scholarly journals Effects of Structural Dimension Variation on the Vibration of MEMS Ring-Based Gyroscopes

Micromachines ◽  
2021 ◽  
Vol 12 (12) ◽  
pp. 1483
Author(s):  
Zhipeng Ma ◽  
Xiaoli Chen ◽  
Xiaojun Jin ◽  
Yiming Jin ◽  
Xudong Zheng ◽  
...  
Keyword(s):  
Young’S Modulus ◽  
Principal Axis ◽  
Young's Modulus ◽  
Dynamical Behavior ◽  
Vibration Modes ◽  
Structural Dimension ◽  
Crystal Silicon ◽  
Deep Trench ◽  
Modal Coupling ◽  
Mode Pair

This study investigated the effects of structural dimension variation arising from fabrication imperfections or active structural design on the vibration characteristics of a (100) single crystal silicon (SCS) ring-based Coriolis vibratory gyroscope. A mathematical model considering the geometrical irregularities and the anisotropy of Young’s modulus was developed via Lagrange’s equations for simulating the dynamical behavior of an imperfect ring-based gyroscope. The dynamical analyses are focused on the effects on the frequency split between two vibration modes of interest as well as the rotation of the principal axis of the 2θ mode pair, leading to modal coupling and the degradation of gyroscopic sensitivity. While both anisotropic Young’s modulus and nonideal deep trench verticality affect the frequency difference between two vibration modes, they have little contribution to deflecting the principal axis of the 2θ mode pair. However, the 4θ variations in the width of both the ring and the supporting beams cause modal coupling to occur and the degenerate 2θ mode pair to split in frequency. To aid the optimal design of MEMS ring-based gyroscopic sensors that has relatively high robustness to fabrication tolerance, a geometrical compensation based on the developed model is demonstrated to identify the geometries of the ring and the suspension.

Heating Effects on The Young's Modulus of Films Sputtered onto Micromachined Resonators

1998 ◽  
Vol 518 ◽  
Author(s):  
H. Kahn ◽  
M.A. Huff ◽  
A.H. Heuer
Keyword(s):  
Temperature Dependence ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Single Crystal Silicon ◽  
Crystal Silicon ◽  
Resonant Structures ◽  
Young’S Moduli ◽  
Heating Effects ◽  
Sputter Deposited ◽  
Dc Current

AbstractSurface-micromachined polysilicon lateral resonant structures were fabricated and used to determine the temperature dependence of the Young's modulus of the polysilicon. This is done by passing a dc current through the beams during resonance testing, resulting in Joule-heating. The temperatures are calibrated by increasing the dc current until the melting point of silicon is attained. The calculated Young's moduli agree well with reported values for single crystal silicon.In addition, metal films were sputter-deposited onto the polysilicon resonators, and similar experiments performed on the composite devices to determine the temperature dependence of the modulus of the sputtered films. Ni films demonstrate a linear decrease in Young's modulus with temperature. TiNi films demonstrate two distinct modulus values with an intermediate transition region, due to the temperature-induced reversible phase transformation exhibited by TiNi.

Modeling Nonlinear MEMS Beams and the Chaotic Duffing Oscillator in SPICE

2017 ◽  
Vol 2017 (DPC) ◽  
pp. 1-90
Author(s):  
Aubrey Nathan Beal
Keyword(s):  
Young’S Modulus ◽  
Complex Dynamics ◽  
Nonlinear Oscillations ◽  
Young's Modulus ◽  
Circuit Simulation ◽  
Duffing Oscillator ◽  
Single Crystal Silicon ◽  
Mems Devices ◽  
Crystal Silicon ◽  
Cross Sectional

Nonlinear MEMS beams have been modeled using SPICE. This allows for the complex dynamics of MEMS resonators to be observed parallel to their supporting electronics via circuit simulation. Silicon generally provides suitably linear parameters for use in MEMS. However, nonlinearities may arise due to issues such as amplitude-frequency (A-F) effect, large displacement of the proof mass, pull-in voltage, fatigue, material or electrical parameters, process variation, simplified beam modeling and nonlinear spring constants. By modeling these effects in SPICE, the design of electronics that automatically test, calibrate, report or even mitigate these effects is aided. Single-crystal silicon is a highly linear material up until its failure, especially type <100>. High quality factor MEMS devices may, however, be affected by even small nonlinear terms in the material's Young's modulus. Geometric deformations may also occur due to decreases in cross-sectional area of beams in reaction to stretching and loading. Specifically, by including nonlinear geometric effects of MEMS beams and nonlinear terms in the Young's modulus of <100> and <110> silicon - nonlinear and chaotic oscillations are shown to arise via SPICE simulation. Using this SPICE modeling method, electronic systems were designed to monitor the nonlinear parameters of MEMS beams that cause A-F effect and chaotic Duffing oscillations. Extracting parameters such as those from the oscillation's Poincare section may yield advantage in built-in self-test (BIST) applications. The features in these nonlinear oscillations extend parameters to monitor and potentially calibrate MEMS devices for reliability, stability and processing variation.

The Stiffest Wire

1995 ◽  
Vol 62 (4) ◽  
pp. 947-951 ◽  
Author(s):  
K. Schulgasser
Keyword(s):  
Young’S Modulus ◽  
Elastic Constants ◽  
Upper Bound ◽  
Principal Axis ◽  
Young's Modulus ◽  
Maximum Modulus ◽  
Axial Direction ◽  
The Individual ◽  
Oriented Parallel ◽  
Individual Crystallite

We consider a polycrystal constituted from orthorhombic single crystals for which one particular principal axis of the crystallites is always oriented parallel to a particular direction; in the plane perpendicular to this direction the crystallites are randomly oriented. Bounds are found for the Young’s modulus in the axial direction. The lower bound on the Young’s modulus, which is realizable, is found to be that of the individual crystallite in the aligned direction. The upper bound determined is necessarily realizable when the single crystal elastic constants satisfy a certain condition. When this condition is not satisfied a bound is found; whether or not this bound is realizable must be examined using the specific elastic constants of the crystal being considered. For all physical examples considered the upper bound was indeed found to be realizable. Thus, generally speaking, a wire constituted as above, with the stiffest direction of the individual crystallites being along the wire, will have a higher Young’s modulus than the maximum modulus of the individual crystallites of which it is composed.

Sign in / Sign up

Export Citation Format

Share Document