Electrostatic tuning of temperature coefficient of frequency of anisotropic disk-shaped resonators

This paper presents an electrostatic mechanism for tuning the temperature coefficient of frequency (TCf) of disk-shaped resonators fabricated in highly doped (100) single-crystalline silicon. Taking advantage of the degenerate nature of “wineglass” mode resonators such as rings and disks, we show that rotating the resonant mode shapes by electrostatically changing the boundary conditions can effectively tune the TCf. In this work, the proof-of-concept is demonstrated by matching the TCf of the drive and sense modes of a disk resonator gyroscope (DRG). By using electrostatic tuning, the two wineglass modes are each rotated by 22.5° from the natural 0° and 45° (with respect to <;110>) positions, resulting in a substantial reduction in the TCf mismatch between two modes. The capability to tune TCf of wineglass mode resonators has potential applications for not only continuous mode-matching operation of vibratory gyroscopes, but also temperature compensation of silicon-based MEMS oscillators.