WO2024055388A1

WO2024055388A1 - Acoustic resonator

Info

Publication number: WO2024055388A1
Application number: PCT/CN2022/128015
Authority: WO
Inventors: Viktor Plesski; Naiqing Zhang
Original assignee: Huawei Technologies Co., Ltd.
Priority date: 2022-09-14
Filing date: 2022-10-27
Publication date: 2024-03-21

Abstract

The present disclosure relates to an acoustic resonator wherein each resonant element is at least partly coated with vertical electrodes on side walls of its top piezoelectric part and solidly mounted with its bottom part on an underlaying supporting substrate. The bottom part of each resonant element has a width smaller than λ/2, where λ is a wavelength of a shear acoustic wave in the bottom part at a resonance frequency determined by the top part. Given this condition, a total width of the top part and the electrodes is greater than the width of the bottom part, and vibrations from the top part cannot propagate through the bottom part, thereby leading to increasing piezo-coupling and providing structural solidity. Moreover, a heat evacuation path can go in each resonant element from its top part to the substrate through its bottom part, which may improve the power-handling properties of the resonator.

Description

ACOUSTIC RESONATOR

CROSS-REFERENCE TO RELATED APPLICATION

The present application claims priority from International Patent Application No. PCT/CN2022/118572, filed on September 14, 2022, entitled "ACOUSTIC RESONATOR WITH VERTICAL ELECTRODES" , which is incorporated by reference herein in its entirety.

TECHNICAL FIELD

The present disclosure relates generally to the field of acoustic devices. In particular, the present disclosure relates to an acoustic resonator in which each resonant element is provided with vertical electrodes on side walls of its top piezoelectric part and solidly mounted with its bottom part on an underlaying supporting substrate, thereby providing high piezo-coupling and improving heat evacuation capability.

BACKGROUND

Acoustic resonators can be used to implement signal processing functions in various electronic applications. For example, the acoustic resonators are used in the existing wireless and wired communication devices, such as mobile phones, to implement frequency filters and/or multiplexers for transmitted and/or received wireless and/or wired signals. Some examples of the acoustic resonators include bulk acoustic wave (BAW) resonators, thin-film bulk acoustic resonators (FBARs) , laterally excited bulk acoustic wave resonators (XBARs) , transversally excited shear wave resonators (YBARs) , stacked bulk acoustic resonators (SBARs) , double bulk acoustic resonators (DBARs) , and solidly mounted resonators (SMRs) .

An XBAR is based on exploiting a suspended piezoelectric (e.g., lithium niobate or LN for short) membrane of submicron thickness and have been proven to be a high piezo-coupling acoustic resonator. In the XBAR, a horizontal electric field is utilized for a horizontal displacement and an A1 mode resonance in a piezoelectric layer of the membrane.

However, since the membrane in the XBAR is extremely thin and needs to be suspended over an air cavity for acoustic isolation, the membrane is a fragile structure. Moreover, since the bottom side of the membrane must be open, this significantly complicates the fabrication process of the whole XBAR. On top of that, the XBAR has poor power-handling properties due to the low thermal conductivity of its suspended piezoelectric membrane (i.e., heat is evacuated mainly along electrodes attached to the membrane) .

SUMMARY

This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features of the present disclosure, nor is it intended to be used to limit the scope of the present disclosure.

It is an objective of the present disclosure to provide an acoustic resonator that provides high piezo-coupling and exhibits improved (e.g., compared to the existing XBARs) power-handing properties.

The objective above is achieved by the features of the independent claim in the appended claims. Further embodiments and examples are apparent from the dependent claims, the detailed description, and the accompanying drawings.

According to an aspect, an acoustic resonator is provided. The acoustic resonator comprises a supporting substrate and at least one resonant element provided on the supporting substrate. Each of the at least one resonant element has a top part and a bottom part. The top part is made of a piezoelectric material and has two opposite side walls each at least partly coated with an electrode. The bottom part has a width smaller than λ/2, where λ is a wavelength of a shear acoustic wave in the bottom part at a resonance frequency which is determined by the top part. In the acoustic resonator thus configured, the shear acoustic wave generated in the top part of each resonant element in response to a radio frequency (RF) electric signal applied to the electrodes may be prevented from leaking into the supporting substrate because the total width of the electrodes and the top part is always greater than the width of the bottom part. This may provide high piezo-coupling

in the acoustic resonator and, thus, a large Resonance-antiResonance (R-a-R) frequency gap which is an important condition for using this resonator in wide-band filters. Moreover, the acoustic resonator thus configured may exhibit excellent power-handling properties due to the presence of a heat evacuation path in each resonant element from its top part to the supporting substrate through its bottom part. The above-indicated advantages may allow the acoustic resonator to operate at a 5 GHz frequency range with comparably high piezo-coupling.

In one exemplary embodiment, each of the at least one resonant element is shaped as a ridge. In this embodiment, the ridge has a transversal (or aperture) dimension and a cross-sectional dimension, and the two opposite side walls coated at least partly with the electrodes in each of the at least one resonant element extend along the transversal dimension. The transversal dimension may be much larger (e.g., at least 10 times) than the cross-sectional dimension. Such ridge-like resonant structures may be easy to implement and less fragile, for example, compared to column-like structures. Furthermore, it is much easier to make electrode connections in such ridge-like resonant structures.

In one exemplary embodiment, each of the two opposite side walls of the top part in each of the at least one resonant element is inclined at an angle from -40° to 40° relative to a normal to the supporting substrate. This wide range of side-wall inclination angles may give tolerance for the fabrication process of the acoustic resonator (e.g., by using photolithography) . It should also be noted that a high Q value and piezoelectric coupling factor

may still be obtained at such side-wall inclination angles.

In one exemplary embodiment, the top part in each of the at least one resonant element has a positively or negatively tapered profile. This may also provide flexibility in the fabrication process of the acoustic resonator and make the acoustic resonator versatile in use (e.g., different top-part profiles of the resonant elements may be used for different acoustic applications, studies, etc. ) .

In one exemplary embodiment, the top part and the bottom part in each of the at least one resonant element are equal in height. This may also provide flexibility in the fabrication process of the acoustic resonator (e.g., the equal heights of the top and bottom parts may simplify the actual fabrication process of the acoustic resonator) .

In another exemplary embodiment, each of the top part and the bottom part in each of the at least one resonant element has a different height. This may also provide flexibility in the fabrication process of the acoustic resonator (e.g., from the fabrication process standpoint, it may be easier to make the top and bottom parts different in height than equal in height) .

In one exemplary embodiment, the top part in each of the at least one resonant element has a height-to-width ratio ranging from 0.4 to 2. The top part with height and width values falling within this range may provide optimal piezo-coupling factor values, as well as may be convenient to fabricate.

In one exemplary embodiment, the bottom part in each of the at least one resonant element has a height-to-width ratio ranging from 0.4 to 2. The bottom part with height and width values falling within this range may provide good heat evacuation from the top part to the supporting substrate, may be used as a strong support for the top part, and may be convenient to fabricate. If the height-to-width ratio for the bottom part is smaller than 0.4, redundant (parasitic) coupling may occur between the top part and the supporting substrate. If the height-to-width ratio for the bottom part is higher than 2, such a high bottom part will be difficult to fabricate, not to mention more fragile.

In one exemplary embodiment, the supporting substrate is made of the piezoelectric material, and the bottom part in each of the at least one resonant element is made of the piezoelectric material. In this embodiment, it is possible to implement the acoustic resonator by using a piezoelectric substrate only –each resonant element may be formed, for example, by etching cavities on the surface of the piezoelectric substrate and forming the electrodes on the side walls of each cavity close to the original surface of the piezoelectric substrate. This embodiment may be useful, for example, when it is required to provide decreased material consumption (i.e., the same piezoelectric material is used for the substrate and each resonant element of the acoustic resonator) , as well as reduced fabrication costs (e.g., one LN substrate is at least one order cheaper than a multi-layered substrate, such as LN/SiO2/submicron-LN) .

In one exemplary embodiment, the supporting substrate is made of a first dielectric material, and the bottom part in each of the at least one resonant element is made of a second dielectric material. In this embodiment, the first dielectric material and the second dielectric material may be the same or different from each other. Again, this may provide flexibility in the fabrication process of the acoustic resonator.

In one exemplary embodiment, the first dielectric material comprises one of silicon (Si) , diamond, silicon carbide (SiC) , and silicon dioxide (SiO2) , and the second dielectric material comprises one of Si, SiO2, quartz, and glass. These materials are good in terms of mechanical properties and thermal conductivity, for which reason they may provide a strong support for the top part in each resonant element and increase heat evacuation capability with almost no loss of piezo-coupling (i.e., avoid the occurrence of the redundant coupling between the top part and the supporting substrate) .

In one exemplary embodiment, the piezoelectric material comprises one of lithium niobate (LN) , lithium tantalate (LT) , Al (Sc) N, lithium iodate (LiIO3) , zinc oxide (ZnO) , lead zirconate titanate (PZT) , and quartz. These materials exhibit proper piezoelectric properties for the efficient operation of the acoustic resonator.

In one exemplary embodiment, the piezoelectric material comprises one of 30°+/-30°-rotated Y-cut LN and 120°+/-30°-rotated Y-cut LN. By using these cuts of LN, it is possible to achieve strong piezo-coupling (e.g., up to

) . 30°-rotated Y-cut LN may be used to obtain a main resonance mode like a SH 1 mode with maximized

while 120°-rotated Y-cut LN may be used to obtain a main resonance mode like an A1 mode with maximized

In one exemplary embodiment, widths of the top part and each of the electrodes in each of the at least one resonant element are selected based on a resonance frequency of the acoustic resonator. Thus, by changing the widths of the top part and the electrodes, it is possible to change or tune the resonance frequency of the acoustic resonator.

In one exemplary embodiment, the bottom part in each of the at least one resonant element comprises a set of alternating low and high acoustic impedance layers each having a thickness of λ/4, where λ is the wavelength of the shear acoustic wave propagating across the set of alternating low and high acoustic impedance layers. By using such a set or stack of layers, it is possible to isolate the active (top) part of the acoustic resonator from the supporting substrate, thereby avoiding acoustic losses (i.e., providing strong piezo-coupling) .

In one exemplary embodiment, the supporting substrate comprises a set of alternating low and high acoustic impedance layers each having a thickness of λ/4, where λ is a wavelength of a shear acoustic wave propagating across the set of alternating low and high acoustic impedance layers. By using such a set or stack of layers, it is also possible to isolate the active (top) part of the acoustic resonator from the supporting substrate, thereby avoiding acoustic losses (i.e., providing strong piezo-coupling) .

In one exemplary embodiment, the at least one resonant element comprises an array of identical resonant elements provided on the supporting substrate. In this embodiment, the array of identical resonant elements has an inter-element spacing selected such that there is no mechanical contact between the electrodes of each two adjacent resonant elements of the array of identical resonant elements. The use of multiple identical resonant elements in the acoustic resonator may be beneficial in some acoustic applications. For example, the number of resonant elements and their geometry (i.e., their width, height, and length/aperture) may be selected in a way to obtain desired parameters of the acoustic resonator (not only its resonance frequency but, e.g., also an impedance at the resonance frequency and a static capacitance, etc. ) .

In one exemplary embodiment, the inter-element spacing is larger than a total width of the top part and the electrodes. Such an inter-element spacing may provide the efficient operation of the acoustic resonator with multiple identical resonant elements.

In another exemplary embodiment, the inter-element spacing is defined as:

where p is the inter-element spacing, V _acoustic is the lowest acoustic wave velocity in the supporting substrate, and F _R is the resonance frequency of the acoustic resonator. Such an inter-element spacing may provide the efficient operation of the acoustic resonator with multiple identical resonant elements. In this resonator configuration, the inter-element spacing may be quite large (up to 5 μm) without the energy leakage from the top part down to the substrate. Such large inter-element spacing may also provide flexibility in the fabrication process of the acoustic resonator.

In one exemplary embodiment, the acoustic resonator comprises a first array of identical resonant elements and a second array of identical resonant elements which are both provided on the substrate. The first array of identical resonant elements and the second array of identical resonant elements differ from each other in at least one of: an inter-element spacing; a profile of the top part; a size of the top part; a size of the bottom part; the piezoelectric material of the top part; a material of the bottom part; a number of resonant elements; and an aperture of each resonant element. By using two different arrays of identical resonant elements, one can implement two acoustic resonators with different resonance frequencies, which is necessary for using such resonators, for example, in “ladder” filters.

Other features and advantages of the present disclosure will be apparent upon reading the following detailed description and reviewing the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure is explained below with reference to the accompanying drawings in which:

FIGs. 1A and 1B show different schematic views of a suspended piezoelectric membrane used in a laterally excited bulk acoustic wave resonator (XBAR) in accordance with the prior art, namely: FIG. 1A shows a perspective view of the membrane, and FIG. 1B shows a magnified side view of the membrane, as taken within the area delimited by circle A in FIG. 1A;

FIG. 2 shows a schematic side view of an acoustic resonator in accordance with a first exemplary embodiment;

FIG. 3 shows a schematic side view of an acoustic resonator in accordance with a second exemplary embodiment;

FIG. 4 shows a schematic side view of an acoustic resonator in accordance with a third exemplary embodiment;

FIG. 5 shows a schematic side view of an acoustic resonator in accordance with a fourth exemplary embodiment;

FIG. 6 shows a dependence of a piezo-coupling factor

on a side-wall inclination angle in a top piezoelectric part of each resonant element included in the acoustic resonator of FIG. 4, with the width of the top piezoelectric part equal to 300 nm; and

FIG. 7 shows an admittance curve of optimized parameters for the acoustic resonator of FIG. 4, which confirms that the acoustic resonator of FIG. 4 has a strong piezo-coupling

parasitic-mode-free and high-frequency (3-4 GHz) configuration.

DETAILED DESCRIPTION

Various embodiments of the present disclosure are further described in more detail with reference to the accompanying drawings. However, the present disclosure may be embodied in many other forms and should not be construed as limited to any certain structure or function discussed in the following description. In contrast, these embodiments are provided to make the description of the present disclosure detailed and complete.

According to the detailed description, it will be apparent to the ones skilled in the art that the scope of the present disclosure encompasses any embodiment thereof, which is disclosed herein, irrespective of whether this embodiment is implemented independently or in concert with any other embodiment of the present disclosure. For example, the apparatus disclosed herein may be implemented in practice by using any numbers of the embodiments provided herein. Furthermore, it should be understood that any embodiment of the present disclosure may be implemented using one or more of the features presented in the appended claims.

The word “exemplary” is used herein in the meaning of “used as an illustration” . Unless otherwise stated, any embodiment described herein as “exemplary” should not be construed as preferable or having an advantage over other embodiments.

Any positioning terminology, such as “left” , “right” , “top” , “bottom” , “above” “below” , “upper” , “lower” , “horizontal” , “vertical” , etc., may be used herein for convenience to describe one element’s or feature's relationship to one or more other elements or features in accordance with the figures. It should be apparent that the positioning terminology is intended to encompass different orientations of the apparatus disclosed herein, in addition to the orientation (s) depicted in the figures. As an example, if one imaginatively rotates the apparatus in the figures 90 degrees clockwise, elements or features described as “left” and “right” relative to other elements or features would then be oriented, respectively, “above” and “below” the other elements or features. Therefore, the positioning terminology used herein should not be construed as any limitation of the invention.

Furthermore, although the numerative terminology, such as “first” , “second” , etc., may be used herein to describe various embodiments, elements or features, it should be understood that these embodiments, elements or features should not be limited by this numerative terminology. This numerative terminology is used herein only to distinguish one embodiment, element or feature from another embodiment, element or feature. For example, a first array of resonant elements discussed below could be called a second array of resonant elements, and vice versa, without departing from the teachings of the present disclosure.

FIGs. 1A and 1B show different schematic views of a suspended piezoelectric membrane 100 used in a laterally excited bulk acoustic wave resonator (XBAR) in accordance with the prior art. More specifically, FIG. 1A shows a perspective view of the membrane 100, while FIG. 1B shows a magnified side view of the membrane 100, as taken within the area delimited by circle A in FIG. 1A. The membrane 100 is assumed to be suspended over an air cavity (not shown) for acoustic isolation. The membrane 100 is a submicron layered structure that comprises a supporting substrate 102 (e.g., a high-acoustic-velocity solid substrate, such as a diamond or SiC substrate) and a piezoelectric (e.g., LN) layer 104 provided on the substrate 102. The substrate 102 and the layer 104 may be made of the same piezoelectric material (e.g., LN) . Vertical positive electrodes 106 (schematically shown by using a zig-zag pattern) and vertical negative electrodes 108 (schematically shown by using a dotted pattern) are assumed to be embedded into the piezoelectric layer 104 (as well as into the substrate 102, if required) , thereby providing a more uniform horizontal electric field to increase piezo-coupling. However, the membrane 100 is fragile from the mechanical standpoint, and the embedded

vertical electrodes

106 and 108 make it even more fragile. Furthermore, it is difficult to fabricate the membrane 100 in practice. Additionally, as shown in FIG. 1B, the membrane 100 suffers from inefficient electric field distribution and redundant (parasitic) coupling between the piezoelectric layer 104 and the substrate 102, which may significantly decrease the piezo-coupling in the XBAR. Also, since the membrane 100 is suspended over the air cavity in the XBAR, heat can be evacuated from the membrane 100 only through the piezoelectric layer 104 having a low thermal conductivity and the

vertical electrodes

106 and 108, for which reason the XBAR using the membrane 100 exhibits poor power-handling properties.

The exemplary embodiments disclosed herein provide a technical solution that allows mitigating or even eliminating the above-indicated drawbacks of the prior art. In particular, the technical solution disclosed herein relates to an acoustic resonator in which each resonant element is at least partly coated with vertical electrodes on side walls of its top piezoelectric part and solidly mounted with its bottom part on an underlaying supporting substrate. The bottom part of each resonant element has a width smaller than λ/2, where λis a wavelength of a shear acoustic wave in the bottom part at a resonance frequency which is determined by the top part. Given this condition, the total width of the top part and the electrodes is always greater than the width of the bottom part, and vibrations from the top part cannot propagate through the bottom part in each resonant element, thereby leading to increasing piezo-coupling and providing structural solidity at the same time. Moreover, in the acoustic resonator thus configured, the heat evacuation path can go in each resonant element from its top part to the substrate through its bottom part, which may significantly improve the power-handling properties of the acoustic resonator.

FIG. 2 shows a schematic side view of an acoustic resonator 200 in accordance with a first exemplary embodiment. The acoustic resonator 200 comprises a supporting substrate 202 and three resonant elements 204 provided on one (top) side of the supporting substrate 202. The supporting substrate 202 may be made of a silicon (Si) or silicon dioxide (SiO2) . Preferably, the supporting substrate 202 is made of a high-acoustic-velocity material, such as diamond, silicon carbide (SiC) , boron nitride (BN) , or any other materials having an acoustic velocity ranging from 4000 m/sto 10000 m/sfor shear acoustic waves. Each of the resonant elements 204 has a top part 206 and a bottom part 208. The top part 206 is made of a piezoelectric material and has two opposite (i.e., left and right) side walls which are fully coated with

vertical electrodes

210, 212. Some examples of the piezoelectric material may include, but not limited to, lithium niobate (LN) , lithium tantalate (LT) , aluminum scandium nitride (AlScN) , lithium iodate (LiIO3) , zinc oxide (ZnO) , lead zirconate titanate (PZT) , and quartz. Preferably, the piezoelectric material of the top part 206 is represented by either 30°+/-30°-rotated Y-cut LN or 120°+/-30°-rotated Y-cut LN. The

vertical electrodes

210, 212 may be made of any metal, such as copper (Cu) , Molybdenum (Mo) , gold (Au) , aluminum (Al) , etc. The

vertical electrodes

210, 212 provide uniform horizontal electric fields near electrodes area, thereby facilitating strong piezo-coupling and providing weaker acoustic parasitic modes. The bottom part 208 may be made of the same material as the supporting substrate 202 or a different material, such as quartz and glass. As also shown in FIG. 2, the bottom part 208 has a width w ₁ smaller than a width w ₂ of the top part 206. Another embodiment is possible, in which w ₁ = w ₂. Irrespective of whether w ₁ = w ₂ or w ₁ < w ₂, a total width w ₃ of the top part 206 and the

electrodes

210, 212 is always greater than w ₁, which, along with the vertical arrangement of the

electrodes

210, 212, is an important condition for the efficient operation of the acoustic resonator 200 (i.e., the achievement of strong piezo-coupling) .

In a preferred embodiment, a resonance frequency F _R is determined by the top part 206 of each resonant element 204. In this embodiment, the bottom part 208 of each resonant element 204 has a width smaller than a half-wavelength of a shear acoustic wave in the material of the bottom part 208 at the resonance frequency F _R. This may prevent vibrations from spreading down to the substrate 202 and, thus, avoid wasting energy of the resonator 200 and decreasing its Q-factor.

In general, each of the resonant elements 204 may be fabricated by using the existing lithography techniques (e.g., photolithography for which the critical dimension of the

electrodes

210, 212 should be more than 0.3 μm) .

During operation, the

electrodes

210, 212 in each of the resonant elements 204 are alternatively connected to two different busbars (not shown) , so that the facing electrodes of each two adjacent resonant elements 204 are connected to the same busbar. After that, a RF voltage signal having a frequency comparable with the resonance frequency of the acoustic resonator 200 is applied to the busbars. As a result of the piezoelectric effect, the top part 206 of each resonant element 204 begins to vibrate, and the width of the top part 206 roughly corresponds to λ/2 of the shear acoustic wave. If the piezoelectric material of the top part 206 is represented by LN, two main vibration modes are possible depending on the LN cut used.

If 30°-rotated Y-cut LN is used, it may provide strong piezo-coupling to shear deformation with displacements perpendicular to the plane of FIG. 2. This situation is preferable, because the shear acoustic wave has an onset frequency and exists in the top part 206 of each resonant element 204 but cannot exist in its bottom part 208.

If 120°-rotated Y-cut LN is used, it provides almost the same strength of piezo-coupling but for other shear deformations: displacements are vertical, asymmetric on the left and the right sides of the top part 206 of each resonant element 204. However, the problem is that such displacements may generate a kind of “flexure” wave, A0, that is able to propagate to the bottom part 208 of any small thickness. This may increase the energy losses in the acoustic resonator 200.

In other words, the main vibration modes are substantially in the top part 206 of each resonant element 204, but 30°-rotated Y-cut LN is preferable.

In one embodiment, each of the resonant elements 204 may be shaped as a ridge-like structure elongated along axis z (i.e., perpendicular to the plane of FIG. 2) . Thus, such a ridge-like structure has a transversal dimension along axis z and a cross-sectional dimension along axis x. In this embodiment, the two opposite side walls coated with the

electrodes

210, 212 in each of the resonant elements 204 extend along the transversal dimension (i.e., along axis z) . The transversal dimension may be at least 40 ×p times the cross-sectional dimension, where p is the pitch of the resonator structure (i.e., its geometric period which is expressed as follows: p= w ₃ + s, where s is the inter-element spacing) . In another embodiment, each of the resonant elements 204 may be shaped as a column-like or tower-like structure, in which the transversal and cross-sectional dimensions are comparable to each other.

The top part 206 and the bottom part 208 in each of the resonant elements 204 may be equal or different in height. It should be noted that the height is measured along axis y in FIG. 2. Preferably, each of the top part 206 and the bottom part 208 in each of the resonant elements 204 has a height-to-width ratio ranging from 0.4 to 2.

The widths of the top part 206 (i.e., w ₂) and each of the

electrodes

210, 212 in each of the resonant elements 204 may be selected based on the resonance frequency F _R of the acoustic resonator 200. I resonance frequency F _R may correspond to the width w ₂ of the top part 206 equal to λ/2 –i.e., the half-wavelength of the shear acoustic wave generated in the top part 206 due to the piezoelectric effect. In general, the selection of w ₂ is a design issue. For example, a necessary resonance frequency may be selected based on some filter specification, and this frequency may be implemented in the acoustic resonator 200 by properly changing the width w ₂ of the top part 206 and the width/thickness of the

vertical electrodes

210 and 212. This may be optimized using suitable Finite Element Method (FEM) software, taking into account many other trade-offs (e.g., other parameters of the acoustic resonator 200, such as an impedance at the resonance frequency and a static capacitance, etc. ) .

It should be noted that the inter-element spacing s or the pitch p does not affect the resonance frequency. Large values of the inter-element spacing (e.g., s > 5 μm) may be used for better metal deposition and lift-off during the fabrication of the side-wall vertical electrodes 210, 212. In one embodiment, the inter-element spacing s may be greater than the total width w ₃ of the top part 206 and the electrodes 210, 212, in order to avoid any mechanical contact between the electrodes of each two adjacent resonant elements 204. In another embodiment, the inter-element spacing s may be defined as:

where V _acoustic is the lowest acoustic wave velocity in the supporting substrate 202.

To additionally decrease acoustic losses (due to parasitic acoustic modes) , the bottom part 208 in each of the resonant elements 204 may comprise a set of alternating low and high acoustic impedance layers (not shown) each having a thickness of λ/4, where λ is the wavelength of the shear acoustic wave propagating across the set of alternating low and high acoustic impedance layers. As an alternative or addition, a similar set of alternating low and high acoustic impedance layers (not shown) may be present in the supporting substrate 202.

FIG. 3 shows a schematic side view of an acoustic resonator 300 in accordance with a second exemplary embodiment. The acoustic resonator 300 comprises a piezoelectric (e.g., LN) substrate 302 and resonant elements 304 provided on the substrate 302 by forming (e.g., by means of etching, stamping, or MEMS technology) cavities on its surface. If the cavities are shaped as elongated (along axis z) grooves, then each of the resonant elements 304 will have a ridge-like shape. Each of the resonant elements 304 may be conveniently divided into top and bottom parts by vertical (e.g., Cu, Au, Mo, or Al)

electrodes

310, 312 which are formed on the side walls of each of the cavities close to the original surface of the substrate 302 (see the dashed line in FIG. 3) . Thus, each of the constructive elements of the acoustic resonator 300 (except for the electrodes 310, 312) may be made of the same piezoelectric material (e.g., LN) . The operational principle of the acoustic resonator 300 is the same as that of the acoustic resonator 200.

FIG. 4 shows a schematic side view of an acoustic resonator 400 in accordance with a third exemplary embodiment. The acoustic resonator 400 comprises a supporting substrate 402 and three resonant elements 404 provided on one (top) side of the supporting substrate 402. Each of the resonant elements 404 has a top part 406 and a bottom part 408. The top part 406 is made of a piezoelectric material and has two opposite (i.e., left and right) side walls which are fully coated with vertical electrodes 410, 412. In general, the acoustic resonator 400 may be implemented similarly to the acoustic resonator 200, i.e., by using the same fabrication materials for the substrate 402 and the resonant elements 404 as those for the substrate 202 and the resonant elements 204, respectively. Additionally, the resonant elements 404 may be sized similarly to the resonant elements 204. The only difference between the acoustic resonator 200 and the acoustic resonator 400 is that the side walls of the top part 406 in each of the resonant elements 404 are inclined at an angle α relative to a normal to the supporting substrate 402, thereby providing a positively tapered profile of the top part 406. The operational principle of the acoustic resonator 400 is the same as that of the acoustic resonator 200.

It should be noted that if each of the resonant elements 404 is shaped as a column-like structure (i.e., its dimensions along axes z and x are comparable) , all (i.e., left, right, front, and back) side walls of the resonant element 404 may be similarly inclined relative to the normal to the substrate 402, thereby providing a mushroom-like profile of the top part 406.

FIG. 5 shows a schematic side view of an acoustic resonator 500 in accordance with a fourth exemplary embodiment. The acoustic resonator 500 comprises a supporting substrate 502 and three resonant elements 504 provided on one (top) side of the supporting substrate 502. Each of the resonant elements 504 has a top part 506 and a bottom part 508. The top part 506 is made of a piezoelectric material and has two opposite (i.e., left and right) side walls which are fully coated with vertical electrodes 510, 512. In general, the acoustic resonator 500 may be implemented similarly to the acoustic resonator 200, i.e., by using the same fabrication materials for the substrate 502 and the resonant elements 504 as those for the substrate 202 and the resonant elements 204, respectively. Additionally, the resonant elements 504 may be sized similarly to the resonant elements 204. The only difference between the acoustic resonator 200 and the acoustic resonator 500 is that the side walls of the top part 506 in each of the resonant elements 504 are inclined at an angle α relative to a normal to the supporting substrate 502 such that the top part 506 has a negatively tapered profile. The operational principle of the acoustic resonator 500 is the same as that of the acoustic resonator 200.

Preferably, the side-wall inclination angle α is from -40° to 40° in each of the

acoustic resonators

400, 500. This wide range of side-wall inclination angles may give tolerance for the actual fabrication process of the

acoustic resonators

400 and 500.

It should be noted that the number, arrangement, and profile of the resonant elements, which are shown in FIGs. 2-5, are not intended to be any limitation of the present disclosure, but merely used to provide a general idea of how the resonant elements may be implemented within the acoustic resonators 200-500. For example, the acoustic resonators 200-500 may comprise much more resonant elements arranged on one or different (e.g., top and bottom) sides of the supporting substrate 202-502, respectively (e.g., the number of the resonant elements may vary from 20 to 200 along the axis x) . Furthermore, the side walls of the top parts in the resonant elements of the acoustic resonator 200-500 may be coated with the vertical electrodes only partly (i.e., not fully) . Other embodiments are possible, in which the vertical electrodes in the resonant elements of the acoustic resonator 200-500 at least partly cover the surface of the substrate 202-502, respectively, between the adjacent bottom parts of the resonant elements.

One has also to keep in mind that the number of resonant elements and their geometry (i.e., their width, height, and length/aperture) may be selected in a way to obtain desired parameters of the acoustic resonators 200-500 (not only their resonance frequencies but, e.g., also certain impedances at the resonance frequencies and certain static capacitances, etc. ) .

FIG. 6 shows a dependence of a piezo-coupling factor

on the side-wall inclination angle α in the top part 406 of each resonant element 404 included in the acoustic resonator 400. The width w ₂ of the top part 406 is assumed to be equal to 300 nm. As can be seen, optimal values of the piezo-coupling factor

are observed within the angular range 0°-40°.

FIG. 7 shows an admittance curve of optimized parameters (i.e., admittance Y11 and its real part Re (Y11) in dB) for the acoustic resonator 400, which confirms that the acoustic resonator 400 has a strong piezo-coupling

parasitic-mode-free and high-frequency (3-4 GHz) configuration. In FIG. 7, the solid curve corresponds to the admittance Y11, and the dashed curve corresponds to Re (Y11) .

Although the exemplary embodiments of the present disclosure are described herein, it should be noted that any various changes and modifications could be made in the embodiments of the present disclosure, without departing from the scope of legal protection which is defined by the appended claims. In the appended claims, the word “comprising” does not exclude other elements or operations, and the indefinite article “a” or “an” does not exclude a plurality. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

Claims

An acoustic resonator comprising:

a supporting substrate; and

at least one resonant element provided on the supporting substrate, each of the at least one resonant element having a top part and a bottom part, the top part being made of a piezoelectric material, the top part having two opposite side walls each at least partly coated with an electrode, and the bottom part having a width smaller than λ/2, where λ is a wavelength of a shear acoustic wave in the bottom part at a resonance frequency of the acoustic resonator, the resonance frequency being determined by the top part of each of the at least one resonant element.
The acoustic resonator of claim 1, wherein each of the at least one resonant element is shaped as a ridge.
The acoustic resonator of claim 1 or 2, wherein each of the two opposite side walls of the top part in each of the at least one resonant element is inclined at an angle from -40° to 40° relative to a normal to the supporting substrate.
The acoustic resonator of any one of claims 1 to 3, wherein the top part in each of the at least one resonant element has a positively or negatively tapered profile.
The acoustic resonator of any one of claims 1 to 4, wherein the top part and the bottom part in each of the at least one resonant element are equal in height.
The acoustic resonator of any one of claims 1 to 4, wherein each of the top part and the bottom part in each of the at least one resonant element has a different height.
The acoustic resonator of any one of claims 1 to 6, wherein the top part in each of the at least one resonant element has a height-to-width ratio ranging from 0.4 to 2.
The acoustic resonator of any one of claims 1 to 7, wherein the bottom part in each of the at least one resonant element has a height-to-width ratio ranging from 0.4 to 2.
The acoustic resonator of any one of claims 1 to 8, wherein the supporting substrate is made of the piezoelectric material, and wherein the bottom part in each of the at least one resonant element is made of the piezoelectric material.
The acoustic resonator of any one of claims 1 to 8, wherein the supporting substrate is made of a first dielectric material, and wherein the bottom part in each of the at least one resonant element is made of a second dielectric material, the first dielectric material and the second dielectric material being the same or different from each other.
The acoustic resonator of claim 10, wherein the first dielectric material comprises one of silicon (Si) , diamond, silicon carbide (SiC) , and silicon dioxide (SiO ₂) , and wherein the second dielectric material comprises one of Si, SiO ₂, quartz and glass.
The acoustic resonator of any one of claims 1 to 11, wherein the piezoelectric material comprises one of lithium niobate (LN) , lithium tantalate (LT) , aluminum scandium nitride (Al (Sc) N) , lithium iodate (LiIO ₃) , zinc oxide (ZnO) , lead zirconate titanate (PZT) , and quartz.
The acoustic resonator of claim 12, wherein the piezoelectric material comprises one of 30°+/-30°-rotated Y-cut LN and 120°+/-30°-rotated Y-cut LN.
The acoustic resonator of any one of claims 1 to 13, wherein widths of the top part and each of the electrodes in each of the at least one resonant element are selected based on a resonance frequency of the acoustic resonator.
The acoustic resonator of any one of claims 1 to 14, wherein the bottom part in each of the at least one resonant element comprises a set of alternating low and high acoustic impedance layers each having a thickness of λ/4, where λ is a wavelength of a shear acoustic wave propagating across the set of alternating low and high acoustic impedance layers.
The acoustic resonator of any one of claims 1 to 15, wherein the supporting substrate comprises a set of alternating low and high acoustic impedance layers each having a thickness of λ/4, where λ is a wavelength of a shear acoustic wave propagating across the set of alternating low and high acoustic impedance layers.
The acoustic resonator of any one of claims 1 to 16, wherein the at least one resonant element comprises an array of identical resonant elements provided on the supporting substrate, and wherein the array of identical resonant elements has an inter-element spacing selected such that there is no mechanical contact between the electrodes of each two adjacent resonant elements of the array of identical resonant elements.
The acoustic resonator of claim 17, wherein the inter-element spacing is larger than a total width of the top part and the electrodes.
The acoustic resonator of claim 17, wherein the inter-element spacing is defined as follows:
where s is the inter-element spacing, V _acoustic is a lowest acoustic wave velocity in the supporting substrate, and F _R is the resonance frequency of the acoustic resonator.
The acoustic resonator of any one of claims 1 to 16, wherein the at least one resonant element comprises a first array of identical resonant elements and a second array of identical resonant elements which are both provided on the supporting substrate, the first array of identical resonant elements and the second array of identical resonant elements differing from each other in at least one of:

an inter-element spacing;

a profile of the top part;

a size of the top part;

a size of the bottom part;

the piezoelectric material of the top part;

a material of the bottom part;

a number of resonant elements; and

an aperture of each resonant element.