Microelectromechanical resonator

Abstract

A microelectromechanical (MEMS) resonator includes a spring mass system having a first mass portion (M1), a second mass portion (M2), and a central spring portion (SP) between the mass portions.

Description

TECHNICAL FIELD

[0001] The present invention relates generally to micro-electro-mechanical (MEMS) resonators. BACKGROUND

[0002] This section provides useful background information on the technology relating to the application described herein without admitting that any technology described herein represents prior art.

[0003] Low frequency clock references are conventionally obtained from quartz tuning fork resonators, such as 32.768 kHz quartz tuning fork resonators.

[0004] Micro-electro-mechanical (MEMS) resonators are developing to provide the same functionality as quartz tuning forks, and have benefits such as reduced cost, smaller chip size, increased robustness to shock and vibration, and better stability over a wide temperature range.

[0005] A key performance parameter in MEMS resonators, such as silicon MEMS resonators, for frequency reference applications is the equivalent series resistance (ESR). The ESR is inversely proportional to the quality factor Q of the resonator, and so it is generally desirable to maximise this parameter. SUMMARY

[0006] It is an aim of certain embodiments of the present invention to provide a micro-electro-mechanical resonator having desirable properties.

[0007] According to a first example aspect of the present invention, there is provided a micro-electro-mechanical resonator, the micro-electro-mechanical resonator comprising:

[0008] a spring mass system having

[0009] a first mass portion,

[0010] a second mass portion, and

[0011] a central spring portion between the mass portions.

[0012] In certain embodiments, the resonator comprises a body of silicon doped to an average impurity concentration of at least 2*10 19 cm -3 and a material portion of the central spring portion is oriented along an x-axis perpendicular to a y-axis in a direction of which the resonator is configured to vibrate, wherein the x-axis extends along or deviates less than 5 degrees from a <100> silicon crystal direction.

[0013] In certain embodiments, the central spring portion comprises arms spaced apart by a trench, aligned with or deviating less than 5 degrees from a <100> silicon crystal direction.

[0014] In certain embodiments, the first and second weight portions are symmetrical weight portions.

[0015] In certain embodiments, the center spring portion is a symmetrical portion.

[0016] In certain embodiments, the center spring portion comprises a meandering structure attached at its first end to the first weight portion and at its opposite end to the second weight portion.

[0017] In certain embodiments, the first and second weight portions are connected to the center spring portion at their edges.

[0018] In certain embodiments, the first and second weight portions comprise a front edge, a back edge, a right edge and a left edge. Among the edges, the front edge is the edge facing the center spring portion. In certain embodiments, the first weight portion is connected to the center spring portion at the corner connecting the front edge and the left edge and at the corner connecting the front edge and the right edge. Similarly, the second weight portion is connected to the center spring portion at the corner connecting the front edge and the left edge and at the corner connecting the front edge and the right edge. In certain embodiments, the first and second weight portions are connected to the center spring portion in a region located in the middle of the front edge.

[0019] In certain embodiments, the resonator supports a foldable mode shape. In certain embodiments, the resonator operates in an in-plane bending mode. However, in certain other embodiments, the resonator operates in an out-of-plane mode. Thus, in certain embodiments, the resonator supports an in-plane bending vibration operating mode or an out-of-plane bending vibration operating mode.

[0020] In certain embodiments, the center spring portion comprises (or is formed by) a symmetrical arrangement of folded springs. In certain embodiments, the center spring portion comprises (or is formed by) unfolded springs attached in series to each other or attached in parallel to each other.

[0021] In certain embodiments, the first and second weight portions are configured to vibrate symmetrically.

[0022] In certain embodiments, the resonator comprises symmetrically positioned anchor points.

[0023] In certain embodiments, in a direction of the resonator along which the resonator vibrates, the resonator comprises an anchor point in the middle of a first edge of the spring portion and an anchor point in the middle of an opposite edge. Depending on the form of the weight portion, said direction (y direction, as defined later in the description) can be the length direction or the width direction of the resonator. The mentioned edges can form the side edges of the resonator.

[0024] In certain embodiments, the number of anchor points within the spring portion is two. In certain embodiments, the anchor points are used to anchor the resonator to the surroundings (or to the surrounding substrate). In certain embodiments, the central spring portion comprises a connecting beam leading to the anchor points. In certain embodiments, the connecting beam is aligned with the center of mass of the central spring portion or the center of mass of the spring mass system. In certain embodiments, the connecting beam extends from the meander shape of the central spring portion to the anchor points.

[0025] In certain embodiments, the resonator comprises an anchor point aligned with the center of mass of the central spring portion or the center of mass of the spring mass system.

[0026] In certain embodiments, the resonator comprises an anchor point for anchoring the central spring portion to the surroundings, the main resonant mode shape of the resonator having a node at the anchor point.

[0027] In certain embodiments, the resonator comprises a semiconductor material. In certain embodiments, the resonator comprises silicon. In certain embodiments, the resonator comprises degenerately doped silicon. In certain embodiments, more than 50% of the resonator mass is constituted by degenerately doped silicon. In certain embodiments, the resonator comprises silicon bodies doped to an average impurity concentration of at least 2*10 19 cm -3 , such as at least 10 20 cm -3 In certain embodiments, the resonator is a (single crystal) silicon MEMS resonator.

[0028] In certain embodiments, the resonator is configured to be piezoelectrically actuated.

[0029] In certain embodiments, the longitudinal axes of the individual spring elements of the central spring portion are oriented along the

[100] crystal direction of the silicon. Thus, in certain embodiments, the (elongated) material portions of the central spring portion are oriented along an x-axis perpendicular to the y-axis direction in which the resonator is configured to vibrate, wherein the x-axis extends along the <100> silicon crystal direction or deviates from this direction by less than 5 degrees. In certain embodiments, the material portions herein comprise straight portions or individual spring elements (in the y-direction) spaced apart from each other by trenches.

[0030] In certain embodiments, the longitudinal axis of the resonator is defined as the direction along which the resonator is vibrated.

[0031] In certain embodiments, the resonator is operated in vacuum.

[0032] In certain embodiments, the trenches at the end (or trailing edge) of the weight portion have a width that reduces the effect of air damping. The width depends on the embodiment in question. In certain embodiments, a width of more than 5 pm is applied.

[0033] In certain embodiments, the back edge of the weight portion is the outer end of the resonator.

[0034] In certain embodiments, the resonator comprises a first weight portion and a second weight portion, the first weight portion and the second weight portion comprising a grid of trenches.

[0035] In certain embodiments, the resonator is fabricated on a silicon-on-insulator (SOI) wafer (or SOI-type wafer). In certain embodiments, the resonator is fabricated on a cavity SOI (C-SOI) wafer.

[0036] In certain embodiments, the resonator is configured to operate at a 32 kHz frequency band, such as at a frequency of 32.768 kHz.

[0037] In certain embodiments, the center spring portion is oriented along a diagonal of the rectangular die.

[0038] In certain embodiments, the spring mass system comprises an additional support spring attached to the first and second weight portions.

[0039] In certain embodiments, the support spring is an additional portion of the spring(s) of the center spring portion. Thus, the support spring is separate from the center spring portion. In certain embodiments, the support spring is attached to the back edges (i.e., the edges opposite the edges facing the center spring portion) of the first and second weight portions.

[0040] In certain embodiments, a first portion of the resonator is in a degenerately doped silicon layer, and a second portion of the resonator is in a SiO2 layer formed below or above or on both sides of the degenerately doped silicon layer.

[0041] In certain embodiments, a silicon oxide (SiO2) layer is positioned immediately adjacent to or in the middle of the degenerately doped silicon layer, such that the SiO2 layer divides the degenerately doped silicon layer into two portions.

[0042] In certain embodiments, the resonator oscillates in the y-axis direction. The first mass portion and the second mass portion connected by the central spring portion experience a periodic movement in which the mass portions are brought closer to each other or further apart from each other. In certain embodiments, the movement is a reciprocating movement. In certain embodiments, the coordinate system is chosen such that the y-axis is in the longitudinal direction of the resonator and the x-axis is perpendicular to the y-axis, but depending on the embodiment, the resonator can be longer in the x-direction than in the y-direction (or as long). The first mass portion is spaced apart from the second mass portion in the y-direction. In certain embodiments, the y-direction is defined as the direction through (by) the center of mass of the first mass portion and through the center of mass of the second mass portion. In certain embodiments, the y-direction is defined as the direction (in the plane of the resonator) along which the central spring portion is allowed to vibrate. In certain embodiments, the resonator oscillates in only a single plane. In certain embodiments, the resonator oscillates in only one dimension (+y and -y directions). In certain other embodiments, the resonator oscillates in an out-of-plane mode (+z and -z directions).

[0043] In certain embodiments, the smaller dimension (width in the y-direction) of the folded springs mentioned in the foregoing is the same as the unfolded springs. In certain embodiments, the folded springs or the unfolded springs form a repeating structure within the central spring portion.

[0044] In certain embodiments, the resonator structure has inversion symmetry. In certain embodiments, the resonator structure has mirror symmetry. In certain embodiments, the mirror symmetry is with respect to the x-axis and / or the y-axis. In certain embodiments, the intersection of the x-axis and the y-axis is in the center of mass of the resonator structure. In certain embodiments, the resonator structure has rotational symmetry.

[0045] In certain embodiments, the resonator comprises a first mass portion and a second mass portion arranged in the shape of a tuning fork with side masses and a central spring portion.

[0046] In certain embodiments, the resonator comprises a set of double-ended tuning fork resonators positioned in a row and connected with a common mass element or connecting beam.

[0047] In certain embodiments, the resonator comprises:

[0048] A material stack with a silicon oxide layer between a top electrode layer and a bottom electrode layer.

[0049] In certain embodiments, the resonator further comprises a third mass portion and a fourth mass portion, wherein the central spring portion is arranged in the form of a cross with the mechanical anchor at its center.

[0050] In certain embodiments, the resonator comprises two top electrodes with opposite polarities, and a bottom electrode (or device layer) that is electrically floating.

[0051] In certain embodiments, a "foldable" type of silicon MEMS resonator is disclosed. Symmetric first and second weight portions vibrate (or oscillate) in a manner controlled (or dictated) by the spring constant of a central spring portion (or spring mass system). In certain embodiments, the conduction of the resonator is based on the use of a piezoelectric thin film.

[0052] In certain embodiments, a resonator structure with low acoustic loss (i.e., high quality factor) and low ESR is disclosed. Good frequency stability over a wide temperature range can be obtained when the resonator is fabricated on highly phosphorous doped silicon with the correct alignment with respect to the Si crystal structure.

[0053] In the foregoing, different non-binding example aspects and embodiments have been presented. The above embodiments and the embodiments described later in this description serve to explain selected aspects or steps that can be utilized in the implementation of the present invention. It should be understood that the corresponding embodiments apply equally to the other example aspects. Any suitable combination of embodiments can be formed. BRIEF DESCRIPTION OF DRAWINGS

[0054] The present invention will now be described, by way of example only, with reference to the accompanying drawings in which:

[0055] FIG. 1A A microelectromechanical (MEMS) resonator according to certain embodiments is shown;

[0056] FIG. 1B A modified MEMS resonator according to certain embodiments is shown;

[0057] FIG. 2 Another MEMS resonator according to certain embodiments is shown;

[0058] FIG. 3 Certain dimensions of the MEMS resonator of FIG. 1A are shown;

[0059] FIG. 4 Experimental results related to the type of MEMS resonator shown in FIG. 1A are shown;

[0060] FIG. 5 Another MEMS resonator according to certain embodiments is shown;

[0061] FIG. 6 A MEMS resonator with a diagonal design according to certain embodiments is shown;

[0062] FIG. 7 A MEMS resonator with additional support springs according to certain embodiments is shown;

[0063] FIG. 8 A cross-sectional view of a piezoelectric actuated MEMS resonator is shown in accordance with certain embodiments;

[0064] FIG. 9 An example of an electrode pattern for a resonator is shown in accordance with certain embodiments; FIG. 8

[0065] FIG. 10 An alternative cross-sectional view of a MEMS resonator is shown in accordance with certain embodiments;

[0066] FIG. 11 An example of an electrode pattern for a resonator is shown in accordance with certain embodiments; FIG. 10

[0067] A cross-sectional view of a MEMS resonator is shown in accordance with other embodiments; FIG. 12A to FIG. 12C

[0068] A MEMS resonator with a trimmed weight layer is shown in accordance with certain embodiments; FIG. 13

[0069] A tuning fork type MEMS resonator is shown in accordance with certain embodiments; FIG. 14

[0070] Another MEMS resonator with a diagonal design is shown in accordance with certain embodiments; FIG. 15

[0071] Another tuning fork resonator is shown in accordance with certain embodiments; FIG. 16A to FIG. 16C Figures 17 to

[0072] A double-ended tuning fork type MEMS resonator is shown in accordance with certain embodiments; and FIG. 21

[0073] A rotating MEMS resonator is shown in accordance with certain embodiments. FIG. 22 DETAILED DESCRIPTION

[0074] In the following description, like reference numbers refer to like elements.

[0075] FIG. 1A A microelectromechanical (MEMS) resonator is shown in accordance with certain embodiments. In more detail, FIG. 1A A top view of the resonator structure is shown. The coordinate system is chosen such that the y-axis is in the longitudinal direction of the resonator, and the x-axis is perpendicular to the y-axis. The resonator oscillates in the y-axis direction.

[0076] FIG. 1A ​​The black parts in the middle (and in the other figures) represent the trenches that are normally etched away, i.e. the parts of the layer (normally the silicon layer of an SOI wafer) that have been removed during the manufacturing process. The white parts in the presented structures represent the material parts, normally silicon or degenerately doped silicon regions. Thus, the resonator geometry is defined. In FIG. 1A The electrode geometry for the piezoelectric actuation has not been drawn in the middle.

[0077] The reference signs A1 and A2 represent the points that are anchored to the surrounding substrate. The MEMS resonator is described as a spring mass system with symmetric weight parts M1 and M2, where the masses M1 = M2 = M. The weight parts are connected by a central spring part SP.

[0078] The central spring part SP comprises a folded spring (or equivalently several unfolded springs attached to each other in series or in parallel). The composite spring constant can be made low to support a resonant mode with low frequency in a small footprint.

[0079] The frequency f of the resonator is f = 1 / (2pi) x sqrt(K / M).

[0080] In the formula, the spring constant of the central spring part is denoted by K.

[0081] The mode shape of the resonator is a "foldable mode", i.e. the weight parts M1 and M2 vibrate symmetrically in the +y and -y direction.

[0082] With respect to the alignment of the resonator, the x- and y-axes preferably extend along the <100> silicon crystal direction (or deviate less than 5 degrees from the <100> silicon crystal direction). In certain embodiments, the length direction of the folded spring (i.e. the x-direction) is oriented along the

[100] crystal direction (or deviates less than 5 degrees from the

[100] crystal direction).

[0083] FIG. 1A The structure disclosed in the middle has mirror symmetry over both the x- and y-axes through the centroid of the structure. By having the symmetry, a good node of the (main) resonant mode shape is obtained at the anchor positions A1 and A2 that are located in the middle of the side edges of the structure, leading to a high quality factor (under vacuum).

[0084] The reference sign T1 denotes a trench on the side of the masses M1 and M2 that is not parallel to the y-direction (direction of vibration in the main resonant mode). In certain embodiments, the trench T1 is larger than 5 pm to reduce the effect of air damping, thereby reducing the dependence of the quality factor on the pressure, and to provide a sufficient quality factor under atmospheric pressure so that the device can be measured even under atmospheric pressure (although the typical final operating condition of the resonator is under vacuum, achieved by vacuum packaging).

[0085] In FIG. 1AIn modifications of the embodiments shown in

[0086] The first weight portion M1 (similarly the second weight portion M2) has a front edge facing the center spring portion K, a right edge on its right side, a left edge on its left side, and a back edge at the end of the resonator structure.

[0087] Although in the embodiments shown in FIG. 1A In the embodiments shown in FIG. 1B Alternative embodiments shown in FIG. 1B The attachment shown in

[0088] In FIG. 1A And FIG. 1B The connecting beams CB extend in the x-direction from the center of mass of the structure to the anchor positions Al and A2. Thus, the center spring portion is attached to the surrounding substrate through two points and to each of the weight portions through one or two points.

[0089] FIG. 2 A similar design as in FIG. 1A is shown, but with mass (weight) portions comprising a grid of small trenches that enable the release of a buried oxide layer when the device is fabricated on an SOI (Silicon on Insulator) wafer. Furthermore, FIG. 2 A slightly different center portion is shown to provide a shorter connecting beam CB length for a stronger anchor of the resonator to the surrounding substrate. The center portion of the center spring portion comprises a spread material area to make the structure stronger. The spread area has no (meandering) springs. The spread area can contain multiple trenches. The trenches can be placed symmetrically.

[0090] FIG. 3 The dimensions of the resonator shown in FIG. 1A are shown. These are example dimensions that can be used, for example, to create a resonator that operates at a frequency of approximately 32 kHz. The width of the resonator is 405 pm, the length of the resonator is 628 pm, and the smaller dimension (width) of the individual spring elements is 9 pm. The thickness of the layer in which the resonator is located (i.e., the device layer) can be in the range of, for example, 4 pm to 20 pm.

[0091] FIG. 4Experimental results are shown, which respond to a test design operating at 44 kHz, measured in vacuum at p < 0.1 mbar. The obtained quality factor is 17000, and the ESR is 133 kOhm.

[0092] FIG. 5 A similar resonator as shown in FIG. 2 is shown, but with different mass M1 and M2 sizes, and with the central spring structure folded in a different way, which makes the connecting beam element CB shorter, to provide stronger support of the resonator to the substrate. The connecting beam CB extends from the outside turning point of the meander spring element to the anchor point A2 (Al).

[0093] FIG. 6 A spring along the diagonal resonator structure is shown. The effective length of the central folded spring structure is maximized by orienting the spring along the diagonal of the die. Thus, the area required for implementing a resonator with e.g. a 32 kHz resonant frequency resonator can be minimized.

[0094] FIG. 7 A MEMS resonator is shown, typically having FIG. 2 the resonator structure shown in

[0095] The spring constant of the support spring with respect to motion along the y-axis is less than 1 / 10 of the main spring constant K of the resonator. There can be multiple support springs SS attached to the masses M1 and M2. The support spring SS can be attached to either (x-oriented or y-oriented) side of the masses M1 and M2.

[0096] The purpose of the support spring SS is to suppress parasitic resonant modes, and to increase the stiffness of the structure with respect to z-oriented (perpendicular to both x- and y-directions) displacement. This can be beneficial for the manufacturability of the component, as well as for the reliability during device operation (a source of unreliability can be the static friction of the structure to the underlying (silicon) handling wafer above the gap.

[0097] FIG. 8 An example cross-section of a resonator device is shown, when fabricated on an SOI wafer 150. The layers L1-L6 are shown in the attached figures with the following explanations:

[0098] L2 = Piezoelectric layer: Conduction is based on the piezoelectric layer. Example layer materials are AlN, ScAlN, and ZnO. The L2 thickness can be e.g. 1 pm.

[0099] L1 = Top electrode layer: The top electrode layer is on the top side of the piezoelectric layer. The material of this layer can be Al, Mo, Au, poly-silicon, or any other suitable conductive material. The L1 thickness can be e.g. 1 pm.

[0100] L3 = bottom electrode layer: a bottom electrode layer on the bottom side of the piezoelectric layer. The material of this layer can be Al, Mo, Au, polysilicon or any other suitable conductive material. The L3 thickness can be e.g. 1 pm.

[0101] L4 = doped silicon layer (resonator body and bottom electrode): Phosphorous doped single crystal silicon forms >50% of the mass of the resonator (or center spring portion). In certain embodiments, the phosphorous doping concentration is greater than 1*10 19 cm -3 . The doped silicon layer can act as a bottom electrode layer, i.e. layers L3 and L4 can be combined into a single silicon layer. The L4 thickness can be in the range of e.g. 2 pm - 20 pm.

[0102] L5 = buried oxide layer: This layer is etched from underneath the resonator structure to release the resonator (resonator area marked by reference 100) to vibrate in its resonance mode.

[0103] L6 = silicon handling layer.

[0104] In other embodiments, there can be additional material layers.

[0105] Reference 201 indicates an electrical connection to the bottom electrode layer, and reference 202 indicates an electrical connection to the top electrode layer. The opening in layer L2 is denoted by reference 120.

[0106] FIG. 9 An example of a top electrode pattern (reference FIG. 8 ) is shown, which can be used to implement the electromechanical conduction of the “foldable” resonance mode. TE denotes the top electrode in the figure.

[0107] FIG. 10 An alternative cross-section of the resonator device is shown, wherein the difference to FIG. 8 is that there are two polarities of the top electrode: 203 [X in ] and 204 [X out ], and the bottom electrode is floating. Since having a top electrode geometry with two polarities requires a cross electrode pattern without electrical connections (see FIG. 11 ), additional material layers are needed: L7 = bridging conductor layer, L8 = bridging dielectric layer.

[0108] FIG. 11 An example of a top electrode pattern (reference FIG. 10 ) is shown, which can be used to have two polarities of the top electrode layer (X in , X outelectromechanical conduction of the "foldable" resonance mode is achieved when the region of the L7 bridge conductor layer and the L8 bridge dielectric layer (not shown in FIG. 11

[0109] FIG. 12A Cross-sectional views of MEMS resonators according to other embodiments are shown. In these embodiments, a thermal oxide layer L4' is provided. The thermal oxide layer, e.g. a silicon oxide Si02 layer, is positioned next to (degenerate) doped silicon layer L4 (below or above the (degenerate) doped silicon layer L4) or on both sides of the layer L4. In other embodiments, the silicon oxide Si02 layer is positioned in the middle of the layer L4, such that the Si02 layer divides the L4 layer in two parts. The thermal oxide layer L4' is used to improve the thermal characteristics of the resonator. In certain embodiments, the (frequency's) linear temperature coefficient TCF1 of the resonator is modified, e.g. increased, by adding the thermal oxide layer. For example, a resonator without thermal oxide layer can have a slightly negative TCF1 (e.g. -5 ppm / °C). By adding a thermal oxide layer with a suitable thickness depending on the embodiment, the TCF1 is increased. A desired TCF1 = 0 can be achieved.

[0110] FIG. 12B FIG. 12C Cross-sectional views of MEMS resonators according to other embodiments are shown. In these embodiments, a silicon oxide (Si02) layer L4' is deposited on the piezoelectric layer L2 (as illustrated in FIG. 12B FIG. 12C FIG. 8 FIG. 10 FIG. 8 In certain embodiments, as discussed above with reference to

[0111] The advantages of these solutions can be understood by considering the following reasoning. To achieve a reduction of the ESR in the resonator, it is advantageous to scale down the mass of the resonator by reducing the film thicknesses while maintaining the condition that the total TCF1 of the material stack is zero. Silicon oxide has a relatively higher positive temperature coefficient than highly phosphorous doped silicon, and thus the resonator material stack total thickness (and mass) can be reduced by replacing parts of the doped silicon by silicon oxide while keeping the total TCF1 = 0. The result of reducing the thickness is a reduction of the ESR and at the same time an increase of the capacitance across the piezoelectric layer. To prevent the capacitance from increasing too much, it is advantageous to place a silicon oxide layer L4' between the bottom electrode and the top electrode, as illustrated in FIG. 12B FIG. 12C ​​​​​​​​

[0112] There are several known methods for growing a silicon oxide layer, such as thermal oxidation of silicon, plasma-enhanced chemical vapor deposition (PECVD) or low-temperature oxide (LTO) methods. For example, PECVD and LTO methods can be used to grow a SiO2 layer for a resonator from a material stack according to FIG. 12B and FIG. 12C .

[0113] In certain embodiments, the bottom electrode layer L3 and the doped silicon layer L4 are combined into a single doped silicon layer L4. In this case, the thermal oxide can conveniently be formed from layer L4 by thermal oxidation, thereby forming a layer L4’ on top of the remaining layer L4.

[0114] FIG. 13 A design similar to the design of FIG. 5 is shown, but with a layer L9: a trimming mass layer on top of masses M1 and M2 (diagonally hatched area / grey area). The purpose of layer L9 is to provide good tunability of the resonance frequency by reducing the thickness of layer L9 (or parts of layer L9), e.g. by ion beam trimming or by laser ablation. The material of L9 can be e.g. Mo or Au. As an example, due to similar dimensions as in FIG. 3 , and a Si device layer thickness of 10 pm, the resonance frequency changes approximately 40,000 ppm per 100 nm of Mo removed.

[0115] FIG. 14 Another (single crystal) silicon MEMS resonator 1400 according to certain embodiments is shown. With respect to the materials, general structure and general functionality of resonator 1400, reference is made to the previously described embodiments. The coordinate system is defined as shown in the figure. Thus, layers of the resonator or resonator structure, such as piezoelectric layers, are typically located in the xy-plane.

[0116] The resonator 1400 can be seen as a tuning fork resonator equipped with additional masses at the end of the vibrating arms to lower the resonant frequency of the spring mass system to the desired value. Thus, in certain embodiments, the resonator 1400 has a general M-shape. The resonator 1400 comprises a spring mass system having a first weight portion 1401, a second weight portion 1402, and a central spring portion between the weight portions. In certain embodiments, the central spring portion comprises a first (left) arm 1403 of the tuning fork and a second (right) arm 1404 of the tuning fork. The arms 1403 and 1404 are aligned with the x-direction. The left arm 1403 is separated from the right arm 1404 by a gap, but is also mechanically connected to the respective end of the right arm 1404 at its end. The tuning fork is further anchored to a mechanical anchor 1409 at the same end(s) of the connecting arms. The portion 1403 (and respectively portion 1404) is connected to the portion 1401 (respectively portion 1402) at the opposite end. In addition to this, there is a first gap between the portions 1401 and 1403, and a respective second gap between the portions 1402 and 1404.

[0117] The preferred mode of vibration is in-plane motion in which the two arms of the resonator 1400 move opposite to each other. The vibrating arms 1403, 1404 thus vibrate such that they move alternately closer to each other and in a symmetric manner further away from each other (as depicted by the double arrow in the y-direction).

[0118] In order to minimize the variation of the frequency with temperature, it is advantageous to dope the single-crystalline silicon layer of the resonator with an n-type dopant, such as phosphorous. In certain embodiments, the doping concentration is greater than 1*10 19 cm -3 In certain embodiments, the doped silicon forms at least 50% of the mass of the vibrating arms 1403, 1404 of the resonator. This is advantageous in striving for high thermal stability. In certain embodiments, the two arms 1403, 1404 are aligned along a <100> crystalline axis (such as a

[100] silicon crystalline axis), which will also help to achieve high thermal stability.

[0119] In certain embodiments, the resonator 1400 is set to vibrate by means of piezoelectric coupling. In certain embodiments, a piezoelectric film (e.g. an AlN thin film) is deposited on top of the single-crystalline silicon layer of the resonator structure. A top electrode is deposited and patterned on the piezoelectric thin film. In certain embodiments, a first portion 1405 of the top electrode is positioned on the vibrating arm 1403, and a second portion 1406 is positioned on the vibrating arm 1404. The material of the electrode can be, for example, Mo, Al, Au, Pt, Ag, polysilicon, or another conductive material.

[0120] In certain embodiments, the doped silicon layer L4 (see e.g. FIG. 8 ,FIG. 10 and FIG. 12A to FIG. 12C ) acts as a bottom electrode layer. In certain alternative embodiments, there is an additional thin layer or layer stack on the single-crystalline silicon that operates as a bottom electrode (see FIG. 8 , FIG. 10 and FIG. 12A to FIG. 12C L3 in). The material stack of the resonator 1400 in certain embodiments thus corresponds to the material stack presented in the foregoing with reference to FIG. 12A to FIG. 12C L4' features as disclosed in FIG. 8 may optionally be compensated for in the foregoing with reference to

[0121] In certain embodiments, the top electrode is patterned as depicted in FIG. 14 so that when an alternating current signal is connected between the top electrode and the bottom electrode, the two arms of the resonator 1400 are subjected to forces that support anti-phase resonance. This can be achieved, for example, by patterning the top electrode as depicted in FIG. 14 so that the regions of the arms 1403, 1404 on top of the piezoelectric layer immediately adjacent to the gap separating the arms 1403, 1404 (i.e. regions 1405 and 1406) are covered by the electrode portions, while the regions of the arms 1403, 1404 closer to the weight portions remain uncovered.

[0122] In certain alternative embodiments, the top electrode is patterned so that the regions of the arms 1403, 1404 on top of the piezoelectric layer closer to the weight portions are covered by the electrode portions, while the regions of the arms 1403, 1404 immediately adjacent to the gap separating the arms 1403, 1404 remain uncovered.

[0123] In certain embodiments, the wiring to the patterned top electrode is arranged from contact pads 1408 positioned on a mechanical anchor 1409 (indicated by reference number 202 of the resonator according to the material stack of FIG. 8 The contact pads 1407 for the bottom electrode (indicated by reference number 201 of the resonator according to the material stack of FIG. 8 may be positioned on the same anchor 1409. (The openings 120 in the piezoelectric layer L2 illustrated in FIG. 14 are not shown in FIG. 8 ).

[0124] FIG. 15 Another tuning fork resonator according to certain embodiments is shown. The length of the tuning fork arms 1403, 1404 can utilize the diagonal dimension of the relevant chip (or die), while the mass elements (weight portions) 1401, 1402 are placed in the corners of the die. In certain embodiments, the two arms 1403, 1404 are aligned along a <100> crystallographic axis (such as the

[100] crystallographic axis of silicon) (or deviate from this direction by less than 5 degrees) to minimize the thermal coefficient.

[0125] The preferred vibration mode is in-plane motion (in the xy-plane) in which the two arms of the resonator move opposite to each other in the y-direction. The vibrating arms 1403, 1404 (aligned with the x-direction) thus vibrate such that they move alternately closer to each other and in a symmetric fashion further away from each other (as depicted by the double arrow in the y-direction). FIG. 15 The material stack of the resonator shown in FIG. 15 corresponds to the material stack of the resonator 1400.

[0126] FIG. 16A Other embodiments of a tuning fork resonator are shown. FIG. 16A The resonator 1600 shown in

[0127] The preferred vibration mode is in-plane motion in which the two arms of the resonator 1600 move opposite to each other in the y-direction. The vibrating arms 1603, 1604 thus vibrate such that they move alternately closer to each other and in a symmetric fashion further away from each other (as depicted by the double arrow).

[0128] The resonator 1600 thus essentially corresponds to the resonator 1400. The difference compared to the resonator 1400 is in the implementation of the actuation method. Instead of a top electrode and a bottom electrode, the resonator structure comprises two top electrodes with opposite polarity and a bottom electrode layer L3 that is electrically floating. The material stack of the resonator 1600 corresponds to the material stack in the foregoing with reference to FIG. 10 and FIG. 12A to FIG. 12C any of the material stacks presented. In certain embodiments, the patterning of the top electrodes is as shown in FIG. 16AThe first and second top electrodes are positioned on the resonator 1600' as depicted in FIG. 16B, such that a first portion 1605 of the first top electrode is positioned on the vibrating arm 1603' and a second portion 1606 is positioned on the vibrating arm 1604'. A first portion 1615 of the second top electrode is positioned on the vibrating arm 1603' and a second portion 1616 is positioned on the vibrating arm 1604'. The regions 1605, 1606 of the arms 1603, 1604 immediately adjacent the gap separating the arms 1603, 1604 are covered by the first top electrode, and the regions 1615, 1616 of the arms 1603, 1604 closer to the respective weight portions 1601, 1602 are covered by the second top electrode.

[0129] In certain embodiments, the wiring to the first top electrode is arranged from a contact pad 1608 positioned on the mechanical anchor 1609. The contact pad 1618 of the second top electrode can be positioned on the same anchor 1609.

[0130] FIG. 16B Other embodiments of a tuning fork resonator are shown. FIG. 16B The resonator 1600' shown in FIG. 16A' includes a spring-mass system having a first weight portion 1601, a second weight portion 1602, and a central spring portion between the weight portions. In certain embodiments, the central spring portion includes a first (left) arm 1603' of a tuning fork and a second (right) arm 1604' of the tuning fork. The left arm 1603' is separated from the right arm 1604' by a gap, but is also mechanically connected at its ends to the respective ends of the right arm 1604'. The tuning fork is further anchored to a mechanical anchor 1609' at the same end(s) of the connecting arms. The portion 1603' (and, correspondingly, the portion 1604') is connected at the opposite end to the portion 1601 (and, correspondingly, the portion 1602). In addition to this, there is a first gap between the portions 1601 and 1603', and a corresponding second gap between the portions 1602 and 1604'.

[0131] In this embodiment, the mode of vibration is an out-of-plane motion in which the two arms of the resonator 1600' move in opposite directions relative to each other. The vibrating arms 1603', 1604' thus vibrate such that when the left arm 1603' moves in the positive z-axis direction, the right arm 1604' moves in the negative z-axis direction (and vice versa).

[0132] In FIG. 16B A preferred implementation of the electromechanical actuation of such a resonator 1600' is illustrated in FIG. 16B. There are two top electrodes with opposite polarities (i.e., electrode 1605' for the left arm and electrode 1606' for the right arm), and a bottom electrode layer L3 that is electrically floating. An electrical signal (X in , X outThe contact pads 1618' and 1608' are connected to the top electrodes 1605' and 1606', respectively. The contact pads are formed on the mechanical anchoring region 1609'. The material stack of the resonator 1600' can correspond to the one referenced above. FIG. 10 and FIG. 12A to FIG. 12C Any material stack in the presented material stack.

[0133] FIG. 16C Other embodiments of the tuning fork resonator are shown. Similar to resonator 1600', FIG. 16C The resonator 1600” shown includes a spring-mass system having a first weight portion 1601, a second weight portion 1602, and a central spring portion between the weight portions. The central spring portion includes a first (left) arm 1603” and a second (right) arm 1604” of the tuning fork. The left arm 1603” is separated from the right arm 1604” by a gap, but is also mechanically connected at its end to the corresponding end of the right arm 1604”. The tuning fork is further anchored to mechanical anchors 1609” at the same(s) ends of the connecting arms. The portions 1603” and 1604” respectively are connected to portions 1601 (and 1602) respectively at opposite ends. In addition, there is a first gap between portions 1601 and 1603”, and a corresponding second gap between portions 1602 and 1604”.

[0134] In some embodiments, such as FIG. 16C As depicted, the top electrode is patterned such that when an AC signal is connected between the top and bottom electrodes, the two arms of the resonator 1600” are subjected to a force supporting out-of-plane motion, in which the two arms of the resonator 1600” move in phase with each other (i.e., the left arm 1603” and the right arm 1604” move in the direction of the positive z-axis or alternatively the negative z-axis). To support this vibration mode, the top electrode includes two portions 1605” and 1606” respectively disposed on the left and right arms. The top electrode portions are connected to contact pads 1608” disposed on mechanical anchors 1609”. Contact pads 1607” of the bottom electrode can be positioned on the same anchors 1609”. In some embodiments, the material stack of the resonator 1600” thus corresponds to optionally being composed of, for example, FIG. 12A to FIG. 12C The publicly available L4' features are supplemented and referenced above. FIG. 8 The material stacking is presented.

[0135] FIG. 17A Another MEMS resonator according to certain embodiments is shown. Regarding the materials, structure, and general function of resonator 1700, refer to the previous description, and in particular to the description of resonator 1400.

[0136] The resonator 1700 can be seen as a double-ended tuning fork resonator, as the general structure of a double-ended tuning fork resonator can be seen as having been formed by connecting two tuning fork resonators at their end portions. The resonator 1700 comprises a spring mass system having a first mass portion 1701, a second mass portion 1702, and a central spring portion between the mass portions. In certain embodiments, the central spring portion comprises a first (left) vibration arm 1703 and a second (right) vibration arm 1704 aligned with the x-direction. The left arm 1703 is separated from the right arm 1704 by a (closed) gap 17, but is also mechanically connected to the respective end of the right arm 1704 at its end portions. In certain embodiments, the two mass portions are the same mass element attached to the middle points of the two vibration arms 1703, 1704 to adjust the value of the resonance frequency to a desired value. In addition to this, there is a gap between portions 1701 and 1703 and between portions 1702 and 1704, respectively. The resonator 1700 is further anchored at one of its ends to a mechanical anchor 1709 and at its opposite end to another mechanical anchor 1719.

[0137] The preferred vibration mode is an in-plane motion in which the two arms of the resonator 1700 move in the y-direction opposite to each other by piezoelectric conduction. The two (bending) vibration arms 1703, 1704 thus vibrate so that they move alternately closer to each other and in a symmetrical manner further away from each other (as depicted by the double arrow). The patterned top electrode is to support this motion. In certain embodiments, the patterned top electrode is to form an alternating pattern in the longitudinal direction of the arms. In certain embodiments, the central longitudinal regions of the arms 1703, 1704 on top of the piezoelectric layer are arranged so that the regions next to the mass portions are covered by the top electrode (i.e. top electrode portions 1705 and 1706), and the regions closer to the gap 17 remain uncovered. The distal longitudinal regions of the arms 1703, 1704 are conversely arranged, i.e. the regions closer to the gap 17 are covered by the top electrode (i.e. top electrode portions 1715, 1725, 1716 and 1726), and the regions next to the mass portions remain uncovered.

[0138] In certain embodiments, the wiring to the patterned top electrode is arranged from a contact pad 1708 positioned on the mechanical anchor 1709. In addition, wiring from the top electrode portions to other portions of the top electrode can be arranged. Also, wiring starting from the opposite anchor 1719 can be arranged. The contact pad 1707 of the bottom electrode can be positioned at one of the anchors 1709, 1719, for example.

[0139] FIG. 17BAnother embodiment of a double-ended tuning fork resonator is shown. The preferred mode of vibration of resonator 1730 is out-of-plane motion, in which the two arms of resonator 1730 move in phase in the z direction relative to each other by piezoelectric conduction. (The notation in gap 17 shows the direction of relative motion, whether in the positive z direction or the negative z direction, for adjacent flexural vibrating arms.) The two (flexural) vibrating arms 1703, 1704 thus vibrate so that the two arms 1703 and 1704 move alternately in the positive z direction or in the negative z direction. The top electrodes are patterned to support this motion. The resonator structure includes two top electrodes with opposite polarity, and a bottom electrode layer L3 that is electrically floating. The material stack of resonator 1730 corresponds to that presented in the foregoing with reference to FIG. 10 and FIG. 12A to FIG. 12C The material stack in any of the presented material stacks. In certain embodiments, the central longitudinal region of arms 1703, 1704 on top of the piezoelectric layer is primarily covered by the first top electrode structure (i.e., top electrode portions 1732 and 1742) and connected to the (first) contact pad 1708, while the distal longitudinal region of arms 1703, 1704 is primarily covered by the second top electrode structure (i.e., top electrode portions 1731, 1733, 1741, and 1743) and connected to the (second) contact pad 1718. In the example shown in FIG. 17B , the contact pad 1708 is positioned at anchor 1709, and the contact pad 1718 is positioned at opposite anchor 1719.

[0140] FIG. 17C Another embodiment of a double-ended tuning fork resonator is shown. The preferred mode of vibration of resonator 1750 is out-of-plane motion, in which the two arms of resonator 1750 move out of phase in the z direction relative to each other by piezoelectric conduction. The two (flexural) vibrating arms 1703, 1704 thus vibrate so that arm 1703 moves in the positive z direction while arm 1704 moves in the negative z direction, or vice versa. The top electrodes are patterned to support this motion. The resonator structure includes two top electrodes with opposite polarity, and a bottom electrode layer L3 that is electrically floating. The material stack of resonator 1750 corresponds to that presented in the foregoing with reference to FIG. 10 and FIG. 12A to FIG. 12CAny of the material stacks presented. In some embodiments, the central longitudinal region of arm 1703 on top of the piezoelectric layer (i.e., top electrode portion 1752) and the distal longitudinal region of arm 1704 on top of the piezoelectric layer (i.e., top electrode portions 1761 and 1763) are primarily covered by a first top electrode structure and connected to contact pad 1708, while the central longitudinal region of arm 1704 on top of the piezoelectric layer (i.e., top electrode portion 1762) and the distal longitudinal region of arm 1703 on top of the piezoelectric layer (i.e., top electrode portions 1751 and 1753) are primarily covered by a second top electrode structure and connected to contact pad 1718.

[0141] exist FIG. 17B and FIG. 17C In the embodiment illustrated, the two top electrodes do not need to cross each other. Therefore, it is not necessary to... FIG. 10 and FIG. 12A to FIG. 12C Layers L7 and L8 in the material stack depicted in the image.

[0142] Similar to the aforementioned tuning fork resonator, FIG. 17A to FIG. 17C The arms of the double-ended tuning fork resonators 1703 and 1704 in the middle are... <100> Crystallization axes (such as the

[100] crystallization axis of silicon) are aligned (or deviated from that direction by less than 5 degrees) to achieve high thermal stability.

[0143] Two-ended tuning fork resonators can be combined to form larger resonator structures with interconnecting elements that enable the components to resonate in a single collective vibration mode. FIG. 18A and FIG. 18B An example of such a two-ended tuning fork resonator assembly is shown in the figure. Individual two-ended tuning fork resonator 1800 ( FIG. 17A to FIG. 17C Five resonators of the type shown are arranged in a row. The double-ended tuning fork resonators 1800 include their own vibrating arms 1803, 1804 separated by gap 18. A common mass element 1802 is positioned between adjacent central spring portions, and end mass elements 1801 are positioned at the ends of the assembly. The assembly includes mechanical anchors 1809, 1819 connected to the respective ends of the central spring portions (double-ended tuning forks). In other embodiments, these anchors may be combined or connected and / or moved closer to the central anchor.

[0144] exist FIG. 18A In the example shown, each individual double-ended tuning fork resonator 1800 vibrates in an in-plane out-of-phase mode (in the xy plane), while the vibration modes of adjacent resonators 1800 are offset from each other by 180 degrees. Therefore, the mass element 1802 (connected to its adjacent double-ended tuning fork resonator arms 1803, 1804) FIG. 18A The four innermost mass elements move synchronously with the adjacent arms.

[0145] In FIG. 18B another embodiment of an assembly of connected double-ended tuning fork resonators is depicted. In this embodiment, the individual double-ended tuning fork resonators 1800 all vibrate in an out-of-plane anti-phase mode, while the vibration modes of the resonators 1800 are offset by 180 degrees from each other (as illustrated by the signs showing motion in the positive and negative z-directions). Thus, the mass elements 1802 (the four innermost mass elements in FIG. 18B ) connected to their adjacent double-ended tuning fork resonator arms 1803, 1804 move in sync with the adjacent arms.

[0146] In certain embodiments, the outermost mass elements 1801 have a volume (e.g., width) that is 50% or substantially 50% of the volume of the innermost mass elements 1802 to facilitate an even distribution of vibration energy between the interconnected double-ended tuning fork resonators 1800. As in the foregoing, the arms 1803, 1804 of the double-ended tuning fork resonators 1800 are aligned with the <100> crystalline axis (such as the

[100] crystalline axis of silicon) (or are offset from this direction by less than 5 degrees).

[0147] FIG. 19A and FIG. 19B Other embodiments of interconnected double-ended tuning fork resonators are shown. In some embodiments, the top electrode structure is patterned so that when an alternating current signal is connected between the top and bottom electrodes, adjacent double-ended tuning fork resonators are subjected to forces that support motion with a 180 degree relative phase shift. In certain embodiments, this is achieved by patterning the top electrode in the manner shown in FIG. 19A . For simplicity, an assembly with (only) three double-ended tuning fork resonators 1800 is drawn. When comparing two adjacent resonators 1800, the top electrode 1850 is patterned on the opposite top surface side of the respective curved arms 1803 (or 1804).

[0148] In certain embodiments, the wiring to the patterned top electrode 1850 is arranged from contact pads 1808 positioned on a combined mechanical anchor 1809. The contact pads 1807 of the bottom electrode can be positioned on the same anchor 1809.

[0149] In other embodiments, such as in the example illustrated in FIG. 19B , the structure of the corresponding resonator 1800' includes two top electrodes (1860 and 1870) with opposite polarity and a bottom electrode layer L3 that is electrically floating. The material stack of the resonator 1800' corresponds to any of the material stacks presented in the foregoing with reference to FIG. 10 and FIG. 12A to FIG. 12C , except for layers L7 and L8 in the material stacks depicted in FIG. 10 and FIG. 12A to FIG. 12C . The material stack of the resonator 1800' corresponds to any of the material stacks presented in the foregoing with reference to FIG. 19BL7 and L8 are not needed in the example of Fig. 18). For simplicity, an assembly with (only) two double-ended tuning fork resonators 1800' is drawn.

[0150] In the left-hand double-ended tuning fork resonator, the central longitudinal region of the arm 1803 on top of the piezoelectric layer is mainly covered by the first top electrode structure 1860 (connected to the contact pad 1868), and the distal longitudinal region of the arm is mainly covered by the second top electrode structure 1870 (connected to the contact pad 1878), while for the arm 1804, the central longitudinal region is mainly covered by the second top electrode structure 1870 and the distal longitudinal region of the arm is mainly covered by the first top electrode structure 1860. In the example shown in Fig. 18, the contact pad 1868 is positioned at the anchor 1809, and the contact pad 1878 is positioned at the opposite anchor 1819. FIG. 19B

[0151] When comparing two adjacent double-ended tuning fork resonators 1800', the respective central longitudinal region and distal longitudinal region are covered by top electrodes with opposite polarity. When an alternating current signal is connected between the two top electrodes, the adjacent double-ended tuning fork resonators are subjected to out-of-plane forces that support a motion with 180 degrees opposite phase shift. The mass element 1802 (the innermost mass element in Fig. 18) connected to its adjacent double-ended tuning fork resonator arms 1803, 1804 moves in synchronism with the adjacent arms. FIG. 19B

[0152] FIG. 20 Some modifications of the embodiment shown in Figs. 18 to 22 are shown. Only the central double-ended tuning fork resonator 1800 (or 1800') is mechanically anchored. Also, the top electrodes to the other double-ended tuning fork resonators are implemented by connecting the electrodes of adjacent resonators via the common mass element 1802, preferably in a symmetric pattern. FIG. 18A to FIG. 18B FIG. 19A to FIG. 19B Another modification of the embodiment shown in Figs. 18 to 22 is shown. The interconnecting mass elements (common mass elements) have been minimized (or omitted) such that the connecting elements between adjacent resonators are implemented only by the connecting beams 2145.

[0153] FIG. 21 FIG. 20 A further modification of the embodiment shown in Figs. 18 to 22 is shown. The interconnecting mass elements (common mass elements) have been minimized (or omitted) such that the connecting elements between adjacent resonators are implemented only by the connecting beams 2145.

[0154] FIG. 22 A rotational resonator 2200 is shown in which there is a central spring structure or portion that is mechanically anchored at its center to a mechanical anchor 2209. The central spring portion is connected to four mass elements 2201, 2202, 2211 and 2212 that are arranged in a surrounding region via four spring elements or arms 2203, 2204, 2213 and 2214. The spring elements form a cross structure, and the spring elements are substantially aligned along the <100> crystal axis (or deviate from this direction by less than 5 degrees).​​​​

[0155] The top electrodes 2205, 2206, 2215 and 2216 are patterned so that when an alternating signal is connected between the top and bottom electrodes, the arms 2203, 2204, 2213 and 2214 are subjected to a rotational (reciprocal) motion about the z-axis so that the central anchor region 2209 remains fixed. This can be achieved, for example, by patterning the top electrodes in a manner as illustrated in FIG. 22 so that the surface areas of the arms 2203, 2204, 2213 and 2214 on the same side of the arm in question (e.g. on the right side as viewed from the anchor 2209), i.e. the areas 2205, 2206, 2215 and 2216, are covered by the electrode parts, while the remaining areas of the arms remain uncovered. In this example, the four mass elements rotate in the same direction (in phase).

[0156] The (preferably metallic) wiring 22 to the top electrodes is arranged from the contact pads 2208. The contact to the bottom electrode is arranged from the contact pads 2207. FIG. 8 The openings 120 in the piezoelectric layer L2 as illustrated in FIG. 22 are not shown in. More generally, the contact pads can represent through-silicon via interconnects, which are part of the wafer-level packaged resonator.

[0157] In certain embodiments, the material stack of the resonator 2200 is implemented similarly as presented in the foregoing with reference to FIG. 12A to FIG. 12C the L4’ feature as disclosed in FIG. 8 may be supplemented.

[0158] In other embodiments, a resonator corresponding to the resonator 2200 is implemented with two top electrodes (X in and X out ) with opposite polarities and a bottom electrode that is electrically floating. In such embodiments, there can be an additional insulating layer (L8) between the top electrodes, which can be implemented similarly as in the embodiments shown in FIG. 10 and FIG. 11 . The technical implementation of the material stack can be implemented similarly as described in any of the embodiments shown in FIG. 10 and FIG. 12A to FIG. 12C .

[0159] 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 below. One technical effect is an optimized silicon MEMS resonator design. One technical effect is to provide a foldable mode MEMS resonator with a desired resonant frequency. Another technical effect is good frequency stability over a wide temperature range. Another technical effect is low equivalent series resistance (ESR). Another technical effect is to provide a resonator with a small footprint.

[0160] The above description has been provided by way of non-limiting examples of particular embodiments and examples of the present application, the full and informative disclosure of which is presently considered by the inventors to be complete and informative, in view of the patenting of the present application. However, to those skilled in the art, to which the application pertains, it will be clear that the application is not limited to the details of the above- presented embodiments, but that it can be implemented in other embodiments using equivalent means, without departing from the characteristics of the application.

[0161] Furthermore, some of the features of the above-disclosed embodiments of this application can be used to advantage without the corresponding use of other features. As such, the foregoing description shall not be interpreted as limiting the scope of the application. Hence, specific embodiments of the application are to be construed as merely illustrative of principles of the present application. Accordingly, the scope of the application is to be limited only by the appended patent claims.

Claims

1. A microelectromechanical resonator comprising: a spring mass system having a first weight portion, a second weight portion, and a center spring portion between the weight portions, the resonator having a piezoelectric layer for actuating the resonator, wherein the resonator comprises a silicon body doped to an average impurity concentration of at least 2 10 19 cm -3 and wherein a material portion of the center spring portion is oriented along an x-axis perpendicular to a y-axis along which the resonator is configured to vibrate, wherein the x-axis extends along a <100> silicon crystal direction or is offset from the <100> silicon crystal direction by less than 5 degrees.

2. The resonator of claim 1, wherein the first weight portion and the second weight portion are symmetrical weight portions.

3. The resonator of claim 1, wherein the center spring portion is a symmetrical portion.

4. The resonator of claim 1, wherein the center spring portion comprises a meandering structure attached at a first end of the meandering structure to the first weight portion and at an opposite end of the meandering structure to the second weight portion.

5. The resonator of claim 4, wherein the first weight portion and the second weight portion are connected to the center spring portion at edges of the first weight portion and the second weight portion.

6. The resonator of claim 1, supporting a foldable mode shape.

7. The resonator of claim 1, comprising an anchor point in a middle of a first edge of the spring portion and an anchor point in a middle of an opposite edge.

8. The resonator of claim 1, comprising an anchor point aligned with a center of mass of the center spring portion or a center of mass of the spring mass system.

9. The resonator of claim 1, comprising one anchor point for anchoring the center spring portion to a surrounding, the resonator's main resonant mode shape having a node at the one anchor point.

10. The resonator of claim 1, wherein the resonator comprises a semiconductor material and / or silicon and / or degenerately doped silicon, and / or more than 50% of the resonator mass is comprised of degenerately doped silicon, and / or the resonator comprises a silicon body that is doped to an average impurity concentration of at least 2 10 19 cm -3 , or at least 10 20 cm -3 .

11. The resonator of claim 1, wherein the resonator is configured to be piezoelectrically actuated.

12. The resonator of claim 1, wherein the center spring portion comprises arms separated by a trench, the arms being aligned with a <100> silicon crystal direction or the arms being misaligned with the <100> silicon crystal direction by less than 5 degrees.

13. The resonator of claim 1, wherein the resonator operates in vacuum.

14. The resonator of claim 1, wherein a trench at an end of the weight portions has a width that reduces air damping effects.

15. The resonator of claim 1, wherein the first weight portion and the second weight portion comprise a grid of trenches.

16. The resonator of claim 1, fabricated on a silicon-on-insulator (SOI) wafer.

17. The resonator of claim 1, configured to operate at a 32 kHz frequency band or at a frequency of 32.768 kHz.

18. The resonator of claim 1, wherein the center spring portion is oriented along a diagonal of a rectangular die.

19. The resonator of claim 1, wherein the spring mass system comprises additional support springs attached to the first weight portion and the second weight portion.

20. The resonator of claim 1, wherein a first portion of the resonator is located in a degenerately doped silicon layer and a second portion of the resonator is located in a Si02 layer formed below or above or on both sides of the degenerately doped silicon layer.

21. The resonator of claim 1, comprising the first and second mass portions and the center spring portion arranged in the shape of a tuning fork with side masses.

22. The resonator of claim 1, comprising a set of double-ended tuning fork resonators positioned in a row and connected with a common mass element or connecting beam.

23. The resonator of claim 1, comprising: a material stack with a silicon oxide layer between a top electrode layer and a bottom electrode layer.

24. The resonator of claim 1, further comprising third and fourth mass portions, wherein the center spring portion is arranged in the form of intersecting with a mechanical anchor at the center of the center spring portion.

25. The resonator of claim 1, comprising two top electrodes with opposite polarities, and a bottom electrode that is electrically floating.

26. The resonator of claim 1, supporting an in-plane bending vibration operating mode or an out-of-plane bending vibration operating mode.

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