Self-Contained Frequency Trimming of Micromachined Silicon Resonators via Localized Thermal Oxidation

An electronically controllable frequency trimming technique based on localized thermal oxidation of single crystalline silicon resonators is demonstrated. Thin layers of silicon dioxide can be thermally grown on silicon surfaces of resonant structures via extreme joule heating of such when biased with relatively large bias currents in an oxygen-rich environment. Changes in structural stiffness or oxidation induced internal stress causes a shift in the resonant frequency of the structures that can be used for post-fabrication frequency trimming of silicon resonators. As an added advantage, the positive temperature coefficient of Young´s modulus for the added silicon dioxide layer can partially compensate the large negative temperature coefficient of frequency (TCF) for the silicon resonators. Frequency trimming as high as ~ 3.7% and TCF as low as 0.2 ppm/^°C has been demonstrated for a 54 MHz I-shaped resonator using this technique. Furthermore, it has been demonstrated that coupling of mechanical resonance to electrical resistance and consequently joule heating of the structure can lead to a cooling effect at mechanical resonant frequency of the structure that allows the localized oxidation to stop automatically as soon as the resonator frequency reaches a targeted actuation frequency applied to the structure. The viability of this concept is demonstrated by application of both off-resonance and at-resonance actuation signals to fabricated resonators showing that as opposed to the off-resonance signals, the at-resonance signals with the same intensity do not lead to further frequency shift.