阅读说明：本技术 Mems谐振器阵列布置 (MEMS resonator array arrangement ) 是由 A·贾克拉 A·奥加 于 2019-02-06 设计创作，主要内容包括：本发明涉及一种微机电谐振器,该微机电谐振器包括：支撑结构；谐振器元件,被悬置到支撑结构,该谐振器元件包括多个子元件；以及致动器,用于将谐振器元件激发到谐振模式。子元件被定尺寸为使得它们在一个方向上可划分为一个或多个基本元件,该一个或多个基本元件具有不同于1的长宽比,使得基本元件中的每个基本元件支持基本谐振模式,这些基本元件一起定义子元件的复合谐振模式。子元件还通过连接元件彼此耦合,并且相对于彼此定位为使得基本元件处于矩形阵列配置,其中每个基本元件占据单个阵列位置,并且阵列配置的至少一个阵列位置没有基本元件。(The invention relates to a microelectromechanical resonator comprising: a support structure; a resonator element suspended to the support structure, the resonator element comprising a plurality of sub-elements; and an actuator for exciting the resonator element into a resonant mode. The sub-elements are dimensioned such that they are divisible in one direction into one or more basic elements having an aspect ratio different from 1, such that each of the basic elements supports a basic resonance mode, the basic elements together defining a complex resonance mode of the sub-element. The sub-elements are further coupled to each other by connecting elements and are positioned relative to each other such that the basic elements are in a rectangular array configuration, wherein each basic element occupies a single array position and at least one array position of the array configuration is free of basic elements.)

1. A microelectromechanical resonator comprising:

-a support structure for supporting the support structure,

a resonator element suspended to the support structure, the resonator element comprising a plurality of sub-elements,

an actuator for exciting the resonator element into a resonant mode,

wherein

-the subelements are dimensioned such that the subelements are divisible in one direction into one or more elementary elements, the one or more elementary elements having an aspect ratio different from 1, such that each of the elementary elements supports a basic resonance mode,

the sub-elements are coupled to each other by a connecting element and are positioned relative to each other such that

Said base elements are in a rectangular array configuration, with each base element occupying a single array position,

o the resonance mode of the resonator element is a collective resonance mode, an

-at least one array position of the array configuration is free of elementary elements.

2. The resonator according to claim 1, wherein at least one free array position is located at a peripheral position of the array, such as at one, two or four corners of the array and/or at a side of the array, thereby providing a non-rectangular resonator element.

3. The resonator according to claim 1 or 2, wherein at least one free array position is located at an internal array position, such as at an array position located at one or both axes of symmetry of the array, thereby providing a resonator element with voids.

4. The resonator of any preceding claim, wherein the at least one free array position comprises transduction circuitry functionally coupled to the resonator element for actuating and/or sensing the resonator element.

5. The resonator according to any of the preceding claims, wherein said at least one free array position comprises a vertical electrical via or a horizontal electrical via functionally connected to said resonator element.

6. The resonator according to any of the preceding claims, wherein the at least one free array position comprises an electrical contact terminal.

7. The resonator according to any of the preceding claims, wherein the resonator elements are suspended to the support structure at the at least one free array position.

8. The resonator according to any of the preceding claims, wherein there are at least two different types of said subelements, a first type having a first length corresponding to a first number of elementary elements and a second type having a second length corresponding to a second number of elementary elements, said second length and said second number corresponding to an integer fraction of said first length and said first number of said first type.

9. The resonator according to claim 8, wherein said resonator element comprises at least one subelement of said second type, positioned between two subelements of said first type.

10. The resonator according to claim 9, wherein said resonator element is suspended from said two subelements of said first type to said support structure.

11. The resonator according to claim 10, wherein said resonator element comprises a void defined by two of said subelements of said second type and said two subelements of said first type, said support structure being at least partially arranged in said void, and said resonator element being suspended to said support structure within said void.

12. The resonator according to claim 10, wherein said resonator element comprises a recess defined by one of said subelements of said second type and said two subelements of said first type, said support structure being at least partly arranged to extend within said recess, and said resonator element being suspended to said support structure within said recess.

13. The resonator according to any of the preceding claims, wherein each of said subelements is adapted to resonate in said fundamental resonance mode, or in a overtone mode of said fundamental resonance mode.

14. The resonator according to any of the preceding claims, wherein said fundamental resonance mode is a fundamental length extended resonance mode and the length-to-width aspect ratio of the fundamental element is higher than 1.

15. The resonator according to any of claims 1-13, wherein the fundamental resonance mode is a fundamental torsional resonance mode or a fundamental bending resonance mode, such as an in-plane bending resonance mode.

16. The resonator according to any of the preceding claims, wherein the connection element is positioned at a non-node of the resonance modes of the subelements for coupling the subelements to each other in order to achieve a collective resonance mode in the resonator element.

17. The resonator according to any of the preceding claims, wherein the subelements are partially separated from each other by intermediate regions, each of the intermediate regions comprising at least one elongated groove, and at least two connecting elements adjoining the groove and mechanically coupling the subelements to each other.

18. The resonator according to any of the preceding claims, wherein the sub-elements and the connection element are formed of monocrystalline silicon, the monocrystalline silicon being doped to at least 2 ＊ 10¹⁹cm^-3Such as at least 10²⁰cm^-3Average impurity ofAnd (4) concentration.

19. The resonator according to any of the preceding claims, wherein the resonator element comprises a silicon crystalline body having a [100] crystallographic direction oriented along a main axis of the array configuration, in particular along a length direction of the subelement, or deviating less than 25 degrees, in particular less than 15 degrees, from the main axis of the array configuration, in particular from the length direction of the subelement.

20. The resonator according to any of the preceding claims, wherein each of the subelements is adapted to resonate in an in-plane length extending resonance mode.

Technical Field

The present invention relates to microelectromechanical (MEMS) resonators.

Background

Electromechanical resistance, also known as Equivalent Series Resistance (ESR), is an important performance parameter of a resonator. ESR tends to be high compared to conventional quartz crystals, particularly in piezoelectrically actuated beam resonators, such as Length Extended (LE) resonators, because the fundamental LE mode can only be present in beam resonators having a length-to-width aspect ratio greater than 1, i.e., in beams having a length greater than the width of the beam, and the nth overtone LE mode can be present in beam resonators having a length-to-width aspect ratio greater than N. Since the ESR of the LE mode decreases as the beam width increases, wider beams are preferred to obtain lower ESR. However, the presence of LE mode coupled with the aspect ratio sets a lower limit for ESR.

An additional task in MEMS resonator design is to make the resonator frequency insensitive to temperature changes, i.e. temperature compensation. In general, a beam resonator made of single crystal silicon can be temperature compensated using: the silicon crystal is doped sufficiently strongly to shape and align the beam appropriately with respect to the crystallographic orientation of the underlying silicon crystal and to select its resonant mode appropriately. Temperature compensation by doping is discussed more extensively in, for example, WO 2012/110708a 1.

The beam may oscillate, for example, in a length-extended (LE) resonant mode, wherein motion occurs primarily in the direction of the length of the beam. The LE mode has the following desirable properties: the resonator beam has a zero or positive first order Temperature Coefficient (TCF) when directed along the [100] crystal direction, and when doped with a sufficiently high doping concentration of an n-type dopant. The positive TCF of silicon allows the use of other materials with negative TCF, which may be needed for piezoelectric actuation purposes, for example, and thus the total TCF of the composite LE-mode resonator may become zero.

Instead of the LE mode, the beam resonator may be excited into a bending or torsion mode. However, these modes face similar problems with ESR and temperature compensation.

Particular challenges are faced when it is desirable to have both a low ESR and a low temperature dependence. Some piezo-actuated resonators having a length-to-width aspect ratio less than 1 (i.e., having a relatively wide beam) may support a resonant mode having a relatively low ESR level comparable to a quartz crystal at the same frequency. For example, Ho et al, "HIGH-ORDER composition BULK ACOUSTIC RESONATES" MEMS 2007, Shenhu, Japan, 2007, 1 month, 21-25 days, and Kuypers J., HIGH Frequency RESONATORS for Mobile Devices, inh.Bhugra, G.Piazza (eds.), Piezoelectric MEMS detectors, Microsystems and N-systems, DOI 10.1007/978-3-319-. However, these resonant modes have a higher temperature dependence than e.g. the LE mode and are therefore less available in piezo actuated resonators.

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

There is a need for an improved resonator that can simultaneously meet as many of the above requirements as possible.

Disclosure of Invention

The object of the present invention is to overcome the above problems. A particular object is to provide a novel resonator structure that is able to provide more design freedom, in particular for realizing resonators with a high quality factor (Q-value) and/or a small footprint.

An additional object is to achieve a resonator with a low ESR.

It is an object to achieve a resonator that provides simultaneously greater design freedom than single beam geometry, and the advantages of a beam resonator. A particular object is to achieve a resonator with a low frequency dependence on temperature.

These objects are achieved as described and claimed herein.

According to one aspect, a microelectromechanical resonator is provided that includes a support structure and a resonator element suspended to the support structure, the resonator element comprising a plurality of sub-elements placed at a distance from each other. An actuator for exciting a resonator element into a resonant mode is also provided. According to the invention, the subelements are dimensioned such that they can be divided in one direction into one or more basic elements having an aspect ratio different from 1, such that each of the basic elements supports a basic resonance mode (or the same basic resonance mode). Furthermore, the sub-elements are coupled to each other by the connecting elements and are positioned relative to each other such that the basic elements are arranged in a rectangular array configuration, wherein each basic element occupies a single array position, and the resonance mode of the resonator element is a collective resonance mode (collective resonance mode) defined by the basic elements. In addition, at least one array position of the array arrangement is free of essential elements.

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

In particular, the length-to-width aspect ratio of the sub-elements is higher than 1, so that they are beam elements. Depending on the length of the subelements, they resonate as a whole in the fundamental mode or in overtones of the fundamental mode. The fundamental mode may be, for example, a length-extended mode, a torsional mode, or a flexural mode.

The present invention provides significant benefits. The coupled sub-elements and thus the entire resonator element defined by the occupied array positions can resonate in a collective resonance mode, which results in a well-defined output frequency for the resonator side. The coupling with the connecting element has the effect of avoiding frequency splitting (splitting) and the occurrence of multiple resonance modes. The free array position may be used for other functional components of the resonator, such as anchor or electrical vias, surface circuitry, or contact pads, to mention a few examples. Thus, the degree of freedom of design is increased without impairing the performance of the resonator.

The design freedom can thus be used to modify the resonator envelope geometry (envelope geometry) for e.g. making room for the central anchoring of the resonator, which minimizes losses and maximizes the quality factor, and/or making room for electrical contacts, which minimizes the area of the resonator component when using rectangular cuts. These schemes will be discussed in detail later.

The resonator is compatible with at least length extension, bending and torsion modes. In addition, by using multiple subelements, the area of the resonator element can be increased for reducing ESR while maintaining the benefits of these modes.

Importantly, the present invention is compatible with doping-based (intrinsic) temperature compensation. This means that by properly aligning the resonator elements on the silicon wafer with respect to the crystal orientation of the silicon wafer, the temperature dependence of the resonator's frequency, i.e. the absolute value of the TCF, can be reduced.

This is particularly important in the case of piezoelectric actuation (which is often required to reduce ESR). Furthermore, the layer of piezoelectric actuator material arranged by the silicon body of the resonator element has an effect on the TCF, whereby an "overcompensation" of the TCF of the silicon body is beneficial.

The invention thus overcomes the limitations of the prior art in a practical manner and allows the realization of new types of resonators.

The dependent claims relate to selected embodiments of the invention.

In some embodiments, the at least one free array location is located at a peripheral location of the array. In practice, the one or more free positions may be at, for example, one, two or four corners of the array and/or at one side of the array. As a result, non-rectangular envelope geometries are formed. Preferably, the symmetry of the resonator with respect to the anchoring position is maintained.

In some embodiments, at least one free array location is located at an internal array location, thereby providing a voided resonator (voided resonator) element. The voids may be located at one or both axes of symmetry of the array. Preferably, the symmetry of the resonator is maintained at least with respect to the anchoring position.

At least one free array position can be used, for example, for

-transduction circuitry functionally coupled to the resonator element for actuating and/or sensing the resonator element, e.g. for driving an oscillator circuit of a resonator, and/or

-an electrical via or circuit functionally connected to the resonator element, such as a via connecting the inside of the sealed Wafer Level Package (WLP) of the resonator to the outside of the package or an internal or external circuit of the package, and/or

Electrical contact terminals, e.g. for bonding wires for activating the assembly, and/or

-a support structure and an anchoring element for suspending the resonator element.

In some embodiments, there are at least two different types of the sub-elements described above, the first type having a first length corresponding to a first number of elementary elements and the second type having a second length corresponding to a second number of elementary elements, the second length and the second number corresponding to (amount to) an integer fraction of the first length and the first number of the first type. The subelement of the second type can be positioned between two subelements of the first type, which leaves space for anchoring a resonator from two subelements of the first type, for example.

In some other embodiments, the resonator element comprises a void defined by two subelements of the second type and two subelements of the first type. The support structure may be arranged to extend in the void, and the resonator element is suspended to the support structure within the void.

Alternatively, the resonator element may comprise a recess defined by one or more subelements of the second type and two subelements of the first type. The support structure is at least partially arranged to extend into the recess, and the resonator element is suspended to the support structure within the recess.

In some embodiments, the resonator element is suspended from a node of a resonance mode of the subelement on opposite lateral sides in a width direction of the resonator element to the support structure. Alternatively or in addition, the resonator element may be suspended from a node between the two sub-elements to the support structure, preferably symmetrically in both the width and length directions of the resonator element. The two subelements are not necessarily adjacent elements, and typically are not adjacent elements, but are separated by a distance corresponding to the width of one or more subelements (and intervening trenches).

Typically, each of the subelements is adapted to resonate in a fundamental resonance mode or in an overtone mode of the fundamental resonance mode. In addition, the connecting element is positioned at a non-node of the resonance mode of the subelement for achieving a rise of the collective resonance mode. This ensures that there are no resonance peaks and the cleanliness of the output signal of the resonator.

In some embodiments, the fundamental resonance mode is a fundamental length-extension (fundamental-extension) resonance mode, and the fundamental element has a length-to-width aspect ratio higher than 1. The LE mode is particularly suited to minimize ESR and temperature compensation.

In some embodiments, each of the subelements is adapted to resonate in an in-plane length-extension (in-plane) resonant mode.

In some embodiments, the fundamental resonant mode is a fundamental torsional resonant mode or a fundamental flexural resonant mode, such as an in-plane flexural resonant mode. Also in this case, the basic element may have a length-to-width aspect ratio higher than 1.

In some embodiments, the sub-elements are separated from each other by an intermediate region comprising one or more grooves defined by the connecting elements between the sub-elements. The number of grooves corresponds to the order of the overtone mode in which the subelement is adapted to resonate.

In some embodiments, the sub-elements and the connecting elements are formed of single crystal silicon doped to at least 2 ＊ 10¹⁹cm^-3Such as at least 10²⁰cm^-3Average impurity concentration of (2). In particular (with an accuracy of 25 degrees) and along the main axis of the array arrangement, typically along the length of the subelement and the silicon crystal [100]]This, in combination with the crystal orientation alignment, allows for efficient temperature compensation of the resonator while achieving a small ESR.

Embodiments of the invention and their advantages are discussed in more detail below with reference to the accompanying drawings.

Drawings

Fig. 1-5 show top views of fully populated resonator array configurations formed from elemental components.

Figure 6 shows a top view of a resonator element suspended to a support structure.

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

Figure 8A shows a top view of one resonator configuration designed for the second order LE mode.

Fig. 8B shows a mode shape diagram of a portion of the resonator element of fig. 8A.

Figure 9A shows a top view of one resonator configuration designed for the fundamental (first order) LE mode.

Fig. 9B shows a mode diagram of a portion of the resonator element of fig. 9A.

Fig. 10 shows a plot of modal frequencies for a plurality of modal orders as a function of beam aspect ratio (width versus length).

Fig. 11 shows a top view of an exemplary high-order (ninth harmonic) mode resonator element configuration.

Fig. 12 shows a top view of a gapped, centrally anchored variant of the arrangement of fig. 11.

Fig. 13 shows a non-rectangular variant of the configuration of fig. 11.

Figures 14A-D show further examples of centrally anchored gapped, split and non-rectangular resonator elements.

Fig. 15A shows a measured broadband range admittance diagram (submittance graph) of the piezoelectrically coupled second harmonic mode resonator of fig. 8A.

Fig. 15B shows a detail of the admittance diagram of the main resonance of fig. 15A.

Fig. 15C shows a measured frequency versus temperature curve for the resonator of fig. 8A.

Figure 16A shows a top view of a multi-branched width-coupled resonator plate.

Figure 16B shows a top view of the longitudinally coupled resonator plates.

Fig. 17A-E show different possible flexible connecting element geometries between longitudinally coupled sub-elements.

Fig. 18A-C show examples of different longitudinal coupling positions.

Fig. 19A-D show additional examples of flexible connecting elements for longitudinal coupling.

Detailed Description

Definition of

By "nodal point" herein is meant a point at the oscillation mode that has an average oscillation amplitude that is less than 20% of the maximum amplitude of the oscillation mode.

"non-nodal point" (or "point displaced from nodal point") refers to a point at the oscillating mode shape that has an average oscillation amplitude that is 20% or more of the maximum amplitude of the oscillating mode shape.

The terms "length" and "longitudinal" are used herein in particular to refer to an in-plane direction which is parallel to the main expansion direction LE mode, the torsion axis of the torsion mode, or the axis perpendicular to the main bending displacement of the bending mode. "width" and "transverse" refer to the in-plane direction orthogonal to this direction.

Aspect ratio (aspect ratio) refers to the ratio of the in-plane dimensions of an element or sub-element. By "effective aspect ratio" is meant the aspect ratio of the entire resonator element, including the plurality of sub-elements, as opposed to the aspect ratio(s) of its individual sub-elements (beams).

A "trench" (trench) refers to an empty space inside a resonator element that allows adjacent subelements to move relative to each other and thus the desired mode occurs in the subelement. An "elongated" (elongated) trench is a trench having an aspect ratio of 3 or more, such as 5 or more, or even 10 or more, depending on the mode the element is adapted to support.

A "connecting element" is any member that mechanically connects two sub-elements, which are located at a distance from each other. The connection element may couple the subelement in the width direction, whereby it is confined to a groove, or alternatively a void or recess, within the resonator element at the longitudinal ends of the resonator element. In this case, the element is typically a substantially rigid element. Alternatively, it may couple the subelements lengthwise, whereby it is generally a flexible element, such as a C-shaped or S-shaped element that can be elastically deformed during resonance. Typically, the connection element is part of a single crystal structure of the resonator element, which is generated by patterning the outer shape of the resonator element and the trenches therein using known MEMS micromachining methods.

The "fundamental (resonant) mode" refers to a first-order resonant mode (also referred to as "first harmonic"). The higher overtone mode is formed by several basic modes.

The "basic element" is the rectangular in-plane part of the resonator, which carries the (carry) basic resonance mode. The base elements may be seamlessly (seamless) connected in the longitudinal direction in an end-to-end configuration (i.e., the "virtual" elements of the beam defined by the mode shape excited therein), or separated by gaps and connected by flexible connecting elements. The higher overtone mode of order N can be considered as a fundamental mode occurring in N fundamental elements coupled end-to-end longitudinally.

A "collective (collective) resonant mode" refers to a compound resonant mode in which all of the fundamental elements of a particular entity of interest resonate in the same fundamental resonant mode and have substantially the same frequency and the same or 180 degree shifted phase. In the collective resonance mode of the entire resonator element, each of the subelements forming the resonator element carries a first-order length-extending, torsional or bending resonance mode or higher overtone mode thereof. In this case, the resonator element may be divided into elementary elements, typically of equal size, each supporting the same elementary mode.

In a typical embodiment, all the basic elements of the resonator are arranged in a rectangular array configuration. An "occupied" array location contains a basic element. The "unoccupied" array locations are free of resonant material.

By "voided" resonator element shape is meant a shape in which at least one array location within the resonator element is unoccupied. The voids may serve as anchoring and/or electrical contact regions. In this context, the desired resonant mode enabling gap (trench) between subelements is not considered to be a void.

A rectangular resonator element is an element whose all peripheral basic element array positions are occupied. The non-rectangular elements have at least one peripheral array position unoccupied.

When looking at the length of a subelement, "integer fraction" means a fraction of N/M, where N and M are both positive integers and N < M. For example, the third harmonic sub-element in the embodiment of the present invention is shorter than the fifth harmonic sub-element by an integer fraction 3/5.

Length Extended (LE) bulk acoustic modes of different orders in the beam elements are known in the art. In such a mode, the elements (subelements) contract and expand primarily along a single axis with one or more nodes on the axis. In a symmetric element, and in a typical case where both longitudinal ends of the element are free (not anchored to the support structure), the nodes are symmetrically located along the length of the element. Similarly, torsional and in-plane bending and out-of-plane (out-of-plane) bending modes are known in the art.

An element that is "temperature compensated" in this context means that the elastic properties of the element, in relation to the mechanical movement of the element, at the present doping level are adapted to have a smaller temperature dependence in at least some temperature ranges than would be the case without such doping¹⁹cm^-3Or larger, such as 10²⁰cm^-3Or larger. The dopant may be an n-type or p-type dopant, such as phosphorus or boron. Temperature compensation in this context also covers so-called "overcompensation", i.e. having the TCF of the element positive such that when the piezoelectric transducer layer and/or some other layer is coupled with the element, the total TCF of the resonator is smaller than without doping.

Description of selected embodiments

In the following, the overall resonator structure and function is first described with reference to fully populated array resonators, then particular attention is given to configurations having one or more free array positions. It should be noted that the principles described with reference to the former apply to the latter. In addition, any fully populated resonator described having an array size of at least 2 x 2 (particularly at least 3 x 2 to maintain symmetry) can be modified to conform to the invention by removing one or more of the elemental elements while maintaining coupling of the remaining elemental elements.

In general, the resonator elements discussed herein may include a plurality of subelements having aspect ratios greater than 1, particularly greater than N, where N is the number of overtones (i.e., mode order) of the collective modes excited therein.

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

The number of elementary elements in the length direction corresponding to the number of mode steps excited in the subelement may for example be 1-20, for example 2-12.

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

More detailed embodiments of the invention are described below primarily with reference to the length extension mode, for which experimental data is also provided to illustrate the feasibility and benefits of the invention, but the same principles can be applied to both torsional and bending modes.

In some embodiments thereof, the present invention provides a length-extended mode resonator comprising a support structure, and a silicon resonator element suspended to the support structure at a node thereof, the resonator element having a length and a width. The resonator element further comprises at least two sub-elements partially separated from each other by intermediate regions, each of the intermediate regions comprising at least one elongated groove and at least two connecting elements adjoining the groove and mechanically coupling the sub-elements to each other at non-nodes thereof. This ensures a strong coupling of the subelements and thus the behaviour of the entire element as a single element with well defined resonance modes and resonance frequencies. The actuator is adapted to excite the resonator element into a length-extending resonance mode, the length-extending resonance mode being parallel to a longitudinal direction of the at least one elongated slot.

In some embodiments, the resonator element comprises a body of doped silicon. Furthermore, [100] of a silicon body]The crystal direction may be oriented along the length extension of the resonator element or may deviate less than 25 degrees, in particular less than 15 degrees, from the length extension of the resonator element, and doping the silicon body of the resonator to at least 2 ＊ 10¹⁹cm^-3Such as at least 10²⁰cm^-3This allows the resonator to be temperature compensated while achieving a low ESR.

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

In some embodiments, there are at least two grooves and three connecting elements in at least one intermediate region, preferably in all intermediate regions. This may be used to manufacture resonator elements that are dedicated to specific higher order LE overtones, for example.

The aspect ratio of the subelement is typically selected to be in the range of 2:1 … 10:1 to keep the number of subelements relatively low and to keep the relative area occupied by the trenches low and to obtain the maximum benefit of the invention. However, the invention is also applicable to higher aspect ratio sub-elements.

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

If each subelement of figure 1 is driven to a first order mode, i.e. the fundamental mode, the resonator elements form a fully populated, rectangular array of 3 x 1 fundamental modes.

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

The element is suspended from the midpoint of its longitudinal outer edges using anchors (anchors) 19A, 19B. The number of anchors may be greater than two. In a typical arrangement, the anchor is located at or symmetrical with respect to the transverse central axis of the element.

Fig. 2 shows an embodiment suitable for second order LE-mode oscillation. Between each sub-element 21A, 21B, 21C there are three connecting elements 22AB/24AB/26AB, 22BC/24BC/26BC and two grooves 23AB/25AB, 23BC/25 BC. This configuration allows the subelement to expand in width in the second LE mode, as well as other even higher order modes. The resonator elements of figure 2 form a rectangular 3 x 2 fundamental mode array.

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

Fig. 3 shows an example in which there are four sub-elements 31A-D separated by non-similar intermediate regions. Between each two most lateral sub-elements 31A/31B, 31C/31D, there are two grooves 33AB/35AB, 33CD/35CD and three connecting elements 32AB/34AB/36AB, 32CD/34CD/36CD, while between the most central sub-elements 31B/31C, there is a single groove 33BC and two connecting elements 32BC/34 BC. Other configurations are also possible. The resonator elements of figure 3 form a (modified) rectangular 4 x 2 fundamental mode array.

Fig. 4 shows an embodiment in which three sub-elements 41A, 41B, 41C are interleaved with intermediate regions 48AB, 48BC, the intermediate regions 48AB, 48BC each having four connecting elements and three grooves symmetrically positioned along the length of the sub-elements. The resonator elements of figure 4 form a rectangular 3 x 3 fundamental mode array.

FIG. 5 shows a variantType, this variant has five subelements 51A-E separated by intermediate areas 58AB-DE of the kind discussed with reference to fig. 2. In this example, the total width W of the element_tGreater than the length of the element, which is equal to the length l of the subelement the resonator elements of figure 5 form a rectangular array of 5 × 2 basic modes.

In a typical implementation, at least one trench between each pair of subelements is centered on a node of the LE pattern.

For an element capable of supporting LE mode, the total length of the trench (es) at each intermediate region between sub-elements should be a significant fraction of the total length L of the element. In some embodiments, the portion is 50% or more, such as 75% or more. In some embodiments, the portion is 90% or more.

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

In some embodiments, the grooves and connecting elements are sized (dimensioned) and positioned such that frequency splitting and the occurrence of multiple simultaneous resonant modes can be avoided. Herein, http may be followed: the principle of "Experimental study of the effects of sizing on piezoelectric transformed MEMS actuators" by A.Jaakkola et al, page 410-414, de dX.doi.org/10.1109/FREQ.2010.5556299, Proc.IEEE International Frequency Control Symposium, 2010.

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

Figure 6 shows a suspended resonator element. The support structure 60 is separated from the resonator element 61 by a gap at all locations except for the anchor point 69 at a node point on the outer longitudinal side of the most lateral sub-element. As described above, this allows the resonator element 61 to freely oscillate in the LE mode.

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

Finally, fig. 7A-7C illustrate the difference of the present resonator with respect to a conventional resonator. Fig. 7A shows a single high aspect ratio beam with two free ends. Fig. 7B shows a beam extending in the width direction, actually making it a rectangular plate. Such resonators have a low ESR and can be used in the [110] direction, but cannot operate in the LE mode when aligned in the [100] crystal direction and therefore cannot be temperature compensated therein. Figure 7C shows a resonator element according to one embodiment of the invention. This scheme works even if the side edges of the element are aligned in the [100] crystal direction, and has the same low ESR in the [110] direction as the plate of FIG. 7B.

Fig. 8A shows a resonator capable of supporting a second LE overtone resonance mode. The resonator element of the resonator is formed by a number (here 11) of sub-elements, which are each separated from the adjacent sub-element by two elongated grooves, which are arranged one after the other, and are connected to the adjacent sub-element by three connecting elements. When the resonator plate is shown as 326 μm by 180 μm in size, the resonant frequency is close to 40 MHz. The resonator elements of figure 8A form a rectangular 11 x 2 fundamental mode array.

FIG. 8B shows the LE mode resonance mode for the geometry of FIG. 8A simulated with FEM software. Due to the symmetry, only half of the entire resonator is shown. The shading in grey indicates the total displacement at each position. As can be seen, each subelement resonates in the same collective mode. In the second order (and other even-order resonances), the mode shape is asymmetric, but one end of the subelement contracts while the other expands.

Figure 9A shows another resonator capable of supporting a fundamental LE resonant mode. When the resonator plate is 300 μm × 180 μm in size, the resonance frequency is close to 20 MHz. The resonator elements of figure 8A form a rectangular 5 x 1 fundamental mode array.

Fig. 9B shows the southeast, symmetric quarter LE mode resonance mode shape of the geometry of fig. 9A simulated with FEM software.

Fig. 10 shows a graph of the modal frequencies of beams (here corresponding to subelements) with aspect ratios between nearly zero (very thin beams) and 1. Dashed lines indicate basic LE mode (LE1) and overtone mode LE2 … … LE 4. Along the LEx modal branch, the LEx pattern in the direction defined by the parameter L is only present at the dashed region.

Fig. 11 shows an example of a high (ninth) overtone length extension resonator element including a plurality of (19) sub-elements 111A, the plurality of sub-elements 111A being stacked in the width direction and anchored with anchor elements 119 from nodes at opposite longitudinal sides thereof. For example, to form a resonator that oscillates at about 120MHz, the size of the element may be set to 225 μm 170 μm.

Fig. 12 shows a similar configuration to fig. 11 in other respects, but now the anchoring has been done by: the anchor element 129 at the center of the resonator is used by providing a void 118 in the resonator element, i.e. "removing" some of the central basic elements of the subelement (in this case 5 x 3 basic elements). Thus, the resulting structure includes two types of subelements 121A, 121B having different lengths. The length of the shorter sub-element 121B is an integer fraction of the length of the longer element 121A. It has been shown that the collective resonant mode properties of the slab are maintained even if the envelope (envelope) geometry has been modified.

In general, the present resonator design allows for the (preferably symmetric) removal of the desired basic elements without losing the desired (collective) mode characteristics of the composite resonator. This has the following advantages: the LE resonant mode characteristics are maintained even if a void is present in the center. The central anchor is beneficial as such from the perspective of minimizing packaging stresses that may affect the resonator element. The central anchor is also beneficial from the standpoint of low acoustic losses, thereby increasing the Q of the resonator. The loss is reduced due to the high degree of symmetry of the structure allowed by the present invention.

Fig. 13 shows an example of a non-rectangular geometry, where the basic elements are omitted at the corners of the resonator plate. Also in this case, the resulting structure comprises two types of subelements 131A, 131B having different lengths. In this case, the collective resonant mode properties of the plates are maintained even though the envelope geometry has been modified. The free area 113 may be used, for example, for electrical interconnection and/or vias of components.

Thus, the gapped and/or non-rectangular resonator elements as illustrated in fig. 12 and 13 are advantageous in that the footprint of the resonator components can be minimized in view of the fact that in a common dicing process, a wafer containing a plurality of components is cut into rectangular portions, each containing a single component. To mention just some potential requirements, the area freed from the resonator area may be used for anchoring or internal or external connection purposes. The embodiments of fig. 12 and 13 may also be combined to provide a gapped, non-rectangular resonator element.

The resonator elements of fig. 11-13 form a rectangular 19 x 11 fundamental mode array. The array locations of fig. 11 have been fully occupied, but are stored in unoccupied array locations in fig. 12 and 13.

Fig. 14A shows an embodiment similar to fig. 12, but now adapted for smaller frequencies (overtone 3). The void 148A is created here by "removing" all the basic elements of one subelement and using longer connecting elements 147A at the longitudinal ends of the void 148A. Central anchoring with the anchoring element 149A is achieved.

Fig. 14B shows a further variation in which the longer coupling element 147A of fig. 14A is omitted so that the resonator is actually a two-element resonator, each single element being of the type currently discussed. This is a simple geometry to process because the substrate anchored to the periphery does not require structural contact to the back or top wafer as in the design of fig. 14A. In order for a collective mode to exist between two elements of a resonator, anchoring needs to be achieved so that the two elements are not too weakly coupled to each other (which may produce two distinct peaks due to manufacturing imperfections).

Fig. 14C and 14D illustrate additional embodiments that combine the advantages of fig. 14A and 14B and provide a central anchor, easy electrical connection to the actuator and overcome the potential problem of weak coupling. The configuration of fig. 14C couples the left and right sides so that there is a compound pattern by using one longer connecting element 147C and supporting structure 148C and anchoring element 149C on the opposite side of the element, structure 148C extending to the central anchoring region. The embodiment of fig. 14D is similar to the embodiment of fig. 14C, but here sufficient coupling is achieved and ensured by one complete basic element comprising a sub-element 141D, which sub-element 141D has an integer fractional length of another sub-element 141C.

The resonator elements of fig. 14A-D form a rectangular 11 x 3 fundamental mode array with 3 unoccupied array positions in fig. 14A-C and 2 unoccupied array positions in fig. 14D. (the embodiment of FIG. 14B can also be viewed as two 5 x 1 arrays depending on the coupling strength).

In general, in some embodiments, as shown in fig. 12, 13 and 14D, there are at least two different types of subelements, a first type having a first length and a second type having a second length, the second length corresponding to an integer fraction of the length of the first type, for exciting the different types of subelements to different overtone modes of a collective fundamental resonant mode.

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

In some examples, like the example of fig. 12, the resonator element comprises a void defined by two or more sub-elements of the second type and two sub-elements of the first type, the support structure is at least partially arranged in the void, and the resonator element is suspended to the support structure within the void. Thus, the resonator element is anchored centrally to surround the anchoring position in the lateral plane.

In some embodiments, like the embodiment shown in fig. 14D, the resonator element comprises a recess (i.e. a lateral depression) which is defined by one or more sub-elements of the second type and two sub-elements of the first type, the support structure is at least partly arranged to extend within the recess, and the resonator element is suspended to the support structure within the recess.

By means of both the void and recess configuration, a central anchoring may be achieved, which may be used to minimize the loss of the resonator. The void configuration has the benefit that it may enable a fully symmetric resonator, while the recess configuration allows simpler electrical access to the surface of the resonator, which typically contains a piezoelectric actuation layer. By means of the recess arrangement, through silicon vias (through silicon vias) in the wafer can be completely avoided. In a void configuration, through-silicon vias may be arranged in the wafer, to the area of the void.

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

Fig. 15B shows a detail of the admittance diagram of the primary resonance of the design of fig. 15A (labeled "11 beams"), and corresponding diagrams of the primary resonance of a resonator similar to that of fig. 15A but with a smaller number of coupled beam elements (labeled "7 beams" and "3 beams," respectively). The resonator quality factor Q, the shunt capacitance C obtained by fitting to the measurements are shown for all three cases₀And an equivalent series resistance R₁(═ ESR). The figure shows how the ESR decreases as the resonator width increases in proportion to the number of coupled beam elements.

FIG. 15C shows measured frequency versus temperature curves for both: resonator of FIG. 15A (Labeled "stacked LE beam overtone 2"), and the same characteristics of a hybrid WE-dome mode resonator similar to that discussed in WO 2018/002439 a1, both prepared with n-type doping of 7 ＊ 10¹⁹cm^-3On the same wafer. It can be seen that: the linear temperature coefficient TCF1 for the resonator of fig. 15A is about 4 units higher than the same parameter for the other resonator. Therefore, there is a high overcompensation, which has the following benefits: for example, a thicker AlN layer may be used for piezoelectric driving purposes to achieve a temperature compensated design.

Figure 16A shows a resonator element configuration with four branches of short subelements coupled side by side, anchored to a central support element at nodes. Each branch element is a 6 x 1 fundamental mode array resonator element with non-nodal internal coupling between its subelements.

In a variation of fig. 16A (not shown in detail), to ensure collective resonance between the branches, the central element is a resonating subelement, and the coupling of the branches to the central subelement may also be at non-nodal points, thereby forming a 13 × 2 fundamental mode array.

Fig. 16B shows a top view of a longitudinally coupled resonator plate comprising three rows and 11 columns of fundamental mode subelements. Each row is coupled to the other row at both ends of the row using flexible longitudinal connecting elements. As discussed above, each row is internally coupled using a rigid connecting element. An 11 x 3 array of elemental elements is formed.

Fig. 17A-E show different possible flexible connecting element geometries between longitudinally coupled sub-elements. The side connectable shape "C" shape also used in the configuration of fig. 16B is shown in fig. 17A. The end connectable shape is shown in fig. 17B-17E. These show the end connectable C shape of fig. 17B, the S shape of fig. 17C and 17D, and the oblique I shape of fig. 17E. It will be appreciated that other flexible shapes and variations of the illustrated shape are possible.

Fig. 18A-C schematically show examples of different longitudinal coupling options at the level of the resonator plate. It can be seen that the longitudinal couplings can be arranged directly between the longitudinal elements in any configuration, preferably a symmetrical configuration, for example using the elements of fig. 17B-E (connection elements not shown in detail in fig. 18A-C).

As shown in the examples discussed above, instead of or in addition to end-to-end connection of subelements in the same column, longer elements extending widthwise above the column boundary may be used to connect subelements of different columns (not shown).

Fig. 19A-D show further examples of flexible connecting elements, each having at least one T-shaped branch.

Reference list

Patent document

WO 2012/110708 A1

WO 2018/002439 A1

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