ksjp, 7/01 MEMS Design & Fab Overview Integrating multiple steps of a single actuator Simple beam theory Mechanical Digital to Analog Converter
ksjp, 7/01 MEMS Design & Fab Limits to electrostatics Residual stress (limits size) Pull-in Gap-closing Comb drive Tooth (for comb and gap-closing) Thermal noise
ksjp, 7/01 MEMS Design & Fab Force/Area n L W
ksjp, 7/01 MEMS Design & Fab Energy-Area Ratio n L W
ksjp, 7/01 MEMS Design & Fab Inchworm Motor Design F F shoe F F shuttle V s1 V a2 V s2 V a1 shoe shuttle FF shoe Add Shoe Actuators
ksjp, 7/01 MEMS Design & Fab guides MUMPs Inchworm Motors Gap Stop Shoe Actuators Shuttle Large Force Large Structures Residual Stress Stiction shoes
ksjp, 7/01 MEMS Design & Fab Silicon Inchworm Motors 1mm
ksjp, 7/01 MEMS Design & Fab Power Dissipation of the Actuator
ksjp, 7/01 MEMS Design & Fab Springs Linear beam theory leads to K a = Ea 3 b / (4L 3 ) K b = Eab 3 / (4L 3 ) L b a FaFa FbFb
ksjp, 7/01 MEMS Design & Fab Springs Linear beam theory leads to K a = Ea 3 b / (12L) K z = Ea 3 b / (3(1+2 ) L) Note that T z results in pure torsion, whereas T a results in bending as well. TaTa TzTz
ksjp, 7/01 MEMS Design & Fab Spring constant worksheet Assume that you have a silicon beam that is 100 microns long, and 2um wide by 20um tall. Calculate the various spring constants. E si ~ 150 GPa; G si = E si / (1+ 2 ) = 80 GPa a 3 b= K a = K b = K a = K z =
ksjp, 7/01 MEMS Design & Fab Damping Two kinds of viscous (fluid) damping Couette: b = A/g ; = 1.8x10 -5 Ns/m 2 Squeeze-film: b ~ W 3 L/g 3 proportional to pressure Dynamics: m a + b v +k x = F ext If x(t) = x o sin( t) then v(t) = x o cos( t) a(t) = - 2 x o sin( t) -m 2 x o sin( t) + b x o cos( t) +kx o sin( t) = F ext
ksjp, 7/01 MEMS Design & Fab Dynamic forces, fixed amplitude x o -m 2 x o sin( t) + b x o cos( t) +kx o sin( t) = F ext frequency Force nn Low damping Q~10 High damping ~10
ksjp, 7/01 MEMS Design & Fab Dynamic forces, fixed amplitude x o -m 2 x o sin( t) + b x o cos( t) +kx o sin( t) = F ext frequency Force nn increase k Increasing k raises n but at cost of more force or less deflection n’
ksjp, 7/01 MEMS Design & Fab Dynamic forces, fixed amplitude x o -m 2 x o sin( t) + b x o cos( t) +kx o sin( t) = F ext frequency Force nn n’ Decreasing m raises n at no cost in force or deflection decrease m
ksjp, 7/01 MEMS Design & Fab Dynamic forces, fixed amplitude o -J 2 o sin( t) + b o cos( t) +k o sin( t) = F ext frequency Torque nn n’ Identical result for angular systems with J (angular momentum) instead of m decrease m
ksjp, 7/01 MEMS Design & Fab Mechanical Digital to Analog Converter
ksjp, 7/01 MEMS Design & Fab Basic Lever Arm Design Stops 6m6m 6m6m Folded spring support Input Beam (digital) Input Beam (analog) Output Beam (analog)
ksjp, 7/01 MEMS Design & Fab 6-bit DAC Implementation (Courtesy of Matthew Last)
ksjp, 7/01 MEMS Design & Fab Output of a 6-bit DAC 19 cycles