Abstract
This paper analyzes the effect of the anisotropy of single crystal silicon on the frequency split of the vibrating ring gyroscope, operated in the wineglass mode. Firstly, the elastic properties including elastic matrices and orthotropic elasticity values of (100) and (111) silicon wafers were calculated using the direction cosines of transformed coordinate systems. The (111) wafer was found to be in-plane isotropic. Then, the frequency splits of the mode ring gyroscopes of two wafers were simulated using the calculated elastic properties. The simulation results show that the frequency split of the (100) ring gyroscope is far larger than that of the (111) ring gyroscope. Finally, experimental verifications were carried out on the micro-gyroscopes fabricated using deep dry silicon on glass technology. The experimental results are sufficiently in agreement with those of the simulation. Although the single crystal silicon is anisotropic, all the results show that compared with the (100) ring gyroscope, the frequency split of the ring gyroscope fabricated using the (111) wafer is less affected by the crystal direction, which demonstrates that the (111) wafer is more suitable for use in silicon ring gyroscopes as it is possible to get a lower frequency split.
Highlights
With the development of the microelectromechanical systems (MEMS) technology, MEMS inertial sensors have been widely adopted into many fields, such as aerospace, vehicle navigation, and consumer electronic products including smartphones, tablets, and wearable sensors [1]
The simulation results show that the frequency split of the (100) ring caused by the anisotropy is obvious, and it has a strong relationship with the geometry of the (100) ring while the (111) wafer is in-plane isotropic
This paper presents how the anisotropy of single crystal silicon (SCS) affects the frequency splits of vibrating ring gyroscope (VRG), which can provide a method to calculate the elastic properties of various SCS wafers
Summary
With the development of the microelectromechanical systems (MEMS) technology, MEMS inertial sensors have been widely adopted into many fields, such as aerospace, vehicle navigation, and consumer electronic products including smartphones, tablets, and wearable sensors [1]. In order to avoid this trouble, some researchers prefer the n = 3 mode rather than the n = 2 mode, because the n = 3 mode is inherently identical, which helps to eliminate the frequency mismatch induced by the anisotropic elastic properties of the SCS [7] Both the angular gain and the effective mass of the n = 3 mode are smaller than those of the n = 2 mode, and the sensitivity of the n = 3 mode is lower [8,9]. In-plane and out-of-plane resonant modes of the circular ring were solved by Lagrange’s equations, and the effect of anisotropy was considered in the strain energy formulation [5] These theories derived from the perspective of the single ring were not concretely combined with a real SCS VRG or confirmed by experiments.
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