Beam resonator

Abstract

A resonator element (100) is provided herein, comprising a plurality of beam elements (101) having a length (L) and a width (W), wherein the plurality of beam elements (101) are placed adjacent to each other and adjacent beam elements are mechanically connected to each other, and wherein the width (W) of the plurality of beam elements (101) varies within the resonator element (100), and wherein the resonator element (100) is configured to mitigate spurious resonant modes of the resonator element (100) by having a varying width (W).

Description

Technical Field

[0001] This disclosure generally relates to the field of semiconductors and semiconductor devices. This disclosure particularly, but not exclusively, relates to beam resonators. Background Technology

[0002] This section provides useful background information, but does not acknowledge that any technology described herein represents prior art.

[0003] A key performance parameter in semiconductor devices (such as resonators, such as silicon MEMS resonators) is the equivalent series resistance (ESR). ESR is inversely proportional to the device's quality factor Q.

[0004] Typically, semiconductor devices are configured to vibrate (oscillate) in a desired primary resonant mode. In some cases, however, the device may employ an undesired resonant mode. The performance of semiconductor devices is often adversely affected by such undesired resonant modes. Summary of the Invention

[0005] The appended claims define the scope of protection. Any examples and technical descriptions of devices, products, and / or methods not covered by the claims in the specification and / or drawings are not presented as embodiments of the invention, but rather as background or examples to aid in understanding the invention.

[0006] The purpose of certain embodiments of this disclosure is to provide solutions to at least one of the problems associated with the prior art, or at least to provide alternatives to the prior art. Therefore, certain disclosed embodiments provide ingenious resonator elements for solving at least one of the problems associated with the prior art.

[0007] According to a first exemplary aspect of this disclosure, a resonator element is provided, comprising a plurality of beam elements having length and width, wherein the plurality of beam elements are positioned adjacent to each other and adjacent beam elements are mechanically connected to each other, and wherein the width of the plurality of beam elements varies within the resonator element, and wherein the resonator element is configured to mitigate stray resonance modes of the resonator element by having width variations.

[0008] In some embodiments, the multiple beam elements are manufactured with varying widths relative to each other. In some embodiments, at least some of the multiple beam elements have different widths from each other. In some embodiments, at least some adjacent beam elements have different widths from each other. In some embodiments, the resonator element includes a beam width gradient (within the width of the beam elements of the resonator element).

[0009] In some embodiments, any two adjacent beam elements of the plurality of beam elements have widths that are different from each other (relative to, corresponding to, compared to). In some embodiments, any three adjacent beam elements of the plurality of beam elements have widths that are different from each other. In some embodiments, any five adjacent beam elements of the plurality of beam elements have widths that are different from each other.

[0010] In some embodiments, the resonator element is an asymmetric resonator element. In some embodiments, the resonator element includes an asymmetric beam element with varying width. In some embodiments, the resonator element is asymmetric in its width direction. In some embodiments, the resonator element is asymmetric with respect to its central axis parallel to its length direction. In some embodiments, the resonator element is asymmetric in terms of beam element width. In some embodiments, multiple beam elements with varying widths are asymmetrically arranged (positioned) within the resonator element.

[0011] In some embodiments, the outermost beam elements of the resonator element have the same width. In some embodiments, the outermost beam element and the center (middle) beam element have the same width. In some embodiments, the outermost beam elements of the resonator element have the same width, while all other beam elements of the resonator element have varying widths (between each other). In some embodiments, the outermost beam element and the center beam element have the same width, while all other beam elements of the resonator element have varying widths.

[0012] In some embodiments, the widths of the plurality of beam elements (each of which) vary from one another by less than 20% of the average width of the beam elements. In some embodiments, the widths of the plurality of beam elements (each of which) vary from one another by less than 15% of the average width of the beam elements. In some embodiments, the widths of the plurality of beam elements vary from one another by more than 1% of the average width of the beam elements. In some embodiments, the widths of the plurality of beam elements vary from one another by more than 5% of the average width of the beam elements. In some embodiments, the widths of the plurality of beam elements vary from one another by more than 10% of the average width of the beam elements.

[0013] In some embodiments, the difference between the widths of the widest beam element and the narrowest beam element is less than 20% of the width of the widest beam element (e.g., less than 15% of the width of the widest beam element). In some embodiments, the difference between the widths of the widest beam element and the narrowest beam element is greater than 5% of the width of the widest beam element (e.g., greater than 10% of the width of the widest beam element).

[0014] In some embodiments, each of the multiple beam elements has a unique (different) width relative to each other.

[0015] In some embodiments, the width of one beam element differs from that of another beam element by 0.1. m to 2 m (width difference within 0.1) m and 2 (between m). In some embodiments, the widths of any two beam elements of the resonator differ from the widths of the other beam elements by 0.3 m. m to 0.5 In some preferred embodiments, the width of any two beam elements of the resonator element differs from the width of the other beam elements by 0.4 m. m. In some embodiments, the width of any two adjacent beam elements of the resonator element differs from that of any other adjacent beam element by 0.1 m. m to 2 m, such as 0.3 m to 0.5 m, preferably differing by 0.4 m. In some embodiments, the width of all beam elements of the resonator element differs from that of the other beam elements by 0.1 m. m to 2 m, such as a difference of 0.3 m to 0.5 m, preferably differing by 0.4 m.

[0016] In some embodiments, the definition of beam element width applies to all beam elements except the outermost beam elements (the rightmost and leftmost beam elements). In other words, in other embodiments, the definition of beam element does not apply to the outermost beam elements.

[0017] In some embodiments, the resonator elements are stacked beam resonator elements. In some embodiments, the stacked beam resonator elements comprise a plurality of beam elements positioned side-by-side in a plane. In some embodiments, the plurality of beam elements are positioned adjacent to each other in their width direction. In some embodiments, the plurality of beam elements are positioned adjacent to each other in the width direction of the resonator elements. In some embodiments, the beam elements are separated by grooves. In some embodiments, the beam elements are connected to each other by connecting elements. In some embodiments, each beam element is mechanically connected to another beam element by (at least) two connecting elements, and adjacent beam elements are separated by grooves. In some embodiments, the grooves between adjacent beam elements have a uniform width.

[0018] In some embodiments, the resonator element comprises multiple beam elements, such as seven, nine, or eleven beam elements. In some embodiments, adjacent beam elements are mechanically connected to each other by connecting elements. In some embodiments, the beam elements of the resonator element are arranged in a rectangular array configuration.

[0019] In some embodiments, the resonator element is rectangular (rectangular in shape). In some embodiments, the resonator element has an aspect ratio (the ratio of length to width when viewed from above) other than 1. In some embodiments, the resonator element has an aspect ratio less than 1. In some embodiments, the resonator element is attached (supported, anchored) to a support structure. In some embodiments, the resonator element is attached to the support structure from the outermost beam element of the resonator element.

[0020] In some embodiments, each beam element is shaped like a (rectangular) beam. In some embodiments, each beam element has an aspect ratio (the ratio of length to width when viewed from above) other than 1. In some embodiments, each beam element has an aspect ratio greater than 1.

[0021] In some embodiments, the resonator element is fabricated on a substrate. In some embodiments, the substrate is a wafer. In some embodiments, the substrate is a silicon-on-insulator (SOI) wafer. In some embodiments, the substrate includes a silicon layer.

[0022] In some embodiments, the resonator element includes a material stack comprising a silicon layer, a piezoelectric layer on top of the silicon layer, and a top electrode on top of the piezoelectric layer. In some embodiments, the resonator element is a piezoelectric resonator element.

[0023] In some embodiments, the resonator element is part of a semiconductor device. In some embodiments, the resonator element is a microelectromechanical system (MEMS) resonator element. In some embodiments, the resonator element is configured to operate in a megahertz frequency region. In some embodiments, the resonator element is sized to operate in a megahertz frequency region. In some embodiments, the resonator element is configured to operate at a 32 MHz frequency. In some embodiments, the resonator element is sized to operate at a 32 MHz frequency.

[0024] In some embodiments, the resonator element includes a resonant element. In some embodiments, each beam element is a resonant beam element. In some embodiments, each beam element is a sub-element of the resonator element.

[0025] In some embodiments, the resonator element is configured to resonate (operate, oscillate, vibrate) in an in-plane resonant mode. In some embodiments, the resonator element is adapted to resonate in a length-extended LE resonant mode. In some embodiments, the resonator element is configured to operate in an in-plane length-extended LE resonant mode. In some embodiments, the length-extended resonant mode is configured to resonate parallel to the length direction of the resonator element. In some embodiments, the length-extended resonant mode is configured to resonate perpendicular to the width direction of the resonator element.

[0026] In some embodiments, the resonator elements are configured to resonate in a collective resonant mode. In some embodiments, each beam element of the resonator elements is configured to resonate in the same collective resonant mode. In some embodiments, the resonator elements are configured to resonate in a desired (primary) resonant mode. In some embodiments, each beam element of the resonator elements is configured to resonate in the same desired resonant mode.

[0027] In some embodiments, the widths of the multiple beam elements vary within the resonator element to (mechanically) mitigate (reduce, remove, eliminate, suppress) stray resonant modes of the resonator element. In some embodiments, the stray resonant mode is an undesired resonant mode. In some embodiments, the stray resonant mode is a resonant mode different from the desired (primary) resonant mode. In some embodiments, the stray resonant mode resonates at a resonant mode different from the desired resonant mode.

[0028] In some embodiments, the spurious resonant mode is a bending resonant mode. In some alternative embodiments, the spurious mode is a width-extended resonant mode. In some alternative embodiments, the spurious mode is a differential resonant mode, such as a differential length-extended resonant mode.

[0029] In some embodiments, the stray resonance mode is an out-of-plane resonance mode. In some alternative embodiments, the stray resonance mode is an in-plane resonance mode.

[0030] In some embodiments, the stray resonance mode is an out-of-plane bending resonance mode. In some embodiments, the stray resonance mode is an in-plane width-extending resonance mode. In some embodiments, the stray resonance mode is an in-plane differential length-extending resonance mode.

[0031] In some embodiments, the resonator element includes more than one stray resonant mode. In some embodiments, the widths of multiple beam elements vary within the resonator element to mitigate the stray resonant modes(s) of the resonator element(s).

[0032] In some embodiments, the resonator element is configured to mitigate disturbances (effects, detrimental effects) caused by stray resonant modes of the resonator element by varying the width of the beam element within the resonator element (width variation). In some embodiments, the resonator element is configured to mitigate disturbances caused by stray resonant modes of the resonator element by asymmetrically varying the width of the beam element within the resonator element. In some embodiments, the resonator element is configured to mitigate disturbances caused by stray resonant modes by modifying (segmenting) the equivalent series resistance (ESR) of the stray resonant modes of the resonator element.

[0033] In some embodiments, the resonator element is configured to eliminate the collective stray resonance mode of the beam element of the resonator element.

[0034] According to a second exemplary aspect of this disclosure, a resonator assembly is provided, comprising at least two (more than one) resonator elements according to the first aspect coupled to each other. In some embodiments, the resonator elements are coupled to each other via a coupler. In some embodiments, the resonator elements are coupled to each other via a coupler comprising multiple discontinuous regions.

[0035] In some embodiments, the resonator assembly includes an extended-mode resonator element. In some embodiments, the resonator assembly includes a flexural-mode resonator. In some embodiments, the resonator assembly includes a mechanical connector element connecting the flexural resonator to the extended-mode resonator element.

[0036] In some embodiments, each resonator element includes a plurality of beam elements having a length and a width, wherein the plurality of beam elements are positioned adjacent to each other and adjacent beam elements are mechanically connected to each other, and wherein the width of the plurality of beam elements varies within the resonator element, and wherein the resonator element is configured to mitigate stray resonance modes of the resonator element by having a width variation.

[0037] According to certain embodiments, embodiments of the second aspect are provided, which include the subject matter in conjunction with any single embodiment presented in the first aspect, or the embodiments include the subject matter in conjunction with any embodiment presented in the first aspect and the subject matter presented in any other one or more embodiments.

[0038] Various non-limiting example aspects and embodiments have been described above. The embodiments described above are only used to explain selected aspects or steps that can be utilized in different implementations. Some embodiments may be presented with reference only to certain example aspects. It should be understood that corresponding embodiments may also be applied to other example aspects. In particular, the embodiments described in the context of the first aspect are applicable to each of the other aspects. Any suitable combination of embodiments may be formed. Attached Figure Description

[0039] Some exemplary embodiments will be described with reference to the accompanying drawings, in which:

[0040] Figure 1 A top view schematically illustrating a resonator element according to an example embodiment, showing its dimensions;

[0041] Figure 2 A top view of a resonator element comprising seven beam elements with varying widths, according to another example embodiment, is schematically shown.

[0042] Figure 3 A top view of a resonator element comprising 1...n beam elements according to yet another exemplary embodiment is schematically shown;

[0043] Figure 4 A top view of a resonator including two resonator elements according to an example embodiment is shown schematically;

[0044] Figure 5 A top view of a resonator including two resonator elements according to another example embodiment is shown schematically;

[0045] Figure 6 A cross-sectional view of a piezoelectrically actuated resonator according to an example embodiment is schematically shown;

[0046] Figure 7a The modification of the frequency of the spurious resonant mode according to the example embodiment is illustrated schematically;

[0047] Figure 7b The modification of the frequency of the stray resonance mode according to another example embodiment is illustrated schematically;

[0048] Figure 7c An illustration of a process defect according to an example embodiment is shown schematically;

[0049] Figure 8a The stray resonance mode is schematically illustrated from a top view according to an example embodiment; and

[0050] Figure 8b Another stray resonance mode is schematically illustrated in a side view according to an example embodiment. Detailed Implementation

[0051] In the following description, the same reference numerals refer to the same elements or steps.

[0052] Figure 1 A schematic top view (from top to bottom) of a resonator element 100 according to some embodiments is shown. The resonator element 100 includes a plurality of beam elements 101 having a length L and a width W. Figure 1 In the illustrated embodiment, the resonator element 100 includes seven beam elements 101, 101' (the number of beam elements 101 may vary depending on the embodiment). In some embodiments, the length L of the beam element 101 is greater than its width W. In some embodiments, a coordinate system is chosen such that the x-axis lies in the width direction W of the beam element 101, and the y-axis lies in the longitudinal direction L of the beam element 101.

[0053] Multiple beam elements 101 are positioned adjacent to each other. In some embodiments, the multiple beam elements 101 are positioned adjacent to each other in their width direction. Adjacent beam elements 100 are mechanically connected to each other. In some embodiments, the resonator element 100 is formed by multiple beam elements 101 and multiple connecting elements 102. In some embodiments, the adjacent beam elements 100 are mechanically connected to each other by connecting elements 102. In some embodiments, adjacent beam elements 101 are separated by a groove 104. In some embodiments, the groove 104 has a length TL (groove length). In some embodiments, the length L of the beam element 101 includes at least the length TL of the groove and the length of at least one connecting element 102.

[0054] In some embodiments, the beam elements 101 of the resonator element 100 are arranged in a rectangular array configuration. In some embodiments, the resonator element has a length L (which is equal to the length of the beam element). In some embodiments, the resonator element has a width RW (the width of the resonator element).

[0055] like Figure 1 As shown, the outermost beam element is represented by the numeral 101'. In all other respects, they correspond to the beam element 101, except that they are located at the outermost position of the resonator element 100. In some embodiments, the resonator element 100 is attached to a support structure (not shown). In some embodiments, the resonator element 100 is attached to the support structure from the outermost beam element 101' of the resonator element 100 ((a plurality of) anchor points 103).

[0056] In some embodiments, the width W of the plurality of beam elements 101 varies within the resonator element 101 to mitigate stray resonant modes of the resonator element. In some embodiments, beam element 101 differs in width from another beam element 101. In some embodiments, each beam element 101 has its respective width W. In some embodiments, the width W of at least one beam element 101 (or multiple beam elements) differs from the width W of another beam element 101.

[0057] In some embodiments, the resonator element 100 is elongated (having a length L less than its width RW). In some embodiments, the resonator element 100 is rectangular (the resonator element 100 has a rectangular shape). In some embodiments, the resonator element 100 has an aspect ratio other than 1 (the ratio of length L to width RW when viewed from above). In some embodiments, the resonator element 100 has an aspect ratio of length to width, and L to RW less than 1.

[0058] In some embodiments, beam element 101 is elongated (having a length L greater than its width W). In some embodiments, each beam element 101 is in the shape of a rectangular beam. In some embodiments, each beam element 101 has a width-to-height ratio (the ratio of length L to width W when viewed from above) different from 1. In some embodiments, each beam element 101 has a length-to-width and L-to-W width-to-height ratio greater than 1.

[0059] Figure 2 A top view of a resonator element 100 according to some embodiments is schematically shown. Figure 2 In the illustrated embodiment, the resonator element 100 includes seven beam elements 101, 101' (the number of beam elements may vary depending on the embodiment).

[0060] In some embodiments, the resonator element 100 includes a width variation between beam elements 101, 101'. In some embodiments, any two adjacent beam elements 101 of the plurality of beam elements have different widths W1, W2, W3, W4, W5, W6, W7 relative to each other. In some embodiments, the resonator element 100 is an asymmetric resonator element (relative to the beam element widths W1, W2, W3, W4, W5, W6, W7). In some embodiments, the plurality of beam elements 101 having varying widths W1, W2, W3, W4, W5, W6, W7 are asymmetrically positioned (arranged, placed) in the resonator element 100. By asymmetrically arranging the beam elements 101 with varying widths W1, W2, W3, W4, W5, W6, W7 in the resonator element 100, the risk of acquiring collective stray resonance modes is reduced.

[0061] In some embodiments, the outermost beam element 101' of the resonator element 100 has the same width. In some other embodiments, the outermost beam element 101' and the center beam element (shown herein as a beam element with width W4) have the same width (shown herein as W1=W4=W7).

[0062] In some embodiments, the widths W1, W2, W3, W4, W5, W6, and W7 of the beam element 101 of the resonator element 100 are in the range of 8. m to 35 The widths W1, W2, W3, W4, W5, W6, and W7 of the beam element 101 of the resonator element 100 vary between m. In some preferred embodiments, the widths W1, W2, W3, W4, W5, W6, and W7 of the beam element 101 of the resonator element 100 are between 20 m and m. m to 26 The value varies between m, preferably between 22. m to 24 Between m, more preferably between 22.6 and m. m to 23.4 Between m. In some embodiments, the resonator element 100 includes a gradient of beam elements 101 with varying widths W1, W2, W3, W4, W5, W6, W7, wherein the width of one beam element 101 differs from that of another beam element 101 by 0.1 m. m to 2 Step sizes between m, such as 0.4 The step size is m. Depending on the embodiment, the widths W1, W2, W3, W4, W5, W6, W7 of the beam element 101 are modified by an appropriate amount (an appropriate width difference), such as in 0.1. m to 2 It is beneficial to reduce the risk of acquiring (adapting to) collective stray resonance modes between m.

[0063] In some embodiments, the widths W1, W2, W3, W4, W5, W6, W7 of the plurality of beam elements 101 vary from each other by less than 20% of the average width of the beam elements 101 (such as less than 15% of the average width of the beam elements 101) and greater than 1% of the average width of the beam elements 101 (such as greater than 5% or greater than 10% of the average width of the beam elements 101).

[0064] In some embodiments, the resonator element 100 includes a first set of beam elements 101 having a first width W. In some embodiments, the first set of beam elements 101 is asymmetrically arranged (positioned) within the resonator element 100.

[0065] In some embodiments, the resonator element 100 includes a second set of beam elements 101 having a second width W. In some embodiments, the first width and the second width are different from each other (the width of the beam elements 101 in the first set is different from the width W of the beam elements 101 in the second set). In some embodiments, the second set of beam elements 101 is asymmetrically arranged within the resonator element 101.

[0066] In some embodiments, the resonator element 101 further includes a third set of beam elements 101 having a third width W. In some embodiments, the third set of beam elements 101 is arranged asymmetrically within the resonator element 100. In some embodiments, the first width, the second width, and the third width are all different from each other (the width W of the beam elements 101 in the third set is different from the width W of the beam elements 101 in the first set and the second set).

[0067] In some embodiments, the above description similarly applies to the beam elements 101 of any fourth, fifth, sixth... group of resonator elements 100, which have fourth, fifth, sixth... widths. In some embodiments, the beam elements 101 of all groups are asymmetrically positioned within the resonator element 100. In some embodiments, the beam elements 101 of all groups have varying widths compared to the beam elements 101 of other groups.

[0068] In some embodiments, each of the plurality of beam elements 101 has a unique width W1, W2, W3, W4, W5, W6, W7 relative to each other.

[0069] Therefore, a resonator element 100 is provided, comprising a plurality of beam elements 101 having a length L and a width W, wherein the plurality of beam elements 101 are positioned adjacent to each other and the adjacent beam elements are mechanically connected to each other, and wherein the width W of the plurality of beam elements 101 varies within the resonator element 100, and wherein the resonator element 100 is configured to mitigate stray resonance modes of the resonator element 100 by having a variation in width W.

[0070] Figure 3 A top view of a resonator element 100 according to some embodiments is schematically shown. The resonator element 100 includes a plurality of adjacent beam elements 101, which are shown herein as 1...n beam elements 101.

[0071] In some embodiments, the resonator element 100 is a stacked beam resonator element. Stacked beam resonator elements typically have a basic geometry in which beam elements of equal width are connected by connecting elements positioned at the edges of the resonator. The geometry of the resonator element of this disclosure differs from this geometry by varying the width of the beam elements.

[0072] In some embodiments, the stacked beam resonator elements 100 include adjacent beam elements 101 (adjacent sub-elements) positioned side-by-side in a plane. In some embodiments, the resonator elements 100 include anchor points 103 to anchor the beam elements to the surrounding area. In some embodiments, the resonant modes of the resonator elements 100 have nodes at the anchor points 103.

[0073] In some embodiments, the resonator element 100 includes n adjacent beam elements 101, wherein the first and nth beam elements 101' have the same width W, which is different from the width W of the other beam elements 101. In some embodiments, the resonator element 100 includes n adjacent beam elements 101, wherein the first, nth, and n / 2th beam elements 101 have the same width W, which is different from the width W of the other beam elements 101 (where n is an odd number). In some embodiments, the resonator element 100 includes n adjacent beam elements 101, wherein the first, nth, and two n / 2th beam elements 101 have the same width W, which is different from the width W of the other beam elements 101 (where n is an even number).

[0074] In some embodiments, resonator element 100 includes a resonant element. As used herein, the term resonant element refers to a portion of a resonator configured to operate in a resonant mode. In some embodiments, the resonant element includes multiple resonant beams (beam elements). As used herein, the term resonator element refers to a structure including multiple resonant portions and multiple stationary portions, such as a support structure.

[0075] In some embodiments, each beam element 101 is a resonant beam element. In some embodiments, the resonator element 100 is configured to resonate in a desired (primary) resonant mode. In some embodiments, the desired resonant mode is a collective resonant mode. In some embodiments, each beam element 101 of the resonator element 100 is configured to resonate in the same resonant mode.

[0076] In some embodiments, resonator element 100 is configured to operate in an in-plane length-extended LE resonant mode. In some embodiments, the in-plane length-extended resonant mode is the dominant resonant mode of resonator element 100. In some embodiments, beam element 101 of resonator element 100 is configured to operate in an in-plane length-extended resonant mode. Beam element 101 (and therefore the entire resonator element 100) oscillates in LE mode in the direction of the y-axis (in the direction parallel to the longitudinal length L).

[0077] In some embodiments, the width W of the plurality of beam elements 101 varies within the resonator element 100 to mitigate stray resonant modes of the resonator element 100. Typically, the resonator element(s) 100 is configured to operate in a desired (collective) dominant resonant mode (resonance, vibration, oscillation). In some cases, the resonator element 100 employs another undesired stray resonant mode. This undesired stray resonant mode typically includes a lower ESR than the desired dominant resonant mode. Therefore, the undesired stray resonant mode typically dissipates less energy than the desired dominant resonant mode, ultimately becoming the dominant resonant mode for self-sustaining oscillation. The performance of the semiconductor device including the resonator element 100 is adversely affected by such undesired (plural) stray resonant modes. In some embodiments, the stray resonant mode is a resonant mode different from the desired dominant resonant mode. In some embodiments, the resonator element 100 includes stray resonant modes (resonating in stray resonant modes) (in addition to the dominant resonant mode).

[0078] Figure 4 and Figure 5 A resonator assembly comprising multiple resonator elements is schematically illustrated according to certain embodiments. In some embodiments, the resonator assembly includes (at least) two resonator elements 100 (stacked beam resonator elements). For a single resonator element... Figure 1 , 2 All embodiments described in the context of 3 also apply herein to the resonator element 100 of the resonator assembly.

[0079] Figure 4 A resonator assembly comprising two resonator elements 100 coupled to each other, according to certain embodiments, is schematically illustrated. The resonator assembly includes at least two extended-mode resonator elements 100 and one or more bent-mode resonators 310. Furthermore, the resonator assembly includes one or more mechanical connector elements 320 that connect the bent resonator 120 to the extended-mode resonator elements. In some embodiments, at least one of the extended-mode resonator elements 100 of the resonator assembly includes a piezoelectric thin-film actuator for exciting the extended-mode resonator to a resonant mode, and thereby exciting the entire resonator assembly to collective resonance due to the mechanical coupling of the extended-mode resonator elements 100.

[0080] In some embodiments, more than 50% of the mass of the resonator assembly comprises a portion of monocrystalline silicon material. In some embodiments, the resonator assembly 100 includes an electrostatic actuator for exciting at least one of the extended-mode resonator elements 100 to a resonant mode, and thereby exciting the entire resonator element to collective resonance due to the mechanical coupling of the extended-mode resonators.

[0081] Figure 5 A resonator assembly comprising two resonator elements 100 coupled to each other, according to certain embodiments, is schematically illustrated. In some embodiments, the resonator assembly comprises at least two resonator elements 100 coupled to each other via a coupler 330. In some embodiments, the coupler 330 is a length-extending coupler. In some embodiments, the resonator elements 100 are implemented in the form of stacked beam resonators having a plurality of adjacent resonant beams connected by connecting elements(multiple) and separated by grooves (thus forming a trapezoidal structure).

[0082] In some embodiments, the coupler 330 includes a discontinuous region 340. In some embodiments, the discontinuous region 340 of the coupler 330 makes the coupler 330 electrically inert.

[0083] In some embodiments, all resonator elements 100 of the resonator assembly are identical to each other. In some embodiments, the resonator elements 100 of the resonator assembly are identical to each other in terms of beam width gradient. As used herein, the term beam width gradient refers to how the beam widths within the resonator elements differ from each other.

[0084] In some embodiments, all resonator elements 100 of the resonator assembly are different from each other. In some embodiments, the resonator elements 100 of the resonator assembly are different from each other in terms of beam width gradient.

[0085] In some embodiments, the resonator assembly includes a plurality of resonator elements. In some embodiments, the resonator assembly includes a plurality of resonator elements positioned adjacent to each other. In some embodiments, each odd-numbered resonator element of the resonator assembly has the same first beam width gradient relative to each other. In some embodiments, each even-numbered resonator element of the resonator assembly has the same second beam width gradient relative to each other. In some embodiments, the first beam width gradient is a mirror image of the second beam width gradient.

[0086] Figure 6 An example cross-section (section view, side view) of a piezoelectrically actuated resonator element located on a substrate is schematically shown.

[0087] In some embodiments, the resonator elements are fabricated on a substrate. Figure 6 In the example embodiment, a silicon-on-insulator (SOI) substrate (wafer) 450 is used. Reference numerals 401 and 402 denote the bottom electrode and top electrode contacts, respectively.

[0088] In some embodiments, the resonator element 100 includes a material stack (formed therefrom). In some embodiments, the resonator element 100 includes a material stack that includes at least a silicon layer L4, a piezoelectric layer L2 on top of the silicon layer, and a top electrode L1 on top of the piezoelectric layer.

[0089] exist Figure 6 In the illustrated example embodiment, the top electrode is implemented in layer L1. In this example embodiment, layer L2 is a piezoelectric layer for piezoelectric actuation of the resonator element located in the region indicated by 100. The opening of L2 is indicated by 420. In this example embodiment, layer L3 represents the layer for the bottom electrode. In this example embodiment, layer L4 is a silicon layer for the resonator element (beam element and its connecting elements). In this example embodiment, layer L5 is the buried oxide layer (SiO2) of the SOI wafer, and layer L6 is a silicon processing layer. In some embodiments, layer L6 includes a cavity C1. In some embodiments, layer L5 follows the following... Figure 6 The shape of cavity C1 is shown.

[0090] In some embodiments, when the doped silicon layer is used as L4, it is possible to omit the separate L3 bottom electrode layer. In this embodiment, the conductive doped silicon layer L4 acts as the bottom electrode. In some embodiments, the silicon layer L4 comprises degraded doped silicon. In some embodiments, more than 50% of the mass of the silicon layer L4 consists of degraded doped silicon. In some embodiments, the silicon layer L4 is doped to at least 2... 10 19 cm -3 The average impurity concentration, such as at least 10 20 cm -3 In some embodiments, silicon layer L4 comprises monocrystalline silicon. In some embodiments, silicon layer L4 is substantially composed of monocrystalline silicon. In some embodiments, silicon layer L4 comprises degraded-doped monocrystalline silicon.

[0091] In some embodiments, the longitudinal axis L of beam element (or all beam elements) 101 is parallel to the longitudinal axis L of beam element (not shown). <100> Crystal orientation alignment, such as alignment with the

[100] crystal orientation of the beam element, or deviation from it of less than 25 degrees, or in some embodiments, deviation from it of less than 15 degrees. In some preferred embodiments, the longitudinal axis L of the beam element (or all beam elements) 101 is aligned with the crystal orientation of the beam element. <100> Crystal orientation alignment, such as alignment with the

[100] crystal orientation of the beam element, or deviation from it by less than 5 degrees, or in some embodiments by less than 2 degrees.

[0092] Figure 7a and 7bThe diagram schematically illustrates an impedance Z (ohms) versus frequency f (MHz) plot showing a modified frequency of the stray resonance mode according to certain embodiments. The stray resonance frequency is a function of the beam width. When all beam elements of the resonator element have the same width, it is possible for the beam elements to resonate at the same frequency. On the other hand, when the beam elements of the resonator element include variations in width, the beam elements are intentionally designed to resonate at a variety of different frequencies using a higher equivalent series resistance (ESR).

[0093] As described above, in some embodiments, the resonator element is configured to mitigate disturbances caused by stray resonant modes of the resonator element by varying the width (asymmetrically) of the beam element within the resonator element. In some embodiments, the resonator element is configured to mitigate disturbances caused by stray resonant modes (shown as large peaks R in the reference (REF) Z-f diagram) by modifying (split, segment, adjust, separate) the stray resonant modes of the resonator element into (a number of) harmless resonant modes by varying the width of the beam element. The stray resonant mode depends on the width dimension of the beam element of the resonator element. Figure 7a and Figure 7b In the reference (REF), the resonator elements consist of beam elements of the same width (with a strong low equivalent series resistance ESR signal). Figure 7a and Figure 7b In the resonator element 100, the widths of multiple beam elements vary within the resonator element 100, and the resonator element 100 is configured to mitigate stray resonance modes of the resonator element 100 by having width variations.

[0094] In some embodiments, the equivalent series resistance (ESR) of the stray modes is adjusted to maintain the dominant resonant mode as the dominant resonant mode. In some embodiments, the dominant resonant mode is an in-plane length-extended resonant mode. In some embodiments, the stray resonant modes(s) have ESR values ​​at least higher than the ESR value of the dominant resonant mode. In some embodiments, the stray resonant modes(s) have ESR values ​​at least three times higher than the ESR value of the dominant resonant mode. In some embodiments, the dominant resonant mode has a lower ESR value than the stray resonant modes(s).

[0095] In other words, in some embodiments, by changing the width of the beam element of the resonator element, a stray resonant mode R with a lower ESR than the main resonant mode is modified (split) into (several) harmless stray resonant modes with higher ESR (such as...). Figure 7a and Figure 7bAs shown, the small peaks R'1, R'2, R'3, R'4, and R'5 in the Z-pair diagram of the resonator element 100 of this disclosure. The modification prevents stray resonance modes from becoming the dominant resonance mode. Therefore, the dominant resonance mode remains the resonance mode with the lowest ESR (the dominant resonance mode). In some embodiments, the resonator element of this disclosure is configured to eliminate the collective stray resonance modes of the beam elements of the resonator element.

[0096] Figure 7c A schematic diagram illustrating 1 / Z (dB) versus frequency f (MHz) of a process defect, according to certain embodiments, is shown.

[0097] Figure 7a and 7b The small changes shown in the REF and 100 Z versus f plots (where the lines are not perfectly aligned at the top of each other) are... Figure 7c The details are shown below. These small variations are typically caused by defects in the resonator elements, resulting from the manufacturing process. These small defects are insufficient to reliably separate the stray resonant modes (multiple modes) into a number of peaks, such as... Figure 7a and Figure 7b As shown.

[0098] like Figure 7c As shown, peak values ​​R1 and R2 represent peak values ​​from a resonator structure that includes some variation in the beam element widths due to the manufacturing process. Peak value R3 represents a peak value from a resonator structure with all beam elements having exactly equal widths.

[0099] Without limiting the scope and interpretation of the patent claims, certain technical effects of one or more exemplary embodiments disclosed herein are listed below. The technical effect is to provide a resonator free from harmful disturbances caused by stray resonant modes. The technical effect is to prevent stray resonant modes from becoming collective resonant modes.

[0100] Another technical effect is to prevent the resonant mode of the resonator element (for which the oscillation is self-sustaining) from harmfully "locking in" to a stray resonant mode instead of the dominant resonant mode. Stray modes typically dissipate less energy and have a smaller ESR compared to the dominant resonant mode. Another technical effect is to prevent stray resonant modes from becoming the dominant resonant mode for self-sustaining oscillations. By changing the beam width of the resonator element, the small ESR of the stray resonant mode is broken down into several high-ESR stray resonant modes, making the dominant resonant mode of the resonator element the smallest ESR resonant mode, thus preventing the stray resonant mode from becoming the dominant resonant mode.

[0101] The increase in ESR of a stray resonant mode depends on the resonance of the beam element of the resonator element along its width dimension. In other words, the ESR of a stray mode is inversely proportional to the number of beams in the collective resonance (because stray resonant modes depend on the beam width). Therefore, changing the beam element width reduces the number of beam elements that contribute to any resonance peak, thus increasing the ESR. The ESR of a stray mode is designed to be higher than that of the dominant resonant mode. Therefore, by changing the beam element width of the resonator element, (multiple) stray resonant modes can be mitigated.

[0102] It should be noted that minute edge defects in the width of the beam element(s) due to errors during the manufacturing process of the resonator element, for example, are insufficient to reliably mitigate the stray resonant modes(s) of the resonator element(s). In this disclosure, the beam element is intentionally designed and manufactured with varying widths.

[0103] Another technical advantage is that it maintains the main resonant mode (in some embodiments, the in-plane length-extended resonant mode) unchanged in terms of performance, and provides resonator elements with stable high performance.

[0104] Stray resonance modes are unintended resonance modes (different from the expected main resonance modes). Figure 8a and Figure 8b An example of a stray resonance mode according to an exemplary embodiment is shown schematically, wherein the main resonance mode is an in-plane length-extended resonance mode. Figure 8a The stray resonance mode is schematically illustrated from a top-down view. In Figure 8a In the example embodiment shown, the stray resonance mode is a width-extended resonance mode, specifically an in-plane width-extended resonance mode. In this example stray resonance mode, displacement occurs in the plane, but in the width direction rather than the desired length direction.

[0105] Figure 8b The stray resonance mode is schematically illustrated in a side view. Figure 8b In the example embodiment shown, the stray resonance mode is a bending resonance mode, specifically an out-of-plane bending resonance mode. In this example stray resonance mode, the displacement occurs out of plane, rather than in the desired length direction. In some alternative embodiments (not shown), the stray mode is a differential resonance mode, such as an in-plane differential length-extending resonance mode.

[0106] Various embodiments have been presented. It should be understood that in this document, the words “comprising,” “including,” and “covering” are used as open-ended expressions and are not exclusive.

[0107] The foregoing description has provided a complete and informative description of the best mode for carrying out the invention as currently contemplated by the inventors, through non-limiting examples of specific implementations and embodiments. However, it will be apparent to those skilled in the art that the invention is not limited to the details of the embodiments presented above, but can be implemented in other embodiments using equivalent components or in different combinations of embodiments without departing from the spirit of the invention.

[0108] Furthermore, some features of the exemplary embodiments disclosed above can be used advantageously without corresponding use of other features. Therefore, the foregoing description should be considered merely as an illustration of the principles of the invention, and not as a limitation thereof. Consequently, the scope of the invention is limited only by the appended patent claims.

Claims

1. A resonator element (100), comprising: Multiple beam elements (101) having length (L) and width (W). The plurality of beam elements (101) are positioned adjacent to each other, and adjacent beam elements are mechanically connected to each other. The width (W) of the plurality of beam elements (101) varies within the resonator element (100), and the resonator element (100) is configured to mitigate stray resonance modes of the resonator element (100) by having the variation in width (W).

2. The resonator element according to claim 1, wherein any two adjacent beam elements (101) of the plurality of beam elements (101) have different widths (W) from each other.

3. The resonator element according to claim 1 or 2, wherein the resonator element (100) is an asymmetric resonator element.

4. The resonator element according to any of the preceding claims, wherein the outermost beam element (101') of the resonator element has the same width (W).

5. The resonator element according to claim 4, wherein the outermost beam element (101') and the innermost beam element (101) have the same width (W).

6. The resonator element according to any of the preceding claims, wherein the width (W) of the plurality of beam elements (101) varies from one another by less than 20% of the average width of the beam elements (101).

7. The resonator element according to any of the preceding claims, wherein each of the plurality of beam elements (101) has a unique width (W) relative to each other.

8. The resonator element according to any of the preceding claims, wherein the width (W) of said beam element (101) differs from that of the other beam element (101) by 0.

1. m to 2 m.

9. The resonator element according to any of the preceding claims, wherein the resonator element (100) is a stacked beam resonator element.

10. The resonator element according to any of the preceding claims, wherein the resonator element (100) is configured to operate in a plane-length-extended LE resonant mode.

11. The resonator element according to any of the preceding claims, wherein the resonator element (100) is configured to mitigate disturbances caused by the stray resonance mode by modifying the equivalent series resistance (ESR) of the stray resonance mode of the resonator element (100).

12. The resonator element according to any of the preceding claims, wherein the resonator element (100) is configured to: eliminate the collective stray resonance mode of the beam element (101) of the resonator element (100).

13. A resonator assembly comprising at least two resonator elements (100) coupled to each other according to any one of claims 1 to 12.

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