Power-insensitive silicon crystal-cut for amplitude-stable frequency synthesis

This paper reports on the theoretical prediction and experimental verification of the existence of a power-insensitive crystal cut in doped single crystal silicon (SCS). The existence of such a cut enables fully harmonic excitation of extensional elastic waves with negligible dispersion. Aligning bulk acoustic resonators to this power-insensitive cut along with suppression of boundary-induced nonlinearities enable realization of vibration-amplitude insensitive frequency references. An analytical formulation is presented to characterize the anisotropic anharmonic behavior of SCS elasticity, predicting the existence of the power-insensitive cut at ~30° offset from <;100> axis. This prediction is experimentally verified through implementation and characterization of an array of waveguide-based resonators aligned to different crystallographic directions. The resonators are optimized for substantial suppression of boundary induced nonlinearities through dispersive energy trapping technique. Among these, the waveguide-based resonator aligned to 22.5° cut shows a 1-dB compression point at 29dBm, which is 50× higher power-handling compared to <;100>/<;110> counterparts. Dispersive energy trapping used for elimination of geometrical nonlinearities simultaneously realizes a high Q of ~7,000 at 80MHz, which is independent of the crystallographic orientation.