MEMS resonator with a coupler

Abstract

A MEMS, microelectromechanical systems, resonator (100) comprising a first in-phase resonating element (101) comprising a top electrode, a second in-phase resonating element (102) comprising a top electrode, and a coupler (112) in between the first in-phase resonating element (101) and the second in-phase resonating element (102), wherein a top electrode of the coupler (112) is at least partially absent.

Description

[0001] MEMS RESONATOR WITH A COUPLER

[0002] FIELD OF THE INVENTION

[0003] The present invention generally relates to microelectromechanical systems, MEMS, resonators which comprise resonating elements coupled with a coupler.

[0004] BACKGROUND OF THE INVENTION

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

[0006] Microelectromechanical systems, MEMS, resonators are being developed to provide the same functionality as quartz resonators with benefits such as smaller chip size, reduced cost, and increased robustness against shock and vibrations.

[0007] A key performance parameter in MEMS resonators is the equivalent series resistance, ESR, whose minimization is often desirable. ESR is inversely proportional to a quality factor Q of the resonator, and thus any attempt at the minimization of ESR requires to maintain a good quality factor Q.

[0008] SUMMARY

[0009] It is a general object of certain embodiments of the invention to reduce ESR of MEMS resonators (while maintaining an optimal quality factor) or at least to provide an alternative to existing technology.

[0010] According to a first example aspect of the invention there is provided a MEMS, microelectromechanical systems, resonator comprising: a first in-phase resonating element comprising a top electrode; a second in-phase resonating element comprising a top electrode; and a coupler in between the first in-phase resonating element and the second in-phase resonating element, the coupler comprising a top electrode, wherein a top electrode of the coupler is at least partially absent.

[0011] The disclosed structure leads to ESR improvement and maintains a good quality factor Q.

[0012] In certain embodiments, the MEMS resonator comprises discontinuity regions in the top electrode of the coupler to render the coupler electrically inert. Accordingly, in certain embodiments, the top electrode of the coupler is not connected to any electrical terminal. In certain embodiments, the top electrode of the coupler is absent in said discontinuity regions.

[0013] In certain embodiments, the top electrode of the coupler is floating. In certain embodiments, the discontinuity regions render the top electrode of the coupler floating.

[0014] In certain embodiments, the top electrodes of the in-phase resonating elements are connected to a same electrical terminal. In certain embodiments, the top electrodes of the in-phase resonating elements are connected to the same electrical terminal through electrically connecting pathway(s) extending via anchor point(s) of the resonator.

[0015] In certain embodiments, the number of discontinuity regions in the top electrode of the coupler is two.

[0016] In certain embodiments, the MEMS resonator comprises discontinuity regions in the top electrode of the coupler, and the top-electrode of the coupler is free from connections to any electrical terminal.

[0017] In certain embodiments, the MEMS resonator comprises the discontinuity regions at both ends of the top electrode of the coupler.

[0018] In certain embodiments, by said ends are meant ends of the coupler (or ends of the top electrode of the coupler) that face the in-phase resonating elements.

[0019] In certain embodiments, the MEMS resonator comprises discontinuity regions in the top electrode of the coupler drawn inwards from ends of the top electrode of the coupler (in the direction of vibration).

[0020] Accordingly, in certain embodiments, the top electrode of the coupler is disconnected from the top electrodes of the in-phase resonating elements. In certain embodiments, there are metal cuts or top electrode removal areas (providing respective discontinuity regions) in the top electrode of the coupler. In certain embodiments, the top electrode of the coupler is patterned to obtain the discontinuity regions. In certain embodiments, a top electrode layer forming the top electrodes is removed at an interface between an in-phase resonating element and the coupler (or at interfaces between the first and second in-phase resonating elements and the coupler). In certain embodiments, a top electrode layer is discontinuous at an interface between an in-phase resonating element (first and / or second in-phase resonating element) and the coupler.

[0021] In certain embodiments, the MEMS resonator comprises discontinuity regions in the top electrode of the coupler drawn inwards from ends of the top electrode of the coupler so much that they meet (at a center region of the coupler) and thereby render the whole top electrode of the coupler absent.

[0022] In certain embodiments, the MEMS resonator comprises the coupler in the form of an out-of-phase resonator.

[0023] In certain embodiments, the MEMS resonator comprises the coupler in the form of a beam. In certain embodiments, the coupler consists of a single beam.

[0024] In certain embodiments, the coupler is in the form of a plurality of beams. In certain embodiments, the plurality of beams are separated by a trench or trenches.

[0025] In certain embodiments, the first in-phase resonating element and the second in-phase resonating element and the coupler together form a symmetric structure.

[0026] In certain embodiments, the first in-phase resonating element and the second in-phase resonating element and the coupler each have a substantially same (or comparable) length.

[0027] In certain embodiments, the length is measured as the length in x-dimension (i.e. in the direction of vibration in certain embodiments).

[0028] In certain embodiments, the first and second in-phase resonating element and the coupler each comprise a beam having an aspect ratio different from 1 , and the beams have substantially identical (or comparable), lengths, widths and heights. Accordingly, in certain embodiments, the length of each of the beams is substantially the same, the width of each the beams is substantially the same, and the height of each of the beams is substantially the same (but the length differs from the width and height in certain embodiments). In certain embodiments, however, the length of the coupler beam is marginally different from (typically longer than) the length of the in-phase resonating element beams to compensate for a frequency shift due to the omission of top electrode metal at the discontinuity regions.

[0029] In certain embodiments, the MEMS resonator comprises the first and second in-phase resonating element in the form of a stacked beam resonator having a plurality of adjacent beams connected by connection element(s).

[0030] In certain embodiments, the MEMS resonator comprises coupler(s) at point(s) at which stacked beam resonator(s) have highest displacement(s).

[0031] In certain embodiments, the MEMS resonator comprises the first in-phase resonating element and the second in-phase resonating element in the form of length extensional, LE, resonance mode resonators.

[0032] In certain embodiments, the MEMS resonator comprises the coupler in the form of LE resonance mode (out-of-phase) resonator(s), such as a LE beam. In other embodiments, the coupler is in the form of a flexural mode resonating beam. In certain embodiments, the flexural mode resonating beam is configured to resonate in an inplane flexural mode.

[0033] In certain embodiments, the first in-phase resonating element and second in-phase resonating element and the coupler comprise an identical material stack.

[0034] In certain embodiments, the material stack comprises a top electrode layer of metal, preferably Au, a piezoelectric layer, and a silicon layer, preferably of single-crystalline silicon.

[0035] In certain embodiments, the MEMS resonator comprises a single-crystalline silicon layer doped to an average impurity concentration of at least 2*1019cm-3, such as at least 1O20cm-3.

[0036] In certain embodiments, the first in-phase resonating element and the second in phase resonating element both comprise a material stack comprising a top electrode layer, preferably of metal such as Au, a piezoelectric layer (underneath the top electrode layer), and a silicon layer (underneath the piezoelectric layer). The silicon layer is preferably a doped silicon layer, most preferably a doped silicon layer of singlecrystalline silicon. In certain embodiments, the coupler comprises a corresponding material stack, i.e., a top electrode layer, preferably of metal such as Au, a piezoelectric layer (underneath the top electrode layer), and a silicon layer (underneath the piezoelectric layer). The silicon layer is preferably a doped silicon layer, most preferably a doped silicon layer of single-crystalline silicon. In certain embodiments, the respective layers of the material stack reside at same vertical level in each of the elements (first and second in-phase resonating elements, and optionally the coupler). In certain embodiments, the coupler mechanically connects said first and second in-phase resonating elements.

[0037] In certain embodiments, the MEMS resonator is configured to resonate at an overtone frequency. In certain embodiments, the MEMS resonator is operational at a MHz frequency range. As an example, the MEMS resonator may be a 24 MHz resonator or a 153 MHz resonator. In certain embodiments, the MEMS resonator is a coupled stacked beam resonator.

[0038] In certain embodiments, the MEMS resonator comprises resonating beams that are aligned with a <100> crystal direction of silicon or deviate less than 25 degrees therefrom.

[0039] In further embodiments, to improve scalability, the MEMS resonator comprises further in-phase resonating element(s) and further coupler(s) to reach higher frequencies. In certain embodiments, the MEMS resonator comprises N in-phase resonating elements coupled by N-1 couplers.

[0040] In certain embodiments, the MEMS resonator comprises N in-phase resonating elements coupled by N-1 intervening couplers, where N = 3, 4, 5, ...

[0041] In certain embodiments, the MEMS resonator comprises a single coupler between neighboring in-phase resonating elements.

[0042] In certain embodiments, the MEMS resonator comprises a coupler at all spots between the resonating beams of adjacent in-phase resonating elements.

[0043] In certain embodiments, a trench separating beams of an in-phase resonating element extends through the whole MEMS resonator structure from respective connection element at a one end of the MEMS resonator structure all the way to a respective connection element at the other end of the MEMS resonator structure.

[0044] In certain embodiments, the top electrode of the coupler comprises a floating region. In certain embodiments, the top electrode of the coupler comprises an electrical path formed outside of the floating region (and connecting neighboring in-phase resonating elements).

[0045] In certain embodiments, the MEMS resonator comprises a pair of anchor connections (or suspenders) at opposite edges of a centermost in-phase resonating element. In certain embodiments, other anchor connections are omitted.

[0046] In certain embodiments, the MEMS resonator comprises a pair of anchor connections (or suspenders) at centermost couplers. In certain embodiments, other anchor connections are omitted.

[0047] Different non-binding example aspects and embodiments have been presented in the foregoing. The above embodiments and embodiments described later in this description are used to explain selected aspects or steps that may be utilized in implementations of the present invention. It should be appreciated that corresponding embodiments apply to other example aspects as well. Any appropriate combinations of the embodiments can be formed.

[0048] BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0050] Fig. 1a shows a schematic top view of a MEMS resonator in accordance with certain embodiments;

[0051] Fig. 1 b shows a schematic cross-sectional view of the MEMS resonator of Fig. 1a in accordance with certain embodiments; and

[0052] Figs. 2-13 show alternative layouts of MEMS resonators in accordance with certain further embodiments.

[0053] DETAILED DESCRIPTION

[0054] In the following description, like numbers denote like elements.

[0055] Fig. 1a shows a schematic top view of a MEMS resonator 100 in accordance with certain embodiments. The resonator 100 comprises a first in-phase resonating element 101 , a second in-phase resonating element 102, and a coupler 112 positioned in between the in-phase resonating elements.

[0056] Fig. 1 b shows a schematic cross-sectional view of the MEMS resonator 100 along section A-A in accordance with certain embodiments. The first in-phase resonating element 101 , the second in-phase resonating element 102, and the coupler 112 are provided as a layered structure, a material stack. The material stack comprises a top electrode layer 144 providing a top electrode for the first in-phase resonating element 101 , a top electrode for the second in-phase resonating element 102, and a top electrode for the coupler 112. A piezoelectric layer 143 resides beneath the top electrode layer 144 for providing the resonator with piezoelectric actuation. A silicon layer 142, preferably of single-crystalline silicon, resides beneath the piezoelectric layer 143.

[0057] In certain embodiments, the silicon layer 142 comprises single-crystalline silicon doped to an average impurity concentration of at least 2*1019cm-3, such as at least 102° cm-3. Accordingly, the single-crystalline layer may function as a bottom electrode layer in certain embodiments.

[0058] The resonating structure (i.e., the first in-phase resonating element 101 , the second in- phase resonating element 102, and the coupler 112) is separated (vertically) from a silicon substrate 130 by a cavity 131. A lateral separation of the resonating structure from a surrounding structure is implemented by trenches 132.

[0059] Fig. 1 b further shows an insulation layer 141 , typically of SiCh, separating the silicon substrate 130 from a device layer (i.e. layers 142-144) of a typical silicon on insulator, SOI, wafer. It should be noted that the structure shown in Figs. 1a and 1 b including the material stack is shown as an example only. The structure may vary depending on the embodiment.

[0060] In certain embodiments, the first in-phase resonating element 101 and the second in- phase resonating element 102 are implemented in the form of stacked beam resonators having a plurality of adjacent resonating beams 110 connected by connection element(s) 111 and separated by trenches 132 (thus forming a ladder-like structure). The first in-phase resonating element 101 and the second in-phase resonating element 102 are attached to a surrounding structure at anchor points 133. The anchor points 133 are preferably positioned at nodal points of the resonating elements 101 , 102.

[0061] The top electrode of the coupler 112 is floating. In certain embodiments, this is achieved by arranging discontinuity regions 121 in the top electrode of the coupler 112 to render the coupler 112 electrically inert. In certain embodiments, the top electrode of the coupler 112 is not connected to any electrical terminal. In certain embodiments, as shown in Figs. 1a and 1b, a discontinuity region is arranged at an interface between an in-phase resonating element and the coupler 112 (or at interfaces between the first and second in-phase resonating elements 101 , 102 and the coupler 112). The top electrode layer 144 contains a discontinuity (or discontinuity region) 121 in between the top electrode of the first in-phase resonating element 101 and the top electrode of the coupler 112. Further, the top electrode layer 144 contains a discontinuity (or discontinuity region) 121 in between the top electrode of the second in-phase resonating element 102 and the top electrode of the coupler 112. The discontinuity (discontinuities) can be implemented e.g. by patterning the top electrode of the coupler 112. The patterning may include top electrode layer removal. In certain embodiments, the coupler 112 is in the form of an out-of-phase resonator (mechanically connected with the in-phase resonating elements 101 , 102). Thus, when the in-phase resonating elements 101 , 102 resonate in-phase the coupler resonates out-of-phase. The resonating motion is preferably in-plane motion. The coupler 112 is preferable in the form of a beam. In certain embodiments, the coupler 112 is a length extensional mode, LE, coupler. In certain embodiments, the LE coupler (beam) is centrally positioned in the middle of the longer edges of the in-phase resonating elements 101 , 102 facing each other. Accordingly, in certain embodiments, the LE coupler is positioned in the middle of the (in-phase) stacked beam resonator(s) as shown in Fig. 1 a.

[0062] In certain embodiments, the first and second in-phase resonating element 101 , 102 and the coupler 112 each comprise a beam having an aspect ratio different from 1 , and the beams have substantially identical (or comparable) lengths (dimension in x-direction), widths (dimension in y-direction), and heights (dimension in z-direction). Accordingly, in certain embodiments, the length of each of the beams is substantially the same, the width of each the beams is substantially the same, and the height of each of the beams is substantially the same (but the length differs from the width and height in certain embodiments). In certain embodiments, however, the length of the coupler beam is marginally different from (typically longer than) the length of the in-phase resonating element beams to compensate for a frequency shift due to the omission of top electrode metal at the discontinuity regions.

[0063] The floating of the top electrode of the coupler 112 has the effect of reducing ESR in resonators having both in-phase and out-of-phase resonating regions. Further, the discontinuities may be conveniently positioned at end regions of the coupler 112 to prevent opposite charges of the coupler from being collected.

[0064] In the embodiments shown in Figs. 1a and 1 b (and in further embodiments of this disclosure) the top electrodes of the in-phase resonating elements are preferably connected to a same electrical terminal, shown in Fig. 1a with reference numeral 135. The connections to the terminal 135 may be implemented for example by electrically connecting pathway(s) extending via anchor points (or suspenders) 133.

[0065] Fig. 2 shows an embodiment with more than one LE coupler (here: three LE couplers 112 separated by trenches) with top electrodes made floating similarly as shown in the preceding. Adding couplers or widening them can be beneficial in optimizing spurious separation. However, it is preferable to implement rather narrower couplers than wider to avoid an increase in ESR.

[0066] Fig. 3, similarly as Figs. 1a and 1 b, shows an embodiment with a single coupler 112 in the middle. In this embodiment, the MEMS resonator 100 comprises the discontinuity regions 121 drawn inwards from ends of the top electrode of the coupler 112 (in the direction of vibration). Accordingly, top electrode layer removal regions (e.g. by means of patterning) have been pushed closer to the center of the coupler 112. This reduces the impact of top electrode metal removal on the resonance frequency but simultaneously increases the collecting of opposite charges.

[0067] In certain embodiments, the in-phase resonating elements may have a highest displacement at points other than at their middle. In those embodiments, couplers 112 may be positioned at these points instead of the middle. Fig. 4 merely illustrates such a positioning of the couplers 112.

[0068] In certain embodiments, as shown in Fig. 5, the two discontinuity regions have joined to form a unified region where the top electrode is absent from the coupler 112. The width of this unified region can be adapted to obtain a tradeoff between transduction efficiency and matching of the nominal frequency as well as frequency sensitivity to top electrode trimming between the coupler 112 and the resonating elements 101 , 102. In effect, if the width of the unified region 121 is increased, less charges from the coupler 112 is collected, improving the transduction and therefore the ESR. However, as the width gets larger, the coupler 112 frequency will deviate more from the frequency of the resonating elements 101 and 102, requiring more length tuning of coupler 112. In addition, the sensitivity to top electrode trimming of the coupler 112 will deviate more from the trimming of the resonating elements 101 and 102 as well.

[0069] It has been observed that e.g. an overtone resonator with in-phase resonating elements coupled with a coupler (e.g. LE coupler beam) such as shown in the preceding can be used e.g. for higher frequency applications. The out-of-phase motion can however cause some ESR loss. But, this can be reduced or even eliminated by the disclosed embodiments. When the (out-of-phase) coupler has the same material stack as the in- phase resonating elements, including e.g. the top electrode layer of metal, better compatibility with frequency trimming remains. Further, by minimizing the area of the out-of-phase region (coupler region) e.g. by using a (narrow) coupler beam and / or by minimizing the number of couplers, an ESR increase can be minimized.

[0070] In further embodiments, to improve scalability, the MEMS resonator 100 comprises further in-phase resonating element(s) and further coupler(s) to reach higher frequencies. Accordingly, in certain embodiments, the MEMS resonator comprises N in-phase resonating elements coupled by N-1 intervening couplers. Fig. 6 shows such a MEMS resonator in which N=3 (with in-phase resonating elements 101 , 102, and 103, and couplers 112 and 113). An overtone resonator is formed of the in-phase resonating elements 101 , 102, and 103, and couplers 112 and 113 (here: 5thovertone) so that the in-phase resonating elements and the (out-of-phase) couplers alternate within the resonator structure. As in other embodiments, the top electrodes of the in-phase resonating elements are preferably connected to a same electrical terminal, shown in Fig. 6 with reference numeral 135.

[0071] In certain embodiments, instead of having only one coupler between the in-phase resonating elements, the MEMS resonator comprises a coupler at all spots between the resonating beams of adjacent in-phase resonating elements. Accordingly, as shown in Fig. 7, each in-phase resonating beam 110 is connected by an out-of-phase coupler 112 or 113 to a respective in-phase resonating beam of an adjacent (parallel) in-phase resonating element 101-103. The discontinuity regions 121 are arranged in the top electrode(s) of the coupler(s) 112, 113 in a manner described in the preceding. In certain embodiments, as shown in Fig. 7, the connection elements 111 between the beams 110 are omitted in central parts of the MEMS resonator structure except for a common central coupler 712 positioned in the middle of the second (here: middle) in- phase resonating element 102. The central coupler 712 extends throughout the resonating element 102 from an anchor point 133 at one side to an anchor point 133 at the opposite side (connecting all the beams of the resonating element in question) thereby allowing charge collection in the region of the resonating element in question. In one implementation, as shown in Fig. 7, the connection elements 111 are only implemented at both ends of the MEMS resonator structure only (overtone resonator outermost beam ends only) and in the central coupler 712 (if applied). In such an embodiment, the trenches 132 separating the beams 110 of the in-phase resonating elements extend through the whole MEMS resonator structure (and extend from respective connection element 111 at a one end of the MEMS resonator structure all the way to the respective connection element 111 at the other end of the MEMS resonator structure) except in the region of the central coupler 712. Accordingly, the trenches 132 thus formed are common to all in-phase resonating elements 101 -103 and respective out-of-phase couplers 112, 113 (except in the region of the central coupler 712).

[0072] In certain embodiments, as shown in Fig. 8, the number of anchors is reduced (and the central coupler can be omitted). The MEMS resonator structure comprises in-phase resonating elements 101 , 103 at ends of the MEMS resonator structure having anchors 133 but anchor(s) of an intervening in-phase resonating element 102 are omitted. For enabling charges to be collected also from the intervening in-phase resonating element 102, an electrical path 115 between the intervening in-phase resonating element 102 and a neighbouring in-phase resonating element (here: in-phase resonating element 101 and / or 103) is implemented. In certain embodiments, the electrical path 115 is implemented via a top electrode of a respective coupler 112 (and / or 113). In certain embodiments, as shown in Fig. 8, the electrical path 115 is implemented on both sides of a floating region 116 of the top electrode of the coupler 112 (the floating region 116 being formed by the discontinuity regions 121 ). The discontinuity regions 121 in this embodiment are preferably obtained by rectangular patterning of the top electrode layer of the respective coupler. Edge regions next to respective trenches 132 are left free of patterning so that they can be used as electrical path(s) 115. The reference numeral 140 depicts border line(s) between in-phase and out-of-phase regions. In certain embodiments, as shown in Fig. 9, the electrical path 115 is implemented only on one side of a floating region 116. The discontinuity regions 121 also in this embodiment are preferably obtained by rectangular patterning of the top electrode layer of the respective coupler (except that it is sufficient to provide the discontinuity regions 121 at both longitudinal ends and only at (or in proximity of) that longer side (or edge) at which the electrical path 115 is formed).

[0073] In certain embodiments, as shown in Fig. 10, the MEMS resonator structure comprises only one anchor point 133 (at both sides of the MEMS resonator structure). In certain embodiments, this central pair of anchors is implemented (at nodal points) at opposite edges of a centermost in-phase resonating element 102. The electrical path(s) 115 between the centermost in-phase resonating element 102 and a neighbouring in-phase resonating element (and further possible in-phase resonating element(s) having no anchor at its / their own) are implemented similarly as shown in connection with the embodiments of Fig. 8 or 9.

[0074] In certain embodiments, as shown in Fig. 11 , the MEMS resonator structure again comprises a central anchor point or points 133 (at both sides of the MEMS resonator structure). However, instead of positioning the anchor at an in-phase resonating element, the anchor point or central pair of anchors is implemented at centermost coupler (or couplers) 112. The outermost coupler(s) which comprises the anchor preferably provides electrical path(s) 115 to neighbouring in-phase resonating element(s) 101 , 102. A floating region 116 of the top electrode of the coupler 112 is provided (the floating region 116 being formed by the discontinuity regions 121 ). The discontinuity regions 121 are preferably obtained by rectangular patterning of the top electrode layer of the respective coupler. Edge regions next to anchors (or suspenders suspending the MEMS resonator structure from a surrounding structure) are left free of patterning. Accordingly, the region left outside of the floating region is, again, used to implement electrical path(s) 115.

[0075] Fig. 12 shows a schematic top view of a further MEMS resonator 100 in accordance with certain embodiments. The resonator 100 comprises a first in-phase resonating element 101 , a second in-phase resonating element 102, and a coupler 112’ positioned in between the in-phase resonating elements. Instead of an LE beam, the coupler 112’ in the embodiment shown in Fig. 12 is a flexural resonator, such as a flexural beam coupler. The coupler 112’ is connected to the in-phase resonating elements by connectors 191 , such as beam connectors 191 shown in Fig. 12. These connectors 191 reside between the flexural beam of the coupler 112’ and the LE beams 110 of the in-phase resonating elements 101 , 102. In certain embodiments, the connectors 191 are positioned at anti-nodal points of the coupler 112’. In certain embodiments, the flexural beam coupler is oriented perpendicular to the length direction (x-direction) of the resonating beams 110.

[0076] The top electrode of the coupler 112’ is made floating by discontinuity regions 121 positioned at the connectors 191 (in the top electrode layer). Accordingly, similar to certain preceding embodiments, the top electrode of the coupler 112’ is separated from the top electrode(s) of the stacked LE beams 110 (separated from the top electrode(s) of the in-phase resonating elements 101 , 102). The top electrodes of the in-phase resonating elements 101 , 102 are preferably connected to a same electrical terminal similarly as in preceding embodiments.

[0077] Fig. 13 illustrates the shape of the MEMS resonator 100 of Fig. 12 at a maximum displacement of a vibration cycle. The in-phase resonating elements 101 , 102 vibrate in a collective length extensional-mode vibration resonance (similarly as in certain preceding embodiments). The dash-dot lines in Fig. 13 represent the resting positions of the distal ends (or distal side walls) of the in-phase resonating elements 101 , 102. At the maximum contraction position of the resonance motion illustrated in Fig. 13, the distal ends of the in-phase resonating elements 101 , 102 have moved in the x-direction towards their (central) symmetry axes as illustrated by the four arrows next to the four dash-dot lines in Fig. 13. The shape of the flexural resonator (coupler 112’) is such that the material portion close to the connector element 191 connecting the flexural resonator to the first in-phase resonating element 101 , and the material portions close to the connector elements 191 connecting the flexural resonator to the second in-phase resonating element 102, move in opposite directions along the x axis. The material portions of the flexural resonator close to the connector elements 191 follow the motion of the respective distal ends of the in-phase resonating elements 101 , 102 thereby causing flexural motion of the flexural resonator.

[0078] In advantageous embodiments, the flexural resonator has a resonance frequency which is substantially equal to the resonance frequencies of the in-phase resonating elements 101 , 102. One possible (overtone) mode shape of the flexural resonator is shown in Fig. 13. The displacement scale in Fig. 13 is magnified for illustrative purposes to highlight the resonance mode shape in comparison to resting position.

[0079] Without limiting the scope and 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 reduction of ESR and maintaining a good quality factor Q in higher frequency resonators. A further technical effect is preventing charges of opposite sign from being collected from out-of-phase regions. In certain embodiments, this is enabled by implementing out-of-phase regions with a floating top electrode or by omitting it. A further technical effect is the reduction of electrical capacitance Co of the resonator. A further technical effect enabling straightforward frequency trimming ability in coupled stacked beam resonators.

[0080] The foregoing description has provided by way of non-limiting examples of particular implementations and embodiments of the invention 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 above, but that it can be implemented in other embodiments using equivalent means without deviating from the characteristics of the invention.

[0081] Furthermore, some of the features of the above-disclosed embodiments of this invention may be used to advantage without the corresponding use of other features. As such, the foregoing description should 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 MEMS, microelectromechanical systems, resonator comprising: a first in-phase resonating element comprising a top electrode; a second in-phase resonating element comprising a top electrode; and a coupler in between the first in-phase resonating element and the second in- phase resonating element, wherein a top electrode of the coupler is at least partially absent.

2. The MEMS resonator of claim 1 , comprising discontinuity regions in the top electrode of the coupler to render the coupler electrically inert.

3. The MEMS resonator of claim 1 or 2, comprising a discontinuity region at both ends of the top electrode of the coupler.

4. The MEMS resonator of any preceding claim, comprising discontinuity regions in the top electrode of the coupler drawn inwards from ends of the top electrode of the coupler.

5. The MEMS resonator of claim 4, comprising discontinuity regions in the top electrode of the coupler drawn inwards from ends of the top electrode of the coupler so much that they meet and thereby render the whole top electrode of the coupler absent.

6. The MEMS resonator of any preceding claim, comprising the coupler in the form of an out-of-phase resonator.

7. The MEMS resonator of any preceding claim, comprising the coupler in the form of a beam, preferably an length extensional, LE, mode beam, or a flexural mode beam.

8. The MEMS resonator of any preceding claim, wherein the first in-phase resonating element and the second in-phase resonating element and the coupler each have a substantially same length.

9. The MEMS resonator of any preceding claim, comprising the first and second in- phase resonating element in the form of a stacked beam resonator having a plurality of adjacent beams connected by connection element(s).

10. The MEMS resonator of claim 9, comprising coupler(s) at point(s) at which stacked beam resonator(s) have highest displacement(s).

11. The MEMS resonator of any preceding claim, comprising the first in-phase resonating element and the second in-phase resonating element in the form of length extensional, LE, resonance mode resonators.

12. The MEMS resonator of any preceding claim, wherein the first in-phase resonating element and second in-phase resonating element and the coupler comprise an identical material stack.

13. The MEMS resonator of claim 12, wherein the material stack comprises a top electrode layer of metal, preferably Au, a piezoelectric layer, and a silicon layer, preferably of single-crystalline silicon.

14. The MEMS resonator of any preceding claim, configured to resonate at an overtone frequency.

15. The MEMS resonator of any preceding claim, wherein the MEMS resonator is a resonator operational at a MHz frequency range.

16. The MEMS resonator of any preceding claim, comprising N in-phase resonating elements coupled by N-1 intervening couplers, where N = 3, 4, 5, ...

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