A resonator is provided that suppresses frequency variations with etching without decreasing the strength of vibration arms. The resonator includes a base portion, a first vibration portion extending from the base portion in a first direction and having a first width, and a second vibration portion extending from the base portion in the first direction with a first gap between the first and second vibration portions and having the first width. The first and second vibration portions perform out-of-plane bending vibration with opposite phases at a predetermined frequency. The predetermined frequency varies in accordance with the first width and the first gap. The ratio of the first gap to the first width is within a range that causes an absolute value of rates of variations in the predetermined frequency with respect to variations in the first width and in the first gap to be not more than about 100 ppm.

An electric measurement circuit possesses an electrical reaction leg for forming an oscillator from a resonator, and furthermore possesses a measurement leg the input of which is supplied by the electrical reaction leg. The measurement leg contains an adjustable phase shifter so that an additional excitation force that is applied to the resonator in the measurement leg can be adjusted in phase quadrature with respect to an excitation force that is applied to the resonator in the electrical reaction leg. Such an electrical measurement circuit is particularly suitable for forming a photoacoustic gas detector.

A resonant member of a MEMS resonator oscillates in a mechanical resonance mode that produces non-uniform regional stresses such that a first level of mechanical stress in a first region of the resonant member is higher than a second level of mechanical stress in a second region of the resonant member. A plurality of openings within a surface of the resonant member are disposed more densely within the first region than the second region and at least partly filled with a compensating material that reduces temperature dependence of the resonant frequency corresponding to the mechanical resonance mode.

According to one embodiment, a vibration device includes a first movable unit including first and second movable portions arranged in a direction parallel to a first axis and enabled to vibrate in the direction parallel to the first axis, a second movable unit enabled to vibrate in a direction parallel to a second axis perpendicular to the first axis, and a connection unit configured to connect the first and second movable units together, wherein the following relationship is satisfied
fi>(1+1/(2Qa))fa
where a resonant frequency of the first movable unit in an in-phase mode is denoted by fi, a resonant frequency of the first movable unit in an anti-phase mode is denoted by fa, and a Q factor of resonance of the first movable unit in the anti-phase mode is denoted by Qa.

A microelectromechanical system (MEMS) resonator includes a resonant semiconductor structure, drive electrode, sense electrode and electrically conductive shielding structure. The first drive electrode generates a time-varying electrostatic force that causes the resonant semiconductor structure to resonate mechanically, and the first sense electrode generates a timing signal in response to the mechanical resonance of the resonant semiconductor structure. The electrically conductive shielding structure is disposed between the first drive electrode and the first sense electrode to shield the first sense electrode from electric field lines emanating from the first drive electrode.

A temperature-compensated resonator including a body used in deformation, and a core of the body is formed by a material that is one of glass, ceramic glass, technical ceramic, and metallic glass. At least one part of the body includes a coating whose Young's modulus variation with temperature is of an opposite sign to that of the material used for the core, so that at least a first order frequency variation with temperature of the resonator is substantially zero.

A method of manufacturing a gyro element as a vibration element is a manufacturing method of processing a quartz crystal substrate to form an outward shape of a gyro element including a vibrating arm and form recessed portions in a vibrating arm. The method includes forming the outward shape of a gyro element from one surface of the quartz crystal substrate using dry etching and forming the recessed portions using wet etching.

A method of forming a capacitive micro-electro-mechanical system (MEMS) sensor device includes at least one capacitive MEMS sensor element with at least one capacitive MEMS sensor cell. A patterned dielectric layer including a thick dielectric region and a thin dielectric region is formed on a top side of a first substrate. A second substrate is bonded to the thick dielectric region to provide at least one sealed micro-electro-mechanical system (MEMS) cavity. The second substrate is thinned to reduce a thickness of said second substrate to provide a membrane layer. Vias are etched through the membrane layer and said thick dielectric region extending into the first substrate to form embedded vias. A dielectric liner which lines the embedded vias is formed within the first substrate. The embedded vias are filed with electrically conductive TSV filler material to form a plurality of through-substrate vias (TSVs), said plurality of TSVs extending to at least a top of said membrane layer. A patterned metal cap layer including metal caps is formed on top of said plurality of TSVs. Trenches are etched through regions of the membrane layer for releasing a first portion of the membrane layer over said MEMS cavity to provide a MEMS electrode and to define a fixed electrode. A third substrate including an inner cavity and outer protruding portions framing said inner cavity is bonded to the thick dielectric. The protruding portions are bonded to the thick dielectric region and, together with said first substrate vacuum, seals said MEMS electrode. The plurality of TSVs on a bottom side of said first substrate are exposed.

A microelectromechanical system (MEMS) resonator includes a resonant semiconductor structure, drive electrode, sense electrode and electrically conductive shielding structure. The first drive electrode generates a time-varying electrostatic force that causes the resonant semiconductor structure to resonate mechanically, and the first sense electrode generates a timing signal in response to the mechanical resonance of the resonant semiconductor structure. The electrically conductive shielding structure is disposed between the first drive electrode and the first sense electrode to shield the first sense electrode from electric field lines emanating from the first drive electrode.

According to one embodiment, a vibration device includes a first movable unit including first and second movable portions arranged in a direction parallel to a first axis and enabled to vibrate in the direction parallel to the first axis, a second movable unit enabled to vibrate in a direction parallel to a second axis perpendicular to the first axis, and a connection unit configured to connect the first and second movable units together, wherein the following relationship is satisfied

fi>(1+1/(2Qa))fa

where a resonant frequency of the first movable unit in an in-phase mode is denoted by fi, a resonant frequency of the first movable unit in an anti-phase mode is denoted by fa, and a Q factor of resonance of the first movable unit in the anti-phase mode is denoted by Qa.