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

Abstract

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.

Highly-symmetric silicon dioxide shallow shell resonators with angstrom-level roughness

“…While thin oxide hemispherical shells can exhibit intrinsic zero frequency split between degenerate resonance modes despite thickness anisotropy [13], support anisotropy sets the minimum achievable, as-fabricated, frequency split. We report a frequency split reduced by more than an order of magnitude down to less than 1Hz for shallow thin SiO2 shells despite anisotropic supports.…”

The influence of shape imperfections on the vibrations of a ring resonator of a wave solid-state gyroscope

“…Резонаторы име-ют динамическую асимметрию, вызванную наличием неизбежных начальных отклонений от идеальной круговой формы [9][10][11][12][13]. Такие несовершенства формы приводят к специфи-ческим особенностям при изгибных колебаниях колец [14][15][16][17], что, в свою очередь, может привести к неустойчивой работе ВТГ [7,[18][19][20][21].…”

Single-crystal diamond micro-cupped resonators made by laser ablation

“…Recently, there has been a growing interest in micro-scale shell resonators including micro-hemispherical shell resonators, due to their potential advantages of high precision, small size, large dynamic range, large bandwidth, high quality factor and high insensitivity to environmental vibrations (Sorenson et al 2013;Cho 2013). made of SCD have not been reported yet, because it is difficult to shape for different application for its high hardness and chemical stability (Litao et al 2010).…”