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19. Micro-Optical-Electro-Mechanical Devices

nMicromachining Technique allows to fabricatemechanical microstructures monolithically on thesame chip as electronic and optical devices.

nSuch devices are called micro-optical-electro-mechanical devices or systems (MOEMs).

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n There are 3 types of MOEMs or MEMs

n Sensors: for detecting or measuring someproperty

n Actuators: have moving parts

n Optical elements: without moving parts

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19.1 Basic Equations of Mechanics19.1.1 Axial Stress and Strainn A solid bar of initial length = L0, andn Diameter = D.n Tensile force = F is uniformly applied to the

end of the bar.n The bar will lengthen by an amount = ΔLn The axial strain εa = ΔL / L0n The stress σ = F/Area = F / (πD/2)2

n Break pointn Hooke’s Law σ = εEn E: Young’s modulus, the slope of stress-

strain curven Shear stress and strain also follow such

equations.n Poisson’s ratio ν = - εl / εa

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19.1.2 Thin Membranesn Usually used in MEMs pressure or vibration sensors.n Deflection type: using rotational mirrors to measure

pressure or vibration by the deflection of light beams.n Reflection type: converting electrical or magnetic energy

into mechanical motion of mirrors to cause phase shift ormodulation of optical beams.

n Square membrane with side length = a, thickness = t,Young’s modulus = E, density = ρ, Poisson’s ratio = ν,pressure = P, and maximum deflection = Wmax

n Wmax= 0.001265 Pa4/D,n D = Et3/12(1- ν2) flexural rigidityn σl = 0.3081 P(a/t)2 longitudinal stressn σt = νσl maximum transverse stressn F0 = (1.654t/a2)[E/ρ(1- ν2)]1/2 resonant frequency

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19.1.3 Cantilever Beamsn Deflection of beams depends on the magnitude of the

force and the nature of the distribution of the force.n Cantilever beam fixed at one end (x = 0), length = L, width

= a, thickness = t, Young’s modulus = E, density = ρ

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n Uniform distributed forcen Uniform distributed force per unit width P = F/an The deflection W(P,x) = Px2(6L2-4Lx+x2)/24EIn I = at3/12 bending momentum of inertian σmax = PL2t/4I maximum stress

n Point loadn Load force = Q, at x = Ln The deflection W(Q,x) = Qx2(3L-x)/6EIn σmax = QLt/2I maximum stressn The frequency of fundamental vibrational

resonant mode of the beamF0 = 0.161 (t/L2)(E/ρ)1/2

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19.1.4 Torsion Plates

n As scanning mirrors and optical switchesn Torsion angle θ, restoring torque Tr , shear modulus G

( )

−=

tw

wt

lGwtTr 2

tanh19213

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3 ππ

θ

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19.2 Thin Membrane Devices

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19.3 Cantilever Beam Devices

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19.4 Torsional Devices

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19.5 Optical Elements

DOE, Microlens

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19.6 Future Directions in MOEMS Development

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19.7 Mechanical Properties of Silicon