Abstract: Mechanical resonators including doped piezoelectric active layers are described. The piezoelectric active layer(s) of the mechanical resonator may be doped with a dopant type and concentration suitable to increase the electromechanical coupling coefficient of the active layer. The increase in electromechanical coupling coefficient may all for improved performance and smaller size mechanical resonators than feasible without using the doping.

Abstract: Methods and apparatus for anchoring resonators, such as microelectromechanical systems (MEMS) resonators. A resonator may include a substrate, a mechanical resonating structure, and at least one anchor. The mechanical resonating structure may be configured to resonate in a resonance mode of vibration at a frequency. The anchor may couple the mechanical resonating structure to the substrate. The anchor may be configured to exhibit an acoustic bandgap at the frequency of the resonance mode of vibration of the mechanical resonating structure. The anchor may be oriented in a direction substantially parallel to a direction of propagation of the resonance mode of vibration of the mechanical resonating structure.

Abstract: Methods are described for constructing a mechanical resonating structure by applying an active layer on a surface of a compensating structure. The compensating structure comprises one or more materials having an adaptive resistance to deform that reduces a variance in a resonating frequency of the mechanical resonating structure, wherein at least the active layer and the compensating structure form a mechanical resonating structure having a plurality of layers of materials A thickness of each of the plurality of layers of materials results in a plurality of thickness ratios therebetween.

Abstract: Suppression of spurious modes of vibration for resonators and related apparatus and methods. A device may include a MEMS resonating structure, a substrate, and anchors between the MEMS resonating structure and the substrate. The MEMS resonating structure may have at least one main eigenmode of vibration and at least one spurious eigenmode of vibration. The anchors may be configured to suppress the response of the at least one spurious mode of vibration.

Abstract: Apparatus and methods for control of the second order temperature dependence of the frequency of a mechanical resonating structure are described. The second order temperature dependence of frequency of the mechanical resonating structure may be non-linear. Control may be provided by doping of a semiconductor layer of the mechanical resonating structure.

Abstract: Microelectromechanical systems (MEMS) resonators and related methods and apparatus are provided. A MEMS resonator may include a first portion and a second portion. The first portion may be configured to resonate, and the second portion may be configured to operate based on an energy trapping principle to prevent energy from traveling therethrough from the first portion. The MEMS resonator may be a Lamb wave resonator. The MEMS resonator may be anchorless. The MEMS resonator may have a side contacted by the anchor, wherein the anchor contacts greater than approximately 50% of the side.

Abstract: Micromechanical resonators having stub anchors are described. The micromechanical resonators may be suspended, being connected to a substrate or support by one or more anchors. The anchor(s) may include one or more stubs which can impact the acoustic impedance of the anchor(s). The stub(s) may have various shapes and sizes. In some instances, multiple resonators may be coupled together by a connector having one or more stubs.

Abstract: Mechanical resonators including doped piezoelectric active layers are described. The piezoelectric active layer(s) of the mechanical resonator may be doped with a dopant type and concentration suitable to increase the electromechanical coupling coefficient of the active layer. The increase in electromechanical coupling coefficient may all for improved performance and smaller size mechanical resonators than feasible without using the doping.

Abstract: Mechanical resonators including doped piezoelectric active layers are described. The piezoelectric active layer(s) of the mechanical resonator may be doped with a dopant type and concentration suitable to increase the electromechanical coupling coefficient of the active layer. The increase in electromechanical coupling coefficient may all for improved performance and smaller size mechanical resonators than feasible without using the doping.

Abstract: Apparatus and methods for control of charge in a semiconductor material of a mechanical resonating structure are described. Controlling the charge of the material may control the material properties of the semiconductor, such as the stiffness. Such control may result in changes in the behavior of the mechanical resonating structure, allowing for control and tuning of the behavior of the mechanical resonating structure.

Abstract: Resonator structures and electrodes are described, as well as methods for manufacturing the same. Resonator electrodes may be formed using two or more photolithographic steps and masks, with different masks being used to define different features of the electrodes. The masks may create self-aligned electrodes, which can be aligned with one or more anchors of the resonator.

Abstract: Aspects of the subject disclosure include, for example, constructing a mechanical resonating structure by applying an active layer on a surface of a compensating structure, wherein the compensating structure comprises one or more materials having an adaptive resistance to deform that reduces a variance in a resonating frequency of the mechanical resonating structure, wherein at least the active layer and the compensating structure form a mechanical resonating structure having a plurality of layers of materials, and wherein a thickness of each of the plurality of layers of materials results in a plurality of thickness ratios therebetween. Other embodiments are disclosed.

Abstract: Aspects of the subject disclosure include, for example, obtaining a mechanical resonating structure comprising a compensating structure, where the compensating structure comprises one or more materials having an adaptive stiffness that reduces a variance in a resonating frequency of the mechanical resonating structure (f0), and adjusting at least one of a value of f0 of the obtained mechanical resonating structure or a value of a temperature for which temperature coefficient of frequency of the obtained mechanical resonating structure is approximately zero (T0) by altering a thickness of at least one targetable material of the mechanical resonating structure. Other embodiments are disclosed.

Abstract: Resonator structures and electrodes are described, as well as methods for manufacturing the same. Resonator electrodes may be formed using two or more photolithographic steps and masks, with different masks being used to define different features of the electrodes. The masks may create self-aligned electrodes, which can be aligned with one or more anchors of the resonator.

Abstract: Mechanical resonating structures are described, as well as related devices and methods. The mechanical resonating structures may have a compensating structure for compensating environmental changes.