High-Q energy trapping of temperature-stable shear waves with Lamé cross-sectional polarization in a single crystal silicon waveguide

Abstract

A multi-port electrostatically driven silicon acoustic cavity is implemented that efficiently traps the energy of a temperature-stable eigen-mode with Lamé cross-sectional polarization. Dispersive behavior of propagating and evanescent guided waves in a ⟨100⟩-aligned single crystal silicon waveguide is used to engineer the acoustic energy distribution of a specific shear eigen-mode that is well known for its low temperature sensitivity when implemented in doped single crystal silicon. Such an acoustic energy trapping in the central region of the acoustic cavity geometry and far from substrate obviates the need for narrow tethers that are conventionally used for non-destructive and high quality factor (Q) energy suspension in MEMS resonators; therefore, the acoustically engineered waveguide can simultaneously serve as in-situ self-oven by passing large uniformly distributed DC currents through its body and without any concern about perturbing the mode shape or deforming narrow supports. Such a stable thermo-structural performance besides large turnover temperatures than can be realized in Lamé eigen-modes make this device suitable for implementation of ultra-stable oven-controlled oscillators. 78 MHz prototypes implemented in arsenic-doped single crystal silicon substrates with different resistivity are transduced by in- and out-of-plane narrow-gap capacitive ports, showing high Q of ∼43k. The low resistivity device shows an overall temperature-induced frequency drift of 200 ppm over the range of −20 °C to 80 °C, which is ∼15× smaller compared to overall frequency drift measured for the similar yet high resistivity device in the same temperature range. Furthermore, a frequency tuning of ∼2100 ppm is achieved in high resistivity device by passing 45 mA DC current through its body. Continuous operation of the device under such a self-ovenizing current over 10 days did not induce frequency instability or degradation in Q.