Combining MEMS resonators

Abstract

To provide a beam-like resonator whose electromechanical resistance can be kept low, a resonator with low dependency of frequency on temperature, and a low-ESR resonator that has a high quality factor (Q-value) and / or a small footprint.SOLUTION: A resonator element includes a plurality of adjacent sub-elements 11A, 11B, 11C each having a length, a width and a length-to-width aspect ratio higher than 1 and resonating in a length-extensional resonance mode, torsional resonance mode, or flexural resonance mode. Further, each of the sub-elements is coupled to at least one other sub-element by one or more connection elements 12AB, 12BC, 14AB, 14BC coupled to non-nodal points of the length-extensional, torsional and flexural resonance modes of the sub-elements for exciting the resonator element into a collective resonance mode.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to Microelectromechanical System (MEMS) resonators. In particular, the present invention relates to length extension mode resonators, torsional mode resonators, or flexural mode resonators. Background of the Invention

[0002] The electromechanical resistance, also known as the equivalent series resistance (ESR), is an important performance parameter of a resonator. Compared to conventional quartz crystals, the ESR tends to be particularly high in piezoelectrically actuated beam resonators, e.g., length-extensional (LE) resonators. This is because the fundamental LE mode can exist in a beam resonator only if the length-to-width aspect ratio is greater than 1, i.e., in beams where the length is greater than the width, and the Nth overtone LE mode can exist in beam resonators where the length-to-width aspect ratio is greater than N. The ESR of the LE mode is reduced as the beam width increases, so a wider beam would be preferable to achieve a lower ESR. However, limiting the existence of the LE mode by the aspect ratio sets a lower limit on the ESR.

[0003] A further challenge in MEMS resonator design is ensuring that the resonator frequency is insensitive to temperature changes, i.e., temperature compensation. Beam resonators made of single crystal silicon can generally be temperature compensated by doping the silicon crystal sufficiently heavily, by properly shaping and orienting the beam with respect to the crystallographic orientation of the underlying silicon crystal, and by properly selecting the resonant mode. Temperature compensation by doping is described in more detail in WO 2012 / 110708.

[0004] The beam can, for example, oscillate in a length-extension (LE) resonant mode, where motion occurs primarily in the length direction of the beam. If the resonator beam is oriented in the 0100 crystallographic direction and doped with n-type dopants at a sufficiently high doping concentration, the LE mode has the desirable property of a zero or positive first order Temperature Coefficient of Frequency (TCF). While silicon has a positive TCF, materials with negative TCFs can also be used (which may be required, for example, for piezoelectric actuation purposes), making the overall TCF of the composite LE mode resonator zero.

[0005] Beam resonators can be excited in flexural or torsional modes instead of LE modes, however these modes suffer from similar problems associated with ESR and temperature compensation.

[0006] Particular problems arise when trying to obtain both low ESR and low temperature dependence at the same time. Some piezoelectrically driven resonators with length-to-width aspect ratios less than 1, i.e., relatively wide beams, can support resonant modes with relatively low ESR levels comparable to those of a quartz crystal at the same frequency. For example, Ho et al, "HIGH-ORDER COMPOSITE BULK ACOUSTIC RESONATORS", MEMS 2007, Kobe, Japan, 21-25 January 2007, and Kuypers J., "High Frequency Oscillators for Mobile Devices", in H. Bhugra, G. Piazza (eds.), Piezoelectric MEMS Resonators, Microsystems and Nanosystems, DOI 10.1007 / 978-3-319-28688-4_15, pp 335-385, show that such resonator designs with low ESR are possible when the beam is oriented in the

[0110] direction of the underlying silicon crystal. However, such resonant modes are more temperature dependent than, for example, the LE modes, making them less applicable in piezoelectrically driven resonators.

[0007] Additional challenges with MEMS resonator design include maintaining the quality factor of the resonator as high as possible while keeping the footprint of the resonator as small as possible to reduce manufacturing costs.

[0008] Therefore, there is a need for improved resonators having advantageous beam characteristics and low ESR, and particularly resonators which are more temperature compensated. Summary of the Invention

[0009] The object of the present invention is to overcome the aforementioned problems, in particular to provide a beam-shaped resonator that allows the electromechanical resistance to be kept low.

[0010] Another object is to realize a resonator whose frequency has a low temperature dependence.

[0011] A further object is to provide a low ESR resonator with a high quality factor (Q) and / or a small footprint.

[0012] The invention is based on coupling multiple beam-shaped subelements to each other using one or more connecting elements coupled to their non-nodal points, allowing the subelements to resonate in a collective mode. Thus, the entire resonator can be excited as a single resonator, and the division into subelements relaxes the geometric and orientation restrictions.

[0013] In particular, the invention has the characteristics stated in the independent claims.

[0014] According to one aspect, a microelectromechanical resonator is provided, comprising a support structure, a resonator element suspended on the support structure, and an actuator for exciting the resonator element in a resonant mode. The resonator element comprises a plurality of adjacent subelements, each subelement having a length, a width, and a length-to-width aspect ratio greater than one (i.e., a beam element). The subelements are configured to resonate in a length-extensional, torsional, or flexural resonance mode at the same or two or more different overtones thereof. Furthermore, to excite the resonator element in a collective resonant mode, each subelement is coupled to at least one other subelement by one or more connecting elements coupled to non-nodal points of the length-extensional, torsional, and flexural resonance modes of the subelements.

[0015] The present invention offers significant advantages. Firstly, by coupling subelements capable of resonating in one of the designated modes to form a resonator element, the area, specifically the width, of the resonator element can be increased to reduce the ESR while still maintaining the benefits of these modes. It has been found that the coupling of the subelements in the above mentioned manner is strong enough that all subelements resonate in the collective resonant mode. Thus, frequency splitting and the occurrence of multiple resonant modes are avoided.

[0016] Importantly, the present invention provides for doping-based (intrinsic) temperature compensation: the temperature dependence of frequency, i.e. absolute value of TCF, of a resonator element is reduced by properly orienting the element along its crystallographic direction on a silicon wafer.

[0017] The aforementioned advantages are particularly important in the case of piezoelectric actuation. When using piezoelectric actuation, it is generally necessary to reduce the ESR. Furthermore, the piezoelectric actuator material layer disposed on the silicon body of the resonator element influences the TCF. In this case, overcompensation of the TCF of the silicon body is beneficial.

[0018] Further advantages of the present invention include the ability to vary the exterior geometry of the resonator to provide space for different fixation schemes (e.g., center fixation to minimize losses) and / or electrical interconnection schemes (e.g., to minimize the area of ​​the resonator components), as will be described in more detail below.

[0019] Thus, the present invention overcomes the limitations of the prior art in a practical manner and enables a new type of resonator to be realized.

[0020] The dependent claims are directed to selected embodiments of the invention.

[0021] In general, embodiments of the present invention allow for both rectangular and non-rectangular resonator shapes, as well as hollow resonator shapes, with low ESR and, optionally, simultaneous temperature compensation. Non-rectangular and / or hollow shapes allow, for example, high quality factor fixturing and optimization of the overall component footprint.

[0022] In a typical embodiment, regardless of the overall shape of the element, the sub-elements have a rectangular shape and are spaced apart from one another in their width and / or length directions and are spaced apart by the connecting elements.

[0023] In some embodiments, at least two of the subelements have a length-to-width aspect ratio greater than 2 and are configured to resonate in an overtone resonance mode of order 2 or greater. In some embodiments, the aspect ratio is greater than 3, such as greater than 5, and the order is 3 or greater, such as 5 or greater.

[0024] In some embodiments, at least two of the subelements are coupled to each other in their width direction, and the connecting element comprises at least two essentially rigid connecting elements bordering elongated trenches between the subelements and extending in the length direction of the subelements. In some embodiments, a plurality of trenches are provided between at least some of the subelements in the length direction, the trenches being defined by the connecting elements. The number of trenches corresponds to the order of the overtone mode in which the subelements are configured to resonate.

[0025] The trenches in the resonator elements allow the elements to expand and contract laterally in addition to longitudinally, even when the overall element has a small aspect ratio. Such subelements cannot support, for example, LE modes if their aspect ratio is too small, but in this way the entire element can support collective LE modes. This is because the connecting elements make the resonator element behave like a single element, i.e. a beam with a small effective aspect ratio, which reduces the ESR of the resonator.

[0026] In some embodiments, at least two of the partial elements are coupled to one another along their length, and the connecting element includes at least one flexible connecting element that spans the gap between the partial elements. The flexible connecting element may be, for example, C-shaped, S-shaped, T-shaped, angled I-shaped, or serpentine-shaped.

[0027] In some embodiments, each subelement is configured to resonate in a length-extension resonance mode, alternatively the resonance mode may be a torsional resonance mode or a bending resonance mode, for example an in-plane bending resonance mode.

[0028] In some embodiments, each subelement is configured to resonate in an in-plane length extension resonance mode.

[0029] In a typical embodiment, the connecting elements together with the subelements are passive elements formed from a single, preferably doped, silicon crystal, i.e., they do not act as actuators as in some known array resonators, but act as passive couplers contributing to a collective mode such that the subelements have the same frequency and fundamental mode shape.

[0030] In some embodiments, the actuators are piezoelectric thin film actuators arranged on the resonator element, preferably distributed over all subelements of the resonator element.

[0031] In some embodiments, the resonator element comprises at least three, for example 3 to 50, typically 5 to 24 subelements coupled side-to-side, end-to-end, or both, by the connecting elements.

[0032] In some embodiments, at least some of the subelements are formed by one or more basic elements having a length-to-width aspect ratio greater than 1 and bordering each other along a length dimension perpendicular to a width dimension, each of the basic elements corresponding to a fundamental resonant mode that combines to become a collective resonant mode of the subelements and further to a collective resonant mode of the entire resonator element. The basic elements are arranged in a rectangular array configuration, with each basic element occupying a single array location. In some embodiments, at least one array location of the array configuration is not used by the basic elements. In other embodiments, each array location is occupied by only one basic element.

[0033] Thus, all resonating basic elements define a collective resonance mode for each subelement, and the coupling of the subelements ensures a collective resonance mode for the entire resonator element. The arrangement ensures that the collective resonance does not disappear even if one or more portions corresponding to one or more adjacent basic elements are removed, thus maintaining the desired properties of the resonator as new designs become available.

[0034] In some embodiments, the resonator element comprises a doped silicon crystalline body with a

[0100] crystallographic direction oriented along the length of the resonator element or offset from the length by less than 25 degrees, particularly less than 15 degrees, to provide temperature compensation of the element and reduced ESR due to the expansion of the width of the resonator element. In some embodiments, the silicon body has a doped silicon crystalline body with a

[0100] crystallographic direction oriented along the length of the resonator element or offset from the length by less than 25 degrees, particularly less than 15 degrees. This provides temperature compensation of the element and reduced ESR due to the expansion of the width of the resonator element. 19 cm -3 , e.g. at least 10 20 cm -3 is doped with an average impurity concentration of

[0035] In some embodiments, the subelements each have a length-to-width aspect ratio greater than or equal to N, where N is the order of a resonant mode of the subelement.

[0036] In some embodiments, the entire resonator element has an effective length to width aspect ratio of less than 2, particularly less than 1.

[0037] In some embodiments, all subelements of the resonator element have substantially the same width. Further, in some embodiments, the subelements have substantially the same length. However, in some embodiments, at least some of the subelements have different lengths and are configured to resonate in different but mutually collective overtone resonance modes. Thus, the subelements correspond to different collective overtones of a single fundamental mode. This allows the exterior geometry of the resonator to be shaped for various purposes, as described below.

[0038] In some embodiments, the resonator element comprises a plurality of adjacent sub-elements configured to accommodate at least a third, such as at least a fifth, overtone mode of the fundamental mode, allowing for high frequencies and low ESR.

[0039] In some embodiments, the resonator element is suspended from the support structure on both sides in the width direction of the resonator element from a node of the resonant mode of the subelement. Alternatively or additionally, the resonator element may be suspended from the support structure between two subelements from a node, preferably symmetrically in both the width direction and the length direction of the resonator element. The two subelements may not be adjacent subelements, and are generally not adjacent elements, but are spaced apart by a distance corresponding to the width of one or more subelements (and the intervening trench). Next, embodiments of the present invention and their advantages will be described in more detail with reference to the accompanying drawings. [Brief description of the drawings]

[0040] [Figure 1] 1 shows a top view of a fully used resonator array configuration formed from basic elements. [Diagram 2]1 shows a top view of a fully used resonator array configuration formed from basic elements. [Diagram 3] 1 shows a top view of a fully used resonator array configuration formed from basic elements. [Figure 4] 1 shows a top view of a fully used resonator array configuration formed from basic elements. [Diagram 5] 1 shows a top view of a fully used resonator array configuration formed from basic elements. [Figure 6] 1 shows a top view of a resonator element suspended on a support structure. [Figure 7] FIG. 7A shows a single beam resonator, FIG. 7B shows a beam expanded in width in a conventional manner, and FIG. 7C shows a resonator element according to the present invention. [Figure 8] Figure 8A shows a top view of one resonator configuration designed for a second order LE mode, and Figure 8B shows a mode shape diagram of a portion of the resonator element shown in Figure 8A. [Figure 9] Figure 9A shows a top view of one resonator configuration designed for the fundamental (first order) LE mode, and Figure 9B shows a mode shape diagram of a portion of the resonator element shown in Figure 9A. [Figure 10] 1 shows a graph of modal frequency as a function of beam aspect ratio (width to length) for several mode orders. [Figure 11] 1 illustrates a top view of an exemplary high-order (9th overtone) mode resonator element configuration. [Figure 12] FIG. 12 shows a top view of a variation of the arrangement shown in FIG. 11 that is hollow and fixed in the center. [Figure 13] 12 illustrates a non-rectangular variation of the configuration shown in FIG. [Figure 14] 14A-14D further show examples of centrally clamped hollow resonator elements, segmented resonator elements, and non-rectangular resonator elements. [Figure 15A]FIG. 15A shows a graph of the broad frequency range admittance measured for the piezoelectrically coupled second overtone mode resonator shown in FIG. 8A. [Figure 15B] FIG. 15B shows a detail of the admittance graph of the main resonance shown in FIG. 15A. [Figure 15C] FIG. 15C shows the frequency versus temperature curve measured for the resonator shown in FIG. 8A. [Figure 16A] 1 shows a top view of a multi-branch, width-coupled resonator plate. [Figure 16B] FIG. 1 shows a top view of longitudinally coupled resonator plates. [Figure 17] 17A to 17E show various possible flexible connecting element shapes between longitudinally joined sub-elements. [Figure 18] 18A-18C show examples of various longitudinal bond locations. [Figure 19] 19A-19D show further examples of flexible connecting elements for longitudinal coupling. Detailed Description of the Embodiments

[0041] [Definition]

[0042] A "node," as used herein, is a point in a vibration mode shape where the average amplitude of vibration at that point is less than 20% of the maximum amplitude of that vibration mode shape.

[0043] A "non-nodal point" (or "off-nodal point") is a point in a vibration mode shape where the average amplitude of vibration at that point is 20% or more of the maximum amplitude of the vibration mode shape.

[0044] The terms "length" and "longitudinal" are used specifically herein to refer to in-plane directions parallel to an axis perpendicular to the primary elongation direction of an LE mode, the torsion axis of a torsion mode, or the primary bending displacement of a bending mode. "Width" and "transverse" refer to in-plane directions perpendicular to the aforementioned in-plane directions.

[0045] Aspect ratio refers to the ratio of the in-plane dimensions of an element or subelement. "Effective aspect ratio" refers to the aspect ratio of the entire resonator element, including multiple subelements, to the aspect ratio of an individual subelement (beam) of the resonator element.

[0046] A "trench" is a space within a resonator element that allows adjacent subelements to move relative to one another to generate a desired mode in the subelement. An "elongated" trench is one that has an aspect ratio of 3 or more, such as 5 or more, or even 10 or more, depending on the mode the element is configured to support.

[0047] A "connecting element" is any member that mechanically connects two separate partial elements to each other. The connecting element may connect the partial elements in the width direction and limit a trench or a void or a recess in the resonator element at its longitudinal ends. In this case, the connecting element is typically an essentially rigid element. Alternatively, it may connect the partial elements in the length direction. In this case, the connecting element is typically a flexible element, for example a C- or S-shaped element that can be elastically deformed during resonance. Typically, the connecting element is part of the single crystal structure of the resonator element and is created by patterning the outline of the resonator element and the trenches therein by known MEMS microfabrication methods.

[0048] "Fundamental (resonant) mode" refers to the first resonant mode (also called the first overtone). Higher overtone modes are made up of several fundamental modes.

[0049] A "fundamental element" is a rectangular in-plane portion of a resonator that has a fundamental resonant mode. The fundamental elements can be connected longitudinally in an end-coupled configuration (i.e., a "virtual" element of the beam defined by the shape of the mode excited therein) or can be spaced apart by gaps and connected by flexible connecting elements. Higher order overtone modes, of order N, can be viewed as multiple fundamental modes arising in N longitudinally end-coupled fundamental elements.

[0050] The "collective resonance mode" refers to a composite resonance mode in which all the basic elements in a related specific entity resonate in the same basic resonance mode, having basically the same frequency and the same or 180-degree phase-shifted phases. In the collective resonance mode of the entire resonator element, each partial element constituting the resonator element has a first-order longitudinal extension resonance mode, a torsional resonance mode, or a bending resonance mode, or a higher-order overtone mode thereof. In this case, the resonator element can be divided into basic elements of generally the same size corresponding to the same basic mode.

[0051] In a typical embodiment, all the basic elements of the resonator are arranged in a rectangular array configuration. There are basic elements at the "occupied" array positions. There is no resonant material at the "empty" array positions.

[0052] The "hollow" resonator element shape means a shape in which at least one array position within the resonator element is empty. The void may be used as a fixed region and / or an electrical contact region. A gap (trench) enabling a desired resonance mode between partial elements is not considered a void in this context.

[0053] A rectangular resonator element is an element in which all the basic element array positions on the outer periphery are occupied. A non-rectangular element has at least one empty outer periphery array position.

[0054] "Integer fraction" (when the length of a partial element is relevant) means a fraction N / M. Here, both N and M are positive integers, and N < M. For example, the length of a third-order overtone partial element in an embodiment of the present invention is the integer fraction 3 / 5 of the fifth-order overtone partial element.

[0055] Length-extensional (LE) bulk acoustic modes of various orders in beam elements are known in the prior art. In such modes, the element (subelement) expands or contracts primarily along one axis. There are one or more nodes on this axis. In symmetric elements, and in the general case where both longitudinal ends of the element are free (not fixed to a support structure), the nodes are symmetrically located along the length of the element. Similarly, torsional, in-plane flexural, and out-of-plane flexural mode shapes are known in the prior art.

[0056] A "temperature compensated" element herein means that the elastic properties of the element, appropriate for the mechanical operation for which the element is designed, have a lower dependence on temperature at the present doping level than they would have without such doping, at least in some temperature range. In general, temperature compensation is achieved by selection of material properties, geometric properties, crystal orientation related properties, and mode shapes. Doping concentrations are in the range of 2×10 19 cm -3 More than, for example, 10 20 cm -3 or more. The dopants may be n-type or p-type dopants, such as phosphorus or boron. Temperature compensation herein also encompasses so-called "overcompensation" i.e. making the TCF of an element positive such that when a piezoelectric transducer layer, and / or any other layer, is coupled with the element, the total TCF of the resonator is less than without doping. Description of Selected Embodiments

[0057] In general, the resonator elements described herein may include multiple subelements with aspect ratios greater than 1, in particular greater than N, where N is the overtone number (i.e., mode number) of the collective mode excited in the element.

[0058] The number of subelements in a resonator element can be 2 or more, for example 2 to 50, in the width direction of the resonator element, and 1 or more, typically 1 to 8, for example 2 to 8, in the length direction.

[0059] The number of basic elements in the length direction corresponds to the number of modes excited in the subelements and can be from 1 to 20, for example from 2 to 12.

[0060] To achieve low ESR, the length-to-width aspect ratio of the resonator elements is typically less than 2. In some embodiments, the aspect ratio is less than 1.

[0061] Detailed embodiments of the present invention are described below primarily with reference to the length extension mode, and experimental data is also presented to illustrate the feasibility and advantages of the present invention, although the same principles can be applied to the torsion and bending modes.

[0062] In some embodiments of the present invention, a length-extension mode resonator is provided. The resonator comprises a support structure and a silicon resonator element, the silicon resonator element being suspended from the support structure at its nodal points and having a length and a width. The resonator element comprises at least two sub-elements partially spaced apart from each other by intermediate zones, each intermediate zone comprising at least one elongated trench and at least two connecting elements bordering the trench and mechanically coupling the sub-elements to each other at non-nodal points of the sub-elements. This ensures that the sub-elements are strongly coupled together and therefore operate as a single element in a well-defined resonant mode and frequency. An actuator is configured to excite the resonator element in a length-extension resonant mode parallel to the longitudinal direction of the at least one elongated trench.

[0063] In some embodiments, the resonator element comprises a doped silicon body, and the silicon body may have a

[0100] crystallographic direction oriented along the longitudinal extension of the resonator element or offset from said direction by less than 25 degrees, in particular by less than 15 degrees. Additionally, the silicon body of the resonator may have a crystallographic direction of at least 2×10 19 cm -3 , e.g. at least 10 20 cm -3By doping the resonator to an average impurity concentration of 0.01 μm, a low ESR can be achieved and at the same time, temperature compensation of the resonator can be achieved.

[0064] In some embodiments, the resonator element is split into three or more subelements arranged side-by-side in the width direction, which allows to keep the ESR of the resonator low while maintaining the ability to accommodate LE modes and the possibility of efficient temperature compensation.

[0065] In some embodiments, at least one intermediate zone, and preferably all intermediate zones, have at least two trenches and three connecting elements, which can be used, for example, to create resonator elements dedicated to specific higher LE overtones.

[0066] The aspect ratio of the subelements is typically selected to be in the range of 2:1 to 10:1 to maximize the benefits of the invention while keeping the number of subelements relatively small and the relative area used by the trenches small, although the invention is also effective with subelements of larger aspect ratios.

[0067] FIG. 1 shows a resonator element corresponding to oscillation in the first or higher LE mode (overtone). The element comprises three partial elements 11A, 11B, and 11C arranged side by side along the width direction. Adjacent partial elements 11A / 11B, 11B / 11C are respectively coupled between the partial elements by two connecting elements 12AB / 14AB, 12BC / 14BC arranged at or near the longitudinal ends of the partial elements. Between the connecting elements 12AB and 14AB there is a trench 13AB, and between the connecting elements 12BC and 14BC there is a trench 13BC. These trenches allow the partial elements 11A, 11B, and 11C to expand in the width direction during LE mode vibration. A first intermediate zone is defined by the linearly arranged connecting elements 12AB, 14AB, and the trench 13AB, and a second intermediate zone is defined by the arrangement of the connecting elements 12BC, 14BC, and the trench 13BC.

[0068] When each subelement in FIG. 1 is driven in its first order, or fundamental, mode, the resonator elements form a rectangular 3×1 fundamental mode array in which all are in use.

[0069] Note that the connecting elements 12AB / 14AB, 12BC / 14BC are not placed at the nodes of the LE vibration mode, but at non-nodal points at or near the vibrating ends of the subelements, so that the entire element becomes a set of strongly coupled resonators capable of resonating in a collective LE mode.

[0070] The element is suspended from the midpoint of its outer longitudinal edge using fasteners 19A, 19B. The number of fasteners may be more than two. In a typical configuration, the fasteners are located at or symmetrically about the lateral central axis of the element.

[0071] Figure 2 shows an embodiment suitable for second-order LE mode vibration. Here, there are three connecting elements 22AB / 24AB / 26AB, 22BC / 24BC / 26BC between the subelements 21A, 21B, 21C, respectively, and two trenches 23AB / 25AB, 23BC / 25BC. This configuration allows the subelements to extend in width in the second-order LE mode and other modes of higher order. The resonator elements in Figure 2 form a rectangular 3x2 fundamental mode array.

[0072] Each subelement has a width W and a length L. These widths and lengths may be the same between the different elements, but need not be. It should also be noted that the connection elements do not have to be located at the same position between each subelement pair, and / or the subelements and / or trenches do not have to be perfectly rectangular, some or all of them may have a tapered shape, for example. These modifications can, for example, tune the TCF of the resonator element, since the aspect ratio of the individual beams affects the TCF of the individual beams and thus the TCF of the entire resonator element. Also, tuning the dimensions and shape of the beams, as well as the location, dimensions and number of the connection elements, provides additional degrees of freedom. This can be used to set the frequency of the parasitic modes to the optimum frequency at which their adverse effects can be minimized.

[0073] Fig. 3 shows an example with four subelements 31A to 31D spaced apart by dissimilar intermediate zones. Between the two outer subelements 31A / 31B, 31C / 31D respectively there are two trenches 33AB / 35AB, 33CD / 35CD and three connecting elements 32AB / 34AB / 36AB, 32CD / 34CD / 36CD, and between the central subelements 31B / 31C there is one trench 33BC and two connecting elements 32BC / 34BC. Other configurations are of course possible. The resonator elements in Fig. 3 form a (modified) rectangular 4x2 fundamental mode array.

[0074] Figure 4 shows an embodiment with three subelements 41A, 41B, 41C separated by intermediate zones 48AB, 48BC. Each intermediate zone has four connecting elements and three trenches arranged symmetrically along the length of the subelement. The resonator elements in Figure 4 form a rectangular 3 x 3 fundamental mode array.

[0075] 5 shows a variant with five partial elements 51A to 51E spaced apart by intermediate zones 58AB to 58DE, similar to the one described with reference to FIG. tis greater than the length of the element in this example, which is equal to the subelement length L. The resonator elements in FIG. 5 form a rectangular 5×2 fundamental mode array.

[0076] In a typical implementation, at least one trench between each pair of subelements is centered on a node of the LE mode.

[0077] In order for the element to be able to support LE modes, the total length of the trenches in each intermediate zone between the sub-elements should make up a large proportion of the total length L of the element. In some embodiments, this proportion is 50% or more, for example 75% or more. In some embodiments, this proportion is 90% or more.

[0078] In a typical configuration, the trench width is 10 μm or less, preferably as narrow as possible given the fabrication method to minimize the trench area.

[0079] In some embodiments, the trenches and connecting elements are sized and positioned to avoid frequency splitting and multiple simultaneous resonant modes, following the principles of A. Jaakkola, et al., "Experimental study of the effects of size variations on piezoelectrically transduced MEMS resonators," Proc. IEEE International Frequency Control Symposium, 2010, pp. 410-414, http: / / dx.doi.org / 10.1109 / FREQ.2010.5556299.

[0080] In some examples, the resonant mode is a fundamental mode and the aspect ratio is between 2 and 4, such as between 2.6 and 3.4. In some examples, the resonant mode is a second or higher order mode and the aspect ratio is between 3 and 10, such as between 4.0 and 8.0 for the second order mode.

[0081] Figure 6 shows a suspended resonator element: the support structure 60 is spaced from the resonator element 61 by gaps everywhere except at the fasteners 69 at the nodes on the outer longitudinal sides of the outer sub-elements, allowing the resonator element 61 to vibrate freely in the LE mode as previously described.

[0082] In each of the above embodiments, at least one, and typically two or more, connecting elements for each subelement are located at the non-nodal points of the resonant mode in which the element is configured to resonate, thereby ensuring that the subelements are coupled together and vibrate in unison.

[0083] Finally, Figures 7A-7C show the difference between the present resonator and conventional resonators. Figure 7A shows a single high aspect ratio beam with two free ends. Figure 7B shows a beam expanded in width to become a virtual rectangular plate. Such a resonator has lower ESR and can be used in a

[0110] orientation, but cannot be temperature compensated because it does not function in LE mode when oriented in the

[0100] crystal direction. Figure 7C shows a resonator element according to an embodiment of the present invention. This approach works even if the side of the element is oriented in the

[0100] crystal direction and has a similar low ESR as the

[0110] oriented plate in Figure 7B.

[0084] FIG. 8A shows a resonator capable of supporting a second LE overtone resonance mode. The resonator element of this resonator is formed of a number of subelements (here 11). Each subelement is separated from the adjacent subelement by two elongated trenches arranged in series and connected to the adjacent subelement by three connecting elements. With the dimensions of the resonator plate shown being 326 μm×180 μm, the resonant frequency is approximately 40 MHz. The resonator elements in FIG. 8A form a rectangular 11×2 fundamental mode array.

[0085] Figure 8B shows the LE mode resonant mode shape for the geometry of Figure 8A, as simulated by FEM software. Due to symmetry, only half of the full resonator is shown. The grey shaded area indicates the total displacement at each location. As shown, each subelement resonates with the same collective mode. At the second order (and other even order resonances), the mode shape is not symmetric, but rather the subelements compress at one end and stretch at the other.

[0086] Figure 9A shows another resonator capable of supporting the fundamental LE resonant mode. With dimensions of the resonator plate of 300 μm×180 μm, the resonant frequency is approximately 20 MHz. The resonator elements in Figure 9A form a rectangular 5×1 fundamental mode array.

[0087] FIG. 9B shows the LE mode resonant mode shape in the southeast symmetric quadrant of the geometry of FIG. 9A, as simulated by FEM software.

[0088] Figure 10 shows a graph of the mode frequencies of a beam (here corresponding to a subelement) with a width-to-length aspect ratio varying from near zero (very thin beam) to 1. The dotted lines indicate the fundamental LE mode (LE1) and the overtone modes LE2 to LE4. Along the LEx mode branch, LEx modes with a direction determined by the parameter L are present only in the dotted region.

[0089] 11 shows an example of a high-order (9th) overtone length extension resonator element comprising a plurality (19) of subelements 111A. These subelements are stacked in the width direction and fixed from the nodal points on both longitudinal sides by fixing elements 119. For example, to form a resonator that vibrates at about 120 MHz, the dimensions of the element can be set to 225 μm by 170 μm.

[0090] Figure 12 shows a similar configuration to Figure 11, but fixed in the centre of the resonator with a fixing element 129 by providing an air gap 118 in the centre of the resonator, i.e. by "removing" some of the central basic elements of the subelements (in this case 5x3 basic elements). The resulting structure therefore comprises two types of subelements 121A, 121B with different lengths. The length of the shorter subelement 121B is an integer fraction of the length of the longer element 121A. It has been found that the collective resonant mode properties of the plate are maintained even when the exterior geometry is modified.

[0091] In general, the resonator design allows for the removal of desired fundamental elements (preferably symmetrically) without losing the desired (collective) modal properties of the composite resonator. This is advantageous since a central air gap maintains the LE resonant mode properties. As regards central fixation, it is beneficial from the point of view of minimizing packaging stresses that may affect the resonator elements. Central fixation is also beneficial from the point of view of low acoustic losses, which improves the Q-factor of the resonator. The high symmetry of the structure according to the invention reduces losses.

[0092] Figure 13 shows an example of a non-rectangular shape where the corner basic elements of the resonator plate are removed. Again, the resulting structure comprises two types of sub-elements 131A, 131B with different lengths. Again, the collective resonant mode properties of the plate are maintained even if the exterior shape is changed. The freed zones 113 can be used for example for electrical interconnections and / or vias of components.

[0093] Therefore, considering that a typical dicing process cuts a wafer containing multiple components into rectangular portions each containing a single component, hollow and / or non-rectangular resonator elements as illustrated in Figures 12 and 13 are beneficial because they can minimize the footprint of the resonator components. The areas not occupied by the resonator regions can be used for fixturing or internal or external connection purposes (these are just some of the possible applications). The embodiments of Figures 12 and 13 can also be combined to provide hollow and non-rectangular resonator elements.

[0094] The resonator elements of Figures 11 to 13 form a rectangular 19 x 11 fundamental mode array. Every array position in Figure 11 is occupied, but there are empty array positions in Figures 12 and 13.

[0095] Figure 14A shows an embodiment similar to Figure 12, but configured for lower frequencies (overtone 3). The air gap 148A in this embodiment is created by "removing" all the base elements in one subelement and using long connecting elements 147A at the longitudinal ends of the air gap 148A. Central fixation by fixing element 149A is provided.

[0096] FIG. 14B shows a further variation in which the long connecting element 147A of FIG. 14A is omitted, making the resonator effectively a two-element resonator, one element each of the type currently described. It is a simple geometry to fabricate, since, like the design of FIG. 14A, fixation to the surrounding substrate does not require structural contact to the backside or top wafer. For a collective mode to exist between the two elements of the resonator, the fixation must be such that the elements are not too weakly coupled to each other (otherwise imperfections in the fabrication process could result in two distinct peaks).

[0097] Figures 14C and 14D show an embodiment that combines the advantages of Figures 14A and 14B, providing both a central fixation and easy electrical access to the actuators, while overcoming the potential problem of weak coupling. In the configuration of Figure 14C, the left and right sides are coupled together using one long connecting element 147C, a support structure 148C that extends to the central fixation zone, and fixation elements 149C on opposite sides of the elements, so that one composite mode exists. The embodiment of Figure 14D is similar to that of Figure 14C, but here sufficient coupling is achieved and ensured by one complete base element, including partial element 141D, whose length is an integer fraction of the other partial element 141C.

[0098] The resonator elements of Figures 14A-14D form a rectangular 11 x 3 fundamental mode array, with three free array positions in Figures 14A-14C and two free array positions in Figure 14D (depending on the coupling strength, the embodiment of Figure 14B can also be considered as two 5 x 1 arrays).

[0099] Generally, in some embodiments, there are at least two different types of subelements, as in Figures 12, 13, and 14D, where the first type has a first length and the second type has a second length that is an integer fraction of the first length, in order to excite the different types of subelements with different overtone modes of the collective fundamental resonant mode.

[0100] In some cases, as in Figures 12 and 14D, at least one subelement of the second (short) type is placed between two subelements of the first (long) type, thereby leaving space for a central fixation. For example, in this case, the resonator element is suspended on the support structure from two subelements of the first type on either side of a subelement of the second type.

[0101] In some examples, such as the example of Fig. 12, the resonator element has a gap defined by two or more subelements of the second type and two subelements of the first type. The support structure is at least partially disposed in the gap, and the resonator element is suspended on the support structure within the gap. Thus, the resonator element is fixed in the center and surrounds the fixed location on the lateral sides.

[0102] In some embodiments, such as the embodiment shown in Fig. 14D, the resonator element has a recess (i.e. a lateral recess) defined by one or more subelements of the second type and two subelements of the first type, and the support structure is at least partially arranged to extend into this recess, and the resonator element is suspended on the support structure within this recess.

[0103] Both the air gap and the dimple configurations allow for a central fixation to be achieved, which can be used to minimize the losses of the resonator. The air gap configuration has the advantage that a perfectly symmetrical resonator can be achieved, whereas the dimple configuration allows easier electrical access to the resonator surface, which typically contains the piezoelectric driving layer. The dimple configuration allows for the through silicon vias in the wafer to be avoided entirely. In the air gap configuration, through silicon vias in the wafer can be placed in the area of ​​the air gap.

[0104] Figure 15A shows a graph of the admittance over a wide frequency range measured in a piezoelectrically coupled 2nd overtone mode resonator, which corresponds to the resonator in Figure 8A. The resonator is fabricated on a wafer with a Si / AlN / Mo material stack of 28 / 1 / 0.3 μm thicknesses, respectively. It can be deduced that the main mode at 42 MHz is excited exactly; there are only a few parasitic resonant modes (e.g. 18 MHz) that are much weaker coupled than the main mode.

[0105] Figure 15B shows a detailed plot of the admittance of the main resonance for the design of Figure 15A (labeled "11 beams") and for resonators similar to Figure 15A but with fewer coupled beam elements (labeled "7 beams" and "3 beams"). The resonator quality factor Q, shunt capacitance C0, and equivalent series resistance R1 (=ESR) obtained by fitting to the measured results are shown for all three cases. These figures show how the ESR decreases when the resonator width is increased in proportion to the number of coupled beam elements.

[0106] FIG. 15C shows the frequency vs. temperature curves measured for the resonator of FIG. 15A (labeled “Stacked LE Beam Overtone 2”) and the same characteristics for a composite WE-Lame mode resonator similar to the one described in WO 2018 / 002439. Both resonators have a 7×10 19 cm -3 The two resonators are fabricated on similar wafers with n-type doping of 1000 Å. It can be seen that the linear temperature coefficient TCF1 of the former resonator is about 4 units higher than the same parameter of the latter resonator. Thus, a higher overcompensation is obtained. This has the advantage that a temperature-compensated design can be achieved, for example, with a thicker AlN layer for piezoelectric actuation purposes.

[0107] Figure 16A shows a resonator element configuration with four branches made of short subelements joined side-to-side, with each branch nodal-mounted to a central support element. Each branch element is a 6x1 fundamental mode array resonator element with non-nodal internal couplings between the subelements.

[0108] In one variation of Figure 16A (details not shown), the central element may be a resonating subelement and the junctions of the branches to the central subelement may be non-nodal to ensure collective resonance between the branches, thus forming a 13x2 fundamental mode array.

[0109] FIG. 16B shows a top view of a longitudinally coupled resonator plate with three rows of eleven fundamental mode subelements. Each row is coupled to the other rows at both ends with flexible longitudinal connecting elements. Each row is internally coupled with rigid connecting elements as previously described. An 11×3 fundamental element array is formed.

[0110] Figures 17A to 17E show various possible flexible connection element shapes between longitudinally joined sub-elements. A side-connectable "C" shape, also used in the configuration of Figure 16B, is shown in Figure 17A. End-connectable shapes are shown in Figures 17B to 17E. These show an end-connectable C shape in Figure 17B, an S shape in Figures 17C and 17D, and an angled I shape in Figure 17E. It will be understood that other flexible shapes and variations than those shown are possible.

[0111] Figures 18A to 18C show schematic examples of different longitudinal coupling options at the resonator plate level. As shown, the longitudinal couplings can be arranged in any configuration, preferably symmetrical, directly between the longitudinal elements, for example using the elements of Figures 17B to 17E (connecting elements not shown in detail in Figures 18A to 18C).

[0112] Instead of or in addition to connecting subelements in the same row end-to-end, as shown in the previous example, subelements in different rows can be connected using long elements that extend widthwise across row boundaries (not shown).

[0113] 19A through 19D each show further examples of flexible connecting elements having at least one T-shaped branch. [Prior art documents] [Patent documents]

[0114] [Patent Document 1] International Application Publication No. 2012 / 110708 [Patent Document 2] International Application Publication No. 2018 / 002439 [Non-patent literature]

[0115] [Non-Patent Document 1] Ho et al, "HIGH-ORDER COMPOSITE BULK ACOUSTIC RESONATORS", MEMS 2007, Kobe, Japan, 21-25 January 2007 [Non-Patent Document 2] Kuypers J., "High Frequency Oscillators for Mobile Devices", in H. Bhugra, G. Piazza (eds.), Piezoelectric MEMS Resonators, Microsystems and Nanosystems, DOI 10.1007 / 978-3-319-28688-4_15, pp 335-385 [Non-Patent Document 3] A. Jaakkola, et al, "Experimental study of the effects of size variations on piezoelectrically transduced MEMS resonators", Proc. IEEE International Frequency Control Symposium, 2010, pp. 410-414, http: / / dx.doi.org / 10.1109 / FREQ.2010.5556299

Claims

1. 1. A microelectromechanical resonator assembly comprising: a first rectangular resonator array; a second rectangular resonator array; Equipped with the first rectangular resonator array and the second rectangular resonator array each have at least two rectangular resonator subelements; the at least two rectangular resonator subelements are coupled to each other by a plurality of connecting elements; the first rectangular resonator array and the second rectangular resonator array are coupled to each other by one or more connecting elements; the rectangular resonator subelements resonate in an in-plane length extension resonance mode; Resonator assembly.

2. The resonator assembly according to claim 1 , wherein the first rectangular resonator array and the second rectangular resonator array are coupled to each other in a short side direction or a long side direction thereof.

3. The resonator assembly of claim 1 , wherein the at least two rectangular resonator subelements are coupled to each other along their short or long sides.

4. The resonator assembly of claim 1 , wherein at least two of the rectangular resonator sub-elements are coupled to each other in their short or long directions.

5. The resonator assembly of claim 1 , wherein the at least two rectangular resonator subelements are longitudinally or transversely coupled to each other by a plurality of connecting elements.

6. a trench extending in a longitudinal direction of the first rectangular resonator array or the second rectangular resonator array or the rectangular resonator subelements; the one or more connection elements include at least two rigid connection elements across the elongated trench; The resonator assembly of claim 1 .

7. The resonator assembly of claim 1 , wherein the first rectangular resonator array and the second rectangular resonator array are coupled to each other by a flexible connecting element that spans a gap therebetween.

8. The resonator assembly of claim 1 , wherein the connecting element is a flexible connecting element that spans a gap between the first rectangular resonator array and the second rectangular resonator array or a gap between the rectangular resonator subelements.

9. The resonator assembly of claim 1 , wherein the connecting elements are straight, curved, or right-angled.

10. The resonator assembly of claim 1 , wherein the connecting element is T-shaped or serpentine-shaped.

11. 10. The resonator assembly of claim 1, comprising a thin film piezoelectric actuator.

12. The resonator assembly of claim 1 , wherein each of the rectangular resonator subelements is coupled to other of the rectangular resonator subelements by a plurality of connecting elements coupled to non-nodal points of a collective resonant mode.

13. The resonator assembly of claim 1 , wherein the aspect ratio of the rectangular resonator subelements is in the range of 2:1 to 10:

1.

14. The resonator assembly of claim 1, wherein the first rectangular resonator array and the second rectangular resonator array are fixed to a central support element.

15. 10. The resonator assembly of claim 1, comprising a silicon crystalline body having a [100] crystallographic direction aligned with a longitudinal direction of the rectangular resonator subelement or aligned less than 15 degrees from the longitudinal direction.

16. 2. The resonator assembly of claim 1, wherein the first rectangular resonator array and the second rectangular resonator array are separated by the plurality of connecting elements and spaced apart from each other in their short and / or long directions.

17. The resonator assembly according to claim 1 , wherein the at least two rectangular resonator sub-elements are separated from each other by the plurality of connecting elements and are spaced apart from each other in their short and / or long directions.

18. The resonator assembly of claim 1 , wherein the first rectangular resonator array and the second rectangular resonator array are oriented parallel in a common plane.

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