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.

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.

Single Crystal Silicon Carbide On Silicon Using A Supersonic Gas Jet Of Methylsilane

1997 ◽  
Vol 483 ◽  
Author(s):  
S. A. Ustin ◽  
C. Long ◽  
L. Lauhon ◽  
W. Ho
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Single Crystal Silicon ◽  
Maximum Growth ◽  
X Ray Diffraction ◽  
Crystal Silicon ◽  
Cross Sectional ◽  
Supersonic Molecular Beam ◽  
Transmission Electron

AbstractCubic SiC films have been grown on Si(001) and Si(111) substrates at temperatures between 600 °C and 900 °C with a single supersonic molecular beam source. Methylsilane (H3SiCH3) was used as the sole precursor with hydrogen and nitrogen as seeding gases. Optical reflectance was used to monitor in situ growth rate and macroscopic roughness. The growth rate of SiC was found to depend strongly on substrate orientation, methylsilane kinetic energy, and growth temperature. Growth rates were 1.5 to 2 times greater on Si(111) than on Si(001). The maximum growth rates achieved were 0.63 μm/hr on Si(111) and 0.375μm/hr on Si(001). Transmission electron diffraction (TED) and x-ray diffraction (XRD) were used for structural characterization. In-plane azimuthal (ø-) scans show that films on Si(001) have the correct 4-fold symmetry and that films on Si(111) have a 6-fold symmetry. The 6-fold symmetry indicates that stacking has occurred in two different sequences and double positioning boundaries have been formed. The minimum rocking curve width for SiC on Si(001) and Si(111) is 1.2°. Fourier Transform Infrared (FTIR) absorption was performed to discern the chemical bonding. Cross Sectional Transmission Electron Microscopy (XTEM) was used to image the SiC/Si interface.

Effects of cross-sessional area and aspect ratio coupled with orientation on mechanical properties and deformation behavior of Cu nanowires

2021 ◽  
Author(s):  
Hui Cao ◽  
Wenke Chen ◽  
Zhiyuan Rui ◽  
Changfeng Yan
Keyword(s):  
Mechanical Properties ◽  
Aspect Ratio ◽  
Yield Stress ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Cu Nanowires ◽  
The Cross

Abstract Metal nanomaterials exhibit excellent mechanical properties compared with corresponding bulk materials and have potential applications in various areas. Despite a number of studies of the size effect on Cu nanowires mechanical properties with square cross-sectional, investigations of them in rectangular cross-sectional with various sizes at constant volume are rare, and lack of multifactor coupling effect on mechanical properties and quantitative investigation. In this work, the dependence of mechanical properties and deformation mechanisms of Cu nanowires/nanoplates under tension on cross-sessional area, aspect ratio of cross-sectional coupled with orientation were investigated using molecular dynamics simulations and the semi-empirical expressions related to mechanical properties were proposed. The simulation results show that the Young’s modulus and the yield stress sharply increase with the aspect ratio except for the <110>{110}{001} Cu nanowires/nanoplates at the same cross-sectional area. And the Young’s modulus increases while the yield stress decreases with the cross-sectional area of Cu nanowires. However, both of them increase with the cross-sectional area of Cu nanoplates. Besides, the Young’s modulus increases with the cross-sectional area at all the orientations. The yield stress shows a mildly downward trend except for the <111> Cu nanowires with increased cross-sectional area. For the Cu nanowires with a small cross-sectional area, the surface force increases with the aspect ratio. In contrast, it decreases with the aspect ratio increase at a large cross-sectional area. At the cross-sectional area of 13.068 nm2, the surface force decreases with the aspect ratio of the <110> Cu nanowires while it increases at other orientations. The surface force is a linearly decreasing function of the cross-sectional area at different orientations. Quantitative studies show that Young’s modulus and yield stress to the aspect ratio of the Cu nanowires satisfy exponent relationship. In addition, the main deformation mechanism of Cu nanowires is the nucleation and propagation of partial dislocations while it is the twinning-dominated reorientation for Cu nanoplates.

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