We demonstrate dome-shaped, radio frequency, micromechanical resonators with integrated thermo-elastic actuators. Such resonators can be used as the frequency-determining element of a local oscillator or as a combination of a mixer and IF filter in a superheterodyne transceiver.
The dome resonators (shallow shell segments clamped on the periphery) are fabricated utilizing pre-stressed thin polysilicon film over sacrificial silicon dioxide. The shell geometry enhances the rigidity of the structure, providing a resonant frequency several times higher than a flat membrane of the same dimensions. The finite curvature of the shell also couples out-of-plane deflection with in-plane stress, providing an actuation mechanism. Out-of-plane motion is induced by employing non-homogeneous, thermomechanical stress, generated in plane by local heating. A metal resistor, lithographically defined on the surface of the dome, provides thermal stress by dissipating 4 μW of Joule heat.
The diminished heat capacity of the MEMS device enables a heating/cooling rate comparable to the frequency of mechanical resonance and allows operation of the resonator by applying AC current through the microheater. Resistive actuation can be readily incorporated into integrated circuit processing and provides significant advantages over traditional electrostatic actuation, such as low driving voltages, matched 50-ohm impedance, and reduced cross talk between drive and detection.
We show that when a superposition of two AC signals is applied to the resistive heater, the driving force can be detected at combinatory frequencies, due to the fact that the driving thermomechanical stress is determined by the square of the heating current. Thus the thermoelastic actuator provides frequency mixing while the resonator itself performs as a high quality (Q~10,000) intermediate frequency filter for the combinatory frequencies. A frequency generator is built by closing a positive feedback loop between the optical detection of the mechanical motion of the dome and the resistive drive. We demonstrate self-sustained oscillation of the dome resonator with frequency stability of 1.5 ppm and discuss the phase noise of the oscillator.
Shell-type micromechanical resonators operating in radio frequency range were fabricated utilizing mechanical stress that is built into polysilicon thin films. Significant increase of the resonant frequency (in comparison with flat, plate-type resonators of the same size) and the rich variety of vibrating modes demonstrate great potential for "2.5-Dimensional" MEMS structures. A finite curvature of the shell also provides a mechanism for driving resonators by coupling in plane stress with out of plane deflection. By modulating the intensity of a low power laser beam (P~10μWatts) focused on the resonator we introduced a time-variable, in-plane, thermomechanical stress. This stress modulation resulted in experimentally observed, large amplitude, out-of-plane, vibrations for a dome-type resonator.
A double laser beam experimental setup was constructed where mechanical motion of a shell-type resonator was actuated by a modulated, sharply focused Ar<sup>+ </sup>ion (blue) laser beam and detected by a red HeNe laser using an interferometric setup. A positive feedback loop was implemented by amplifying the red laser signal (related to the oscillator deflection) and applying it to modulate the blue (driving) laser beam. Stable self-sustained vibrations were observed providing that the feedback gain was high enough. Employing a frequency selective amplifier in the feedback loop allowed excitation of different modes of vibrations. Fine frequency tuning was realized by adjusting the CW component of either lasers' intensity or a phase shift in the feedback loop. Frequency stability better than 1 ppm (10<sup>-6</sup>) at 9 MHz was demonstrated for self-sustained vibrations for certain modes of the dome-shaped oscillators.
High frequency and high quality factor, <i>Q</i>, (defined as a half-width of the resonant peak) are the key factors that determine applications of microelectromechanical (MEMS) oscillators for supersensitive force detection or as elements for radio frequency signal processing. By shrinking the dimensions of MEMS resonators to the sub-micron range one increases the resonant frequency of the devices. Shrinking the devices, however, also increases the surface-to-volume ratio leading to a significant degradation of the quality factor (to below 5,000) due to the increased contribution of surface-related losses.
We demonstrate that local annealing performed by focused low-power laser beams can improve the quality factor of MEMS resonators by more than an order of magnitude, which we attribute to the alteration of the surface state. Quality factors over 150,000 were achieved after laser annealing 3.1 MHz disc-type oscillators (radius R=10 micrometers, thickness h=0.25 micrometer) compared with a Q=6,000 for the as-fabricated device. The mushroom-type design of our resonator (a single-crystal silicon disc supported by a thin silicon dioxide pillar at the center) provides low heat loss and also confines the electron-hole gas created by laser excitation, enhancing light absorption. The combined power of a red HeNe laser (P<sub>red</sub>=4mW) and a blue Ar+ ion laser (P<sub>blue</sub>=5mW) focused on the periphery of the mushroom provides enough energy for surface modification. The post-treatment quality factor, exceeding 100,000 for MHz-range resonators, boosts the performance of MEMS to be comparable to that of lower frequency single-crystal quartz devices. The local nature of laser annealing, safe for surrounding electronics, is a crucial element for integration of MEMS resonators into an integrated circuit environment.