1. Are mechanical laws different at small scales? YES! If we scale quantities by a factor ‘S’ Area  S 2 Volume  S 3 Surface tension  SElectrostatic forces  S 2  agnetic forces  S 3 Gravitational forces  S 4 Surface Area/Volume effects Stiction: “Sticky friction”, due to molecular forces - surface tension pulls things together SCALING OF: Mechanical systems Fluidic systems Thermal systems Electrical and Magnetic systems Chemical and Biological systems

2. Which dynamical variables are scaled? - depends on our choice e.g. Mechanical systems Constant stress  Scale independent elastic deformation, scale independent shape Electromagnetic systems Constant electrostatic stresses/field strengths Thermal systems Constant heat capacity & thermal conductivity

3. Scaling Issues in Fluids Viscosity & Surface Tension Definition: A fluid cannot resist shear stresses Re is the ratio of inertial and viscous forces, v: velocity,  : density. l: linear dimension Viscosity dominates at: Re < 1 Re for whale swimming at 10 m/second ~ 300,000,000 Re for a mosquito larva, moving at 1mm/sec ~ 0.3 Re marks the transition between Laminar/Smooth flow & Turbulent Flow (mixing) In MEMS: always laminar flow!

4. Thermal Issues Thermal Mass (specific heat X Volume) scales as l 3, but heat removal scales as l 2 (proportional to area) Evaporation or Heat loss increases as Surface Area/Volume increases Easier to remove heat from a smaller sample

5. Electrophoresis - Stirring vs. Diffusion, Diffusion is the dominant mixing process in MEMS - Separation of bio-molecules, cells by the application of electric fields Separation of different types of blood cells E = 0 E > 0

6. Micro-fabricated DNA capture chip (Cepheid, CA) Fast, on-site, real time testing Miniature Clinical Diagnostic Systems Polymerase Chain Reaction (PCR) for DNA amplification Principle: High Isolation, Low Mass, Localized heating possible Scaling of Minimal Analytic Sample Size

7. Scaling in Electricity and Magnetism Potentiometric devices (measure voltage) are scale invariant Amperometric devices (measure current) are more sensitive when miniaturized e.g.,  -array electrochemical detectors (Kel-F) for trace amounts of ions Electroplating is faster in MEMS Courtesy: M. Schoning

8. Scaling in electromagnetic systems Voltage  Electrostatic field · length  L Resistance  Length  L -1 Ohmic current  Voltage  L 2 Current density (I/A) is scale invariant Constant electrostatic stresses/field strengths Area Resistance

9. Scaling in Electricity and Magnetism Electric:  : dielectric permittivity (8.85. 10 -12 F/m) E: electric field (Breakdown for air: 30 kV/cm) Magnetic:  : permeability (4     ) B: Magnetic field Rotor Stator Human Hair ! Sandia MEMS

10. Judy, Smart Mater. Struc, 10, 1115, (2001) Electrostatics is more commonly used in MEMS Macroscopic machines: Magnetic based Microscopic machines: Electrostatics based

11. Electrostatic force  Area · (Electrostatic field) 2  L 2 Electrostatic energy  Volume · (Electrostatic field) 2  L 3 Electrostatics vs. magnetostatics Magnetic field  Current  L distance Magnetic force  Area · (magnetic field) 2  L 4 Magnetic forces are much weaker compared to electrostatic forces Magnetic energy  Volume · (Magnetic field) 2  L 5

12. Power and Power density scaling Power  Force · speed  L 2 Power density  Power  L -1 Volume Small devices made through strong materials can have very large power densities e.g. 10 nN force in a 1  m 3 volume  ~ 10 3 J/mm 2 c.f. a thin-film battery  ~ 1J/mm 2

13. Power in MEMS Compact power sources needed, but Power scales by mass Energy stored in 1 mm 3 Currently: Fuel cells, micro-combustors, Radio frequency/optical sources Power capacitor 4  J/mm 3 1  W for 4 s Thick Film Battery1 J/mm 3 270  W for 1 hour Thin Film Battery2.5 J/mm 3 0.7 mW for 1 hour Solar Cell (1 X 1 X 0.1 mm 3 )0.1 mW Gasoline300 J/mm 3 3 mW for 1 day 178 Hf> 10 MJ/mm 3 160 mW

14. MEMS devices: How do we make them? Sandia MEMS Gear chain Hinge Gear within a gear A mechanism

15. Making MEMS How to make a MEMS device - deposit and etch out materials Introduction to Micro-machining - Wet and Dry etching - Bulk and surface micro-machining What kinds of materials are used in MEMS? -Semiconductors - Metals - Polymers