Transversely-excited film bulk acoustic resonators

Abstract

There is disclosed acoustic resonators and filter devices. An acoustic resonator device includes a piezoelectric plate, a portion of the piezoelectric plate forming a diaphragm, a thickness of the piezoelectric plate is greater than or equal to 300 nm and less than or equal to 500 nm, and an interdigital transducer (IDT) with interleaved fingers of the IDT on the diaphragm. The piezoelectric plate and the IDT are configured such that a radio frequency signal applied to the IDT excites a primary shear acoustic mode in the diaphragm.

Description

NOTICE OF COPYRIGHTS AND TRADE DRESS

A portion of the disclosure of this patent document contains material which is subject to copyright protection. This patent document may show and/or describe matter which is or may become trade dress of the owner. The copyright and trade dress owner has no objection to the facsimile reproduction by anyone of the patent disclosure as it appears in the Patent and Trademark Office patent files or records, but otherwise reserves all copyright and trade dress rights whatsoever.

BACKGROUND

Field

This disclosure relates to radio frequency filters using acoustic wave resonators, and specifically to bandpass filters with high power capability for use in communications equipment.

Description of the Related Art

A radio frequency (RF) filter is a two-port device configured to pass some frequencies and to stop other frequencies, where “pass” means transmit with relatively low signal loss and “stop” means block or substantially attenuate. The range of frequencies passed by a filter is referred to as the “pass-band” of the filter. The range of frequencies stopped by such a filter is referred to as the “stop-band” of the filter. A typical RF filter has at least one pass-band and at least one stop-band. Specific requirements on a pass-band or stop-band depend on the specific application. For example, a “pass-band” may be defined as a frequency range where the insertion loss of a filter is less than a defined value such as 1 dB, 2 dB, or 3 dB. A “stop-band” may be defined as a frequency range where the rejection of a filter is greater than a defined value such as 20 dB, 30 dB, 40 dB, or greater depending on application.

RF filters are used in communications systems where information is transmitted over wireless links. For example, RF filters may be found in the RF front-ends of cellular base stations, mobile telephone and computing devices, satellite transceivers and ground stations, IoT (Internet of Things) devices, laptop computers and tablets, fixed point radio links, and other communications systems. RF filters are also used in radar and electronic and information warfare systems.

RF filters typically require many design trade-offs to achieve, for each specific application, the best compromise between performance parameters such as insertion loss, rejection, isolation, power handling, linearity, size and cost. Specific design and manufacturing methods and enhancements can benefit simultaneously one or several of these requirements.

Performance enhancements to the RF filters in a wireless system can have broad impact to system performance. Improvements in RF filters can be leveraged to provide system performance improvements such as larger cell size, longer battery life, higher data rates, greater network capacity, lower cost, enhanced security, higher reliability, etc. These improvements can be realized at many levels of the wireless system both separately and in combination, for example at the RF module, RF transceiver, mobile or fixed sub-system, or network levels.

High performance RF filters for present communication systems commonly incorporate acoustic wave resonators including surface acoustic wave (SAW) resonators, bulk acoustic wave (BAW) resonators, film bulk acoustic wave resonators (FBAR), and other types of acoustic resonators. However, these existing technologies are not well-suited for use at the higher frequencies proposed for future communications networks.

The desire for wider communication channel bandwidths will inevitably lead to the use of higher frequency communications bands. Radio access technology for mobile telephone networks has been standardized by the 3GPP (3^rd Generation Partnership Project). Radio access technology for 5^th generation mobile networks is defined in the 5G NR (new radio) standard. The 5G NR standard defines several new communications bands. Two of these new communications bands are n77, which uses the frequency range from 3300 MHz to 4200 MHz, and n79, which uses the frequency range from 4400 MHz to 5000 MHz. Both band n77 and band n79 use time-division duplexing (TDD), such that a communications device operating in band n77 and/or band n79 use the same frequencies for both uplink and downlink transmissions. Bandpass filters for bands n77 and n79 must be capable of handling the transmit power of the communications device. The 5G NR standard also defines millimeter wave communication bands with frequencies between 24.25 GHz and 40 GHz.

DESCRIPTION OF THE DRAWINGS

FIG. 1 includes a schematic plan view and two schematic cross-sectional views of a transversely-excited film bulk acoustic resonator (XBAR).

FIG. 2 is an expanded schematic cross-sectional view of a portion of the XBAR of FIG. 1.

FIG. 3A is an alternative schematic cross-sectional view of the XBAR of FIG. 1.

FIG. 3B is another alternative schematic cross-sectional view of the XBAR of FIG. 1.

FIG. 3C is an alternative schematic plan view of an XBAR

FIG. 4 is a graphic illustrating a primary acoustic mode in an XBAR.

FIG. 5 is a schematic circuit diagram of a band-pass filter using acoustic resonators in a ladder circuit.

FIG. 6 is a graph showing the relationship between piezoelectric diaphragm thickness and resonance frequency of an XBAR.

FIG. 7 is a plot showing the relationship between coupling factor Gamma (F) and IDT pitch for an XBAR.

FIG. 8 is a graph showing the dimensions of XBAR resonators with capacitance equal to one picofarad.

FIG. 9 is a graph showing the relationship between IDT finger pitch and resonance and anti-resonance frequencies of an XBAR, with dielectric layer thickness as a parameter.

FIG. 10 is a graph comparing the admittances of three simulated XBARs with different IDT metal thicknesses.

FIG. 11 is a graph illustrating the effect of IDT finger width on spurious resonances in an XBAR.

FIG. 12 is a graph comparing XBARs with aluminum and molybdenum IDT fingers.

FIG. 13 is an expanded portion of the graph of FIG. 12 comparing XBARs with aluminum and molybdenum IDT fingers.

FIG. 14 is a graph identifying preferred combinations of molybdenum IDT thickness and IDT pitch for XBARs without a front dielectric layer.

FIG. 15 is a graph identifying preferred combinations of molybdenum IDT thickness and IDT pitch for XBARs with front dielectric layer thickness equal to 0.25 times the XBAR diaphragm thickness.

FIG. 16 is a cross-section view and two detailed cross-sectional views of a portion of an XBAR with two-layer IDT fingers.

FIG. 17 is a graph of S-parameters S11 and S21 of an exemplary bandpass filter using XBARs with molybdenum conductors.

Throughout this description, elements appearing in figures are assigned three-digit or four-digit reference designators, where the two least significant digits are specific to the element and the one or two most significant digit is the figure number where the element is first introduced. An element that is not described in conjunction with a figure may be presumed to have the same characteristics and function as a previously-described element having the same reference designator.

DETAILED DESCRIPTION

Description of Apparatus

FIG. 1 shows a simplified schematic top view and orthogonal cross-sectional views of a transversely-excited film bulk acoustic resonator (XBAR) 100. XBAR resonators such as the resonator 100 may be used in a variety of RF filters including band-reject filters, band-pass filters, duplexers, and multiplexers. XBARs are particularly suited for use in filters for communications bands with frequencies above 3 GHz.

The XBAR 100 is made up of a thin film conductor pattern formed on a surface of a piezoelectric plate 110 having parallel front and back surfaces 112, 114, respectively. The piezoelectric plate is a thin single-crystal layer of a piezoelectric material such as lithium niobate, lithium tantalate, lanthanum gallium silicate, gallium nitride, or aluminum nitride. The piezoelectric plate is cut such that the orientation of the X, Y, and Z crystalline axes with respect to the front and back surfaces is known and consistent. In the examples presented in this patent, the piezoelectric plates are Z-cut, which is to say the Z axis is normal to the front and back surfaces 112, 114. However, XBARs may be fabricated on piezoelectric plates with other crystallographic orientations.

The back surface 114 of the piezoelectric plate 110 is attached to a surface of the substrate 120 except for a portion of the piezoelectric plate 110 that forms a diaphragm 115 spanning a cavity 140 formed in the substrate. The portion of the piezoelectric plate that spans the cavity is referred to herein as the “diaphragm” 115 due to its physical resemblance to the diaphragm of a microphone. As shown in FIG. 1, the diaphragm 115 is contiguous with the rest of the piezoelectric plate 110 around all of a perimeter 145 of the cavity 140. In this context, “contiguous” means “continuously connected without any intervening item”. In other configurations, the diaphragm 115 may be contiguous with the piezoelectric plate are at least 50% of the perimeter 145 of the cavity 140.

The substrate 120 provides mechanical support to the piezoelectric plate 110. The substrate 120 may be, for example, silicon, sapphire, quartz, or some other material or combination of materials. The back surface 114 of the piezoelectric plate 110 may be bonded to the substrate 120 using a wafer bonding process. Alternatively, the piezoelectric plate 110 may be grown on the substrate 120 or attached to the substrate in some other manner. The piezoelectric plate 110 may be attached directly to the substrate or may be attached to the substrate 120 via one or more intermediate material layers (not shown in FIG. 1).

“Cavity” has its conventional meaning of “an empty space within a solid body.” The cavity 140 may be a hole completely through the substrate 120 (as shown in Section A-A and Section B-B) or a recess in the substrate 120 under the diaphragm 115. The cavity 140 may be formed, for example, by selective etching of the substrate 120 before or after the piezoelectric plate 110 and the substrate 120 are attached.

The conductor pattern of the XBAR 100 includes an interdigital transducer (IDT) 130. The IDT 130 includes a first plurality of parallel fingers, such as finger 136, extending from a first busbar 132 and a second plurality of fingers extending from a second busbar 134. The first and second pluralities of parallel fingers are interleaved. The interleaved fingers overlap for a distance AP, commonly referred to as the “aperture” of the IDT. The center-to-center distance L between the outermost fingers of the IDT 130 is the “length” of the IDT.

The first and second busbars 132, 134 serve as the terminals of the XBAR 100. A radio frequency or microwave signal applied between the two busbars 132, 134 of the IDT 130 excites a primary acoustic mode within the piezoelectric plate 110. As will be discussed in further detail, the primary acoustic mode is a bulk shear mode where acoustic energy propagates along a direction substantially orthogonal to the surface of the piezoelectric plate 110, which is also normal, or transverse, to the direction of the electric field created by the IDT fingers. Thus, the XBAR is considered a transversely-excited film bulk wave resonator.

The IDT 130 is positioned on the piezoelectric plate 110 such that at least the fingers of the IDT 130 are disposed on the portion 115 of the piezoelectric plate that spans, or is suspended over, the cavity 140. As shown in FIG. 1, the cavity 140 has a rectangular shape with an extent greater than the aperture AP and length L of the IDT 130. A cavity of an XBAR may have a different shape, such as a regular or irregular polygon. The cavity of an XBAR may more or fewer than four sides, which may be straight or curved.

For ease of presentation in FIG. 1, the geometric pitch and width of the IDT fingers is greatly exaggerated with respect to the length (dimension L) and aperture (dimension AP) of the XBAR. A typical XBAR has more than ten parallel fingers in the IDT 110. An XBAR may have hundreds of parallel fingers in the IDT 110. Similarly, the thickness of the fingers in the cross-sectional views is greatly exaggerated.

FIG. 2 shows a detailed schematic cross-sectional view of the XBAR 100. The piezoelectric plate 110 is a single-crystal layer of piezoelectrical material having a thickness ts. Thickness ts may be, for example, 100 nm to 1500 nm. When used in filters for LTE™ bands from 3.4 GHz to 6 GHz (e.g. bands 42, 43, 46), the thickness ts may be, for example, 200 nm to 1000 nm.

A front-side dielectric layer 214 may optionally be formed on the front side of the piezoelectric plate 110. The “front side” of the XBAR is, by definition, the surface facing away from the substrate. The front-side dielectric layer 214 has a thickness tfd. The front-side dielectric layer 214 may be formed only between the IDT fingers (e.g. IDT finger 238b) or may be deposited as a blanket layer such that the dielectric layer is formed both between and over the IDT fingers (e.g. IDT finger 238a). The front-side dielectric layer 214 may be a non-piezoelectric dielectric material, such as silicon dioxide or silicon nitride. tfd may be, for example, 0 to 500 nm. tfd is typically less than the thickness ts of the piezoelectric plate. The front-side dielectric layer 214 may be formed of multiple layers of two or more materials.

The IDT fingers 238a and 238b may be aluminum, an aluminum alloy, copper, a copper alloy, beryllium, gold, tungsten, molybdenum or some other conductive material. The IDT fingers are considered to be “substantially aluminum” if they are formed from aluminum or an alloy comprising at least 50% aluminum. The IDT fingers are considered to be “substantially copper” if they are formed from copper or an alloy comprising at least 50% copper. The IDT fingers are considered to be “substantially molybdenum” if they are formed from molybdenum or an alloy comprising at least 50% molybdenum. Thin (relative to the total thickness of the conductors) layers of other metals, such as chromium or titanium, may be formed under and/or over and/or as layers within the fingers to improve adhesion between the fingers and the piezoelectric plate 110 and/or to passivate or encapsulate the fingers and/or to improve power handling. The busbars (132, 134 in FIG. 1) of the IDT may be made of the same or different materials as the fingers.

Dimension p is the center-to-center spacing or “pitch” of the IDT fingers, which may be referred to as the pitch of the IDT and/or the pitch of the XBAR. Dimension w is the width or “mark” of the IDT fingers. The geometry of the IDT of an XBAR differs substantially from the IDTs used in surface acoustic wave (SAW) resonators. In a SAW resonator, the pitch of the IDT is one-half of the acoustic wavelength at the resonance frequency. Additionally, the mark-to-pitch ratio of a SAW resonator IDT is typically close to 0.5 (i.e. the mark or finger width is about one-fourth of the acoustic wavelength at resonance). In an XBAR, the pitch p of the IDT is typically 2 to 20 times the width w of the fingers. In addition, the pitch p of the IDT is typically 2 to 20 times the thickness is of the piezoelectric slab 212. The width of the IDT fingers in an XBAR is not constrained to be near one-fourth of the acoustic wavelength at resonance. For example, the width of XBAR IDT fingers may be 500 nm or greater, such that the IDT can be readily fabricated using optical lithography. The thickness tm of the IDT fingers may be from 100 nm to about equal to the width w. The thickness of the busbars (132, 134 in FIG. 1) of the IDT may be the same as, or greater than, the thickness tm of the IDT fingers.

FIG. 3A and FIG. 3B show two alternative cross-sectional views along the section plane A-A defined in FIG. 1. In FIG. 3A, a piezoelectric plate 310 is attached to a substrate 320. A portion of the piezoelectric plate 310 forms a diaphragm 315 spanning a cavity 340 in the substrate. The cavity 340 does not fully penetrate the substrate 320. Fingers of an IDT are disposed on the diaphragm 315. The cavity 340 may be formed, for example, by etching the substrate 320 before attaching the piezoelectric plate 310. Alternatively, the cavity 340 may be formed by etching the substrate 320 with a selective etchant that reaches the substrate through one or more openings (not shown) provided in the piezoelectric plate 310. In this case, the diaphragm 315 may contiguous with the rest of the piezoelectric plate 310 around a large portion of a perimeter 345 of the cavity 340. For example, the diaphragm 315 may contiguous with the rest of the piezoelectric plate 310 around at least 50% of the perimeter 345 of the cavity 340. An intermediate layer (not shown), such as a dielectric bonding layer, may be present between the piezo electric plate 340 and the substrate 320.

In FIG. 3B, the substrate 320 includes a base 322 and an intermediate layer 324 disposed between the piezoelectric plate 310 and the base 322. For example, the base 322 may be silicon and the intermediate layer 324 may be silicon dioxide or silicon nitride or some other material. A portion of the piezoelectric plate 310 forms a diaphragm 315 spanning a cavity 340 in the intermediate layer 324. Fingers of an IDT are disposed on the diaphragm 315. The cavity 340 may be formed, for example, by etching the intermediate layer 324 before attaching the piezoelectric plate 310. Alternatively, the cavity 340 may be formed by etching the intermediate layer 324 with a selective etchant that reaches the substrate through one or more openings provided in the piezoelectric plate 310. In this case, the diaphragm 315 may be contiguous with the rest of the piezoelectric plate 310 around a large portion of a perimeter 345 of the cavity 340 (see FIG. 3C). For example, the diaphragm 315 may be contiguous with the rest of the piezoelectric plate 310 around at least 50% of the perimeter 345 of the cavity 340 as shown in FIG. 3C. Although not shown in FIG. 3B, a cavity formed in the intermediate layer 324 may extend into the base 322.

FIG. 3C is a schematic plan view of another XBAR 350. The XBAR 350 includes an IDT formed on a piezoelectric plate 310. A portion of the piezoelectric plate 310 forms a diaphragm spanning a cavity in a substrate. In this example, the perimeter 345 of the cavity has an irregular polygon shape such that none of the edges of the cavity are parallel, nor are they parallel to the conductors of the IDT. A cavity may have a different shape with straight or curved edges.

FIG. 4 is a graphical illustration of the primary acoustic mode of interest in an XBAR. FIG. 4 shows a small portion of an XBAR 400 including a piezoelectric plate 410 and three interleaved IDT fingers 430 which alternate in electrical polarity from finger to finger. An RF voltage is applied to the interleaved fingers 430. This voltage creates a time-varying electric field between the fingers. The direction of the electric field is predominantly lateral, or parallel to the surface of the piezoelectric plate 410, as indicated by the arrows labeled “electric field”. Due to the high dielectric constant of the piezoelectric plate, the RF electric energy is highly concentrated inside the plate relative to the air. The lateral electric field introduces shear deformation which couples strongly to a shear primary acoustic mode (at a resonance frequency defined by the acoustic cavity formed by the volume between the two surfaces of the piezoelectric plate) in the piezoelectric plate 410. In this context, “shear deformation” is defined as deformation in which parallel planes in a material remain predominantly parallel and maintain constant separation while translating (within their respective planes) relative to each other. A “shear acoustic mode” is defined as an acoustic vibration mode in a medium that results in shear deformation of the medium. The shear deformations in the XBAR 400 are represented by the curves 460, with the adjacent small arrows providing a schematic indication of the direction and relative magnitude of atomic motion at the resonance frequency. The degree of atomic motion, as well as the thickness of the piezoelectric plate 410, have been greatly exaggerated for ease of visualization. While the atomic motions are predominantly lateral (i.e. horizontal as shown in FIG. 4), the direction of acoustic energy flow of the excited primary acoustic mode is substantially orthogonal to the surface of the piezoelectric plate, as indicated by the arrow 465.

Considering FIG. 4, there is essentially no RF electric field immediately under the IDT fingers 430, and thus acoustic modes are only minimally excited in the regions 470 under the fingers. There may be evanescent acoustic motions in these regions. Since acoustic vibrations are not excited under the IDT fingers 430, the acoustic energy coupled to the IDT fingers 430 is low (for example compared to the fingers of an IDT in a SAW resonator) for the primary acoustic mode, which minimizes viscous losses in the IDT fingers.

An acoustic resonator based on shear acoustic wave resonances can achieve better performance than current state-of-the art film-bulk-acoustic-resonators (FBAR) and solidly-mounted-resonator bulk-acoustic-wave (SMR BAW) devices where the electric field is applied in the thickness direction. Such devices are usually based on AlN thin films with the C axis of the AlN perpendicular to the surfaces of the film. The acoustic mode is compressive with atomic motions and the direction of acoustic energy flow in the thickness direction. In addition, the piezoelectric coupling for shear wave XBAR resonances can be high (>20%) compared to other acoustic resonators. High piezoelectric coupling enables the design and implementation of microwave and millimeter-wave filters with appreciable bandwidth.

FIG. 5 is a schematic circuit diagram of a band-pass filter 500 using five XBARs X1-X5. The filter 500 may be, for example, a band n79 band-pass filter for use in a communication device. The filter 500 has a conventional ladder filter architecture including three series resonators X1, X3, X5 and two shunt resonators X2, X4. The three series resonators X1, X3, X5 are connected in series between a first port and a second port. In FIG. 5, the first and second ports are labeled “In” and “Out”, respectively. However, the filter 500 is bidirectional and either port may serve as the input or output of the filter. The two shunt resonators X2, X4 are connected from nodes between the series resonators to ground. All the shunt resonators and series resonators are XBARs.

The three series resonators X1, X3, X5 and the two shunt resonators X2, X4 of the filter 500 maybe formed on a single plate 530 of piezoelectric material bonded to a silicon substrate (not visible). Each resonator includes a respective IDT (not shown), with at least the fingers of the IDT disposed over a cavity in the substrate. In this and similar contexts, the term “respective” means “relating things each to each”, which is to say with a one-to-one correspondence. In FIG. 5, the cavities are illustrated schematically as the dashed rectangles (such as the rectangle 535). In this example, an IDT of each resonator is disposed over a respective cavity. In other filters, the IDTs of two or more resonators may be disposed over a common cavity. Resonators may also be cascaded into multiple IDTs which may be formed on multiple cavities.

Each of the resonators X1 to X5 has a resonance frequency and an anti-resonance frequency. In simplified terms, each resonator is effectively a short circuit at its resonance frequency and effectively an open circuit at its anti-resonance frequency. Each resonator X1 to X5 creates a “transmission zero”, where the transmission between the in and out ports of the filter is very low. Note that the transmission at a “transmission zero” is not actually zero due to energy leakage through parasitic components and other effects. The three series resonators X1, X3, X5 create transmission zeros at their respective anti-resonance frequencies (where each resonator is effectively an open circuit). The two shunt resonators X2, X4 create transmission zeros at their respective resonance frequencies (where each resonator is effectively a short circuit). In a typical band-pass filter using acoustic resonators, the anti-resonance frequencies of the series resonators create transmission zeros above the passband, and the resonance frequencies of the shunt resonators create transmission zeros below the passband.

A band-pass filter for use in a communications device, such as a cellular telephone, must meet a variety of requirements. First, a band-pass filter, by definition, must pass, or transmit with acceptable loss, a defined pass-band. Typically, a band-pass filter for use in a communications device must also stop, or substantially attenuate, one or more stop band(s). For example, a band n79 band-pass filter is typically required to pass the n79 frequency band from 4400 MHz to 5000 MHz and to stop the 5 GHz WiFi™ band and/or the n77 band from 3300 MHz to 4200 MHz. To meet these requirements, a filter using a ladder circuit would require series resonators with anti-resonance frequencies about or above 5100 MHz, and shunt resonators with resonance frequencies about or below 4300 MHz.

The resonance and anti-resonance frequencies of an XBAR are strongly dependent on the thickness ts of the piezoelectric diaphragm (115 in FIG. 1). FIG. 6 is a graph 600 of resonance frequency of an XBAR versus piezoelectric diaphragm thickness. In this example, the piezoelectric diaphragm is z-cut lithium niobate. The solid curve 610 is plot of resonance frequency as a function of the inverse of the piezoelectric plate thickness for XBARs with IDT pitch equal to 3 microns. This plot is based on results of simulations of XBARs using finite element methods. The resonance frequency is roughly proportional to the inverse of the piezoelectric plate thickness.

The resonance and anti-resonance frequencies of an XBAR are also dependent on the pitch (dimension p in FIG. 2) of the IDT. Further, the electromechanical coupling of an XBAR, which determines the separation between the resonance and anti-resonance frequencies, is dependent on the pitch. FIG. 7 is a graph 700 of gamma (F) as a function of normalized pitch, which is to say IDT pitch p divided by diaphragm thickness ts. Gamma is a metric defined by the equation:

$\Gamma =\frac{1}{{\left(\mathrm{Fa}/\mathrm{Fr}\right)}^2-1}$ where Fa is the antiresonance frequency and Fr is the resonance frequency. Large values for gamma correspond to smaller separation between the resonance and anti-resonance frequencies. Low values of gamma indicate strong coupling which is good for design of wideband ladder filters.

In this example, the piezoelectric diaphragm is z-cut lithium niobate, and data is presented for diaphragm thicknesses of 300 nm, 400 nm, and 500 nm. In all cases, the IDT is aluminum with a thickness of 25% of the diaphragm thickness, the duty factor (i.e. the ratio of the width w to the pitch p) of the IDT fingers is 0.14, and there are no dielectric layers. The “+” symbols, circles, and “x” symbols represent diaphragm thicknesses of 300 nm, 400 nm, and 500 nm, respectively. Outlier data points, such as those for relative IDT pitch about 4.5 and about 8, are caused by spurious modes interacting with the primary acoustic mode and altering the apparent gamma. The relationship between gamma and IDT pitch is relatively independent of diaphragm thickness, and roughly asymptotic to Γ=3.5 as the relative pitch is increased.

Another typical requirement on a band-pass filter for use in a communications device is the input and output impedances of the filter have to match, at least over the pass-band of the filter, the impedances of other elements of the communications device to which the filter is connected (e.g. a transmitter, receiver, and/or antenna) for maximum power transfer. Commonly, the input and output impedances of a band-pass filter are required to match a 50-ohm impedance within a tolerance that may be expressed, for example, as a maximum return loss or a maximum voltage standing wave ratio. When necessary, an impedance matching network comprising one or more reactive components can be used at the input and/or output of a band-pass filter. Such impedance matching networks add to the complexity, cost, and insertion loss of the filter and are thus undesirable. To match, without additional impedance matching components, a 50-Ohm impedance at a frequency of 5 GHz, the capacitances of at least the shunt resonators in the band-pass filter need to be in a range of about 0.5 picofarads (pF) to about 1.5 picofarads.

FIG. 8 is a graph 800 showing the area and dimensions of XBAR resonators with capacitance equal to one picofarad. The solid line 810 is a plot of the IDT length required to provide a capacitance of 1 pF as a function of the inverse of the IDT aperture when the IDT pitch is 3 microns. The dashed line 820 is a plot of the IDT length required to provide a capacitance of 1 pF as a function of the inverse of the IDT aperture when the IDT pitch is 5 microns. The data plotted in FIG. 8 is specific to XBAR devices with lithium niobate diaphragm thickness of 400 nm.

For any aperture, the IDT length required to provide a desired capacitance is greater for an IDT pitch of 5 microns than for an IDT pitch of 3 microns. The required IDT length is roughly proportional to the change in IDT pitch. The design of a filter using XBARs is a compromise between somewhat conflicting objectives. As shown in FIG. 7, a larger IDT pitch may be preferred to reduce gamma and maximize the separation between the anti-resonance and resonance frequencies. As can be understood from FIG. 8, smaller IDT pitch is preferred to minimize IDT area. A reasonable compromise between these objectives is 6≤p/ts≤12.5. Setting the IDT pitch p equal to or greater than six times the diaphragm thickness ts provides Fa/Fr greater than 1.1. Setting the maximum IDT pitch p to 12.5 times the diaphragm thickness ts is reasonable since Fa/Fr does not increase appreciably for higher values of relative pitch.

As will be discussed is greater detail subsequently, the metal fingers of the IDTs provide the primary mechanism for removing heat from an XBAR resonator. Increasing the aperture of a resonator increases the length and the electrical and thermal resistance of each IDT finger. Further, for a given IDT capacitance, increasing the aperture reduces the number of fingers required in the IDT, which, in turn, proportionally increases the RF current flowing in each finger. All of these effects argue for using the smallest possible aperture in resonators for high-power filters.

Conversely, several factors argue for using a large aperture. First, the total area of an XBAR resonator includes the area of the IDT and the area of the bus bars. The area of the bus bars is generally proportional to the length of the IDT. For very small apertures, the area of the IDT bus bars may be larger than the area occupied by the interleaved IDT fingers. Further, some electrical and acoustic energy may be lost at the ends of the IDT fingers. These loss effects become more significant as IDT aperture is reduced and the total number of fingers is increased. These losses may be evident as a reduction in resonator Q-factor, particularly at the anti-resonance frequency, as IDT aperture is reduced.

As a compromise between conflicting objectives, resonators apertures will typically fall in the range from 20 μm and 60 μm for 5 GHz resonance frequency. Resonator aperture may scale inversely with frequency.

The resonance and anti-resonance frequencies of an XBAR are also dependent on the thickness (dimension tfd in FIG. 2) of the front-side dielectric layer applied between (and optionally over) the fingers of the IDT. FIG. 9 is a graph 900 of anti-resonant frequency and resonant frequency as a function of IDT finger pitch p for XBAR resonators with z-cut lithium niobate piezoelectric plate thickness is =400 nm, with front-side SiO₂ dielectric layer thickness tfd as a parameter. The solid lines 910 and 920 are plots of the anti-resonance and resonance frequencies, respectively, as functions of IDT pitch for tfd=0. The dashed lines 912 and 922 are plots of the anti-resonance and resonance frequencies, respectively, as functions of IDT pitch for tfd=30 nm. The dash-dot lines 914 and 924 are plots of the anti-resonance and resonance frequencies, respectively, as functions of IDT pitch for tfd=60 nm. The dash-dot-dot lines 916 and 926 are plots of the anti-resonance and resonance frequencies, respectively, as functions of IDT pitch for tfd=90 nm. The frequency shifts are approximately linear functions of tfd.

In FIG. 9, the difference between the resonance and anti-resonance frequencies is 600 to 650 MHz for any particular values for front-side dielectric layer thickness and IDT pitch. This difference is large compared to that of older acoustic filter technologies, such as surface acoustic wave filters. However, 650 MHz is not sufficient for very wide band filters such as band-pass filters needed for bands n77 and n79. As described in U.S. patent application Ser. No. 16/230,443, the front-side dielectric layer over shunt resonators may be thicker than the front-side dielectric layer over series resonators. A thicker dielectric layer over shunt resonators shifts the resonance frequency of the shunt resonators downward and thus increases the frequency difference between the resonant frequencies of the shunt resonators and the anti-resonance frequencies of the series resonators.

Communications devices operating in time-domain duplex (TDD) bands transmit and receive in the same frequency band. Both the transmit and receive signal paths pass through a common bandpass filter connected between an antenna and a transceiver. Communications devices operating in frequency-domain duplex (FDD) bands transmit and receive in different frequency bands. The transmit and receive signal paths pass through separate transmit and receive bandpass filters connected between an antenna and the transceiver. Filters for use in TDD bands or filters for use as transmit filters in FDD bands can be subjected to radio frequency input power levels of 30 dBm or greater and must avoid damage under power.

The required insertion loss of acoustic wave bandpass filters is usually not more than a few dB. Some portion of this lost power is return loss reflected back to the power source; the rest of the lost power is dissipated in the filter. Typical band-pass filters for LTE bands have surface areas of 1.0 to 2.0 square millimeters. Although the total power dissipation in a filter may be small, the power density can be high given the small surface area. Further, the primary loss mechanisms in an acoustic filter are resistive losses in the conductor patterns and acoustic losses in the IDT fingers and piezoelectric material. Thus, the power dissipation in an acoustic filter is concentrated in the acoustic resonators. To prevent excessive temperature increase in the acoustic resonators, the heat due to the power dissipation must be conducted away from the resonators through the filter package to the environment external to the filter.

In traditional acoustic filters, such as surface acoustic wave (SAW) filters and bulk acoustic wave (BAW) filters, the heat generated by power dissipation in the acoustic resonators is efficiently conducted through the filter substrate and the metal electrode patterns to the package. In an XBAR device, the resonators are disposed on thin piezoelectric diaphragms that are inefficient heat conductors. The large majority of the heat generated in an XBAR device must be removed from the resonator via the IDT fingers and associated conductor patterns.

To minimize power dissipation and maximize heat removal, the IDT fingers and associated conductors should be formed from a material that has low electrical resistivity and high thermal conductivity. Some metals having both low resistivity and high thermal conductivity are listed in the following table:

		Electrical	Thermal
		resistivity	conductivity
	Metal	(10−6 Ω-cm)	(W/m-K)
	Silver	1.55	419
	Copper	1.70	385
	Gold	2.2	301
	Aluminum	2.7	210
	Molybdenum	5.34	138

Silver offers the lowest resistivity and highest thermal conductivity but is not a viable candidate for IDT conductors due to the lack of processes for deposition and patterning of silver thin films. Appropriate processes are available for copper, gold, aluminum, and molybdenum. Aluminum offers the most mature processes for use in acoustic resonator devices and potentially the lowest cost, but with higher resistivity and reduced thermal conductivity compared to copper and gold. For comparison, the thermal conductivity of lithium niobate is about 4 W/m-K, or about 2% of the thermal conductivity of aluminum. Aluminum also has good acoustic attenuation properties which helps minimize dissipation.

Molybdenum has very low acoustic attenuation compared to the other metals. The acoustic losses in molybdenum may be as little as 2% of the acoustic losses in equivalent aluminum electrodes. Molybdenum has the highest electrical resistivity and lowest thermal conductivity of the metals listed in the table above.

The electric resistance of the IDT fingers can be reduced, and the thermal conductivity of the IDT fingers can be increased, by increasing the cross-sectional area of the fingers to the extent possible. As described in conjunction with FIG. 4, unlike SAW or BAW, for XBAR there is little coupling of the primary acoustic mode to the IDT fingers. Changing the width and/or thickness of the IDT fingers has minimal effect on the primary acoustic mode in an XBAR device. This is a very uncommon situation for an acoustic wave resonator. However, the IDT finger geometry does have a substantial effect on coupling to spurious acoustic modes, such as higher order shear modes and plate modes that travel laterally in the piezoelectric diaphragm.

FIG. 10 is a chart 1000 illustrating the effect that IDT finger thickness can have on XBAR performance. The solid curve 1010 is a plot of the magnitude of the admittance of an XBAR device with the thickness of the IDT fingers tm=100 nm. The dashed curve 1030 is a plot of the magnitude of the admittance of an XBAR device with the thickness of the IDT fingers tm=250 nm. The dot-dash curve 1020 is a plot of the magnitude of the admittance of an XBAR device with the thickness of the IDT fingers tm=500 nm. The three curves 1010, 1020, 1030 have been offset vertically by about 1.5 units for visibility. The three XBAR devices are identical except for the thickness of the IDT fingers. The piezoelectric plate is lithium niobate 400 nm thick, the IDT electrodes are aluminum, and the IDT pitch is 4 microns. The XBAR devices with tm=100 nm and tm=500 nm have similar resonance frequencies, Q-factors, and electromechanical coupling. The XBAR device with tm=250 nm exhibits a spurious mode at a frequency near the resonance frequency, such that the resonance is effectively split into two low Q-factor, low admittance peaks separated by several hundred MHz. The XBAR with tm=250 nm (curve 1030) is not be useable in a filter.

FIG. 11 is a chart 1100 illustrating the effect that IDT finger width w can have on XBAR performance. The solid curve 1110 is a plot of the magnitude of the admittance of an XBAR device with the width of the IDT fingers w=0.74 micron. Note the spurious mode resonance at a frequency about 4.9 GHz, which could lie within the pass-band of a filter incorporating this resonator. Such effects could cause an unacceptable perturbation in the transmittance within the filter passband. The dashed curve 1120 is a plot of the magnitude of the admittance of an XBAR device with the width of the IDT fingers w=0.86 micron. The two resonators are identical except for the dimension w. The piezoelectric plate is lithium niobate 400 nm thick, the IDT electrodes are aluminum, and the IDT pitch is 3.25 microns. Changing w from 0.74 micron to 0.86 micron suppressed the spurious mode with little or no effect on resonance frequency and electromechanical coupling.

As previously described, molybdenum IDT fingers will have much lower acoustic losses than aluminum or copper IDT fingers. Although the electrical and thermal conductivity of molybdenum is low compared to other metals, molybdenum IDT electrodes can be as thick as required to achieve adequate thermal and electrical conductivity. FIG. 12 is a chart 1200 comparing the magnitude of the admittance of XBARs with molybdenum and aluminum IDT fingers. The solid line 1210 is a plot of the magnitude of admittance of a representative XBAR with molybdenum IDT fingers as a function of frequency. The dashed line 1220 is a plot of the magnitude of admittance of a representative XBAR with aluminum IDT fingers as a function of frequency. In both cases, the thickness of the IDT fingers is sufficient to reduce resistive losses to a negligible level, and the width of the IDT fingers is selected to minimize spurious effect between the resonance and anti-resonance frequencies. Comparison of the two plots shows that the XBAR with molybdenum IDT fingers (solid curve 1210) has sharper resonance and anti-resonance peaks than the XBAR with aluminum fingers (dashed curve 1220). Sharper resonance and anti-resonance peaks are indicative of significantly higher Q-factor. The higher Q-factor is primarily due to the lower acoustic losses in the molybdenum. The XBAR with molybdenum fingers (solid curve 1210) also has more and larger spurious effects, which may imply that acoustic losses damp or attenuate spurious effects in the XBAR with aluminum fingers (dashed curve 1220).

FIG. 13 is a chart 1300 showing an expanded portion of the chart 1200 of FIG. 12. The solid line 1310 is a plot of the magnitude of admittance of an XBAR with molybdenum IDT fingers as a function of frequency. The dashed line 1320 is a plot of the magnitude of admittance of an XBAR with aluminum IDT fingers as a function of frequency. Both curves show the admittance peak that occurs at the resonance frequency of the XBARs. Comparison of the two plots shows that the XBAR with molybdenum IDT fingers (solid curve 1310) has a sharper and higher admittance peak, which is indicative of significantly higher Q-factor, than the XBAR with aluminum fingers (dashed curve 1320). The higher Q-factor is primarily due to the lower acoustic losses in the molybdenum.

Given the complex dependence of spurious mode frequency and amplitude on diaphragm thickness ts, IDT metal thickness tm, IDT pitch p and IDT finger width w, the inventors undertook an empirical evaluation, using two-dimensional finite element modeling, of a large number of hypothetical XBAR resonators. For each combination of diaphragm thickness ts, IDT finger thickness tm, and IDT pitch p, the XBAR resonator was simulated for a sequence of IDT finger width w values. A figure of merit (FOM) was calculated for each value of w to estimate the negative impact of spurious modes. The FOM is calculated by integrating the negative impact of spurious modes across a defined frequency range. The FOM and the frequency range depend on the requirements of a particular filter. The frequency range typically includes the passband of the filter and may include one or more stop bands. Spurious modes occurring between the resonance and anti-resonance frequencies of each hypothetical resonator were given a heavier weight in the FOM than spurious modes at frequencies below resonance or above anti-resonance. Hypothetical resonators having a minimized FOM below a threshold value were considered potentially “useable”, which is to say probably having sufficiently low spurious modes for use in a filter. Hypothetical resonators having a minimized FOM above the threshold value were considered not useable.

U.S. patent application Ser. No. 16/578,811, entitled TRANSVERSELY-EXCITED FILM BULK ACOUSTIC RESONATORS FOR HIGH POWER APPLICATIONS, contains charts showing combinations of IDT pitch and IDT finger thickness that may provide useable resonators with aluminum and copper IDT conductors. FIG. 14 and FIG. 15 of the present patent are similar charts for molybdenum conductors.

FIG. 14 is a chart 1400 showing combinations of IDT pitch and IDT finger thickness that may provide useable resonators. This chart is based on two-dimensional simulations of XBARs with lithium niobate diaphragm thickness is =400 nm, molybdenum conductors, and front-side dielectric thickness tfd=0. XBARs with IDT pitch and thickness within shaded regions 1410, 1420, 1430 are likely to have sufficiently low spurious effects for use in filters. For each combination of IDT pitch and IDT finger thickness, the width of the IDT fingers was selected to minimize the FOM. The black dots 1450 represent XBARs used in a filter to be discussed subsequently. Resonators with acceptably low spurious effects exist for IDT finger thickness greater than or equal to 0.25 times the diaphragm thickness and less than or equal to 2.5 times the diaphragm thickness. However, low spurious effects are not the only requirement. Resonators for use in filters must also have acceptably low resistive losses and adequate removal of heat from the IDT and diaphragm. Resonators for use in filters will typically have IDT finger thickness greater than or equal to the diaphragm thickness and less than or equal to 2.5 times the diaphragm thickness.

As previously discussed, wide bandwidth filters using XBARs may use a thicker front-side dielectric layer on shunt resonators than on series resonators to lower the resonance frequencies of the shunt resonators with respect to the resonance frequencies of the series resonators. The front-side dielectric layer on shunt resonators may be as much as several hundred nm thicker than the front side dielectric on series resonators. For ease of manufacturing, it may be preferable that the same IDT finger thickness be used on both shunt and series resonators.

FIG. 15 is another chart 1500 showing combinations of IDT pitch and IDT finger thickness that may provide useable resonators. This chart is based on simulations of XBARs with lithium niobate diaphragm thickness=400 nm, molybdenum conductors, and tfd=100 nm (0.25 times the diaphragm thickness). XBARs having IDT pitch and thickness within shaded regions 1510, 1520, 1530 are likely to have sufficiently low spurious effects for use in filters. For each combination of IDT pitch and IDT finger thickness, the width of the IDT fingers was selected to minimize the FOM. The black dots 1550 represent XBARs used in a filter to be discussed subsequently. Usable resonators exist for IDT finger thickness greater than or equal to 0.25 times the diaphragm thickness and less than or equal to 2.5 times the diaphragm thickness, except that usable resonators do not exist for IDT thicknesses between about 0.4 times the diaphragm thickness to 0.65 times the diaphragm thickness.

Assuming that a filter is designed with no front-side dielectric layer on series resonators and 100 nm of front-side dielectric on shunt resonators, FIG. 14 and FIG. 15 jointly define the combinations of metal thickness and IDT pitch that result in useable resonators. Specifically, FIG. 14 defines useable combinations of metal thickness and IDT pitch for series resonators, and FIG. 15 defines useable combinations of metal thickness and IDT for shunt resonators. Since only a single metal thickness is desirable for ease of manufacturing, the overlap between the ranges defined in FIG. 14 and FIG. 15 defines the range of metal thicknesses for filter using a front-side dielectric to shift the resonance frequency of shunt resonator. Comparing FIG. 14 and FIG. 15, IDT molybdenum thickness between 0.65 times the diaphragm thickness and 2.5 times the diaphragm thickness provides at least two different useable pitch values for both series and shunt resonators. A larger minimum finger thickness may be dictated by consideration of resistive losses and heat removal. Resonators for use in filters will typically have IDT finger thickness greater than or equal to the diaphragm thickness and less than or equal to 2.5 times the diaphragm thickness.

FIG. 16 is a cross-sectional view of a portion of an XBAR with two-layer IDT fingers. FIG. 16 shows a cross section though a portion of a piezoelectric diaphragm 1610 and two IDT finger 1620. Each IDT finger 1620 has two metal layers 1630, 1640. The lower (as shown in FIG. 16) layer 1630 may be molybdenum or another metal with low acoustic loss, such as tungsten. The lower layer 1630 may be adjacent the diaphragm 1610 or separated from the diaphragm 1610 by a thin intermediate layer (not shown) used to improve adhesion between the diaphragm 1610 and the lower layer 1630. The upper layer 1640 may be a material such as aluminum, copper, or gold having high electrical and thermal conductivity. The use of a metal with low acoustic losses for the lower layer 1630 closest to the piezoelectric diaphragm 1610, where the acoustic stresses are greatest, reduces acoustic losses in the XBAR. The addition of an upper layer 1640 of high conductivity metal can reduce electrical losses and improve thermal conductivity. Having two metal layers 1630, 1640 allows the designer to have somewhat independent control of acoustic and electrical losses in the XBAR.

Further, the two metal layers need not have the same thickness or cross-sectional shape, as shown in Detail A and Detail B of FIG. 16. In Detail A, the second metal layer 1640A of each IDT finger has the form of a narrow rib on top of a thinner, wider first metal layer 1630A. In Detail B, each IDT finger has a “T” cross section form by a narrow first metal layer 1630B and a wider second metal layer 1640B. The cross-section shapes of the first and second metal layers are not limited to rectangular as shown in FIG. 16. Other cross-sectional shapes including trapezoidal and (at least for the second metal layer) triangular may be used and may be beneficial to minimize or control spurious acoustic modes.

FIG. 17 is a chart 1700 showing simulated performance of an exemplary high-power XBAR band-pass filter for band n79. The circuit of the band-pass filter is a five-resonator ladder filter, similar to that of FIG. 5. The XBARs are formed on a Z-cut lithium niobate plate. The thickness is of the lithium niobate plate is 400 nm. The substrate is silicon, the IDT conductors are molybdenum, the front-side dielectric, where present, is SiO2. The thickness tm of the IDT fingers is 500 nm, such that tm/ts=1.25. The other physical parameters of the resonators are provided in the following table (all dimensions are in microns; p=IDT pitch, w=IDT finger width, AP=aperture, L=length, and tfd=front-side dielectric thickness):

	Series Resonators	Shunt Resonators
Parameter	X1	X3	X5	X2	X4
p	4.02	4.2	3.1	4.475	4.275
w	0.875	0.95	.925	.925	.675
AP	41.2	55.4	19.4	44.5	45.8
L	520	250	235	350	325
tfd	0	0	0	0.100	0.100

The series resonators correspond to the filled circles 1350 in FIG. 13, and the shunt resonators correspond to the filled circles 1450 in FIG. 14.

Closing Comments

Throughout this description, the embodiments and examples shown should be considered as exemplars, rather than limitations on the apparatus and procedures disclosed or claimed. Although many of the examples presented herein involve specific combinations of method acts or system elements, it should be understood that those acts and those elements may be combined in other ways to accomplish the same objectives. With regard to flowcharts, additional and fewer steps may be taken, and the steps as shown may be combined or further refined to achieve the methods described herein. Acts, elements and features discussed only in connection with one embodiment are not intended to be excluded from a similar role in other embodiments.

As used herein, “plurality” means two or more. As used herein, a “set” of items may include one or more of such items. As used herein, whether in the written description or the claims, the terms “comprising”, “including”, “carrying”, “having”, “containing”, “involving”, and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of” and “consisting essentially of”, respectively, are closed or semi-closed transitional phrases with respect to claims. Use of ordinal terms such as “first”, “second”, “third”, etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements. As used herein, “and/or” means that the listed items are alternatives, but the alternatives also include any combination of the listed items.

Claims

1. An acoustic resonator device comprising: a piezoelectric plate, a portion of the piezoelectric plate forming a diaphragm, a thickness of the piezoelectric plate is greater than or equal to 300 nm and less than or equal to 500 nm; andan interdigital transducer (IDT) with interleaved fingers of the IDT on the diaphragm, the piezoelectric plate and the IDT configured such that a radio frequency signal applied to the IDT excites a primary shear acoustic mode in the diaphragm.

2. The acoustic resonator device of claim 1, wherein the interleaved fingers of the IDT are substantially molybdenum.

3. The acoustic resonator device of claim 1, further comprising a first dielectric layer between the fingers of the IDT.

4. The acoustic resonator device of claim 3, further comprising a second dielectric layer over the first dielectric layer.

5. The acoustic resonator device of claim 4, wherein a material of the first dielectric layer is different from a material of the second dielectric layer.

6. The acoustic resonator device of claim 1, wherein a thickness of the interleaved fingers of the IDT is greater than or equal to 0.25 times the thickness of the piezoelectric plate and less than or equal to 2.5 times the thickness of the piezoelectric plate.

7. The acoustic resonator device of claim 6, wherein the thickness of the interleaved fingers of the IDT is greater than or equal to 0.65 times the thickness of the piezoelectric plate and less than or equal to 2.5 times the thickness of the piezoelectric plate.

8. The acoustic resonator device of claim 7, wherein the thickness of the interleaved fingers of the IDT is greater than or equal to the thickness of the piezoelectric plate and less than or equal to 2.5 times the thickness of the piezoelectric plate.

9. The acoustic resonator device of claim 1, wherein a pitch of the interleaved fingers of the IDT is greater than or equal to 6 times the thickness of the piezoelectric plate and less than or equal to 12.5 times the thickness of the piezoelectric plate.

10. The acoustic resonator device of claim 1, wherein a direction of acoustic energy flow of the primary acoustic mode is substantially normal to the front and back surfaces of the diaphragm.

11. A filter device, comprising: at least one piezoelectric plate, portions of the at least one piezoelectric plate forming one or more diaphragms, a thickness of the at least one piezoelectric plate is greater than or equal to 300 nm and less than or equal to 500 nm; anda conductor pattern including a plurality of interdigital transducers (IDTs) of a respective plurality of acoustic resonators, interleaved fingers of each of the plurality of IDTs on one of the one or more diaphragms, the at least one piezoelectric plate and all of the IDTs configured such that respective radio frequency signal applied to each IDT excite respective shear primary acoustic modes in the respective diaphragm.

12. The filter device of claim 11, wherein the interleaved fingers of all of the plurality of IDTs are substantially molybdenum.

13. The filter device of claim 11, further comprising a first dielectric layer between the fingers of at least some of the IDTs.

14. The filter device of claim 13, further comprising a second dielectric layer deposited over the first dielectric layer.

15. The filter device of claim 14, wherein a material of the first dielectric layer is different from a material of the second dielectric layer.

16. The filter device of claim 11, wherein the interleaved fingers of all of the plurality of IDTs have a common finger thickness, which is greater than or equal to 0.25 times the thickness of the at least one piezoelectric plate and less than or equal to 2.5 times the thickness of the piezoelectric plate.

17. The filter device of claim 16, wherein the common finger thickness is greater than or equal to 0.65 times the thickness of the at least one piezoelectric plate and less than or equal to 2.5 times the thickness of the piezoelectric plate.

18. The filter device of claim 17, wherein the common finger thickness is greater than or equal to the thickness of the at least one piezoelectric plate and less than or equal to 2.5 times the thickness of the piezoelectric plate.

19. The filter device of claim 11, wherein respective pitches of the interleaved fingers of all of the plurality of IDTs are greater than or equal to 6 times the thickness of the at least one piezoelectric plate and less than or equal to 12.5 times the thickness of the piezoelectric plate.

20. The filter device of claim 11, wherein a direction of acoustic energy flow of the respective primary acoustic modes excited by all of the IDTs is substantially normal to the front and back surfaces of the diaphragm.