1.52-GHz micromechanical extensional wine-glass mode ring resonators.

Vibrating polysilicon micromechanical ring resonators, using a unique extensional wine-glass-mode shape to achieve lower impedance than previous UHF resonators, have been demonstrated at frequencies as high as 1.2 GHz with a Q of 3,700, and 1.52 GHz with a Q of 2,800. The 1.2-GHz resonator exhibits a measured motional resistance of 1 MOmega with a dc-bias voltage of 20 V, which is 2.2 times lower than the resistance measured on radial contourmode disk counterparts at the same frequency. The use of larger rings offers a path toward even lower impedance, provided the spurious modes that become more troublesome as ring size increases can be properly suppressed using methods described herein. With spurious modes suppressed, the high-Q and low-impedance advantages, together with the multiple frequency on-chip integration advantages afforded by capacitively transduced micromechanical resonators, make this device an attractive candidate for use in the front-end RF filtering and frequency generation functions needed by wireless communication devices.

1.156-GHz self-aligned vibrating micromechanical disk resonator.

A new fabrication methodology that allows self-alignment of a micromechanical structure to its anchor(s) has been used to achieve vibrating radial-contour mode polysilicon micromechanical disk resonators with resonance frequencies up to 1.156 GHz and measured Q's at this frequency >2,650 in both vacuum and air. In addition, a 734.6-MHz version has been demonstrated with Q's of 7,890 and 5,160 in vacuum and air, respectively. For these resonators, self-alignment of the stem to exactly the center of the disk it supports allows balancing of the resonator far superior to that achieved by previous versions (in which separate masks were used to define the disk and stem), allowing the present devices to retain high Q while achieving frequencies in the gigahertz range for the first time. In addition to providing details on the fabrication process, testing techniques, and experimental results, this paper formulates an equivalent electrical circuit model that accurately predicts the performance of these disk resonators.

A negative-capacitance equivalent circuit model for parallel-plate capacitive-gap-transduced micromechanical resonators.

A small-signal equivalent circuit for parallel-plate capacitive-gap-transduced micromechanical resonators is introduced that employs negative capacitance to model the dependence of resonance frequency on electrical stiffness in a way that facilitates circuit analysis, that better elucidates the mechanisms behind certain potentially puzzling measured phenomena, and that inspires circuit topologies that maximize performance in specific applications. For this work, a micromechanical disk resonator serves as the vehicle with which to derive the equivalent circuits for both radial-contour and wine-glass modes, which are then used in circuit simulations (via simulation) to match measurements on actual fabricated devices. The new circuit model not only correctly predicts the dependence of electrical stiffness on the impedances loading the input and output electrodes of parallel-plate capacitive- gap-transduced micromechanical device, but does so in a visually intuitive way that identifies current drive as most appropriate for applications that must be stable against environmental perturbations, such as acceleration or power supply variations. Measurements on fabricated devices confirm predictions by the new model of up to 4× improvement in frequency stability against dc-bias voltage variations for contour- mode disk resonators as the resistance loading their ports increases. By enhancing circuit visualization, this circuit model makes more obvious the circuit design procedures and topologies most beneficial for certain mechanical circuits, e.g., filters and oscillators.