Elastic wave device and filter
The elastic wave apparatus with a lithium niobate piezoelectric layer, dielectric layer, and acoustic reflector structure addresses unwanted wave generation, improving resonance and electromechanical coupling for better performance.
Patent Information
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2025-09-30
- Publication Date
- 2026-04-16
AI Technical Summary
Existing elastic wave apparatuses suffer from unwanted wave generation near the resonant frequency, degrading resonant characteristics.
The apparatus incorporates a piezoelectric layer made of lithium niobate with specific Euler angles and a dielectric layer, along with a support member featuring an acoustic reflector, to improve resonance characteristics by utilizing a bulk wave of the thickness-slip first mode and optimizing the thickness and electrode pitch ratios.
This configuration enhances resonance characteristics by suppressing unwanted waves and maintaining high electromechanical coupling coefficients, suitable for broadband applications.
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Figure JP2025034749_16042026_PF_FP_ABST
Abstract
Description
Elastic wave apparatus and filters
[0001] This invention relates to an elastic wave apparatus and a filter.
[0002] Patent Document 1 describes an elastic wave apparatus designed such that the ratio of the distance between electrode fingers to the thickness of the piezoelectric layer is within a predetermined range.
[0003] U.S. Patent Application Publication No. 2022 / 0123720
[0004] In the elastic wave apparatus shown in Patent Document 1, unwanted waves may be generated near the resonant frequency, potentially degrading the resonant characteristics.
[0005] The present invention aims to provide an elastic wave device and filter that can improve resonance characteristics.
[0006] An elastic wave apparatus according to one embodiment comprises a piezoelectric layer containing lithium niobate, having a first main surface and a second main surface opposite to the first main surface; an IDT electrode provided on at least one of the main surfaces of the first and second main surfaces of the piezoelectric layer; a dielectric layer provided on at least one of the main surfaces of the first and second main surfaces of the piezoelectric layer; and a support member provided on the second main surface side of the piezoelectric layer. The IDT electrode has a first busbar and a second busbar facing each other, at least one first electrode finger whose base end is connected to the first busbar, and at least one second electrode finger whose base end is connected to the second busbar. The support member has an acoustic reflector on the second main surface side. When the thickness of the piezoelectric layer is d and the average distance between the centers of adjacent first and second electrode fingers is p, d / p is 0.5 or less, and when the sum of the thickness of the piezoelectric layer and the thickness of the dielectric layer is T, p / T is 3.0 or more and 6.0 or less.
[0007] A filter according to one embodiment is a filter comprising a resonator, wherein at least one of the resonators is the elastic wave device.
[0008] According to the elastic wave apparatus and filter of the present invention, resonance characteristics can be improved.
[0009] Figure 1 is a plan view showing the elastic wave apparatus of the first embodiment. Figure 2 is a cross-sectional view taken along line II-II' of Figure 1. Figure 3 is an enlarged cross-sectional view showing the intersection region C shown in Figure 2. Figure 4 is a schematic cross-sectional view illustrating the bulk wave of the first-order thickness-slip mode propagating through the piezoelectric layer of the first embodiment. Figure 5 is a schematic cross-sectional view illustrating the amplitude direction of the bulk wave of the first-order thickness-slip mode propagating through the piezoelectric layer of the first embodiment. Figure 6 is an explanatory diagram showing an example of the resonance characteristics of the elastic wave apparatus of the first embodiment. Figure 7 is an explanatory diagram showing the relationship between d / 2p and the specific bandwidth as a resonator, where p is the distance between the centers of adjacent electrodes or the average distance between the centers, and d is the average thickness of the piezoelectric layer, in the elastic wave apparatus of the first embodiment. Figure 8 is a plan view showing an example in which a pair of electrodes are provided in the elastic wave apparatus of the first embodiment. Figure 9 is a reference diagram showing an example of the resonance characteristics of the elastic wave apparatus of the first embodiment. Figure 10 is an explanatory diagram showing the relationship between the relative bandwidth of the elastic wave apparatus of the first embodiment when a large number of elastic wave resonators are configured, and the phase rotation amount of the spurious impedance normalized by 180 degrees as the spurious magnitude. Figure 11 is an explanatory diagram showing the relationship between d / 2p, the metallization ratio MR, and the relative bandwidth. Figure 12 shows LiNbO when d / p approaches 0. 3 This is an explanatory diagram showing the relative bandwidth map for the Euler angle (0°, θ, ψ). Figure 13 shows the simulation results of the elastic wave apparatus according to the embodiment. Figure 14 shows the simulation results of the elastic wave apparatus according to the comparative example. Figure 15 shows the relationship between p / T and the frequency of unwanted waves for the embodiment and the comparative example. Figure 16 shows the relationship between p / T and the effective electromechanical coupling coefficient K of the elastic wave apparatus according to the embodiment. eff 2 This figure shows the relationship between t / d and the effective electromechanical coupling coefficient K of the elastic wave apparatus according to the embodiment. eff 2 This figure shows the relationship between the Euler angle of lithium niobate and the effective electromechanical coupling coefficient K of the elastic wave apparatus according to the embodiment. eff 2This is a diagram showing the relationship between the two. Figure 19 is a schematic plan view showing the IDT electrodes of the elastic wave apparatus of the second embodiment. Figure 20A is a schematic diagram showing an example of the relationship between the electrode pitch and the order of the electrode fingers in the elastic wave apparatus of the second embodiment. Figure 20B is a schematic diagram showing an example of the relationship between the electrode pitch and the order of the electrode fingers in the elastic wave apparatus of the second embodiment. Figure 20C is a schematic diagram showing an example of the relationship between the electrode pitch and the order of the electrode fingers in the elastic wave apparatus of the second embodiment. Figure 20D is a schematic diagram showing an example of the relationship between the electrode pitch and the order of the electrode fingers in the elastic wave apparatus of the second embodiment. Figure 20E is a schematic diagram showing an example of the relationship between the electrode pitch and the order of the electrode fingers in the elastic wave apparatus of the second embodiment. Figure 21 is a cross-sectional view showing the elastic wave apparatus of the third embodiment. Figure 22 is a cross-sectional view showing the elastic wave apparatus of the fourth embodiment. Figure 23 is a cross-sectional view showing the elastic wave apparatus of the fifth embodiment. Figure 24 is a cross-sectional view showing the elastic wave apparatus of the sixth embodiment. Figure 25 is a cross-sectional view showing the elastic wave apparatus of the seventh embodiment. Figure 26 is a cross-sectional view showing the elastic wave apparatus of the eighth embodiment. Figure 27 is a cross-sectional view showing the elastic wave apparatus of the ninth embodiment. Figure 28 is a circuit diagram showing a filter according to the tenth embodiment. Figure 29 is a diagram illustrating the resonance characteristics of the resonators used in the filters according to Examples 1 to 3. Figure 30A is a diagram showing the simulation results of the filters according to Examples 1 to 3. Figure 30B is a diagram showing the simulation results of the filters according to Examples 1 to 3. Figure 31 is a circuit diagram showing a filter according to the eleventh embodiment. Figure 32A is a diagram showing the simulation results of the filters according to Examples 4 to 6. Figure 32B is a diagram showing the simulation results of the filters according to Examples 4 to 6.
[0010] Embodiments of the present disclosure will be described in detail below with reference to the drawings. However, these embodiments do not limit the present disclosure. Each embodiment described in this disclosure is illustrative, and partial substitution or combination of configurations is possible between different embodiments. In modifications and subsequent embodiments, descriptions of matters common to the first embodiment will be omitted, and only the differences will be described. In particular, similar effects and benefits due to similar configurations will not be mentioned sequentially for each embodiment.
[0011] (First Embodiment) Figure 1 is a plan view showing an elastic wave apparatus according to the first embodiment. Figure 2 is a cross-sectional view taken along line II-II' in Figure 1. Figure 3 is an enlarged cross-sectional view showing region A shown in Figure 2.
[0012] As shown in Figures 1 and 2, the elastic wave apparatus 10 according to the first embodiment includes a piezoelectric layer 20, an IDT electrode 30, a support member, a first dielectric layer 41, and a second dielectric layer 42. As shown in Figure 2, in the elastic wave apparatus 10, the second dielectric layer 42, piezoelectric layer 20, IDT electrode 30, and first dielectric layer 41 are stacked in the Z direction on the support substrate 11 in that order.
[0013] (Piezoelectric layer) The piezoelectric layer 20 is a flat plate-shaped layer having a first main surface 20a and a second main surface 20b on the opposite side of the first main surface 20a. The piezoelectric layer 20 is made of lithium niobate (LiNbO 3 ) is included. In the first embodiment, the piezoelectric layer 20 is formed of a single crystal of lithium niobate with a rotational Y cut.
[0014] In the first embodiment, when the Euler angles of lithium niobate in the piezoelectric layer 20 are (φ, θ, ψ), it is preferable that -10°≦φ≦10°, 5°≦θ≦60°, and -10°≦ψ≦10° be satisfied. Here, it is more preferable that θ be satisfied with 15°≦θ≦50°, and even more preferable that θ be satisfied with 20°≦θ≦45°. Furthermore, it is more preferable that φ=ψ=0° be satisfied for φ and ψ. This improves the effective electromechanical coupling coefficient, thereby improving the resonance characteristics.
[0015] Furthermore, the same effect can be obtained even when the range of the second component θ of the Euler angle of lithium niobate in the piezoelectric layer 20 (φ, θ, ψ) differs by 180°. Specifically, it is preferable that -10°≦φ≦10°, 185°≦θ≦240°, and -10°≦ψ≦10° be satisfied. Here, for θ, it is more preferable that 195°≦θ≦230° be satisfied, and even more preferable that 200°≦θ≦225° be satisfied. Also, for φ and ψ, it is more preferable that φ=ψ=0° be satisfied. This improves the effective electromechanical coupling coefficient, and thus improves the resonance characteristics.
[0016] (Support Member) The support member is provided on the second main surface 20b side with respect to the piezoelectric layer 20. In the first embodiment, the support member consists of a support substrate 11 and is provided on the side of the second dielectric layer 42 opposite to the piezoelectric layer 20.
[0017] The support member has an acoustic reflective portion on the second main surface 20b side of the piezoelectric layer 20. In the first embodiment, the acoustic reflective portion is a recess 14 on the piezoelectric layer 20 side of the support substrate 11. More specifically, the support substrate 11 has a bottom surface on the piezoelectric layer 20 side and a wall surface provided in a frame shape on the upper surface of the bottom surface, and the recess 14 is formed by the bottom surface and the wall surface. Here, the recess 14 is also called a cavity portion or hollow portion. In the example of Figure 1, the acoustic reflective portion is provided so as to overlap with the intersection region C of the IDT electrode 30, which will be described later, when viewed in plan in the Z direction. Therefore, the elastic wave device 10 has a so-called membrane structure in which the recess 14 is provided on the second main surface 20b side of the piezoelectric layer 20. In the example of Figure 2, the support substrate 11 is in direct contact with the second dielectric layer 42 at the peripheral portion where the recess 14 is not provided.
[0018] In the first embodiment, the support substrate 11 is made of silicon (Si). The plane orientation of the Si on the side facing the piezoelectric layer 20 may be (100) or (110), or it may be (111). Preferably, high-resistivity Si with a resistivity of 4 kΩ or more is desirable. However, the support substrate 11 can also be made of an appropriate insulating material or semiconductor material. As materials for the support substrate 11, for example, piezoelectric materials such as aluminum oxide, lithium tantalate, lithium niobate, and quartz, various ceramics such as alumina, magnesia, sapphire, silicon nitride, aluminum nitride, silicon carbide, zirconia, cordierite, mullite, steatite, and forsterite, dielectrics such as diamond and glass, and semiconductors such as gallium nitride can be used.
[0019] (IDT electrode) The IDT (Interdigital Transducer) electrode 30 is provided on at least one of the first main surface 20a and the second main surface 20b of the piezoelectric layer 20. That is, the IDT electrode 30 may be directly provided on at least one of the first main surface 20a and the second main surface 20b, or it may be indirectly provided on at least one of the first main surface 20a and the second main surface 20b via a dielectric layer or the like. In the first embodiment, the IDT electrode 30 is provided on the first main surface 20a. As shown in Figure 1, the IDT electrode 30 has a first electrode finger 31, a second electrode finger 32, a first busbar electrode 33, and a second busbar electrode 34. The plurality of first electrode fingers 31 extend in the Y direction, and one end in the extending direction is connected to the first busbar electrode 33. Multiple second electrode fingers 32 extend in the Y direction, and their other ends in the extending direction are connected to the second busbar electrode 34. Multiple first electrode fingers 31 and multiple second electrode fingers 32 are arranged alternately in the X direction with spacing between them. The first busbar electrode 33 and the second busbar electrode 34 each extend in the X direction and are arranged opposite each other in the Y direction. Multiple first electrode fingers 31 and multiple second electrode fingers 32 are arranged between the first busbar electrode 33 and the second busbar electrode 34.
[0020] Furthermore, the IDT electrode 30 is not limited to a configuration having a plurality of first electrode fingers 31 and a plurality of second electrode fingers 32, and may also include a configuration with at least one first electrode finger 31 whose base end is connected to the first busbar electrode 33 and at least one second electrode finger 32 whose base end is connected to the second busbar electrode 34.
[0021] In the following description, the thickness direction of the piezoelectric layer 20 may be referred to as the Z direction, the extension direction of the first electrode finger 31 and the second electrode finger 32 as the Y direction, and the arrangement direction of the first electrode finger 31 and the second electrode finger 32 as the X direction. In the first embodiment, the X direction is perpendicular to the extension direction of the first electrode finger 31 and the second electrode finger 32. Also, in the following description, "up" refers to the direction from the support substrate 11 toward the outermost IDT electrode 30, and "down" refers to the direction from the IDT electrode 30 toward the support substrate 11.
[0022] The distance between the centers of the first electrode finger 31 and the second electrode finger 32 (electrode pitch) is not particularly limited, but is preferably in the range of 1 μm to 10 μm. Here, the electrode pitch refers to the distance between the center line of the dimensions of the first electrode finger 31 in the direction perpendicular to the extending direction (Y direction) of the first electrode finger 31 (X direction) and the center line of the dimensions of the second electrode finger 32 in the direction perpendicular to the extending direction (Y direction) of the second electrode finger 32 (X direction). In addition, the width of the first electrode finger 31 and the second electrode finger 32 (electrode width), that is, the dimensions in the direction perpendicular to the extending direction (Y direction) of the first electrode finger 31 and the second electrode finger 32 (X direction), is not particularly limited, but is preferably in the range of 150 nm to 1000 nm.
[0023] When there are multiple first electrode fingers 31 and second electrode fingers 32, that is, when the first electrode fingers 31 and second electrode fingers 32 are considered as a pair of electrode sets, there are 1.5 or more pairs of electrode sets, the arithmetic mean of the center-to-center distances of adjacent first electrode fingers 31 and second electrode fingers 32 among the 1.5 or more pairs of first electrode fingers 31 and second electrode fingers 32 may be described as the average center-to-center distance between the first electrode fingers 31 and second electrode fingers 32 (average electrode pitch).
[0024] In the first embodiment, the electrode spacing between electrode pairs consisting of a first electrode finger 31 and a second electrode finger 32 was made equal for all pairs. That is, the first electrode finger 31 and the second electrode finger 32 were arranged at equal pitches.
[0025] In the first embodiment, the IDT electrode 30, i.e., the first electrode finger 31, the second electrode finger 32, the first busbar electrode 33, and the second busbar electrode 34, are made of a suitable metal or alloy such as Al or AlCu alloy. Alternatively, the IDT electrode 30 may be a laminate in which an Al film is laminated on an adhesion layer such as a titanium (Ti) film. Note that an adhesion layer other than a Ti film may also be used.
[0026] Here, the crossing region C (excitation region) shown in Figure 1 is the region where the first electrode finger 31 and the second electrode finger 32 overlap when viewed in the X direction. The length of the crossing region C is the dimension in the extending direction of the first electrode finger 31 and the second electrode finger 32 in the crossing region C. In this embodiment, the length of the crossing region C is, for example, 30 μm.
[0027] During operation, an AC voltage is applied between a plurality of first electrode fingers 31 and a plurality of second electrode fingers 32. More specifically, an AC voltage is applied between a first busbar electrode 33 and a second busbar electrode 34. This makes it possible to obtain resonance characteristics using the bulk wave of the thickness-slip first mode excited in the piezoelectric layer 20.
[0028] Furthermore, in the elastic wave apparatus 10, when the thickness of the piezoelectric layer 20 is d and the average electrode pitch is p, d / p is set to 0.5 or less. Therefore, the bulk wave of the thickness-slip first mode described above is effectively excited, and good resonance characteristics can be obtained. More preferably, d / p is 0.24 or less, in which case even better resonance characteristics can be obtained. Regarding the thickness d of the piezoelectric layer 20, if the piezoelectric layer 20 has thickness variations, the average value of its thickness is adopted.
[0029] In the elastic wave device 10 of the first embodiment, since it has the above-described configuration, even if the number of pairs of the first electrode fingers 31 and the second electrode fingers 32 is reduced in an attempt to reduce the propagation loss and miniaturize the device, a decrease in the Q value is unlikely to occur. This is because the bulk wave of the thickness-slip primary mode is utilized.
[0030] (Dielectric layer) The dielectric layer is a layer containing a dielectric provided on at least one of the first main surface 20a and the second main surface 20b of the piezoelectric layer 20. That is, the dielectric layer is provided so as to contact at least one of the first main surface 20a and the second main surface 20b of the piezoelectric layer 20. In the first embodiment, the dielectric layer includes a first dielectric layer 41 provided on the first main surface 20a and a second dielectric layer 42 provided on the second main surface 20b. Thereby, higher-order modes generated in the thickness direction of the piezoelectric layer 20 can be suppressed, and the resonance characteristics can be improved.
[0031] As shown in FIGS. 2 and 3, the first dielectric layer 41 is provided on the first main surface 20a side of the piezoelectric layer 20. In the examples of FIGS. 2 and 3, the first dielectric layer 41 is provided so as to cover the IDT electrode 30 provided on the first main surface 20a. That is, the IDT electrode 30 is provided between the first dielectric layer 41 and the first main surface 20a of the piezoelectric layer 20 in the Z direction.
[0032] The first dielectric layer 41 is silicon oxide (SiO X ), silicon nitride (Si 3 N 4 ), aluminum nitride (AlN), aluminum oxide (Al 2 O 3 ), tantalum oxide (Ta 2 O 5 ), niobium oxide (Nb 2 O 5 ) and contains at least one kind. Further, the first dielectric layer 41 may be a laminate of a plurality of layers.
[0033] As shown in FIGS. 2 and 3, the second dielectric layer 42 is provided on the second main surface 20b side of the piezoelectric layer 20. In the examples of FIGS. 2 and 3, the second dielectric layer 42 is provided so as to cover the second main surface 20b.
[0034] The second dielectric layer 42 contains at least one of silicon oxide, silicon nitride, aluminum nitride, aluminum oxide, tantalum oxide, and niobium oxide. The material of the second dielectric layer 42 may be the same as or different from that of the first dielectric layer 41.
[0035] The following describes the relationship between the thickness of the piezoelectric layer 20, the thickness of the dielectric layers (first dielectric layer 41 and second dielectric layer), and the average electrode pitch p of the elastic wave apparatus 10 according to the first embodiment. In the following description, the thicknesses of the first dielectric layer 41 and the second dielectric layer 42 are denoted as t1 and t2, respectively, the sum of the thicknesses of the dielectric layers is denoted as t, and the sum of the thicknesses of the piezoelectric layer and the dielectric layers is denoted as T. In the first embodiment, the dielectric layer includes the first dielectric layer 41 and the second dielectric layer 42, so t = t1 + t2. Also, T = d + t. Here, the thickness of the dielectric layer refers to the average thickness of the dielectric layer in the region of the intersection region C that does not overlap with the IDT electrode 30 when viewed in plan in the Z direction. Furthermore, the thickness t2 of the second dielectric layer 42 refers to the distance in the Z direction from the second main surface 20b of the piezoelectric layer 20 in contact with the second dielectric layer 42 to the upper end of the acoustic reflection portion (recess 14) where the main surface of the second dielectric layer 42 is located.
[0036] In the first embodiment, p / T is 3.0 or more and 6.0 or less. A p / T of 3.0 or more improves the effective electromechanical coupling coefficient, thereby improving the resonance characteristics. A p / T of 6.0 or less keeps the frequency of unwanted waves away from the main wave, thereby suppressing the deterioration of the resonance characteristics due to unwanted waves.
[0037] t / d is preferably greater than 0 and less than or equal to 0.98, and more preferably between 0.3 and 0.6. This improves the effective electromechanical coupling coefficient, thereby improving the resonance characteristics.
[0038] Here, the thickness of the dielectric layer with the smaller thickness among the first dielectric layer 41 and the second dielectric layer 42 is preferably 30% or more of the total thickness t of the dielectric layers, and it is more preferable that the thicknesses of the first dielectric layer 41 and the second dielectric layer 42 are equal. In the examples of Figures 2 and 3, t1 / t = t2 / t = 0.5. This makes it possible to suppress higher-order modes that occur in the thickness direction of the piezoelectric layer 20 and improve the resonance characteristics.
[0039] Figure 4 is a schematic cross-sectional view illustrating the bulk wave of the first-order thickness-slip mode propagating through the piezoelectric layer of the first embodiment. Figure 5 is a schematic cross-sectional view illustrating the amplitude direction of the bulk wave of the first-order thickness-slip mode propagating through the piezoelectric layer of the first embodiment.
[0040] As shown in Figure 4, in the elastic wave device 10 of the first embodiment, since the vibration displacement is in the thickness sliding direction, the wave propagates almost entirely in the direction connecting the first main surface 20a and the second main surface 20b of the piezoelectric layer 20, i.e., in the Z direction, and resonates. That is, the X-direction component of the wave propagation direction is significantly smaller than the Z-direction component. And since the resonance characteristics are obtained by the propagation of this wave in the Z direction, a reflector is not required. Therefore, no propagation loss occurs when the wave propagates to the reflector. Accordingly, even if the number of logarithms of electrode pairs consisting of the first electrode finger 31 and the second electrode finger 32 is reduced in an attempt to miniaturize the device, a decrease in the Q value is unlikely to occur.
[0041] In the first embodiment, the amplitude direction of the bulk wave in the thickness-slip primary mode is approximately opposite in the first region 251 and the second region 252, both included in the intersection region C (see Figure 1) of the piezoelectric layer 20, as shown in Figure 5. Figure 5 schematically shows the bulk wave when a voltage is applied between the first electrode finger 31 and the second electrode finger 32 such that the second electrode finger 32 is at a higher potential than the first electrode finger 31. Here, the virtual plane VP1 is a plane that is perpendicular to the thickness direction of the piezoelectric layer 20 and divides the piezoelectric layer 20 into two. The first region 251 is the region between the virtual plane VP1 and the first main surface 20a within the intersection region C. The second region 252 is the region between the virtual plane VP1 and the second main surface 20b within the intersection region C.
[0042] In the elastic wave device 10, at least one pair of electrodes consisting of a first electrode finger 31 and a second electrode finger 32 are arranged. However, since waves are not propagated in the X direction, it is not necessarily required that there be multiple pairs of electrodes consisting of the first electrode finger 31 and the second electrode finger 32. In other words, it is sufficient that at least one pair of electrodes is provided.
[0043] For example, the first electrode finger 31 is an electrode connected to a hot potential, and the second electrode finger 32 is an electrode connected to a ground potential. However, the first electrode finger 31 may be connected to a ground potential and the second electrode finger 32 may be connected to a hot potential. In the first embodiment, at least one pair of electrodes are either connected to a hot potential or to a ground potential, as described above, and no floating electrodes are provided.
[0044] Figure 6 is an explanatory diagram showing an example of the resonance characteristics of the elastic wave apparatus of the first embodiment. The design parameters of the elastic wave apparatus 10 that obtained the resonance characteristics shown in Figure 6 are as follows.
[0045] Piezoelectric layer 20: LiNbO with Euler angles (0°, 0°, 90°) 3 Piezoelectric layer 20 thickness: 400 nm Support substrate 11: Si Length of cross region C: 40 μm Number of electrode pairs consisting of first electrode finger 31 and second electrode finger 32: 21 pairs Pitch between first electrode finger 31 and second electrode finger 32: 3 μm Width of first electrode finger 31 and second electrode finger 32: 500 nm d / p: 0.133
[0046] As is clear from Figure 6, good resonance characteristics with a relative bandwidth of 12.5% are obtained despite the absence of a reflector.
[0047] By the way, if the thickness of the piezoelectric layer 20 is d and the average (average distance) of the electrode pitch between the first electrode finger 31 and the second electrode finger 32 is p, then in the first embodiment, d / p is 0.5 or less, more preferably 0.24 or less. This will be explained with reference to Figure 7.
[0048] Figure 7 is an explanatory diagram showing the relationship between d / 2p and the specific bandwidth of the resonator in the elastic wave apparatus of the first embodiment, where p is the distance between the centers of adjacent electrodes or the average distance between the centers, and d is the average thickness of the piezoelectric layer. In Figure 7, multiple elastic wave apparatuses were obtained in the same manner as the elastic wave apparatus that obtained the resonance characteristics shown in Figure 6, except that d / 2p was changed.
[0049] As shown in Figure 7, when d / 2p exceeds 0.25, i.e., d / p > 0.5, the relative bandwidth is less than 5% even when d / p is adjusted. In contrast, when d / 2p ≤ 0.25, i.e., d / p ≤ 0.5, the relative bandwidth can be increased to 5% or more by changing d / p within that range, i.e., a resonator with a high coupling coefficient can be constructed. Furthermore, when d / 2p is 0.12 or less, i.e., when d / p is 0.24 or less, the relative bandwidth can be increased to 7% or more. In addition, by adjusting d / p within this range, a resonator with an even wider relative bandwidth can be obtained, and a resonator with an even higher coupling coefficient can be realized. Therefore, it can be seen that by setting d / p to 0.5 or less, a resonator with a high coupling coefficient can be constructed using the bulk wave of the thickness-slip first mode described above.
[0050] Figure 8 is a plan view showing an example in which a pair of electrodes is provided in the elastic wave apparatus of the first embodiment. In the elastic wave apparatus 10, a pair of electrodes having a first electrode finger 31 and a second electrode finger 32 are provided on the first main surface 20a of the piezoelectric layer 20. In Figure 8, K is the crossover width. As mentioned above, in the elastic wave apparatus 10 of this disclosure, the number of electrode finger pairs may be one. Even in this case, if the above d / p is 0.5 or less, the bulk wave of the thickness-slip first mode can be effectively excited.
[0051] In the elastic wave apparatus 10, it is preferable that the metallization ratio MR of the adjacent first electrode finger 31 and second electrode finger 32 with respect to the crossing region C satisfies MR ≤ 1.75 (d / p) + 0.075. In this case, spurious emissions can be effectively reduced. This will be explained with reference to Figures 8 and 9.
[0052] Figure 9 is a reference diagram showing an example of the resonance characteristics of the elastic wave apparatus of the first embodiment. As shown in Figure 9, the spurious signal indicated by arrow B appears between the resonant frequency and the anti-resonant frequency. Note that d / p = 0.08 and LiNbO 3 The Euler angles were set to (0°, 0°, 90°). Furthermore, the metallization ratio MR was set to 0.35.
[0053] The metallization ratio MR will be explained with reference to Figure 1. In the electrode structure of Figure 1, if we focus on a pair of first electrode fingers 31 and second electrode fingers 32, we assume that only this pair of first electrode fingers 31 and second electrode fingers 32 are provided. In this case, the area enclosed by the dashed line becomes the intersection region C. This intersection region C is the area on the first electrode finger 31 that overlaps with the second electrode finger 32 when viewed in a direction perpendicular to the extending direction of the first electrode finger 31 and the second electrode finger 32, i.e., in an opposing direction, the area on the first electrode finger 31 that overlaps with the first electrode finger 32, the area on the second electrode finger 32 that overlaps with the first electrode finger 31, and the area between the first electrode finger 31 and the second electrode finger 32 that overlaps. The area of the first electrode finger 31 and the second electrode finger 32 within the intersection region C relative to the area of the intersection region C is the metallization ratio MR. In other words, the metallization ratio MR is the ratio of the area of the metallized portion to the area of the cross region C.
[0054] Furthermore, if multiple pairs of first electrode fingers 31 and second electrode fingers 32 are provided, the ratio of the metallized portion to the total area of the crossing region C should be defined as MR.
[0055] Figure 10 is an explanatory diagram showing the relationship between the relative bandwidth of the elastic wave device of the first embodiment, when a large number of elastic wave resonators are configured, and the phase rotation amount of the spurious impedance normalized to 180 degrees as the spurious magnitude. The relative bandwidth was adjusted by changing various aspects of the thickness of the piezoelectric layer 20 and the dimensions of the first electrode fingers 31 and the second electrode fingers 32. Also, Figure 10 shows the Z-cut LiNbO 3 The results shown are for the case where a piezoelectric layer 20 consisting of the above is used, but a similar trend is observed when piezoelectric layers 20 with other cut angles are used.
[0056] In the region enclosed by the ellipse J in Figure 10, the spurious emission is large at 1.0. As is clear from Figure 10, when the relative bandwidth exceeds 0.17, that is, when it exceeds 17%, large spurious emissions with a spurious emission level of 1 or more appear within the passband, even if the parameters constituting the relative bandwidth are changed. In other words, as shown in the resonance characteristics in Figure 9, large spurious emissions indicated by arrow B appear within the bandwidth. Therefore, it is preferable that the relative bandwidth be 17% or less. In this case, the spurious emissions can be reduced by adjusting the thickness of the piezoelectric layer 20 and the dimensions of the first electrode finger 31 and the second electrode finger 32.
[0057] Figure 11 is an explanatory diagram showing the relationship between d / 2p, the metallization ratio MR, and the relative bandwidth. In the elastic wave apparatus 10 of the first embodiment, various elastic wave apparatuses 10 with different d / 2p and MR were configured and the relative bandwidth was measured. The hatched area to the right of the dashed line D in Figure 11 is the region where the relative bandwidth is 17% or less. The boundary between this hatched region and the unhatched region is represented by MR = 3.5(d / 2p) + 0.075. That is, MR = 1.75(d / p) + 0.075. Therefore, preferably, MR ≤ 1.75(d / p) + 0.075. In that case, it is easy to keep the relative bandwidth at 17% or less. More preferably, it is the region to the right of MR = 3.5(d / 2p) + 0.05, shown by the dashed line D1 in Figure 11. In other words, if MR ≤ 1.75 (d / p) + 0.05, the relative bandwidth can be reliably reduced to 17% or less.
[0058] Figure 12 shows the LiNbO2 when d / p approaches 0. 3 This is an explanatory diagram showing the relative bandwidth map for Euler angles (0°, θ, ψ). The hatched area in Figure 12 is the region where a relative bandwidth of at least 5% is obtained. Approximating the range of this region, it is represented by the following equations (1), (2), and (3).
[0059] (0°±10°, 0°~20°, any ψ) ...Equation (1) (0°±10°, 20°~80°, 0°~60° (1-(θ-50)) 2 / 900) 1/2) or (0°±10°, 20°~80°, [180°-60°(1-(θ-50) 2 / 900) 1/2 ]~180°) ...Formula (2) (0°±10°, [180°-30°(1-(ψ-90) 2 ( / 8100) 1/2 ] ~180°, any ψ) ...Equation (3)
[0060] Therefore, in the case of the Euler angle range of equation (1), equation (2), or equation (3) above, the relative bandwidth can be made sufficiently wide, which is preferable.
[0061] Furthermore, even when the range of the second component θ in equations (1), (2), and (3) differs by 180°, similar propagation characteristics are observed, and similar effects can be obtained. Specifically, for example, the Euler angles (φ, θ, ψ) of the lithium niobate constituting the piezoelectric layer are preferably within the range of equations (1A), (2A), or (3A) below. This allows for a sufficiently wide specific bandwidth.
[0062] (0°±10°, 180°~200°, any ψ) ...Equation (1A) (0°±10°, 200°~260°, 0°~60° (1-(θ-50)) 2 / 900) 1/2 ) or (0°±10°, 200°~260°, [180°-60°(1-(θ-50) 2 / 900) 1/2 ]~180°) ...Formula (2A) (0°±10°, [360°-30°(1-(ψ-90) 2 ( / 8100) 1/2 ] ~360°, any ψ) ...Equation (3A)
[0063] (Examples) Examples of the first embodiment will be described below. However, the embodiments are not limited by these examples. Here, the resonance characteristics of the elastic wave apparatus according to the examples and comparative examples were investigated by simulation.
[0064] The elastic wave apparatus according to the embodiment is an elastic wave apparatus according to the first embodiment. The elastic wave apparatus according to the embodiment was designed as follows. Here, in the elastic wave apparatus according to the embodiment, p / T = 3.92 and t / d = 0.50. In addition, in the elastic wave apparatus according to the embodiment, the electrode pitch is the same for all pairs of first electrode fingers 31 and second electrode fingers 32. Piezoelectric layer 20: Material: LiNbO 3 Euler angles: (0°, 30°, 0°) Thickness: 332 nm IDT electrode 30: Material: Al Average electrode pitch: 1.95 μm Electrode width: 0.325 μm Thickness: 100 nm First dielectric layer 41: Material: SiO 2 Thickness: 83 nm Second dielectric layer 42: Material: SiO 2 Thickness: 83 nm
[0065] The comparative example elastic wave apparatus has a Z-cut piezoelectric layer 20 and does not have a dielectric layer. The comparative example elastic wave apparatus was designed as follows. Here, in the comparative example elastic wave apparatus, p / T = 7.50 and t / d = 0. In the comparative example elastic wave apparatus, the electrode pitch is the same for all pairs of first electrode fingers 31 and second electrode fingers 32. Piezoelectric layer 20: Material: LiNbO 3 Euler angles: (0°, 0°, 90°) Thickness: 400 nm IDT electrode 30: Material: Al Average electrode pitch: 3.0 μm Electrode width: 0.5 μm Thickness: 100 nm
[0066] Figure 13 shows the simulation results of the elastic wave apparatus according to the embodiment. Figure 14 shows the simulation results of the elastic wave apparatus according to the comparative example. As shown in Figure 13, in the embodiment where p / T ≤ 6.0, unwanted waves S, which are higher-order modes of the main wave M along the electrode finger alignment direction (X direction), appeared at 7136 MHz. On the other hand, as shown in Figure 14, in the comparative example where p / T > 6.0, unwanted waves S appeared at 6231 MHz. Therefore, it can be seen that by setting p / T ≤ 6.0, the unwanted waves S can be moved away from the main wave M to the higher frequency side, thereby improving the resonance characteristics.
[0067] Furthermore, regarding the elastic wave apparatus according to the embodiment in Figure 13 and the comparative example in Figure 14 described above, the effective electromechanical coupling coefficient K eff 2 Here, the effective electromechanical coupling coefficient K was calculated. eff 2 F is a parameter that represents the efficiency of the piezoelectric effect, as shown in equation (4) below. In equation (4), F r F is the resonant frequency. a This represents the anti-resonance frequency. The effective electromechanical coupling coefficient K. eff 2 The larger the coefficient of capacitance, the more efficient the piezoelectric effect, and the more suitable the elastic wave device is for broadband applications.
[0068]
[0069] In the elastic wave apparatus according to the embodiment shown in Figure 13, which is provided with a dielectric layer, the resonant frequency F r The frequency is 4808 MHz, and the anti-resonant frequency is F. a The frequency is 5562 MHz, and the effective electromechanical coupling coefficient K eff 2 This was 29.2%, exceeding 25%. On the other hand, in the elastic wave apparatus according to the comparative example in Figure 14, which did not have a dielectric layer, the resonant frequency F r The frequency is 4815 MHz, and the anti-resonant frequency is F. a The frequency is 5385 MHz, and the effective electromechanical coupling coefficient K eff 2 The ratio was 23.9%, which is below 25%. Therefore, by providing a dielectric layer, even if p / T ≤ 6.0, the effective electromechanical coupling coefficient K eff 2 This shows that it is possible to improve performance and obtain an elastic wave device suitable for broadband applications.
[0070] Figure 15 shows the relationship between p / T and the frequency of unwanted waves for the examples and comparative examples. More specifically, the resonant frequency of the main wave is F. Main The frequency F of the unwanted wave S shown in Figures 13 and 14. Spurious In this case, Figure 15 shows the relationship between p / T and the frequency ratio F. Spurious / F Main This graph shows the relationship between the frequency ratio F. Spurious / F MainThe larger the value, the further the unwanted wave S is from the main wave M on the higher frequency side. In the simulation shown in Figure 15, the average electrode pitch p of the elastic wave apparatus described in the example in Figure 13 and the comparative example in Figure 14 is changed to change p / T, and the frequency ratio F at each p / T value is changed. Spurious / F Main I investigated it.
[0071] As shown in Figure 15, in the embodiment with a dielectric layer, as in the comparative example without a dielectric layer, the smaller the p / T, the higher the frequency ratio F. Spurious / F Main The frequency ratio F increased. Spurious / F Main It can be seen that this depends on p / T and is independent of the presence or absence of a dielectric layer.
[0072] As shown in Figure 15, in the elastic wave apparatus according to the embodiment, when p / T ≤ 6.0, the frequency ratio F Spurious / F Main The value became greater than 1.35. Therefore, by satisfying p / T ≤ 6.0, the unwanted wave S can be sufficiently separated from the main wave M on the higher frequency side, and the resonance characteristics can be improved.
[0073] Figure 16 shows the p / T ratio and effective electromechanical coupling coefficient K of the elastic wave apparatus according to the embodiment. eff 2 This figure shows the relationship. In the simulation shown in Figure 16, the average electrode pitch p of the elastic wave apparatus according to the embodiment shown in Figure 13 above is changed to change p / T, and the effective electromechanical coupling coefficient K at each p / T value is determined. eff 2 I investigated it.
[0074] As shown in Figure 16, when p / T ≥ 3.0, the effective electromechanical coupling coefficient K eff 2 The ratio exceeds 25%, indicating that a seismic wave device suitable for broadband applications can be obtained.
[0075] Figure 17 shows the t / d and effective electromechanical coupling coefficient K of the elastic wave apparatus according to the embodiment. eff 2is a diagram showing the relationship therewith. In the simulation according to FIG. 17, by changing the total thickness t of the first dielectric layer 41 and the second dielectric layer 42 according to the above-described embodiment of FIG. 13, t / d is changed, and the effective electromechanical coupling coefficient K with respect to the value of t / d eff 2 was examined.
[0076] As shown in FIG. 17, when 0 < t / d ≤ 0.98 is satisfied, the effective electromechanical coupling coefficient K eff 2 exceeds the case where t / d = 0, that is, the case where the dielectric layer is not provided. Therefore, it can be seen that by satisfying 0 < t / d ≤ 0.98, an elastic wave device suitable for broadband can be obtained.
[0077] As shown in FIG. 17, when 0.3 ≤ t / d ≤ 0.6 is satisfied, the effective electromechanical coupling coefficient K eff 2 became 25% or more. Therefore, it can be seen that by satisfying 0.3 ≤ t / d ≤ 0.6, an elastic wave device more suitable for broadband can be obtained.
[0078] FIG. 18 is a diagram showing the relationship between the Euler angles of lithium niobate of the elastic wave device according to the embodiment and the effective electromechanical coupling coefficient K eff 2 In the simulation according to FIG. 18, the second component θ of the Euler angle of lithium niobate of the piezoelectric layer 20 according to the above-described embodiment of FIG. 13 is changed, and the effective electromechanical coupling coefficient K with respect to the value of θ eff 2 was examined. Note that the comparative example indicated by the one-dot chain line in FIG. 18 refers to the comparative example of FIG. 14 described above.
[0079] As shown in FIG. 18, when 5° ≤ θ ≤ 60° is satisfied, the effective electromechanical coupling coefficient K eff 2 exceeds the comparative example in which the piezoelectric layer 20 is Z-cut. Therefore, it can be seen that by setting the piezoelectric layer 20 to a rotated Y-cut and satisfying 5° ≤ θ ≤ 60°, an elastic wave device suitable for broadband can be obtained.
[0080] As shown in FIG. 18, when 15° ≤ θ ≤ 50° is satisfied, the effective electromechanical coupling coefficient K eff2 became 25% or more. Therefore, it can be seen that by satisfying 15° ≤ θ ≤ 50°, an elastic wave device more suitable for broadbanding can be obtained.
[0081] As shown in FIG. 18, when 20° ≤ θ ≤ 45° is satisfied, the effective electromechanical coupling coefficient K eff 2 became 28% or more. Therefore, it can be seen that by satisfying 20° ≤ θ ≤ 45°, an elastic wave device even more suitable for broadbanding can be obtained.
[0082] (Second Embodiment) That is, in the second embodiment, the center-to-center distance of at least one set of adjacent first electrode fingers 31 and second electrode fingers 32 is different from the center-to-center distance of other adjacent sets of first electrode fingers 31 and second electrode fingers 32. In the following description, the set of first electrode fingers 31 and second electrode fingers 32 will be simply described as a set of electrode fingers.
[0083] FIG. 19 is a schematic plan view showing the IDT electrodes of the elastic wave device of the second embodiment. The elastic wave device according to the second embodiment is different from the elastic wave device according to the first embodiment in that the center-to-center distance of at least one set of adjacent first electrode fingers 31 and second electrode fingers 32 is different from the center-to-center distance of other adjacent sets of first electrode fingers 31 and second electrode fingers 32. In the following description, the set of first electrode fingers 31 and second electrode fingers 32 will be simply described as a set of electrode fingers.
[0084] In the following description, the total number of sets of electrode fingers included in the IDT electrode 30A is represented by N, the order of the sets of electrode fingers counted from one side in the X direction is represented by k (or l), and the electrode pitch is represented by p k and is represented by the following formula (5) using the total number of sets of electrode fingers N, the order of the sets of electrode fingers k, and the electrode pitch p k
[0085]
[0086] In the second embodiment, the center-to-center distance of at least one set of electrode fingers is different from the center-to-center distance of other sets of electrode fingers. In other words, k ≠ l and p k ≠ p lThere exists at least one pair of k and l such that this condition is met. This suppresses unwanted waves caused by modes whose frequency is easily changed by the inter-electrode pitch of the first electrode finger 31 and the second electrode finger 32, and improves the resonance characteristics because the main wave M is hardly transformed by the inter-electrode pitch.
[0087] Figures 20A to 20E are schematic diagrams showing an example of the relationship between the electrode pitch and the order of the electrode fingers in the elastic wave apparatus of the second embodiment. In Figures 20A to 20E, the normalized electrode pitch is defined as the electrode pitch p k Ratio p to average electrode pitch p k / refers to p. Figures 20A to 20E show the normalized inter-electrode pitch p with respect to the order k of the electrode finger pairs. k This figure schematically represents a graph in which the plots of a scatter plot showing the value of / p are connected by lines. In the second embodiment, the inter-electrode pitch p of the electrode finger pair is relative to the order k of the electrode finger pair. k The relative magnitudes of these can be any of those shown in Figures 20A to 20E, for example.
[0088] As shown in Figure 20A, the electrode pitch p k The value can be increased stepwise from k=1 until it reaches a maximum value near the center in the X direction, i.e., k=(N+1) / 2 or (N+1) / 2, and then gradually decrease towards k=N.
[0089] As shown in Figure 20B, the electrode pitch p k The value of k may be gradually decreased from k=1 until it is minimized at a k closest to the center in the X direction, i.e., k=(N+1) / 2 or (N+1) / 2, and then gradually increased up to k=N.
[0090] As shown in Figure 20C, the electrode pitch p k k may vary with each k. In the example in Figure 20C, the design is such that k increases from k=1, reaching a maximum at the k closest to the center in the X direction, i.e., k=(N+1) / 2 or (N+1) / 2, and then decreasing to k=N.
[0091] As shown in Figure 20D, the electrode pitch p k The interval between electrodes p may vary monotonically. k While it is shown as monotonically increasing with respect to k, it is not limited to this and may also be monotonically decreasing.
[0092] As shown in Figure 20E, the electrode pitch p k There may be multiple values of k at which the interval is smallest or largest. In the example in Figure 20E, the inter-electrode pitch p is p when k = 1. k The electrode pitch p is at its minimum, and thereafter increases with increasing k. k The inter-electrode pitch p is increased and then decreased until it reaches a minimum near the center in the X direction, i.e., at the k closest to k = (N+1) / 2 or (N+1) / 2, and then again increases as k increases. k The inter-electrode pitch p increases and then decreases, and then at k=N, it returns to its original value. k This is the minimum value. Note that the example shown in Figure 20E is just one example and is not limited to this.
[0093] (Third Embodiment) Figure 21 is a cross-sectional view showing an elastic wave apparatus of the third embodiment. As shown in Figure 21, the elastic wave apparatus 10A according to the third embodiment differs from the first embodiment in that a first dielectric layer 41 is provided as a dielectric layer between the IDT electrode 30 and the piezoelectric layer 20. That is, the IDT electrode 30 is laminated on the first dielectric layer 41 that is in contact with the first main surface 20a, and the upper surface of the IDT electrode 30 is exposed. Even in this case, the resonance characteristics can be improved.
[0094] Furthermore, the third embodiment can be combined with the second embodiment described above.
[0095] (Fourth Embodiment) Figure 22 is a cross-sectional view showing an elastic wave apparatus of the fourth embodiment. As shown in Figure 22, the elastic wave apparatus 10B according to the fourth embodiment differs from the first embodiment in that the IDT electrode 30 is embedded in the first dielectric layer 41. That is, the IDT electrode 30 is laminated on the lower part of the first dielectric layer 41 that is in contact with the first main surface 20a, and the upper surface of the IDT electrode 30 is covered by the upper part of the first dielectric layer 41. In this case as well, the resonance characteristics can be improved.
[0096] Furthermore, the fourth embodiment can be combined with the second embodiment described above.
[0097] (Fifth Embodiment) Figure 23 is a cross-sectional view showing the elastic wave apparatus of the fifth embodiment. As shown in Figure 23, the elastic wave apparatus 10C according to the fifth embodiment differs from the first embodiment in that the upper surface of the first dielectric layer 41 is flush with the surface. In this case as well, the resonance characteristics can be improved.
[0098] Furthermore, the fifth embodiment can be combined with the second embodiment described above.
[0099] (Sixth Embodiment) Figure 24 is a cross-sectional view showing the elastic wave apparatus of the sixth embodiment. As shown in Figure 24, the elastic wave apparatus 10D according to the sixth embodiment differs from the first embodiment in that the first dielectric layer 41 is not provided. In this case as well, the resonance characteristics can be improved.
[0100] Furthermore, the sixth embodiment can be combined with the second embodiment described above.
[0101] (Seventh Embodiment) Figure 25 is a cross-sectional view showing the elastic wave apparatus of the seventh embodiment. As shown in Figure 25, the elastic wave apparatus 10E according to the seventh embodiment differs from the first embodiment in that the second dielectric layer 42 is not provided. In this case as well, the resonance characteristics can be improved.
[0102] Furthermore, the seventh embodiment can be combined with the embodiments described above.
[0103] (Eighth Embodiment) Figure 26 is a cross-sectional view showing an elastic wave apparatus of the eighth embodiment. In the embodiments described above, a structure in which the support substrate 11 has a recess 14 has been described, but the invention is not limited thereto.
[0104] As shown in Figure 26, in the elastic wave apparatus 10F according to the eighth embodiment, the support member further has an intermediate layer 12. The intermediate layer 12 is made of, for example, silicon oxide. The intermediate layer 12 is provided on the piezoelectric layer 20 side of the support substrate 11. In the example of Figure 26, there is a recess 14 on the piezoelectric layer 20 side of the intermediate layer 12. Even in this case, the recess 14 can confine the bulk wave of the thickness-slip first mode within the piezoelectric layer 20.
[0105] In the eighth embodiment, when the support substrate 11 is made of silicon, it is preferable that the support member further comprises a coating layer on the intermediate layer 12 side of the support substrate 11. The coating layer is a layer containing at least one of amorphous silicon and polycrystalline silicon. This makes it possible to suppress the generation of a highly electrically conductive layer on the intermediate layer 12 side of the support substrate 11 due to contact with the intermediate layer 12 during the manufacture of the elastic wave apparatus, thereby suppressing degradation of the device's characteristics.
[0106] Furthermore, the eighth embodiment can be combined with the embodiments described above.
[0107] (Ninth Embodiment) Figure 27 is a cross-sectional view showing an elastic wave apparatus of the ninth embodiment. In the embodiments described above, a so-called membrane structure was described in which the support substrate 11 has a recess 14 and the recess 14 is provided on the second main surface 20b side of the piezoelectric layer 20, but the invention is not limited thereto.
[0108] As shown in Figure 27, in the elastic wave apparatus 10G according to the ninth embodiment, an acoustic multilayer film 43 is laminated on the second main surface 20b of the piezoelectric layer 20. The acoustic multilayer film 43 has a laminated structure of first layers 43b, 43d and second layers 43a, 43c, 43e. Here, the first layers 43b, 43d and the second layers 43a, 43c, 43e are made of different materials. The first layers 43b, 43d have a relatively higher acoustic impedance than the second layers 43a, 43c, 43e. For example, the first layers 43b, 43d are made of tungsten carbide (WC), tantalum carbide (TaC), rhenium oxide (ReO 3 ), carbon silicon chromium (CrCSI), niobium carbide (NbC), zinc carbide (ZrC), zinc nitride (TiC), lanthanum boride (LaB 6 ), vanadium carbide (VC), aluminum nitride (AlN), silicon carbide (SiC), yttrium oxide (Y 2 O 3 ), magnesium oxide (MgO), silicon nitride (Si 3 N 4 ), boron carbide (B 4 C), Strontium fluoride (SrF 2 ), barium fluoride (BaF 2 ), tantalum oxide (Ta2 O 5 ), hafnium oxide (HfO 2 ), tungsten oxide (WO 3 The second layer 43a, 43c, 43e may be, for example, silicon oxide (SiO2). X ) and aluminum (Al) can be at least one of these. When the acoustic multilayer film 43 is used, the bulk wave of the thickness-slip first mode can be confined within the piezoelectric layer 20 without using the recess 14. In the ninth embodiment, the first layers 43b, 43d and the second layers 43a, 43c, 43e are formed of a different material from the first dielectric layer 41.
[0109] In addition, the number of layers of the first layers 43b, 43d and the second layers 43a, 43c, 43e in the acoustic multilayer film 43 is not particularly limited. It is sufficient that at least one of the first layers 43b, 43d is located further from the piezoelectric layer 20 than the second layers 43a, 43c, 43e.
[0110] The first layers 43b, 43d and the second layers 43a, 43c, 43e can be made of any suitable material, as long as the acoustic impedance relationship described above is satisfied.
[0111] The configuration of the ninth embodiment can be combined with the embodiments described above.
[0112] (Tenth Embodiment) Figure 28 is a circuit diagram showing a filter according to the tenth embodiment. As shown in Figure 28, the filter 1 according to the tenth embodiment is a so-called ladder type filter.
[0113] In the tenth embodiment, filter 1 is a so-called bandpass filter that allows waves of a specific frequency band to pass through. Examples of the frequency bands of filter 1 include the n77 band (3300 MHz - 4200 MHz), the n79 band (4400 MHz - 5000 MHz), the n96 band (5925 MHz - 7125 MHz), the n102 band (5925 MHz - 6425 MHz), the n104 band (6425 MHz - 7125 MHz), the Wi-Fi® 5 GHz band (5170 MHz - 5815 MHz), the Wi-Fi 6 GHz band (6105 MHz - 7125 MHz), and the Wi-Fi Full band (5150 MHz - 7125 MHz).
[0114] Filter 1 includes a plurality of series arm resonators S1, S2, S3, S4 and a plurality of parallel arm resonators P11, P12, P21, P22. The plurality of series arm resonators S1, S2, S3, S4 are connected in series to the signal path (series arm) between the input terminal IN and the output terminal OUT. The plurality of parallel arm resonators P11, P12, P21, P22 are connected in parallel to the signal path (parallel arm) connecting each of the series arm nodes N11, N12, N21, N22 to ground.
[0115] The series arm nodes N11, N12, N21, and N22 include the first nodes N11 and N12 and the second nodes N21 and N22. The first nodes N11 and N12 are located between the series arm resonators. The second nodes N21 and N22 are located between the series arm resonators and the input terminal IN or output terminal OUT. The multiple parallel arm resonators P11, P12, P21, and P22 include the first parallel arm resonators P11 and P12 and the second parallel arm resonators P21 and P22. The first parallel arm resonators P11 and P12 are located in the signal path (parallel arm) connecting the first nodes N11 and N12 to ground, respectively. The second parallel arm resonators P21 and P22 are located in the signal path (parallel arm) connecting the second nodes N21 and N22 to ground, respectively.
[0116] One terminal of each of the series-connected series arm resonators S1, S2, S3, and S4 is electrically connected to the input terminal IN, and the other terminal is electrically connected to the output terminal OUT. One terminal of the parallel arm resonator P21 is electrically connected to node N21 located between the input terminal IN and series arm resonator S1, and the other terminal is electrically connected to ground. One terminal of the parallel arm resonator P11 is electrically connected to node N11 located between series arm resonators S1 and S2, and the other terminal is electrically connected to ground. One terminal of the parallel arm resonator P12 is electrically connected to node N12 located between series arm resonators S3 and S4, and the other terminal is electrically connected to ground. One terminal of the parallel arm resonator P22 is electrically connected to node N22 located between series arm resonator S4 and output terminal OUT, and the other terminal is electrically connected to ground.
[0117] In the tenth embodiment, at least one of the resonators S1, S2, S3, S4, P11, P12, P21, and P22 included in the filter 1 is the elastic wave device 10 according to the first embodiment. The elastic wave device 10 according to the first embodiment has a large electromechanical coupling coefficient, which improves the filter characteristics of the filter 1, particularly when the filter 1 is used in a band requiring broadband, such as the n79 band (4400 MHz - 5000 MHz).
[0118] In the tenth embodiment, it is preferable that at least one of the parallel arm resonators P11, P12, P21, and P22 is the elastic wave device 10 according to the first embodiment, and it is more preferable that all of the parallel arm resonators P11, P12, P21, and P22 are the elastic wave device 10 according to the first embodiment. In the elastic wave device 10 according to the first embodiment, the unwanted waves are located at a higher frequency than the frequency of the main wave, so the frequency of the unwanted waves of the parallel arm resonators can be moved away from the bandwidth of the filter 1 at a higher frequency, and the influence of the unwanted waves of the parallel arm resonators on the filter characteristics can be suppressed.
[0119] For example, if the filter 1 according to the 10th embodiment is a filter for the n79 band (4400 MHz - 5000 MHz), the resonant frequency F of the main wave of the parallel arm resonator is MainThe frequency F of unwanted waves Spurious Ratio F Spurious / F Main If the value is 1.35 or higher, the resonant frequency of the main wave of the parallel arm resonator can be set to around 4400 MHz, while the frequency of the unwanted waves of the parallel arm resonator can be made sufficiently larger than 5000 MHz. As a result, the frequency of the unwanted waves of the parallel arm resonator falls outside the n79 band, and the influence of the unwanted waves of the parallel arm resonator on the filter characteristics can be suppressed.
[0120] In the tenth embodiment, it is preferable that at least one of the first parallel arm resonators P11 and P12 is the elastic wave device 10 according to the first embodiment, and it is more preferable that all of the first parallel arm resonators P11 and P12 are the elastic wave device 10 according to the first embodiment. As a result, the loss due to unwanted waves S of the parallel arm resonators is reduced compared to a filter in which only the second parallel arm resonators P21 and P22 are the elastic wave device 10 according to the first embodiment, and thus the filter characteristics can be improved.
[0121] The following describes an embodiment according to the tenth embodiment. Note that the embodiment is not limited to this example. Here, the resonance characteristics of the filter according to the embodiment were investigated by simulation.
[0122] Figure 29 illustrates the resonance characteristics of the resonators used in the filters according to Examples 1 to 3. In the filters according to Examples 1 to 3, the filters were designed using resonators PA, PB, and SA having the resonance characteristics shown in Figure 29. Resonator PA is a resonator with a resonant frequency of 4500 MHz and an anti-resonant frequency of 5500 MHz. Resonator PB is a resonator with a resonant frequency of 4500 MHz and an anti-resonant frequency of 5500 MHz, and has an unwanted wave S at 6200 MHz. Resonator SA is a resonant frequency of 5500 MHz and an anti-resonant frequency of 6500 MHz.
[0123] Table 1 shows the combinations of resonators used in Examples 1 to 3. In Examples 1 to 3, the filters were designed by applying the resonators PA to PC in the combinations shown in Table 1 to the circuit shown in Figure 28.
[0124]
[0125] Figures 30A and 30B show the simulation results of the filters according to Examples 1 to 3. More specifically, Figure 30A is a graph showing the S-parameter S21 of the filters according to Examples 1 to 3, and Figure 30B is a graph showing the S-parameter S21 after removing the loss due to mismatch of the filters according to Examples 1 to 3.
[0126] As shown in Figures 30A and 30B, in Examples 1 and 2, where the first parallel arm resonators P11 and P12 use resonators PA without unwanted waves S, the loss L due to unwanted waves S is smaller compared to Example 3, where the first parallel arm resonators P11 and P12 use resonators PB with unwanted waves S. Therefore, in the filter 1 according to the 10th embodiment, by applying an elastic wave device 10 in which unwanted waves S within the filter band are suppressed to the first parallel arm resonators P11 and P12, the loss L due to unwanted waves S can be reduced and the filter characteristics can be improved.
[0127] As shown in Figures 30A and 30B, in Example 1, which uses a resonator PA without unwanted waves S in all of the parallel arm resonators P11, P12, P21, and P22, the loss L due to unwanted waves S is smaller compared to Examples 2 and 3, which use a resonator PB with unwanted waves S in one of the parallel arm resonators P11, P12, P21, and P22. Therefore, in the filter 1 according to the tenth embodiment, by applying an elastic wave device 10 in which unwanted waves S within the filter band are suppressed in all of the parallel arm resonators P11, P12, P21, and P22, the loss L due to unwanted waves S can be reduced and the filter characteristics can be improved.
[0128] The tenth embodiment can be combined with each of the embodiments described above.
[0129] (Eleventh Embodiment) Figure 31 is a circuit diagram showing a filter according to the eleventh embodiment. The filter 1A according to Figure 31 differs from the tenth embodiment in that the first nodes N11 and N12 are located between the series arm resonator S2 and the series arm resonator S3.
[0130] The following describes an embodiment according to the eleventh embodiment. Note that this embodiment does not limit the available embodiments. Here, the resonance characteristics of the filters according to Examples 4 to 6 were investigated by simulation.
[0131] Table 2 shows the combinations of resonators used in Examples 4 to 6. In Examples 4 to 6, the filters were designed by applying resonators PA to SA in the combinations shown in Table 2 to the circuit shown in Figure 31. Here, resonators PA to SA are the same resonators used in Examples 1 to 3 according to the ninth embodiment.
[0132]
[0133] Figures 32A and 32B show the simulation results of the filters according to Examples 4 to 6. More specifically, Figure 32A is a graph showing the S-parameter S21 of the filters according to Examples 4 to 6, and Figure 32B is a graph showing the S-parameter S21 after removing the loss due to mismatch of the filters according to Examples 4 to 6.
[0134] As shown in Figures 32A and 32B, in Examples 4 and 5, where the first parallel arm resonators P11 and P12 use resonators PA without unwanted waves S, the loss L due to unwanted waves S is smaller compared to Example 6, where the first parallel arm resonators P11 and P12 use resonators PB with unwanted waves S. Therefore, in the filter 1 according to the 11th embodiment, by applying an elastic wave device 10 in which unwanted waves S within the filter band are suppressed to the first parallel arm resonators P11 and P12, the loss L due to unwanted waves S can be reduced and the filter characteristics can be improved.
[0135] As shown in Figures 32A and 32B, in Example 4, which uses a resonator PA without unwanted waves S in all of the parallel arm resonators P11, P12, P21, and P22, the loss L due to unwanted waves S is smaller compared to Examples 5 and 3, which use a resonator PB with unwanted waves S in one of the parallel arm resonators P11, P12, P21, and P22. Therefore, in the filter 1 according to the 11th embodiment, by applying an elastic wave device 10 in which unwanted waves S within the filter band are suppressed in all of the parallel arm resonators P11, P12, P21, and P22, the loss L due to unwanted waves S can be reduced and the filter characteristics can be improved.
[0136] The eleventh embodiment can be combined with each of the embodiments described above.
[0137] The embodiments described above are provided to facilitate understanding of the present invention and are not intended to limit its interpretation. The present invention may be modified or improved without departing from its spirit, and equivalents thereof are also included.
[0138] For example, the width of at least one electrode finger may differ from the width of the other electrode fingers. Here, the relationship between the ratio of the electrode width to the average electrode width and the order of the electrode fingers is, for example, the inter-electrode pitch p shown in Figures 20A to 20E above. k Ratio p to average electrode pitch p k The relationship between / p and the order of the electrode fingers can be similar.
[0139] For example, in the elastic wave apparatus according to the first to ninth embodiments, the IDT electrode may be provided on both the first main surface 20a and the second main surface 20b, or it may be provided only on the second main surface 20b.
[0140] Furthermore, this disclosure may also take the following form. <1> An elastic wave apparatus comprising: a piezoelectric layer having a first main surface and a second main surface opposite to the first main surface, and containing lithium niobate; an IDT electrode provided on at least one of the main surfaces of the first and second main surfaces of the piezoelectric layer; a dielectric layer provided on at least one of the main surfaces of the first and second main surfaces of the piezoelectric layer; and a support member provided on the second main surface side of the piezoelectric layer, wherein the IDT electrode has a first busbar facing each other, a second busbar, at least one first electrode finger whose base end is connected to the first busbar, and at least one second electrode finger whose base end is connected to the second busbar; the support member has an acoustic reflector on the second main surface side; when the thickness of the piezoelectric layer is d and the average distance between the centers of adjacent first and second electrode fingers is p, d / p is 0.5 or less; and when the sum of the thickness of the piezoelectric layer and the thickness of the dielectric layer is T, p / T is 3.0 or more and 6.0 or less. <2> The elastic wave apparatus according to <1>, wherein when the total thickness of the dielectric layers is t, t / d is greater than 0 and 0.98 or less. <3> The elastic wave apparatus according to <2>, wherein t / d is 0.3 or more and 0.6 or less. <4> The elastic wave apparatus according to any one of <1> to <3>, wherein when the Euler angle of the lithium niobate of the piezoelectric layer is (φ, θ, ψ), -10°≦φ≦10°, 5°≦θ≦60° and -10°≦ψ≦10°. <5> The elastic wave apparatus according to <4>, further satisfying 15°≦θ≦50°. <6> The elastic wave apparatus according to <4>, further satisfying 20°≦θ≦45°. <7> The elastic wave apparatus according to any one of <1> to <6>, wherein the dielectric layer includes a first dielectric layer provided on the first main surface side of the piezoelectric layer and a second dielectric layer provided on the second main surface side of the piezoelectric layer. <8> The elastic wave apparatus according to <7>, wherein the thickness of the dielectric layer with the smaller thickness among the first dielectric layer and the second dielectric layer is 30% or more of the total thickness of the dielectric layers.<9> The elastic wave apparatus according to any one of <1> to <8>, wherein at least one of the first electrode fingers and the second electrode fingers is provided in multiple quantities, and the distance between the centers of at least one pair of adjacent first electrode fingers and second electrode fingers is different from the distance between the centers of other adjacent pairs of first electrode fingers and second electrode fingers. <10> The elastic wave apparatus according to any one of <1> to <9>, wherein the IDT electrode is provided between the dielectric layer and the piezoelectric layer. <11> The elastic wave apparatus according to any one of <1> to <10>, wherein the dielectric layer is provided between the IDT electrode and the piezoelectric layer. <12> The elastic wave apparatus according to any one of <1> to <11>, wherein the acoustic reflection portion is a recess on the piezoelectric layer side of the support member. <13> The acoustic wave apparatus according to any one of <1> to <11>, wherein the acoustic reflection portion is an acoustic reflection film provided between the support member and the piezoelectric layer, the acoustic reflection film includes a first layer and a second layer, and the first layer has a relatively higher acoustic impedance than the second layer. <14> The acoustic wave apparatus according to any one of <1> to <11>, wherein the acoustic reflection portion is an acoustic reflection film provided between the support member and the piezoelectric layer, the acoustic reflection film comprises a first layer and a second layer, the first layer comprises at least one of tungsten carbide, tantalum carbide, rhenium oxide, silicon chromium, niobium carbide, zinc carbide, zinc nitride, lanthanum boride, vanadium carbide, aluminum nitride, silicon carbide, yttrium oxide, magnesium oxide, silicon nitride, boron carbide, strontium fluoride, barium fluoride, tantalum oxide, hafnium oxide, tungsten oxide, hafnium nitride, tungsten nitride, platinum, tungsten, copper, gold, and silver, and the second layer comprises at least one of silicon oxide and aluminum. <15> The acoustic wave apparatus according to any one of <1> to <14>, wherein the d / p is 0.24 or less.<16> The elastic wave apparatus according to any one of <1> to <15>, wherein, when viewed from a direction perpendicular to the extending direction of the first electrode finger and the second electrode finger, the region in which adjacent first electrode finger and second electrode finger overlap, and the region between the centers of adjacent first electrode finger and second electrode finger in a direction perpendicular to the extending direction of the first electrode finger and second electrode finger is defined as the excitation region, and when the metallization ratio of the first electrode finger and second electrode finger with respect to the excitation region is MR, the condition MR ≤ 1.75 (d / p) + 0.075 is satisfied. <17> The elastic wave apparatus according to any one of <1> to <16>, wherein the Euler angle (φ, θ, ψ) of the lithium niobate constituting the piezoelectric layer is within the range of the following equations (1), (2), or (3). (0°±10°, 0°~20°, any ψ) ...Equation (1) (0°±10°, 20°~80°, 0°~60° (1-(θ-50)). 2 / 900) 1/2 ) or (0°±10°, 20°~80°, [180°-60°(1-(θ-50) 2 / 900) 1/2 ]~180°) ...Formula (2) (0°±10°, [180°-30°(1-(ψ-90) 2 ( / 8100) 1/2] ~180°, any ψ) ...Equation (3) <18> A filter comprising a resonator, wherein at least one of the resonators is an elastic wave device according to any one of <1> to <17>. <19> A filter according to <18> comprising a plurality of resonators, having an input terminal, an output terminal, a series arm connecting the input terminal and the output terminal, and a parallel arm connecting the node of the series arm to ground, wherein the plurality of resonators include a series arm resonator provided on the series arm and a parallel arm resonator provided on the parallel arm, wherein at least one of the parallel arm resonators is the elastic wave device. <20> The filter according to <19>, wherein the node includes a first node located between the series arm resonators and a second node located between the series arm resonators and the input terminal or the output terminal, and the parallel arm resonators include a first parallel arm resonator provided on a parallel arm connecting the first node and ground, and a second parallel arm resonator provided on a parallel arm connecting the second node and ground, and at least one of the first parallel arm resonators is the elastic wave device.
[0141] 1, 1A Filter 10, 10A-10G Acoustic wave device 11 Support substrate 12 Intermediate layer 14 Recess 20 Piezoelectric layer 20a First main surface 20b Second main surface 30, 30A IDT electrode 31 First electrode finger 32 Second electrode finger 33 First busbar electrode 34 Second busbar electrode 41 First dielectric layer 42 Second dielectric layer 43 Acoustic multilayer film
Claims
1. A piezoelectric layer comprising a lithium niobate having a first main surface and a second main surface opposite to the first main surface; an IDT electrode provided on at least one of the main surfaces of the first and second main surfaces of the piezoelectric layer; a dielectric layer provided on at least one of the main surfaces of the first and second main surfaces of the piezoelectric layer; and a support member provided on the second main surface side of the piezoelectric layer, wherein the IDT electrode has a first busbar facing each other, a second busbar, at least one first electrode finger whose base end is connected to the first busbar, and at least one second electrode finger whose base end is connected to the second busbar; the support member has an acoustic reflector on the second main surface side, the acoustic reflector is a recess on the piezoelectric layer side of the support member, and when the thickness of the piezoelectric layer is d and the average distance between the centers of adjacent first and second electrode fingers is p, d / p is 0.5 or less. An elastic wave apparatus in which, when T is the sum of the thickness of the piezoelectric layer and the thickness of the dielectric layer, p / T is 3.0 or more and 6.0 or less.
2. A piezoelectric layer comprising lithium niobate having a first main surface and a second main surface opposite to the first main surface; an IDT electrode provided on at least one of the main surfaces of the first and second main surfaces of the piezoelectric layer; a dielectric layer provided on at least one of the main surfaces of the first and second main surfaces of the piezoelectric layer; and a support member provided on the second main surface side of the piezoelectric layer, wherein the IDT electrode has a first busbar facing each other, a second busbar, at least one first electrode finger whose base end is connected to the first busbar, and at least one second electrode finger whose base end is connected to the second busbar; the support member has an acoustic reflector on the second main surface side, the acoustic reflector is an acoustic multilayer film provided between the support member and the piezoelectric layer, and the acoustic multilayer film includes a first layer and a second layer made of a different material from the first layer. An elastic wave apparatus in which, when the thickness of the piezoelectric layer is d and the average distance between the centers of adjacent first and second electrode fingers is p, d / p is 0.5 or less, and when the sum of the thickness of the piezoelectric layer and the thickness of the dielectric layer is T, p / T is 3.0 or more and 6.0 or less.
3. The elastic wave apparatus according to claim 2, wherein the first layer has a relatively higher acoustic impedance than the second layer.
4. The elastic wave apparatus according to claim 2, wherein the first layer comprises at least one of tungsten carbide, tantalum carbide, rhenium oxide, silicon chromium, niobium carbide, zinc carbide, zinc nitride, lanthanum boride, vanadium carbide, aluminum nitride, silicon carbide, yttrium oxide, magnesium oxide, silicon nitride, boron carbide, strontium fluoride, barium fluoride, tantalum oxide, hafnium oxide, tungsten oxide, hafnium nitride, tungsten nitride, platinum, tungsten, copper, gold, and silver, and the second layer comprises at least one of silicon oxide and aluminum.
5. The elastic wave apparatus according to any one of claims 1 to 4, wherein when the total thickness of the dielectric layers is t, t / d is greater than 0 and 0.98 or less.
6. The elastic wave apparatus according to claim 5, wherein the t / d is 0.3 or more and 0.6 or less.
7. The elastic wave apparatus according to any one of claims 1 to 6, wherein when the Euler angle of lithium niobate in the piezoelectric layer is (φ, θ, ψ), -10°≦φ≦10°, 5°≦θ≦60°, and -10°≦ψ≦10°.
8. The elastic wave apparatus according to claim 7, further satisfying 15° ≤ θ ≤ 50°.
9. The elastic wave apparatus according to claim 7, further satisfying 20° ≤ θ ≤ 45°.
10. The elastic wave apparatus according to any one of claims 1 to 3, wherein when the Euler angle of lithium niobate in the piezoelectric layer is (φ, θ, ψ), -10°≦φ≦10°, 185°≦θ≦240°, and -10°≦ψ≦10°.
11. The elastic wave apparatus according to claim 4, further satisfying 195° ≤ θ ≤ 230°.
12. The elastic wave apparatus according to claim 4, further satisfying 200° ≤ θ ≤ 225°.
13. The elastic wave apparatus according to any one of claims 1 to 12, wherein the dielectric layer includes a first dielectric layer provided on the first main surface side of the piezoelectric layer and a second dielectric layer provided on the second main surface side of the piezoelectric layer.
14. The elastic wave apparatus according to claim 13, wherein, when the sum of the thicknesses of the dielectric layers is t, the thickness of the dielectric layer with the smaller thickness among the first dielectric layer and the second dielectric layer is 30% or more of t.
15. The elastic wave apparatus according to any one of claims 1 to 14, wherein at least one of the first electrode fingers and the second electrode fingers is provided in multiple quantities, and the distance between the centers of at least one pair of adjacent first electrode fingers and second electrode fingers is different from the distance between the centers of other adjacent pairs of first electrode fingers and second electrode fingers.
16. The elastic wave apparatus according to any one of claims 1 to 15, wherein the IDT electrode is provided between the dielectric layer and the piezoelectric layer.
17. The elastic wave apparatus according to any one of claims 1 to 16, wherein the dielectric layer is provided between the IDT electrode and the piezoelectric layer.
18. The elastic wave apparatus according to any one of claims 1 to 17, wherein the d / p is 0.24 or less.
19. The elastic wave apparatus according to any one of claims 1 to 18, wherein, when viewed from a direction perpendicular to the extending direction of the first electrode finger and the second electrode finger, the region in which adjacent first electrode finger and second electrode finger overlap, and the region between the centers of adjacent first electrode finger and second electrode finger in a direction perpendicular to the extending direction of the first electrode finger and second electrode finger is defined as the excitation region, and when the metallization ratio of the first electrode finger and second electrode finger with respect to the excitation region is denoted as MR, the condition MR ≤ 1.75 (d / p) + 0.075 is satisfied.
20. The elastic wave apparatus according to any one of claims 1 to 19, wherein the Euler angle (φ, θ, ψ) of the lithium niobate constituting the piezoelectric layer is within the range of the following equations (1), (2), or (3): (0°±10°, 0° to 20°, any ψ) ...Equation (1) (0°±10°, 20° to 80°, 0° to 60° (1 - (θ - 50)) 2 / 900) 1/2 ) or (0°±10°, 20°~80°, [180°-60°(1-(θ-50) 2 / 900) 1/2 ]~180°) ...Formula (2) (0°±10°, [180°-30°(1-(ψ-90) 2 ( / 8100) 1/2 ] ~180°, any ψ) ...Equation (3) 21. The elastic wave device according to any one of claims 1 to 19, wherein the Euler angles (φ, θ, ψ) of the lithium niobate constituting the piezoelectric layer are within the range of the following formula (1), formula (2) or formula (3). (0° ± 10°, 180° to 200°, any ψ) … formula (1) (0° ± 10°, 200° to 260°, 0° to 60° (1 - (θ - 50) 2 / 900) 1/2 ) or (0° ± 10°, 200° to 260°, [180° - 60° (1 - (θ - 50) 2 / 900) 1/2 to 180°) … formula (2) (0° ± 10°, [360° - 30° (1 - (ψ - 90) 2 / 8100) 1/2 to 360°, any ψ) … formula (3) 22. A filter comprising a resonator, wherein at least one of the resonators is an elastic wave apparatus according to any one of claims 1 to 21.
23. The filter according to claim 22, comprising a plurality of resonators, having an input terminal, an output terminal, a series arm connecting the input terminal and the output terminal, and a parallel arm connecting the node of the series arm to ground, wherein the plurality of resonators include a series arm resonator provided on the series arm and a parallel arm resonator provided on the parallel arm, and at least one of the parallel arm resonators is the elastic wave device.
24. The filter according to claim 23, wherein the node includes a first node located between the series arm resonators and a second node located between the series arm resonators and the input terminal or the output terminal, and the parallel arm resonators include a first parallel arm resonator provided on a parallel arm connecting the first node and ground, and a second parallel arm resonator provided on a parallel arm connecting the second node and ground, and at least one of the first parallel arm resonators is the elastic wave device.
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