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.

Multiple degenerately-doped silicon layers are implemented within resonant structures to control multiple orders of temperature coefficients of frequency.

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 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.

Multiple degenerately-doped silicon layers are implemented within resonant structures to control multiple orders of temperature coefficients of frequency.

A continuous or distributed resonator geometry is defined such that the fabrication process used to form a spring mechanism also forms an effective mass of the resonator structure. Proportional design of the spring mechanism and/or mass element geometries in relation to the fabrication process allows for compensation of process-tolerance-induced fabrication variances. As a result, a resonator having increased frequency accuracy is achieved.

A bulk-acoustic-mode MEMS resonator has a first portion with a first physical layout, and a layout modification feature. The resonant frequency is a function of the physical layout, which is designed such that the frequency variation is less than 150 ppm for a variation in edge position of the resonator shape edges of 50 nm. This design combines at least two different layout features in such a way that small edge position variations (resulting from uncontrollable process variation) have negligible effect on the resonant frequency.

Embodiments of multi-frequency excitation are described. In various embodiments, a natural frequency of a device may be determined. In turn, a first voltage amplitude and first fixed frequency of a first source of excitation can be selected for the device based on the natural frequency. Additionally, a second voltage amplitude of a second source of excitation can be selected for the device, and the first and second sources of excitation can be applied to the device. After applying the first and second sources of excitation, a frequency of the second source of excitation can be swept. Using the methods of multi-frequency excitation described herein, new operating frequencies, operating frequency ranges, resonance frequencies, resonance frequency ranges, and/or resonance responses can be achieved for devices and systems.

A method of making a temperature-compensated resonator is presented. The method comprises the steps of: (a) providing a substrate including a device layer; (b) replacing material from the device layer with material having an opposite temperature coefficient of elasticity (TCE) along a pre-determined region of high strain energy density for the resonator; (c) depositing a capping layer over the replacement material; and (d) etch-releasing the resonator from the substrate. The resonator may be a part of a micro electromechanical system (MEMS).

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.