MEMS resonator with improved temperature stability and method thereof

Abstract

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

Description

Technical Field

[0001] This invention relates to MEMS resonators. Background Technology

[0002] MEMS-based sensors typically use resonators with resonant frequencies that are sensitive to inputs such as acceleration and pressure. These sensors monitor physical quantities by outputting frequency shifts in these quantities (i.e., changes in the resonant frequency). Furthermore, resonators are used as timing references to provide signals for tracking time, synchronizing events in digital integrated circuits (ICs), and processing signals.

[0003] A potential drawback of silicon MEMS resonators is their lack of temperature stability. Due to the softening of silicon, the resonant frequency of a silicon resonator varies with temperature. The thermal frequency stability of a resonator is characterized by its temperature coefficient of frequency (“TCF”). The change in the resonant frequency of silicon with respect to temperature is given by the following expression: (1) Where: f0 is the resonant frequency of the resonator at the reference temperature. TCF1 is the first-order frequency temperature coefficient. TCF2 is a second-order frequency temperature coefficient, and ΔT is the absolute value of the difference between the temperature of interest and the reference temperature.

[0004] Silicon has an inherent first-order temperature drift of approximately -30 ppm / °C. Over the entire operating range of the resonator (typically -40°C to 85°C), this drift equals 3500 ppm.

[0005] The resonant frequency of a resonator also varies with its internal stress. This stress can occur, for example, when different parts of the resonator are made of different materials. More specifically, each material has a characteristic response to temperature changes, such as the amount of change in its dimensions. This particular response is called the material's coefficient of thermal expansion ("CTE"). Because different materials may have different CTEs, MEMS resonators composed of more than one material may exhibit CTE mismatch.

[0006] When different materials expand / contract at different rates with respect to temperature, this CTE mismatch leads to stress, referred to in this paper as "thermal stress." This typically occurs during the microfabrication of the resonator and during its normal operation as temperatures rise / fall. The bonding temperature between the two materials is the reference temperature. As the absolute value of the difference between the ambient temperature and the reference temperature increases, the magnitude of the thermal stress also increases. Tensile stress increases the frequency, while compressive stress has the opposite effect. Because the stress caused by CTE mismatch is temperature-dependent, the TCF of a resonator subjected to thermal stress will change.

[0007] The coefficient of thermal expansion (CTE) is a temperature-dependent material property. CTE is typically given as a single value, but the order of the CTE as a function of temperature varies depending on the material and temperature range of interest. For an Nth-order CTE that does not match the temperature function, the resulting frequency-temperature relationship will be of order N+1. In the industrial and military temperature ranges (-40°C to 85°C and -55°C to 125°C, respectively), the CTE of most materials can be well approximated as a first-order function.

[0008] Expression (2) shows the relationship between frequency and temperature when N=1: (2) in: It is substrate CTE, It is the strain of the substrate. It is the strain of the device layer Ð It is the device layer CTE, and ΔT is the absolute value of the difference between the temperature of interest and the reference temperature (i.e., the temperature at which the material first came into contact).

[0009] Regarding silicon: These data points can be used to determine the CTE slope within the range of interest. Therefore, unless the selected substrate has the same CTE slope as silicon, the TCF2 of the resonator will be affected by thermal stress.

[0010] Attempts have been made to address the thermal frequency stability issue, such as by using highly doped substrates and / or composite materials. In fact, doping alone can reduce the temperature-frequency response of MEMS resonators to less than 5 ppm / °C. However, the performance of these resonators is affected by the variability in doping concentration.

[0011] Alternatively, CTE mismatch can be considered to address thermal frequency stability issues. In fact, the judicious use of CTE mismatch enables the production of temperature-compensated resonators requiring much lower doping levels. This is desirable because MEMS devices requiring lower doping levels are more readily available and mass-produced. Doping is also used to alter the frequency-temperature inflection point, allowing the resonator to achieve frequency stabilization through isothermal treatment. Using thermal stress to reduce TCF can also lower the doping concentration level required for this frequency stabilization technique.

[0012] As described above, "thermal stress" does not vary with the absolute CTE value, but rather with the difference in CTE between two or more materials. Resonators that can be designed using thermal stress fall into one of two categories: the substrate has a higher CTE than the device layer, or the substrate has a lower CTE than the device layer. The latter category is referred to herein as "low-CTE substrates." These resonators are simpler to fabricate because many materials typically available in wafer form have low CTE (e.g., silicon, pyrex glass, fused silica, titania-silica glass, etc.). These materials are also well-suited for many microfabrication processes. A limitation of using low-CTE substrates stems from the difficulty in reducing the resonator's TCF using device layer materials that naturally have a negative TCF (such as silicon).

[0013] As previously mentioned, silicon has a natural negative TCF1 of approximately -30 ppm / °C. To reduce temperature-induced frequency drift, the resonator will need to withstand tensile stress that increases with temperature (or conversely, compressive stress that is inversely proportional to temperature). Designing such a resonator is not easy. Resonators with multiple anchors connected to a low CTE substrate will adversely experience tensile stresses inversely proportional to temperature. Consider... Figure 1 The conventional arrangement depicted in the diagram shows a strip 100 anchored at both ends to a substrate 102 via anchors 104A and 104B. If the substrate 102 has a relatively lower CTE than the anchors 104A and 104B and the strip 100, the strip will contract relative to the anchors as the temperature decreases, thus experiencing a tensile load. Therefore, the tensile stress is inversely proportional to the temperature, which is contrary to the desired response. Therefore, using multiple anchors to apply thermal stress to the resonator to reduce its TCF is problematic. Summary of the Invention

[0014] This invention provides a method for designing temperature-compensated MEMS devices, and a temperature-compensated device formed by this method. Devices formed according to this teaching have improved temperature stability.

[0015] According to exemplary embodiments, the TCF of the MEMS resonator is reduced via a suitable resonator architecture, including a low CTE substrate. More specifically, the resonator architecture suitable for achieving the desired level of temperature compensation includes: (a) a low CTE substrate, (b) a single anchor, and (c) a continuous outer region connected to the anchor by at least two tethers, wherein: (i) the outer region is rigid compared to the tethers (its stiffness is approximately 3 times or more than that of the tethers), and (ii) the intrinsic modes are driven by the tethers. One or more tethers may also be characterized by 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.

[0016] The method disclosed herein is based on CTE mismatch; that is, a resonator design in which the CTE of the substrate and the CTE of the device layer differ. With a suitable architecture, (i) the CTE difference leads to thermal stress in the resonator, and (ii) the desired eigenmode is driven by the tether. More specifically, the desired eigenmode is the eigenmode in which the resonant frequency of the resonant structure depends primarily on the size of the tether. Therefore, for a resonator according to an embodiment of the invention, changing the size of the tether will have a significant impact on the resonant frequency. Among any other benefits, a resonator design with CTE mismatch requires less doping than is required to achieve a given temperature compensation level. This is advantageous because MEMS devices with lower doping levels are easier to obtain and mass-produce. Furthermore, reducing the TCF via thermal stress can reduce the doping concentration level required to change the frequency-temperature inflection point (to produce a frequency-stable resonator via isothermal treatment).

[0017] Simply loading the resonator region is insufficient to produce a resonator with a reduced TCF. For the resonator's oscillation frequency to be affected by stress, the region of the resonator deformed due to oscillation must also be the same region under thermal load. In this regard, it is worth noting that two different types of associated stress exist. There is static stress caused by CTE mismatch between different layers; this is referred to herein as "thermal stress." There is also stress caused by vibration. In embodiments of the invention, where the intrinsic mode is driven by a tether, the region of the resonator stressed during vibration (i.e., the tether) is the same region under thermal stress. Therefore, to reduce the resonator's TCF, the frequency of the intrinsic mode must depend on the stiffness of the region loading the resonator.

[0018] The method for designing a temperature-compensated resonator according to this teaching includes the following steps: (a) developing an initial architecture consistent with that described in paragraphs

[0013] -

[0014] ; (b) calculating the TCF, and if the TCF is acceptable, the design is complete; if not, then (c) structurally modifying the design to stiffen the surrounding region relative to the tether; (d) if all candidate structural modifications have been made and the TCF is still unacceptable, then (e) changing the doping amount of the dopant type.

[0019] Regarding step "(a)" above, the resonant structure has an infinite number of eigenmodes. This design effectively defines and optimizes the structure for only one of these eigenmodes. Specifically, under this eigenmode, the resonant frequency of the resonant structure depends primarily on the dimensions of the tethering element.

[0020] Embodiments of the present invention are particularly suitable for low-frequency resonators (i.e., operating at about 1 MHz or below), where the resonant frequency depends largely on the size of the tether. Specifically, in order for the forces generated by CTE mismatch to produce significant stress, the cross-section of the tether must be small relative to the cross-section of the outer region. Since silicon has a relatively low average CTE value at room temperature (i.e., 2.6 ppm / °C), there are practical limitations on the stress that may be generated in resonators with low CTE substrates using the design methods described herein. Furthermore, as mentioned above, in order for the resonator to have a stress-dependent TCF, the strained regions during oscillation must be regions subjected to thermal stress. Since it is desirable to thin the cross-section of these strained regions (i.e., the tether), the frequencies of the eigenmodes with reduced TCF will tend to be lower.

[0021] Prior art has disclosed MEMS resonators that use CTE mismatch between the substrate and the device layer to compensate for the TCF of the resonant component. For example, U.S. Patents 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 resonant component connected to a stress inverter component, and the stress inverter component is anchored to the substrate. In the '853 patent, the stress inverter component has a symmetrical structure; in the '517 patent, the stress inverter component has an asymmetrical structure; and in the '124 patent, two different materials, each with a different CTE, are integrated into the stress inverter component (referred to herein as a "frame").

[0022] In the cited patent, the stress inverter component is depicted as 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 unclear how the stress inverter component (i.e., the "frame") of the '124 patent is supported by a single anchor, nor is there any disclosure regarding how this is achieved. In any case, having two or more anchors introduces the possibility that the positioning of these anchors will shift relative to each other (due to reasons other than thermal stress), thus affecting the stress in the resonant component and therefore also the TCF. The farther the anchors are placed, the greater the possibility of positioning variation. The positioning of the anchors can be altered by many factors, including stress from the packaging material, stress from thin-film and microfabrication processes, process variability, etc.

[0023] In the cited patent, the resonant component is a suspended feature, meaning it is only connected to the stress inverter component, which in turn is anchored to the substrate. This can lead to several performance issues, including static friction and susceptibility to shocks due to the narrow suspended feature being far from the anchor point. Additionally, the resonant component may be less sensitive to rapid temperature changes because it is not located near the interface between the device layer and the substrate layer. Finally, the device footprint increases because the stress inverter component is not configured to be directly actuated and sensed.

[0024] Regarding the '124 patent, the introduction of a second material with a second CTE into the stress inverter components increases manufacturing complexity, manufacturing cost, and aging-related failures. For ease of manufacturing, it is desirable to utilize a single material in the mechanical components (excluding any electrical components) of the device layer.

[0025] Furthermore, the double-ended fork architecture of the resonator elements disclosed in the aforementioned patents is limited to in-plane resonant modes. This is not desirable for all applications. First, MEMS devices with out-of-plane (OOP) resonant modes typically have capacitive electrodes located above / below the device layer, and therefore benefit from a relatively smaller device footprint compared to MEMS devices with in-plane resonant modes where the electrodes are located within the device layer. Second, in some cases, it is easier to form small capacitive gaps in the OOP direction than in the in-plane direction, thereby reducing motion resistance and insertion loss. Finally, double-ended fork resonators may be incompatible with complementary passive temperature compensation techniques, such as using geometric modifications to reduce the temperature coefficient of the first-order frequency to approximately 0 ppm / °C.

[0026] Some embodiments of the present invention provide a MEMS device comprising: having a first coefficient of thermal expansion (CTE) s The substrate and the substrate having a second coefficient of thermal expansion (CTE) d The device layer of ) where CTE s <CTE d Furthermore, the device layer is configured to form a resonant 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 not adjacent to the anchor; and (c) at least two tethers, each tether coupling the outer region to the anchor.

[0027] Some other embodiments of the present invention provide a method for manufacturing a resonator having a desired temperature coefficient of frequency (“TCF”), the method comprising: a) Develop a resonator architecture to achieve the desired level of temperature compensation, based on: i. Low CTE substrate, ii. A resonant structure defined in a device layer, the resonant structure comprising a single anchor, an outer region not adjacent to the anchor, and at least two tethering elements physically coupling the outer region to the anchor. iii. The stiffness of the outer region is at least three times that of the bolt, and iv. Eigenmodes sensitive to thermal stress; b) Calculate the TCF and manufacture the resonator if the TCF is acceptable; c) When TCF is unacceptable, structurally modify the resonator architecture, where structural modifications can be selected from reducing the width of the tether, reducing the thickness of the device layer, increasing the size of the anchor, or bonding the anchor to a group consisting of the overlay and the underlay layers. d) Calculate the TCF and manufacture the resonator if the TCF is acceptable; e) When all structural changes to the group have been made and TCF is unacceptable, change the amount or type of dopant; and f) Fabricate the resonator.

[0028] Other embodiments of the present invention are described below with reference to the accompanying drawings. Attached Figure Description

[0029] Figure 1 The MEMS structure anchored at two locations according to existing technology is depicted.

[0030] Figure 2 A MEMS resonator according to an exemplary embodiment of the present invention is depicted.

[0031] Figure 3A Depicting Figure 2 A perspective view of the resonant structure of a MEMS resonator.

[0032] Figure 3B Depicting Figure 3A Von Mises stress in a resonant structure.

[0033] Figure 3C Depicting Figure 3A The eigenmodes of the resonant structure.

[0034] Figure 4 The von Mises stress in a resonant structure inconsistent with this teaching is depicted.

[0035] Figure 5A A method for designing MEMS resonators based on this teaching is described.

[0036] Figure 5B Depicting Figure 5A One of the steps of the method is a sub-operation.

[0037] Figure 6 The effect of device layer thickness on the maximum deformation of the anchor region and the von Mises stress in the resonator is depicted.

[0038] Figure 7A The case where the lower surface of the resonator is fixed to a low CTE substrate is depicted. Figure 3A A cross-sectional view of the resonator along axis AA when it deforms due to thermal stress.

[0039] Figure 7B The case is depicted where the lower surface of the resonator is fixed to a low-CTE substrate and the upper surface is fixed to a low-CTE capping layer. Figure 3A The resonant structure is shown in a cross-sectional view along axis AA when it deforms due to thermal stress.

[0040] Figure 8A A first alternative embodiment of the resonant structure for a MEMS resonator according to this teaching is depicted.

[0041] Figure 8B Depicting Figure 8A The resonator undergoes out-of-plane deformation along axis BB under thermal stress.

[0042] Figure 9A A second alternative embodiment of the resonant structure for a MEMS resonator according to this teaching is depicted.

[0043] Figure 9B The resonator under thermal stress was depicted along... Figure 9A The out-of-plane deformation of the axis CC of the resonator is depicted in the figure.

[0044] Figure 9C and Figure 9D Depicted respectively Figure 9A The eigenmodes and thermal stress of the resonant structure.

[0045] Figure 10A A third alternative embodiment of the resonant structure for a MEMS resonator according to this teaching is described.

[0046] Figure 10B and Figure 10C Depicted respectively Figure 7A The eigenmodes and thermal stress of the resonant structure.

[0047] Figure 11A A fourth alternative embodiment of the resonant structure for a MEMS resonator according to this teaching is depicted.

[0048] Figure 11B and Figure 11C Depicted respectively Figure 8A The intrinsic modes and thermal stress of MEMS resonators.

[0049] Figure 12 Depicting Figure 3A The temperature response of the resonant structure.

[0050] Figure 13 Depicting Figure 9A The temperature response of the resonant structure.

[0051] Figure 14 Depicting Figure 10A The temperature response of the resonant structure.

[0052] Figure 15 Depicting Figure 11A The temperature response of the resonant structure.

[0053] Figures 16A to 16D depict the final device cross-sections of various resonator designs based on this teaching. Detailed Implementation

[0054] Definitions. The following terms are defined for use in this specification and the appended claims: ● “About” or “basically” means + / - 20% relative to the stated number or nominal value.

[0055] ● “Low CTE substrate” refers to a substrate with a lower coefficient of thermal expansion (“CTE”) than the device layer of a MEMS device.

[0056] ● “Stiffness” is defined as the amount of force required to produce a given displacement.

[0057] In the context of this specification, other definitions may be provided elsewhere. All patents and published patent applications referenced in this disclosure are incorporated herein by reference.

[0058] Figure 2 A resonator 200 according to an exemplary embodiment of the present invention is depicted. The resonator 200 includes a substrate 202 and a device layer 204 attached via eutectic bonding (a eutectic bond 203 between the substrate and the device layer is shown). Various eutectic bonding methods, such as Au-Si, Al-Ge, or Al-Si, can be used. Alternatively, other bonding methods, such as direct bonding or glass powder bonding, can be used, provided the bonding method is suitable for the device and substrate wafer. The substrate 202 is a low-CTE substrate, meaning it has a lower CTE than the device layer 204. Defined within the device layer 204 are a resonant structure 206, a drive electrode 208, and a sensing electrode 210. Electrical contacts 212 are electrically connected to the drive electrode and the sensing electrode, as well as a portion of the resonant structure 206. The various drive electrodes and sensing electrodes are connected via an actuation gap G ( Figure 2 Only one of the actuation gaps is specifically identified in the diagram, and it is separated from the resonant structure 206. The undepicted capping layer typically covers the device layer 204.

[0059] A simple single-anchored resonator will be largely unaffected by any CTE substrate because the outer edge of the resonator expands / contracts freely, resulting in no significant stress within the resonator. However, stress may be generated within a single-anchored resonant structure (such as resonant structure 206) having two or more regions that produce stresses of opposite signs. Figure 3A Depicting Figure 2 Further details of the resonant structure 206 shown.

[0060] like Figure 3A As depicted, the resonant structure 206 includes a rectangular outer region 320 with a central opening. Within the opening are a centrally positioned anchor 322 and two fasteners 324A and 324B. The fasteners couple the outer region 320 to the anchor 322.

[0061] As previously stated, substrate 202 is a low CTE substrate. Therefore, as the temperature decreases, the anchor 322 bonded to substrate 202 will shrink less than the outer region 320. Thus, as resonator 200 cools, the "free" outer region 320 will tend to "close" towards the centrally positioned anchor 322. Since anchor 322 will not shrink relative to the rest of resonant structure 206, the rigid outer region 320 will compress tethers 324A and 324B. As discussed further below, this architecture results in compressive stress (in the tethers) that is inversely proportional to temperature, as needed. In one embodiment, the resonator structure applies compressive stress to the tethers when the temperature of the resonant structure (such as ambient or operating temperature) is lower than a reference temperature at which the substrate and device layers are bonded to each other.

[0062] According to this teaching, it is important that the outer region 320 is significantly stiffer than the tethering elements 324A and 324B. This ensures that stress is concentrated in the tethering elements. Here, "stiffness" is defined as the amount of force required to produce a set displacement. In this context, stiffness varies with the aspect ratio (length to width ratio) and geometry of the relevant elements of the resonant structure 206. The closed-loop / square geometry of the outer region 320 is actually stiffer than that of the tethering elements 324A and 324B. As a guideline, the stiffness ratio of the outer region 320 to the tethering elements 324A and 324B should be at least 3 / 1.

[0063] like Figure 3A As depicted, the aspect ratios of tethering components 324A and 324B are significantly larger than that of the outer region 320. Therefore, the outer region 320 is much stiffer than tethering components 324A and 324B. Typically, but not necessarily, tethering components 324A and 324B will have an aspect ratio of 10 / 1 or greater (tethering length T). L Width T of the fastenerW (ratio). Figure 3B The von Mises stress in the resonant structure 206 is depicted, showing the stress concentrated in the fasteners 324A and 324B. It is noteworthy that in embodiments of the invention, the outer region 320 is continuous; if the resonant structure 206 includes two isolated sub-regions 420A and 420B, such as in… Figure 4 In the resonant structure 406, substantially less stress will be generated in the tether (showing the greatly reduced von Mises stress in the tether).

[0064] In the context of embodiments of the invention, another way to visualize stress generation in the tether is to assume that, due to the much larger width of the outer region, the deformation of the outer region (e.g., outer region 320) will be largely unaffected by the tether. Upon cooling, the outer region 320 will contract relative to the center of the resonant structure 206, as it is a continuous region anchored at the center. And despite the fact that the tether will also contract, because the dimensions of the centrally located anchor 322 are substantially stable with respect to temperature, the tether will experience compressive loads due to the contraction of the outer region 320 onto the centrally located anchor 322. Therefore, the outer region 320 will experience stresses of equal magnitude and opposite sign (opposite to those of the tether), but its deformation will be minimal due to its stiffness and size.

[0065] It is important to note that simply loading any region of the resonator is insufficient to produce a resonator with a reduced TCF. For the resonator's oscillation frequency to be affected by stress, the region deformed due to oscillation must be the same region under thermal load. To reduce the resonator's TCF, the frequency of the intrinsic mode must depend on the stiffness of the region loading the resonator. Figure 3C The compensated eigenmodes of the resonant structure 206 are shown.

[0066] like Figure 3B and Figure 3C As shown, the von Mises stress and eigenmodes are based on the following design of the resonant structure 206 and the resonator 200: Figure 5A A method 500 for designing a temperature-compensated MEMS resonator according to this teaching is described. In step S501, an architecture for the resonant structure (e.g., resonant structure 206, etc.) is proposed. This architecture is based on the following design parameters: (a) Low CTE substrate; (b) A single anchor; (c) Connected to a continuous outer area of ​​the anchor by at least two tethering elements; (d) The outer region is rigid compared to the tether (its stiffness is approximately 3 times or more than that of the tether); and (e) Eigenmodes sensitive to thermal stress. More specifically, the resonant frequency of the resonant structure depends primarily on the dimensions of the tethering element.

[0067] As previously described and as used herein, the descriptor “low” in the phrase “low CTE substrate” does not imply any specific CTE value; rather, it indicates that the CTE of the substrate is less than the CTE of the device layer of the resonator. Importantly, this design produces a resonant structure in which the eigenmodes are driven by the tether. In other words, it is important that the tether deforms at resonance. Consider that resonator 200 has many eigenmodes, but only those eigenmodes in which the tether deforms will have a TCF affected by thermal stress. In other words, according to this teaching, the desired eigenmodes are those in which the resonant frequency of the resonant structure depends primarily on the size of the tether. Therefore, for a resonator according to an embodiment of the invention, changing the size of the tether will have a significant effect on the resonant frequency. For the purposes of this document and the appended claims, the use of the word “primarily” in this context means that changing the size of the tether (i.e., length, width, thickness) by a certain amount (e.g., 10%) will change the resonant frequency of the resonant structure more than changing the size of any other region of the resonant structure by the same amount.

[0068] In step S501, the layout and dimensions of all elements of the resonant structure (e.g., resonant structure 206, etc.) are defined, and the materials for the substrate (e.g., substrate 202, etc.) and the materials for the device layers (e.g., device layer 204, etc.), as well as the concentration of any impurities (dopants), are selected. Suitable materials for the substrate layer include, but are not limited to: fused silica, borosilicate glass, titania silicate, silicon carbide, polycrystalline silicon, undoped silicon, and doped silicon. Simulations are performed to calculate the von Mises stress and eigenmodes of the resonant structure. The von Mises stress can be calculated using commercially available software such as SOLIDWORKS and COMSOL.

[0069] Typically, the device layer is formed of silicon, which can be doped (P-type or N-type) or undoped. In some alternative embodiments, the device layer is formed of polysilicon or aluminum nitride. The dopant concentration in P-type doped silicon is approximately 9.0 × 10⁻⁶. 18 ions / cm 3 To approximately 3.0 × 10 20 ions / cm 3 Within the range, and the dopant concentration in N-type doped silicon is approximately 2.5 × 10⁻⁶. 18 ions / cm 3 To approximately 2.0 × 10 20 ions / cm 3Within the range.

[0070] In some alternative embodiments, the device layer is formed of silicon carbide, polycrystalline silicon, aluminum nitride, or diamond. Although not in... Figure 2 The resonator described herein includes a capping layer (see, for example, Figures 16A to 16D). Suitable materials for the capping layer include, but are not limited to, fused silica, borosilicate glass, titania silicate, diamond, polycrystalline silicon, undoped silicon, and doped silicon.

[0071] In step S502, the TCF is calculated. In step S503, it is determined whether the TCF is acceptable. The TCF will vary depending on the application. In some embodiments, a TCF of 0 is desired. In such embodiments, acceptable TCF values ​​are as follows: the absolute value of the first-order TCF of the device layer (|TCF1|) < 5 ppm / ℃; and the absolute value of the second-order TCF of the substrate (|TCF2|) < 25 ppb / ℃. 2 In some implementations, the substrate and device layers are selected such that the coefficient of thermal expansion (CTE) of the substrate is such that... s ) and the coefficient of thermal expansion (CTE) of the device layer d This is sufficient to set the absolute value of the frequency temperature coefficient of MEMS devices to be less than 5 ppm / ℃ at 25℃.

[0072] In some other cases, it is expected that the TCF value will result in an inflection point in the frequency-temperature curve, thereby allowing for isothermal treatment of the resonator. Simulation software such as COMSOL can be used to identify the frequencies of the resonator's eigenmodes. As those skilled in the art will understand, information relating to the change of silicon's elastic constants with temperature is used to predict the TCF.

[0073] If the TCF is determined to be acceptable in step S503, the design is completed in S516. If the TCF is unacceptable, various changes to the resonator design can be considered.

[0074] In step S504, it is inquired whether the resonator design has been structurally changed. If various changes have been made, as discussed further below, then in step S514 it is inquired whether the amount or type of dopant has been changed. If the answer to the inquiry is "yes," then return to step S501 and propose a new resonator structure. If the answer to the inquiry is "no," then in step S515 the dopant amount and / or type is changed, and in step S502 the TCF is recalculated.

[0075] If the answer to the question in step S504 is "no", then the resonator is structurally modified in step S505. Figure 5BA series of sub-steps are described to make various physical changes to the resonant structure. These changes include reducing the anchor width (steps S506 / S507), reducing the device layer thickness (steps S508 / S509), increasing the anchor size (steps S510 / S511), and bonding the anchor to both the top (capping layer) and the bottom (substrate) (steps S512 / S513). Regarding the bonding of the anchor, it will be bonded to at least the substrate (typically) or the capping layer. Therefore, step S513 involves bonding the anchor to a second surface, which is typically the capping layer. After one or more of steps S507, S509, S511, or S513 have been performed, the TCF is recalculated in step S502.

[0076] As a guideline, when reducing the tether width in step S507, the tether should be made as thin as possible. If the tether width has been reduced too much when recalculating the TCF, the tether width should be increased. If the TCF is still unacceptable, the same dimensional reduction method is used in S509 to reduce the device layer thickness. This process is repeated until a change produces the desired TCF, or a change does not produce the desired TCF. In the latter case, the doping dose and / or type is changed.

[0077] Besides reducing or otherwise altering the TCF of a MEMS resonator, some of the physical changes in step S505 can increase the reliability of the resonator and increase the extent to which the TCF can be altered. For example, one problem limiting the amount of stress generated in the tether and thus the ability to alter the TCF via this method is that the anchor deforms beyond the (low)CTE substrate. Considering that only one face of the resonant structure is fixed to the substrate in the architecture, the anchor deforms in the out-of-plane direction. This reduces the amount of stress that may be generated in the tether. In such architectures, the amount of out-of-plane deformation can be reduced in several ways.

[0078] One way to reduce out-of-plane distortion is to reduce the number of device layers in the resonator (e.g., Figure 2 The thickness of device layer 204 in the image. See, for example... Figure 5B Step S509 in the process. Figure 6 A graph depicts the displacement of the anchor and the von Mises stress in the resonant structure according to this teaching as a function of the device layer thickness. The graph shows that as the device layer thickness decreases from 30 micrometers to 10 micrometers, the von Mises stress increases by approximately 60 percent, and the anchor displacement decreases by approximately 50 percent.

[0079] Out-of-plane deformation of the anchor in a resonant structure can also be reduced by bonding both the upper and lower surfaces of the anchor to the corresponding substrate (i.e., the lower substrate and the upper capping layer). See, for example... Figure 5BStep S513 in the process. Figure 7A An anchor 722 is depicted connected to two fasteners 724A and 724B, and the anchor 722 is bonded to the underlying substrate (not depicted) via a eutectic bond 703A. Figure 7B Anchors 722 are depicted bonded to the underlying substrate and the upper capping layer (neither depicted) via corresponding eutectic bonds 703A and 703B. When only one surface of the anchor 722 is bonded, the anchor 722 undergoes out-of-plane (downward) deflection, as... Figure 7A As shown. When both the upper and lower surfaces of the anchor 722 are bonded, the anchor 722 essentially does not undergo out-of-plane deflection, as... Figure 7B As shown.

[0080] Another method to reduce out-of-plane deformation of anchors is to increase the size of the anchor relative to the surrounding external region. Figure 8A A first alternative embodiment of the resonant structure for a MEMS resonator is depicted: resonant structure 806. This resonant structure includes an outer region 820, an anchor 822, and four tethering elements 824. Figure 9A A second alternative embodiment of the resonant structure for a MEMS resonator is depicted: a resonant structure 906, which includes an outer region 920, an anchor 922, and four fasteners 924. The anchor 922 of the resonant structure 906 is larger than the anchor 822 of the resonant structure 806.

[0081] Compare Figure 8B and Figure 9B (A cross-sectional view is depicted through the corresponding axes BB and CC), anchor 822 deflects significantly more out-of-plane than anchor 922 (as shown by the downward deflection of the tether). It is worth noting that caution must be exercised when increasing the size of the anchor, as relatively larger anchors are more prone to deformation due to encapsulation and machining operations (compared to relatively smaller anchors). Anchors according to the embodiments can be manufactured in various shapes, such as, but not limited to, quadrilaterals, discs, crosses, etc.

[0082] As described above, limiting out-of-plane deformation can significantly reduce TCF. Furthermore, it reduces unwanted vertical displacement in the resonator's eigenmodes, thereby reducing the likelihood of any static friction between the resonant structure and the lower surface of the capping layer or the upper surface of the substrate.

[0083] Figure 3A The resonant structure 206 Figure 8A The resonant structure 806 and Figure 9A The resonant structure 906 depicts three embodiments of the resonant structure for MEMS resonators according to this teaching. Additionally, Figure 10A The resonant structure 1006 according to this teaching is depicted, and Figure 11A A resonant structure 1106 according to this teaching is depicted. These five exemplary embodiments of the resonant structure can, for example, be used with... Figure 2 Other components depicted herein are used in combination to provide a MEMS resonator according to this teaching.

[0084] Figure 9C The compensated eigenmodes of resonator structure 906 are depicted, and Figure 9D The thermal stress in the resonator structure is described. Figure 9A The tethering element of the resonator depicted is configured to be directly actuated and sensed. As correspondingly... Figure 9C and Figure 9D As shown, the compensation for intrinsic modes and von Mises stress is based on the following design of the resonant structure 906 (and various other elements of the resonator, such as those depicted in resonator 200): Figure 10A A fourth alternative embodiment of the resonant structure according to this teaching is depicted. Figure 10A The resonant structure 1006 includes an outer region 1020, an anchor 1022, and four tethering elements 1024. Figure 10B The compensated eigenmodes of resonator structure 1006 are depicted, and Figure 10C The thermal stress in the resonator structure is described. Figure 10A The resonator depicted is configured for electrostatic actuation on all four sides (including the inner and outer sides) of the outer region 1020. As correspondingly... Figure 10B and Figure 10C As shown, the compensation for intrinsic modes and von Mises stress is based on the following design of resonant structure 1006 (and resonator 200): Figure 11A A fifth alternative embodiment of the resonant structure according to this teaching is depicted. Figure 11A The resonant structure 1106 includes an outer region 1120, an anchor 1122, and four fasteners 1124. Figure 11B The compensated eigenmodes of resonator structure 1106 are depicted, and Figure 11C The thermal stress in the resonator structure is described. Figure 11A The resonator depicted is configured to resonate with out-of-plane eigenmodes, which allows the capacitor electrodes to be positioned above or below the device layer, thereby minimizing the resonator's footprint. As correspondingly... Figure 11B and Figure 11C As shown, the compensation for intrinsic modes and von Mises stress is based on the following design of resonant structure 1106 (and resonator 200): Figures 12 to 15 Temperature responses at the resonant frequencies of temperature-compensated resonant structures 206, 906, 1006, and 1106 are depicted. In each figure, the curve on the left shows the effect of doping on the TCF (dotted line) of the resonant structure and the effect of thermal stress (i.e., due to CTE mismatch) on the TCF. Additionally, the solid line depicts the total TCF (i.e., net temperature response) resulting from these two factors. The curve on the right reproduces the total TCF at a scale more suitable for illustrating the temperature response (e.g., the shape of the curve, etc.). Resonant structures 206, 906, 1006, and 1106 are designed to provide 0 ppm TCF at 20 °C. In other embodiments, it may be desirable to design resonant structures that meet the following requirements: i) substantially zero first-order, second-order, third-order, and fourth-order TCF terms, or any two of them; ii) exhibit a non-zero first-order TCF value; or iii) exhibit one or more “turning points” within an industrial or military temperature range.

[0085] Figure 12 The temperature response of the resonant structure 206 was plotted. The response curve is linear with a negative TCF of approximately -0.4 ppm / ℃. Within the normal operating range, the TCF varies from approximately 24 ppm at -40℃ to approximately -33 ppm at 100℃.

[0086] Figure 13 The temperature response of the resonant structure 906 was plotted. The response curve has a positive TCF of approximately 0.065 ppm / ℃. Within the normal operating range, the TCF varies from approximately 153 ppm at -40℃ to approximately 145 ppm at 100℃.

[0087] Figure 14 The temperature response of the resonant structure 1006 was depicted. The response curve approximates a parabola (opening upwards), with a frequency inflection point at approximately 30°C. Within the normal operating range, the TCF varies from approximately -5.4 ppm at -40°C to approximately 3.7 ppm at 100°C.

[0088] Figure 15 The temperature response of the resonant structure 1106 is depicted. The response curve exhibits a negative TCF of approximately -4.7 ppm / °C. The graph shows a frequency cutoff at approximately 83°C. Therefore, the resonant structure 1106 can be isothermally treated to produce an over-temperature stable resonator. Within the normal operating range, the TCF varies from approximately 410 ppm at -40°C to approximately -145 ppm at 100°C.

[0089] Figures 16A to 16D depict device cross-sections of embodiments of MEMS resonators. These device cross-sections do not correspond to any of the previously described resonant structures / resonators. Rather, these embodiments illustrate several methods for fabricating temperature-compensated MEMS resonators according to this teaching.

[0090] Figure 16A depicts a capacitively actuated MEMS resonator according to this teaching. The resonator includes a substrate 1602A and a capping layer 1614A both made of molten silicon dioxide, and a device layer 1604A made of doped silicon sandwiched between them. A eutectic bond 1603 hermetically seals the cavity and encloses the device layer 1604A between the substrate and the capping layer. A getter 1616 is used to improve the eutectic bond after vacuum. Defined within the device layer 1604A is a resonant structure including an anchor 1622A, an outer region 1620A, and a tether (not depicted). The anchor 1622A is bonded to the substrate 1602A and the capping layer 1614A. An actuation gap G separates the resonant structure from the drive electrode 1608A and the sensing electrode 1610A. An electrical contact 1612 is electrically coupled to the drive electrode 1608A, the sensing electrode 1610A, and the anchor 1622A.

[0091] Figure 16B depicts another embodiment of a capacitively actuated MEMS resonator according to this teaching. In this embodiment, the resonator includes a substrate 1602B made of titania silicate glass and a capping layer 1614B made of doped silicon. The substrate and capping layer sandwich a device layer 1604B made of doped silicon. Eutectic bonds 1603 couple the substrate 1602B to the device layer 1604B. Fusion bonds (not shown) couple the device layer 1604B to the capping layer 1614B. A getter 1616 is used to improve eutectic bonding after vacuum.

[0092] Defined within device layer 1604B is a resonant structure comprising an anchor 1622B, an outer region 1620B, and a tether (not depicted). Anchor 1622B is bonded to substrate 1602B and capping layer 1614B. An actuation gap G separates the resonant structure from drive electrode 1608B and sensing electrode 1610B. Electrical contact 1612 is electrically coupled to drive electrode 1608B, sensing electrode 1610B, and anchor 1622B. Capping layer 1614B includes a through-silicon via (TSV) 1628B with an isolation trench comprising a silicon dioxide liner 1625 and in-situ doped polysilicon (ISDP) filler 1626.

[0093] Figure 16C illustrates an embodiment of a piezoelectrically actuated MEMS resonator according to this teaching. In this embodiment, the resonator includes a substrate 1602C made of molten silicon dioxide, a capping layer 1614C, and a device layer 1604C made of doped silicon sandwiched in between. Eutectic bonds 1603 hermetically seal the cavity and enclose the device layer 1604A between the substrate and the capping layer.

[0094] Defined within device layer 1604C is a resonant structure comprising an anchor 1622C, an outer region 1620C, and a tether (not depicted). Anchor 1622C is bonded to capping layer 1614C. Piezoelectric material 1630 is disposed on anchor 1622C, tether, and outer region 1620C. Electrode 1613 is disposed on piezoelectric material 1630, which is disposed on anchor 1622C and outer region 1620C. Electrical contacts 1612 disposed adjacent to anchor 1622C are adjacent to via 1628C, which is made of doped silicon and extends through capping layer 1614C. Another set of electrical contacts 1612 is electrically coupled to via 1628C on top of capping layer 1614C.

[0095] Figure 16D Another embodiment of a capacitively actuated MEMS resonator according to this teaching is depicted. In this embodiment, the resonator includes a substrate 1602D made of molten silicon dioxide and a capping layer 1614D made of doped silicon. The substrate and the capping layer sandwich a device layer 1604D made of doped silicon. A eutectic bond 1603 hermetically seals the cavity and encloses the device layer 1604D between the substrate and the capping layer. A getter 1616 is used to improve the eutectic bond after vacuum.

[0096] Defined within device layer 1604D is a resonant structure comprising an anchor 1622D, an outer region 1620D, and a tether (not depicted). Anchor 1622D is bonded to substrate 1602D. Actuation gap G separates the resonant structure from drive electrode 1608D and sensing electrode 1610D.

[0097] An electrical contact 1612 disposed on the bottom surface of substrate 1602D is electrically coupled to a via 1628D made of doped silicon. The via 1628D extends through substrate 1602D to be electrically coupled to drive electrode 1608D, sensing electrode 1610D and anchor 1622D.

[0098] It should be understood that this disclosure describes some embodiments, and those skilled in the art can readily devise many variations of the invention after reading this disclosure, and the scope of the invention is defined by the appended claims.

Claims

1. A MEMS device, the MEMS device comprising: It has the first coefficient of thermal expansion (CTE) s (substrate); and It has the second coefficient of thermal expansion (CTE) d The device layer, where CTE s <CTE d Furthermore, the device layer includes a resonant structure, the resonant structure comprising: (a) A single anchor, wherein the anchor is bonded to the substrate. (b) An outer region, wherein the outer region is continuous and not adjacent to the anchor, and (c) At least two tethering elements, each tethering element having a first end and a second end, wherein the first end of each tethering element is physically connected to the anchoring element, and the second end of each tethering element is physically connected to the outer region.

2. The device of claim 1, wherein the resonant structure applies compressive stress to the at least two tethering members at ambient temperature.

3. The device according to claim 1, wherein the stiffness of the outer region is at least three times that of the tethering member.

4. The device of claim 1, wherein the device includes a capping layer, wherein the capping layer is bonded to the device layer.

5. The device of claim 4, wherein the capping layer has a third coefficient of thermal expansion (CTE). c CTE c <CTE d And wherein the anchor is bonded to the capping layer.

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

7. The device of claim 1, wherein the substrate comprises a material selected from the group consisting of fused silicon dioxide, borosilicate glass, titanium dioxide silicate, silicon carbide, polycrystalline silicon, undoped silicon, and doped silicon.

8. The device of claim 1, wherein the device layer comprises polysilicon, aluminum nitride, undoped silicon, at a concentration of about 9.0 × 10⁻⁶. 18 ions / cm 3 With approximately 3.0 × 10 20 ions / cm 3 The P-type doped silicon and the concentration are between approximately 2.5 × 10⁻⁶. 18 ions / cm 3 With approximately 2.0 × 10 20 ions / cm 3 Materials consisting of N-type doped silicon.

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

10. The device according to claim 1, wherein the anchor has a shape selected from the group consisting of quadrilaterals, discs, and crosses.

11. The device of claim 1, wherein the device includes a capacitor electrode for actuating the resonant structure and for sensing a resonant mode in the resonant structure.

12. The device of claim 1, wherein the device includes a piezoelectric electrode for actuating the resonant structure and for sensing a resonant mode in the resonant structure.

13. The device according to claim 1, wherein the resonant mode of the resonant structure is an out-of-plane mode.

14. The device according to claim 1, wherein the resonant mode of the resonant structure is an in-plane mode.

15. The device according to claim 1, wherein the resonant frequency of the resonant structure is less than about 1 MHz.

16. The device of claim 1, wherein the first coefficient of thermal expansion (CTE) s ) and the second coefficient of thermal expansion (CTE) d This is sufficient to set the absolute value of the frequency temperature coefficient of the MEMS device to be less than 5 ppm / ℃ at 25℃.

17. A MEMS device, the MEMS device comprising: It has the first coefficient of thermal expansion (CTE) s (substrate); It has the second coefficient of thermal expansion (CTE) d The device layer, where CTE s <CTE d The device layer includes a resonant structure, the resonant structure comprising: (a) A single anchor, wherein the anchor is bonded to the substrate. (b) An outer region, wherein the outer region is continuous and not adjacent to the anchor, and (c) At least two tethering elements, each tethering element coupling the outer region to the anchoring element; Furthermore, the device layer is structurally configured such that: (i) More than 50 percent of the thermal stress experienced in the resonant structure is experienced in the at least two fasteners, and (ii) The resonant frequency of the resonant structure depends primarily on the size of the tethering element.

18. The device of claim 17, wherein the outer region is harder than the tether.

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

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

21. The device of claim 17, wherein the resonant frequency of the resonant structure is less than about 1 MHz.

22. A method for manufacturing a resonator having a desired temperature coefficient of frequency ("TCF"), the method comprising: a) Develop a resonator architecture to achieve the desired level of temperature compensation, the resonator architecture being based on: i. Low CTE substrate, ii. A resonant structure defined in a device layer, the resonant structure comprising a single anchor, an outer region not adjacent to the anchor, and at least two tethering elements physically coupling the outer region to the anchor, and iii. The stiffness of the outer region is at least three times that of the tethering member; b) Calculate the TCF, and manufacture the resonator if the TCF is acceptable; c) When the TCF is unacceptable, structurally modify the resonator architecture, wherein the structural modification is selected from reducing the width of the tether, reducing the thickness of the device layer, increasing the size of the anchor, or bonding the anchor to the group consisting of the overlay layer; d) Calculate the TCF, and manufacture the resonator if the TCF is acceptable; e) When all structural changes to the group have been made and the TCF is unacceptable, change the amount or type of dopant; and f) Fabricate the resonator.

Images