Lamb wave resonator and filter

WO2024207825A9PCT designated stage expired Publication Date: 2025-08-21SHANGHAI INST OF MICROSYSTEM & INFORMATION TECH CHINESE ACAD OF SCI
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Patent Information

Application Number
PCT/CN2023/142048
Authority / Receiving Office
WO · WO
Patent Type
Applications
Current Assignee / Owner
Priority Date
2023-04-04
Filing Date
2023-12-26
Publication Date
2025-08-21

AI Technical Summary

Technical Problem

Thickness discontinuities in existing Lamb wave resonators lead to the generation of spurious modes, which reduces the passband performance of the filter and limits its application in commercial filters.

Method used

By setting grooves in the first material area of ​​the piezoelectric film or forming a dielectric layer under the second material area, the local thickness is adjusted so that the first material area and the second material area are staggered along the thickness direction, thereby suppressing stray modes. and build responsive filters to improve passband performance.

Benefits of technology

It effectively suppresses spurious modes, improves the acoustic impedance matching of Lamb wave resonators and the passband performance of filters, and promotes the development of high-frequency and large-bandwidth acoustic resonators.

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Abstract

Provided in the present invention are a Lamb wave resonator and a filter, which improve the matching performance of acoustic impedance by means of adjusting and controlling local thin film thickness. Providing recesses in a piezoelectric thin film in first material areas, or forming a dielectric layer below a piezoelectric thin film in second material areas achieves local thickness adjustment for a Lamb wave resonator constituted by interdigital electrodes and having a thickness difference, such that the first material areas and the second material areas are offset with respect to each other in the thickness direction, thus suppressing a stray mode of the Lamb wave resonator; and the response filter is constructed on the basis of the resonator, so as to suppress the phenomenon of passband performance deterioration caused by the stray mode, thereby facilitating development of high-frequency large-bandwidth acoustic resonators.
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Description

Lamb wave resonators and filters Technical Field

[0001] The invention belongs to the technical field of semiconductor manufacturing and relates to a Lamb wave resonator and a filter. Background Art

[0002] Radio frequency MEMS (micro-electromechanical systems) resonators based on the piezoelectric effect play an important role in the communications field and are widely used. Lamb wave resonators are a new type of piezoelectric RF MEMS resonator. They feature small size, high quality factor, high frequency, and wide bandwidth, making them an ideal resonator structure for developing single-chip integrated filters.

[0003] The device structure of a conventional Lamb wave resonator is shown in Figures 1 and 2 , and includes a supporting substrate 100, an air gap 101 embedded within the supporting substrate 100, a piezoelectric film 200 suspended above the supporting substrate 100, and a metal electrode 300 located above the piezoelectric film 200. As shown in Figure 2 , the metal electrode 300 includes a bus bar 302 and interdigital electrodes 301, with the piezoelectric film regions corresponding to the interdigital electrodes 301 being suspended.

[0004] Because the interdigital electrodes 301 in the Lamb wave resonator are placed on the piezoelectric film 200, this causes discontinuity in the thickness direction of the resonator. As shown in Figure 3, the material layer located above the air gap 101 includes the piezoelectric film 200 and the interdigital electrodes 301 located on the first material region Q1, and the corresponding material layer has a thickness of D1. In the second material region Q2, the material layer above the air gap 101 only includes the piezoelectric film 200, and the corresponding material layer has a thickness of D2. As a result, the material layers in different areas on the air gap 101 have a thickness difference, namely the difference between D1 and D2. This will cause an acoustic impedance mismatch in the sound field mode, leading to the generation of spurious modes. A filter composed of resonators with spurious modes will have larger spurious modes within the passband, which will reduce the passband performance.

[0005] Therefore, the existing Lamb wave resonator cannot form a large-scale commercial filter due to its many heterogeneous modes, poor stability, and greater design difficulty. Therefore, it is necessary to improve the existing Lamb wave resonator and filter.

[0006] Summary of the Invention

[0007] In view of the above-mentioned shortcomings of the prior art, an object of the present invention is to provide a Lamb wave resonator and a filter to solve the application problems of the Lamb wave resonator and the filter in the prior art caused by thickness discontinuity.

[0008] To achieve the above-mentioned and other related purposes, the present invention provides a Lamb wave resonator, comprising:

[0009] a supporting substrate;

[0010] a piezoelectric film, wherein the piezoelectric film is located on the supporting substrate, and an air gap is formed between the piezoelectric film and the supporting substrate;

[0011] a metal electrode, the metal electrode being located on the piezoelectric film and comprising a corresponding bus bar and interdigitated electrodes, the interdigitated electrodes being connected to the bus bar and located above the air gap;

[0012] The material layer above the air gap is divided into a first material region and a second material region, the interdigitated electrodes are located in the first material region, and the first material region and the second material region are staggered along the thickness direction.

[0013] Optionally, the piezoelectric film located in the first material area has a groove extending from the lower surface to the upper surface, and the first material area and the second material area are staggered along the thickness direction due to the groove.

[0014] Optionally, the depth of the groove is 4% to 35% of the thickness of the piezoelectric film in the second material region.

[0015] Optionally, the shape of the groove is the same as that of the corresponding interdigital electrode; or the groove has the same width as that of the corresponding interdigital electrode, and the length of the groove extends to the edge of the bus bar.

[0016] Optionally, the second material region comprises a dielectric layer located below the piezoelectric film, and the first material region and the second material region are staggered along the thickness direction through the dielectric layer.

[0017] Optionally, the thickness of the dielectric layer is 4% to 35% of the thickness of the piezoelectric film in the second material region.

[0018] Optionally, the dielectric layer includes one or a combination of a single crystal silicon layer, a polycrystalline silicon layer, an aluminum oxide layer, a silicon oxide layer, and an aluminum nitride layer.

[0019] Optionally, it further includes a dielectric layer covering the metal electrode and the piezoelectric film; the dielectric layer includes one or a combination of a single crystal silicon layer, a polycrystalline silicon layer, an aluminum oxide layer, a silicon oxide layer, and an aluminum nitride layer.

[0020] Optionally, the piezoelectric film includes one or a combination of lithium niobate film, lithium tantalate film, quartz film, and aluminum nitride film; the supporting substrate includes a single crystal silicon substrate, a polycrystalline silicon substrate, and a sapphire substrate; the material of the metal electrode includes one or a combination of aluminum, copper, gold, nickel, molybdenum, and platinum, and the metal electrode includes a single layer or a stacked layer.

[0021] The present application also provides a filter, which comprises any of the above-mentioned Lamb wave resonators in a topological cascade connection.

[0022] As described above, the Lamb wave resonator and filter of the present invention improve the matching of acoustic impedance by regulating the thickness of the local film, including providing a groove in the piezoelectric film in the first material region, or forming a dielectric layer under the piezoelectric film in the second material region, so as to adjust the local thickness of the Lamb wave resonator with a thickness difference composed of interdigitated electrodes, so that the first material region and the second material region are staggered in the thickness direction to suppress the stray mode of the Lamb wave resonator, and construct a corresponding filter based on the resonator to suppress the deterioration of the passband performance caused by the stray mode, thereby contributing to the development of high-frequency and large-bandwidth acoustic resonators. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] FIG1 is a schematic diagram showing the structure of a Lamb wave resonator in the prior art.

[0024] FIG. 2 is a schematic diagram showing a top view of the metal electrode in FIG. 1 .

[0025] FIG3 shows a material layer (upper half) located above the air gap in a Lamb wave resonator in the prior art and a schematic diagram of the thickness distribution of the material layer (lower half).

[0026] FIG4 is a schematic structural diagram of a material layer located above an air gap in a Lamb wave resonator according to the first embodiment of the present invention.

[0027] FIG5 shows a schematic diagram of the material layer located on the air gap in FIG4 (upper half) and the thickness distribution of the material layer (lower half).

[0028] FIG6 is a schematic structural diagram of a material layer located above the air gap in a Lamb wave resonator according to a second embodiment of the present invention.

[0029] FIG7 is a schematic structural diagram of a material layer located above the air gap in a Lamb wave resonator according to a third embodiment of the present invention.

[0030] FIG8 is a schematic diagram showing the structure of the filter of the present invention.

[0031] FIG9 is a comparison diagram of the admittance response curves of the Lamb wave resonator of the present invention and the conventional Lamb wave resonator.

[0032] FIG. 10 is a comparison diagram of the admittance response curves of the filter of the present invention and the conventional filter.

[0033] Component number description

[0034] 100 Support substrate

[0035] 101 Air Gap

[0036] 200 Piezoelectric Film

[0037] 201 groove

[0038] 300 Metal Electrode

[0039] 301 interdigitated electrodes

[0040] 302 busbar

[0041] 400, 500 dielectric layer

[0042] 10 Series Lamb wave resonators

[0043] 20 Parallel Lamb Wave Resonators

[0044] D1, D2, D3, D4 thickness

[0045] H Depth

[0046] Q1 First Material Area

[0047] Q2 Second Material Area

[0048] A, A', B, B' curves DETAILED DESCRIPTION

[0049] The following describes the embodiments of the present invention through specific examples. Those skilled in the art will readily understand the other advantages and benefits of the present invention from the disclosure herein. The present invention may also be implemented or applied through various other specific embodiments, and the details in this specification may be modified or altered based on different viewpoints and applications without departing from the spirit of the present invention.

[0050] For example, when describing the embodiments of the present invention, cross-sectional views of device structures may be partially enlarged to scale for ease of explanation. Furthermore, these schematic views are merely illustrative and should not limit the scope of the present invention. Furthermore, in actual manufacturing, three-dimensional dimensions, including length, width, and depth, should be included.

[0051] For convenience of description, spatially relative terms such as "under," "below," "below," "below," "over," and the like may be used herein to describe the relationship of one element or feature to other elements or features illustrated in the drawings. It will be understood that these spatially relative terms are intended to encompass orientations of the device in use or operation in addition to the orientation depicted in the drawings, and may include embodiments in which the first and second features are formed in direct contact, as well as embodiments in which additional features are formed between the first and second features so that the first and second features may not be in direct contact. In addition, when a layer is referred to as being "between" two layers, it can be the only layer between the two layers, or one or more intervening layers may also be present.

[0052] It should be noted that the illustrations provided in this embodiment are only used to schematically illustrate the basic concept of the present invention. Therefore, the illustrations only show components related to the present invention and are not drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component can be changed at will, and the component layout type may also be more complicated.

[0053] Example 1

[0054] This embodiment provides a Lamb wave resonator, which includes: a supporting substrate, a piezoelectric film, and a metal electrode; the piezoelectric film is located on the supporting substrate, and an air gap is defined between the piezoelectric film and the supporting substrate; the metal electrode is located on the piezoelectric film and includes a corresponding bus bar and interdigitated electrodes, the interdigitated electrodes are connected to the bus bar and are located above the air gap; wherein the material layer above the air gap is divided into a first material region and a second material region, the interdigitated electrodes are located within the first material region, and the first material region and the second material region are alternately disposed along the thickness direction.

[0055] 4 and 5 , in this embodiment, the piezoelectric film 200 in the first material region Q1 has a groove 201 extending from the bottom surface to the top surface. The groove 201 allows the first material region Q1 and the second material region Q2 to be staggered along the thickness direction.

[0056] The Lamb wave resonator of this embodiment specifically includes:

[0057] Referring to Figure 1, the piezoelectric film 200 is located on the supporting substrate 100, and an air gap 101 is provided between the piezoelectric film 200 and the supporting substrate 100; referring to Figures 1 and 2, the metal electrode 300 is located on the piezoelectric film 200, and includes a corresponding bus bar 302 and an interdigitated electrode 301, the interdigitated electrode 301 being connected to the bus bar 302 and being located above the air gap 101; referring to Figures 4 and 5, the material layer above the air gap 101 is divided into the first material region Q1 and the second material region Q2, the interdigitated electrode 301 being located in the first material region Q1, and the first material region Q1 and the second material region Q2 being staggered along the thickness direction.

[0058] Referring to Figures 3 and 5, in this embodiment, based on the structure of the Lamb wave resonator of Figure 1, a groove 201 extending from the lower surface to the upper surface of the piezoelectric film 200 is formed in the piezoelectric film 200 to locally reduce the thickness of the material layer located in the first material region Q1, forming a staggered and locally dislocated material layer located above the air gap 101 along the thickness direction, thereby suppressing the spurious mode of the Lamb wave resonator. A filter responsive to the resonator can be constructed based on the resonator, as shown in Figure 8, which is a filter composed of a plurality of series-connected Lamb wave resonators 10 or parallel-connected Lamb wave resonators 20 through a topological cascade to suppress the passband performance degradation caused by the spurious mode, thereby contributing to the development of high-frequency, wide-bandwidth acoustic resonators. Preferably, the antiresonance frequency of the series-connected Lamb wave resonator 10 is close to the resonant frequency of the parallel-connected Lamb wave resonator 20, and the series-connected Lamb wave resonator 10 and the parallel-connected Lamb wave resonator 20 are prepared based on the same piezoelectric film 20. Among them, the crystal cut of the piezoelectric film 200 in the Lamb wave resonator can be a rotated Y cut, and the corresponding Euler angle is (0, β, 0), where -80°<β<20°; it can also be a Z cut, and the corresponding Euler angle is (α, 0, 0), where α is an arbitrary angle.

[0059] As an example, the depth H of the groove 201 may be 4% to 35% of the thickness of the piezoelectric film 200 in the second material region Q2 .

[0060] Specifically, referring to Figures 4 and 5, the piezoelectric film 200 in this embodiment maintains the thickness of the piezoelectric film 200 in the second material area Q2 at D2, and forms the groove 201 with a depth of H in the piezoelectric film 200 in the first material area Q1 by methods such as photolithography and etching, and the depth H of the groove 201 is preferably 4% to 35%, such as 4%, 5%, 10%, 20%, 30%, 35%, etc., so that the material layer located in the first material area Q1 is converted from a thickness of D1 to D3, and the first material area Q1 and the second material area Q2 are staggered, as shown in Figure 5.

[0061] As an example, the morphology of the groove 201 is the same as the morphology of the corresponding interdigital electrode 301 .

[0062] Specifically, referring to Figures 2 and 4, the morphology of the groove 201 formed can have the same morphology as the interdigitated electrode 301. Of course, as needed, the groove 201 can also have the same width as the corresponding interdigitated electrode 301 (the width direction of the groove is perpendicular to the thickness of the piezoelectric film and the depth direction of the groove and parallel to the plane of the piezoelectric film), but the length of the groove 201 can extend to the edge of the bus bar 302, that is, the morphology of the groove 201 can be the morphology formed by extending the interdigitated electrode 301 to contact the edge of the bus bar 302 in Figure 2.

[0063] As an example, the piezoelectric film 200 may include one or a combination of lithium niobate film, lithium tantalate film, quartz film, and aluminum nitride film; the supporting substrate 100 may include a single crystal silicon substrate, a polycrystalline silicon substrate, or a sapphire substrate; the material of the metal electrode 300 may include one or a combination of aluminum, copper, gold, nickel, molybdenum, and platinum, and the metal electrode 300 may include a single layer or a stacked layer.

[0064] Specifically, the thickness of the piezoelectric film 200 may be between 200 nm and 1 μm, such as 200 nm, 500 nm, 1 μm, etc., as shown in FIG4 . The frequency satisfies Among them, v t , v lare the longitudinal (thickness direction of the film) velocity and transverse (perpendicular to the interdigital electrodes and parallel to the film plane) velocity of the acoustic wave excitation mode, respectively. Where m and n are the mode orders perpendicular to the longitudinal (thickness direction of the film) and transverse (perpendicular to the interdigital electrodes and parallel to the film plane) directions. The order of the Lamb wave is usually defined by the size of m. When m ≥ 1, it is called a high-order Lamb wave. For a high-order Lamb wave resonator, a major feature is that the center spacing l between adjacent interdigital electrodes, such as the interdigital electrodes 301 in Figure 4, is between 2μm and 20μm, such as 2μm, 10μm, 20μm, etc. The metallization rate of the interdigital electrodes can be 5% to 45%, such as 5%, 15%, 25%, 35%, 45%, etc. There is no excessive restriction on the selection of the material and structure of the supporting substrate 100, the piezoelectric film 200, and the metal electrode 300.

[0065] Example 2

[0066] 6 , this embodiment further provides a Lamb wave resonator, which differs from the first embodiment primarily in that in this embodiment, a dielectric layer 400 is provided below the piezoelectric film 200 in the second material region Q2. The additional dielectric layer 400 at the bottom of the piezoelectric film 200 modifies the shape of the lower surface profile of the material layer above the air gap 101, thereby increasing the degree of misalignment in the thickness of the material layer, such that the first material region Q1 and the second material region Q2 are staggered in the thickness direction.

[0067] Specifically, as shown in Figures 3 and 6, in this embodiment, based on the structure of the Lamb wave resonator in Figure 1, the dielectric layer 400 is formed below the piezoelectric film 200 in the second material area Q2 to locally thicken the thickness of the material layer located in the second material area Q2, forming a staggered and locally dislocated material layer located above the air gap 101 along the thickness direction, thereby suppressing the stray mode of the Lamb wave resonator, and a responsive filter can be constructed based on the resonator. As shown in Figure 8, a filter is formed by topological cascading of several Lamb wave resonators 10 in series or Lamb wave resonators 20 in parallel, so as to suppress the deterioration of the passband performance caused by the stray mode, thereby contributing to the development of high-frequency and large-bandwidth acoustic resonators.

[0068] As an example, the thickness D4 of the dielectric layer 400 may be 4% to 35% of the thickness D2 of the piezoelectric film 200 in the second material region Q2 .

[0069] Specifically, referring to Figure 6, in this embodiment, while the piezoelectric film 200 maintains a thickness of D2 and the thickness of the material layer in the first material area Q1 is D1, a dielectric layer 400 with a thickness of D4 is formed below the piezoelectric film 200 in the second material area Q2 using methods such as PVD and CVD, and the thickness D4 of the dielectric layer 400 is preferably 4% to 35%, such as 4%, 5%, 10%, 20%, 30%, 35%, etc.

[0070] As an example, the dielectric layer 400 may include one or a combination of a single crystal silicon layer, a polycrystalline silicon layer, an aluminum oxide layer, a silicon oxide layer, and an aluminum nitride layer, and the specific selection can be made according to needs.

[0071] Regarding the selection of other structural layers of the Lamb wave resonator, please refer to Example 1 and will not be described in detail here.

[0072] Example 3

[0073] 7 , this embodiment further provides a Lamb wave resonator, which differs from the first embodiment mainly in that this embodiment further includes a dielectric layer 500 covering the metal electrode 300 and the piezoelectric film 200 .

[0074] Specifically, according to the requirements of device functions and performance, such as heat dissipation and passivation, the dielectric layer 500 can be formed above the metal electrode 300 and the piezoelectric film 200, wherein the dielectric layer 500 may include one or a combination of a single crystal silicon layer, a polycrystalline silicon layer, an aluminum oxide layer, a silicon oxide layer, and an aluminum nitride layer. For other structures of the Lamb wave resonator, please refer to Example 1 and will not be described here.

[0075] In this embodiment, by covering the surface with the dielectric layer 500, the profile of the upper surface of the material layer above the air gap 101 can be raised, thereby increasing the overall thickness of the Lamb wave resonator. The thickness of the dielectric layer 500 can be selected as needed and is not excessively limited herein.

[0076] Regarding the selection of other structural layers of the Lamb wave resonator, please refer to Example 1 and will not be described in detail here.

[0077] FIG9 shows a comparison of the admittance response curve A of the Lamb wave resonator with thickness staggered regions, made of the same material, and the admittance response curve A' of a conventional Lamb wave resonator without thickness staggered regions. For example, the piezoelectric film is made of lithium niobate with a YX124° cut, the sound wave propagation direction is along the positive direction of the material's X-axis, the piezoelectric film thickness is 0.5 μm, and the metal electrode thickness is 60 nm. As can be seen from the figure, the present invention significantly suppresses the appearance of spurious modes between 4.3 GHz and 4.66 GHz after the thickness staggering is implemented, achieving excellent results. Furthermore, referring to FIG10 , a comparison of the admittance response curve B of a Lamb wave filter constructed using the Lamb wave resonator of the present invention and the admittance response curve B' of a Lamb wave filter constructed using a conventional Lamb wave resonator, made of the same material, is shown. As can be seen from the figure, the passband performance of the Lamb wave filter of the present invention is significantly optimized, and the interference caused by spurious modes is significantly reduced.

[0078] In summary, the Lamb wave resonator and filter of the present invention improve the matching of acoustic impedance by regulating the thickness of the local film, including providing a groove in the piezoelectric film in the first material region, or forming a dielectric layer under the piezoelectric film in the second material region, so as to adjust the local thickness of the Lamb wave resonator with a thickness difference composed of interdigitated electrodes, so that the first material region and the second material region are staggered in the thickness direction to suppress the stray mode of the Lamb wave resonator, and construct a responsive filter based on the resonator to suppress the deterioration of the passband performance caused by the stray mode, thereby contributing to the development of high-frequency and large-bandwidth acoustic resonators.

[0079] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the present invention. Anyone skilled in the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by one of ordinary skill in the art without departing from the spirit and technical principles disclosed herein are intended to be covered by the claims of the present invention.

Claims

1. A Lamb wave resonator, characterized in that: The Lamb wave resonator comprises: a supporting substrate; A piezoelectric film, wherein the piezoelectric film is located on the supporting substrate, and an air gap is formed between the piezoelectric film and the supporting substrate; A metal electrode, the metal electrode is located on the piezoelectric film, and includes a bus bar and interdigitated electrodes that are correspondingly arranged, the interdigitated electrodes are connected to the bus bar and the interdigitated electrodes are located above the air gap; The material layer above the air gap is divided into a first material region and a second material region, the interdigitated electrodes are located in the first material region, and the first material region and the second material region are staggered along the thickness direction.

2. The Lamb wave resonator according to claim 1, characterized in that: The piezoelectric film located in the first material area has a groove extending from the lower surface to the upper surface, and the first material area and the second material area are staggered along the thickness direction through the groove.

3. The Lamb wave resonator according to claim 2, characterized in that: The depth of the groove is 4% to 35% of the thickness of the piezoelectric film in the second material area.

4. The Lamb wave resonator according to claim 2, characterized in that: The morphology of the groove is the same as that of the corresponding interdigital electrode; or the groove has the same width as that of the corresponding interdigital electrode, and the length of the groove extends to the edge of the bus bar.

5. The Lamb wave resonator according to claim 1, characterized in that: The second material area has a dielectric layer located below the piezoelectric film, and the first material area and the second material area are alternately arranged along the thickness direction through the dielectric layer.

6. The Lamb wave resonator according to claim 5, characterized in that: The thickness of the dielectric layer is 4% to 35% of the thickness of the piezoelectric film in the second material region.

7. The Lamb wave resonator according to claim 5, characterized in that: The dielectric layer includes one or a combination of a single crystal silicon layer, a polycrystalline silicon layer, an aluminum oxide layer, a silicon oxide layer, and an aluminum nitride layer.

8. The Lamb wave resonator according to claim 1, characterized in that: It also includes a dielectric layer covering the metal electrode and the piezoelectric film; the dielectric layer includes one or a combination of a single crystal silicon layer, a polycrystalline silicon layer, an aluminum oxide layer, a silicon oxide layer, and an aluminum nitride layer.

9. The Lamb wave resonator according to claim 1, characterized in that: The piezoelectric film includes one or a combination of lithium niobate film, lithium tantalate film, quartz film, and aluminum nitride film; the supporting substrate includes a single crystal silicon substrate, a polycrystalline silicon substrate, and a sapphire substrate; the material of the metal electrode includes one or a combination of aluminum, copper, gold, nickel, molybdenum, and platinum, and the metal electrode includes a single layer or a stacked layer.

10. The Lamb wave resonator according to claim 1, characterized in that: The Lamb wave resonator is a first-order or high-order Lamb wave resonator.

11. The Lamb wave resonator according to claim 1, characterized in that: The thickness of the piezoelectric film is between 200 nm and 1 μm.

12. The Lamb wave resonator according to claim 1, characterized in that: The center distance between adjacent interdigital electrodes is between 2 μm and 20 μm.

13. A filter, characterized in that: The filter is formed by a topological cascade connection of Lamb wave resonators as described in any one of claims 1 to 12.

14. The filter according to claim 13, characterized in that: The filter is formed by topologically cascading a plurality of Lamb wave resonators connected in series and / or a plurality of Lamb wave resonators connected in parallel.

15. The filter according to claim 14, characterized in that: The anti-resonance frequency of the series-connected Lamb wave resonator is close to the resonant frequency of the parallel-connected Lamb wave resonator, and the series-connected Lamb wave resonator and the parallel-connected Lamb wave resonator are prepared based on the same piezoelectric film.