MEMS resonator with improved temperature stability and method therefor

Abstract

A temperature-compensated MEMS resonator includes a substrate and a device layer, wherein the coefficient of thermal expansion of the substrate is lower than that of the device. The device layer is configured to form a resonating structure, the resonating structure comprising a single anchor that is bonded to the substrate, and an outer region, wherein the outer region is continuous and does not abut the anchor, and at least two tethers, each of which tethers couple the outer region to the anchor.

Description

MEMS RESONATOR WITH IMPROVED TEMPERATURE STABILITY AND METHOD THEREFORField of the Invention[oooi] The present invention relates to MEMS resonators.Background

[0002] MEMS-based sensors typically use a resonator having a resonant frequency that is sensitive to an input, such as acceleration, pressure, etc. Such sensors monitor these physical quantities by outputting their frequency drift ( / '.e., the change in resonant frequency). Also, resonators are used as timing references to provide signals for keeping track of time, synchronize events in digital integrated circuits (ICs), and process signals.

[0003] A potential drawback of a silicon MEMS resonator is a lack of temperature stability. The resonant frequency of a silicon resonator changes with temperature due to the material softening of silicon. The thermal frequency stability of a resonator is characterized by its temperature coefficient of frequency ("TCF"). The change in resonant frequency with respect to temperature of silicon is given by the expression: f(T) = fo[TCFl * (AT) + TCF2 * (AT)2+ ••• ]( 1)where: fo is the resonance frequency of the resonator at a reference temperature, TCF1 is the first order temperature coefficient of frequency, TCF2 is the second order temperature coefficient of frequency, and AT is the absolute value of the difference between the temperature of interest and the reference temperature.The inherent first-order temperature drift of silicon is around -30 ppm / °C. Over the full operational range of a resonator, typically -40°C to 85°C, that drift equates to 3500 ppm.

[0004] The resonant frequency of a resonator also varies with its internal stress. Such stress may arise, for example, when different portions of the resonator are composed of different materials. More particularly, each material has characteristic responses to a change a temperature, such as the amount by which its dimensions are altered. This particular response is the material's coefficient of thermal expansion ("CTE"). Since different materials are likely to have a different CTE, a MEMS resonator comprised of more than one material is likely to exhibit a CTE mismatch.

[0005] This CTE mismatch results in stresses, referenced herein as "thermal stresses," as the different materials expand / contract at different rates with respect totemperature. This commonly occurs as temperatures are raised / lowered during microfabrication of the resonator, as well as during normal operation thereof. The temperature at which two materials are bonded is the reference temperature. As the absolute value of the difference between the ambient temperature and the reference temperature increases, the magnitude of thermal stresses also increases. Tensile stresses increase frequency, while compressive stresses have the opposite effect. As stresses resulting from CTE mismatch have a temperature dependence, the TCF of resonators subject to thermal stresses will be altered.

[0006] The coefficient of thermal expansion is a temperature-dependent material property. CTE is often given as a single value, but the order of the CTE vs temperature function varies based on the material and temperature range of interest. For a CTE mismatch vs temperature function of order N, the order of the resulting frequency vs temperature relationship will be of order N + l. In the industrial and military temperature ranges (-40 to 85°C and -55 to 125°C, respectively), the CTE of most materials can be well approximated as a 1storder function.

[0007] Expression (2) shows frequency vs temperature relationship for N = 1 :where: asis the substrate CTE, esis the strain of the substrate edis the strain of the device layer adis the device layer CTE, andAT is the absolute value of the difference between the temperature of interest and the reference temperature ( / .e., the temperature at which the materials initially come into contact).In the case of silicon: a_73= 1.36 * 10-6 / °C, a+83= 2.92 * 10-6. These data points can be used to determine the slope of CTE within the range of interest. Thus, unless a chosen substrate has the same CTE slope as silicon, the TCF2 of the resonator will be affected by thermal stress.

[0008] There have been attempts to address the thermal-frequency stability issue, such as by using highly doped substrates and / or compound materials. In fact, the temperature-frequency response of MEMS resonators can be reduced using doping alone to less than 5 ppm / °C. However, the performance of these resonators is subject to variability in doping concentration.

[0009] Additionally, CTE mismatch can be considered for addressing the thermalfrequency stability issue. In fact, judicious use of CTE mismatch enables the creation oftemperature-compensated resonators that require much lower levels of doping. This is desirable because MEMS devices requiring lower doping level are easier to procure and manufacture at scale. Doping is also used to shift the frequency-temperature turnover point such that a resonator can be frequency stable using ovenization. Reducing TCF using thermal stress can reduce the doping concentration levels necessary for this frequency stability technique as well.[ooio] As described above, "thermal stress" is not a function of absolute CTE value, but rather of the CTE difference between two or more materials. The types of resonators that can be designed using thermal stress fall in one of two categories: either the CTE of the substrate is higher than the CTE of the device layer, or the substrate has a lower CTE than the device layer. The latter category is referred to herein as a "low CTE substrate." The latter category of resonator is simpler to fabricate since many materials that are commonly available in wafer form have low CTEs (e.g., silicon, pyrex, fused silica, titania silica glass, etc.). These materials are also well adapted to use in many microfabrication processes. A limitation of using a low CTE substrate comes from the difficulty of reducing the TCF of resonators using device layer materials that naturally have a negative TCF, such as silicon.[ooii] As previously noted, silicon has a naturally negative TCF1 of around -30 ppm / °C. To reduce its frequency drift due to temperature, a resonator would need to be subject to a tensile stress which increases with temperature (or inversely, a compressive stress that is inversely proportional to temperature). Designing such a resonator is not trivial. Resonators with multiple anchors connected to a low CTE substrate will disadvantageously be subject to tensile stresses that are inversely proportional to temperature. Consider the conventional arrangement depicted in FIG. 1, wherein bar 100 is anchored at both ends to substrate 102 by anchors 104A and 104B. If substrate 102 has a relatively lower CTE than anchors 104A and 104B and bar 100, the bar will shrink relative to the anchors as temperature decreases, experiencing a tensile load. Thus, the tensile stresses are inversely proportional to temperature, which is opposite to the desired response. It is thus problematic to use multiple anchors to thermally stress a resonator to reduce its TCF.Summary

[0012] The present invention provides methods for designing temperature- compensated MEMS devices, and temperature-compensated devices formed from the method. Devices formed in accordance with the present teachings have improved temperature stability.

[0013] In accordance with an illustrative embodiment, the TCF of a MEMS resonator is reduced via an appropriate resonator architecture, including a low CTE substrate. More particularly, a resonator architecture suitable for achieving a desired level of temperature compensation includes: (a) a low CTE substrate, (b) a single anchor, (c) a continuous outer region connected to the anchor by at least two tethers, wherein: (i) the outer region is stiff compared to the tethers (c.a., by a factor of 3 or more), and (ii) the eigenmode is driven by the tethers. The one or more tethers may also be characterized as having first and second ends, with the first end of each tether is physically connected to the anchor and the second end of each tether physically connected to the outer region.

[0014] Methods disclosed herein are based on CTE mismatch; that is, a resonator design wherein the CTE of the substrate and the CTE of the device layer differ. With an appropriate architecture, (i) the CTE difference results in thermal stresses in the resonator, and (ii) the desired eigenmode is driven by the tethers. More particularly, the desired eigenmode is one in which the resonance frequency of the resonating structure primarily depends on the dimensions of the tethers. So, for resonators in accordance with the embodiments of the invention, changing the dimensions of the tethers will have a significant impact on resonant frequency. Among any other benefits, resonator designs having CTE mismatch require less doping than would otherwise be required to achieve a given level of temperature compensation. This is advantageous because MEMS devices having lower doping levels are easier to procure and manufacture at scale. Moreover, reducing TCF via thermal stress can reduce the doping concentration levels necessary for shifting the frequency-temperature turnover point (to create a frequency-stable resonator via ovenization).

[0015] Merely loading regions of a resonator is insufficient to create a resonator with a reduced TCF. For a resonator to have its oscillation frequency affected by stress, the regions of the resonator that are deforming due to oscillation must additionally be the same regions that are under thermal load. In this regard, it is notable that there are two distinct stresses of relevance. There is the static stress that is caused by the CTE mismatch between the different layers; this is referred to herein as "thermal stress." There is also the stress from vibration. For embodiments of the invention, wherein the eigenmode is driven by tethers, the regions of the resonator ( / .e., the tethers) stressed during vibration are the same regions that are thermally stressed. Thus, for the TCF of a resonator to be reduced, the frequency of the eigenmode must be dependent on the stiffness of the loaded resonator region.

[0016] A method for designing a temperature-compensated resonator in accordance with the present teachings includes the steps of: (a) developing an initial architectureconsistent with what is described in paragraphs

[0013] -

[0014] ; (b) calculating TCF, and if it's acceptable, the design is complete; if not, then (c) structurally altering the design to stiffen the surrounding region relative to the tethers; (d) if all candidate structural alterations have been made and the TCF remains unacceptable, then (e) altering doping amount of type of dopant.

[0017] With respect to step "(a)" above, resonating structures have an infinite amount of eigenmodes. The design effectively defines and optimizes the structure for only one of these eigenmodes. In particular, one in which the resonance frequency of the resonating structure primarily depends on the dimensions of the tethers.

[0018] Embodiments of the invention are particularly well suited for low-frequency resonators ( / .e., operating at or below about 1 MHz), wherein the resonance frequency is largely dependent on the dimensions of the tethers. In particular, for the forces generated by CTE mismatch to generate significant stresses, the cross section of the tethers must be small relative to that of the exterior region. Since the average CTE value of silicon at room temperature is relatively low ( / .e., 2.6ppm / °C), there is a practical limit to the amount of stress that can generated in a resonator having a low CTE substrate and using the design methodology described herein. Additionally, as mentioned above, for the resonator to have a TCF affected by stress, the regions that are strained during oscillation must be the ones that are thermally stressed. Since it is desirable to make the cross-section of these strained regions ( / .e., the tethers) thin, the frequency of the eigenmodes with reduced TCF will tend to be low.

[0019] The prior art has disclosed MEMS resonators that use the mismatch in CTE between the substrate and the device layer to compensate the TCF of the resonating member. For example, U.S. Pats. 7,514,853, 7,956,517, and 7,944,124 disclose MEMS devices having a device layer and a substrate layer, wherein the device layer includes a resonating member connected to a stress-inverter member, and the stress-inverter member is anchored to the substrate. In the '853 patent, the stress-inverter member has a symmetric configuration, in the '517 patent, the stress-inverter member has an asymmetric structure, and in the '124 patent, two different materials each having a different CTE are integrated into the stress-inverter member (referenced therein as a "frame").

[0020] In the referenced patents, the stress-inverter member is depicted as being anchored to the substrate via at least two anchors, although the '124 patent indicates that in some embodiments, only a single anchor may be used. It is not clear how the stress inverter member ( / .e., "frame") of the '124 patent could be supported by a single anchor, nor is there any disclosure as to how that could be accomplished. In any case, having two or more anchors introduces the possibility that the position of these anchorswill move relative to one another (due to causes other than thermal stress), affecting the stress in the resonating member, and therefore affecting the TCF as well. Position changes are increasingly likely the further apart the anchors are placed. The position of the anchors can be altered by many factors, including stress from packaging materials, stress from thin films and microfabrication processes, process variability, etc.

[0021] In the referenced patents, the resonating member is a suspended feature, meaning the resonating member is connected only to the stress-inverter member, and the stress-inverter member is, in turn, anchored to the substrate. This may lead to several performance issues including stiction and susceptibility to shock due to the narrow features suspended far from anchor points. Additionally, the resonating member may be less sensitive to rapid changes in temperature, since it is not near to the interface of the device layer and the substrate layer. Finally, the device footprint is increased as the stress inverter member is not configured to be actuated and sensed directly.

[0022] Regarding the '124 patent, introducing a second material having a second CTE in the stress-inverter member increases manufacturing complexity, manufacturing cost and aging-related failures. For manufacturing ease, it is desirable to utilize a single material in the mechanical components of the device layer (excluding any electrical components).

[0023] Moreover, the double-ended fork architecture of the resonator element disclosed in the aforementioned patents is limited to in-plane resonance modes. This is not desirable for all applications. First, MEMS devices having out-of-plane (OOP) resonance modes typically have capacitive electrodes located above / below the device layer, and thus facilitate a relatively smaller device footprint than for MEMS device having in-plane resonance modes with electrodes located in the device layer. Second, in some cases, forming small capacitive gaps in the OOP direction is easier than in the inplane direction, decreasing motional resistance and insertion loss. Finally, double-ended fork resonators may not be compatible with complementary passive temperaturecompensation techniques such as using geometric modification to reduce the first order temperature coefficient of frequency to approximately 0 ppm / °C.

[0024] Some embodiments of the invention provide a MEMS device comprising : a substrate having a first coefficient of thermal expansion (CTES), and a device layer having a second coefficient of thermal expansion (CTEd), wherein CTES< CTEd, and further wherein the device layer is configured to form a resonating structure, the resonating structure having (a) a single anchor, wherein the anchor is bonded to the substrate, (b) an outer region, wherein the outer region is continuous and does not abutthe anchor, and (c) at least two tethers, each of which tethers couple the outer region to the anchor.

[0025] Some other embodiments of the invention provide a method for fabricating a resonator having a desired temperature coefficient of frequency ("TCF"), comprising : a) developing a resonator architecture for achieving a desired level of temperature compensation, the resonator architecture based on: i a low CTE substrate,II a resonating structure defined in a device layer, the resonating structure including a single anchor, an outer region that does not abut the anchor, and at least two tethers that physically couple the outer region to the anchor, ill the outer region is at least three times as stiff as the tethers, and iv an eigenmode that is sensitive to thermal stress; b) calculating the TCF and fabricating the resonator when the TCF is acceptable; c) structurally altering the resonator architecture when the TCF is not acceptable, wherein structural alterations are selected from the group consisting of reducing a width of the tethers, reducing a thickness of the device layer, increasing a size of the anchor, bonding the anchor to an overlying layer and an underlying layer; d) calculating the TCF and fabricating the resonator when the TCF is acceptable; e) altering an amount or type of type dopant when all structural alterations of the group have been made and the TCF is not acceptable; and f) fabricating the resonator.

[0026] Further embodiments of the invention are described below in conjunction with the appended drawings.Brief Description of the Drawings

[0027] FIG. 1 depicts a MEMS structure that is anchored at two locations, in accordance with the prior art.

[0028] FIG. 2 depicts a MEMS resonator in accordance with the illustrative embodiment of the invention.

[0029] FIG. 3A depicts a perspective view of the resonating structure of the MEMS resonator of FIG. 2.

[0030] FIG. 3B depicts the von Mises stress in the resonating structure of FIG. 3A.

[0031] FIG. 3C depicts an eigenmode of the resonating structure of FIG. 3A.

[0032] FIG. 4 depicts the von Mises stress in a resonating structure inconsistent with the present teachings.

[0033] FIG. 5A depicts a method for designing a MEMS resonator in accordance with the present teachings.

[0034] FIG. 5B depicts suboperations for one of the steps of the method of FIG. 5A.

[0035] FIG. 6 depicts the effect of device layer thickness on maximal deformation of the anchor region and von Mises stress in the resonator.

[0036] FIG. 7A depicts a sectional view of the resonator of FIG. 3A along the axis A- A when deformed by thermal stress in a case in which the lower surface of the resonator is fixed to a low CTE substrate.

[0037] FIG. 7B depicts a sectional view of the resonating structure of FIG. 3A along the axis A-A when deformed by thermal stress in a case in which the lower surface of the resonator is fixed to a low CTE substrate, and the upper surface is fixed to a low CTE cap layer.

[0038] FIG. 8A depicts a first alternative embodiment of a resonating structure for a MEMS resonator in accordance with the present teachings.

[0039] FIG. 8B depicts, along axis B-B, out-of-plane deformation of the resonator of FIG. 8A under thermal stress.

[0040] FIG. 9A depicts a second alternative embodiment of a resonating structure for a MEMS resonator in accordance with the present teachings.

[0041] FIG. 9B depicts, along axis C-C of the resonator depicted in FIG. 9A, out-of- plane deformation of that resonator under thermal stress.

[0042] FIGs. 9C and 9D depict an eigenmode and thermal stress, respectively, of the resonating structure of FIG. 9A.

[0043] FIG. 10A depicts a third alternative embodiment of a resonating structure for a MEMS resonator in accordance with the present teachings.

[0044] FIGs. 10B and IOC depict an eigenmode and thermal stress, respectively, of the resonating structure of FIG. 7A.

[0045] FIG. 11A depicts a fourth alternative embodiment of a resonating structure for a MEMS resonator in accordance with the present teachings.

[0046] FIGs. 11B and 11C depict an eigenmode and thermal stress, respectively, of the MEMS resonator of FIG. 8A.

[0047] FIG. 12 depicts a temperature response of the resonating structure of FIG. 3A.

[0048] FIG. 13 depicts a temperature response of the resonating structure of FIG.9A.

[0049] FIG. 14 depicts a temperature response of the resonating structure of FIG. 10A.

[0050] FIG. 15 depicts a temperature response of the resonating structure of FIG. 11A.

[0051] FIGs. 16A through 16D depict final device cross sections for various resonator designs in accordance with the present teachings.Detailed Description

[0052] Definitions. The following terms are defined for use in this description and the appended claims:• "About" or "Substantially" means + / - 20% with respect to a stated figure or nominal value.• "low CTE substrate" means a substrate having a lower coefficient of thermal expansion ("CTE") than that of a device layer of a MEMS device.• "stiffness" is defined as the amount of force needed to produce a set displacement.

[0053] Additional definitions may be provided, in context, elsewhere in this specification. All patents and published patent applications referenced in this disclosure are incorporated by reference herein.

[0054] FIG. 2 depicts resonator 200 in accordance with an illustrative embodiment of the present invention. Resonator 200 includes substrate 202 and device layer 204, attached via eutectic bonding (showing eutectic bond 203 between the substrate and device layer). Various eutectics can be used such as Au-Si, Al-Ge or Al-Si. Additionally, other bonding methods can be used such as direct bonding or glass frit bonding providing the bonding method is suitable for the device and substrate wafers. Substrate 202 is a low-CTE substrate, meaning that is has a CTE lower than device layer 204. Defined within device layer 204 are resonating structure 206, drive electrodes 208, and sense electrodes 210. Electrical contacts 212 are electrically connected to the drive and sense electrodes, as well as a portion of resonating structure 206. The various drive and sense electrodes are separated from resonating structure 206 via actuation gaps G (only one of which is specifically identified in FIG. 2). A cap layer, not depicted, typically covers device layer 204.

[0055] A simple single-anchored resonator will be largely unaffected by a substrate of any CTE, since the outer edge of the resonator is free to expand / contract, such that no significant stress is created within the resonator. However, stress can be created within a single-anchored resonating structure, such as resonating structure 206, which has two or more regions that develop stresses opposite in sign. FIG. 3A depicts further detail of resonating structure 206 shown in FIG. 2.

[0056] As depicted in FIG. 3A, resonating structure 206 includes outer region 320 having a rectangular shape with a central opening. Within the opening is centrally located anchor 322 and two tethers 324A and 324B. The tethers couple outer region 320 to anchor 322.

[0057] As previously noted, substrate 202 is a low-CTE substrate. Consequently, anchor 322, which is bonded to substrate 202, will shrink less than outer region 320 as temperature decreases. Thus, as resonator 200 cools, the "free" outer region 320 will tend to "close in" towards centrally located anchor 322. Since anchor 322 will not be shrinking relative to the rest of resonating structure 206, stiff outer region 320 will compress tethers 324A and 324B. As discussed further below, this architecture results in a compressive stress (in the tethers) that is inversely proportional to temperature, as desired. In an embodiment, the resonator structure exerts a compressive stress on the tethers when a temperature (such as ambient temperature or operating temperature) of the resonating structure is less than a reference temperature at which the substrate layer and the device layer are bonded to one another.

[0058] In accordance with the present teachings, it is important that outer region 320 is considerably stiffer than tethers 324A and 324B. This ensures that stress is concentrated in the tethers. Here, "stiffness" is defined as the amount of force needed to produce a set displacement. In the present context, stiffness is a function of the aspect ratio (length to width) and the geometry of the relevant elements of the resonating structure 206. The closed ring / square geometry of outer region 320 is indeed stiffer than the tethers 324A and 324B. As a guideline, the ratio of the stiffness of outer region 320 to tethers 324A and 324B should be at least 3 / 1.

[0059] As depicted in FIG. 3A, the aspect ratio of tethers 324A and 324B is considerably greater than the aspect ratio of outer region 320. Consequently, outer region 320 is considerably stiffer than tethers 324A and 324B. Typically, but not necessarily, tethers 324A and 324B will have an aspect ratio (tether length TL to tether width Tw) of 10 / 1 or greater. FIG. 3B depicts von Mises stresses in resonating structure 206, showing stresses concentrating in tethers 324A and 324B. It is notable that in embodiments of the invention, outer region 320 is continuous; substantially less stress would be generated in the tethers if resonating structure 206 included two isolated sub-regions 420A and 420B, such as in resonating structure 406 of FIG. 4 (showing far reduced von Mises stresses in the tethers).

[0060] In the context of embodiments of the invention, another way of visualizing stress generation in the tethers is to assume that deformation of the outer region (e.g., outer region 320) will be largely unaffected by the tethers due to the far greater width of the outer region. Upon cooling, outer region 320 will shrink with respect to the center of resonating structure 206, since it is a continuous region anchored at the center. And notwithstanding the fact that the tethers will also be shrinking, because the dimensions of the centrally located anchor 322 are essentially stable with respect to temperature, the tethers will experience a compressive load due to the shrinking of outer region 320 onto the centrally located anchor 322. Outer region 320 will be thus experience a stress equal in magnitude and opposite in sign (to the tethers), but due to its stiffness and size, the deformation thereof will be minimal.

[0061] It is notable that simply loading any region of a resonator is not sufficient to create a resonator with a reduced TCF. For a resonator to have its oscillation frequency affected by stress, the regions that are deforming due to oscillation must be the same regions that are under thermal load. For the TCF of a resonator to be reduced, the frequency of the eigenmode must be dependent on the stiffness of the loaded resonator region. FIG. 3C shows the compensated eigenmode of resonating structure 206.

[0062] The von Mises stress and eigenmode, as shown in FIG. 3B and FIG. 3C, is based on the following design for resonating structure 206 and resonator 200:Device Layer 204 P-doped silicon; 2.6 x 1019cm3Substrate 202 Titania silicate glassLength, L 260 micronsWidth, W 200 micronsThickness, T 25 micronsResulting Simulated Temperature Stability ± 30 ppm

[0063] FIG. 5A depicts method 500 for designing a temperature-compensated MEMS resonator in accordance with the present teachings. In step S501, an architecture is proposed for the resonating structure (e.g., resonating structure 206, etc.). The architecture is based on the following design parameters:(a) a low CTE substrate;(b) a single anchor;(c) a continuous outer region connected to the anchor by at least two tethers;(d) the outer region is stiff compared to the tethers (c.a., by a factor of 3 or more); and(e) an eigenmode that is sensitive to thermal stress. More particularly, the resonance frequency of the resonating structure primarily depends on the dimensions of the tethers.

[0064] As previously described, as used herein, the descriptor "low" in the phrase "low CTE substrate" is not meant to indicate any particular value of CTE; rather, it indicates that the CTE of the substrate is less than the CTE of the device layer of the resonator. It is important that the design results in a resonating structure in which the eigenmode(s) are driven by the tethers. In other words, it is important that the tethers are being deformed at resonance. Consider that resonator 200 has many eigenmodes, but only those in which the tethers are deforming will have a TCF that is affected by thermal stress. In other words, in accordance with the present teachings, a desired eigenmode is one in which the resonance frequency of the resonating structure primarily depends on the dimensions of the tethers. So, for resonators in accordance with the embodiments of the invention, changing the dimensions of the tethers will have a significant impact on resonant frequency. For use herein and the appended claims, the use of the word "primarily" in this context means that changing the dimensions ( / .e., length, width, thickness) of the tethers by some amount (say 10%), will alter the resonant frequency of the resonating structure more than if the dimensions of any other region of the resonating structure were changed by the same amount.

[0065] In step S501, the layout and dimensions of all elements of the resonating structure (e.g., resonating structure 206, etc.) are defined, and a material for the substrate (e.g., substrate 202, etc.) and a material for the device layer (e.g., device layer 204, etc.) are selected, as well as any impurity (dopant) concentration. Suitable materials for the substrate layer include, without limitation: fused silica, borosilicate glass, titania silicate, silicon carbide, polysilicon, undoped silicon, doped silicon. Simulations are conducted to calculate the von Mises stresses and eigenmodes of the resonating structure. Software, such as is commercially available from SOLIDWORKS, COMSOL, and others, may be used to calculate the von Mises stresses.

[0066] Typically, the device layer will be formed from silicon, which may be doped (either P-type or N-type) or undoped. In some alternative embodiments, the device layer is formed from polysilicon or aluminum nitride. The concentration of dopant in P-type doped silicon is in a range of about 9.0 x 1018ions per cm3to about 3.0 x 1020ions per cm3, and the concentration of dopant in N-type doped silicon is in a range of about 2.5 x 1018ions per cm3to about 2.0 x 1020ions per cm3.

[0067] In some alternative embodiments, the device layer is formed from silicon carbide, polysilicon, aluminum nitride, or diamond. Although not depicted in FIG. 2, resonators in accordance with the present teachings include a cap layer (see, e.g., FIGs.16A - 16D). Suitable materials for the cap layer include, without limitation: fused silica, borosilicate glass, titania silicate, diamond, polysilicon, undoped silicon and doped silicon.

[0068] The TCF is calculated in step S502. In step S503, query whether the TCF is acceptable. The TCF will vary based on use case. In some embodiments, a TCF of 0 is desired. In such embodiments, acceptable values of TCF are as follows: an absolute value of the first order TCF (|TCF1 | ) of the device layer < 5 ppm / °C; and an absolute value of the second order TCF (|TCF2| ) of the substrate < 25 ppb / °C2. In some embodiments, substrate and device layer are selected such that the coefficient of thermal expansion of the substrate (CTES) and the coefficient of thermal expansion of the device layer (CTEd) are sufficient to set an absolute value of a temperature coefficient of frequency of the MEMS device is less than 5 ppm / °C at 25°C.

[0069] In some other situations, a value of the TCF will be desired that results in a turnover point in the Frequency vs. Temperature curve, allowing for ovenization of the reasonator. A simulation software, such as COMSOL can be used to identify the frequencies of the eigenmodes of a resonator. As will be appreciated by those skilled in the art, information pertaining to the variation of elastic constants of silicon with temperature is used to predict TCF.

[0070] If it is determined in step S503 that TCF is acceptable, then the design is complete at S516. If TCF is not acceptable, then various alterations to the resonator design can be considered.

[0071] In step S504, query whether the resonator design has been structurally altered. If various alterations have been made, as discussed further below, then query at step S514 whether dopant amount or type have been altered. If the answer to the query is "Yes," then return to step S501 and new resonator structure is proposed. If the answer to the query is "No," then alter dopant amount and / or type at step S515, and recalculate TCF at step S502.

[0072] If answer to the query at step S504 is "No," then structurally alter the resonator at step S505. FIG. 5B depicts a series of sub-steps in which various physical alterations to the resonating structure are made. The alterations include reducing tether width (steps S506 / S507), reducing device layer thickness (steps S508 / S509), increasing anchor size (steps S510 / S510), and bonding the anchor to both the top (cap layer) and bottom (substrate) (steps S512 / S513). As to the bonding of the anchor, it will, at a minimum, be bonded to either the substrate (typically) or the cap layer. As such, step S513 involves bonding the anchor to the second surface, which is typicallythe cap layer. After an alteration is performed at one or more of steps S507, S509, S511, or S513, TCF is recalculated at step S502.

[0073] As a guideline, when reducing tether width at step S507, the tethers should be made as thin as practical. If, upon recalculating TCF, tether width has been reduced too much, then tether width should be increased. If TCF remains unacceptable, then reduce device layer thickness at S509, using the same approach to size reduction. This procedure is repeated until alterations result in a desirable TCF, or they do not. In the latter case, the dopant amount and / or type is altered.

[0074] Beyond an ability to reduce or otherwise alter the TCF of a MEMS resonator, some of the physical alterations of step S505 can increase the reliability of the resonator and increase the extent to which the TCF can be altered. For example, one issue limiting the amount of stress generated in the tethers, and hence the ability to alter the TCF via the present methods, is the extent to which the anchor deforms more than the (low) CTE substrate. Consider that in architectures in which only one face of the resonating structure is fixed to the substrate, the anchor deforms in an out-of-plane direction. This reduces the amount of stress that can be generated in the tethers. In such architectures, the amount of out-of-plane deformation can be reduced in several ways.

[0075] One way in which to reduce out-of-plane deformation is by reducing the thickness of the device layer (e.g., device layer 204 in FIG. 2) of the resonator. See, e.g., step S509 in FIG. 5B. FIG. 6 depicts plots of the displacement of the anchor and the von Mises stress in the resonator as a function of the thickness of the device layer, for a resonating structure in accordance with the present teachings. This figure shows von Mises stress increasing by about 60 percent, and the displacement of the anchor decreasing by about 50 percent, as the thickness of the device layer decreases from 30 microns to 10 microns.

[0076] Out-of-plane deformation of the anchor of the resonating structure can also be reduced by bonding both the upper and lower surface of the anchor to respective substrates ( / .e., an underlying substrate and an overlying cap layer). See, e.g., step S513 in FIG. 5B. FIG. 7A depicts an anchor 722 connected with two tethers 724A and 724B and the anchor 722 bonded to underlying substrate (not depicted) via eutectic bond 703A, and FIG. 7B depicts anchor 722 bonded to an underlying substrate and overlying cap layer (neither depicted) via respective eutectic bonds 703A and 703B. Out-of-plane (downward) deflection of anchor 722 occurs when only one surface of anchor 722 is bonded, as in FIG. 7A. Substantially no out-of-plane deflection of anchor 722 occurs when both the upper and lower surfaces of anchor 722 are bonded, as in FIG. 7B.

[0077] A further approach for reducing out-of-plane deformation of the anchor is by increasing the size of the anchor relative to the surrounding outer region thereof. FIG. 8A depicts a first alternative embodiment of a resonating structure for a MEMS resonator: resonating structure 806. This resonating structure includes outer region 820, anchor 822, and four tethers 824. FIG. 9A depicts second alternative embodiment of a resonating structure for a MEMS resonator: resonating structure 906, which includes outer region 920, anchor 922, and four tethers 924. Anchor 922 of resonating structure 906 is larger than anchor 822 of resonating structure 806.

[0078] Comparing FIGs. 8B and 9B, which depicts cross-sectional views through respective axes B-B and C-C, anchor 822 deflects out-of-plane considerably more than anchor 922 (as shown by the downward deflection of the tethers). It is notable that care must be taken when increasing the size of an anchor, since relatively larger anchors are more prone to deformation (than relatively smaller anchors) due to packaging and processing operations. The anchors in accordance with embodiments may be fabricated to assume a variety of shapes, such as, but not limited to a quadrilateral, a disk, a cross, etc.

[0079] Limiting out-of-plane deformation as described, above enables a relatively larger reduction in TCF. Furthermore, it reduces unwanted vertical displacement in the eigenmode of the resonator, thereby decreasing any likelihood of stiction between the resonating structure and the lower surface of the cap layer or the upper surface of the substrate.

[0080] Resonating structure 206 of FIG. 3A, resonating structure 806 of FIG. 8A, and resonating structure 906 of FIG. 9A depict three embodiments of a resonating structure for a MEMS resonator in accordance with the present teachings. Additionally, FIG. 10A depicts resonating structure 1006 and FIG. 11A depicts resonating structure 1106 in accordance with the present teachings. These five exemplary embodiments of resonating structures can be used, for example, in conjunction with other elements depicted in FIG. 2 to provide a MEMS resonator in accordance with the present teachings.

[0081] FIG. 9C depicts the compensated eigenmode and FIG. 9D depicts the thermal stress in resonator structure 906. The tethers of the resonator depicted in FIG. 9A are configured to be directly actuated and sensed. The compensated eigenmode and von Mises stress, as shown in respective FIGs. 9C and 9D, are based on the following design for resonating structure 906 (and various other elements of a resonator, such as depicted in resonator 200) :Device Layer N-doped silicon; 3.6 x 1018cm3Substrate Fused silicaLength 270 micronsWidth 270 micronsThickness 30 micronsResulting Simulated Temperature Stability ± 5 ppm

[0082] FIG. 10A depicts a fourth alternative embodiment of a resonating structure in accordance with the present teachings. Resonating structure 1006 of FIG. 10A includes outer region 1020, anchor 1022, and four tethers 1024. FIG. 10B depicts the compensated eigenmode and FIG. IOC depicts the thermal stress in resonator structure 1006. The resonator depicted in FIG. 10A is configured for electrostatic actuation on all four sides of outer region 1020, both inside and out. The compensated eigenmode and von Mises stress, as shown in respective FIGs. 10B and IOC, are based on the following design for resonating structure 1006 (and resonator 200) :Device Layer undoped siliconSubstrate Fused silicaLength 320 micronsWidth 320 micronsThickness 15 micronsResulting Simulated Temperature Stability ± 75 ppm Frequency turnover point 30°C

[0083] FIG. 11A depicts a fifth alternative embodiment of a resonating structure in accordance with the present teachings. Resonating structure 1106 of FIG. 11A includes outer region 1120, anchor 1122, and four tethers 1124. FIG. 11B depicts the compensated eigenmode and FIG. 11C depicts the thermal stress in resonator structure 1106. The resonator depicted in FIG. 11A is configured to resonate with an out-of-plane eigenmode, which allows for the capacitive electrodes to be positioned above or below the device layer, minimizing the resonator footprint. The compensated eigenmode and von Mises stress, as shown in respective FIGs. 11B and 11C, are based on the following design for resonating structure 1106 (and resonator 200) :Device Layer undoped siliconSubstrate titania silicate glassLength 260 micronsWidth 260 micronsThickness 10 micronsResulting Simulated Temperature Stability ± 300 ppm Frequency turnover point 83°C

[0084] FIGs. 12 through 15 depict the temperature response of the resonant frequency of temperature-compensated resonating structures 206, 906, 1006, and1106, respectively. In each figure, the plot on the left shows the effect of doping on TCF (dashed and dotted line) of resonant structure and the effect of thermal stress ( / '.e., due to CTE mismatch) on the TCF. Additionally, the solid line depicts the overall TCF ( / .e., net temperature response) due to these two factors. The plot on the right reproduces the overall TCF on a scale that is more suitable for illustrating the temperature response (e.g., shape of the curve, etc.). Resonating structures 206, 906, 1006, and 1106 were designed to provide a TCF of 0 ppm at 20°C. In further embodiments, it may be desirable to design resonating structures that i) substantially zero the first, second, third and fourth order TCF terms or any two of those, ii) exhibit a nonzero value of the first order TCF, or iii) exhibit one or more 'turn-over temperatures' in the industrial or military temperature ranges.

[0085] FIG. 12 depicts the temperature response of resonating structure 206. The response curve is linear, with a negative TCF of about -0.4 ppm / °C. Over a normal operating range, TCF varies from about 24 ppm at -40°C to about -33 ppm at 100°C.

[0086] FIG. 13 depicts the temperature response of resonating structure 906. The response curve has a positive TCF of about 0.065 ppm / °C. Over a normal operating range, TCF varies from about 153 ppm at -40°C to about 145 ppm at 100°C.

[0087] FIG. 14 depicts the temperature response of resonating structure 1006. The response curve is approximately parabolic (opening upwards), with a frequency turnover at about 30°C. Over a normal operating range, TCF varies from about -5.4 ppm at - 40°C to about 3.7 ppm at 100°C.

[0088] FIG. 15 depicts the temperature response of resonating structure 1106. The response curve has negative TCF of about -4.7 ppm / °C. The plot shows a frequency turnover at about 83°C. Resonating structure 1106 could thus be ovenized to yield a super-temperature stable resonator. Over a normal operating range, TCF varies from about 410 ppm at -40°C to about -145 ppm at 100°C.

[0089] FIGs. 16A through 16D depict device cross sections for embodiments of MEMS resonators. These device cross sections do not correspond to any resonating structure / resonator previously described. Rather, these embodiments illustrate several approaches for fabricating temperature-compensated MEMS resonators in accordance with the present teachings.

[0090] FIG. 16A depicts a capacitively actuated MEMS resonator in accordance with the present teachings. The resonator includes substrate 1602A and cap layer 1614A, both composed of fused silica, sandwiching device layer 1604A, which is composed of doped silicon. Eutectic bonds 1603 hermetically seal the cavity and enclose the device layer 1604A between the substrate and cap layer. Getters 1616 are used to improvevacuum post eutectic bond. Defined within device layer 1604A is the resonating structure, which includes anchor 1622A, outer region 1620A, and tethers (not depicted). Anchor 1622A is bonded to substrate 1602A and cap layer 1614A. Actuation gaps G separate the resonating structure from drive electrode(s) 1608A and sense electrode(s) 1610A. Electrical contacts 1612 are electrically coupled to drive electrode(s) 1608A, sense electrodes 1610A, as well as anchor 1622A.

[0091] FIG. 16B depicts another embodiment of a capacitively actuated MEMS resonator in accordance with the present teachings. In this embodiment, the resonator includes substrate 1602B composed of titania silicate glass and cap layer 1614B composed of doped silicon. The substrate and cap layer sandwich device layer 1604B, which is composed of doped silicon. Eutectic bonds 1603 couple substrate 1602B to device layer 1604B. Fusion bonds (not depicted) couple device layer 1604B to cap layer 1614B. Getters 1616 are used to improve vacuum post eutectic bond.

[0092] Defined within device layer 1604B is the resonating structure, which includes anchor 1622B, outer region 1620B, and tethers (not depicted). Anchor 1622B is bonded to substrate 1602B and cap layer 1614B. Actuation gaps G separate the resonating structure from drive electrode(s) 1608B and sense electrode(s) 1610B. Electrical contacts 1612 are electrically coupled to drive electrode(s) 1608B, sense electrodes 1610B, as well as anchor 1622B. Cap layer 1614B includes through silicon vias (TSV) 1628B with an isolating trench comprising a silicon dioxide liner layer 1625 and in-situ doped polysilicon (ISDP) filler 1626.

[0093] FIG. 16C depicts an embodiment of a piezoelectrically actuated MEMS resonator in accordance with the present teachings. In this embodiment, the resonator includes substrate 1602C and cap layer 1614C composed of fused silica, sandwiching device layer 1604C, which is composed of doped silicon. Eutectic bonds 1603 hermetically seal the cavity and enclose the device layer 1604A between the substrate and cap layer.

[0094] Defined within device layer 1604C is the resonating structure, which includes anchor 1622C, outer region 1620C, and tethers (not depicted). Anchor 1622C is bonded to cap layer 1614C. Piezoelectric material 1630 is disposed on anchor 1622C, tethers, and outer region 1620C. Electrodes 1613 are disposed on piezo material 1630, which is disposed on anchor 1622C and on outer region 1620C. Electrical contacts 1612 that are disposed proximate to anchors 1622C abut vias 1628C, which are composed of doped silicon and extend through cap layer 1614C. An additional set of electrical contacts 1612 electrically couple to vias 1628C at the top of cap layer 1614C.

[0095] FIG. 16D depicts yet a further embodiment of a capacitively actuated MEMS resonator in accordance with the present teachings. In this embodiment, the resonator includes substrate 1602D composed of fused silica and cap layer 1614D composed of doped silicon. The substrate and cap layer sandwich device layer 1604D, which is composed of doped silicon. Eutectic bonds 1603 hermetically seal the cavity and enclose the device layer 1604A between the substrate and cap layer. Getters 1616 are used to improve vacuum post eutectic bond.

[0096] Defined within device layer 1604D is the resonating structure, which includes anchor 1622D, outer region 1620D, and tethers (not depicted). Anchor 1622D is bonded to substrate 1602D. Actuation gaps G separate the resonating structure from drive electrode(s) 1608D and sense electrode(s) 1610D.

[0097] Electrical contacts 1612 disposed on the bottom surface of substrate 1602D electrically couple to vias 1628D composed of doped silicon. Vias 1628D extend through substrate 1602D to electrically couple to drive electrode(s) 1608D, sense electrode(s) 1610D, and anchor 1622D.

[0098] It is to be understood that the disclosure describes a few embodiments and that many variations of the invention can easily be devised by those skilled in the art after reading this disclosure and that the scope of the present invention is to be determined by the following claims.

Claims

What is claimed:

1. A MEMS device, comprising : a substrate having a first coefficient of thermal expansion (CTES); and a device layer having a second coefficient of thermal expansion (CTEd), wherein CTES< CTEd, and further wherein the device layer includes a resonating structure that comprises:(a) a single anchor, wherein the anchor is bonded to the substrate,(b) an outer region, wherein the outer region is continuous and does not abut the anchor, and(c) at least two tethers, each tether having a first end and a second end, wherein the first end of each tether is physically connected to the anchor and the second end of each tether is physically connected to the outer region.

2. The device of claim 1, wherein the resonating structure exerts a compressive stress on the at least two tethers at ambient temperature.

3. The device of claim 1, wherein the outer region is at least three times as stiff as the tethers.

4. The device of claim 1 comprising a cap layer, wherein the cap layer is bonded to the device layer.

5. The device of claim 4, wherein the cap layer has third coefficient of thermal expansion CTEc, wherein CTEc< CTEd, and wherein the anchor is bonded to the cap layer.

6. The device of claim 4, wherein the cap layer comprises a material selected from the group consisting of fused silica, borosilicate glass, titania silicate, diamond, polysilicon, undoped silicon and doped silicon.

7. The device of claim 1, wherein the substrate layer comprises a material selected from the group consisting of fused silica, borosilicate glass, titania silicate, silicon carbide, polysilicon, undoped silicon and doped silicon.

8. The device of claim 1, wherein the device layer comprises a material selected from the group consisting of polysilicon, aluminum nitride, undoped silicon, P-type doped silicon with a concentration between about 9.0 x 1018ions per cm3and about 3.0 x 102°ions per cm3, and N-type doped silicon with a concentration between about 2.5 x 1018ions per cm3and about 2.0 x 1020ions per cm3.

9. The device of claim 1 wherein the anchor is located at a center of the outer region.

10. The device of claim 1 wherein the anchor has a shape selected from the group consisting of a quadrilateral, a disk, and a cross.

11. The device of claim 1 comprising capacitive electrodes for actuating the resonating structure and for sensing a resonance mode in the resonating structure.

12. The device of claim 1 comprising piezoelectric electrodes for actuating the resonating structure and for sensing a resonance mode in the resonating structure.

13. The device of claim 1 wherein a resonance mode of resonating structure is an out-of-plane mode.

14. The device of claim 1 wherein a resonance mode of resonating structure is an inplane mode.

15. The device of claim 1 wherein a resonance frequency of the resonating structure is below about 1 MHz.

16. The device of claim 1 wherein first coefficient of thermal expansion (CTES) and the second coefficient of thermal expansion (CTEd) are sufficient to set an absolute value of a temperature coefficient of frequency of the MEMS device is less than 5 ppm / °C at 25°C.

17. A MEMS device, comprising : a substrate having a first coefficient of thermal expansion (CTEs); a device layer having a second coefficient of thermal expansion (CTEd), wherein CTEs< CTEd, wherein the device layer includes a resonating structure that comprises:(a) a single anchor, wherein the anchor is bonded to the substrate,(b) an outer region, wherein the outer region is continuous and does not abut the anchor, and(c) at least two tethers, each of which tethers couple the outer region to the anchor; and further wherein the device layer is structurally configured so that:(i) greater than 50 percent of thermal stress experienced in the resonating structure is experienced in the at least two tethers, and(ii) a resonance frequency of the resonating structure primarily depends on dimensions of the tethers.

18. The device of claim 17 wherein the outer region is stiffer than the tethers.

19. The device of claim 17 wherein a ratio of a length of each tether to a width of each tether is at least 10.

20. The device of claim 17 comprising a cap layer, wherein the anchor is bonded to the cap layer.

21. The device of claim 17 wherein a resonance frequency of the resonating structure is less than about 1 MHz.

22. A method for fabricating a resonator having a desired temperature coefficient of frequency ("TCF"), comprising : a) developing a resonator architecture for achieving a desired level of temperature compensation, the resonator architecture based on: i a low CTE substrate,II a resonating structure defined in a device layer, the resonating structure including a single anchor, an outer region that does not abut the anchor, and at least two tethers that physically couple the outer region to the anchor, and ill the outer region is at least three times as stiff as the tethers; b) calculating the TCF and fabricating the resonator when the TCF is acceptable; c) structurally altering the resonator architecture when the TCF is not acceptable, wherein structural alterations are selected from the group consisting of reducing a width of the tethers, reducing a thickness of the device layer, increasing a size of the anchor, bonding the anchor to an overlying layer; d) calculating the TCF and fabricating the resonator when the TCF is acceptable; e) altering an amount or type of type dopant when all structural alterations of the group have been made and the TCF is not acceptable; and f) fabricating the resonator.

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