Acoustic resonators and filter devices, and method of making acoustic resonators and filter devices. An acoustic resonator includes a substrate having a surface and a piezoelectric plate having front and back surfaces, the back surface attached to the surface of the substrate except for a portion of the piezoelectric plate forming a diaphragm that spans a cavity in the substrate. An interdigital transducer (IDT) is formed on the front surface of the piezoelectric plate such that interleaved fingers of the IDT are disposed on the diaphragm. The interleaved fingers have an irregular hexagon cross-sectional shape.

A substrate for a surface acoustic wave device or bulk acoustic wave device, comprising a support substrate and an piezoelectric layer on the support substrate, wherein the support substrate comprises a semiconductor layer on a stiffening substrate having a coefficient of thermal expansion that is closer to the coefficient of thermal expansion of the material of the piezoelectric layer than that of silicon, the semiconductor layer being arranged between the piezoelectric layer and the stiffening substrate.

To provide a vibrator made of a piezoelectric crystal having a larger electromechanical coupling coefficient and a more satisfactory frequency-temperature characteristic than those of quartz, a vibrating piece (101) is made of a Ca.sub.3Ta(Ga.sub.1-xAl.sub.x).sub.3Si.sub.2O.sub.14 single crystal (0<x≤1). In the single crystal, letting θ be a rotation angle from an X-Z plane about an X-axis serving as a rotation axis, 18x+17.5≤θ≤24x+24.5 is set. In addition, the vibrating piece (101) is made of a Ca.sub.3Nb(Ga.sub.1-xAl.sub.x).sub.3Si.sub.2O.sub.14 single crystal (0<x≤1). In the single crystal of this arrangement, letting θ be a rotation angle from an X-Z plane about an X-axis serving as a rotation axis, 25x+23.083≤θ≤32x+26.167 is set.

To provide a vibrator made of a piezoelectric crystal having a larger electromechanical coupling coefficient and a more satisfactory frequency-temperature characteristic than those of quartz, a vibrating piece (101) is made of a Ca.sub.3Ta(Ga.sub.1-xAl.sub.x).sub.3Si.sub.2O.sub.14 single crystal (0<x≤1). In the single crystal, letting θ be a rotation angle from an X-Z plane about an X-axis serving as a rotation axis, 18x+17.5≤θ≤24x+24.5 is set. In addition, the vibrating piece (101) is made of a Ca.sub.3Nb(Ga.sub.1-xAl.sub.x).sub.3Si.sub.2O.sub.14 single crystal (0<x≤1). In the single crystal of this arrangement, letting θ be a rotation angle from an X-Z plane about an X-axis serving as a rotation axis, 25x+23.083≤θ≤32x+26.167 is set.

A vibration element includes a base and a vibrating arm extending from the base. The vibrating arm includes an arm positioned between the base and a weight. A weight film is disposed on the weight. The weight has a first principal surface and a second principal surface in a front and back relationship with respect to a center plane of the arm. A center of gravity of the weight is located between the first principal surface and the center plane of the arm. A center of gravity of the weight film is located between the second principal surface and the center plane of the arm.

A vibration element includes a base and a vibrating arm extending from the base. The vibrating arm includes an arm positioned between the base and a weight. A weight film is disposed on the weight. The weight has a first principal surface and a second principal surface in a front and back relationship with respect to a center plane of the arm. A center of gravity of the weight is located between the first principal surface and the center plane of the arm. A center of gravity of the weight film is located between the second principal surface and the center plane of the arm.

Provided is an oscillator including: a resonator; a first circuit device electrically coupled to the resonator; and a second circuit device. The first circuit device generates a first clock signal by causing the resonator to oscillate, and performs first temperature compensation processing for temperature compensating a frequency of the first clock signal. The second circuit device receives the first clock signal from the first circuit device, generates a second clock signal based on the first clock signal, and performs second temperature compensation processing for temperature compensating a frequency of the second clock signal.

Provided is an oscillator including: a resonator; a first circuit device electrically coupled to the resonator; and a second circuit device. The first circuit device generates a first clock signal by causing the resonator to oscillate, and performs first temperature compensation processing for temperature compensating a frequency of the first clock signal. The second circuit device receives the first clock signal from the first circuit device, generates a second clock signal based on the first clock signal, and performs second temperature compensation processing for temperature compensating a frequency of the second clock signal.

A microelectromechanical resonator device is provided having two-dimensional resonant rods. The resonator device has a piezoelectric layer formed with a plurality of alternating rods and trenches. A bottom electrode is in contact with a bottom surface of the piezoelectric layer. A top electrode metal grating of conductive strips is aligned in contact with corresponding rods of the piezoelectric layer.

A microelectromechanical resonator device is provided having two-dimensional resonant rods. The resonator device has a piezoelectric layer formed with a plurality of alternating rods and trenches. A bottom electrode is in contact with a bottom surface of the piezoelectric layer. A top electrode metal grating of conductive strips is aligned in contact with corresponding rods of the piezoelectric layer.