Effect of thickness anisotropy on degenerate modes in oxide micro-hemispherical shell resonators

The effect of thickness anisotropy on the degenerate elliptical resonance modes of micro-hemispherical shell resonators (μHSRs) created using the thermal oxidation process is investigated. This anisotropy arises from the variation in wet thermal oxide growth according to the exposed crystal planes of the single-crystal-silicon hemispherical mold used to generate the μHSRs. It is shown that, despite the presence of thickness anisotropy, the degenerate resonance modes of oxide μHSRs can exhibit zero intrinsic frequency split depending on the particular resonance mode and symmetry of the thickness anisotropy imparted from the underlying silicon wafer. Measured results verified by simultaneous electrical excitation on the 0° and 45° axes demonstrate less than 94 Hz intrinsic m=3 frequency split for a 1240 μm oxide μHSR (limited by measurement conditions), which is to the authors' knowledge the smallest as-fabricated frequency split reported to date for any μHSR.