An ultra low power thermally-actuated oscillator and driving circuit thereof are provided. The ultra low power thermally-actuated oscillator includes proof masses, thermally-actuated element and a plurality of driving elements. The proof masses is symmetrically disposed and suspended from a substrate by spring structure. The thermally-actuated element is a line structure to effectively reduce the motional impedance and direct current power. Wherein, the thermally-actuated element is connected to the proof masses or the spring structure. The plurality of driving elements are respectively disposed on both sides of the thermally-actuated element to provide a driving current. When the driving current flows through the thermally-actuated element, the thermally-actuated element will be deformed and thus the proof masses will be driven to produce a harmonic oscillation.

A microelectromechanical system (MEMS) device includes a temperature compensating structure including a first beam suspended from a substrate and a second beam suspended from the substrate. The first beam is formed from a first material having a first Young's modulus temperature coefficient. The second beam is formed from a second material having a second Young's modulus temperature coefficient. The body may include a routing spring suspended from the substrate. The routing spring may be coupled to the first beam and the second beam. The routing spring may be formed from the second material. The first beam and the second beam may have lower spring compliance than the routing spring. The MEMS device may be a resonator and the temperature compensating structure may have dimensions and a location such that the temperature compensation structure modifies a temperature coefficient of frequency of the resonator independent of a mode shape of the resonator.

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.

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.

A silicon microelectromechanical system, MEMS, resonator assembly, includes four flexural beam elements forming a rectangular frame, each beam element being connected at an end thereof to an end of a neighboring one of the beam elements. The resonator assembly further includes connection elements for connecting the rectangular frame to at least one mechanical anchor, and the resonator assembly supporting an in-plane flexural collective resonance mode.

A dual-mode resonator assembly includes a plurality of electrodes disposed around the resonator and configured to transduce information related to a first mode of operation of the dual-mode resonator assembly and a second mode of operation of the dual-mode resonator assembly. The plurality of electrodes includes electrodes associated with the first mode of operation and electrodes associated with the second mode of operation. The plurality of electrodes are disposed symmetrically and centered to nodes and antinodes of the first mode of operation and/or the second mode of operation. The electrodes are configured to also minimize feedback and noise from the first and second mode of operation.

A resonator element includes three vibrating arms. Each of the three vibrating arms includes an arm extending from a base and a wide section positioned at a tip end portion of the arm. The wide section is wider than the arm. When, of the three vibrating arms, the vibrating arm positioned at a center of an arrangement is provided with the arm having a width denoted by W1 which is defined as a length of the arm in the second direction, and the vibration arms positioned on both sides of the arrangement are provided with the arms each having a width denoted by W2 which is defined as a length of the arms in the second direction, a relationship 1W1/W22 is satisfied. When a length of the three vibrating arms in the first direction is denoted by L and a length of the wide sections in the first direction is denoted by Lh, a relationship Lh/L0.49 is satisfied.

A resonator element includes first to third vibrating arms and weights disposed at respective tip end portions of the first to third vibrating arms. When a weight mass ratio A represented by M1/M2 is plotted on a horizontal axis and an arm width ratio B represented by W1/W2 is plotted on a vertical axis, where M1 is a mass of the weight disposed on the first vibrating arm, M2 is a mass of the weight disposed on each of the second and third vibrating arms, W1 is a width of the first vibrating arm, and W2 is a width of each of the second and third vibrating arms, a point (A, B) is located in a region surrounded by a polygon formed by connecting six points of (A, B)=(2.39, 2), (0.01, 2), (0.23, 1.6), (1.65, 1), (7.15, 1), and (4.02, 1.6) with straight lines.

A MEMS resonator includes a pantograph that is a parallelogram, an oscillator connected to each vertex of the pantograph, and an electrode disposed opposite each oscillator, and forming a capacitor with the oscillator. A set of the electrodes disposed opposite to a set of the oscillators along an extension direction of a diagonal line of the pantograph that is the parallelogram have applied thereto a voltage differing in phase by 180 from another set of the electrodes disposed opposite to another set of the oscillators along an extension direction of another diagonal line of the pantograph. At least two of the MEMS resonators are connected so as to share one oscillator.