A multiple coil spring MEMS resonator includes a center anchor and a resonator body including two or more coil springs extending in a spiral pattern from the center anchor to an outer closed ring. Each pair of coil springs originates from opposing points on the center anchor and extends in the spiral pattern to opposing points on the outer ring. The number of coil springs, the length and the width of the coil springs and the weight of the outer ring are selected to realize a desired resonant frequency.

A micro-mechanical resonator die includes: micro-mechanical resonator die layers; a cavity formed in at least one of the micro-mechanical resonator die layers; and a micro-mechanical resonator suspended in the cavity. The micro-mechanical resonator includes: a base; a first resonator portion extending from the base along a first plane; and a second resonator portion extending from the base along a second plane. The first resonator portion is configured to operate in an out-of-plane flexural mode that displaces at least part of the first resonator portion out of the first plane. The second resonator portion is configured to operate in an out-of-plane flexural mode that displaces at least part of the second resonator portion out of the second plane and out-of-phase relative to the first resonator portion.

A vibration device includes: a vibration substrate that includes a base, a flexural vibration arm joined to the base, and a torsional vibration arm joined to the base; a flexural vibration driver that causes the flexural vibration arm to perform a flexural vibration, the flexural vibration driver being disposed on the vibration substrate; and a torsional vibration driver that causes the torsional vibration arm to perform a torsional vibration, the torsional vibration driver being disposed on the vibration substrate.

A method comprises: forming a die including a cavity; coupling an anchor to the die; coupling a first resonator to a side of the anchor, in which the first resonator is suspended over the cavity and is operable to bend towards or away from a bottom of the cavity; and coupling a second resonator to the side of the anchor, in which the second resonator is suspended over the cavity, at least a part of the first resonator is laterally between the side of the anchor and a part of the second resonator, and the first resonator is operable to bend in an opposite direction from the second resonator.

Embodiments of the invention include micromechanical resonators. These resonators can be fabricated from thin silicon layers. Both rotational and translational resonators are disclosed. Translational resonators can include two plates coupled by two resonate beams. A stable DC bias current can be applied across the two beams that causes the plates to resonate. In other embodiments, disk resonators can be used in a rotational mode. Other embodiments of the invention include using resonators as timing references, frequency sources, particle mass sensors, etc.

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.