Characterization and modeling of electro-thermal frequency tuning in a mechanical resonator with integral crossbar heaters

This paper investigates the efficiency of frequency tuning in a silicon-based mechanical resonator through joule heating owing to the temperature coefficient of modulus of silicon. We here employ a flexural mode resonator that is suspended by a simple crossbar heater in contrast to more complex serpentine heater designs reported previously. To provide further insight into the effect of geometrical and material parameters on the heating (as well as frequency tuning) efficiency, we have developed a model in this work to describe and predict the effect of joule heating in our test structure. The theoretical predictions from our model agree well with both the results from finite element computation as well as measurements from fabricated devices. A tuning range of up to 1.1% from the nominal frequency of 39.2 kHz with 54 mW power was obtained in this work. Given the good match between our model with both simulation and measurements, further optimization can be made depending on the specific application where in-built heaters from an integral part of a resonator.