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					Micro-Electro-Mechanical
        Systems
         Scaling in MEMS
       Balaji Panchapakesan
Department of Electrical and Computer
            Engineering
     Reasons for Miniaturization
•   Low energy and little resources consumed
•   Arrays of sensors
•   Small in size and minimally invasive
•   Favorable scaling laws
•   Batch fabrication
•   Disposable
•   Breakdown of macroscopic laws
•   Increased sensitivity and smaller time scales
•   Smaller building blocks
          Nature as a Guide
• Reducing a system in size alters the
  relative influence of various physical
  effects
• As objects shrink, ratio of surface area to
  volume becomes important!
• Largest Animal : African Elephant: 3.80 m
  tall (Land), Whale: 20 m
• Smallest Bacteria: 0.2 microns
   How does Scaling Limit Life
• Large animals are limited in few
  environments
• They are fewer in number
• They are slow
• For land animals the size is limited by
  gravitational influences
    How does Scaling Limit Life
• For smaller animals heat
  loss is a problem
• Heat loss scales as S2
  and rate of heat
  generation scales as S3
• As animals gets smaller,
  they have to keep eating
  or freeze to death
• Example: Very small
  pygmy shrew, smaller
  then some insects,
• 40 mm and 4 grams:
  about the same size as a
  penny coin
   How does Scaling Limit Life
• Environment: Wet or Dry
• Dry environment with high surface area to
  volume poses a problem to retain fluids
• Water based life don’t have fluid loss
  problems
• They can be as small as land animals and
  can grow much larger
         Scaling in Swimming
• Gravity scales as S3 while skin friction scales as
  S2
• For swimming overcoming skin friction is
  important than gravity
• Larger size has advantages in swimming
• Larger the size faster the animal can swim and
  cover greater distances
• Energy E~ R x V2, E~S3, R ~S2, V~S1/2
• Hence longer the animal faster is its velocity
• Larger ships can also move faster
Scaling in Swimming




  E~ R x V2, E~S3, R ~S2, V~S1/2
              Scaling in Flying
•   Flying is harder than swimming
•   Lower air density means faster flight
•   But larger force is needed to keep it aloft
•   Drag force Dg = Cd* ½ (ρAV2)
    – Cd = drag coefficient is a parameter that
      describes the resistance to motion
    – ρ = density of fluid
    – A = area of the body
    – V = velocity
            Scaling in Flying
• Lower the drag, faster the flight
• For example, Drag coefficient Cd =0.34 for a
  Porsche 924 Turbo and Cd=0.54 for Toyota
  Tercel
• Drag is also a function of Reynolds number
  which is the ratio of inertial to viscous forces
• So this ratio determines the speed and length of
  flight
• Smaller the viscous forces it is easier to swim
  and fly
           Scaling in Flying
• For flying Lift forces are also important
• This is similar to Drag forces and depends
  on the surface area
• Lift forces depends on angle of attack,
  geometric shape and Reynolds number
• Examples: Fruit fly: 3 mph
• Bumble Bee: 10-12 mph
• Boeing 747: 967 kmph
           Scaling in Flying
• Lift to drag ratio determines flying
  – For larger airplanes this ratio is 10-100
  – For micromachined airplanes this ratio is
    about 0.4
  – Hence as we scale down airplanes, it doesn’t
    give us favorable lift to drag ratio
  – This is the reason smaller birds while they can
    generate lift easily, they cannot overcome the
    viscous forces for making significant headway
   Scaling in Surface Tension
• Surface Tension = (δG/ δA)p,T where G is
  the free energy and A is the area
• G scales as S3 and A scales as S2.
• Surface Tension scales as S1
• Hence as things get miniaturized surface
  tension forces are more pronounced
• How does an insect walk on water?
• Answer: Surface Tension
    Scaling in Surface Tension
• Weight scales as S3 and
  surface tension scales as
  S1
• Hence weight decreases
  more rapidly than surface
  tension
• Hence insects can walk
  on water and coins can
  float on water
         Scaling and Diffusion
• As things get smaller diffusion plays a big role
• At molecular scales diffusion is more
  predominant
• Mixing, and sorting are aided by diffusion at the
  molecular scales
• D =kT/6πηr, where k is the Boltzman’s constant
  (J/K), T is the temperature in K, η (kg/m-s) is the
  viscosity and r is the hydrodynamic radius
• D scales as 1/S3 !
         Scaling and Diffusion
• Mixing through diffusion at the micro-scales can
  be really fast
• Smallest animals rely on molecular transport
  through diffusion
• Mixing small amount of liquids in micro-reactors
  is more efficient and much higher mixing than
  mixing in macro-reactors
• Large chemical reactors that are built using
  small micro-reactor building blocks can result in
  much better reaction efficiency and kinetics
            Scaling and Optics
• Optical absorption measurements are based on Beer’s
  law:
• A= εCL, where ε is the absorptivity, C is the
  concentration and L is the path length
• Hence longer the path length, larger the absorptivity
• Smaller L= smaller absorption
• Doesn’t scale very well
• Can improve the path length by making small mirrors
  and bouncing light from one mirror to another
• But the limitations are the reflectivity of the mirror.
Scaling of Strength to Weight Ratio
• Strength to weight ratio scales as area oer
  weight ~S2/S3 = S-1
• Smaller things can be stronger
• An ant can carry 50 times its weight
• Its more slender compared to a human
• A human reduced to the size of an ant can
  carry 300 times his own weight
• An ant increased to human size will not be
  able to support its own weight

				
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Description: MEMS (Micro-Electro-Mechanical Systems) is the name for the United States, in Japan, known as MEMS, in Europe known as the micro-system, which is available in volume production, the set of micro-institutions, micro-sensors, micro actuators and signal processing and control circuit, until the interface, communication and power is one of the micro-devices or systems. MEMS is a micro-processing technology with semiconductor integrated circuits and ultra-precision machining technology and developed, the current processing technology is also widely used in MEMS microfluidic chips and synthetic biology and other fields, so the biochemistry laboratory chip technology integration process.