Postfabrication Electrical Trimming of Silicon Micromechanical Resonators via Joule Heating

This paper presents a method to electrically trim the resonance frequency of a silicon bulk acoustic resonator (SiBAR) after its fabrication is completed. The small volume of the microresonator can be Joule heated to a sufficiently high temperature to allow for diffusion of deposited metals from its surface onto its bulk. Such high temperatures also facilitate the formation of silicon-metal bonds which, depending on the metal, are either stronger or weaker compared to the existing silicon-silicon bonds. The former leads to an overall increased stiffness of the resonating element thereby trimming up its resonance frequency, while the latter does the opposite. Both trimming-up and trimming-down by ~400 kHz have been demonstrated at a resonance frequency of 100 MHz (i.e., trimming range of 4000 ppm) using gold and aluminum, respectively. The possibility of increasing the trimming range to ~4 MHz (i.e., 40 000 ppm) by engineering the resonator geometry is also discussed and demonstrated.