Design and Characterization of a Dual-Mode CMOS-MEMS Resonator for TCF Manipulation

A novel complimentary metal-oxide-semiconductor-microelectormechanical systems (CMOS-MEMS) composite ring resonator capable of a dual-mode operation has been proposed to enable temperature coefficient of frequency (TC
_f
$ manipulation. To study the temperature dependence between dual modes, two resonant modes of a single resonator vibrating in the orthogonal axes (i.e., in-plane and out-of-plane) are chosen to enable a large difference of their TC
_f
's while not to sacrifice its form factor. By adjusting the constituent ratio and position of the composed metals and dielectrics through the computer-aided-design layout, different TC
_f
's have been successfully demonstrated in a single CMOS-MEMS resonator. By concurrently measuring the TC
_f
's of the in-plane and out-of-plane modes with a divider-based scaling concept, estimated minimum first- and second-order temperature sensitivities (0.53 and 0.29 ppm/°C
²
, respectively) of their beat frequency can be obtained under proper scaling numbers for temperature-compensated clock applications. This paper also suggests that the first-order temperature coefficient of the beat frequency could be maximized under proper divider numbers. The process variations of the CMOS-MEMS resonators in terms of frequency, quality factor, and transmission magnitude are also intensively studied with an applicable amount of devices. The characterization result shows 1-σ frequency variations of 2,574 and 5,414 ppm for in-plane and out-of-plane modes, respectively.