The present disclosure describes micromechanical resonator, a resonator element for the resonator, and a method for trimming the resonator. The resonator comprises a resonator element having a length, a width, and a thickness, where the length and the width define a plane of the resonator element. The resonator element comprises at least two regions (52, 53) in the plane of the resonator element, wherein the at least two regions have different thicknesses.

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 vibrator device includes a vibration element including a vibration portion and a fixed portion, a supporting member to which the fixed portion is attached to support the vibration element, and a first substrate to which the supporting member is attached, the supporting member includes a attaching portion attached to the first substrate, and A1?A2 is satisfied in a case where an area of a rectangular region including the fixed portion is A1 and an area of a rectangular region including the attaching portion is A2 in a plan view seen from a thickness direction of the vibration element.

Provided are micromechanical resonators and resonator systems including the micromechanical resonators. The micromechanical resonators may each include a supporting beam including a fixed end fixed on a supporting member and a loose end configured to vibrate, and a lumped mass arranged on the loose end, wherein the loose end has a width greater than a width of the fixed end, and a width of the lumped mass is greater than that the width of the fixed end.

An electromechanical amplifying method including a transducing an electrical signal to a mechanical resonator having a mechanical resonance mode with an angular frequency .sub.0; transducing the non-linear oscillations of the resonator into a transduced electrical signal; and filtering the transduced electrical signal to obtain an output signal, the signal transduced to the resonator being obtained by adding a first input signal of a first amplitude and a first angular frequency o.sub.s and a second pump signal of a second amplitude greater than the first amplitude and of a second angular frequency .sub.s that is different from the first angular frequency, the first and second angular frequencies being close to the angular frequency .sub.0 of the mechanical resonator and the second pump signal being chosen from a range of angular frequencies .sub.p and amplitudes in which the resonator is actuated in a non-linear regime.

A microelectromechanical device having a mobile structure including mobile arms formed from a composite material and having a fixed structure including fixed arms capacitively coupled to the mobile arms. The composite material includes core regions of insulating material and a silicon coating.

A vibrator device includes a vibration element including a vibration portion and a fixed portion, a supporting member to which the fixed portion is attached to support the vibration element, and a first substrate to which the supporting member is attached, the supporting member includes a attaching portion attached to the first substrate, and A1?A2 is satisfied in a case where an area of a rectangular region including the fixed portion is A1 and an area of a rectangular region including the attaching portion is A2 in a plan view seen from a thickness direction of the vibration element.

A microelectromechanical system (MEMS) resonator includes a substrate having a substantially planar surface and a resonant member having sidewalls disposed in a nominally perpendicular orientation with respect to the planar surface. Impurity dopant is introduced via the sidewalls of the resonant member such that a non-uniform dopant concentration profile is established along axis extending between the sidewalls parallel to the substrate surface and exhibits a relative minimum concentration in a middle region of the axis.

A MEMS (microelectromechanical system) resonator (150) comprising a substrate (105), a resonator element (100), and a cavity (110). The resonator element (100) is separated from the substrate (105) by said cavity (110), and the resonator element (100) comprises a layer of single-crystalline silicon (101). The layer of single-crystalline silicon (101) is doped with phosphorus atoms to obtain a specific doping profile.

A MEMS resonator device includes: (i) a support structure, (ii) a resonator element doped with at least one of N-type or P-type dopants, wherein a doping concentration of the at least one of N-type or P-type dopants causes a closely temperature-compensated mode in which (a) an absolute value of a first order temperature coefficient of frequency of the resonator element is reduced to a first value below a threshold value and (b) an absolute value of a second order temperature coefficient of frequency of the resonator element is reduced to about zero, and wherein an anchor decoupler region formed on the resonator element causes the absolute value to be further reduced to a second value, and (iii) at least one anchor coupling the resonator element to the support structure, wherein the anchor decoupler region is formed on the resonator element at least partially surrounding the at least one anchor.