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1Scaling in the MicroworldDr. Thara SrinivasanLecture 6Picture credit: Irene Tsai, MITPolymer thin film after electric field and reactive ion etching, 200x2Lecture Outline• Reading• From reader: W.S.N Trimmer, “Microrobots and Micromechanical Systems,” pp. 267-87.• H. Fujita, “Microactuators and Micromachines,” pp. 1721-32.• Watch the movie “Microcosmos” • Today’s Lecture• Scaling in Nature• Trimmer’s Matrix Notation • Scaling of Forces• Scaling of Mechanical, Electrical, and Fluidic SystemsNikon Small World Photo Competition WinnersMarine diatom 160xEmbryo seeds within fruit capsule (25x)23Scaling• Why is scaling important for MEMS?• MEMS are often >1000× smaller than macro counterparts.• We need to develop new intuition of microscale phenomena.• Otherwise, different scaling of any one property can be a big roadblock!• Dependence on length scale s• Length [s1] →• Surface area [s2] →• Volume [s3] →• Constraints on life• Land-based life contends with gravity at large scale, drying out at small scale.• Water-based life increases range of sizes by evading gravity and drying out.8V4A2L2s3.8 m20 mMite on Sandia microengine4Swimming and Flying221AvcFDDρ=221AvcFLLρ=Ian Thorpe• Swimming• Mass of muscles ~ [s3]• Drag force FD ~ [s2]• Larger creatures have greater swimming speed• Flying is more complex• Mass of muscles ~ [s3]• Weight ~ [s3]• Drag force FD ~ [s2]• Lift force FL ~ [s2]• Larger means faster flight but more power to keep weight aloftDickinson group, UCB35Bug’s Life• Most abundant creatures are 1-2 mm in size.• Walking on water is possible as surface tension supports small weights, but swimming is not fun.• Bugs are cold-blooded to manage faster cooling and heating.• Bugs are not easily injured. • They can lift 10-50× their weight.• They jump roughly as high as people do!• Work = weight × height• Force ~ muscle massWater striderAntzMexican ant, Cornell Integrated Microscopy Center6Why Miniaturize?• Motivation• Batch fabrication, lower cost per device• Less energy, less material consumed, disposable (or better, recyclable!)• Arrays of sensors possible, minimally invasive• Similar size scale as individual cells• Can take advantage of different scaling laws (e.g., electrostatic forces)• Breakdown of macroscale laws of physics• Performance• Integration with circuitry can reduce noise and improve sensitivity• Yield and reliability may be improved, fewer defects per chip • 106defects/cm3→ 1 defect for every 106µm3478Challenges to Miniaturization• Harder to interface with the macroscopic world • Fragility• Interconnect issues • Smaller device requires higher sensitivity to sense smaller input• Chemical sensors, accelerometers, gyros• May need to take into account • Molecular forces (i.e., Brownian motion) • Quantum mechanical effects (i.e., phonons)59Matrix Notation• Matrix shows dependence on length scale [s] for different cases in simple format, Trimmer 1989.[][]3/−==ssmFaF()2/12/1)/2(/2 Fxmaxt==[][][]()2/131 Fssst−=tFxP /==4321ssssF10Scaling Results• Scaling of forces•[s1] ~ surface tension, electrostatic I• [s2] ~ pressure, muscle, electrostatic II, magnetic I• [s3] ~ gravitational, magnetic II• [s4] ~ magnetic III=4321ssssF=−−1012ssssa=05.015.1sssst=−−25.015.2ssssVPvolume forces (s3)surface forces (s2)line forces (s1)Microscale ~µmMesoscale ~mmLog DimensionLog ForceNanoscale ~nmJudyMacroscale ~m611Power• Power generated• Force laws with scaling higher than s2, power generated per volume degrades as scale decreases=−−−05.015.111114321ssssssssssssP=55.325.0ssssP=−−25.015.2ssssVPMIT12Electrostatic ForcesxUF∂∂−=20022121wldEUEdVdwlCCVUεε====• Calculate the force exerted between the plates of a parallel plate capacitorFig A6 Trimmer713Electrostatic Forces[]2021wldExF∂∂−=ε[]dVEEsF == ;22[][]05.0sorsEb−=[][]21sorsF=• Two regimes in breakdown voltage Vbvs. spacing dcurve• As d approaches mean free path λ of insulator molecules, fewer molecules are around to be ionized[][]15.0sorsVb=14Magnetic Forces[][][]220sssJAdAJI===∫⋅= •[]402sdIIFba==lπµFig A1, A2 Trimmer...20+=dlIIFba𵕠Constant current density ~ [s1]−=−−05.01sssJmagnetic−=432sssFmagnetic815Electrostatic vs. Magnetic Microactuation• Electrostatics + Generally better scaling at microscale+ Simple actuation with pair of electrodes separated by insulator+ Voltage switching easier than current switching+ Energy loss through Joule heating is lower+ High-force short-range motion concatenated, as in stepper motor• Magnetics+ Absolute forces, displacements larger+ Can operate in harsh environments – Magnetic materials not standard– 3D magnets harder to microfabricate using planar IC processes– High currents, power dissipation−=432sssFmagnetic−−=21ssFticelectrosta16Electrostatic ActuatorsOffenberg et al., Bosch Brosnihan et al.xtlVFandtwVFryrx222020εεεε==• Laterally driven resonators• Electrostatic force proportional to number of comb fingers • For largest deflection operate at resonant frequency917Surface Tension• Surface tension (γwater~ 72 mN/m)• 20 µm hydrophilic channel filled with water, ∆P across meniscus is 12.5 kPa• Capillary condensation: d ~ 3 nm for 50% humidity• Surface tension or capillary forces scale with perimeter of wetted area ~ [s1]• Bug (10 mg) needs 1 mm of foot edge to walk on water• Human (60 kg) would need feet with 8000 m perimeter• Implications for MEMS• Release and in-use stiction are major challenges• Can it be harnessed? +=∆2111RRPγ[][][]121sFssPAF==∆=−Fig18Surface Tension for Self-Assembly• Use surface tension of liquid polymer and molten metal droplets to self-assemble hinged MEMS into desired positions.• γwater = 72 mN/m, γpolystyrene = 39 mN/m at 25°C• γSn-Bi


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