Geometric stress compensation for enhanced thermal stability in micromechanical resonators

A design technique based upon competition between the thermal dependencies of geometrically tailored stresses and Young´s modulus has been demonstrated that (1) reduces the temperature coefficient (TC_f ) of the resonance frequencies of folded-beam micromechanical resonators by almost an order of magnitude without any additional power consumption; and (2) introduces a zero TC_f temperature at which subsequent oven controlled resonators may be biased. In particular, using this design technique, the overall frequency variation of a nickel-plated micromechanical resonator over a 27°C to 117°C range has been reduced from 2519 ppm to 342 ppm, and zero TC _f points have been introduced at temperatures ranging from 27°C to 57°C, specifiable by design. In the preparation of micromechanical devices, localized rapid thermal annealing was found to greatly increase the Q (>13000) and drift stability of the nickel resonators used in this work