Gradient residual stress induced elastic deformation of multilayer MEMS structures

Huang, Shusen; Zhang, Xin

doi:10.1016/j.sna.2006.05.026

Cited by 41 publications

(29 citation statements)

References 34 publications

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“…In the first method the curvature of a flat substrate is measured after the film deposition and the residual stress is evaluated using the Stoney formula [4,7,14,29].…”

Section: Discussionmentioning

confidence: 99%

“…The second technique involves the measurement of the bending of the multilayer structure when all the constraints are removed [14]. This is the method usually used to evaluate the residual stress in released cantilevers.…”

Section: Discussionmentioning

confidence: 99%

“…Causes of stress are the mismatch of thermal expansion coefficients between the different layers (thermal stress), the mismatch of lattice constants between the different materials (misfit stress) and the presence of defects in the layers [14]. The theory predicts that an epitaxial layer having a lattice parameter mismatch f with the underneath layer of less than ≈ 9% (as in our case), would grow elastically strained to have the same interatomic spacing of the substrate up to some critical film thickness d c .…”

Section: Theoretical Values For the Residual Stressmentioning

confidence: 99%

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Residual stress analysis of all perovskite oxide cantilevers

et al. 2011

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We have used a method to experimentally determine the curvature of thin film multilayers in all oxide cantilevers. This method is applicable for large deflections and enables the radius of curvature of the beam, at a certain distance from the anchor, to be determined accurately. The deflections of the suspended beams are measured at different distances from the anchor point using SEM images and the expression of the deflection curve is calculated for each cantilever. With this expression it is possible to calculate the value of the radius of curvature at the free end of the cantilever. Together with measured values for the Youngs Modulus, this enabled us to determine the residual stress in each cantilever. This analysis has been applied to Sr RuO 3 /BaTiO 3 /Sr RuO 3 , BaTiO 3 /MgO/SrTiO 3 and BaTiO 3 /SrTiO 3 piezoelectric cantilevers and the results compared to two models in which the stresses are determined by lattice parameter mismatch or differences in thermal expansion coefficient. Our analysis shows that the bending of the beams is mainly due the thermal stress generated

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“…In the first method the curvature of a flat substrate is measured after the film deposition and the residual stress is evaluated using the Stoney formula [4,7,14,29].…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Theoretical Values For the Residual Stressmentioning

confidence: 99%

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Residual stress analysis of all perovskite oxide cantilevers

et al. 2011

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“…These structures have been used as capacitors for transistors and sensors. [7][8][9][10] This process has also been used to fabricate multilayer microscale polymeric vesicles for drug delivery. 11,12 Here, we employ scrolling in the fabrication of adaptable polymer particles that can alter their geometry when triggered by given stimuli, such as temperature, thus altering flow characteristics and adsorption properties, provide understanding of how the materials and processing conditions alter the particle geometry, and quantify the responsive kinetics for these particles.…”

mentioning

confidence: 99%

Adaptive polymer particles

Kalaitzidou

Crosby

2008

Applied Physics Letters

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Adaptable polymer particles that can change geometry, flow characteristics, and adsorption properties upon the stimulation of an environmental change, such as temperature, are fabricated by utilizing the residual stress developed at the interface of a bilayer. We propose a phase diagram that can be used to predict the shape and size of the adaptive polymer particles as a function of the material modulus, thickness ratio, and the bilayer’s lateral dimensions. The materials used are gold/titanium and polydimethylsiloxane, but the method is applicable to a wide range of material combinations. Initial demonstrations of this responsive control and its impact on properties of the adaptive polymer particles are also presented.

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“…Later on, based on Stoney formula various models have been developed [12][13][14][15][16][17][18] to address numerical computations of uniform residual strain in the coating. Recently, a model using computational techniques identified that the corrosion at the interface of coating and substrate is inhibited by compressive residual stress in coating due to the contraction of open corrosion paths in the coatings [19].…”

Section: Introductionmentioning

confidence: 99%

Analysing the coupled effects of compressive and diffusion induced stresses on the nucleation and propagation of circular coating blisters in the presence of micro-cracks

Nazir

Khan

Stokes

2016

Engineering Failure Analysis

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This paper presents the delamination of coating with micro-cracks under compressive residual stress coupled with diffusion induced stress. Micro-cracks in coating provide a passage for corrosive species towards the coating-substrate interface which in turn produces diffusion induced stress in the coating. Micro-cracks contract gradually with increasing compressive residual stress in coating due to thermal expansion mismatch which blocks the species diffusion towards the interface. This behaviour reduces the diffusion induced stress in the coating while the compressive residual stress increases. With further increase in compressive residual stress, micro-cracks reach to the point, where they cannot be constricted any further and a high compressive residual stress causes the coating to buckle away from the substrate resulting in delamination and therefore initiating blistering. Blistering causes the contracted micro-cracks to wide open again which increases diffusion induced stress along with high compressive residual stress. The high resultant stress in coating causes the blister to propagate in an axis-symmetric circular pattern. A two-part theoretical approach has been utilised coupling the thermodynamic concepts with the mechanics concepts. The thermodynamic concepts involve the corrosive species transportation through micro-cracks under increasing compression, eventually causing blistering, while the fracture mechanics concepts are used to treat the blister growth as circular defect propagation. The influences of moduli ratio, thickness ratio, thermal mismatch ratio, poisson's ratio and interface roughness on blister growth are discussed. Experiment is reported for blistering to allow visualisation of interface and to permit coupled (diffusion and residual) stresses in the coating over a full range of interest. The predictions from model show excellent, quantitative agreement with the experimental results.

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Gradient residual stress induced elastic deformation of multilayer MEMS structures

Cited by 41 publications

References 34 publications

Residual stress analysis of all perovskite oxide cantilevers

Residual stress analysis of all perovskite oxide cantilevers

Adaptive polymer particles

Analysing the coupled effects of compressive and diffusion induced stresses on the nucleation and propagation of circular coating blisters in the presence of micro-cracks

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