Influence of Support Compliance and Residual Stress on the Shape of Doubly-Supported Surface-Micromachined Beams

1999 ◽  
Author(s):  
Mauro J. Kobrinsky ◽  
Erik R. Deutsch ◽  
Stephen D. Senturia
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
Finite Element Method ◽  
Residual Stress ◽  
Gradual Increase ◽  
The Other ◽  
Elastic Model ◽  
Dimensional Model ◽  
Stable States ◽  
One Dimensional

Abstract Doubly-supported surface-micromachined beams are increasingly used to study the mechanical properties of thin films. Residual stresses in the beams cause significant vertical deflections, which affect the performance of these devices. We present here both experimental results for doubly-supported polysilicon surface-micromachined beams, and an elastic model of the devices that takes into account the compliance of the supports and the geometrical non-linear dependence of the vertical deflections on the stress in the beam. An elastic one-dimensional model was used for the beams, and the response of the supports to forces and moments was obtained using Finite Element Method simulations. The model explains a previously observed gradual increase of the maximum vertical deflections of the beams with increasing length at a given constant residual stress, and, in agreement with experimental observations, predicts two stable states for compressively stressed beams: one with the beam bent up, the other down.

Residual stress and mechanical properties of polyimide thin films

2009 ◽  
Vol 113 (2) ◽  
pp. 976-983 ◽  
Author(s):  
Wonbong Jang ◽  
Jongchul Seo ◽  
Choonkeun Lee ◽  
Sang-Hyon Paek ◽  
Haksoo Han
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
Residual Stress

scholarly journals Influence of the Mechanical Properties of Elastoplastic Materials on the Nanoindentation Loading Response

Materials ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 4842
Author(s):  
Huanping Yang ◽  
Wei Zhuang ◽  
Wenbin Yan ◽  
Yaomian Wang
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
The Other ◽  
Equivalent Model ◽  
Strain Hardening Exponent ◽  
Mechanical Parameters ◽  
The Finite Element Method ◽  
Fem Simulations ◽  
Elastoplastic Materials

The nanoindentation loading response of elastoplastic materials was simulated by the finite element method (FEM). The influence of the Young’s modulus E, yield stress σy, strain hardening exponent n and Poisson’s ratio ν on the loading response was investigated. Based on an equivalent model, an equation with physical meaning was proposed to quantitatively describe the influence. The calculations agree well with the FEM simulations and experimental results in literature. Comparisons with the predictions using equations in the literature also show the reliability of the proposed equation. The investigations show that the loading curvature C increases with increasing E, σy, n and ν. The increase rates of C with E, σy, n and ν are different for their different influences on the flow stress after yielding. It is also found that the influence of one of the four mechanical parameters on C can be affected by the other mechanical parameters.

scholarly journals Action minimization and macroscopic interface motion under forced displacement

2018 ◽  
Vol 24 (2) ◽  
pp. 765-792 ◽  
Author(s):  
Panagiota Birmpa ◽  
Dimitrios Tsagkarogiannis
Keyword(s):  
Stochastic Process ◽  
Evolution Equation ◽  
Fixed Time ◽  
Companion Paper ◽  
The Other ◽  
Final Position ◽  
Dimensional Model ◽  
Interface Motion ◽  
One Dimensional ◽  
Non Local

We study an one dimensional model where an interface is the stationary solution of a mesoscopic non local evolution equation which has been derived by a microscopic stochastic spin system. Deviations from this evolution equation can be quantified by obtaining the large deviations cost functional from the underlying stochastic process. For such a functional, derived in a companion paper, we investigate the optimal way for a macroscopic interface to move from an initial to a final position distant by R within fixed time T. We find that for small values of R∕T the interface moves with a constant speed, while for larger values there appear nucleations of the other phase ahead of the front.

Measurements of Residual Stresses in Low-Stress Silicon Nitride Thin Films Using Micro-Rotating Structures

1996 ◽  
Vol 444 ◽  
Author(s):  
Xin Zhang ◽  
Yitshak Zohar ◽  
Tong-Yi Zhang
Keyword(s):  
Thin Films ◽  
Finite Element Method ◽  
Residual Stress ◽  
Finite Element ◽  
Silicon Nitride ◽  
Film Thickness ◽  
Strain Measurement ◽  
Strain Measurements ◽  
Micro Structures ◽  
Gas Ratio

AbstractA variety of rotating micro structures were designed, fabricated and characterized for residual-stress (or strain) measurements in low-stress silicon nitride thin films, deposited by LPCVD on silicon wafers. The sensitivities of the micro structures were calculated by finite element method (FEM) and verified experimentally. The results were further confirmed by utilizing the wafer-curvature method for stress measurements. The size of the structures enables local residual-stress (or strain) measurement. The stress level depends on both the film thickness and the gas ratio and also varies with the location on the wafer.

Research on some Key Mechanical Properties of Silicon Nitride Thin Films Deposited by PECVD

2015 ◽  
Vol 742 ◽  
pp. 773-777
Author(s):  
Qun Feng Yang ◽  
Jian Yi Zheng ◽  
Jun Qing Wang ◽  
Jun Hui Lin ◽  
Xue Nan Zhao ◽  
...  
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
Residual Stress ◽  
Silicon Nitride ◽  
Mechanical Characteristics ◽  
Dielectric Films ◽  
Rotating Beam ◽  
Atomic Force ◽  
Scanning Electron

The purpose of this work is to study the mechanical characteristics of the silicon nitride(SiNx) thin films prepared by PECVD technique, some researches as follows were carried out. First, the SiNx thin films were deposited on the two different substrates. Then, the atomic force microscope (AFM) was adopted to test the surface quality of the SiNxfilms, and the scanning electron microscope (SEM) was used to test the section morphology of the SiNxthin films. Finally, the rotating beam structures was applied to measure the residual stress in the SiNx films. The SiNxthin films with low stress can be fabricated through PECVD, in which the surface roughness values(Ra) are 1.261 nm and 2.383nm, and the residual stress is 43.5 kPa. Therefore, the SiNxthin films deposited by PECVD are suitable for the preparation of device dielectric films in MEMS.

Influence of residual stress on mechanical properties of TiAlN thin films

2013 ◽  
Vol 228 ◽  
pp. S328-S330 ◽  
Author(s):  
Guo-an Cheng ◽  
Dong-yan Han ◽  
Chang-lin Liang ◽  
Xiao-ling Wu ◽  
Rui-ting Zheng
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
Residual Stress

scholarly journals Multiple Steady States in Ice-Water-Till Systems

1990 ◽  
Vol 14 ◽  
pp. 1-5 ◽  
Author(s):  
Richard B. Alley
Keyword(s):  
Steady State ◽  
Ice Sheet ◽  
Steady States ◽  
The Other ◽  
Surface Slope ◽  
Dimensional Model ◽  
Climatic Forcing ◽  
Fixed Boundary ◽  
One Dimensional ◽  
Ice Water

An ice sheet with fixed boundary conditions may have two steady configurations, as shown by a new one-dimensional model including the physics and continuity of ice, water, and deforming subglacial till. In one steady state, a steep surface slope causes rapid internal ice shearing but forces basal water through subglacial aquifers, suppressing basal velocity; in the other steady state, a gentle surface slope causes only slow ice shearing but allows water to lubricate the ice-bed interface and cause rapid basal velocities. Small climatic forcing may cause large ice-sheet response during a switch between steady states.

scholarly journals Multiple Steady States in Ice-Water-Till Systems

1990 ◽  
Vol 14 ◽  
pp. 1-5 ◽  
Author(s):  
Richard B. Alley
Keyword(s):  
Steady State ◽  
Ice Sheet ◽  
Steady States ◽  
The Other ◽  
Surface Slope ◽  
Dimensional Model ◽  
Climatic Forcing ◽  
Fixed Boundary ◽  
One Dimensional ◽  
Ice Water

An ice sheet with fixed boundary conditions may have two steady configurations, as shown by a new one-dimensional model including the physics and continuity of ice, water, and deforming subglacial till. In one steady state, a steep surface slope causes rapid internal ice shearing but forces basal water through subglacial aquifers, suppressing basal velocity; in the other steady state, a gentle surface slope causes only slow ice shearing but allows water to lubricate the ice-bed interface and cause rapid basal velocities. Small climatic forcing may cause large ice-sheet response during a switch between steady states.

Measuring the elastic modulus and residual stress of freestanding thin films using nanoindentation techniques

2009 ◽  
Vol 24 (9) ◽  
pp. 2974-2985 ◽  
Author(s):  
Erik G. Herbert ◽  
Warren C. Oliver ◽  
Maarten P. de Boer ◽  
George M. Pharr
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
Residual Stress ◽  
Thermal Expansion ◽  
Elastic Modulus ◽  
Dimensional Analysis ◽  
Experimental Verification ◽  
Cu Films ◽  
Proposed Model ◽  
The Difference

A new method is proposed to determine the elastic modulus and residual stress of freestanding thin films based on nanoindentation techniques. The experimentally measured stiffness-displacement response is applied to a simple membrane model that assumes the film deformation is dominated by stretching as opposed to bending. Dimensional analysis is used to identify appropriate limitations of the proposed model. Experimental verification of the method is demonstrated for Al/0.5 wt% Cu films nominally 22 µm wide, 0.55 µm thick, and 150, 300, and 500 µm long. The estimated modulus for the four freestanding films match the value measured by electrostatic techniques to within 2%, and the residual stress to within 19.1%. The difference in residual stress can be completely accounted for by thermal expansion and a modest change in temperature of 3 °C. Numerous experimental pitfalls are identified and discussed. Collectively, these data and the technique used to generate them should help future investigators make more accurate and precise measurements of the mechanical properties of freestanding thin films using nanoindentation.

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