Ladder Filters and Multiplexers

Abstract

To provide a ladder-type filter capable of improving characteristics and suppressing an increase in manufacturing processes.SOLUTION: A ladder-type filter includes a plurality of piezoelectric thin film resonators between a first terminal T1 and a second terminal T2, and inductors L1, L2. The plurality of piezoelectric thin film resonators include series resonators S1-S3, and parallel resonators P1-P3. A first series resonator S3 electrically closest to the second terminal T2 has the thinnest insertion film among the plurality of series resonators, and at least one second series resonator other than the first series resonator has a thicker insertion film than that of the first series resonator. A first parallel resonator P3 electrically closest to the second terminal T2 has the thinnest insertion film among the plurality of parallel resonators, and at least one second parallel resonator other than the first parallel resonator has an insertion film thicker than that of the first parallel resonator.SELECTED DRAWING: Figure 7

Description

[Technical field]

[0001] The present invention relates to a ladder-type filter and a multiplexer, for example, to a ladder-type filter and a multiplexer having a film bulk acoustic resonator. [Background technology]

[0002] Ladder-type filters having piezoelectric thin-film resonators are known as filters used in communication devices such as mobile phones. A piezoelectric thin-film resonator has a structure in which a piezoelectric film is sandwiched between a lower electrode and an upper electrode. The region where the lower electrode and the upper electrode overlap, sandwiching at least a part of the piezoelectric film, is the resonance region. It is known to insert an insertion film between the lower electrode and the upper electrode in the resonance region (e.g., Patent Documents 1 to 3). It is known to use a piezoelectric thin-film resonator in a ladder-type filter (e.g., Patent Documents 4 to 7). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2015-95729 A [Patent Document 2] JP 2016-29766 A [Patent Document 3] JP 2017-34358 A [Patent Document 4] JP 2003-22074 A [Patent Document 5] JP 2004-173236 A [Patent Document 6] JP 2005-223808 A [Patent Document 7] JP 2007-324823 A Summary of the Invention [Problem to be solved by the invention]

[0004] In ladder type filters, the electromechanical coupling coefficients of the piezoelectric thin film resonators are sometimes made different in order to increase the steepness of the skirt characteristics and broaden the bandwidth. In order to manufacture a ladder type filter having piezoelectric thin film resonators with different electromechanical coupling coefficients, the number of manufacturing steps increases, resulting in higher manufacturing costs.

[0005] The present invention has been made in consideration of the above problems, and has an object to improve characteristics and suppress an increase in the number of manufacturing steps. [Means for solving the problem]

[0006] The present invention relates to a piezoelectric thin film resonator comprising: a substrate; a piezoelectric film provided on the substrate; and a first electrode and a second electrode which sandwich at least a part of the piezoelectric film and form a resonance region overlapping each other, at least a part of the piezoelectric thin film resonators having an insertion film provided between the first electrode and the second electrode in the resonance region; a plurality of series resonators connected in series between a first terminal and a second terminal, the plurality of series resonators being included in the plurality of piezoelectric thin film resonators and electrically closest to the second terminal, the first series resonator having the thinnest insertion film among the plurality of series resonators, and at least one second series resonator other than the first series resonator having a thicker insertion film than the first series resonator; and a first parallel resonator included in the plurality of piezoelectric thin film resonators and electrically closest to the second terminal, the first parallel resonator having the thinnest insertion film or no insertion film among the plurality of parallel resonators, and at least one second parallel resonator other than the first parallel resonator having a thicker insertion film than the first parallel resonator; an inductor having one end connected to at least one first resonator among the plurality of parallel resonators and the other end grounded; and a second resonator which is at least one of the plurality of parallel resonators and a parallel resonator to which the grounded inductor is not connected, the second resonator having an insertion film substantially the same thickness as the insertion film of the parallel resonator to which the inductor is connected.

[0007] In the above configuration, the first resonator may include the first parallel resonator, and the second resonator may include the first series resonator.

[0008] In the above configuration, of the plurality of series resonators and the plurality of parallel resonators, the first parallel resonator may have the thinnest insertion film, and the second series resonator may have the second thinnest insertion film.

[0009] In the above configuration, a third parallel resonator, which is electrically closest to the first terminal among the multiple parallel resonators, may be configured to have the thickest insertion film among the multiple series resonators and the multiple parallel resonators.

[0010] The present invention relates to a piezoelectric resonator comprising: a substrate; a piezoelectric film provided on the substrate; and a first electrode and a second electrode which sandwich at least a part of the piezoelectric film and form a resonance region overlapping each other, at least a part of the piezoelectric film being sandwiched between the first electrode and the second electrode in the resonance region; a plurality of piezoelectric thin film resonators connected in series between a first terminal and a second terminal, at least a first series resonator included in the plurality of piezoelectric thin film resonators and electrically closest to the second terminal has the thinnest insertion film among the plurality of series resonators, and at least one second series resonator other than the first series resonator has a thicker insertion film than the first series resonator; and one end of the plurality of series resonators connected to a path between the first terminal and the second terminal. a first parallel resonator, which is included in the plurality of piezoelectric thin-film resonators and is electrically closest to the second terminal, has the thinnest insertion film or does not have an insertion film among the plurality of parallel resonators, and the other end is grounded, and at least one second parallel resonator other than the first parallel resonator has a thicker insertion film than the first parallel resonator; a capacitor connected in parallel to the plurality of series resonators and at least one first resonator among the plurality of parallel resonators; and a second resonator, which is at least one of the plurality of series resonators and the plurality of parallel resonators, has no capacitor connected in parallel and has an insertion film having substantially the same thickness as the insertion film of the resonator to which the capacitor is connected in parallel.

[0011] In the above configuration, the first resonator may include the first series resonator, and the second resonator may include the first parallel resonator.

[0012] In the above configuration, of the plurality of series resonators and the plurality of parallel resonators, the first parallel resonator may have the thinnest insertion film, and the second series resonator may have the second thinnest insertion film.

[0013] In the above configuration, a third parallel resonator, which is electrically closest to the first terminal among the multiple parallel resonators, may be configured to have the thickest insertion film among the multiple series resonators and the multiple parallel resonators.

[0014] In the aforementioned configuration, the first resonator can include the third parallel resonator.

[0015] In the above configuration, the piezoelectric films of the multiple piezoelectric thin film resonators may have substantially the same thickness, the first electrodes may have substantially the same thickness, and the second electrodes may have substantially the same thickness.

[0016] The present invention relates to a method for manufacturing a piezoelectric thin film resonator, the method comprising: providing a piezoelectric film on the substrate; and a first electrode and a second electrode that sandwich at least a portion of the piezoelectric film and form a resonance region that overlaps with each other; a first series resonator that is connected in series between a first terminal and a second terminal and is included in the plurality of piezoelectric thin film resonators, the first series resonator being electrically closest to the second terminal and having the largest single electromechanical coupling coefficient among the plurality of series resonators, and at least one second series resonator other than the first series resonator having a smaller single electromechanical coupling coefficient than the first series resonator; and a second series resonator having one end connected to a path between the first terminal and the second terminal and the other end grounded and included in the plurality of piezoelectric thin film resonators, the The ladder-type filter includes: a first parallel resonator electrically closest to the second terminal has the largest single-unit electromechanical coupling coefficient among the multiple parallel resonators, and at least one second parallel resonator other than the first parallel resonator has a single-unit electromechanical coupling coefficient smaller than that of the first parallel resonator; an inductor having one end connected to at least one first resonator among the multiple parallel resonators and the other end grounded; and a second resonator which is at least one of the multiple series resonators and a parallel resonator to which the grounded inductor is not connected, and has a single-unit electromechanical coupling coefficient substantially the same as that of the parallel resonator to which the inductor is connected.

[0017] The present invention relates to a method for manufacturing a piezoelectric thin film resonator, the method comprising: providing a plurality of piezoelectric thin film resonators each including a substrate, a piezoelectric film provided on the substrate, and a first electrode and a second electrode that sandwich at least a portion of the piezoelectric film and form a resonance region that overlaps with each other; a first series resonator included in the plurality of piezoelectric thin film resonators and electrically closest to the second terminal, the first series resonator having the largest single-unit electromechanical coupling coefficient among the plurality of series resonators, and at least one second series resonator other than the first series resonator having a single-unit electromechanical coupling coefficient smaller than that of the first series resonator; and a second series resonator having one end connected to a path between the first terminal and the second terminal and the other end grounded, the second series resonator included in the plurality of piezoelectric thin film resonators, the first series resonator being electrically closest to the second terminal and having the largest single-unit electromechanical coupling coefficient among the plurality of series resonators. The ladder-type filter includes: a first parallel resonator electrically closest to a terminal has the largest single-unit electromechanical coupling coefficient among the multiple parallel resonators, and at least one second parallel resonator other than the first parallel resonator has a single-unit electromechanical coupling coefficient smaller than that of the first parallel resonator; a capacitor connected in parallel to the multiple series resonators and at least one first resonator among the multiple parallel resonators; and a second resonator which is at least one of the multiple series resonators and the multiple parallel resonators, has no capacitor connected in parallel, and has a single-unit electromechanical coupling coefficient substantially the same as the single-unit electromechanical coupling coefficient of the resonator to which the capacitor is connected in parallel.

[0018] The present invention is a multiplexer including the above ladder-type filter. Effect of the Invention

[0019] According to the present invention, it is possible to improve the characteristics and suppress an increase in the number of manufacturing steps. [Brief description of the drawings]

[0020] [Figure 1] FIG. 1(a) is a circuit diagram of a ladder-type filter, and FIG. 1(b) is a circuit diagram in which the ladder-type filter of FIG. 1(a) is divided into sections. [Diagram 2] FIG. 2(a) shows the pass characteristic of a filter designed using the simultaneous Chebyshev approximation, and FIG. 2(b) shows an equivalent circuit of a piezoelectric thin film resonator. [Diagram 3] 3(a) and 3(b) are circuit diagrams of the ladder filter in Simulation 1. [Figure 4] FIG. 4(a) is a diagram showing the electromechanical coupling coefficients of the resonators in the filters A1 to A3, and FIG. 4(b) is a diagram showing the electromechanical coupling coefficients of the resonators in the filters A4 to A6. [Diagram 5] 5(a) and 5(b) are cross-sectional views of the piezoelectric thin film resonator in the first embodiment. [Figure 6] FIG. 6 is a diagram showing the electromechanical coupling coefficient k2 versus the thickness T8 of the insertion film. [Figure 7] FIG. 7 is a circuit diagram of the ladder filter according to the first embodiment. [Figure 8] FIG. 8(a) is an equivalent circuit when an inductance Lg is connected in series to a resonator, and FIG. 8(b) is a diagram showing the electromechanical coupling coefficient versus the magnitude of the inductance Lg. [Figure 9] 9(a) and 9(b) are diagrams showing the pass characteristics of the filters B1 to B3 in the simulation 2. In FIG. [Figure 10] 10(a) and 10(b) are circuit diagrams of ladder filters according to first and second modifications of the first embodiment, respectively. [Figure 11] FIG. 11(a) is a diagram showing an equivalent circuit when a capacitance Cp is connected in parallel to a resonator, and FIG. 11(b) and FIG. 11(c) are diagrams showing the electromechanical coupling coefficient versus the magnitude of the capacitance Cp. [Figure 12] 12(a) and 12(b) are diagrams showing the pass characteristics of the filters B1, C1 and C2 in Simulation 3. FIG. [Figure 13] 13(a) and 13(b) are diagrams showing the pass characteristics of the filters B1, C3 and C4 in Simulation 3. FIG. [Figure 14] 14(a) and 14(b) are cross-sectional views of film bulk acoustic resonators according to third and fourth modifications of the first embodiment, respectively. [Figure 15]FIG. 15 is a circuit diagram of a duplexer in accordance with the second embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0021] Hereinafter, embodiments of the present invention will be described with reference to the drawings. EXAMPLES

[0022] [Ladder type filters and design methods] Before describing the first embodiment, a design method of a ladder filter will be described. Fig. 1(a) is a circuit diagram of a ladder filter. As shown in Fig. 1(a), in the ladder filter, a plurality of series resonators S1 to S3 are connected in series between terminals T1 (first terminal) and T2 (second terminal). A plurality of parallel resonators P1 to P3 are connected in parallel between terminals T1 and T2. One end of the parallel resonators P1 to P3 is connected to a path between terminals T1 and T2, and the other end is connected (grounded) to a ground terminal Gnd. One of the terminals T1 and T2 is an input terminal to which a high-frequency signal is input, and the other of the terminals T1 and T2 is an output terminal to which a filtered high-frequency signal is output.

[0023] [Image impedance method] FIG. 1(b) is a circuit diagram in which the ladder filter of FIG. 1(a) is divided into sections. As shown in FIG. 1(b), the series resonator S1 is divided into two series resonators S1a and S1b, and the series resonator S2 is divided into two series resonators S2a and S2b. The parallel resonator P2 is divided into two parallel resonators P2a and P2b, and the parallel resonator P3 is divided into two parallel resonators P3a and P3b. Sections 21-25 including one parallel resonator and one series resonator are set. In this way, the ladder filter of FIG. 1(a) is a five-stage ladder filter having five sections 21-25. In the image impedance method, the filter is designed using sections 21-25. In the design of the constant k type, the impedance of the sections 21-25 is designed to be a desired value. In the design of the induced m type, in addition to the constant k type, an attenuation pole is provided to make the skirt characteristic steep. However, the attenuation away from the passband is less than that of the constant-k type.

[0024] The image impedance method is widely used in the design of ladder filters because the design calculations are simple. In a ladder filter having piezoelectric thin film resonators designed using the image impedance method, the electromechanical coupling coefficients of multiple series resonators are almost the same, and the electromechanical coupling coefficients of multiple parallel resonators are almost the same. However, ladder filters designed using the image impedance method have a large number of piezoelectric thin film resonators, which deteriorates the characteristics. There are limitations to the design of ladder filters that have steep skirt characteristics and a wide bandwidth.

[0025] [Dynamic Parameter Method] The dynamic parameter method is a method for directly calculating the parameters of a filter circuit that most closely resembles the desired characteristics. The filter can be constructed with a smaller number of resonators, which improves characteristics. As an example of the dynamic parameter method, we considered designing a ladder filter using the simultaneous Chebyshev approximation. In the simultaneous Chebyshev approximation, a steep skirt characteristic can be obtained by forming a ripple in the passband and an attenuation pole in the attenuation band. We considered using the simultaneous Chebyshev approximation to design a ladder filter using piezoelectric thin film resonators.

[0026] FIG. 2(a) is a diagram showing the pass characteristic of a filter designed using the simultaneous Chebyshev approximation. As shown in FIG. 2(a), the maximum loss in the passband Pass of the filter is PdB. The bandwidth at the loss PdB is BW1. The minimum attenuation in the attenuation band Att is AdB. The bandwidth at the attenuation AdB is BWn. The slope of the skirt between the passband Pass and the attenuation band Att is the filter drop rate θ. The reflection coefficient ρ [%] = (10 RdB / 1 -1) / (10 RdB / 10), and θ=arcsin(BW1 / BWn), where n is the order. In the simultaneous Chebyshev approximation, a reference LPF (Low Pass Filter) is determined by determining three values ​​out of four: characteristic parameters ρ, θ, and AdB, and design parameter n. A BPF (Band Pass Filter) with the desired characteristics can be designed by converting the circuit of the reference LPF.

[0027] The BVD (Butterworth-Van Dyke) model is used for the equivalent circuit of a piezoelectric thin film resonator. Figure 2(b) shows the equivalent circuit of a piezoelectric thin film resonator. As shown in Figure 2(b), motional inductance Lm and motional capacitance Cm are connected in series between terminals T01 and T02. Capacitance C0 is connected in parallel to motional inductance Lm and motional capacitance Cm. Using the BVD model as the equivalent circuit of the piezoelectric thin film resonator, a ladder filter is designed based on the simultaneous Chebyshev approximation. The resonant frequency fr of the resonator is fr = 1 / (2π√(Lm × Cm)), the anti-resonant frequency fa is fa = fr√(1 + Cm / C0), and the electromechanical coupling coefficient k 2 k 2 =(π / 2) 2 It becomes (fr / fa)(fa-fr) / fa.

[0028] [Simulation 1] Six filters A1 to A6 were designed based on the simultaneous Chebyshev approximation by changing the characteristic parameters and design parameters. The parameters of each filter A1 to A6 are as follows. Filter A1: θ=60°, AdB=59dB, ρ=20%, number of stages: 5 Filter A2: θ=70°, AdB=44dB, ρ=20%, number of stages: 5 Filter A3: θ=80°, AdB=29dB, ρ=20%, number of stages: 5 Filter A4: θ=51°, AdB=48dB, ρ=20%, number of stages: 3 Filter A5: θ=51°, AdB=73dB, ρ=20%, number of stages: 5 Filter A6: θ=51°, AdB=98dB, ρ=20%, number of stages: 7

[0029] FIG. 1(a) shows a circuit diagram of a ladder filter having five stages. FIG. 3(a) and FIG. 3(b) show circuit diagrams of ladder filters in Simulation 1. As shown in FIG. 3(a), in a ladder filter having three stages, two series resonators S1 and S2 are connected in series between terminals T1 and T2, and two parallel resonators P1 and P2 are connected in parallel. As shown in FIG. 3(b), in a ladder filter having seven stages, four series resonators S1 to S4 are connected in series between terminals T1 and T2, and four parallel resonators P1 to P4 are connected in parallel. The other configurations are the same as those in FIG. 1(a), and therefore will not be described.

[0030] Tables 1 to 6 show the capacitance C0, the dynamic inductance Lm, the dynamic capacitance Cm, the resonant frequency fr, the anti-resonant frequency fa, and the electromechanical coupling coefficient k in the filters A1 to A6. 2 1 is a table showing the above.

[0031] [Table 1]

[0032] [Table 2]

[0033] [Table 3]

[0034] [Table 4]

[0035] [Table 5]

[0036] [Table 6]

[0037] 4(a) is a diagram showing the electromechanical coupling coefficients of the resonators in the filters A1 to A3, and FIG. 4(b) is a diagram showing the electromechanical coupling coefficients of the resonators in the filters A4 to A6. As shown in FIG. 4(a) and FIG. 4(b), the electromechanical coupling coefficients k 2 The electromechanical coupling coefficient k 2 The resonator with the largest electromechanical coupling coefficient k 2 The resonator with the largest electromechanical coupling coefficient k is the series resonator closest to terminal T2 among the series resonators. 2 The resonator with the smallest electromechanical coupling coefficient k is the parallel resonator closest to the terminal T1 among the parallel resonators. 2 is the smallest electromechanical coupling coefficient k 2 In this way, in a ladder filter designed using the simultaneous Chebyshev approximation, the electromechanical coupling coefficient k 2 In addition, the electromechanical coupling coefficient k 2 The terminal T2 may be either an input terminal or an output terminal.

[0038] Electromechanical coupling coefficient k 2Examples of piezoelectric thin film resonators having different shapes will be described. Fig. 5(a) and Fig. 5(b) are cross-sectional views of the piezoelectric thin film resonator in Example 1. As shown in Fig. 5(a), resonators 11a and 11b are provided on a substrate 10. A cavity 30 consisting of a recess is provided on the upper surface of the substrate 10. A lower electrode 12 (first electrode) is provided on the substrate 10 and the cavity 30, a piezoelectric film 14 is provided on the lower electrode 12, and an upper electrode 16 (second electrode) is provided on the piezoelectric film 14. A region where the lower electrode 12 and the upper electrode 16 overlap (face each other) through at least a part of the piezoelectric film 14 is a resonance region 50. The planar shape of the resonance region 50 can be set to any shape such as an ellipse, a polygon (rectangle or pentagon), etc. The resonator 11a does not have an insertion film 18. In the resonator 11b, the piezoelectric film 14 includes a lower piezoelectric film 14a provided on the lower electrode 12 and an upper piezoelectric film 14b provided on the lower piezoelectric film 14a. An insertion film 18 is provided between the lower piezoelectric film 14a and the upper piezoelectric film 14b.

[0039] In the resonator 11a, the thicknesses of the lower electrode 12, the piezoelectric film 14, and the upper electrode 16 are T2, T4, and T6, respectively. In the resonator 11b, the thicknesses of the lower piezoelectric film 14a, the upper piezoelectric film 14b, and the insertion film 18 are T4a, T4b, and T8, respectively. T4=T4a+T4b. In the resonator 11b where the insertion film 18 is not provided, the thickness T8 of the insertion film 18 is 0. In the resonators 11a and 11b, the lower electrode 12, the piezoelectric film 14, and the upper electrode 16 are formed simultaneously. Therefore, the thicknesses T2 of the lower electrodes 12 are substantially the same within the manufacturing error range in the resonators 11a and 11b, the thicknesses T4 of the piezoelectric films 14 are substantially the same within the manufacturing error range, and the thicknesses T6 of the upper electrodes 16 are substantially the same within the manufacturing error range.

[0040] As shown in Fig. 5(b), in the resonator 11a, the piezoelectric film 14 includes a lower piezoelectric film 14a provided on the lower electrode 12 and an upper piezoelectric film 14b provided on the lower piezoelectric film 14a. An insertion film 18 is provided between the lower piezoelectric film 14a and the upper piezoelectric film 14b. The thickness T8 of the insertion film 18 of the resonator 11a is thinner than the thickness T8 of the insertion film 18 of the resonator 11b. The other configurations are the same as those in Fig. 4(a), and therefore description thereof will be omitted.

[0041] The substrate 10 is an insulating substrate or a semiconductor substrate, such as a silicon substrate, a sapphire substrate, a spinel substrate, an alumina substrate, a quartz substrate, a glass substrate, a crystal substrate, a ceramic substrate, a GaAs substrate, etc. The lower electrode 12 and the upper electrode 16 are a single layer film of a metal, such as ruthenium (Ru), chromium (Cr), aluminum (Al), titanium (Ti), copper (Cu), molybdenum (Mo), tungsten (W), tantalum (Ta), platinum (Pt), rhodium (Rh), iridium (Ir), etc., or a laminate film of these metals.

[0042] The piezoelectric film 14 is a film mainly composed of aluminum nitride (AlN), zinc oxide (ZnO), lead zirconate titanate (PZT), lead titanate (PbTiO3), single crystal lithium tantalate (LiTaO3), single crystal lithium niobate (LiNbO3), or the like. For example, the piezoelectric film 14 may mainly be composed of aluminum nitride and contain other elements to improve resonance characteristics or piezoelectricity. For example, the piezoelectricity of the piezoelectric film 14 is improved by using scandium (Sc), two elements of a group 2 element and a group 4 element, or two elements of a group 2 element and a group 5 element as an additive element. Therefore, the effective electromechanical coupling coefficient of the piezoelectric thin film resonator can be improved. The group 2 element is, for example, calcium (Ca), magnesium (Mg), strontium (Sr), or zinc (Zn). The group 4 element is, for example, titanium, zirconium (Zr), or hafnium (Hf). The Group 5 element is, for example, tantalum, niobium (Nb) or vanadium (V). Furthermore, the piezoelectric film 14 may be mainly composed of aluminum nitride and may contain boron (B).

[0043] The acoustic impedance of the insertion film 18 is preferably smaller than the acoustic impedance of the piezoelectric film 14. When the piezoelectric film 14 is mainly composed of aluminum nitride, the insertion film 18 is, for example, a silicon oxide film, an aluminum film, a gold film, a copper film, a titanium film, a platinum film, or a tantalum film.

[0044] Figure 6 shows the electromechanical coupling coefficient k 26. The lower electrode 12 is a ruthenium film having a thickness T2 of 130 nm, the piezoelectric film 14 is an aluminum nitride film having a thickness T4 of 800 nm, the upper electrode 16 is a ruthenium film having a thickness T6 of 145 nm, and the insertion film 18 is a silicon oxide film. As shown in FIG. 6, the electromechanical coupling coefficient k 2 When the thickness T8 of the insertion film 18 is set to about 100 nm, the electromechanical coupling coefficient k 2 is about half of that of a resonator without the insertion film 18. In this way, by making the thickness T8 of the insertion film 18 different, the electromechanical coupling coefficient k 2 can vary greatly.

[0045] Fig. 7 is a circuit diagram of the ladder filter in the first embodiment. As shown in Fig. 7, inductors L1 and L2 are provided. One end of the inductor L1 is connected to the parallel resonator P2, and the other end is connected to the ground terminal Gnd. One end of the inductor L2 is connected to the parallel resonator P3, and the other end is connected to the ground terminal Gnd. The other circuit configuration is the same as that in Fig. 1(a), and therefore description thereof will be omitted.

[0046] Fig. 8(a) is an equivalent circuit when an inductance Lg is connected in series to a resonator, and Fig. 8(b) is a diagram showing the electromechanical coupling coefficient versus the magnitude of the inductance Lg. As shown in Fig. 8(a), the inductance Lg is connected between a node N01, to which the motional capacitance Cm and the capacitance C0 are connected, and a terminal T01. The resonant frequency fr' of the resonator to which the inductance Lg is connected is fr'=1 / (2π√(Lm×Cm+Lg×Cm)). The anti-resonant frequency fa is the same as in Fig. 2(b) where the inductance Lg is not provided, and is fa=fr√(1+Cm / C0).

[0047] FIG. 8(b) shows the change in the electromechanical coupling coefficient Δk 2 FIG. 2 is the electromechanical coupling coefficient k of a single resonator without inductance Lg connected in series. 2The effective electromechanical coupling coefficient k 2 That is, the change in Δk 2 = (effective k 2 -Single k 2 ) / (effective k 2 ) × 100[%]. The electromechanical coupling coefficient k 2 are 3.3% and 5.6%, respectively. As shown in Fig. 8(b), the electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k 2 In the parallel resonator P3, which has a large inductance, the change amount Δk for the same inductance Lg is smaller than that of the parallel resonator P2. 2 is large.

[0048] In the case of a piezoelectric thin film resonator, the number of steps is increased in order to vary the thickness T8 of the insertion film 18. Therefore, if a ladder-type filter designed based on the simultaneous Chebyshev approximation is to be realized using a piezoelectric thin film resonator, the number of manufacturing steps increases, and the manufacturing cost becomes high. Therefore, the electromechanical coupling coefficient k 2 In the resonators having similar thicknesses, the thickness T8 of the insertion film 18 is set to be approximately the same, and the electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k 2 Among piezoelectric thin film resonators with approximately the same effective electromechanical coupling coefficient k 2 Inductance Lg is connected to the parallel resonator where the inductance Lg should be increased. This allows the thickness T8 of the insertion film 18 to be reduced, and the number of manufacturing steps can be reduced.

[0049] [Simulation 2] The pass characteristics of a ladder filter were simulated using a transmit filter for LTE (Long Term Evolution) band 7 as an example. In LTE band 7, the transmit band is 2500MHz to 2570MHz, and the receive band is 2620MHz to 2690MHz. The width of the guard band between the transmit band and the receive band is 50MHz. Meanwhile, the width of the transmit band and the receive band is each 70MHz, and the relative bandwidth, which is the bandwidth relative to the frequency, is 2.7%. Thus, filters used in bands with small guard band widths are required to have steep skirt characteristics. In addition, the passband width is required to be large at 70MHz, and ripples within the passband are required to be suppressed.

[0050] The pass characteristics of the filters B1 to B3 were simulated. The filters B1 and B2 are comparative examples, and the filter B3 corresponds to the first embodiment.

[0051] Filter B1 does not include inductors L1 and L2 as in Fig. 1(a), and the electromechanical coupling coefficients k 2 is a value designed based on the simultaneous Chebyshev approximation. In filter B1, the electromechanical coupling coefficient k 2 (i.e., the thickness T8 of the insertion film 18) is used.

[0052] Filter B2 does not include inductors L1 and L2 as shown in Fig. 1(a), and has an electromechanical coupling coefficient k 2 The closest one with the same electromechanical coupling coefficient k 2 The piezoelectric thin film resonators are used with the same electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k 2 In filter B2, the electromechanical coupling coefficient k 2 (i.e., the thickness T8 of the insertion film 18) is used.

[0053] Filter B3 includes inductors L1 and L2 as shown in Fig. 7. The electromechanical coupling coefficient k 2 is the same as that of filter B2. The electromechanical coupling coefficient k 2 (i.e., the thickness T8 of the insertion film 18) is four levels. By connecting the inductors L1 and L2 in series to the parallel resonators P2 and P3, the effective electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k 2 As a result, the effective electromechanical coupling coefficient k 2 Let be a value designed based on the simultaneous Chebyshev approximation.

[0054] Tables 7 to 9 show the capacitance C0, the dynamic inductance Lm, the dynamic capacitance Cm, the resonant frequency fr, the anti-resonant frequency fa, and the electromechanical coupling coefficient k in the filters B1 to B3. 2 In Table 9, the inductance Lg and the element k in the filter B3 are 2 In Table 9, k 2 is the effective k of the resonator with inductors L1 and L2 connected. 2 And simplex k 2 is the k of the resonator alone 2 It is.

[0055] [Table 7]

[0056] [Table 8]

[0057] [Table 9]

[0058] As shown in Tables 7 and 9, the parameters of the resonators in filters B1 and B3 are almost the same. As shown in Tables 7 to 9, the parameters of the parallel resonators P2 and P3 in filter B2 are different from those in filters B1 and B3.

[0059] 9(a) and 9(b) are diagrams showing the pass characteristics of filters B1 to B3 in simulation 2. FIG. 9(b) is an enlarged view of the vicinity of the pass band in FIG. 9(a). As shown in FIG. 9(a) and FIG. 9(b), filters B1 and B3 have approximately the same pass band width, ripples in the pass band, and steepness of the skirt on the low frequency side. Filter B2 has a narrower pass band width than filters B1 and B3, and the steepness of the skirt on the low frequency side is reduced.

[0060] Thus, in filter B1, the passband width is wide and the skirt steepness is high, but the six levels of electromechanical coupling coefficient k 2 In filter B2, the electromechanical coupling coefficient k 2 Since the number of manufacturing steps is reduced by setting the number of resonators at four levels, the manufacturing cost can be reduced. However, the filter characteristics are deteriorated. In filter B3, the electromechanical coupling coefficient k 2 By connecting inductors L1 and L2, the effective electromechanical coupling coefficient k 2 can be made to be approximately the same as that of filter B1. This makes it possible to make the filter characteristics approximately the same as that of filter B1.

[0061] [Modification 1 of Example 1] Fig. 10(a) is a circuit diagram of a ladder filter in Modification 1 of Example 1. As shown in Fig. 10(a), capacitors C1 and C2 are provided. Capacitor C1 is connected in parallel to series resonator S2, and capacitor C2 is connected in parallel to series resonator S3. The other circuit configurations are the same as those in Fig. 1(a), and therefore description thereof will be omitted.

[0062] [Modification 2 of Example 1] Fig. 10(b) is a circuit diagram of a ladder filter in Modification 2 of Example 1. As shown in Fig. 10(b), capacitors C3 and C4 are provided. Capacitor C3 is connected in parallel to parallel resonator P1, and capacitor C4 is connected in parallel to parallel resonator P4. The other circuit configurations are the same as those in Fig. 1(a), and therefore description thereof will be omitted.

[0063] Fig. 11(a) shows an equivalent circuit when a capacitance Cp is connected in parallel to a resonator, and Fig. 11(b) and Fig. 11(c) show the electromechanical coupling coefficient versus the magnitude of the capacitance Cp. As shown in Fig. 11(a), the capacitance Cp is connected in parallel to the capacitance C0. The anti-resonant frequency fa' of the resonator to which the capacitance Cp is connected is fa' = fr√(1 + Cm / (C0 + Cp)). The resonant frequency fr is the same as in Fig. 2(b) where no capacitance Cp is provided, and is fr = 1 / (2π√(Lm × Cm)).

[0064] FIG. 11(b) shows the change in the electromechanical coupling coefficient Δk 2 FIG. 2 is the electromechanical coupling coefficient k of a single resonator without parallel connection of capacitance Cp 2 The effective electromechanical coupling coefficient k 2 The change in the electromechanical coupling coefficient k 2 are 3.8% and 6.7%, respectively.

[0065] FIG. 11(c) shows the change in the electromechanical coupling coefficient Δk 2 1 is a diagram showing the calculation results of the electromechanical coupling coefficient k 2 are 3.4% and 4.5%, respectively.

[0066] As shown in Fig. 11(b) and (c), increasing the capacitance Cp reduces the electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k of the resonator alone becomes smaller. 2 In a resonator with a large capacitance, the change Δk 2 In this way, by providing the capacitance Cp in parallel, the effective electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k 2 It can be made smaller.

[0067] [Simulation 3] The pass characteristics of filters C1 to C4 were simulated using as an example a transmission filter for LTE band 7. Filters C1 and C3 are comparative examples, filter C2 corresponds to modified example 1 of the first embodiment, and filter C3 corresponds to modified example 2 of the first embodiment.

[0068] The filters C1 and C3 do not include the capacitors C1 to C4 as in FIG. 1(a), and the electromechanical coupling coefficients k 2 The electromechanical coupling coefficient k designed based on the simultaneous Chebyshev approximation 2 The closest one with the same electromechanical coupling coefficient k 2 A piezoelectric thin film resonator having the same structure is used.

[0069] In the filter C1, the electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k 2 (i.e., the thickness T8 of the insertion membrane 18) is four levels.

[0070] In the filter C3, the electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k 2 (i.e., the thickness T8 of the insertion membrane 18) is four levels.

[0071] The filter C2 has an electromechanical coupling coefficient k 2 is the same as filter C1, and the electromechanical coupling coefficient k 2 As shown in FIG. 10(a), the effective electromechanical coupling coefficient k 2 is made smaller than the electromechanical coupling coefficient of each of the series resonators S2 and S3. 2 Let be a value designed based on the simultaneous Chebyshev approximation.

[0072] The filter C4 has an electromechanical coupling coefficient k 2 is the same as filter C3, and the electromechanical coupling coefficient k 2 As shown in FIG. 10(b), the parallel resonators P1 and P2 are connected in parallel to the capacitors C3 and C4, so that the effective electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k 2 This reduces the electromechanical coupling coefficient k 2 Let be a value designed based on the simultaneous Chebyshev approximation.

[0073] Tables 10 to 13 show the capacitance C0, the dynamic inductance Lm, the dynamic capacitance Cm, the resonant frequency fr, the anti-resonant frequency fa, and the electromechanical coupling coefficient k in the filters C1 to C4. 2 In Tables 11 and 13, the capacitances Cp and k in the filters C2 and C4 are 2 The k in Tables 11 and 13 is shown. 2 is the effective k of the resonator in which the capacitors C1 to C4 are connected in parallel. 2 And simplex k 2 is the k of the resonator alone 2 It is.

[0074] [Table 10]

[0075] [Table 11]

[0076] [Table 12]

[0077] [Table 13]

[0078] As shown in Tables 11 and 13, the parameters of the resonators in filters C2 and C4 are almost the same as those of filter B1 in Table 7. As shown in Tables 10 and C12, the parameters of the series resonators S2 and S3 in filter C1 are different from those of filters B1 and C2. The parameters of the parallel resonators P1 and P2 in filter C3 are different from those of filters B1 and C4.

[0079] 12(a) and 12(b) are diagrams showing the pass characteristics of filters B1, C1, and C2 in simulation 3. FIG. 12(b) is an enlarged view of the pass band of FIG. 12(a). As shown in FIG. 12(a) and FIG. 12(b), the pass characteristics of filters B1 and C2 almost overlap. Filter C1 has a wider pass band than filters B1 and C2, but ripples are formed within the pass band, and the steepness of the skirt on the high frequency side is low.

[0080] 13(a) and 13(b) are diagrams showing the pass characteristics of filters B1, C3, and C4 in simulation 3. FIG. 13(b) is an enlarged view of the vicinity of the pass band in FIG. 13(a). As shown in FIG. 13(a) and FIG. 13(b), the pass characteristics of filters B1 and C4 almost overlap. In filter C3, a ripple is formed on the shoulder on the high frequency side of the pass band compared to filters B1 and C4. This narrows the width of the pass band.

[0081] In this way, in the filters C2 and C4, the electromechanical coupling coefficient k 2 Since the number of manufacturing steps can be reduced by setting the number of manufacturing steps to four levels, the manufacturing cost can be reduced. 2 can be made to be approximately the same as that of filter B1. This makes it possible to make the filter characteristics approximately the same as that of filter B1.

[0082] According to the first embodiment and its modified example, when a ladder filter is designed based on the simultaneous Chebyshev approximation, as in the filters A1 to A6 in Simulation 1, the series resonator S3 (first series resonator) that is electrically closest to the terminal T2 has a smaller electromechanical coupling coefficient k 2 That is, the series resonator S3 has the thinnest insertion film 18 among the multiple series resonators S1 to S3. At least one of the series resonators S1 and S2 (second series resonators) other than the series resonator S3 has a smaller single-unit electromechanical coupling coefficient k 2 is small. That is, the series resonators S1 and S2 have thicker insertion films 18 than the series resonator S3. Note that the resonator provided with the insertion film 18 is expressed as having a thicker insertion film 18 than the resonator not provided with the insertion film 18. Also, the resonator not provided with the insertion film 18 is expressed as having a thinner insertion film 18 than the resonator provided with the insertion film 18.

[0083] Similarly, the parallel resonator P3 (first parallel resonator) electrically closest to the terminal T2 has an electromechanical coupling coefficient k 2That is, the parallel resonator P3 has the thinnest insertion film 18 among the parallel resonators P1 to P3 or does not have an insertion film 18. At least one of the parallel resonators P1 and P2 (second parallel resonators) other than the parallel resonator P3 has a smaller electromechanical coupling coefficient k 2 That is, the parallel resonators P1 and P2 have thicker insertion films 18 than the parallel resonator P3.

[0084] In the first embodiment, as shown in FIG. 7, one end of each of the inductors L1 and L2 is connected to at least one of the parallel resonators P2 and P3 (first resonator) among the parallel resonators P1 to P3, and the other end is grounded. As a result, the substantial electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k of at least one resonator (second resonator) among the plurality of series resonators S1 to S3 and the parallel resonator P1 to which a grounded inductor is not connected can be made larger than the above. 2 The electromechanical coupling coefficient k 2 That is, the parallel resonator P3 and the series resonator S3 have a single electromechanical coupling coefficient k 2 are substantially the same (5.6% in the filter B3) (i.e., the thickness of the insertion film 18 is substantially the same). 2 is substantially the same (3.3% in filter B3) (i.e., the thickness of the insertion film 18 is substantially the same). This makes it possible to reduce the electromechanical coupling coefficient k 2 By connecting the inductors L1 and L2 in series to the parallel resonators P2 and P3, the effective electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k 2 This can improve the filter characteristics, thereby improving the characteristics and suppressing an increase in the manufacturing process.

[0085] When a ladder filter is designed based on the simultaneous Chebyshev approximation, as in filters A1 to A6 in Simulation 1, the electromechanical coupling coefficient k 2 is larger than the electromechanical coupling coefficient of the parallel resonator P3. Therefore, the parallel resonator (first resonator) to which the inductor L2 is connected is defined as the parallel resonator P3 (first parallel resonator), and the series resonator S3 (first series resonator) is defined as having substantially the same electromechanical coupling coefficient k 2 That is, the thickness T8 of the insertion film 18 of the series resonator S3 (first series resonator) and the parallel resonator P3 (first parallel resonator) is made substantially the same. This makes it possible to improve the characteristics and suppress an increase in the number of manufacturing steps.

[0086] In addition, when a ladder filter is designed based on the simultaneous Chebyshev approximation, the parallel resonator P3 closest to the terminal T2 among the multiple series resonators S1 to S3 has the lowest electromechanical coupling coefficient k 2 The series resonator S3 closest to the terminal T2 has the second largest electromechanical coupling coefficient k 2 That is, the parallel resonator P3 has the thinnest insertion film 18, and the series resonator S3 has the second thinnest insertion film. 2 is the smallest electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k 2 is the smallest electromechanical coupling coefficient k 2 The thickness difference between the insertion film 18 of the series resonator S3 and the thickest insertion film 18 of the multiple parallel resonators S1 to S3 is 5 nm or more and 10 nm or more. The thickness difference between the insertion film 18 of the parallel resonator P3 and the thickest insertion film 18 of the multiple parallel resonators P1 to P3 is 5 nm or more and 10 nm or more.

[0087] Furthermore, when a ladder filter is designed based on the simultaneous Chebyshev approximation, as in the filters A1 to A6 in Simulation 1, in which the number of stages is five or less, the parallel resonator P1 (third parallel resonator) electrically closest to the terminal T1 has the smallest electromechanical coupling coefficient k 2 is small (i.e., the insertion membrane 18 is the largest).

[0088] In the first and second modifications of the first embodiment, as shown in the filters C2 and C4 and in Fig. 10(a) and Fig. 10(b), the capacitors C1 to C4 are connected in parallel to at least one resonator (first resonator) among the series resonators S1 to S3 and the parallel resonators P1 to P3. The electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k of the same unit 2 (i.e., the thickness T8 of the insertion film 18 is substantially the same) is provided. For example, in the filter C2, the series resonator S2 in which the capacitor C1 is connected in parallel and the parallel resonator P2 in which the capacitor is not connected in parallel have substantially the same single-unit electromechanical coupling coefficient k 2 (3.8%). The series resonator S3 with the capacitor C2 connected in parallel and the parallel resonator P3 with no capacitor connected in parallel have substantially the same single-unit electromechanical coupling coefficient k 2 In the filter C4, the parallel resonator P1 to which the capacitor C3 is connected in parallel and the series resonator S2 to which no capacitor is connected have substantially the same single-unit electromechanical coupling coefficient k 2 (3.4%). The parallel resonator P2 to which the capacitor C4 is connected in parallel and the series resonator S1 to which no capacitor is connected have substantially the same single-unit electromechanical coupling coefficient k 2 (4.5%). This allows the electromechanical coupling coefficient k 2 By connecting the capacitors C1 to C4 in parallel with the resonator, the effective electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k 2This can improve the filter characteristics, thereby improving the characteristics and suppressing an increase in the manufacturing process.

[0089] When a ladder filter is designed based on the simultaneous Chebyshev approximation, as in filters A1 to A6 in Simulation 1, the electromechanical coupling coefficient k 2 is the electromechanical coupling coefficient k of the parallel resonator P3 2 Therefore, in the filter C2, the resonator (first resonator) to which the capacitor C2 is connected in parallel is designated as a series resonator S3 (first series resonator), and the parallel resonator P3 (first parallel resonator) has a single electromechanical coupling coefficient k 2 That is, the thickness of the insertion film 18 of the parallel resonator P3 (first parallel resonator) and the series resonator S3 (first series resonator) is made substantially the same. This makes it possible to improve characteristics and suppress an increase in the number of manufacturing steps.

[0090] In addition, when a ladder filter is designed based on the simultaneous Chebyshev approximation, as in the filters A1 to A6 in Simulation 1, in which the number of stages is five or less, the parallel resonator P1 (third parallel resonator) electrically closest to the terminal T1 has the smallest electromechanical coupling coefficient k 2 Therefore, as in the filter C4, the electromechanical coupling coefficient k 2 The electromechanical coupling coefficient k 2 and a capacitor C3 is connected in parallel to the parallel resonator P1. This makes it possible to improve the characteristics and suppress an increase in the number of manufacturing steps.

[0091] The electromechanical coupling coefficient k of a single resonator 2"Substantially the same" means that, when the maximum single electromechanical coupling coefficient of the multiple resonators is kmax and the minimum single electromechanical coupling coefficient is kmin, (kmax-kmin) / (kmax+kmin) is, for example, 0.1 or less or 0.05 or less. "Substantially the same thickness of a layer in multiple resonators" means that, when the maximum thickness of a layer in multiple resonators is Tmax and the minimum thickness is Tmin, (Tmax-Tmin) / (Tmax+Tmin) is, for example, 0.1 or less or 0.05 or less.

[0092] Electromechanical coupling coefficient k in piezoelectric thin film resonators 2 As a method for making the piezoelectric film 14 different in thickness, impurities may be added to the piezoelectric film 14 to make the piezoelectricity different, or the ratio of the planar area of ​​the insertion film 18 in the resonance region 50 to the planar area of ​​the resonance region 50 may be changed. When a ladder filter is designed based on the simultaneous Chebyshev approximation like the filters A1 to A6, the electromechanical coupling coefficient k 2 is the smallest electromechanical coupling coefficient k 2 In this way, the electromechanical coupling coefficient k 2 A preferred method for making the difference between the thicknesses T2 of the insertion membrane 18 is to make the thicknesses T2 different.

[0093] [Modification 3 of Example 1] Modifications 3 and 4 of Example 1 are examples in which the configuration of the gap is changed. Fig. 14(a) and Fig. 14(b) are cross-sectional views of piezoelectric thin film resonators according to Modifications 3 and 4 of Example 1, respectively. As shown in Fig. 14(a), in Modification 3 of Example 1, the upper surface of the substrate 10 is flat, and a dome-shaped gap 30 is provided between the substrate 10 and the lower electrode 12. The other configurations are the same as those in Fig. 5(a) of Example 1, and therefore description thereof will be omitted.

[0094] [Variation 4 of Example 1] As shown in FIG. 14(b), in the fourth modification of the first embodiment, an acoustic reflection film 31 is formed under the lower electrode 12 in the resonance region 50. The acoustic reflection film 31 is formed by alternately providing a film 31a having a low acoustic impedance and a film 31b having a high acoustic impedance. The thickness of each of the films 31a and 31b is, for example, approximately λ / 4 (λ is the wavelength of the elastic wave). The number of layers of the films 31a and 31b can be set arbitrarily. The acoustic reflection film 31 may be formed by laminating at least two types of layers having different acoustic characteristics with a gap therebetween. The substrate 10 may be one of the at least two types of layers having different acoustic characteristics of the acoustic reflection film 31. For example, the acoustic reflection film 31 may be configured such that one film having a different acoustic impedance is provided in the substrate 10. The other configurations are the same as those in FIG. 5(a) of the first embodiment, and description thereof will be omitted.

[0095] As in the first embodiment and its first to third modifications, the piezoelectric thin film resonator may be an FBAR (Film Bulk Acoustic Resonator) in which a gap 30 is formed between the substrate 10 and the lower electrode 12 in the resonance region 50. As in the fourth modification of the first embodiment, the piezoelectric thin film resonator may be an SMR (Solidly Mounted Resonator) including an acoustic reflection film 31 that reflects an elastic wave propagating through the piezoelectric film 14 under the lower electrode 12 in the resonance region 50. The acoustic reflection layer including the resonance region 50 may include the gap 30 or the acoustic reflection film 31. EXAMPLES

[0096] FIG. 15 is a circuit diagram of a duplexer according to a second embodiment. As shown in FIG. 15, a transmission filter 40 is connected between a common terminal Ant and a transmission terminal Tx. A reception filter 42 is connected between the common terminal Ant and a reception terminal Rx. The transmission filter 40 passes signals in a transmission band among signals input from the transmission terminal Tx to the common terminal Ant as transmission signals, and suppresses signals of other frequencies. The reception filter 42 passes signals in a reception band among signals input from the common terminal Ant to the reception terminal Rx as reception signals, and suppresses signals of other frequencies. At least one of the transmission filter 40 and the reception filter 42 can be the filter of the first embodiment and its modified examples.

[0097] Although a duplexer has been described as an example of a multiplexer, a triplexer or a quadplexer may also be used.

[0098] Although the embodiments of the present invention have been described in detail above, the present invention is not limited to such specific embodiments, and various modifications and variations are possible within the scope of the gist of the present invention described in the claims. [Explanation of symbols]

[0099] 10 Substrate 12 Lower electrode 14 Piezoelectric film 16 Upper electrode 18 Insertion membrane 40 Transmission Filter 42 Receiving Filter 50 resonance area

Claims

1. a plurality of piezoelectric thin film resonators comprising a substrate, a piezoelectric film provided on the substrate, and a first electrode and a second electrode that sandwich at least a portion of the piezoelectric film and form a resonance region that overlaps with each other, at least some of the piezoelectric thin film resonators comprising an insertion film provided between the first electrode and the second electrode within the resonance region; a plurality of series resonators connected in series between a first terminal and a second terminal, the plurality of series resonators including a first series resonator electrically closest to the second terminal, the first series resonator having the thinnest insertion film among the plurality of series resonators, and at least one second series resonator other than the first series resonator having a thicker insertion film than the first series resonator; a first parallel resonator, one end of which is connected to a path between the first terminal and the second terminal and the other end of which is grounded and which is included in the plurality of piezoelectric thin film resonators and is electrically closest to the second terminal, has the thinnest insertion film or does not have an insertion film among the plurality of parallel resonators, and at least one second parallel resonator other than the first parallel resonator has a thicker insertion film than the first parallel resonator; an inductor having one end connected to at least one first resonator among the plurality of parallel resonators and the other end grounded; a second resonator which is at least one of the plurality of series resonators and a parallel resonator to which no grounded inductor is connected and has an insertion film having substantially the same thickness as an insertion film of the parallel resonator to which the inductor is connected; A ladder type filter comprising:

2. the first resonator includes the first parallel resonator, 2. The ladder filter according to claim 1, wherein the second resonator includes the first series resonator.

3. 3. The ladder-type filter according to claim 1, wherein, among the plurality of series resonators and the plurality of parallel resonators, the first parallel resonator has the thinnest insertion film, and the second series resonator has the second thinnest insertion film.

4. 4. The ladder-type filter according to claim 1, wherein a third parallel resonator, which is electrically closest to the first terminal among the plurality of parallel resonators, has a thickest insertion film among the plurality of series resonators and the plurality of parallel resonators.

5. a plurality of piezoelectric thin film resonators comprising a substrate, a piezoelectric film provided on the substrate, and a first electrode and a second electrode that sandwich at least a portion of the piezoelectric film and form a resonance region that overlaps with each other, at least some of the piezoelectric thin film resonators comprising an insertion film provided between the first electrode and the second electrode within the resonance region; a plurality of series resonators connected in series between a first terminal and a second terminal, the plurality of series resonators including a first series resonator electrically closest to the second terminal, the first series resonator having the thinnest insertion film among the plurality of series resonators, and at least one second series resonator other than the first series resonator having a thicker insertion film than the first series resonator; a first parallel resonator, one end of which is connected to a path between the first terminal and the second terminal and the other end of which is grounded and which is included in the plurality of piezoelectric thin film resonators and is electrically closest to the second terminal, has the thinnest insertion film or does not have an insertion film among the plurality of parallel resonators, and at least one second parallel resonator other than the first parallel resonator has a thicker insertion film than the first parallel resonator; a capacitor connected in parallel to at least one first resonator among the plurality of series resonators and the plurality of parallel resonators; a second resonator, which is at least one of the plurality of series resonators and the plurality of parallel resonators, in which a capacitor is not connected in parallel and which has an insertion film having substantially the same thickness as an insertion film of a resonator in which the capacitor is connected in parallel; A ladder type filter comprising:

6. the first resonator includes the first series resonator, 6. The ladder filter according to claim 5, wherein the second resonator includes the first parallel resonator.

7. 7. The ladder-type filter according to claim 5, wherein, among the plurality of series resonators and the plurality of parallel resonators, the first parallel resonator has the thinnest insertion film, and the second series resonator has the second thinnest insertion film.

8. 8. The ladder-type filter according to claim 5, wherein a third parallel resonator, which is electrically closest to the first terminal among the plurality of parallel resonators, has a thickest insertion film among the plurality of series resonators and the plurality of parallel resonators.

9. 9. The ladder filter according to claim 8, wherein the first resonator includes the third parallel resonator.

10. 10. The ladder filter according to claim 1 , wherein in the plurality of piezoelectric thin film resonators, the piezoelectric films have substantially the same thickness, the first electrodes have substantially the same thickness, and the second electrodes have substantially the same thickness.

11. A multiplexer comprising the ladder filter according to any one of claims 1 to 10.

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