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.

Transverse Young's Moduli and Cell Shapes in Coniferous Early Wood

Holzforschung ◽  
2002 ◽  
Vol 56 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Ugai Watanabe ◽  
Minoru Fujita ◽  
Misato Norimoto
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Bending Moment ◽  
Cell Models ◽  
Young’S Moduli ◽  
Cell Shapes ◽  
The Difference ◽  
Square Cells ◽  
Experimental Values ◽  
The Relationship

Summary The relationship between transverse Young's moduli and cell shapes in coniferous early wood was investigated using cell models constructed by two dimensional power spectrum analysis. The calculated values of tangential Young's modulus qualitatively explained the relationship between experimental values and density as well as the difference in experimental values among species. The calculated values of radial Young's modulus for the species having hexagonal cells agreed well with the experimental values, whereas, for the species having square cells, the calculated values were much larger than the experimental values. This result was ascribed to the fact that the bending moment on the radial cell wall of square cell models was calculated to be small. It is suggested that the asymmetrical shape of real wood cells or the behavior of nodes during ell deformation is an important factor in the mechanism of linear elastic deformation of wood cells.

TEMPERATURE DEPENDENCE OFRHSIN ALUMINUM‐IMPLANTED LAYER INn‐TYPE SINGLE CRYSTAL SILICON

1969 ◽  
Vol 14 (9) ◽  
pp. 255-258 ◽  
Author(s):  
Tadatsugu Itoh ◽  
Taroh Inada ◽  
Masao Ishiki ◽  
Kenshi Menabe
Keyword(s):  
Single Crystal ◽  
Temperature Dependence ◽  
Single Crystal Silicon ◽  
Crystal Silicon

Temperature coefficient of Young’s modulus of silver microwhiskers determined by a laser Doppler vibration measurement

2021 ◽  
pp. 2150350
Author(s):  
Yijun Jiang ◽  
Mingyuan Lu ◽  
Shiliang Wang ◽  
Han Huang
Keyword(s):  
Temperature Dependence ◽  
Temperature Coefficient ◽  
Single Crystals ◽  
Young’S Modulus ◽  
Vapor Deposition ◽  
Physical Vapor Deposition ◽  
Young's Modulus ◽  
Laser Doppler Vibrometer ◽  
Laser Doppler ◽  
Vibration Measurement

Temperature dependence of Young’s modulus of Ag microwhiskers was determined by a laser Doppler vibrometer. The Ag whiskers with diameters in sub-microns were synthesized by the use of physical vapor deposition (PVD). They have a five-fold twinned structure grown along the [1 1 0] direction. The temperature coefficient of Young’s modulus was measured to be [Formula: see text] ppm/K in the range of 300 K to 650 K. The measured values are very close to the reported values of [Formula: see text] ppm/K for bulk Ag single crystals. This finding can benefit the design of Ag-based micro/nano-electromechanical systems or micro/nano-interconnectors operated at elevated or lowered temperatures.

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