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MEMS AND NEMS THE PHYSICS OF THE MICROWORLD IS DOMINATED BY SURFACE EFFECTS. RATIO OF SURFACE AREA TO THE VOLUME >&gt

MEMS AND NEMS THE PHYSICS OF THE MICROWORLD IS DOMINATED BY SURFACE EFFECTS. RATIO OF SURFACE AREA TO THE VOLUME >> 1 FRICTION IS MORE IMPORTANT THAN INERTIA, MOLECULAR ATTRACTIONS EXCEED RESTORING FORCES, ELECTROSTATIC FORCES BECOME LARGE. DIMENSIONAL ANALYSIS AND SCALING

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MEMS AND NEMS THE PHYSICS OF THE MICROWORLD IS DOMINATED BY SURFACE EFFECTS. RATIO OF SURFACE AREA TO THE VOLUME >&gt

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  1. MEMS AND NEMS THE PHYSICS OF THE MICROWORLD IS DOMINATED BY SURFACE EFFECTS. RATIO OF SURFACE AREA TO THE VOLUME >> 1 FRICTION IS MORE IMPORTANT THAN INERTIA, MOLECULAR ATTRACTIONS EXCEED RESTORING FORCES, ELECTROSTATIC FORCES BECOME LARGE.

  2. DIMENSIONAL ANALYSIS AND SCALING PROBLEMS OF INTEREST TO MEMS AND NEMS RESEARCHERS ARE COUPLED DOMAIN PROBLEMS. THE DESIGN OF A MICROSCALE THERMAL ANEMOMETER COUPLES HEAT TRANSFER, ELECTROSTATICS, FLUID DYNAMICS. THE MAIN STUMBLING BLOCK TO SUCCESSFUL PREDICTION OF SUCH SYSTEMS IS NOT DETERMINING WHAT TO PUT IN, BUT DETERMINING WHAT TO LEAVE OUT. ANSWER: NON-DIMENSIONALIZE SCALING

  3. PROJECTILE PROBLEM d2y / dt2 = - (1 + ey)-2 WITH INITIAL CONDITIONS: y(0) = 0, dy(0) / dt = 1 WHERE: y = gx / v2, t = gt / v, e = v2 / gR SOLUTION: y(t; e) FIND THE TIME FOR THE OBJECT TO REACH MAXIMUM HEIGHT, SAY tm. THIS OCCURS WHEN dy / dt = 0, AND tm = f(e)

  4. RANGE OF HUMAN SENSORY LENGTH (0.1 mm - 10 m) FIVE ORDERS TIME (0.3 sec - 1 year) NINE ORDERS TEMPERATURE (230 K - 1200 K) ONE ORDER MAGNETIC FIELD NO SENSORY EXPERIENCE HOW THE QUALITATIVE CHARACTERISTCS OF SOME PHYSICAL PHENOMENA CHANGE AS LENGTH SCALES DECREASE? HOW PARTICULAR QUANTITY CHANGES WITH RESPECT TO A CHARACTERISTIC LENGTH?

  5. SCALING LAW • VISCOSITY OF FLUIDS • REYNOLDS NUMBER Re = rva / n • << 1 - LAMINAR FLOW OR CREEPING FLOW • Re = • >> 1 - TURBULENT FLOW • – dynamic viscosity, a – radius, v – velocity, r – density, T – time • SUPPOSE v = aa / T • THEN Re = ba2, (a,b - CONSTANTS) • FOR A SMALL ENOUGH SPHERE THE FLOW WILL ALWAYS BE LAMINAR (Re << 1).

  6. SPHERE IN A CONSTANT GRAVITATIONAL FIELD FOR THE VISCOUS DRAG FORCE ON THE SPHERE (STOKE’S LAW) F = 6pnav = 4/3 pa3g (ro - r) THE TIME IT TAKES FOR THE SPHERE TO TRAVEL THE GIVEN DISTANCE d IS T = 9dn / ( 2ga2 (ro - r) ) = C (1 / a) (d = aa) VERY SMALL PARTICLES TAKE A VERY LONG TIME TO PRECIPITATE OUT OF SOLUTION.

  7. HEATING AND COOLING ANY ENGINE WILL GENERATE WASTE HEAT ALONG WITH THRUST. SUPPOSE, WE TURN THE ENGINE OFF AND LET THE SPHERE COOL DOWN TO THE BATH TEMPERATURE. HOW LONG DOES THIS TAKE? t ~ a2 ON SMALL LENGTH SCALES DIFFUSION CAN BE VERY FAST. THIS RESULTS IN THE RAPID COOLING OF SMALL OBJECTS. THE DISSIPATION OF WASTE HEAT IS NOT PROBLEMATIC IN MANY CASES. CONDUCTION IS THE DOMINANT FORM OF HEAT TRANSFER.

  8. RIGIDITY OF STRUCTURES CONSIDER A LONG THIN BEAM OF LENGTH L AND SQUARE CROSS-SECTION OF SIDE LENGTH a WITH a = eL (e << 1). LET THE BEAM HAVE UNIFORM YOUNG’S MODULUS E, DENSITY r, AND LET ONE FACE OF THE BEAM SUPPORT AN EVENLY DISTRIBUTED LOAD OF MAGNITUDE rga2 (rge2L2). IF THE BEAM IS FIXED AT ONE END AND FREE AT THE OTHER (A CANTILEVER BEAM), THEN THE MAXIMUM DEFLECTION OCCURS AT THE TIP OF THE BEAM umax = - 3rgL / 2e3E ~ L (BODY FORCES) umax ~ INDEPENDENT OF L (SURFACE FORCES) SMALL STRUCTURES ARE RELATIVELY RIGID AND DIFFICULT TO DEFORM.

  9. ELECTROSTATICS WE WISH TO LEVITATE A SMALL SPHERE OF RADIUS a AND MASS DENSITY r IN A UNIFORM, UPWARD POINTING ELECTRIC FIELD OF MAGNITUDE E. Q = 4pa3rg / 3E (CONDITION FOR LEVITATION) IF THE SPHERE HAS AN EMBEDDED VOLUME CHARGE DENSITY m, m = rg / E (INDEPENDENT OF THE LENGTH SCALE a) IF THE SPHERE HAS A NET SURFACE CHARGE DENSITY s, s = pga / 3E (IT SCALES AS a) SMALL SPHERES NEED A VERY LOW SURFACE CHARGE DENSITY TO CREATE LEVITATION.

  10. WE HAVE A CONDUCTING WIRE IN THE PRESENCE OF A CONSTANT MAGNETIC FIELD. LET THE WIRE HAVE LENGTH L AND RADIUS a WITH a = eL (e << 1) AND LET THE FIELD HAVE CONSTANT MAGNITUDE B. THE WIRE CARRYING CURRENT I IS PERPENDICULAR TO BOTH THE MAGNETIC AND GRAVITATIONAL FIELDS. I = pe2rgL2 / B J = I / (pa2) = rg / B (INDEPENDENT OF L) SUPPOSE WE ARE ABLE TO GENERATE A SURFACE CURRENT IN THE WIRE K = I / (2pa) = erLg / B (IT SCALES AS L) LEVITATION BECOMES POSSIBLE WITH A VERY SMALL SURFACE CURRENT.

  11. FLUID INTERFACES THE SURFACE TENSION OF A FLUID INTERFACE IS DEFINED AS THE ENERGY REQUIRED TO INCREASE THE AREA OF THE INTERFACE BY A UNIT AMOUNT. SURFACE TENSION IS CAUSED BY AN IMBALANCE OF VAN DER WAALS FORCES ON THE MOLECULES OF THE FLUID AT THE INTERFACE. THE IMBALANCE OF FORCES NORMAL TO THE SURFACE MEANS THAT THERE MUST BE A PRESSURE DROP ACROSS A FLUID INTERFACE IN ORDER FOR THE INTERFACE TO BE IN EQUILIBRIUM.

  12. THE CHANGE IN PRESSURE (YOUNG-LAPLACE EQ.) DP = 2s / R (CAPILLARY EFFECT) s - SURFACE TENSION, R - RADIUS OF THE INTERFACE CURVATURE. BUBBLES AND DROPLETS PROVIDE GOOD EXAMPLES. CONSIDER AN AIR BUBBLE ONE MICRON IN DIAMETER IN WATER. s = 73 mN / m2 HENCE, THE PRESSURE DROP ACROSS THE BUBBLE SURFACE DP = 1.5 x 105 Pa = 1.5 atm

  13. AN ELECTROSTATIC ACTUATOR SUPPOSE WE HAVE A DEVICE THAT DEPENDS FOR ITS OPERATION ON A PAIR OF PARALLEL, ELECTROSTATICALLY CHARGED RODS THAT REPEL EACH OTHER. (IT CAN BE AN ELECTROSTATIC - MECHANICAL - FLUIDIC SYSTEM)

  14. THERMALLY DRIVEN DEVICES - THERMOELASTIC V-BEAM ACTUATOR (ACTUATION IS BASED ON THERMAL EXPANSION) AN ELASTIC BEAM (V-SHAPE) IS HELD FIXED BETWEEN TWO RIGID SUPPORTS. - AN ELECTRIC CURRENT PROVIDES A HEAT SOURCE BY UTILIZING JOULE HEATING, - A RATIO OF OUTPUT FORCE TO SYSTEM SIZE IS UNFAVORABLE FOR THIS DESIGN.

  15. - THERMAL BIMORPH ACTUATOR THE HOT AND COOL ARMS ARE ANCHORED AT ONE END AND FREE TO MOVE ELSEWHERE. SINCE THE HOT ARM IS VERY THIN COMPARED TO THE COOL ARM, ITS RESISTANCE TO CURRENT FLOW IS MUCH GREATER. JOULE HEATING WILL CAUSE A LARGE TEMPERATURE INCREASE IN THE HOT ARM. IN TURN, LARGE THERMAL STRESSES WILL DEVELOP IN THE HOT ARM CAUSING THE ENTIRE SYSTEM TO DEFLECT.

  16. - THERMOPNEUMATIC VALVE IT RELIES UPON THE CHANGE IN VOLUME OF A HEATED FLUID TO PROVIDE A FORCE. A RESISTIVE HEATING ELEMENT IS EMBEDDED IN A RIGID SUBSTRATE. A FLUID RESIDES IN A CAVITY ABOVE THE HEATING ELEMENT. THE TOP OF THE CAVITY IS COVERED BY AN ELASTIC MEMBRANE. AS A CURRENT PASSES THROUGH THE HEATING ELEMENT, JOULE HEATING OCCURS AND THE FLUID’S TEMPERATURE INCREASES. THIS INCREASES THE PRESSURE IN THE FLUID AND THE ELASTIC MEMBRANE IS PUSHED UPWARD. THE MEMBRANE THEN ACTS AS A VALVE REGULATING THE FLOW IN A MICROCHANNEL.

  17. THERMAL ANEMOMETER A HEAT SOURCE IS PLACED IN A FLOW BETWEEN A PAIR OF TEMPERATURE SENSORS. BY MEASURING THE DIFFERENCE IN TEMPERATURE UPWIND AND DOWNWIND OF THE HEAT SOURCE, THE SPEED OF THE FLOW CAN BE INFERRED.

  18. THERMAL DATA STORAGE DEVICE THE RESISTIVE HEATING OF AN ATOMIC FORCE MICROSCOPE TIP CREATES A THERMAL DATA STORAGE SYSTEM. A RESISTIVELY HEATED AFM TIP IS USED TO MAKE INDENTATIONS IN A POLYCARBONATE DISK. THE PRESENCE OF AN INDENTATION CORRESPONDS TO a 1, WHILE THE ABSENCE CORRESPONDS TO a 0 (BINARY DATA RECORDING). DATA DENSITY NEAR 100 Gb/in2 HAS BEEN DEMONSTRATED USING THIS SYSTEM. A TYPICAL CD-ROM RECORDS DATA WITH A DENSITY OF ABOUT 30 Gb/in2.

  19. SHAPE MEMORY ACTUATOR A MATERIAL UNDERGOES A PHASE CHANGE IN RESPONSE TO A TEMPERATURE CHANGE. IN THE AUSTENITE, OR “REMEMBERED” PHASE, WHICH OCCURS AT HIGH TEMPERATURE, THE MATERIAL IS STIFF AND NOT EASILY DEFORMED. IN THE MARTENSITE PHASE, WHICH OCCURS AT LOW TEMPERATURE, THE MATERIAL DEFORMS PLASTICALLY. UPON HEATING A DEFORMED MATERIAL IN THE MARTENSITE PHASE, IT TRANFORMS TO THE AUSTENITE PHASE AND ASSUMES ITS PREVIOUS HIGH-TEMPERATURE SHAPE. THIS PROCESS CREATES LARGE FORCES THAT MAY BE UTILIZED IN AN ACTUATOR. THE RESISTIVE HEATING IS APPLIED HERE TO PROVIDE THE TEMPRATURE CHANGE.

  20. ELASTIC STRUCTURES IN MEMS / NEMS CARBON NANOTUBE CAPS YAO AND LORDI SHOWED THAT CARBON NANOTUBE CAPPED WITH A HEMISPHERICAL CARBON STRUCTURE CAN BE USED AS A NANOSCALE HOOKEAN SPRING. RECENT WORK HAS SHOWN THAT THIS EFFECT MAY DEPEND ON TEMPERATURE AND CAN BE MODIFIED BY FILLING THE NANOTUBE WITH DIFFERENT MATERIALS.

  21. PRESSURE SENSORS THE PRESSURE SENSOR IS A STAPLE OF MEMS ENGINEERING. THE DIFFERENCE IN PRESSURE BETWEEN OPPOSING SIDES OF THE DIAPHRAGM CAUSES A STRESS AND POSSIBLY A DISPLACEMENT OF THE DIAPHRAGM. A VARIETY OF METHODS HAVE BEEN DEVELOPED TO DETECT THE STRESS OR DISPLACEMENT. - CAPACITANCE CHANGE, - PIEZORESISTIVE EFFECT (ELECTRICAL RESISTANCE VS. STRESS), - ELASTIC DEFLECTION.

  22. MICRO- AND NANOTWEEZERS PHILIP KIM AND CHARLES LIEBER FROM HARVARD UNIVERSITY DEVELOPED NANOTWEEZER. A PAIR OF CNs ARE ATTACHED TO GOLD ELECTRODES, WHICH IN TURN, ARE FASTENED TO A TAPERED GLASS MICROPIPETTE. UNDERSTANDING THE DEFORMATION OF ELASTIC BEAMS SUBJECTED TO VARIOUS LOADS IS ESSENTIAL FOR UNDERSTANDING AND DESIGNING TWEEZERS.

  23. NANOMECHANICAL RESONATOR RECENTLY ELECTROMECHANICAL RESONATOR INVENTED BY BENJAMIN FRANKLIN HAS BEEN REPLICATED ON THE NANOSCALE AS THE CENTERPIECE OF A CHARGE DETECTION DEVICE. THE POTENTIAL DIFFERENCE INDUCES CHARGE ON THE TWO BELLS (EQUAL BUT OPPOSITE SIGN). A STIFF SILICON BEAM SUPPORTS A NANOSCALE “ISLAND” BETWEEN A PAIR OF ELECTRODES. THE NANOSCALE ISLAND HAS A CHARACTERISTIC LENGTH OF 100 nm. NANOSCALE RESONATORS OPERATE AT FREQUENCIES OF ABOVE 500 MHz AND WITH QUALITY FACTORS AS LARGE AS 250,000.

  24. DESCRIPTION OF COUPLED THERMAL-ELASTIC STRUCTURES THERMOELASTIC V-BEAM ACTUATOR WE CONSIDER THE STRUCTURE AS A PART OF ACTUATOR DESIGN. WE WOULD LIKE TO KNOW THE DEFLECTION OF OUR ACTUATOR AS A FUNCTION OF ROD TEMPERATURE. THE DEFLECTION OF AN ELASTIC BEAM, IN THE STEADY-STATE, SATISFIES d2/dx2 (EI d2v/dx2) + P d2v/dx2 = F F - APPLIED LOAD DUE TO THERMAL STRESSES PLUS AN EXTRA APPLIED LOAD, P - TENSION IN THE BEAM (PRESSURE), v - STEADY-STATE DEFLECTION, EI - FLEXURAL RIGIDITY OF THE BEAM.

  25. THE CRITICAL VALUE OF P (EULER LOAD) WHEN BUCKLING HAS OCCURRED: Pc = p2EI / L2 ASSUMING THE ENDS OF THE ROD DO NOT MOVE, THE THERMOELASTIC DUHAMEL-NEUMANN RELATION BETWEEN P AND T IS P = aAE (T - To) AND BUCKLING CRITICAL TEMPERATURE IS Tc = To + (p2I / aAL2) To - AMBIENT TEMPERATURE, a - COEFFICIENT OF THERMAL EXPANSION, A - CROSS-SECTIONAL AREA OF THE BEAM.

  26. THE APPROXIMATE BUCKLED SHAPE ASSUMED BY OUR V-BEAM ACTUATOR IS v(x) = (2L / p) [a (T - Tc)]1/2 sin(px / L) WITH MAXIMUM DISPLACEMENT OCCURING AT x = L / 2 AND HAVING VALUE v(L / 2) = (2L / p) [a (T - Tc)]1/2

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