-merit relative to the state-of-the-art in terms of power consumption and close-to-carrier phase noise.
F: Multi-Resonator Oscillator
Within many microwave and RF applications and timing applications a circuit may be required to either operate upon multiple discrete frequencies outside the tuning range of single oscillator or support operation over a bandwidth wider than that of a single oscillator. Accordingly, it would be beneficial to provide a multi-resonator oscillator wherein multiple resonator/oscillators are employed with a combining circuit allowing one or more of the resonators/oscillators to provide an output signal providing either multiple discrete frequencies concurrently or a single frequency over a bandwidth wider than each individual resonator/oscillator.
Accordingly, referring to
Within an embodiment of the invention the MUX 5220 may comprise a M:1 switch array to actively select a single resonator or alternatively it may be a M:1 combiner with M on/off switches disposed on each input to the MUX 5220 allowing multiple resonators to be coupled concurrently to the output. Optionally, the TIA 5230 may be replaced with a TIA after each resonator. Optionally, subsets of the resonators may be combined with multiplexers wherein the outputs of these multiplexers are then combined with a further multiplexer. Optionally, TIAs may be distributed within such circuits or a single TIA employed. Accordingly, the MRO 5200 can dynamically select which resonator(s) in the bank is/are used in real-time using the Control Circuit 5250. Whilst not depicted it would be evident that the Control Circuit 5250 would receive control signals from an external controller controlling the overall system within which the MRO 5200 forms part.
Accordingly, an MRO 5200 may:
Optionally, the TIA 5230 or others within the MRO 5200 may adjust their bandwidth dynamically as well in order to optimally match the resonant frequency of the selected resonator(s) in order to achieve the best oscillation and power consumption performance metrics.
Accordingly, an MRO according to an embodiment of the invention may be used in PLLs in order to provide a reference frequency for the PLL that is highly tunable or even completely different. This allows for a PLL to be designed with agile reference frequencies, with minimal cost and size impact as a MEMS resonator bank would require only a small die footprint. This can be used for instance to have a PLL lock to a high reference frequency to provide wide loop bandwidth in conditions where this is required, or lock to a very low reference frequency to provide very narrow loop bandwidth but high output frequency granularity. Essentially, the variable frequency MEMS oscillator achieved using the resonator bank allows for another design degree of freedom for PLLs and can lead to novel system architectures in RF transceivers or timing circuits.
Within embodiments of the invention where electrostatic resonators are employed within the resonator bank then the control bias voltage of those resonators can be used to select them as the bias voltage of electrostatic resonators can be used to modulate their losses and accordingly disable them if required. Accordingly, this could remove the requirement for a multiplexer design, especially if the resonator is designed to mitigate feed-through capacitance, which would otherwise cause spurious oscillation paths in the MEMS oscillator. Alternatively, a multiplexer may be used if piezoelectric resonators are used, the feed-through capacitance of electrostatic resonators is an issue or if independent selection is required.
G: Hybrid Transducer Resonators
With the descriptions of embodiments of the invention above resonators have been described with piezoelectric actuation and electrostatic actuation. However, within other embodiments of the invention the piezoelectric and electrostatic actuation (transducers) may be combined in order to achieve a further reduction in the insertion loss of the MEMS resonator.
This may be achieved as the forces generated by both piezoelectric transduction for actuation and electrostatic transduction for actuation can be combined within a resonator to excite the same mode of oscillation, for example Lamé mode or wine glass.
Alternatively, the piezoelectric actuation and electrostatic actuation can be implemented using two coupled inputs to a single resonator such that there are two oscillator loops with a single resonator. These resonator loops therefore being coupled to one another.
The foregoing disclosure of the exemplary embodiments of the present invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many variations and modifications of the embodiments described herein will be apparent to one of ordinary skill in the art in light of the above disclosure. The scope of the invention is to be defined only by the claims appended hereto, and by their equivalents.
Further, in describing representative embodiments of the present invention, the specification may have presented the method and/or process of the present invention as a particular sequence of steps. However, to the extent that the method or process does not rely on the particular order of steps set forth herein, the method or process should not be limited to the particular sequence of steps described. As one of ordinary skill in the art would appreciate, other sequences of steps may be possible. Therefore, the particular order of the steps set forth in the specification should not be construed as limitations on the claims. In addition, the claims directed to the method and/or process of the present invention should not be limited to the performance of their steps in the order written, and one skilled in the art can readily appreciate that the sequences may be varied and still remain within the spirit and scope of the present invention.
This patent application claims the benefit of priority from U.S. Provisional Patent Application 62/583,589 filed on Nov. 9, 2017 entitled “Microelectromechanical System Resonator Devices and Oscillator Control Circuits”, the entire contents of this being incorporated herein by reference.
| Number | Date | Country | |
|---|---|---|---|
| 62583589 | Nov 2017 | US |
