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 nn 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 nn 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 nn  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 nn  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 6m6m 6m6m 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