Configuration of beams in a MEMS resonator having coupled beams resonating in a longitudinal-extensional mode

Abstract

Herein is provided a resonator (100), comprising a resonating element (101), wherein the resonating element (101) comprises a plurality of non-rectangular resonating beam elements (101), the plurality of beam elements (101) being positioned adjacent to each other, wherein the adjacent beam elements are mechanically connected to each other by connection elements (102) and separated from each other by non-linear trenches (104) Herein is further provided an apparatus, such as a resonator array, comprising at least one resonator (100).

Description

[0001] BEAM CONFIGURATION

[0002] TECHNICAL FIELD

[0003] The present disclosure generally relates to the field of semiconductors and semiconductor apparatuses. The disclosure relates particularly, though not exclusively, to beam configurations of resonators.

[0004] BACKGROUND

[0005] This section illustrates useful background information without admission of any technique described herein representative of the state of the art.

[0006] A key performance parameter in semiconductor apparatuses, such as resonators, such as silicon MEMS resonators is the equivalent series resistance (ESR). ESR is inversely proportional to the quality factor Q of the apparatus.

[0007] Typically, semiconductor apparatuses are configured to vibrate (oscillate) in a desired main resonance mode. In certain occasions, the apparatus may adopt another, unwanted resonance mode. The performance of the semiconductor apparatus is typically adversely affected by such unwanted resonance modes.

[0008] SUMMARY

[0009] The appended claims define the scope of protection. Any examples and technical descriptions of apparatuses, products and / or methods in the description and / or drawings not covered by the claims are presented not as embodiments of the invention but as background art or examples useful for understanding the invention. It is an object of certain embodiments of the present disclosure to provide a scheme to solve at least one of the problems related to the prior art, or at least to provide an alternative to existing technology. Accordingly, certain disclosed embodiments provide for an ingenious resonator solving at least one of the problems related to the prior art.

[0010] According to a first example aspect of the present disclosure there is provided a resonator, comprising a resonating element, wherein the resonating element comprises a plurality of non-rectangular resonating beam elements, the plurality of beam elements being positioned adjacent to each other, wherein the adjacent beam elements are mechanically connected to each other by connection elements and separated from each other by non-linear trenches.

[0011] In certain embodiments, the resonating beam elements are non-rectangular in shape. In certain embodiments, the resonating beam elements have non-rectangular shape. In certain embodiments, the resonating beam elements are non-rectangular in shape. In certain embodiments, a resonating beam element comprises width variation within the beam element (itself).

[0012] In certain embodiments, each resonating beam element is non-rectangular in shape. In certain embodiments, each resonating beam element has non-rectangular shape. In certain embodiments, each resonating beam element is non-rectangular in shape. In certain embodiments, each resonating beam element comprises width variation within the beam element (itself).

[0013] In certain embodiments, (any) two adjacent beam elements are different in shape with each other. In certain embodiments, (any) two adjacent beam elements differ in shape from one another. In certain embodiments, the resonating beam elements are non-rectangular elongated elements. In certain embodiments, the resonating beam elements are of triangle wave shaped. In certain embodiments, the resonating beam elements are of elliptical shape, an hourglass shape, a tapered shape, or a rotated hourglass shape. In certain embodiments, the adjacent beam elements have varied shapes (in comparison to the adjacent beam elements).

[0014] In certain embodiments, the resonating beam element has (comprises) non-linear (nonstraight) edge(s). In certain embodiments, the resonating beam element has (comprises) sine-wave shaped edge(s). In certain embodiments, an edge (long edge, long side) of the resonating beam element has (comprises) a shape of wave, such as sine-wave that creates beam width variation within the beam element (itself). In certain embodiments, both opposing edges of the resonating beam element have (comprise) a shape of a wave, wherein the waves of the opposing edges have opposing phases with one another. In certain embodiments, in the embodiments of the both opposing edges having sine-wave shape, the sine-waves (of the opposite edges) are in opposite phases with respect to each other. In certain embodiments, both opposing edges of the resonating beam element have a shape of sine-wave (and said sine-waves oppose one another in phase) such that the beam element comprises width variation within itself. What is disclosed above for a sine-wave, is applicable also to other wave or bent shapes of beam element edges, such as waves other than sine-shaped, or triangle wave edges.

[0015] In certain embodiments, the opposing edges of the resonating beam element have the same but opposing shapes with each other. In certain embodiments, the opposing edges of the resonating beam element have the same shape, such as a sine-wave of triangular wave shape, but in opposite (phase) with one another. In certain embodiments, the opposing edges of the resonating beam element have the same shape, but in opposite phase with one another such that the beam element comprises width variation within itself.

[0016] In certain embodiments, the resonating beam elements comprise width variation within the beam element (itself). In certain embodiments, the resonating beam elements have interchanging width within the beam element (within itself).

[0017] In certain embodiments, the (each, all) resonating beam element has a symmetrical shape (mirror symmetry). In certain embodiments, the (each, all) resonating beam element has a symmetrical shape (is symmetrical) along the central length axis of the beam element. In certain embodiments, the (each, all) resonating beam element has a symmetrical shape along the central width axis of the beam element.

[0018] Typically, the beam elements comprise four sides, wherein two sides are longer in length than two. As used herein, the two longer sides are called ‘long sides’ and the two shorter sides are called ‘short sides’. In certain embodiments, the resonating beam elements comprise non-straight long sides (the long sides being parallel to the length direction of the beam element). In certain embodiments, the resonating beam elements comprise curved (bendy, wavy, angled, meandering, having multiple turns / curves / waves / meanders / angles) long sides.

[0019] In certain embodiments, the non-rectangular beam element comprises at least one nonlinear side. In certain embodiments, the non-rectangular beam element comprises at least two non-linear sides, such as two non-linear parallel sides. In certain embodiments, the plurality of non-rectangular beam elements match with each other. In certain embodiments, the (any) two adjacent beam elements match each other (in shape). In certain embodiments, the (any) two adjacent beam elements mirror each other (in shape). In certain embodiments, a beam element mirrors in shape its immediately adjacent beam elements (at both sides of the beam element). In certain embodiments, a beam element has a bendy shape matching the shape(s) of its immediately adjacent beam elements (at both sides of the beam element). In certain embodiments, the (any) two adjacent beam elements follow the contours of one another (in shape). In certain embodiments, the (any) two adjacent beam elements conform to each other's shape. In certain embodiments, the (any) two adjacent beam elements complement each other's shape. In certain embodiments, the (any) two adjacent beam elements conform to each other's shape, thereby creating the non-linear trench therebetween. In certain embodiments, the (any) two adjacent beam elements follow the contours of one another, thereby creating the non-linear trench therebetween.

[0020] In certain embodiments, the (any) two adjacent beam elements follow each other’s shape. In certain embodiments, the (any) two adjacent beam elements adapt each other’s shape. In certain embodiments, the (any) two non-rectangular beam elements are separated from one another by a non-linear trench. In certain embodiments, the (any) two non-rectangular beam elements are separated from one another by a non-linear trench, wherein the beam elements’ edges (edges adjacent to the trench, long sides) and the non-linear trench share the same shape.

[0021] In certain embodiments, the trench is non-linear. In certain embodiments, the trench is a non-straight trench. In certain embodiments, the non-linear trench comprises a wavy shape (bendy, angled, meandering, having multiple turns / curves / waves / meanders / angles). In certain embodiments, the non-linear trenches have a bendy (wavy, curvy, meandering) shape, matching the shape of the adjacent beam elements.

[0022] In certain embodiments, the non-linear trench is formed in between the non-rectangular resonating beam elements. In certain embodiments, the non-linear trench is formed in between the non-straight long sides of the resonating beam elements. In certain embodiments, the long side(s) of the resonating elements and the non-linear trench share the same shape. In certain embodiments, the long side(s) of the resonating elements and the non-linear trench mirror each other (in shape).

[0023] In certain embodiments, the non-linear trench follows (copies, adopts) the shape of the adjacent beam elements. In certain embodiments, each non-linear trench has a uniform width. In certain embodiments, each non-linear trench has a uniform width everywhere in between two resonating beam elements. In certain embodiments, the (any) adjacent beam elements are equidistant from one another. In certain embodiments, the (any) adjacent beam elements are equally far (equal distance) from one another (in all locations in between thereof, meaning that the trench is of uniform width). In certain embodiments, the (any) adjacent beam elements are evenly spaced (apart from one another).

[0024] In certain embodiments, the resonating element comprises (at least) two non-rectangular adjacent resonating beam elements, wherein the two adjacent beam elements are different from each other (in shape). In certain embodiments, the non-rectangular resonating beam elements are provided adjacent to one another, thereby creating a non-linear trench therebetween.

[0025] In certain embodiments, the beam elements are placed alternatingly within the resonating element. In certain embodiments, the beam elements of the resonating element are arranged in an alternating configuration. In certain embodiments, the beam elements of the resonating element are arranged in a repeating pattern. In certain embodiments, the alternating configuration comprises at least two (a plurality of, such as three) beam elements of different shape alternating within the resonating element. In certain embodiments, the repeating pattern comprises at least two (a plurality of, such as three) beam elements of different shape repeating within the resonating element.

[0026] In certain embodiments, the adjacent beam elements are different from one another (with each other). In certain embodiments, the two adjacent beam elements (a pair of beam elements) are different from one another (with each other). In certain embodiments, the three adjacent beam elements are different from one another (with each other).

[0027] In certain embodiments, every other beam element is identical with each other. In certain embodiments, every third (fourth, fifth...) beam element is identical with each other.

[0028] In certain embodiments, any two adjacent beam elements of the resonating elements form a pair of resonating beam elements. In certain embodiments, no part of resonating beam elements comprises two identical beam elements. In certain embodiments, each pair of beam elements comprises beam elements with different shapes. In certain embodiments, each pair of beam elements comprises beam elements of different shapes such that the adjacent beam elements follow each other’s shape (thereby forming a non-linear trench in between). In certain embodiments, the resonating element comprises a plurality of said pairs adjacent to each other. In certain embodiments, said adjacent pairs form an alternating configuration of beam elements. In certain embodiments, every other beam element is identical with each other, and the adjacent beam elements are different from one another.

[0029] In certain embodiments, the resonating element is formed of two groups of beam elements, a first group and a second group. In certain embodiments, the beam elements of the first group are identical with one another and the beam elements of the second group is identical with one another. In certain embodiments, the beam elements of the first group and the beam elements of the second group are different in comparison to each other. In certain embodiments, the beam elements of the first group and the second group are arranged in an alternating configuration (first-second-first-second-first-second ... and so on).

[0030] In certain embodiments, the resonating element comprises a top electrode (layer) on the resonating element. In certain embodiments, the top electrode (layer) is the topmost layer (surface) of the resonating element. In certain embodiments, the top electrode is configured to cover essentially the entire resonating element.

[0031] In certain embodiments, the resonating element is symmetrical (mirror symmetry). In certain embodiments, the resonating element is symmetrical along the central length axis of the resonating element (same as the length axis of the beam element). In certain embodiments, the resonating element is symmetrical along the central width axis of the resonating element (same direction as the width of the beam element).

[0032] In certain embodiments, the top electrode is implemented by a layer of metal. In certain embodiments, the top electrode comprises (is of) metal, preferably gold (Au). In certain embodiments, the top electrode is of gold, preferably doped gold. In certain embodiments, the top electrode is of gold alloy.

[0033] In certain embodiments, the top electrode (layer) is implemented by a layer of doped silicon. In certain embodiments, the silicon layer is of single-crystal silicon. In certain embodiments, the top electrode (layer) is implemented by a layer of doped polysilicon.

[0034] In certain embodiments, the resonating element comprises a piezoelectric layer, wherein the piezoelectric layer is beneath the top electrode layer. In certain embodiments, the resonating element comprises a bottom electrode on the opposite side of the piezoelectric layer than the top electrode layer. In certain embodiments, the resonating element comprises a top electrode layer, a piezoelectric layer, and a bottom electrode, wherein the piezoelectric layer is beneath the top electrode layer, and the bottom electrode on the opposite side of the piezoelectric layer than the top electrode layer. In certain embodiments, the resonating element comprises a piezoelectric layer, wherein the top electrode is on the piezoelectric layer, and a bottom electrode on the opposite side of the piezoelectric layer than the top electrode. In certain embodiments, the bottom electrode comprises silicon, preferably doped silicon, such as ultra-heavily doped, UHD, silicon. In certain preferred embodiments, the silicon is of single-crystal silicon. In certain embodiments, the bottom electrode (layer) is implemented by an UHD silicon layer.

[0035] In certain embodiments, the doping level of the silicon is above 1019cm-3. In certain embodiments, the doping level of the silicon is above 1O20cm-3. In certain embodiments, the doped silicon is of N-type or P-type doping.

[0036] In certain embodiments, the resonator comprises a material stack, the material stack comprising the silicon layer (the bottom electrode), the piezoelectric layer on top of the silicon layer, and a top electrode on top of the piezoelectric layer. In certain embodiments, the resonator is a piezoelectric resonator. In certain embodiments, the piezoelectric layer comprises aluminum nitride.

[0037] In certain embodiments, the resonator comprises at least one resonating element. In certain embodiments, the resonator comprises a resonating plate element. In certain embodiments, the resonating element comprises a plurality of resonating beam elements. In certain embodiments, each beam element is a sub-element of the resonating element.

[0038] In certain embodiments, the resonating element comprises a plurality of beam elements having a length and a width. In certain embodiments, each beam element has a length and a width. In certain embodiments, the plurality of beam elements are positioned adjacent to each other. In certain embodiments, adjacent beam elements are mechanically connected to each other by connection elements. In certain embodiments, the resonating element comprises a plurality of resonating beam elements having a length and a width, the plurality of beam elements being positioned adjacent to each other, wherein the adjacent beam elements are mechanically connected to each other by connection elements, such as by two connection elements.

[0039] In certain embodiments, the resonating element is a stacked beam resonating element. In certain embodiments, the stacked beam resonating element comprises a plurality of beam elements positioned side-by-side in a plane. In certain embodiments, the plurality of beam elements are positions adjacent to each other in a width direction thereof. In certain embodiments, the plurality of beam elements are positioned adjacent to each other in a width direction of the resonator. In certain embodiments, the beam elements are separated by trenches. In certain embodiments, the beam elements are separated by vertical trenches. In certain embodiments, the beam elements are separated by vertical trenches extending through the beam element (whole, entire) thickness. In certain embodiments, the beam elements are mechanically separated by trenches. In certain embodiments, the beam elements are electrically separated by trenches. In certain embodiments, the beam elements are entirely separated by trenches.

[0040] In certain embodiments, the beam elements are connected to each other by connection elements. In certain embodiments, the beam elements are connected to each other by at least two connection elements. In certain embodiments, the beam elements are connected to each other by two connection elements. In certain embodiments, the beam elements are connected to each other by connection elements at both ends. In certain embodiments, the beam elements are entirely separated by trenches, except that said beam elements are mechanically connected to each other by connection elements. In certain embodiments, the beam elements are entirely separated by trenches, except that said beam elements are mechanically connected to each other by connection elements at both ends.

[0041] In certain embodiments, the resonating element comprises a plurality of beam elements, such as seven, nine, or eleven beam elements. In certain embodiments, said adjacent beam elements are mechanically connected to each other by at least two connection elements. In certain embodiments, the beam elements of the resonating element are arranged in a rectangular array configuration.

[0042] In certain embodiments, the resonating element is in a shape of a rectangle. In certain embodiments, the resonating element is in a shape of an elongated rectangle (beamshaped). In certain embodiments, the resonating element has an aspect ratio (ratio of length to width, when observed from above) different from 1 .

[0043] In certain embodiments, the resonating element has a length-to-width aspect ratio of less than 1. In certain embodiments, the resonating element is attached (supported, anchored, suspended) to a support structure. In certain embodiments, the resonating element is attached to a support structure from the outermost beam elements of the resonating element. In certain embodiments, the resonating element comprises at least one anchor configured to connect the resonating element to, and suspend the resonating element from surrounding layers (support structure). In certain embodiments the at least one anchor comprises portions of the piezoelectric layer, the top electrode and the bottom electrode. In certain embodiments, the resonating element is separated from the substrate by a cavity (cavity being beneath the resonating element).

[0044] In certain embodiments, each beam element is in a shape of an elongated beam (not limited to rectangular shape). In certain embodiments, each beam element has an aspect ratio (ratio of length to width, when observed from above) different from 1. In certain embodiments, each beam element has a length-to-width aspect ratio of more than 1.

[0045] In certain embodiments, the resonator is fabricated on a substrate. In certain embodiments, the substrate is a wafer. In certain embodiments, the substrate is a silicon-on-insulator, SOI, wafer. In certain embodiments, the substrate comprises a silicon layer. In certain embodiments, the bottom electrode (layer) is referred to as a substrate or as a silicon layer.

[0046] In certain embodiments, the resonating beam element(s) are longitudinally aligned within 25 degrees of a <100> crystal direction of silicon (of the bottom electrode). Within at least some embodiments the resonating beam element(s) are longitudinally aligned with a <100 crystal direction of the silicon (of the bottom electrode) such that a longitudinal axis of each resonating beam is within 25 degrees of the <100> crystal direction of the silicon (of the bottom electrode).

[0047] In certain embodiments, the resonating beam element(s) are longitudinally aligned within 45 degrees, or 50 degrees of a <100> crystal direction of silicon (of the bottom electrode). Within at least some embodiments the resonating beam element(s) are longitudinally aligned with a <100> crystal direction of the silicon (of the bottom electrode) such that a longitudinal axis of each resonating beam is within 45 degrees, or 50 degrees of the <100> crystal direction of the silicon (of the bottom electrode).

[0048] In certain embodiments, the resonating beam element(s) are longitudinally aligned within 25 degrees of a

[0100] crystal direction of silicon (of the bottom electrode). Within at least some embodiments the resonating beam element(s) are longitudinally aligned with a

[0100] crystal direction of the silicon (of the bottom electrode) such that a longitudinal axis of each resonating beam is within 25 degrees of the

[0100] crystal direction of the silicon (of the bottom electrode).

[0049] In certain embodiments, the resonating beam element(s) are longitudinally aligned within 25 degrees of a

[0110] crystal direction of silicon (of the bottom electrode). Within at least some embodiments the resonating beam element(s) are longitudinally aligned with a

[0110] crystal direction of the silicon (of the bottom electrode) such that a longitudinal axis of each resonating beam is within 25 degrees of the

[0110] crystal direction of the silicon (of the bottom electrode).

[0050] In certain embodiments, the resonating beam element(s) are longitudinally aligned within 25 degrees of a

[0111] crystal direction of silicon (of the bottom electrode). Within at least some embodiments the resonating beam element(s) are longitudinally aligned with a

[0111] crystal direction of the silicon (of the bottom electrode) such that a longitudinal axis of each resonating beam is within 25 degrees of the

[0111] crystal direction of the silicon (of the bottom electrode).

[0051] In certain embodiments, the resonator (resonating element) is configured to resonate (operate, oscillate, vibrate) in an in-plane resonance mode. In certain embodiments, the resonating element is configured to resonate in a length-extensional, LE, resonance mode. In certain embodiments, the resonator is configured to resonate in an in-plane lengthextensional, LE, (main) resonance mode. In certain embodiments, the length extensional resonance mode is configured to resonate parallel to the length direction of the resonator. In certain embodiments, the length extensional resonance mode is configured to resonate perpendicular to the width direction of the resonator.

[0052] In certain embodiments, the resonating element is configured to resonate in a squareextensional, SE, resonance mode. In certain embodiments, the resonating element is configured to resonate in a width-extensional, WE, resonance mode.

[0053] In certain embodiments, the resonator (resonating element) is configured to resonate in a collective resonance mode. In certain embodiments, each resonating element of the resonator is configured to resonate in the (same) collective resonance mode. In certain embodiments, the resonator is configured to resonate in a desired (main) resonance mode. In certain embodiments, each beam element of the resonator is configured to resonate in the (same) desired resonance mode.

[0054] In certain embodiments, the resonating element comprises a spurious resonance mode. In certain embodiments, the spurious resonance mode is an unwanted resonance mode. In certain embodiments, the spurious resonance mode is a resonance mode other than the desired (main) resonance mode. In certain embodiments, the spurious resonance mode resonates in a resonance mode other than the desired resonance mode.

[0055] In certain embodiments, the spurious resonance mode is a flexural resonance mode. In certain alternative embodiments, the spurious mode is a width-extensional resonance mode. In certain alternative embodiments, the spurious mode is a differential resonance mode, such as a differential length-extensional resonance mode. In certain embodiments, the resonating element comprises a width-extensional, WE, spurious resonance mode and / or a flexural spurious resonance mode. In certain embodiments, the resonating element comprises an in-plane width-extensional, WE, spurious resonance mode and / or an out-of- plane flexural spurious resonance mode.

[0056] In certain embodiments, the spurious resonance mode is an out of plane resonance mode. In certain alternative embodiments, the spurious resonance mode is an in-plane resonance mode. In certain embodiments, the spurious resonance mode is an out of plane flexural resonance mode. In certain embodiments, the spurious resonance mode is an in-plane width-extensional resonance mode. In certain embodiments, the spurious resonance mode is an in-plane differential length extensional resonance mode. In certain embodiments, the resonating element comprises more than one spurious resonance mode.

[0057] In certain embodiments, the resonating element is configured to suppress spurious resonance mode(s). In certain embodiments, the resonating element is configured to suppress spurious (unwanted) resonance mode(s), such as higher frequency spurious resonance modes in resonators. In certain embodiments, the resonating element is configured to eliminate (alleviate, suppress) a collective spurious resonance mode (of the beam elements) of the resonating element.

[0058] In certain embodiments, the resonator is a microelectromechanical systems, MEMS, resonator. In certain embodiments, the resonator is (part of) a semiconductor device. In certain embodiments, the resonator is configured to operate in a megahertz frequency area. In certain embodiments, the resonator is configured to operate at 32 MHz frequency.

[0059] In certain embodiments, the resonator comprises a plurality of resonating elements adjacent to each other in a plane, connected to one another by a coupler. In certain embodiments, the resonator is a multi-ladder resonator, comprising a plurality of stacked beam resonating elements (forming a ladder-like configuration). In certain embodiments, each resonator comprises a plurality of resonating elements having 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 by connection elements. In certain embodiments, the plurality of beam elements are separated from each other by trenches.

[0060] In certain embodiments, the resonator comprises a plurality of extensional-mode resonating elements. In certain embodiments, the resonator comprises a plurality of length extensionalmode resonating elements. In certain embodiments, the resonator comprises a plurality of flexural-mode resonating elements. In certain embodiments, the resonator comprises a mechanical coupler which connects the resonating elements to one another.

[0061] In certain embodiments, the width of the plurality of beam elements varies within the resonating element In certain embodiments, the resonating element comprises the plurality of beam elements, wherein at least two of the beam elements have a different thickness with each other. In certain embodiments, the resonating element comprises beam width gradation in between the beams. In certain embodiments, the resonating element is configured to alleviate a spurious resonance mode of the resonating element mechanically through having the width variation. In certain embodiments, any two / three, four, five...) adjacent beam elements of the plurality of beam elements are of different width with (respect to, respective to, in comparison to) each other. In certain embodiments, the resonating beam elements comprise width variation with respect to other beam element (compared to other beam elements). In certain embodiments, the resonating beam elements have interchanging widths within the resonating element (compared to other beam elements, amongst each other).

[0062] In certain embodiments, the plurality of beam elements have varying widths with one another are arranged (positioned) asymmetrically in the resonating element. In certain embodiments, each of the plurality of beam elements has a unique (different) width in comparison to each other. In certain embodiments, outermost beam elements of the resonating element have same widths whilst all other beam elements of the resonating element have varying widths (amongst each other).

[0063] In certain embodiments, the width of (each of) the plurality of beam elements varies with each other less than 20%, such as less than 15% of the average width of the beam elements. In certain embodiments, the width of the plurality of beam elements varies with each other more than 1 %, such as more than 5% or more than 10% of the average width of the beam elements. In certain embodiments, the width of the beam elements varies from another beam element by 0.1 pm to 2 pm (a width difference being in between 0.1 pm and 2 pm), such as by 0.3 pm to 0.5 pm, such as by 0.4 pm.

[0064] In certain further embodiments, the resonating element is configured to alleviate a disturbance (effect, harmful effect) caused by a spurious resonance mode of the resonating element by varying the width of the beam elements (width variation) within the resonating element. In certain further embodiments, the resonating element is configured to alleviate a disturbance caused by a spurious resonance mode by varying the width of the beam elements asymmetrically within the resonating element. In certain embodiments, the resonating element is configured to alleviate the disturbance caused by the spurious resonance mode by modifying (splitting) equivalent series resistance, ESR, of said spurious resonance mode of the resonating element.

[0065] According to a second example aspect of the present disclosure there is provided an apparatus, such as a resonator array (an apparatus), comprising at least one resonator according to the first aspect or any of its embodiments. In certain embodiments, the apparatus comprises (at least) two (more than one) resonators of the first aspect or any of its embodiments coupled to each other. In certain embodiments, the apparatus is a semiconductor apparatus.

[0066] In certain embodiments, the apparatus comprises extensional-mode resonator(s). In certain embodiments, the apparatus comprises flexural mode resonator(s). In certain embodiments, (all, some of) the resonators of the apparatus are identical with one another (each other). In certain alternative embodiments, (all, some of) the resonators of a resonator are different from one another.

[0067] In accordance with certain embodiments, embodiments of the second aspect are provided, the embodiments comprising subject matter of any single embodiment presented in connection with the first aspect, or the embodiments comprising subject matter of any of the embodiments presented in connection with the first aspect combined with subject matter presented in any other embodiment or embodiments.

[0068] Different non-binding example aspects and embodiments have been illustrated in the foregoing. The embodiments in the foregoing are used merely to explain selected aspects or steps that may be utilized in different implementations. Some embodiments may be presented only with reference to certain example aspects. It should be appreciated that corresponding embodiments may apply to other example aspects as well. In particular, the embodiments described in the context of the first aspect are applicable to each further aspect. Any appropriate combinations of the embodiments may be formed.

[0069] BRIEF DESCRIPTION OF THE FIGURES

[0070] Some example embodiments will be described with reference to the accompanying figures, in which:

[0071] Fig. 1 schematically shows a top view of a conventional resonating element in a top view according to an example embodiment; Fig. 2 schematically shows a cross-section of the material stack of an example resonator according to an example embodiment;

[0072] Fig. 3a schematically shows a top view of a resonating element having triangular wave beam elements according to an example embodiment;

[0073] Fig. 3b schematically shows a top view of a resonator having multiple resonating elements having sine-wave edged beam elements coupled by a coupler according to an example embodiment;

[0074] Fig. 4a schematically shows triangular wave edged beam elements according to example embodiments;

[0075] Fig. 4b schematically shows sine-wave edged beam elements according to example embodiments;

[0076] Fig. 4c schematically shows beam elements having one opposing edge different from the other according to example embodiments; Fig. 5a schematically shows an example of spurious resonance mode from top view according to an example embodiment;

[0077] Fig. 5b schematically shows another example of spurious resonance mode from side view according to an example embodiment; and

[0078] Fig. 6 schematically shows an example illustration of resonance mode splitting according to an example embodiment.

[0079] DETAILED DESCRIPTION

[0080] In the following description, like reference signs denote like elements or steps.

[0081] As used herein, the term “beam” or “beam-shaped” is used to refer to a beam-like elongated shape. Accordingly, the “beam” or “beam-shaped” refers to a (relatively) long and narrow shaped element, such that the beam element has a length-to-width, L-to-W, aspect ratio of more than 1 . It should be noted that in the context of the present disclosure, the “beam” elements are not limited to rectangular shaped elements.

[0082] As used herein, the term “width of the resonating (beam) element” or “width-wise” refers to the horizontal direction, meaning the direction of left to right (or right to left), when observing the resonator or the resonating element from above. This refers to the x-direction according to the chosen coordinate system. In the example embodiments shown in Fig. 1 , the x- direction is equal to the width direction of the resonating element and the resonating beam element.

[0083] Analogously, as used herein, the term “length of the resonating (beam) element” or “lengthwise” refers to the vertical direction, meaning the direction of up and down (or down to up, when observing the resonator or the resonating element from above). This refers to the y- direction according to the chosen coordinate system. In the example embodiments shown in Fig. 1 , the y-direction is equal to the length direction of the resonating element and the resonating beam element.

[0084] Yet analogously, as used herein, herein is also used a direction of left to right (or right to left), when observing the resonator of the resonating element from the side (cross-sectional view), meaning the z-direction according to the chosen coordinate system. In the example embodiments shown in Fig. 2, the z-direction is referred as a “height” direction of the resonator.

[0085] As used herein, the term “material stack” refers to the resonator materials that form the cross-sectional layer structure of the resonator. Thus, the term stack refers to a cross- sectional stack, meaning that the materials can be seen on top of each other once observing the cross-section of the resonator. When observed from the top, only the topmost layer of the particular region can be seen. In accordance with certain embodiments, some of the materials of the material stack originate from the substrate itself (such as the silicon layer), and some of the materials are provided / deposited onto the substrate.

[0086] As used herein, the notation ‘the layer X beneath the layer Y’ refers to the layer X being underneath the layer Y within the material stack / pile in question. Synonyms for the notation are, by way of example, under, underneath, and below. As used herein, the notation “the layer X on the layer Y” refers to the layer X being above the layer Y within the material stack in question. Synonyms for the notation are, by way of example, on top of, onto and above. In certain embodiments, these notations can be understood as “the layer X being in contact with the layer Y”. However, the instant solution is not limited to those embodiments.

[0087] Fig. 1 schematically shows a top view (from above, from up to down) of a conventional resonating element 101.

[0088] In certain embodiments, the resonator 100 comprises at least one resonating element 101. In certain embodiments, the resonator 100 comprises a resonating plate element 101 (not shown in Fig. 1). In certain embodiments, the resonator 100 comprises a plurality of resonating elements 101 (not shown in Fig. 1).

[0089] The resonating element 101 according to embodiment shown in Fig. 1 comprises a plurality of resonating beam elements having a length L and a width W. In certain embodiments, the resonating beam elements are beam-shaped. In the conventional embodiment shown in Fig. 1 , each resonating beam element is in the shape of a rectangular beam (beam-shaped).

[0090] In the embodiment shown in Fig. 1 , the resonating element 101 comprises seven resonating beam elements (the number of beam elements may vary depending on the embodiment). In certain embodiments, the resonating beam elements are longer L than they are wide W. In certain embodiments, the coordinate system is selected so that the x-axis resides in the width direction W of the resonating elements 101 and the y-axis in the longitudinal direction L of the resonating beam elements.

[0091] According to the example embodiment shown in Fig. 1 , the plurality of resonating beam elements are positioned adjacent to each other. In certain embodiments, the plurality of resonating beam elements form a ladder-like configuration (stacked beam resonator). In certain embodiments, the plurality of resonating beam elements are positioned adjacent to each other in a width direction thereof. The adjacent resonating beam elements are mechanically connected to each other.

[0092] In certain embodiments, the resonating element 101 is formed of the plurality of resonating beam elements and a plurality of connection elements 102. In certain embodiments, said adjacent resonating beam elements are mechanically connected to each other by connection elements 102. In certain embodiments, the resonating beam elements are connected to each other (one another) by (at least) two connection elements 102. In certain embodiments, each resonating beam element is connected to another resonating beam element by (at least) two connection elements 102. In certain embodiments, the adjacent resonating beam elements are separated by trenches 104. In certain embodiments, the trenches 104 extend vertically through the material stack of the beam elements, in certain embodiments, the trenches are “through”-trenches (extending all the way through the material stack). In certain embodiments, the beam elements are coupled to each other by at least two connection elements, and otherwise separated from each other by trenches 104. In certain embodiments, the beam elements are mechanically coupled to each other by at least two connection elements, and otherwise mechanically separated from each other by trenches 104. In certain embodiments, the trenches 104 have a length TL (trench length). In certain embodiments, the length L of the beam element comprises at least the length of the trench TL and the length of at least one connection element 102.

[0093] In certain preferred embodiments, the resonating element 101 is a stacked beam resonating element comprising a plurality of resonating beam elements positioned side-by-side in a plane, separated by trenches 104 and connected by (at least two, or two) connection elements 102. In at least some stacked beam resonating elements, the resonating beam elements are positioned in the same plane. In certain stacked beam resonating elements, no two resonating beam elements are positioned atop each other.

[0094] In certain embodiments, the resonating beam elements of the resonating element 101 are arranged in a rectangular array configuration. In certain embodiments, the resonating elements 101 of the resonator 100 are arranged in a rectangular array configuration. In certain embodiments, the resonating element 101 has a length L (which is equal to the length of the beam element). In certain embodiments, the resonating element 101 has a width RW (resonating element width).

[0095] In certain embodiments, the resonating element 101 is attached to a support structure (not shown in Fig. 1). In certain embodiments, the resonating element 101 is attached to the support structure 110 from the outermost resonating beam elements of the resonating element 101 by anchoring point(s) 103. In certain embodiments, the resonator 100 comprises electrical terminal(s) at anchoring points 103. In certain embodiments, the resonating element(s) 101 is separated from the support structure 110 by (an external) trench 104’.

[0096] In certain embodiments, the resonating element 101 is of an elongated shape (having the length L smaller than their width RW). In certain embodiments, the resonating element 101 is in the shape of a rectangle (the resonating element 101 has a shape of a rectangle). In certain embodiments, the resonating element 101 has an aspect ratio (ratio of length L to width RW, when observed from above) different from 1. In certain embodiments, the resonating element 101 has a length-to-width, L-to-RW, aspect ratio of less than 1.

[0097] In certain embodiments, the resonating beam elements are of an elongated shape (having their length L larger than their width W). In certain embodiments, each resonating beam element has an aspect ratio (ratio of length L to width W, when observed from above) different from 1. In certain embodiments, each resonating beam element has a length-to- width, L-to-W, aspect ratio of more than 1. In certain example embodiments, each resonating beam element has a length-to-width, L-to-W, aspect ratio of more than 2, such as 5, 8, or 10.

[0098] In certain embodiments, each beam element is a resonating beam element. In certain embodiments, the resonating element is configured to resonate in a desired (main) resonance mode. In certain embodiments, the desired resonance mode is a collective resonance mode. In certain embodiments, each beam element of the resonating element 101 is configured to resonate in the same resonance mode.

[0099] In certain embodiments, the resonator 100 (the resonating element 101) is configured to operate in an in-plane length extensional, LE, resonance mode. In certain embodiments, the in-plane length extensional resonance mode is a main resonance mode of the resonating element 101. In certain embodiments, the beam elements of the resonating element 101 are configured to operate in an in-plane length extensional resonance mode. The beam elements (and thus the whole resonating element 101) oscillate in the LE-mode in the direction of the y-axis (in the direction of the length L direction, parallel to the longitudinal direction).

[0100] Typically, resonating element(s) 101 are configured to operate (resonate, vibrate, oscillate) in a desired (collective) main resonance mode. In certain occasions, the resonating element 101 adopts another, unwanted, spurious resonance mode. This unwanted spurious resonance mode typically comprises a lower ESR than the desired main resonance mode. Therefore, the unwanted spurious resonance mode typically dissipates less energy than the desired main resonance mode, making it eventually a dominant resonance mode for selfsustained oscillation. The performance of the resonator 100 is adversely affected by such unwanted, spurious resonance mode(s). In certain embodiments, the spurious resonance mode is a resonance mode other than the desired main resonance mode. In certain embodiments, the resonating element 101 comprises (resonates in) a spurious resonance mode (in addition to the main resonance mode).

[0101] Fig. 2 schematically shows a cross-section of the material stack of a resonator 100 according to an example embodiment. Fig. 2 schematically shows an example cross section (sectional view, side view) of the resonator 100 residing on a substrate 450.

[0102] In certain embodiments, the resonator 100 is fabricated on a substrate. In the example embodiment of Fig. 2, a silicon on insulator (SOI) substrate (wafer) 450 is used. The reference numerals 401 and 402 denote bottom electrode and top electrode contacts, respectively. The reference numeral 101 denotes the location of the resonating element 101. In certain embodiments, the resonating element(s) 101 is separated from its surroundings by (an external) trench 104’. In certain embodiments, the trench 104 isolates the resonating element 101 mechanically from its surroundings. In certain embodiments, the trench 104’ extends vertically through the material stack of the resonating element 101 . In certain embodiments, the resonating element 101 is suspended from its surroundings by anchoring point(s) 103 (not visible in Fig. 2).

[0103] In certain embodiments, the resonator 100 (and the resonating element 101) comprises a material stack, the material stack comprising at least the silicon layer L4, the piezoelectric layer L2 on top of the silicon layer, and a top electrode L1 on top of the piezoelectric layer. In certain embodiments, the piezoelectric layer comprises doping, such as scandium doping.

[0104] In the example embodiment shown in Fig. 2, the top electrode is implemented in layer L1. In this example embodiment, layer L2 is a piezoelectric layer for piezoelectric actuation of the resonator. An opening in L2 is denoted by 420. In this example embodiments, layer L3 denotes a layer for the bottom electrode. In this example embodiment, layer L4 is a silicon layer for the resonator (for example resonating beam elements and their connecting elements according to certain embodiments). In this example embodiments, layer L5 is a buried oxide layer (SiO2) of the SOI wafer, and layer L6 is a silicon handle layer. In certain embodiments layer L6 comprises a cavity C1. In certain embodiments, the layer L5 follows the cavity C1 shape as shown in Fig. 2.

[0105] In certain embodiments, when a doped silicon layer is used as L4, it is possible to leave out the separate L3 bottom electrode. In such embodiments, the conductive doped silicon layer L4 acts as the bottom electrode. In certain embodiments, the silicon layer L4 comprises degenerately doped silicon. In certain embodiments, more than 50 % of the silicon layer L4 mass consists of degenerately doped silicon. In certain embodiments, the silicon layer L4 is doped to an average impurity concentration of at least 2*1019cm-3, such as at least 102° cm-3. In certain embodiments, the doped silicon is of N-type or P-type doping. In certain embodiments, the bottom electrode comprises ultra-heavily doped, UHD, silicon.

[0106] In certain embodiments, the silicon layer L4 comprises single crystalline silicon. In certain embodiments, the silicon layer L4 consists essentially of single crystalline silicon. In certain embodiments, the silicon layer L4 comprises degenerately doped single crystalline silicon. In certain preferred embodiments, the resonator 100 comprises a material stack, the material stack comprising the silicon layer L4 (the bottom electrode), the piezoelectric layer L2 on top of the silicon layer L4, and a top electrode L1 on top of the piezoelectric layer L1. In certain embodiments, the resonator 100 is a piezoelectric resonator. In certain embodiments, the piezoelectric layer L2 comprises aluminum nitride.

[0107] In certain embodiments, the longitudinal axis L of a resonating element 101 (the resonating beam elements) is aligned with <100> crystal direction of the silicon (of the bottom electrode), such as aligned with

[0100] crystal direction of silicon (of the bottom electrode), or deviates less than 25 degrees therefrom, or less than 15 degrees therefrom in certain embodiments. In certain preferable embodiments, the longitudinal axis L of the resonating element (the resonating beam elements) 101 is aligned with <100> crystal direction of the silicon (of the bottom electrode), such as aligned with

[0100] crystal direction of the silicon (of the bottom electrode), or deviates less than 5 degrees therefrom, or less than 2 degrees therefrom in certain embodiments.

[0108] Fig. 3a schematically shows a top view of a resonating element 101 having beam elements with triangular wave shaped edges according to an example embodiment. The resonating element 101 of Fig. 3a corresponds with the resonating element 101 shown in Fig. 1 , except that Fig. 3a shows the non-linear trenches 104 in between the non-rectangular beam elements in accordance with the embodiment of the present disclosure.

[0109] As shown in Fig. 3a, in certain embodiments, each resonating beam element of the resonating element 101 has non-rectangular shape. In certain embodiments, the non- rectangular shape is provided by interchanging (varying, changing) the width of the beam element within the beam element itself. This means that the non-rectangular beam element has a different width in one point thereof in comparison to some other point. As shown in Fig. 3a, every other beam elements are wider in the length-wise central area, and narrower at the beam ends (tapered beam). On the other hand, every other beam element is narrower in the length-wise central area, and wider in the beam end areas (hour-glass beam).

[0110] The Fig. 3a shows an embodiment, wherein the beam elements are triangular wave beam elements. Typically, the beam elements comprise four edges or sides, wherein two sides are longer in length than two. As used herein, the two longer sides are called ‘long edges / sides’ and the two shorter sides are called ‘short edges / sides’. As shown in Fig. 3a, the resonating beam elements have angled long edges / sides (edges / sides having an angle), more specifically triangular arranged long edges / sides. According to certain embodiments, the beam elements have edges of triangular wave shapes such that the shapes of the edges oppose each other (are in opposite phases with one another), as shown in Fig. 3a.

[0111] In certain embodiments, the non-rectangular beam elements are separated from one another by non-linear trenches 104. As shown in Fig. 3a, the non-linear trenches 104 are non-straight trenches 104. In certain embodiments, the non-linear trenches 104 are of wavy shape, having multiple (subtle) bends. As shown in Fig. 3a, in certain embodiments, the non-linear trenches 104 are formed in between the non-rectangular resonating beam elements. Accordingly, the resonating beam elements (more particularly, their long sides) and the non-linear trench 104 therebetween mirror each other’s shape. In other words, they follow or copy each other’s shape, and follow the contours of one another, in accordance with certain embodiments. In further words, the resonating beam elements (more particularly, their long sides) and the non-linear trench 104 therebetween conform to each other's shape, or complement each other's shape, in accordance with certain embodiments.

[0112] Following the previous point, in certain embodiments, each non-linear trench 104 has a uniform width, such that the adjacent beam elements are equidistant from one another.

[0113] As shown in Fig. 3a, in certain embodiments, any two adjacent beam elements of the plurality of resonating beam elements are different from each other in shape. This is a result of the provision of the non-rectangular beam elements, separated from one another by nonlinear trenches 104.

[0114] In accordance with certain embodiments, the beam elements of the resonating element 101 are arranged in an alternating configuration, wherein the alternating configuration comprises two beam elements of different shape alternating within the resonating element 101 . In the embodiment shown in Fig. 3a, the hourglass and the tapered beam elements alternate within the resonating element.

[0115] In certain embodiments, such as shown in Fig. 3a, the leftmost and / or the rightmost beam elements of the resonating element are rectangular beam elements. In certain embodiments, such as shown in Fig. 3a, the two leftmost and / or the two rightmost beam elements of the resonating element differ from the centrally located beam elements.

[0116] Accordingly, herein is provided a resonator 100, comprising a resonating element 101 , wherein the resonating element 101 comprises a plurality of non-rectangular resonating beam elements having a length L and a width W, the plurality of beam elements being positioned adjacent to each other, wherein the adjacent beam elements are mechanically connected to each other by connection elements 102 and separated from each other by non-linear trenches 104.

[0117] By providing non-rectangular beam elements separated by non-linear trenches 104, the resonating element 101 enables suppressing (or partially suppressing, or alleviating, or lessening the effect of) spurious resonance mode(s) within the resonating element 101 , especially high frequency spurious resonance mode(s). Typically, in a case for a constant width, such as rectangular, beam element, larger portion(s) of the beam resonates with a given frequency. In accordance with certain embodiments, for a beam element having beam width variation (within the beam itself), smaller portion(s) of the beam element resonate at said frequency. Thereby, in accordance with certain embodiments, the non-rectangular beam elements having width variation within the beam element itself, separated by nonlinear trenches 104 enable suppressing (at least partially) the spurious resonance mode(s) since the spurious resonance mode(s) are arranged into only the smaller portion(s) of the resonating beam element. Thus, in certain embodiments, the spurious resonance mode suppression occurs mechanically. The resonating element 101 enables suppressing said spurious resonance mode(s), but does not adversely affect (or ruin) the main resonance mode in accordance with certain embodiments. In certain embodiments, the resonating element 101 is configured to alleviate the spurious resonance mode by suppressing said spurious resonance mode of the resonating element by providing non-rectangular resonating beam elements adjacent to one another, thereby creating a non-linear trench 104 therebetween.

[0118] Figs. 3b schematically shows a resonator 100 comprising a plurality of resonating elements 101 in accordance with certain embodiments. In certain embodiments, the resonator 100 comprises (at least) two resonating elements 101a, 101b (stacked beam resonating elements). All embodiments described in context of a single resonating element 101 apply herein as well for the plurality of resonating elements 101 of the resonator 100 as shown herein.

[0119] In certain embodiments, such as shown in Fig. 3b, the resonator 100 comprises a mechanically coupled assembly with multiple ‘ladders’ 101 to achieve higher resonator area and improved quality factor (Q). In certain embodiments, the resonator is a multi-ladder resonator 100, comprising a plurality of stacked resonating elements 101a, 101b. In certain embodiments, the resonating elements 101a, 101b comprise a plurality of resonating beam elements positioned adjacent to each other and adjacent beam elements are mechanically connected to each other by connection elements 102, and the resonating beam elements are separated from each other by trenches 104 (forming a ladder-like configuration). In certain embodiments, the resonator 100 is separated from a support structure by an external trench 104’. In certain embodiments, the resonator 100 is coupled to (suspended from) a support structure via anchoring point(s) 103.

[0120] Analogously with Fig. 3a, Fig. 3b shows resonating elements having plurality of non- rectangular beam elements separated from one another by non-linear trenches 104. Both the edges of the beam elements (the long sides thereof) and the non-linear trenches 104 share the sine-wave shape. The Fig. 3b shows an embodiment, wherein the edges of the beam elements have sine-wave shapes. As shown in Fig. 3b, the resonating beam elements have bendy edges (long edges, long sides), more specifically sine-wave shaped edges. As used herein, the term "sine-wave" edges of the beam elements are used to refer to the resonating beam element’s edge having a sine-wave shape. It should be noted that the beam element itself does not need to be sine wave shaped. As seen from the Fig. 3b, the beam elements themselves are not in a shape of sine-wave, but their edges have that shape.

[0121] In certain embodiments, an edge (long edge, long side) of the resonating beam element comprises a shape of sine-wave that creates beam width variation within the beam element (itself). In certain embodiments, both opposing edges (long edges, long sides) of the resonating beam element comprise a shape of sine-wave that creates beam width variation within the beam element.

[0122] As shown in Fig. 3b, in the embodiments of the both opposing edges having sine-wave shape, the sine-waves (of the opposite edges) are in opposite phases with respect to each other. It should be noted that what is herein disclosed for a sine-wave, applies analogously to any wavy or bendy shaped edge of the beam element. The embodiments are not limited to only sine-wave shapes, but comprise any wavy or bendy shapes, such as irregular bendy shapes, or regular but non-sine-wave shapes.

[0123] In certain embodiments, the adjacent beam elements are different in shape from one another, but their shapes match with one another. Accordingly, as shown in Fig. 3b, the beam element’s edge comprises an opposing shape in comparison to the adjacent beam element’s edge. In certain embodiments, the two adjacent beam elements both have a wavy shapes edges, but the waves oppose each other with the edge of the adjacent beam element. This enables providing the non-linear trench therebetween with uniform width. In accordance with certain embodiments, such as shown in Fig. 3b, every other beam element has an identical shape with each other. Thus, in certain embodiments, the beam elements are in a repeating pattern, the repeating pattern comprising two beam elements of different shape repeating (in an alternating manner) within the resonating element. By way of an example, herein the alternating repeating pattern of the two types of beams, denoted as T1 and T2 here, beams can be described by: T1-T2-T1-T2-T1-T2... and so on. In certain embodiments, the outermost beam elements differ from the other (alternating) beam elements.

[0124] In certain embodiments, the resonator 100 comprises a mechanical coupler 310 which connects the resonating elements 101a, 101 b to one another. The embodiment of Fig. 5b shows a flexural mode coupler 310. Other alternatives for the coupler include, but are not limited to rigid coupler 310, such as a beam coupler, length extensional, LE, coupler 310, and Lame mode coupler 310 (not shown).

[0125] Accordingly, in certain embodiments, the resonator 100 comprises (at least) two extensional-mode resonating elements 101a, 101b, and a (one or more) flexural mode coupler 310. Further, the resonator assembly comprises a (one or more) mechanical connector element 320 which connects the flexural coupler 310 to the extensional mode resonating elements 101a, 101b. In certain embodiments, at least one of the extensionalmode resonating elements 101a / 101b of the resonator 100 comprises a piezoelectric thin- film actuator for exciting the said extensional-mode resonating element 101a / 101b to a resonance mode and thereby the whole resonator 100 to a collective resonance due to mechanical coupling of the extensional-mode resonating elements 101a, 101 b. In certain alternative embodiments, the resonator 100 comprises an electrostatic actuator for exciting at least one of the extensional-mode resonating elements 101a / 101 b to a resonance mode and thereby the whole resonator 100 to a collective resonance due to mechanical coupling of the extensional-mode resonating elements 101a / 101b.

[0126] In certain embodiments, more than 50% of the mass of the resonator 100 comprise material portions of single-crystalline silicon. In certain embodiments, the coupler 310 comprises discontinuity regions (not shown). In certain embodiments, the discontinuity regions of the coupler 310 render the coupler 310 electrically inert.

[0127] In certain embodiments, (all) the resonating elements 101a, 101b of a resonator 100 are identical with one another (each other). In certain embodiments, (all, some of) the resonating elements 101a, 101b of a resonator assembly are different from one another. Figs. 4a, 4b and 4bc schematically show different shapes for the resonating non-rectangular beam elements according to example embodiments. Figs. 4a, 4b and 4c show alternatives of one beam element. A plurality of said beam elements are shown adjacent to each other within a resonating element 101 in example embodiments of Figs. 3a and 3b.

[0128] As shown in Figs. 4a, 4b and 4c, each non-rectangular beam element is in the shape of an elongated beam. In certain embodiments, each beam element has an aspect ratio (ratio of length to width, when observed from above) different from 1 . In certain embodiments, each beam element has a length-to-width aspect ratio of more than 1 .

[0129] In certain embodiments, each resonating beam element shown in Figs. 4a and 4b has a symmetrical shape. In certain embodiments, the symmetrical shape comprises mirror symmetry along its central y-axis (length direction of the beam element) and / or along its central x-axis (width direction of the beam element). These axes are shown in the left side beam element of Fig. 4a as dashed lines SY and Sx.

[0130] It should be noted that the beam elements are not limited to symmetrical beam elements. In certain embodiments, asymmetrical non-rectangular beam elements are provided (with respect to x-axis, and / or y-axis).

[0131] Fig. 4a shows a triangular (wave) shaped beam element (left side in Fig. 4a) and an hourglass shaped beam element (right side in Fig. 4a). In certain embodiments, a resonating element 101 having the beam elements as shown in Fig. 4a comprises the triangular shaped beam elements and the hour-glass shaped beam elements alternatingly adjacent to each other, thereby forming non-linear trenches 104 in therebetween. The triangular shape and the hour-glass shape of the beam elements adjacently with one another in an alternating sequence enable providing the uniform width of the non-linear trench 104. Accordingly, the triangular beam element and the hour-glass beam element positioned adjacent to each other follow each other’s shape, rendering the trench 104 therebetween curved (non-linear) and of uniform width. The embodiment shown in Figs. 3a comprises these two types of beam elements placed alternatingly adjacent to each other.

[0132] Fig. 4b shows various sine-wave beam elements according to example embodiments. As used herein, the term “sine-wave” is used to refer to a curve representing periodic oscillations of constant amplitude as given by a sine function. In certain embodiments, beam elements having sine-wave edges are provided herein. It should be noted that the wavy or bendy beams are not limited to sine-wave beams. In certain embodiments, the beam elements are of any wavy, bendy, or curvy shape that matches the wavy, bendy or curvy shape of the adjacent beam element.

[0133] In certain embodiments, the opposing edges of a wavy beam element are of different wave shape (resulting in an irregular beam element having width variation therein). In certain embodiments, the opposing edges of a wavy beam element share the same wavy shape but in opposite phase (resulting in a regular beam element having width variation therein).

[0134] As shown in Fig. 4b, the edge of the beam element having a wavy shape may comprise the one or more crests (and similarly troughs). As used herein, the highest part of a wave is called the crest, and the lowest part is the trough. The location of the crest is also the location of the maximum amplitude of the wave.

[0135] The leftmost beam in Fig. 4b shows a beam element with sine-wave shaped edges that oppose each other, having one crest and two troughs within the length of the beam. The second beam from left in Fig. 4b shows a beam element with sine-wave shaped edges that oppose each other having two crests and one trough within the length of the beam. The second beam from the right in Fig. 4b shows a beam element with sine-wave shaped edges that oppose each other having two crests and three troughs within the length of the beam. The rightmost beam in Fig. 4b shows a beam element with sine-wave shaped edges that oppose each other having three crests and two troughs within the length of the beam.

[0136] The leftmost beam and the second beam from the left in Fig. 4b when placed adjacent to each other provide a non-linear trench 104 therebetween, wherein the trench 104 is of uniform width. These beam elements mirror each other’s shape. The embodiment shown in 3b comprises these two types of beam elements placed alternatingly adjacent to each other.

[0137] Similarly, the rightmost beam and the second beam from the right in Fig. 4b fulfil the same, when placed adjacent to each other they provide a non-linear trench 104 therebetween, wherein the trench 104 is of uniform width.

[0138] Fig. 4c schematically shows beam elements having one opposing edge different from the other according to example embodiments. As shown in Fig. 4c, in certain embodiments, (only) one edge of the resonating beam element has a non-linear shape.

[0139] As shown on the left side in Fig. 4c, in certain embodiments, one edge of the resonating beam element has a non-linear shape, such as a triangular wave shape. As shown on the right side in Fig. 4c, in certain embodiments, one edge of the resonating beam element has the shape of wave, such as sine-wave. By having one linear and one non-linear opposing edge, the beam element comprises width variation within itself along its length.

[0140] In certain embodiments, each resonating beam element shown in Fig. 4c has an asymmetrical shape, more particularly mirror symmetry along its central y-axis (length direction of the beam element).

[0141] The spurious resonance mode is an unwanted resonance mode (other than the desired main resonance mode). Figs. 5a and 5b schematically show examples of spurious resonance modes according to an example embodiment, in which the main resonance mode is an in-plane length extensional, LE, resonance mode. In certain embodiments, each beam element of the resonating element 101 is configured to resonate in the (same) main resonance mode, namely in the in-plane length extensional, LE, resonance mode.

[0142] Fig. 5a schematically shows an example of a spurious resonance mode from a top view. Fig. 5a shows a resonating element 101 having rectangular beam elements. In the example embodiment shown in Fig. 5a, the spurious resonance mode is a width-extensional, WE, resonance mode, in particular an in-plane width-extensional resonance mode. In this example spurious resonance mode, the displacement occurs in-plane, but in width direction instead of the desired length direction.

[0143] Fig. 5b schematically shows another example of spurious resonance mode from a side view. Fig. 5b shows a resonating element 101 having rectangular beam elements. In the example embodiments shown in Fig. 5b, the spurious resonance mode is a flexural resonance mode, in particular an out of plane flexural resonance mode. In this example spurious resonance mode, the displacement occurs out of plane, instead of the desired length direction. In this example, the spurious resonance mode is beam-width directional flexural mode, BW-flex, mode. In accordance with certain embodiments, the cut(s) where the top electrode layer is absent are configured to suppress both WE and BW-flex spurious modes.

[0144] In certain alternative embodiments (not shown), the spurious mode is a differential resonance mode, such as an in-plane differential length-extensional resonance mode.

[0145] Accordingly, in certain preferred embodiments, the main resonance mode of the resonating element (and thereby the resonance mode of each resonating beam element) is an in-plane length-extensional, LE, resonance mode. In certain cases, the spurious resonance mode(s) (of the resonating element or the resonating beam element) comprise an out-of-plane flexural resonance mode and / or an in-plane width-extensional, WE, resonance mode.

[0146] Fig. 6 schematically shows an example illustration of resonance mode splitting according to an example embodiment. The upper part of Fig. 6 shows a conventional rectangular beam element (left side) and its one possible spurious resonance mode (right side). The lower part of Fig. 6 shows a non-rectangular beam element (left side) and its possible split spurious resonance modes.

[0147] In certain occasions, the spurious resonance mode is present in a large portion of, or the entire resonating element 101 , such as shown in Figs. 5a and 5b. However, in certain occasions, the spurious resonance mode is present in only a single resonating beam element. In certain cases, this single beam spurious resonance mode may be strong, due to its low impedance. In accordance with the present disclosure, the instant solution enables weakening the transduction of the spurious resonance mode(s) of the single beam elements, such as the width-extensional WE, and / or the beam-width directional flexural spurious resonance mode(s), by varying the beam element width within the beam element. According to certain embodiments, herein is provided non-rectangular beam elements having varying width within each beam element, separated by non-linear trenches 104.

[0148] As shown in the upper part of Fig. 6, a large portion of the conventional rectangular beam element is involved in the spurious resonance mode shape. This leads to a large number of electrical charges accumulated within the resonating beam element.

[0149] In contrast, as shown in the lower part of Fig. 6, for the non-rectangular beam element having beam width variation within the beam itself, the spurious resonance mode shape is split into smaller spurious resonance modes. In the ‘smaller’ spurious resonance modes, a smaller portion (in comparison to the rectangular beam) of the non-rectangular beam element is involved in the spurious resonance mode shape. This leads to a smaller number (in comparison to the rectangular beam) of electrical charges accumulated within the resonating beam element. Accordingly, the embodiment of lower part of Fig. 6 shows reducing the harmful electrical charge collection of the beam element, by splitting the spurious resonance mode shape into smaller spurious resonance modes. In certain embodiments, the resonating beam element comprises at least two (split, less harmful, smaller) spurious resonance modes after said splitting of the (original, non-splitted, larger, harmful) spurious resonance mode (as the term "splitting" suggests). The arrows from the upper right side resonating beam towards the lower part resonating beams of Fig. 6 represent said splitting of the spurious resonance mode.

[0150] In certain embodiments, the resonating element 101 is configured to suppress spurious resonance mode(s), such as higher frequency spurious resonance modes in resonators 100. In accordance with certain embodiments, the resonating element 101 comprises means for suppressing the spurious resonance mode(s) of the resonating beam elements by reducing the harmful charge collection (of the beam element) by splitting the spurious resonance mode shape into smaller spurious resonance modes. These smaller spurious resonance modes are less harmful.

[0151] In certain embodiments, the resonator 100 is configured to alleviate a disturbance caused by a spurious resonance mode of the resonating element(s) by varying the width of the beam elements of the resonating element. The said beam width variation comprises the provision of non-rectangular resonating beam elements having interchanging width within the beam element, adjacent to one another, thereby creating a non-linear trench 104 therebetween, and / or the provision of beam elements with different width in comparison to other beam elements (widths differ amongst the beam elements).

[0152] In certain embodiments, the resonating beam elements of the resonating element(s) comprise beam width gradation. As used herein, the term beam width gradation refers to how the beam width differs from another beam within the resonating element (i.e not within a beam, but in between beams). In accordance with certain embodiments of the present disclosure, the non-rectangular beam elements refer to changing the beam width within a beam.

[0153] Accordingly, the resonator 100 is configured to mechanically alleviate (suppress) spurious resonance mode(s) of the resonating element(s) 101 by providing non-rectangular resonating beam elements adjacent to one another, thereby creating a non-linear trench 104 therebetween, and / or varying the width of the beam elements (asymmetrically) within the resonating element. In certain embodiments, the resonating element is configured to mechanically alleviate the spurious resonance mode by modifying (splitting, dividing, adjusting, separating) said spurious resonance mode of the resonating element into (several) non-harmful resonance mode(s) by varying the width of the beam elements of the resonating element. Accordingly, in certain embodiments, the spurious resonance mode(s) are alleviated mechanically by beam width variation, within the beam element itself and in between the different beam elements. Without limiting the scope and the interpretation of the patent claims, certain technical effects of one or more of the example embodiments disclosed herein are listed in the following. A technical effect is providing a good resonator product over a wide frequency range, with no harmful disturbance caused by a spurious resonance mode. A technical effect is prevention and / or suppression of a spurious resonance mode from becoming a collective resonance mode.

[0154] A further technical effect is avoiding harmful ‘locking’ of resonance mode (oscillations are self-sustained for this resonance mode) of a resonating element to a spurious resonance mode instead of the main resonance mode. A further technical effect is avoiding the spurious resonance mode from becoming a dominant resonance mode for self-sustained oscillation.

[0155] A further technical effect is leaving the main resonance mode (in certain embodiments, the in-plane length extensional resonance mode) intact in terms of performance, as well as providing a resonating element with stable high performance.

[0156] Various embodiments have been presented. It should be appreciated that in this document, words comprise, include, and contain are each used as open-ended expressions with no intended exclusivity.

[0157] The foregoing description has provided by way of non-limiting examples of particular implementations and embodiments a full and informative description of the best mode presently contemplated by the inventors for carrying out the invention. It is however clear to a person skilled in the art that the invention is not restricted to details of the embodiments presented in the foregoing, but that it can be implemented in other embodiments using equivalent means or in different combinations of embodiments without deviating from the characteristics of the invention.

[0158] Furthermore, some of the features of the afore-disclosed example embodiments may be used to advantage without the corresponding use of other features. As such, the foregoing description shall be considered as merely illustrative of the principles of the present invention, and not in limitation thereof. Hence, the scope of the invention is only restricted by the appended patent claims.

Claims

CLAIMS1 . A resonator (100), comprising a resonating element (101), wherein the resonating element (101) comprises a plurality of non-rectangular resonating beam elements (101), the plurality of beam elements (101) being positioned adjacent to each other, wherein the adjacent beam elements are mechanically connected to each other by connection elements (102) and separated from each other by non-linear trenches (104).

2. The resonator (100) of claim 1 , wherein each non-linear trench (104) has a uniform width.

3. The resonator (100) of claim 1 or 2, wherein any two adjacent beam elements are different in shape with each other.

4. The resonator (100) of any preceding claim, wherein any two adjacent beam elements mirror each other in shape.

5. The resonator (100) of any preceding claim, wherein the non-linear trenches (104) have a bendy shape, matching the shape of the adjacent beam elements.

6. The resonator (100) of any preceding claim, wherein an edge of the resonating beam element has a shape of a wave, such as a sine-wave that creates beam width variation within the beam element.

7. The resonator of claim 6, wherein both opposing edges of the resonating beam element have a shape of a wave, wherein the waves of the opposing edges have opposing phases with one another.

8. The resonator (100) of any preceding claim, wherein the resonating beam elements are longitudinally aligned within 25 degrees of a <100> crystal direction of silicon.

9. The resonator (100) of any preceding claim, wherein the resonating element (101) comprises a top electrode layer (L1), a piezoelectric layer (L2), and a bottom electrode (L4), wherein the piezoelectric layer (L2) is beneath the top electrode layer (L1), and the bottom electrode (L4) on the opposite side of the piezoelectric layer (L2) than the top electrode layer (L1).

10. The resonator (100) of claim 9, wherein the bottom electrode (L4) comprises silicon, preferably doped silicon, such as ultra-heavily doped, UHD, silicon.

11. The resonator (100) of claim 9 or 10, wherein the top electrode layer (L1) comprises metal, preferably gold.

12. The resonator (100) of any preceding claim, wherein the resonating element (101) is configured to resonate in an in-plane length-extensional, LE, main resonance mode.

13. The resonator (100) of any preceding claim, wherein the resonating element (101) is configured to suppress spurious resonance mode(s).

14. The resonator (100) of claim 13, wherein the resonating element (101) comprises an in-plane width-extensional, WE, spurious resonance mode and / or an out-of-plane flexural spurious resonance mode.

15. An apparatus, such as a resonator array, comprising at least one resonator (100) according to any of claims 1-14.

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