Coupled MEMS Resonators

Abstract

The present invention relates to a micro-electromechanical resonator, which comprises a support structure, a resonator element suspended from the support structure, and an actuator for exciting the resonator element to a resonant mode. According to the present invention, the resonator element comprises a plurality of adjacent sub-elements, each sub-element having a length and a width and an aspect ratio higher than 1, and each sub-element is adapted to resonate in a length extension resonant mode, a torsional resonant mode or a bending resonant mode. In addition, each of the sub-elements is coupled to at least one other sub-element by one or more connecting elements for exciting the resonator element to a collective resonant mode, the one or more connecting elements being coupled to non-nodes of the above-mentioned resonant modes of the sub-element.

Description

Technical Field

[0001] The present invention relates to microelectromechanical (MEMS) resonators. In particular, the present invention relates to length extensional mode, torsional mode or bending mode resonators. Background Art

[0002] Electromechanical resistance, also known as equivalent series resistance (ESR), is an important performance parameter of a resonator. Compared to conventional quartz crystals, especially in piezoelectrically actuated beam resonators such as length-extended (LE) resonators, the ESR tends to be high because the fundamental LE mode can only exist in beam resonators with an aspect ratio of length to width greater than 1, i.e., in a beam with a length greater than the width of the beam, and the Nth overtone LE mode can exist in beam resonators with an aspect ratio of length to width greater than N. Since the ESR of the LE mode decreases as the beam width increases, wider beams are preferred to obtain lower ESR. However, the combination of the presence of LE modes and the aspect ratio sets a lower limit on the ESR.

[0003] An additional task in the design of MEMS resonators is to make the frequency of the resonator insensitive to temperature changes, i.e. temperature compensation. Typically, beam resonators made from single crystal silicon can be temperature compensated by doping the silicon crystal sufficiently strongly, by properly shaping and aligning the beam with respect to the crystal orientation of the underlying silicon crystal, and by properly selecting its resonant mode. Temperature compensation by doping is discussed more extensively in, for example, WO 2012 / 110708 A1.

[0004] The beam may oscillate, for example, in a length extension (LE) resonant mode, where the motion occurs primarily in the length direction of the beam. The LE mode has the desirable property of having a zero or positive first-order temperature coefficient of frequency (TCF) when the resonator beam is directed along the

[100] crystal direction and when doped with a sufficiently high doping concentration of n-type dopants. The positive TCF of silicon allows the use of other materials with negative TCF, which may be required, for example, for piezoelectric actuation purposes, and thus the overall TCF of the composite LE mode resonator can become zero.

[0005] Instead of LE modes, beam resonators can be excited into bending or torsional modes. However, these modes face similar problems related to ESR and temperature compensation.

[0006] Special challenges are faced when it is desired to have both low ESR and low temperature dependence. Some piezoelectrically actuated resonators with an aspect ratio of length to width of less than 1 (i.e., with a relatively wide beam) can support a resonant mode with a relatively low ESR level comparable to a quartz crystal at the same frequency. For example, Ho et al., "HIGH-ORDER COMPOSITE BULK ACOUSTIC RESONATORS" MEMS 2007, Kobe, Japan, January 21-25, 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 can be achieved when the beam is aligned with the

[110] direction of the underlying silicon crystal. However, these resonant modes have a higher temperature dependence than, for example, the LE modes and are therefore less useful in piezoelectrically actuated resonators.

[0007] Additional challenges associated with MEMS resonator design include keeping the quality factor of the resonator as high as possible, and keeping the footprint of the resonator as small as possible in order to save manufacturing costs.

[0008] There is therefore a need for an improved resonator which has the advantageous properties of the beam and still has a low ESR, in particular there is a need for a resonator which can additionally be temperature compensated. Summary of the invention

[0009] The object of the present invention is to overcome the above mentioned problems. A particular object is to provide a beam resonator whose electromechanical resistance can be kept low.

[0010] An additional object is to achieve a resonator with a low dependence of the frequency on temperature.

[0011] Further objects include providing a low ESR resonator with a high quality factor (Q value) and / or a small footprint.

[0012] The invention is based on coupling multiple beamformed sub-elements to each other using one or more connecting elements coupled to their non-nodes, allowing them to resonate in a collective mode. Thus, the entire resonator can be excited as a single resonator, but due to the division into sub-elements, the shape and orientation constraints of the entire resonator are alleviated.

[0013] The invention is particularly characterized by what is stated in the independent claims.

[0014] According to one aspect, a microelectromechanical resonator is provided, the microelectromechanical resonator comprising a support structure, a resonator element suspended from the support structure, and an actuator for exciting the resonator element into a resonant mode. The resonator element comprises a plurality of adjacent subelements, each subelement having a length and a width and an aspect ratio greater than 1 (i.e., being a beam element). The subelements are adapted to resonate in a length extension resonant mode, a torsional resonant mode, or a bending resonant mode, resonating in overtones of the same, or two or more different resonant modes. In addition, each of the subelements is coupled to at least one other subelement via one or more connecting elements for exciting the resonator element into a collective resonant mode, the one or more connecting elements being coupled to non-nodes of the resonant modes of the subelement.

[0015] The present invention provides significant benefits. Firstly, by forming a resonator element from coupled sub-elements that are capable of resonating in one of the specified modes, the area, in particular the width, of the resonator element can be increased for reducing the ESR while maintaining the benefits of these modes. It has been found that coupling the sub-elements in this manner is strong enough that all of the sub-elements resonate in a collective resonant mode. Thus, frequency splitting and the occurrence of multiple resonant modes is avoided.

[0016] Importantly, the invention is compatible with doping-based (intrinsic) temperature compensation. This means that by properly aligning the resonator elements on a silicon wafer with respect to its crystal direction, the temperature dependence of the resonator frequency, ie the absolute value of the TCF, can be reduced.

[0017] The above advantages are particularly important in the case of piezoelectric actuation, which generally requires a reduced ESR. Furthermore, the piezoelectric actuator material layer disposed by the silicon body of the resonator element has an influence on the TCF, whereby an "overcompensation" of the TCF of the silicon body is beneficial.

[0018] Other advantages of the present invention include the ability to modify the resonator envelope geometry to allow for different anchoring schemes (particularly central anchoring for loss minimization) and / or electrical interconnection schemes (particularly for minimizing the area of ​​the resonator assembly). These schemes will be discussed in detail below.

[0019] The invention thus overcomes the limitations of the prior art in a practical way and allows the realization of new types of resonators.

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

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

[0022] In a typical embodiment, the sub-elements have a rectangular shape, independently of the shape of the entire element, and are arranged at a distance from each other in the width direction and / or in the length direction of the sub-elements separated by the connecting element.

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

[0024] In some embodiments, at least two of the subelements are coupled to each other in the width direction thereof, whereby the connecting element comprises at least two substantially rigid connecting elements adjoining elongated grooves, the elongated grooves remaining between the subelements and extending in the length direction of the subelements. In some embodiments, a plurality of grooves are provided, the plurality of grooves being defined in the length direction by the connecting element between at least some of the subelements, the number of grooves corresponding to the order of an overtone mode, the subelements being adapted to resonate in the overtone mode.

[0025] When the element as a whole has a low aspect ratio, the grooves in the resonator element allow the element to shrink and expand in the transverse direction in addition to shrinking and expanding in the longitudinal direction. If the aspect ratio is too low, a sub-element such as this cannot support, for example, an LE mode, but in the present manner, the entire element can support a collective LE mode. This is because the connecting elements ensure that the resonator element behaves like a single element, i.e., like a beam with a low effective aspect ratio, which in turn reduces the ESR of the resonator.

[0026] In some embodiments, at least two of the sub-elements are coupled to each other in their length direction, whereby the connecting element comprises at least one flexible connecting element spanning the gap between the sub-elements. The flexible connecting element may, for example, have a C-shape, an S-shape, a T-shape, an inclined I-shape or a meander shape.

[0027] In some embodiments, each sub-element is adapted to resonate in a length-extensional resonant mode.Alternatively, the resonant mode may be torsional or bending, such as an in-plane bending resonant mode.

[0028] In some embodiments, each sub-element is adapted to resonate in an in-plane length-extension resonant mode.

[0029] In a typical embodiment, the connecting element is a passive element formed by a single silicon crystal body, preferably doped silicon crystal body, and the sub-elements. This means that the connecting element does not act as an actuator as in some known array resonators, but rather acts as a passive coupler that ensures that the sub-elements share the same frequency and fundamental mode shape and therefore contribute to the collective mode.

[0030] In some embodiments, the actuator is a piezoelectric thin film actuator arranged on top of the resonator element, preferably distributed on top of all sub-elements in the resonator element.

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

[0032] In some embodiments, at least some of the subelements are formed from one or more base elements having an aspect ratio of length to width higher than 1 and adjoining each other along a length dimension perpendicular to the width dimension, whereby each of the base elements supports a basic resonant mode, the base elements together defining a collective resonant mode of the subelements and also defining a collective resonant mode of the entire resonator element. The base elements are arranged in a rectangular array configuration, wherein each base element occupies a single array position. In some embodiments, at least one array position of the array configuration is free of a base element. In an alternative embodiment, each array position is occupied by exactly one base element.

[0033] Thus, the resonant basic elements together define a collective resonant mode in each subelement, and the coupling of the subelements ensures a collective resonant mode of the entire resonator element. Due to the array configuration, the collective resonance is not destroyed by removing one or more portions corresponding to one or more adjacent basic elements, respectively. Thus, the desired properties of the resonator are maintained while new design possibilities are available.

[0034] In some embodiments, the resonator element comprises a doped silicon crystal body whose

[100] crystal direction is oriented along the length direction of the resonator element or deviates from the length direction of the resonator element by less than 25 degrees, in particular less than 15 degrees. This allows temperature compensation of the element and low ESR by widening the resonator element. In some embodiments, the silicon body is doped to at least 2*10 19 cm -3 , such as at least 10 20 cm -3 The average impurity concentration.

[0035] In some embodiments, each of the sub-elements has an aspect ratio of N or more, where N is the order of the resonant mode of the sub-element.

[0036] In some embodiments, the entire resonator element has an effective aspect ratio of less than 2, in particular less than 1.

[0037] In some embodiments, all subelements in a resonator element have approximately the same width. Further, in some embodiments, all subelements in a resonator element have approximately the same length. On the other hand, in some embodiments, at least some of the subelements have different lengths and are adapted to resonate in different but mutually collective overtone resonance modes. Thus, the subelements support different collective overtones of a single fundamental mode. As described later, this allows the encapsulation geometry of the resonator to be shaped for various purposes.

[0038] In some embodiments, the resonator element comprises a plurality of adjacent sub-elements adapted to support at least a third overtone mode, such as at least a fifth overtone mode, of the fundamental mode. In this way, high frequencies as well as low ESR can be achieved.

[0039] In some embodiments, the resonator element is suspended from a support structure from nodes of a resonant mode of a sub-element on opposite sides of the resonator element in the direction of its width. Alternatively or in addition, the resonator element may be suspended from a support structure from a node between two sub-elements, preferably symmetrically in both the width and length directions of the resonator element. The two sub-elements are not necessarily adjacent elements, and typically are not adjacent elements, but are separated by a distance that is equivalent to (and the amount to) one or more of the sub-element (and intervening groove) widths.

[0040] Next, embodiments of the present invention and their advantages are discussed in more detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1-5 A top view of a fully occupied resonator array configuration formed by elementary elements is shown.

[0042] Figure 6 A top view of a resonator element suspended to a support structure is shown.

[0043] Fig. 7A , 7B 7C show a single beam resonator, a beam extending in the width direction in a conventional manner, and a resonator element according to the present invention, respectively.

[0044] Fig. 8A Shown is a top view of a resonator configuration designed for the second-order LE mode.

[0045] Figure 8B Shows Fig. 8A Mode shape diagram of a portion of a resonator element.

[0046] Fig. 9A Shown is a top view of a resonator configuration designed for the fundamental (first-order) LE mode.

[0047] Fig. 9B Shows Fig. 9A Mode shape diagram of a portion of a resonator element.

[0048] Fig.10 Plots of modal frequency as a function of beam aspect ratio (width to length) are shown for a number of modal orders.

[0049] Fig.11 A top view of an exemplary higher-order (ninth overtone) mode resonator element configuration is shown.

[0050] Fig.12 Shows Fig.11 Top view of a configuration with a gap and central anchoring variant.

[0051] Fig.13 Shows Fig.11 Non-rectangular variants of the configuration.

[0052] Fig.14A -D shows another example of a centrally anchored gapped, split and non-rectangular resonator element.

[0053] Fig.15A Shows Fig. 8AMeasured wide-frequency range admittance graph of the second overtone mode resonator of a piezoelectrically coupled resonator.

[0054] Fig. 15B Shows Fig.15A Detail of the admittance plot of the main resonance.

[0055] Fig. 15C Shows Fig. 8A Measured frequency-versus-temperature curve of a resonator.

[0056] Fig.16A A top view of a multi-branch width-coupled resonator plate is shown.

[0057] Fig. 16B A top view of the longitudinally coupled resonator plates is shown.

[0058] Fig.17A -E shows different possible flexible connection element geometries between longitudinally coupled sub-elements.

[0059] Fig.18A -C shows examples of different longitudinal coupling positions.

[0060] Fig.19A -D shows a further example of a flexible connection element for longitudinal coupling. DETAILED DESCRIPTION

[0061] definition

[0062] A "nodal point" as used herein means a point on an oscillation mode shape having an average oscillation amplitude that is less than 20% of the maximum amplitude of the oscillation mode shape.

[0063] A "non-node" (or a "point displaced from a node") is a point on an oscillation mode shape that has an average oscillation amplitude that is 20% or more of the maximum amplitude of the oscillation mode shape.

[0064] The terms "length" and "longitudinal" are used herein to refer to an in-plane direction that is parallel to the main extension direction LE mode, the torsion axis of the torsion mode, or perpendicular to the axis of the main bending displacement of the bending mode. "Width" and "transverse" refer to in-plane directions orthogonal to this direction.

[0065] Aspect ratio refers to the ratio of the in-plane dimensions of an element or sub-element. "Effective aspect ratio" refers to the aspect ratio of the entire resonator element including multiple sub-elements, as opposed to the aspect ratio(s) of its individual sub-element (beams).

[0066] A "trench" refers to an empty space inside a resonator element that allows adjacent subelements to move relative to each other and thus allow a desired mode to occur in the subelements. 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 adapted to support.

[0067] A "connecting element" is any member that mechanically connects two sub-elements that are located at a distance from each other. The connecting element may couple the sub-elements in the width direction, whereby it is confined to a groove, or alternatively a gap or recess, within the resonator element at the longitudinal ends of the resonator element. In this case, the element is typically a substantially rigid element. Alternatively, it may couple the sub-elements in the length direction, whereby it is typically a flexible element, such as a C-shaped 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, which is generated by patterning the outer shape of the resonator element and the grooves therein using known MEMS micromachining methods.

[0068] "Fundamental (resonant) mode" refers to the first-order resonant mode (also called the "first overtone"). Higher overtone modes are formed from several fundamental modes.

[0069] A "primary element" is a rectangular in-plane portion of a resonator that carries the fundamental resonant mode. The primitives may be seamlessly connected in an end-to-end configuration in the longitudinal direction (i.e., "virtual" elements of the beam defined by the mode shapes excited therein), or separated by gaps and connected by flexible connecting elements. Higher overtone modes of order N may be viewed as fundamental modes occurring in N primitives coupled end-to-end in the longitudinal direction.

[0070] A "collective resonant mode" refers to a composite resonant mode in which all elementary elements of a particular entity of interest resonate in the same fundamental resonant mode and have approximately the same frequency and the same or 180 degrees shifted phase. In the collective resonant mode of the entire resonator element, each subelement forming the resonator element carries a first-order length extension, torsional or bending resonant mode or its higher overtones. In this case, the resonator element can be divided into elementary elements of generally equal size, each elementary element supporting the same fundamental mode.

[0071] In a typical embodiment, all primitives of the resonator are arranged in a rectangular array configuration. An "occupied" array position contains a primitive. An "unoccupied" array position has no resonant material.

[0072] A "gapped" resonator element shape means a shape in which at least one array position within the resonator element is unoccupied. The gaps may serve as anchoring and / or electrical contact areas. In this context, desired resonant mode-enabling gaps (grooves) between subelements are not considered gaps.

[0073] A rectangular resonator element is one in which all of its peripheral primitive element array positions are occupied. A non-rectangular element has at least one peripheral array position unoccupied.

[0074] When focusing on the length of a subelement, "integer fraction" means a fraction N / M, where N and M are both positive integers and N < M. For example, the third overtone subelement in an embodiment of the present invention is shorter than the fifth overtone subelement by an integer fraction 3 / 5.

[0075] Length-extended (LE) bulk acoustic wave modes of various orders in beam elements are known in the art. In such modes, the element (sub-element) contracts and expands primarily along a single axis, with one or more nodes on that axis. In symmetrical elements, and in the typical case where both longitudinal ends of the element are free (not anchored to a support structure), the nodes are symmetrically located along the length of the element. Similarly, torsional and in-plane and out-of-plane bending modes are known in the art.

[0076] A "temperature compensated" element in this context means that the elastic properties of the element, which are related to the mechanical movement of the element, are adapted, at the present doping level, to have a smaller dependence on temperature in at least some temperature ranges than would be the case without such doping. In general, temperature compensation is the result of the selection of material properties, geometrical properties, crystal orientation-related properties and vibration modes. The doping concentration may be 2*10 19 cm -3 or larger, such as 10 20 cm -3 or greater. The dopant may be an n-type or p-type dopant, such as phosphorus or boron. Temperature compensation in this context also encompasses so-called "overcompensation", i.e., making the TCF of the element such a positive value that when the piezoelectric transducer layer and / or some other layer is coupled to the element, the overall TCF of the resonator is smaller than in the absence of doping.

[0077] Description of Selected Embodiments

[0078] In general, the resonator elements discussed herein may include a plurality of subelements having an aspect ratio greater than 1, in particular greater than N, where N is the number of overtones of the collective mode excited therein (ie, the modal order).

[0079] The number of sub-elements in the resonator element may be two or more, such as 2-50, in the width direction of the resonator element, and may be one or more, typically 1-8, such as 2-8, in the length direction.

[0080] The number of elementary elements in the length direction corresponding to the number of mode orders excited in the sub-element may be, for example, 1-20, such as 2-12.

[0081] To achieve low ESR, the aspect ratio of the effective length to width of the resonator element is typically less than 2. In some embodiments, the aspect ratio is less than 1.

[0082] More detailed embodiments of the present invention are described below mainly with reference to the length extension mode, for which experimental data are also provided to illustrate the feasibility and benefits of the present invention, but the same principles can also be applied to the torsion and bending modes.

[0083] In some of its embodiments, the present invention provides a length extension mode resonator, which includes a support structure, and a silicon resonator element suspended to the support structure at its nodes, the resonator element having a length and a width. The resonator element also includes at least two sub-elements partially separated from each other by an intermediate region, each of the intermediate regions including at least one elongated groove and at least two connecting elements, the at least two connecting elements adjoining the grooves and mechanically coupling the sub-elements to each other at their non-nodes. This ensures a strong coupling of the sub-elements and, therefore, the behavior of the entire element as a single element with a well-defined resonant mode and resonant frequency. The actuator is suitable for exciting the resonator element to a length extension resonant mode, the length extension resonant mode being parallel to the longitudinal direction of at least one elongated groove.

[0084] In some embodiments, the resonator element comprises a body of doped silicon. Furthermore, the

[100] crystal direction of the silicon body can be oriented along the length extension direction of the resonator element or deviate from the length extension direction of the resonator element by less than 25 degrees, in particular less than 15 degrees. 19 cm -3 , such as at least 10 20 cm -3 Together with the average impurity concentration, this allows the resonator to be temperature compensated while achieving low ESR.

[0085] In some embodiments, the resonator element is divided into three or more sub-elements side by side along its width. In this way, the ESR of the resonator can be kept low while maintaining the ability to support LE mode and the possibility for efficient temperature compensation.

[0086] In some embodiments, there are at least two grooves and three connecting elements in at least one intermediate region, preferably in all intermediate regions. This can be used to make resonator elements dedicated to specific high-order LE overtones, for example.

[0087] The aspect ratio of the subelements is typically chosen to be in the range 2:1 ... 10:1 to keep the number of subelements relatively low and the relative area occupied by the trenches low, and to obtain the maximum benefit of the invention. However, the invention is also applicable to higher aspect ratio subelements.

[0088] Figure 1 A resonator element supporting oscillation in the first and higher order LE modes (overtones) is shown. The element comprises three sub-elements 11A, 11B, 11C, which are placed side by side in the width direction. Adjacent sub-elements 11A / 11B, 11B / 11C are coupled to each other by two connecting elements 12AB / 14AB, 12BC / 14BC, which are located between the sub-elements at or near the longitudinal ends of the sub-elements. Between the connecting elements 12AB / 14AB, 12BC, 14BC, there are grooves 13AB, 13BC, which allow the sub-elements 11A, 11B, 11C to expand in the width direction during LE mode oscillation. The linear sequence of connecting elements 12AB, 14AB and grooves 13AB defines a first intermediate region, and the sequence of connecting elements 12BC, 14BC and grooves 13BC defines a second intermediate region.

[0089] If Figure 1 With each sub-element of driven to the first-order mode, ie the fundamental mode, the resonator elements form a fully occupied, rectangular 3×1 fundamental mode array.

[0090] It should be noted that the connecting elements 12AB / 14AB, 12BC / 14BC are not located at the nodes of the LE oscillation mode, but at non-nodes, which are at or near the oscillation ends of the sub-elements, which makes the entire element a group of strongly coupled resonators that can resonate in a collective LE mode.

[0091] The element is suspended from the midpoint of the longitudinal outer edges of the element using anchors 19A, 19B. The number of anchors may be greater than two. In a typical configuration, the anchors are located at or symmetrically relative to the transverse median axis of the element.

[0092] Figure 2An embodiment suitable for second order LE mode oscillation is shown. There are three connecting elements 22AB / 24AB / 26AB, 22BC / 24BC / 26BC and two grooves 23AB / 25AB, 23BC / 25BC between each sub-element 21A, 21B, 21C. This configuration allows the sub-element to expand in the width direction with the second LE mode, as well as other even higher order modes. Figure 2 The resonator elements form a rectangular 3×2 fundamental mode array.

[0093] Each subelement has a width W and a length L, which may be the same but not necessarily the same between different elements. It should also be noted that the connecting elements are not necessarily located at the same position between each pair of subelements, and / or the subelements and / or the grooves are not necessarily perfectly rectangular, but some or all of them may have a shape such as a tapering. These variations allow, for example, the TCF of the resonator element to be adjusted, since the aspect ratio of each individual beam affects the TCF of each individual beam and thus the TCF of the entire resonator element. In addition, adjusting the size and shape of the beams and the position, size and number of the connecting elements may provide additional degrees of freedom, which may be used to set the frequency of the parasitic mode to an optimal frequency, where the deleterious effects of the parasitic mode may be minimized.

[0094] Figure 3 An example is shown where there are four sub-elements 31A-D separated by a non-similar middle region. Between each two lateral sub-elements 31A / 31B, 31C / 31D, there are two grooves 33AB / 35AB, 33CD / 35CD and three connecting elements 32AB / 34AB / 36AB, 32CD / 34CD / 36CD, while between the middlemost sub-elements 31B / 31C, there is a single groove 33BC and two connecting elements 32BC / 34BC. Other configurations are also possible. Figure 3 The resonator elements form a (modified) rectangular 4×2 fundamental mode array.

[0095] Figure 4 An embodiment is shown in which three sub-elements 41A, 41B, 41C are interleaved with intermediate regions 48AB, 48BC each having four connecting elements and three grooves symmetrically positioned along the length of the sub-elements. Figure 4 The resonator elements form a rectangular 3×3 fundamental mode array.

[0096] Figure 5 A variation is shown, which has a Figure 2 The intermediate region 58AB-DE of the type in question separates five sub-elements 51A-E. In this example, the total width W of the elementt Greater than the length of the element, the length of the element is equal to the length L of the subelement. Figure 5 The resonator elements form a rectangular 5×2 fundamental mode array.

[0097] In a typical implementation, at least one trench between each pair of subelements is centered at a node of the LE mode.

[0098] For an element to be able to support LE mode, the total length of the groove(s) at each intermediate region between sub-elements should be a significant portion of the element's total length L. In some embodiments, this portion is 50% or more, such as 75% or more. In some embodiments, this portion is 90% or more.

[0099] In a typical configuration, the trench width is 10 μm or less, and is preferably as narrow as possible depending on the fabrication method used, thereby minimizing the area of ​​the trench.

[0100] In some embodiments, the grooves and connecting elements are dimensioned and positioned so as to avoid frequency splitting and the occurrence of multiple simultaneous resonant modes. Herein, the principles of A. Jaakkola et al., "Experimental study of the effects of size variations on piezoelectrically transduced MEMS resonators", http: / / dx.doi.org / 10.1109 / FREQ.2010.5556299, Proc. IEEE International Frequency Control Symposium, 2010, pp. 410-414, may be followed.

[0101] In some examples, the resonant mode is a fundamental mode and the aspect ratio is 2-4. For example, it can be 2.6-3.4. In some examples, the resonant mode is a second-order mode or higher and the aspect ratio is 3-10. For a second-order mode, the aspect ratio can be, for example, 4.0-8.0.

[0102] Figure 6 A suspended resonator element is shown. The support structure 60 is separated from the resonator element 61 by a gap at all locations except for the anchor points 69 at the nodes on the outer longitudinal sides of the lateralmost sub-element. As described above, this allows the resonator element 61 to oscillate freely in the LE mode.

[0103] In each of the embodiments discussed above, at least one connecting element, and typically more than one connecting element, of each subelement is located at a non-node of a resonant mode in which the element is adapted to resonate. This ensures that the subelements are coupled and oscillate in tandem.

[0104] at last, Figures 7A-7C The difference of the present resonator relative to the conventional resonator is shown. Fig. 7A A single high aspect ratio beam with two free ends is shown. Figure 7B A beam extending in the width direction is shown, effectively making it a rectangular plate. Such a resonator has a low ESR and can be used in the

[110] orientation, but cannot operate in the LE mode when aligned in the

[100] crystal direction and therefore cannot be temperature compensated therein. Figure 7C A resonator element according to one embodiment of the invention is shown. This scheme works even if the sides of the element are aligned in the

[100] crystal direction and has the same Figure 7B The same low ESR of the board.

[0105] Fig. 8A A resonator capable of supporting a second LE overtone resonance mode is shown. The resonator element of the resonator is formed by a plurality (here 11) of sub-elements, each of which is separated from an adjacent sub-element by two elongated grooves and connected to an adjacent sub-element by three connecting elements, the two elongated grooves being arranged one after another. When the size of the resonator plate shown is 326 μm×180 μm, the resonance frequency is close to 40 MHz. Fig. 8A The resonator elements form a rectangular 11×2 fundamental mode array.

[0106] Figure 8B The simulation using FEM software shows Fig. 8A Figure 1. LE mode resonance vibration mode shapes of the geometry of the 1000 MHz quartz crystal. Due to symmetry, only half of the entire resonator is shown. The grey shading indicates the total displacement at each position. As can be seen, each subelement resonates in the same collective mode. In the second order (and other even-order resonances), the vibration mode shapes are asymmetric, but one end of the subelement contracts while the other expands.

[0107] Fig.9A Another resonator capable of supporting the fundamental LE resonance mode is shown. When the size of the resonator plate is 300 μm×180 μm, the resonance frequency is close to 20 MHz. Fig. 8A The resonator elements form a rectangular 5×1 fundamental mode array.

[0108] Fig. 9B The simulation using FEM software shows Fig. 9AThe geometry of the southeast, symmetrical quarter LE mode resonant vibration shape.

[0109] Fig.10 A graph of the modal frequencies of a beam (here corresponding to a subelement) is shown, with an aspect ratio between close to zero (very thin beam) and 1. The dashed lines indicate the fundamental LE mode (LE1) and the overtone modes LE2 ... LE4. Along the LEx modal branch, the LEx modes in the direction defined by the parameter L exist only in the dashed region.

[0110] Fig.11 An example of a high (ninth) overtone length extended resonator element is shown, comprising a plurality of (19) subelements 111A stacked in the width direction and anchored from nodes at opposite longitudinal sides thereof with anchor elements 119. For example, to form a resonator oscillating at approximately 120 MHz, the dimensions of the element may be set to 225 μm x 170 μm.

[0111] Fig.12 Shown in other aspects Fig.11 A similar configuration, but now the anchoring has been accomplished by using an anchoring element 129 at the center of the resonator by providing a gap 118 in the resonator element, i.e. "removing" some of the central elementary elements of the sub-elements (in this case 5×3 elementary elements). The resulting structure thus comprises two types of sub-elements 121A, 121B with different lengths. The length of the shorter sub-element 121B is an integer fraction of the length of the longer element 121A. It has been shown that the collective resonant mode properties of the plate are maintained even though the encapsulation geometry has been modified.

[0112] In general, the present resonator design allows for the removal of desired basic elements (preferably symmetrically) without losing the desired (collective) mode properties of the composite resonator. This has the advantage that the LE resonant mode properties are maintained even in the presence of a gap in the center. Central anchoring is beneficial in its own right from the point of view of minimizing packaging stresses that may affect the resonator elements. Central anchoring is also beneficial from the point of view of low acoustic losses, thereby increasing the Q value of the resonator. Due to the high degree of symmetry of the structure allowed by the present invention, losses are reduced.

[0113] Fig.13 An example of a non-rectangular geometry is shown, where at the corners of the resonator plate, the basic elements are omitted. Again, in this case, the resulting structure comprises two types of sub-elements 131A, 131B with different lengths. In this case, the collective resonant mode properties of the plate are maintained even though the encapsulation geometry has been modified. The free areas 113 can be used, for example, for electrical interconnections and / or vias of the components.

[0114] Therefore, if Fig.12 and 13 The illustrated interstitial and / or non-rectangular resonator elements are beneficial because the area occupied by the resonator components can be minimized, considering that in a common dicing process, a wafer containing multiple components is cut into rectangular sections, each containing a single component. The area freed up from the resonator area can be used for anchoring or internal or external connection purposes, just to mention some potential needs. Fig.12 and Fig.13 The embodiments may also be combined to provide gapped, non-rectangular resonator elements.

[0115] Figure 11-13 The resonator elements form a rectangular 19×11 fundamental mode array. Fig.11 The array position is already fully occupied, but in Fig.12 and 13 are stored in unoccupied array locations.

[0116] Fig.14A Shows something like Fig.12 , but now adapted to smaller frequencies (overtone 3). The gap 148A here is created by "removing" all the basic elements of one subelement and using longer connecting elements 147A at the longitudinal ends of the gap 148A. Central anchoring using anchoring elements 149A is achieved.

[0117] Fig. 14B Another variation is shown, in which Fig.14A The longer coupling element 147A is omitted so that the resonator is actually a two-element resonator, each single element being of the type currently discussed. This is a simple geometry to process since anchoring to the surrounding substrate does not require Fig.14A The design is the same as the structural contact to the back or top wafer. In order for the collective mode to exist between the two elements of the resonator, the anchoring needs to be achieved so that the two elements are not too weakly coupled to each other (which could produce two different peaks due to manufacturing defects).

[0118] Fig. 14C and 14D Another embodiment is shown, which combines Fig.14A and 14B The advantages of and provide central anchoring, easy electrical connection to the actuator and overcome potential problems with weak coupling. Fig. 14C The configuration couples the left and right sides so that there is a composite pattern that extends to the central anchoring region by using a longer connecting element 147C, and supporting structure 148C and anchoring elements 149C on opposite sides of the element. Fig.14D Examples and Fig. 14C The embodiment of is similar, but here, sufficient coupling is achieved and ensured by a complete basic element including a subelement 141D, which has an integer fraction length of another subelement 141C.

[0119] Fig.14A -D resonator elements form a rectangular array of 11 × 3 fundamental modes, in Fig.14A -C has 3 unoccupied array positions, and Fig.14D There are 2 unoccupied array positions in the . (Depending on the coupling strength, Fig. 14B The embodiment can also be viewed as two 5×1 arrays).

[0120] Generally speaking, in some embodiments, Fig.12 , 13 As shown in FIG. 14D , there are at least two different types of sub-elements, a first type having a first length, and a second type having a second length, wherein the second length is equivalent to an integer fraction of the length of the first type, so as to excite different types of sub-elements to different overtone modes of the collective fundamental resonant mode.

[0121] In some examples, like Fig.12 and 14D In those examples, at least one subelement of the second (shorter) type is located between two subelements of the first (longer) type. This leaves room, for example, for a central anchoring, in which case the resonator element is suspended from the two subelements of the first type to the support structure on the opposite side of the subelement of the second type.

[0122] In some examples, like Fig.12 In an example of a method of manufacturing a resonator element, the resonator element comprises a void defined by two or more subelements of the second type and two subelements of the first type, the support structure is at least partially arranged in the void, and the resonator element is suspended to the support structure within the void. Thus, the resonator element is centrally anchored to surround an anchoring position in a transverse plane.

[0123] In some embodiments, Fig.14D In the illustrated embodiment, the resonator element comprises a recess (i.e. a lateral depression) defined by one or more subelements of the second type and two subelements of the first type, the support structure being at least partially arranged to extend within the recess, and the resonator element being suspended to the support structure within the recess.

[0124] By means of both the gap and recess configurations, a central anchoring can be achieved, which can be used to minimize the losses of the resonator. The gap configuration has the benefit that a completely symmetrical resonator can be achieved, while the recess configuration allows simpler electrical access to the surface of the resonator, which typically contains the piezoelectric actuation layer. By means of the recess configuration, through silicon vias in the wafer can be completely avoided. In the gap configuration, the through silicon vias can be arranged in the wafer, to the region of the gap.

[0125] Fig.15A shows that when prepared on a wafer with a Si / AlN / Mo material stack with a thickness of 28 / 1 / 0.3 μm, Fig. 8A Figure 2 shows the measured wide frequency admittance plot of the piezoelectric coupled second overtone mode resonator corresponding to the resonator of . It can be inferred that the main mode at 42 MHz is cleanly excited. That is, there are only a few parasitic resonant modes (e.g., at 18 MHz), and the parasitic resonant mode coupling is much weaker than the main mode.

[0126] Fig. 15B Shows Fig.15A Details of the admittance plot of the main resonances of the design (labeled "11 beams"), and Fig.15A 1 and 2, but with a smaller number of coupled beam elements (labeled "7 beams" and "3 beams", respectively). 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. The figure shows how the ESR decreases when the resonator width increases proportionally to the number of coupled beam elements.

[0127] Fig. 15C The frequency versus temperature curves for the measurements of: Fig.15A The resonator (labeled as “Stacked LE Beam Overtone 2”) and the same characteristics as the hybrid WE-Lame mode resonator discussed in WO 2018 / 002439 A1, both of which were prepared in an n-type doped 7*10 19 cm -3 It can be seen that: Fig.15A The linear temperature coefficient TCF1 of the resonator is about 4 units higher than the same parameter of the other resonator. Therefore, there is a higher overcompensation, which has the following benefits: for example, thicker AlN layers can be used for piezoelectric drive purposes to achieve a temperature compensated design.

[0128] Fig.16AA resonator element configuration is shown having four branches of short sub-elements coupled side by side, anchored at nodes to a central support element. Each branch element is a 6×1 fundamental mode array resonator element with non-nodal internal coupling between its sub-elements.

[0129] exist Fig.16A In a variation (not shown in detail), in order to ensure collective resonance between the branches, the central element is a resonant sub-element, and the coupling of the branches to the central sub-element can also be at non-nodes, thereby forming a 13×2 basic mode array.

[0130] Fig. 16B A top view of a longitudinally coupled resonator plate is shown, comprising three rows of 11 columns of fundamental mode subelements. Each row is coupled to another row using flexible longitudinal connecting elements at both ends of the row. As discussed above, each row is coupled internally using rigid connecting elements. An 11×3 array of fundamental elements is formed.

[0131] Fig.17A -E shows different possible flexible connection element geometries between longitudinally coupled sub-elements. Fig. 16B The side of the configuration can be connected to the shape of the "C" shape in Fig.17A The end can be connected to the shape of Figures 17B-17E These show Fig. 17B The end can be connected to a C shape, Fig. 17C and 17D The S shape, and Fig.17E An inclined I shape. It will be appreciated that other flexible shapes and variations of the shapes illustrated are possible.

[0132] Fig.18A -C schematically shows examples of different longitudinal coupling options at the resonator plate level. It can be seen that the longitudinal coupling can be used, for example, Fig. 17B -E element (in Fig.18A - connecting elements (not shown in detail in C) are arranged directly between the longitudinal elements in any configuration, preferably a symmetrical configuration.

[0133] As shown in the examples discussed above, instead of or in addition to end-to-end connection of subelements in the same column, longer elements extending over the column boundaries in the width direction may be used to connect subelements of different columns (not shown).

[0134] Fig.19A -D shows further examples of flexible connection elements, each of which has at least one T-shaped branch.

[0135] Reference List

[0136] Patent Literature

[0137] WO 2012 / 110708 A1

[0138] WO 2018 / 002439 A1

[0139] Non-patent literature

[0140] Ho et al., "HIGH-ORDER COMPOSITE BULK ACOUSTIC RESONATORS", MEMS 2007, Kobe, Japan, January 21 - 25, 2007

[0141] Kuypers J., High Frequency Oscillators for Mobile Devices, in H. Bhugra, G. Piazza (eds.), Piezoelectric MEMS Resonators, Microsystems and Nanosystems, DOI10.1007 / 978 - 3 - 319 - 28688 - 4_15, pp. 335 - 385

[0142] A. Jaakkola et al., “Experimental study of the effects of size variationson piezoelectrically transduced MEMS resonators”, Proc. IEEE InternationalFrequency Control Symposium, 2010, pp. 410—414, http: / / dx.doi.org / 10.1109 / FREQ.2010.5556299

Claims

1. A micro-electromechanical resonator, comprising: - supporting structure, - a resonator element, suspended to the support structure, - an actuator for exciting the resonator element into a resonant mode, in - the resonator element comprises a plurality of adjacent sub-elements, each sub-element having a length and a width and an aspect ratio higher than 1, and each sub-element resonates in an in-plane length-extended resonant mode, - Each of the sub-elements is coupled to at least one other sub-element by one or more connecting elements for exciting the resonator element into a collective resonant mode, the one or more connecting elements being coupled to non-nodes of the resonant modes of the sub-elements.

2. The resonator of claim 1 , wherein at least two of the subelements are coupled to each other in a width direction of the at least two subelements, whereby the connecting element comprises at least two substantially rigid connecting elements adjoining elongated grooves which are retained between the subelements and extend in a length direction of the at least two subelements.

3. The resonator of claim 1, wherein at least two of the subelements have an aspect ratio of length to width of more than 2 and are adapted to resonate in an overtone resonance mode having an order of 2 or higher.

4. The resonator according to claim 3, wherein the sub-elements adapted to resonate in an overtone resonance mode having an order of 2 or higher are separated in the width direction of the sub-elements by a plurality of elongated grooves, the plurality of elongated grooves being defined by the connecting element in the length direction of the at least two sub-elements, the number of the grooves being equal to or higher than the order of the overtone resonance mode, the sub-elements being adapted to resonate.

5. The resonator according to claim 1 or 2, wherein at least two of the sub-elements are coupled to each other in the length direction of the at least two sub-elements by a flexible connection element, the flexible connection element spanning a gap between the sub-elements.

6. The resonator according to claim 1 or 2, wherein each of the sub-elements has a rectangular shape, and the sub-elements are arranged at a distance from each other separated by the connecting element in a width direction and / or a length direction of the sub-elements.

7. The resonator of claim 1 or 2, wherein the connecting element is a passive element formed from a single doped silicon crystal body together with the sub-elements.

8. The resonator of claim 1 or 2, wherein the actuator is a piezoelectric actuator, the piezoelectric actuator being arranged on top of the resonator element.

9. The resonator of claim 8, wherein the actuators are distributed on top of all sub-elements of the resonator element.

10. The resonator of claim 1 or 2, comprising at least 3 sub-elements.

11. The resonator according to claim 1 or 2, comprising: At least two sub-elements are coupled to each other in a width direction thereof, and at least two sub-elements are coupled to each other in a length direction thereof.

12. The resonator of claim 3 or 4, wherein each of the sub-elements has an aspect ratio of length to width of N or more, wherein N is the order of the resonant mode of the sub-element.

13. A resonator according to claim 1 or 2, wherein the entire resonator element has an effective length to width aspect ratio of less than 1.

14. The resonator of claim 1 or 2, wherein all sub-elements of the resonator element have the same width.

15. The resonator of claim 1 or 2, wherein all sub-elements of the resonator element have the same length.

16. The resonator of claim 1 or 2, wherein at least some of the subelements have different lengths and are adapted to collectively resonate in different overtone resonance modes.

17. The resonator of claim 1 or 2, wherein at least two of the subelements have an aspect ratio of length to width of more than 3, and the at least two subelements are respectively adapted to resonate in an overtone resonance mode having an order of 3 or higher.

18. The resonator of claim 1 or 2, wherein the resonator element comprises a quartz crystal doped to at least 2*10 19 cm -3 The average impurity concentration of the silicon bulk.

19. The resonator of claim 1 or 2, wherein the resonator element comprises a silicon crystal having a [100] crystal direction oriented along a length direction of the resonator element or deviating from the length direction of the resonator element by less than 25 degrees.

20. The resonator of claim 1 or 2, wherein the resonator element is suspended to the support structure from nodes of the resonant mode of the sub-element on opposite sides of the resonator element in a width direction of the resonator element.

21. A resonator according to claim 1 or 2, wherein the resonator element is suspended from a node of the resonant mode of the sub-element between two sub-elements to the support structure between two sub-elements.

22. The resonator according to claim 1 or 2, wherein at least some of the subelements are formed by one or more elementary elements having an aspect ratio of length to width higher than 1 and adjoining each other along a length dimension perpendicular to the width dimension, whereby each of the elementary elements supports a elementary resonance mode, the one or more elementary elements together defining a collective resonance mode of the subelements and also of the entire resonator element, - The base elements are arranged in a rectangular array configuration, wherein each base element occupies a single array position.

23. The resonator of claim 22, wherein at least one array position of the array configuration is devoid of the base element.

24. The resonator of claim 22, wherein each array position is occupied by one primitive.

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