Abstract: In an elastic wave device, a first piezoelectric substrate and a second piezoelectric substrate are joined to each other with a joining portion so as to face each other across a cavity. A first set of a plurality of filters located on a facing surface of the first piezoelectric substrate and a second set of a plurality of filters located on a facing surface of the second piezoelectric substrate define a plurality of pairs of filters and face each other across the cavity. An absolute value of a difference between center frequencies of a filter of the first set of filters and a filter of the second set of filters in each pair of filters is larger than a minimum value among absolute values of differences between center frequencies of pairs of filters selected from a group including the first set of filters and the second set of filters.

Abstract: In one embodiment of the invention, a semiconductor optical amplifier (SOA) in a laser ring is chosen to provide low polarization-dependent gain (PDG) and a booster semiconductor optical amplifier, outside of the ring, is chosen to provide high polarization-dependent gain. The use of a semiconductor optical amplifier with low polarization-dependent gain nearly eliminates variations in the polarization state of the light at the output of the laser, but does not eliminate the intra-sweep variations in the polarization state at the output of the laser, which can degrade the performance of the SS-OCT system.

Abstract: A MEMS array structure including a plurality of bulk mode resonators may include at least one resonator coupling section disposed between the plurality of bulk mode resonators. The plurality of resonators may oscillate by expansion and/or contraction in at least one direction/dimension. The MEMS array structure may include a plurality of sense electrodes and drive electrodes spaced apart from the plurality of bulk mode resonators by a gap. Each of at least one of the plurality of bulk mode resonators may be mechanically coupled to a substrate via or approximately at a respective at least one nodal point.

Abstract: A contour mode micromechanical piezoelectric resonator. The resonator has a bottom electrode; a top electrode; and a piezoelectric layer disposed between the bottom electrode and the top electrode. The piezoelectric resonator has a planar surface with a cantilevered periphery, dimensioned to undergo in-plane lateral displacement at the periphery. The resonator also includes means for applying an alternating electric field across the thickness of the piezoelectric resonator. The electric field is configured to cause the resonator to have a contour mode in-plane lateral displacement that is substantially in the plane of the planar surface of the resonator, wherein the fundamental frequency for the displacement of the piezoelectric resonator is set in part lithographically by the planar dimension of the bottom electrode, the top electrode or the piezoelectric layer.

Abstract: A nano electromechanical integrated circuit filter and method of making. The filter comprises a silicon substrate; a sacrificial layer; a device layer including at least one resonator, wherein the resonator includes sub-micron excitable elements and wherein the at least one resonator possess a fundamental mode frequency as well as a collective mode frequency and wherein the collective mode frequency of the at least one resonator is determined by the fundamental frequency of the sub-micron elements.

Abstract: A resonator, an elastic wave transmission element and a method for fabricating the transmission element are provided. The elastic wave transmission element has a first side and a second side. The elastic wave transmission element includes a plurality of structures sequentially arranged along a direction from the first side toward the second side. Each of the structures has a different defect which is different to each other. The impedance of the structures decreases gradually along the direction. As such, the elastic wave transmission element has an impedance match function.

Abstract: A nano-resonator device comprising at least one fixed element and at least one mobile element with respect to the fixed element, first electromagnetic means, integrated or fixed on the fixed element, and second electromagnetic means, integrated or fixed on the mobile element, to generate an oscillating movement of the mobile element.

Abstract: A resonator comprising a beam formed from a first material having a first Young's modulus and a first temperature coefficient of the first Young's modulus, and a second material having a second Young's modulus and a second temperature coefficient of the second Young's modulus, a sign of the second temperature coefficient being opposite to a sign of the first temperature coefficient at least within operating conditions of the resonator, wherein the ratio of the cross sectional area of the first material to the cross sectional area of the second material varies along the length of the beam, the cross sectional areas being measured substantially perpendicularly to the beam.

Abstract: A resonator comprising a resonator body and actuation electrodes for driving the resonator into a resonant mode, in which the resonator body vibrates parallel to a first axis. The resonator comprises means to apply a voltage to the resonator in a direction perpendicular to the first axis direction. This serves to shift the frequency of resonant modes other than the principal resonant mode, and this allows increased amplitude of output signal from the resonator.

Abstract: A resonator comprises a resonator mass (34), a first connector (30) on a first side of the mass connected between the resonator mass and a first fixed mounting and a second connector (32) on a second, opposite, side of the mass connected between the resonator mass and a second fixed mounting. Drive means drives the mass (34) into a resonant mode in which it oscillates in a sideways direction, thereby compressing one of the first and second connectors while extending the other of the first and second connectors.

Abstract: Crystal devices are disclosed, of which an exemplary device includes a crystal frame comprising a crystal vibrating piece having an electrode pattern and an outer frame supporting the crystal vibrating piece. The device also includes a crystal package base including at least one connection electrode formed on a first main surface and at least one external electrode formed on a second main surface, wherein the second main surface is opposite the first main surface. The crystal frame and crystal base are layered together with a lid wafer to form a 3-layer sandwich. The layers of the sandwich are bonded together by siloxane bonding, which results in the connection electrodes contacting the electrode pattern on the crystal vibrating piece.

Abstract: A microelectromechanical systems (MEMS) device includes a tuning electrode, a drive electrode, and a resonator. The resonator is anchored to a substrate and is configured to resonate in response to a signal on the drive electrode. The MEMS device includes a tuning plate coupled to the resonator and positioned above the tuning electrode. The tuning plate is configured to adjust a resonant frequency of the resonator in response to a voltage difference between the resonator and the tuning electrode. In at least one embodiment of the MEMS device, the tuning plate and the tuning electrode are configured to adjust the resonant frequency of the resonator substantially independent of the signal on the drive electrode.

Abstract: A dielectric ceramic which is capable of stably having a desired relative dielectric constant (?r), while having high Q value and good temperature coefficient of the resonance frequency. Specifically disclosed is a dielectric ceramic which contains lanthanum, magnesium, calcium and titanium, and when the compositional formula of the components is expressed as ?La2Ox.?MgO.?CaO.?TiO2 (wherein 3?x?4), the molar ratios ?, ?, ? and ? satisfy the formulae below. The dielectric ceramic also contains aluminum in an amount of 5% by mass or less (excluding 0% by mass) in terms of oxides relative to 100% by mass of the above-mentioned components. 0.160???0.270 0.050???0.100 0.260???0.390 0.360???0.

Abstract: A method for manufacturing a quartz crystal unit comprises the steps of forming a quartz crystal tuning fork resonator vibratable in a flexural mode of an inverse phase and having a quartz crystal tuning fork base and first and second quartz crystal tuning fork tines connected to the quartz crystal tuning fork base, forming at least one groove having at least three stepped portions in at least one of opposite main surfaces of each of first and second quartz crystal tuning fork tines, disposing an electrode on a surface of one of the at least three stepped portions of the at least one groove and an electrode on one of opposite side surfaces of each of the first and second quartz crystal tuning fork tines, mounting the quartz crystal tuning fork resonator on a mounting portion of a case, and connecting a lid to the case to cover an open end of the case, wherein the step of forming the quartz crystal tuning fork base and the first and second quartz crystal tuning fork tines is performed before the step of formin

Abstract: One embodiment of the present invention sets forth a method for decreasing a temperature coefficient of frequency (TCF) of a MEMS resonator. The method comprises lithographically defining slots in the MEMS resonator beams and filling the slots with oxide. By growing oxide within the slots, the amount of oxide growth on the outside surfaces of the MEMS resonator may be reduced. Furthermore, by situating the slots in the areas of large flexural stresses, the contribution of the embedded oxide to the overall TCF of the MEMS resonator is increased, and the total amount of oxide needed to decrease the overall TCF of the MEMS resonator to a particular target value is reduced. As a result, the TCF of the MEMS resonator may be reduced in a manner that is more effective relative to prior art approaches.

Abstract: A high Q resonator device is disclosed. The device includes a substrate, a resonator tethered to the substrate by a tether, and an acoustic reflector etched into the substrate and positioned proximate the tether so as to reflect a substantial portion of planar acoustic energy received from the tether back into the tether.

Abstract: A microelectromechanical resonator may include one or more resonator masses that oscillates in a bulk mode and that includes a first plurality of regions each having a density, and a second plurality of regions each having a density, the density of each of the second plurality of regions differing from the density of each of the first plurality of regions. The second plurality of regions may be disposed in a non-uniform arrangement. The oscillation may include a first state in which the resonator mass is contracted, at least in part, in a first and/or a second direction, and expanded, at least in part, in a third and/or a fourth direction, the second direction being opposite the first direction, the fourth direction being opposite the third direction.

Abstract: Method and apparatus for lowering capacitively-transduced resonator impedance within micromechanical resonator devices. Fabrication limits exist on how small the gap spacing can be made between a resonator and the associated input and output electrodes in response to etching processes. The present invention teaches a resonator device in which these gaps are then fully, or more preferably partially filled with a dielectric material to reduce the gap distance. A reduction of the gap distance substantially lowers the motional resistance of the micromechanical resonator device and thus the capacitively-transduced resonator impedance. Micromechanical resonator devices according to the invention can be utilized in a wide range of UHF devices, including integration within ultra-stable oscillators, RF filtering devices, radar systems, and communication systems.

Abstract: System and method for a microelectromechanical system (MEMS) is disclosed. A preferred embodiment comprises a first anchor region, a vibrating MEMS structure fixed to the first anchor region, a first electrode adjacent the vibrating MEMS structure, a second electrode adjacent the vibrating MEMS structure wherein the vibrating MEMS structure is arranged between the first and the second electrode.

Abstract: An integrated MEMS device is disclosed. The system comprises a MEMS resonator; and a MEMS device coupled to a MEMS resonator. The MEMS resonator and MEMS device are fabricated on a common substrate so that certain characteristics of the MEM resonator and MEMS device track each other as operating conditions vary.

Abstract: A resonator includes a substantially disk shaped portion having a plurality of axes of symmetry and is configured to resonate in a plurality of resonant modes by symmetrically deforming about the plurality of axes of symmetry.

Abstract: A MEMS resonator, comprising a planar resonator body formed of two different materials with opposite sign temperature coefficient of Young's modulus. A first portion of one material extends across the full thickness of the resonator body. This provides a design which allows reduced temperature drift.

Abstract: A MEMS notch filter comprises a frame; a movable mass; resilient members connecting the mass to the frame; electrodes connected to the frame; and a comb drive connected to the frame and the mass which operates to drive the mass, wherein the filter is adapted to oscillate at least one resonant frequency. A mechanism is positioned below the mass, wherein the mechanism is adapted to maintain a neutral position of the mass and to expel fluid onto the mass. The comb drive is adapted to receive an applied voltage signal from the electrodes. This voltage signal is applied to the comb drive at a resonant frequency of the notch filter and induces the mass to oscillate in a geometric plane of the frame (or optionally in some other resonant mode); resulting in dissipation of energy and voltage attenuation. Other voltage components not at the notch frequency are not attenuated.

Abstract: A microelectromechanical filter is provided. The microelectromechanical filter includes an input electrode, an output electrode, one or several piezoelectric resonators, one or several high quality factor resonators, and one or several coupling beams. The input electrode and the output electrode are disposed on the piezoelectric resonators. The high quality factor resonator is silicon or of piezoelectric materials, and there is no metal electrode on top of the resonator. The coupling beam is connected between the piezoelectric resonator and the high quality factor resonator. The coupling beam transmits an acoustic wave among the resonators, and controls a bandwidth of filter. The microelectromechanical filter with low impedance and high quality factor fits the demand for next-generation communication systems.

Abstract: A method for manufacturing a quartz crystal unit comprises the steps of adjusting an oscillation frequency of a quartz crystal tuning fork resonator that is vibratable in a flexural mode of an inverse phrase and that has first and second quartz crystal tuning fork tines, forming at least one groove in each of two of opposite main surfaces of each of first and second quartz crystal tuning fork tines, disposing an electrode on a surface of the at least one groove formed in each of two of the opposite main surfaces and each of two of opposite side surfaces of each of the first and second quartz crystal tuning fork tines so that the electrodes of the grooves of the first quartz crystal tuning fork tine are connected to the electrodes of the side surfaces of the second quartz crystal tuning fork tine and the electrodes of the grooves of the second quartz crystal tuning fork tine are connected to the electrodes of the side surfaces of the first quartz crystal tuning fork tine, the quartz crystal tuning fork resonat

Abstract: A tunable nanostructure such as a nanotube is used to make an electromechanical oscillator. The mechanically oscillating nanotube can be provided with inertial clamps in the form of metal beads. The metal beads serve to clamp the nanotube so that the fundamental resonance frequency is in the microwave range, i.e., greater than at least 1 GHz, and up to 4 GHz and beyond. An electric current can be run through the nanotube to cause the metal beads to move along the nanotube and changing the length of the intervening nanotube segments. The oscillator can operate at ambient temperature and in air without significant loss of resonance quality. The nanotube is can be fabricated in a semiconductor style process and the device can be provided with source, drain, and gate electrodes, which may be connected to appropriate circuitry for driving and measuring the oscillation. Novel driving and measuring circuits are also disclosed.

Abstract: System and method for a microelectromechanical system (MEMS) is disclosed. A preferred embodiment comprises a first anchor region, a vibrating MEMS structure fixed to the first anchor region, a first electrode adjacent the vibrating MEMS structure, a second electrode adjacent the vibrating MEMS structure wherein the vibrating MEMS structure is arranged between the first and the second electrode.

Abstract: A tunable MEMS filter is disclosed, having a substrate with first and second isolated substrate areas. First and second anchor points are coupled to the substrate. A base is coupled to the first and second anchor points by first and second coupling beams, respectively. A dielectric layer is coupled to the base. An input conductor is coupled to the at least one dielectric layer. An output conductor is coupled to the at least one dielectric layer. A method of tuning a center frequency and a bandwidth of a MEMS resonator filter is also disclosed. A first bias voltage is adjusted between a base layer and input and output conductor layers. A second bias voltage is adjusted between the base layer and isolated substrate areas. The center frequency and the bandwidth are determined until the adjustments to the bias voltages provide a desired center frequency and a desired bandwidth.

Abstract: Micro-electromechanical acoustic resonators include a substrate having a cavity therein and a resonator body suspended over the cavity. The resonator body is anchored on opposing sides thereof (by support beams) to first and second portions of the substrate. These first and second portions of the substrate, which extend over the cavity as first and second ledges, respectively, each have at least one perforation therein disposed over the cavity. These perforations may be open or filled. The first and second ledges are formed of a first material (e.g., silicon) and the first and second ledges are filled with a second material having a relatively high acoustic impedance relative to the first material. This second material may include a material selected from a group consisting of tungsten (W), copper (Cu), molybdenum (Mo).

Abstract: A resonant circuit includes a substrate; a MEMS resonator including a fixed electrode and a movable electrode formed above the substrate and having a first terminal and a second terminal, the movable electrode having a movable portion opposing at least a part of the fixed electrode; a first input-output terminal connected to the first terminal connected to one of the fixed electrode and the movable electrode of the MEMS resonator; a second input-output terminal connected to the second terminal connected to an other one of the fixed electrode and the movable electrode of the MEMS resonator; a voltage applying unit supplying a potential to at least the first terminal to apply a bias voltage between the first and the second terminals; and a variable capacitance connected between the first terminal and the first input-output terminal to allow a capacitance value to be changed by a change in a potential difference between opposite ends of the variable capacitance.

Abstract: A groove is formed on a handling member, on a face to be fixed to an element, the groove making up a portion of a channel that externally communicates in the state of being fixed to the element. In the fixing process of the substrate and then handling member, the handling member is fixed so that the edge direction of the vibrating membrane supporting portion and the edge direction of the groove of the handling member intersect. Thus, the probability that a membrane will break during handling or processing of the substrate is reduced, and the handling member can be quickly removed from the substrate.

Abstract: The invention relates to design of micromechanical resonators and, more precisely, to the design of microelectromechanical systems (MEMS) resonators. The invention provides an improved design structure for a microelectromechanical systems (MEMS) resonator in which the width of the spring elements (3), (23-24), (27-30) is greater than the width of the electrode fingers (5-9), (25-26), (31-34), said widths specifically dimensioned so that the sensitivity of the resonant frequency change with respect to dimensional manufacturing variations d(??0/?0)/d? approaches zero. The improved structure is frequency robust to manufacturing variations and enables reliable frequency referencing with good performance, particularly in small size solutions.

Abstract: A handling member is prepared that provides a channel that can withstand subsequent back face processing as to a substrate having elements made up of a substrate and a membrane, and the handling member is fixed to the substrate so that at least a portion within the elements are supported by the handling member. This provides a manufacturing method wherein the physical strength of an element at the time of manufacturing an electromechanical transducing apparatus is strengthened, and the handling member is easily detached in a short time after processing of the element.

Abstract: A groove is formed on a handling member, on a face to be fixed to an element, the groove making up a portion of a channel that externally communicates in the state of being fixed to the element. The handling member is fixed so that the cleavage direction of the vibrating membrane and the edge direction of the groove of the handling member intersect. Thus, the probability that a membrane will break during handling or processing of the substrate is reduced, and the handling member can be quickly removed from the substrate.

Abstract: A micro-electromechanical resonator includes an electrically-trimmed resonator body having at least one stiffness-enhanced semiconductor region therein containing metal-semiconductor lattice bonds. These metal-semiconductor lattice bonds may be gold-silicon lattice bonds and/or aluminum-silicon lattice bonds. A surface of the resonator body is mass-loaded with the metal, which may be provided by a plurality of spaced-apart metal islands. These metal islands may be aligned along a longitudinal axis of the resonator body. A size of the at least one stiffness-enhanced polycrystalline semiconductor region may be sufficient to yield an increase in resonant frequency of the resonator body relative to an otherwise equivalent resonator having a single crystal resonator body that is free of mass-loading by the metal.

Abstract: A microelectromechanical (MEMs) resonator includes a concave bulk acoustic resonator (CBAR). One embodiment of a CBAR includes a substrate and a resonator body suspended over the substrate by a pair of fixed supports that attach to first and second opposing ends of the resonator body. The resonator body has a first concave-shaped side extending between the first and second ends of the resonator body and a second concave-shaped side extending opposite the first concave-shaped side. The resonator body may be configured to have a minimum spacing of ?/2 between the first and second concave-shaped sides, where ? is a wavelength associated with a resonant frequency of said resonator body.

Abstract: A dual in-situ mixing approach for extended tuning range of resonators. In one embodiment, a dual in-situ mixing device tunes an input radio-frequency (RF) signal using a first mixer, a resonator body, and a second mixer. In one embodiment, the first mixer is coupled to receive the input RF signal and a local oscillator signal. The resonator body receives the output of the first mixer, and the second mixer is coupled to receive the output of the resonator body and the local oscillator signal to provide a tuned output RF signal as a function of the frequency of local oscillator signal.

Abstract: The invention relates to a MEMS resonator comprising a first electrode, a movable element (48) comprising a second electrode, the movable element (48) at least being movable towards the first electrode, the first electrode and the movable element (48) being separated by a gap (46, 47) having sidewalls. According to the invention, the MEMS resonator is characterized in that the gap (46, 47) has been provided with a dielectric layer (60) on at least one of the sidewalls.

Abstract: Phononic crystal wave structures and methods of making same are discussed in this application. According to some embodiments, an acoustic structure can generally comprise a phononic crystal slab configured as a micro/nano-acoustic wave medium. The phononic crystal slab can define an exterior surface that bounds an interior volume, and the phononic crystal slab can be sized and shaped to contain acoustic waves within the interior volume of the phononic crystal slab. The phononic crystal slab can comprise at least one defect portion. The defect portion can affect periodicity characteristics of the phononic crystal slab. The defect portion can be shaped and arranged to enable confinement and manipulation of acoustic waves through the defect portion(s) of phononic crystal slab. Other aspects, features, and embodiments are also claimed and described.

Abstract: A resonator includes a translator, a stator, and a control circuit. The control circuit is configured to provide first and second translator voltages and first through third stator voltages, wherein the translator is configured to move with respect to the stator at a resonant frequency of the resonator in response to the control circuit.

Abstract: An array of micromechanical oscillators have different resonant frequencies based on their geometries. In one embodiment, a micromechanical oscillator has a resonant frequency defined by an effective spring constant that is modified by application of heat. In one embodiment, the oscillator is disc of material supported by a pillar of much smaller diameter than the disc. The periphery of the disc is heated to modify the resonant frequency (or equivalently the spring constant or stiffness) of the disc. Continuous control of the output phase and frequency may be achieved when the oscillator becomes synchronized with an imposed sinusoidal force of close frequency. The oscillator frequency can be detuned to produce an easily controlled phase differential between the injected signal and the oscillator feedback. A phased array radar may be produced using independent phase controllable oscillators.

Abstract: A nano-resonator including a beam having a composite structure may include a silicon carbide beam and/or a metal conductor. The metal conductor may be vapor-deposited on the silicon carbide beam. The metal conductor may have a density lower than a density of the silicon carbide beam.

Abstract: The invention relates to MEMS devices. In one embodiment, a micro-electromechanical system (MEMS) device comprises a resonator element having a circumference, an anchor region, and a plurality of beam elements coupling the anchor region and the resonator element. Further embodiments comprise additional devices, systems and methods.

Abstract: A resonant circuit includes a substrate; a MEMS resonator including a fixed electrode and a movable electrode formed above the substrate and having a first terminal and a second terminal, the movable electrode having a movable portion opposing at least a part of the fixed electrode; and a voltage applying unit applying a bias voltage to the MEMS resonator, the voltage applying unit including a voltage divider circuit that includes a compensation resistance formed of a same layer as that of the movable portion to allow a resistance value to be changed by a thickness of the layer and a reference resistance formed of a layer different from that of the movable portion and connected to the compensation resistance to output a junction potential between the compensation resistance and the reference resistance to at least one of the first and the second terminals of the MEMS resonator.

Abstract: A mechanical micro system comprising a flexible bending beam extending along a direction, and at least one magnetic element for creating a magnetic field. The flexible beam includes: a first circuit having a first topology for generating, in response to one current flowing through the first circuit, a force having an effect on the beam at one particular place so as to cause a first vibratory mode; a second circuit having a second topology for generating, in response to one current flowing through the second circuit, a force having an effect on the beam at one particular second position so as to cause a second vibratory mode.

Abstract: An object is to provide a resonator and a vibrator with a high Q value in which dissipation of vibration energy in vibration of the vibrator is small, and a thickness of a support part of the vibrator of a beam structure is made thicker than a thickness of the vibrator and the support part is formed in axisymmetry with respect to a length direction of a beam. By this configuration, brittleness of the support part is improved and loss of vibration energy from the support part is reduced and also loss of vibration energy resulting from surface roughness of a surface of the vibrator can be reduced, so that a resonator having a high Q value can be provided.

Abstract: A ladder type filter includes series resonators S1˜S4 connected in series between an input terminal In and an output terminal Out, parallel resonators P1˜P3 connected in parallel between the input terminal In and the output terminal Out, a resonator RP connected in series with the series resonators S1˜S4 between the input terminal and the output terminal, the resonator RP having a resonance frequency lower than resonance frequencies of the series resonators S1˜S4, and an inductor Lp connected in parallel with the resonator. According to the present ladder filter, signals having frequencies away from the pass band can be suppressed by an attenuation pole formed by the inductor. It is further possible to suppress the insertion loss in the pass band by the resonator.

Abstract: An RF device is provided. The RF device includes a vibratile carbon nanotube having a nanotube natural frequency (f0), a negative electrode fixed to a first end of the carbon nanotube, a vibratile tuning electrode having a variable resonance frequency and facing a second end of the carbon nanotube, and a positive electrode electrically connected to a first end of the tuning electrode. A second end of the tuning electrode is adjacent to the second end of the carbon nanotube, and the carbon nanotube vibrates at a carrier frequency according to an external electromagnetic wave having the carrier frequency, and the tuning electrode having variable resonance frequency characteristics amplifies distance variation between the second end of the carbon nanotube and the second end of the tuning electrode to increase an electron emission sensitivity according to field emission.

Abstract: A micro-electro-mechanical transducer (such as a cMUT) is disclosed. The transducer has a base, a spring layer placed over the base, and a mass layer connected to the spring layer through a spring-mass connector. The base includes a first electrode. The spring layer or the mass layer includes a second electrode. The base and the spring layer form a gap therebetween and are connected through a spring anchor. The mass layer provides a substantially independent spring mass contribution to the spring model without affecting the equivalent spring constant. The mass layer also functions as a surface plate interfacing with the medium to improve transducing performance. Fabrication methods to make the same are also disclosed.

Abstract: An SH wave type surface acoustic wave device includes a piezoelectric substrate and an IDT electrode provided on the piezoelectric substrate and constituted of Al or an alloy mainly containing Al and that uses a SH wave as an excitation wave. The piezoelectric substrate is a crystal plate in which a cut angle ? of a rotary Y cut quartz substrate is set in a range of ?64.0°<?<?49.3° in a counter-clockwise direction from a crystal axis Z and in which a surface acoustic wave propagation direction is set at 90°±5° with respect to a crystal axis X. An electrode film thickness H/? standardized by a wavelength of the IDT electrode is 0.04<H/?<0.12, where ? is a wavelength of the surface acoustic wave to be excited, and a main surface of the piezoelectric substrate is etched by a thickness of 0.002 ?m or more.