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Experimental-Numerical Comparison of the Cantilever MEMS Frequency Shift in presence of a Residual Stress Gradient

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ABSTRACT

The dynamic characterization of a set of gold micro beams by electrostatic excitation in presence of residual stress gradient has been studied experimentally. A method to determine the micro-cantilever residual stress gradient by measuring the deflection and curvature and then identifying the residual stress model by means of frequency shift behaviour is presented. A comparison with different numerical FEM models and experimental results has been carried out, introducing in the model the residual stress of the structures, responsible for an initial upward curvature. Dynamic spectrum data are measured via optical interferometry and experimental frequency shift curves are obtained by increasing the dc voltage applied to the specimens. A good correspondence is pointed out between measures and numerical models so that the residual stress effect can be evaluated for different configurations.

No MeSH data available.


Upper profile and frequency shift variation in cantilever beams of set 3.
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f7-sensors-08-00767: Upper profile and frequency shift variation in cantilever beams of set 3.

Mentions: To obtain an analytical model of the cantilever bending, g(x) is introduced as a variable gap, defined using equations (5) and (6)(10)g(x)=u(x)+g0=c2x2+g0 is calculated from equations (5) and (10) using experimental data, g0 is the gap in ideally flat conditions, also known from specimen profilometry. In Figures 7 and 8 a comparison between experimental and analytically calculated profiles of the upper side of the microbeams is presented. In Figure 7 specimens of wafer 1 are disposed by increasing length while in Figure 8 specimens of wafer 2 are disposed by increasing thickness.


Experimental-Numerical Comparison of the Cantilever MEMS Frequency Shift in presence of a Residual Stress Gradient
Upper profile and frequency shift variation in cantilever beams of set 3.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3927528&req=5

f7-sensors-08-00767: Upper profile and frequency shift variation in cantilever beams of set 3.
Mentions: To obtain an analytical model of the cantilever bending, g(x) is introduced as a variable gap, defined using equations (5) and (6)(10)g(x)=u(x)+g0=c2x2+g0 is calculated from equations (5) and (10) using experimental data, g0 is the gap in ideally flat conditions, also known from specimen profilometry. In Figures 7 and 8 a comparison between experimental and analytically calculated profiles of the upper side of the microbeams is presented. In Figure 7 specimens of wafer 1 are disposed by increasing length while in Figure 8 specimens of wafer 2 are disposed by increasing thickness.

View Article: PubMed Central - PubMed

ABSTRACT

The dynamic characterization of a set of gold micro beams by electrostatic excitation in presence of residual stress gradient has been studied experimentally. A method to determine the micro-cantilever residual stress gradient by measuring the deflection and curvature and then identifying the residual stress model by means of frequency shift behaviour is presented. A comparison with different numerical FEM models and experimental results has been carried out, introducing in the model the residual stress of the structures, responsible for an initial upward curvature. Dynamic spectrum data are measured via optical interferometry and experimental frequency shift curves are obtained by increasing the dc voltage applied to the specimens. A good correspondence is pointed out between measures and numerical models so that the residual stress effect can be evaluated for different configurations.

No MeSH data available.