Explain Young$'$s modulus

Mumbai University > Electronics Engineering > Sem 8 > MEMS Technology

Marks: 3M

1 Answer
  • Young’s modulus, E which is the proportionality between stress (σ), and strain (ε)and the essential parameter for calculation of the stiffness of structures, is necessary for design.
  • Young’s modulus E= stress (σ)/strain (ε)
  • This modulus may be obtained by directly testing the thin-film material using specialized devices such as a nanoindenter,which plunges a diamond tip into the material and measures the deformation.

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  • Alternatively, a lateral electrostatic resonator (Figure 3.35) may be used to extract the value of Young’s modulus.
  • The lateral resonator moves parallel to the substrate and thus minimizes damping effects and allows observation with anoptical microscope. The resonator structure is driven by opposed interdigitatedelectrostatic comb drives.
  • The resonator is suspended by a pair of folded beamsthat minimize the effect of residual stress.
  • The stiffness of the suspension and Resonance is the frequencyf, at which the resonator obtains its largest amplitude of motion.
  • The resonance frequency is a function of the resonator mass, M,and spring stiffness, K. -The mass of the resonator is readily obtained by thedimension of the moving structure and density of the material. Young’s modulusis estimated from the spring stiffness equations.

$$f = \frac{1}{2 \pi} \sqrt{\frac{K}{M}}$$

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