Patent Application
20230264946
The advent of the Internet of Things (IoT) has given rise to a myriad of sensor-based devices used in wearables, smartphones, and remote sensing for industrial and consumer applications. Timing resonators are ubiquitous in these devices and help provide signals used to keep track of time, synchronize events in digital integrated circuits (ICs), and process signals. High-accuracy timing resonators may be desirable for such high-performance electronic applications.
Microelectromechanical (MEMS) resonators are promising candidates for such applications. MEMS resonators are mechanical structures which require an electrical input in order to operate. Their output is a mechanical vibration which is converted into an electrical signal in order to be “sensed” and subsequently utilized.
It is an aim of the present disclosure to achieve an improved temperature compensated MEMS device, such as a resonator. In particular, an aim of the present disclosure is to achieve a MEMS resonator design which offers second-order temperature compensation. The disclosure also provides methods to design second-order temperature compensated MEMS resonators for various purposes.
Features, aspects, and advantages of the presently disclosed technology may be better understood with regard to the following description, appended claims, and accompanying drawings, as listed below. A person skilled in the relevant art will understand that the features shown in the drawings are for purposes of illustrations, and variations, including different and/or additional features and arrangements thereof, are possible.
The drawings are for the purpose of illustrating example embodiments, but those of ordinary skill in the art will understand that the technology disclosed herein is not limited to the arrangements shown in the drawings.
While quartz crystal oscillators have been the foundation of timing and frequency reference applications for the past century, the rapid development of sensor-based electronics has highlighted certain limitations of this technology, such as power consumption, robustness, size, and CMOS compatibility. Over the past two decades, MEMS resonators fabricated with silicon have drawn significant attention due to their small size, low cost, and integration compatibility. However, MEMS resonators still have not been able to replace their quartz counterparts in multiple applications.
A limitation of MEMS resonators fabricated from silicon that has curbed widespread adoption is their lack of temperature stability as compared to quartz. MEMS resonators fabricated from silicon have an inherent first order temperature-induced frequency drift of approximately −30 ppm/° C., resulting in a temperature stability of approximately 3750 ppm over the industrial temperature range of −40° C. to 85° C. In comparison, AT-cut quartz resonators have a temperature stability of approximately 20 ppm over the industrial temperature range of operation.
The change in frequency with respect to temperature of a MEMS resonator is given by the equation:
f(T)=fo[TCF1*(ΔT)+TCF2*(ΔT)2+. . . ]
where f0 is the resonance frequency of the resonator at a reference temperature, ΔT is the deviation from the reference temperature, TCF1 is the first order temperature coefficient of frequency, and TCF2 is the second order temperature coefficient of frequency. For single crystal silicon, the value of TCF2 is typically within the range of −25 to −80 ppb/° C. 2, which can result in a temperature-induced frequency drift of approximately 400 ppm over the industrial temperature range, depending on the resonance mode of operation. While this second order temperature-induced frequency drift is relatively small compared to the uncompensated temperature-induced frequency drift of silicon (˜3,750 ppm based on −30 ppm/° C.), it is still significantly worse than the typical temperature-induced frequency drift of AT-cut quartz crystals. As such, it is desirable to further reduce the temperature-induced frequency drift of MEMS resonators fabricated from silicon in order enable their wide adoption in the timing market.
There have been several attempts to limit the temperature-induced frequency drift of MEMS resonators fabricated from silicon, including techniques involving the use of highly doped silicon substrates and composite materials. However, these techniques are limited to devices that operate in the frequency range of tens of MHz which presents a problem due to the growing need for stable 5G and radio frequency-based (RF-based) ultra-high frequency (UHF) devices. In the 300 MHz to 3 GHz UHF range, existing techniques add fabrication complications, increase production costs, and reduce manufacturability. To a lesser extent, these problems can also appear at the higher end of the 30 MHz to 299 MHz very-high frequency (VHF) range. Consequently, temperature-induced frequency drift compensation in the VHF and UHF range is not yet fully resolved. The present disclosure helps address these issues by providing techniques for mitigating the temperature-induced frequency drift in devices operating at the VHF and UHF range.
The UHF timing market is dominated by the thin-film bulk acoustic resonator (FBAR). An FBAR is a thickness-extensional bulk acoustic wave (BAW) resonator which can be made of a thin piezoelectric substrate such as AlN, ScAlN, or ZnO layered between two electrodes over a cavity in a substrate. Because the frequency of vibration is inversely proportional to the thickness of the piezoelectric substrate, the thin substrates employed in FBARs enable operation at ultra-high frequencies. To date, FBARs are the only type of BAW resonators that are sufficiently reliable in the GHz range to enable commercial applications such as Wi-Fi, positioning (e.g., GPS), and telecommunications. Additional benefits of FBARs include long-term (i.e., on the order of years) frequency stability, power handling capacity, fabrication compatibility, and purity of the desired resonance frequency.
There have been numerous attempts to compensate for temperature-induced frequency drifts in BAW resonators, including FBARs, with both passive and active approaches. These approaches are generally extensions of the same techniques used for other MEMS resonators fabricated with silicon.
One passive temperature compensation technique includes the addition of an SiO2 layer to compensate for temperature-induced frequency drifts in Si or AlN based FBARs. This approach exploits material-specific TCF1 values in order to produce a composite material with a reduced temperature dependency. For example, within the industrial temperature range of −40° C. to 85° C., both AlN and Si have negative first order TCFs (approximately −25 ppm/° C. and −30 ppm/° C., respectively), while SiO2 has a positive first order TCF of approximately 85 ppm/° C. Thus, composite materials composed of AlN and SiO2, or Si and SiO2 can reduce the absolute value of TCF1 as compared to AlN or Si alone. Examples of this technique can be found in R. Tabrizian, G. Casinovi, and F. Ayazi, “Temperature-Stable Silicon Oxide (SilOx) Micromechanical Resonators,” IEEE Trans. Electron Devices, vol. 60, no. 8, pp. 2656-2663, 2013. In other types of BAW resonators, passive temperature compensation techniques to reduce the first order temperature coefficient of frequency by fine tuning the frequency variation across batch fabrication have been implemented, see Yen et al., “Integrated High-frequency Reference Clock Systems Utilizing Mirror-encapsulated BAW Resonators,” IEEE Int. Ultrason. Symp. IUS, vol. 2019-October, pp. 2174-2177, 2019. Such techniques may involve locally frequency trimming resonators by removing material from the layers and adding alternating stacks of SiO2 and tungsten-titanium (TiW). While a temperature-induced frequency drift of approximately ±80 ppm has been shown by this technique in the industrial temperature range, it adds significant complexity to the fabrication process and increases the cost of manufacturing. Furthermore, the addition of layers comprising other materials can degrade the resonator quality factor (Q) and affect the long-term stability of the resonator.
Active techniques for temperature-induced frequency drift compensation include using temperature sensors and oven-controlled heating to maintain a constant temperature of the FBAR. While such techniques have achieved favorable results, including a ±3 ppm temperature-induced frequency drift from 0° C. to 90° C., see Sankaragomathi et al., “A ±3 ppm 1.1 mW FBAR Frequency Reference with 750 MHz Output and 750 mV Supply,” pp. 436-437, 2015, these techniques can more than double the power consumption required to operate the FBAR. In the ±3 ppm case, active compensation techniques increase power consumption from 450 μW to 1100 μW, which is not desirable for many applications such as Wi-Fi and GPS.
Further improving the passive temperature-induced frequency drift compensation of MEMS resonators operating at ultra-high frequencies is desirable. Recently, square Lamé mode resonators have gained popularity for their ability to generate high Qs on the order of 1-5 million due to their low thermoelastic damping (TED). However, motional impedance requirements for low-noise oscillators restrict the practically allowable size of square Lamé mode resonators, limiting them to frequencies of approximately 10 MHz. Nevertheless, some design implementations may leverage the high Q and low TED of square Lamé mode resonators, while circumventing their motional impedance limitations.
While both the cross-sectional Lamé mode resonator 100 and the distributed Lamé mode resonator 105 have various advantages over conventional square Lamé mode resonators, designing them at UHF ranges is still challenging due to their capacitive transduction mechanism, which results in large motional impedances at high frequencies. Additionally, effective capacitive transduction across nanoscale electrode-resonator gaps requires the resonator to be packaged in a low vacuum process to prevent thin-film damping, which adds to the fabrication complexity and cost of manufacturing. As such, it may be beneficial to consider alternative transduction mechanisms for UHF applications, such as piezoelectric transduction. While piezoelectric versions of cross-sectional Lamé mode resonators have been fabricated, such resonators have been implemented at fairly low operational frequencies of around 67 MHz. See Shahraini et al., “Temperature Coefficient of Frequency in Silicon-Based Cross-Sectional Quasi Lamé Mode Resonators,” IFCS 2018-IEEE Int. Freq. Control Symp. (2018).
In addition to the motional impedance requirements, the temperature-induced frequency drift compensation requirements must be considered when designing MEMS resonators operating in the UHF range. The temperature coefficients of frequency of square Lamé mode resonators exhibit a relationship with silicon substrate doping when the dopant concentration is on the order of 1019 cm−3 and higher. As such, the square Lamé mode is considered to be a good candidate for the development of MEMS resonators with reduced temperature-induced frequency drifts. At a certain doping concentration, it may be possible to fully compensate for the first order temperature coefficient of frequency and be left with only the second order temperature coefficient of frequency (and higher order terms), thereby reducing the overall temperature-induced frequency drift substantially. Temperature-induced frequency drifts as small as 200 ppm over the industrial temperature range have been achieved by this method. See Ng et al., “Temperature Dependence of the Elastic Constants of Doped Silicon,” J. Microelectromechanical Syst., vol. 24, no. 3, pp. 730-741 (2015). Additionally, using this approach, both cross-sectional Lamé mode resonators and distributed Lamé mode resonators have been fabricated to compensate for the first order temperature coefficient of frequency. While this technique provides a significant improvement over the temperature-induced frequency drift seen in resonators without TCF1 compensation (i.e., approximately 3,750 ppm over the industrial temperature range), it still does not match the performance of AT-cut quartz. Therefore, it may be beneficial to use another method for lowering the temperature-induced frequency drift inherent in silicon to meet high-end consumer and industrial requirements. The present disclosure addresses this need by providing new techniques for designing MEMS resonators with both first and second order passive temperature-induced frequency drift compensation in the UHF and VHF range.
The present disclosure provides a distributed Lamé mode resonator actuated in the cross-section of the substrate, referred to herein as a “distributed cross-sectional Lamé mode resonator”. Such a device may be transduced by piezoelectric or capacitive means. The device may be fabricated using a homogeneous base material such as silicon. Alternatively, the device may be fabricated using both a base material and a secondary material, where the secondary material may be SiO2, undoped silicon or other materials.
In line with the discussion above, highly-doped silicon substrates can help engineer the TCF1 of square Lamé mode resonators, distributed Lamé mode resonators, and cross-sectional Lamé mode resonators to be almost zero. In the techniques described herein, however, the high doping concentration of the silicon substrate compensates for TCF2 instead of TFC1, and various geometric or material composition modifications compensate for TCF1. In the examples described in this section of the disclosure, modifications to the ratio of elongation of the cross-section of the resonator element 205 may help compensate for TCF1. Using this technique can provide at least second-order temperature compensation to the piezoelectrically-transduced distributed cross-sectional Lamé mode resonator 200, leading to reduced temperature-induced frequency drifts, possibly less than 1 ppm over the industrial temperature range with proper design.
To facilitate this, the technique involves determining, or otherwise defining, an initial geometry of a resonator element with a set of at least one associated eigenmodes. Next, one may determine (i) a type of dopant, (ii) a doping concentration, and (iii) an eigenmode from the set of at least one associated eigenmode, at which TCF2 is about equal to zero for the resonator. While many eigenmodes may be supported by a given resonator element, they need not be exhaustively tested, and may be narrowed by the resonator design parameters such as desired type of mode in the propagating series of modes. For example, because square Lamé modes only exist in resonator elements with edges aligned to the <100> and <110> directions with respect to the crystal axis of silicon, no other orientations may need to be considered. Using various finite element method (FEM) modeling tools, or any other capable modeling tools now known or later developed, a range of doping concentrations and type of dopants can be tested for each eigenmode, and thus a plurality of sets of parameters which result in a TCF2 about equal to zero can be identified.
Below, Table 1 shows the simulated TCF1 values when TCF2 is about equal to zero, for a square Lamé mode resonator element aligned in the <100> and <110> directions with respect to the silicon crystal lattice, for both N-type and P-type dopants. It is important to note that the value of TCF1 for a Lamé mode measured from FEM is the same whether measured for a single square Lamé mode or a propagating series of square Lamé modes. As noted above, the values in Table 1 can be determined using various FEM modeling tools now known or later developed.
Here, we see that for TCF2≅0 ppb/° C. 2, the smallest absolute value (deviation from zero) of TCF1 is seen in a P-doped silicon substrate with a resonator element aligned in the <110> direction (row 3 of Table 1). Thus, the P-doped resonator element aligned in the <110> direction requires less TCF1 compensation as compared to the other three choices. Hence, the P-doped <110> silicon substrate is chosen to serve as the resonator element substrate in the present example.
Certain geometric modifications to a square resonator element operating in a Lamé mode (thereby distorting the Lamé mode slightly) can modify the first order temperature coefficient of frequency. This is because, in the ideal case, the elastic modulus of a Lamé mode aligned in the <110> direction only depends on the elastic constant C44, but any slight geometric distortion begins adding small contributions of other elastic constants C11 and C12 to it. In the particular case of a square Lamé mode resonator element, the resonator element must have a height, H, and width, W, that are equal. However, any slight change to one of the dimensions H or W adds a small contribution of a length extensional mode. By choosing an appropriate H/W ratio of elongation, it is possible to reduce TCF1 from approximately 4.57 ppm/° C. when H/W=1, to a TCF1 of 0 ppm/° C. Using this technique in combination with an appropriate type of dopant and doping concentration can provide both first order and second order temperature compensation for an initially square Lamé mode resonator. This effect can also be extended to a propagating series of square Lamé modes, as found in the piezoelectrically-transduced distributed cross-sectional Lamé mode resonator 200, wherein after a dopant type and concentration is chosen to reduce TCF2 to about zero, a small change in the width of sub-elements 304a-d can be chosen to reduce TCF1 to be about zero.
To illustrate, consider the cross-sectional view 304 of
Additionally, the temperature dependency of the piezoelectric material should be considered when designing piezoelectrically-transduced distributed cross-sectional Lamé mode resonators based on FEM modeling. Including piezoelectric material in the model slightly alters the calculated temperature-induced frequency drift as compared to silicon alone. However, as the volume of the piezoelectric material is significantly smaller compared silicon, the change in temperature-induced frequency drift due to the addition of a piezoelectric material is often significantly smaller than the change caused by the real-world variation in dopant concentration alone, and may be neglected in certain embodiments depending on the design of the resonator.
Practically, the supply of highly doped <110> silicon substrate may be limited by wafer suppliers. This could make the large-scale fabrication of these resonators prohibitively expensive. Therefore, in the following section, an additional method is described in order to achieve temperature compensation using the <100> silicon substrate, which is more readily available from wafer suppliers.
In the techniques described herein, the high doping concentration of the silicon substrate compensates for TCF2 instead of TCF1, and various other geometric or material composition modifications compensate for TCF1, in line with the discussion above. In the examples described in this section of the disclosure, modifications to the material composition of the resonator element 205 may help compensate for TCF1. The TCF1 of a resonator element formed from a base material such as silicon can be altered by embedding a secondary material such as SiO2 into the resonator element. Using this technique can provide at least second-order temperature compensation to either a capacitively-transduced or piezoelectrically-transduced distributed cross-sectional Lamé mode resonator, leading to reduced temperature-induced frequency drifts, possibly less than 1 ppm over the industrial temperature range with proper design.
To facilitate this, the technique involves determining, or otherwise defining, an initial geometry of a resonator element with a set of at least one associated eigenmodes. Next, one may determine (i) a type of dopant, (ii) a doping concentration, and (iii) an eigenmode from the set of at least one associated eigenmode at which TCF2 is about equal to zero for the resonator. As in the previous example, using FEM, or any other capable modeling tools now known or later developed, a range of doping concentrations and type of dopants can be tested for each eigenmode, and thus a plurality of sets of parameters which result in a TCF2 about equal to zero can be identified. Table 1 above shows the simulated TCF1 values when TCF2 is about equal to zero, for a square Lamé mode resonator element aligned in the <100> and <110> directions with respect to the silicon crystal lattice, for both N-type and P-type dopants. In the present example, as the secondary material SiO2 is known to have a positive TCF1 (approximately 85 ppm/° C.), a doped silicon substrate base material with a negative TCF1 is chosen from Table 1 so that these positive and negative values of TCF1 can offset one another. Thus, the P-doped <100> silicon substrate with a negative TCF1=−12.65 ppm/° C. is chosen to serve as the resonator element substrate as it will require requires less TCF1 compensation as compared to the other option with a negative TCF1 (N-doped <110> silicon).
By choosing an appropriate ratio of the volume of SiO2 (VSiO2) and P-doped <100> silicon (VSi) to the volume of tahe resonator element (Vtotal, where Vtotal=VSiO2+VSi), it is possible to increase TCF1 from approximately −12.65 ppm/° C., to a TCF1 of 0 ppm/° C. To achieve this, one may measure the effect of systematically changing VSiO2/Vtotal via a parametric sweep approach, where Vtotal=VSi and VSiO2=0 before the resonator element is modified. However, it is also important to take into consideration the orientation and distribution of the secondary material on or within the resonator element, as the addition of a secondary material like SiO2 may disrupt the mode shape. Many designs are possible, including but not limited to: a sheet of SiO2 on the top of the resonator element, conformal deposition on the sidewalls of the resonator element, or SiO2 beams embedded in the resonator element. For a DCQLM, adding a sheet of SiO2 on the surface or the sidewalls of the resonator element can be considered, however as the thickness of these sheets is increased (as determined by the volume ratio VSiO2/Vtotal required to make TCF1=0), detrimental distortion of the mode may be possible.
Embedding multiple SiO2 beams along the length of the resonator element, wherein each SiO2 beam spans at least most of the width of the resonator element, is another possible design. This placement may be preferable to adding SiO2 to the surface or the sidewalls of the resonator element, as these embedded SiO2 beams run parallel to the cross-section of the eigenmode. This maintains a “square” Lame shape at any cross-section across the resonator element, which minimally distorts the mode. The optimal number, length, and spacing between SiO2 beams required to minimize mode distortion while reaching the VSiO2/Vtotal ratio required for TCF1 to equal zero may be determined with a parametric sweep approach using FEM. In the present example, the length of the SiO2 beam was set to a reasonable value according to practical limitations of microfabrication (i.e., 0.6 μm), while the number of beams were varied. Using this technique in combination with an appropriate type of dopant and doping concentration can provide both first order and second order temperature compensation.
The resonator design 700 in this example may be transduced by either capacitive or piezoelectric means. However, in the piezoelectric case, the temperature dependency of the piezoelectric material should be considered, as including piezoelectric material in the FEM model of resonator element 205 slightly alters the calculated temperature-induced frequency drift as compared to the resonator element 205 alone. However, as the volume of the piezoelectric material is significantly smaller compared to the volume of the resonator element 205, the change in temperature-induced frequency drift due to the addition of a piezoelectric material is often significantly smaller than the change caused by the real-world variation in dopant concentration alone, and may be neglected in certain embodiments depending on the design of the resonator.
The present disclosure also provides an energy-trapped distributed cross-sectional Lamé mode resonator formed by acoustically engineering the dispersion characteristics of propagating and evanescent waves in the resonator element and acoustically-engineered flanks, as well as a method of designing such a resonator. In the examples described in this section of the disclosure, the piezoelectrically-transduced distributed cross-sectional Lamé mode resonator 200 is used, however, other capacitively-transduced and piezoelectrically-transduced resonators may be used. As noted above in connection with
The aim of the waveguide design of the acoustically-engineered flank 1006 is to acoustically couple the mode under consideration in the resonator element 205 with an exponentially decaying wave in Waveguide 1004. In other words, propagating waves in the resonator element 205 are coupled to evanescent waves in Waveguide 1004 to concentrate acoustic energy in the resonator element 205 and reduce losses to the substrate. This is done by the intermediate Waveguide 1002, which supports a propagating wave with a large wave number (small wavelength) at the resonance frequency. As described in further detail below, the design of the waveguides may be performed using a parametric sweep approach in FEM.
As the total width is incrementally increased across Waveguide 1002, and the H/W ratio of elongation of the cross-section becomes incrementally smaller, the DCQLM has additional non-Lamé contributions added to the mode. Thus, the DCQLM dispersion curve will be slightly altered, and the propagating and evanescent waves which a certain frequency fres can excite will exhibit slightly altered wavenumbers. In the depicted example embodiment, as the width of Waveguide 1002 is incrementally increased to W1, the dispersion curve will shift such that only a propagating wave with a positive wave number at fres will be produced (dashed line in
After the width transition face between Waveguide 1002 and Waveguide 1004, the width is incrementally decreased across Waveguide 1004. Thus, the H/W ratio of elongation of the cross-section becomes incrementally larger, and again the DCQLM has additional non-Lamé contributions added to the mode. In the depicted example embodiment, as the width of Waveguide 1004 is incrementally decreased to W2, the dispersion curve will shift such that only an exponentially decaying evanescent wave will be produced (dot-dashed line in
In practice, W1, W2, and the rate of width change in the waveguides (ΔW/Δx) are designed using a parametric sweep conducted with FEM modeling tools.
Finally, by calculating the quality factor of the example resonator with FEM modeling tools, the advantage of this energy trapping technique can be demonstrated. In the present example, the quality factor of anchor damping, QANC, is approximately 320 k, the quality factor of TED, QTED, is approximately 4 M, while the quality factor of Akhiezer damping, QAKH, is approximately 30 k. Without the waveguides of the acoustically-engineered flank 206, FEM results indicate that QANC is only 15 k. The benefits of energy trapping are evident from these results, as even at a relatively high resonance frequency of 830 MHz, the resonator element with Waveguide 1002 and Waveguide 1004 has a large QANC and thus a small anchor damping loss, which is defined by 1/QANC. As Lamé modes inherently show large QTED, the total Q can be designed close to Akhiezer damping limits with the only Q losses being due to the addition of the piezoelectric material on the resonator. Finally, as the QANC is much larger than the total Q, the resonator is completely decoupled from the substrate, or said to be “quasi-levitated.”
At block 1104, the method involves determining, for the distributed cross-sectional resonator element, a plurality of sets of parameters, wherein each set of parameters of the plurality of sets of parameters defines a respective combination of (i) a type of dopant, (ii) a doping concentration, and (iii) a particular eigenmode from the set of associated eigenmodes, that causes an absolute value of a second order temperature coefficient of frequency of the distributed cross-sectional resonator element to be about zero. Examples of these sets of parameters are described above in connection with Table 1.
At block 1106, the method involves selecting, from among the plurality of sets of parameters, a particular set of parameters that results in the smallest absolute value of a first order temperature coefficient of frequency of the distributed cross-sectional resonator element. For instance, in Table 1, the set of parameters that results in the TCF1 with the smallest absolute value are the set of parameters in the third row.
At block 1108, the method involves applying the particular set of parameters to the distributed cross-sectional resonator element.
At block 1110, the method may involve, after applying the particular set of parameters to the distributed cross-sectional resonator element, modifying the initial geometry of the distributed cross-sectional resonator element to a modified geometry that causes an absolute value of the first order temperature coefficient of frequency of the distributed cross-sectional resonator element to be about zero. In line with the discussion above, this may involve modifying the width and/or the height of the plurality of sub-elements. For instance, in the examples described herein, modifying the geometry involves decreasing the width of the sub-elements until the height-to-width ratio of each sub-element is about 1.19. However, for other examples that do not exactly conform to the examples presented herein, other modifications to the height and/or width of each sub-element of the plurality of sub-elements may be applied to cause TCF1 to be about zero.
Alternatively, at block 1110, the method may involve, after applying the particular set of parameters to the distributed cross-sectional resonator element, modifying the material composition of the distributed cross-sectional resonator element to a modified composition that causes an absolute value of the first order temperature coefficient of frequency of the distributed cross-sectional resonator element to be about zero. In line with the discussion above, this may involve adding and/or modifying SiO2 beams in the resonator element to change the VSiO2/Vtotal ratio. For instance, in the examples described herein, modifying the VSiO2/Vtotal ratio involves increasing the volume of the SiO2 beams until the VSiO2/Vtotal ratio of each sub-element is about 0.11. However, for other examples that do not exactly conform to the examples presented herein, other modifications to the VSiO2/Vtotal ratio may be applied to cause TCF1 to be about zero.
It should be understood that the techniques described herein to reduce TCF2 or TCF1 to zero or about zero do not necessarily involve reducing TCF2 and TCF1 to exactly zero. Rather, it is sufficient to reduce TCF2 and/or TCF1 to be as close to zero as is practically possible. In some embodiments, reducing TCF2 and/or TCF1 to “about zero” may involve reducing TCF2 to be less than 1 ppb/° C. 2 and/or reducing TCF1 to be less than 1 ppm/° C. In other embodiments, this may involve reducing TCF2 to be less than 0.1 ppb/° C. 2 and/or reducing TCF1 to be less than 0.1 ppm/° C. Still in other embodiments, this may involve reducing TCF2 to be less than 0.01 ppb/° C. 2 and/or reducing TCF1 to be less than 0.01 ppm/° C.
The techniques described herein can be used to design a piezoelectrically or capacitively-transduced MEMS resonator and fabricate a piezoelectrically or capacitively-transduced MEMS resonator according to the design. For instance, once the piezoelectrically or capacitively-transduced MEMS resonator has been designed using the techniques described herein, it may be fabricated using any semiconductor fabrication techniques now known or later developed. Such a piezoelectrically-transduced MEMS resonator can include a support structure such as a silicon substrate, a distributed cross-sectional resonator element having a cross-section that includes a propagating series of modes, at least one anchor coupling the distributed cross-sectional resonator element to the support structure, at least one piezoelectric drive electrode for actuation of the resonator element, and at least one piezoelectric sense electrode for sensing the resonator element. Such a capacitively-transduced MEMS resonator can include a support structure such as a silicon substrate, a distributed cross-sectional resonator element having a cross-section that includes a propagating series of modes, at least one anchor coupling a first end of the distributed cross-sectional resonator element to the support structure, at least one in-plane capacitive drive electrode for actuation, at least one in-plane capacitive sense electrode for sensing, at least one out-of-plane capacitive drive electrode for actuation of the resonator element, and at least one out-of-plane capacitive sense electrode for sensing the resonator element. In some examples, the resonator can be configured to operate as an oscillator.
While various aspects and embodiments have been disclosed herein, other aspects and embodiments will be apparent to those skilled in the art. The various aspects and embodiments disclosed herein are for purposes of illustration and are not intended to be limiting, with the true scope and spirit being indicated by the following claims.
This application claims priority to U.S. Provisional Application No. 63/312,171, filed Feb. 21, 2022, which is incorporated herein by reference in its entirety.
| Number | Date | Country | |
|---|---|---|---|
| 63312171 | Feb 2022 | US |
