Sub-100ppb/°C temperature stability in thermally actuated high frequency silicon resonators via degenerate phosphorous doping and bias current optimization

In this work, we study temperature drift behavior of thermally actuated high frequency single crystalline silicon resonators and demonstrate temperature compensation of such via a combination of N-type degenerate doping and adjustment of the operating bias current. Significant suppression of the large negative temperature coefficient of frequency (TCF) for the resonators (-40ppm/°C) has been demonstrated using phosphorous degenerate doping resulting in even slightly positive TCF for some of the devices. Furthermore, it is shown that the TCF for such resonators can be fine tuned by changing the operating bias current enabling very close to zero TCF to be realized. Temperature compensation results for several resonators with different frequencies ranging from 3MHz to 60MHz are presented. TCF as low as -0.05ppm/°C (-50ppb/°C) has been demonstrated for an 8.2MHz resonator, which to the best of our knowledge is the lowest reported value for silicon-based micromechanical resonators.