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Micro/Nano Gas Flows and Their Impact on MEMS/NEMS Wenjing Ye MAE, HKUST

Micro/Nano Gas Flows and Their Impact on MEMS/NEMS Wenjing Ye MAE, HKUST. Micro Resonators. Resonant structure fabricated with microfabrication technology Driven mechanism: electrical, piezoelectric Sensing: capacitive, piezoresistive Applications Sensors Filters, oscillators.

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Micro/Nano Gas Flows and Their Impact on MEMS/NEMS Wenjing Ye MAE, HKUST

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  1. Micro/Nano Gas Flows and Their Impact on MEMS/NEMSWenjing YeMAE, HKUST

  2. Micro Resonators • Resonant structure fabricated with microfabrication technology • Driven mechanism: electrical, piezoelectric • Sensing: capacitive, piezoresistive • Applications • Sensors • Filters, oscillators

  3. Examples - Resonators Temperature sensor Bio sensor IF filter or oscillator Doms, et al. JMM 2005

  4. Resonator – 1-D Macro Model • Macro model meff x + cx + kx = Factuator meff: effective mass dashpot damping coefficient stiffness of the spring

  5. Resonator – 1-D Macro Model • Macro model • Quality factor (Q): meff x + cx + kx = Factuator meff: effective mass dashpot damping coefficient stiffness of the spring 1-D model

  6. Influence of Gas on MEMS/NEMS • Momentum exchange • Damping force (viscous damping, squeeze-film damping) • Inertia force (added mass) • Knudsen force • Energy exchange • Heat flux • Damping

  7. Fundamentals of Gas Transport • Knudsen number: mean free path of gas molecules characteristic length of flow field Bulk region Bulk region e.g., air at room temperature, 1 atm

  8. Fundamentals of Micro/Nano Gas Flows - Flow Regimes • Continuum flow with no-slip BCs • Continuum flow with slip BCs • Transition regime • Free-molecule regime Knudsen Number:

  9. Continuum Regime – Governing Equations and BC

  10. Slip Regime – Governing Equations and BC

  11. Non-continuum Gas Regime • Boltzmann equation • Analytical methods - Moment methods, etc • Numerical methods – Discrete velocity method, etc • Kinetic methods • Particle methods • Molecule Dynamics – Free-molecule flows • Direct Simulation Monte Carlo – Flows in the transition regime f velocity distribution function 11

  12. Example 1 – Air Damping on a Laterally Oscillating Resonator • Damping forces: primarily fluidic • viscous drag force is dominant • Squeeze-film damping is insignificant

  13. Experimental Measurement:Computer Microvision f0=19200 Hz ; Q = 27

  14. Air Damping on Laterally Oscillating Micro Resonators • Damping forces: primarily fluidic Continuum regime Reynolds number << 1 Navier-Stokes Stoke equations • Boundary condition – non-slip and slip

  15. Steady Stokes Flow Governing Equations where BC: 1D Couette Model: Tang, et al, 1989, 1990

  16. 1D - Steady (Couette) Theoryvs. Experiment

  17. 1D Stokes Model: Cho, et al, 1993 Unsteady Stokes Flow Governing Equations where BC:

  18. 1D - Unsteady (Stokes) Theoryvs. Experiment

  19. FastStokes Results • Number of Panels: 23424 • CPU (Pentium III) time: 30 minutes • kinematic viscosity: • density: • Drag Force: 207.58 nN • Q: 29.1

  20. Comparison of Different Models and Experiment

  21. FastStokes: Force Distribution • Top force: • Bottom force: • Side force (inter-finger + pressure):

  22. Example 2 – Squeeze-film Damping on Micro Plate/Beam Resonator in Partial Vacuum • Free-Molecule Regime • Low pressure: vacuum environment • Small scale: nano devices • Monte Carlo Simulation Courtesy: Prof. O. Brand 22

  23. Monte Carlo Approach • Based on the momentum and energy transfer between the free molecules and the walls • Assumptions: • Gas reservoir at equilibrium • Oscillation mode shape is not affect by collisions

  24. MC Simulation Approach • Initialization: Generate Molecules • At each time interval • Generatingnew gas molecules entering the interaction region • Tracking each gas molecule inside the interaction region • Detecting collisions and calculating energy change during each collision • Summing all the energy losses in each cycle • Ensemble averaging

  25. Particle Generation • Particle initialization • , Ideal gas law • Randomly, uniformly distributed over the entire interaction region • Velocities follow Maxwell-Boltzmann distribution

  26. Particle Generation • At each small time interval: • Tangential velocities  Maxwell-Boltzmann distribution • Normal velocities  Maxwell-Stream distribution

  27. Collision Detection • Determine the time and position of each collision • Collide with substrate or fixed walls • Solved analytically • Collide with the moving resonator • Solved numerically • Stability • Multiple roots

  28. Collision Model Specular reflection Diffuse reflection • Maxwell gas-wall interaction model • Specular reflection • Mirror-like • Diffuse reflection • Particle accommodated to the wall conditions Accommodation coefficient s

  29. Computation of Quality Factor

  30. Sumali’s Resonator Specular reflection; Frequency: 16.91 kHz H. Sumali, "Squeeze-film damping in the free molecular regime: model validation and measurement on a MEMS," J.Micromech Microeng., Vol. 17, pp. 2231-2240, 2007.

  31. Minikes’s Micro Mirror Agree well Viscous flow Other losses dominate A. Minikes, I. Bucher and G. Avivi, "Damping of a mirco-resonator torsion mirror in rarefied gas ambient," J.Micromech Microeng., Vol. 15, pp. 1762-1769, 2005.

  32. Examples – Thermal sensing AFM AFM TSAFM IBM Millipede

  33. Thermal Sensing AFM TSAFM

  34. Heat Transfer Modes Transfer Paths Length Scales Semi-Infinite g < 500 nm

  35. Multiscale Modeling • Path 1 – Continuum • Path 2 – Continuum • Path 3 – Direct Simulation Monte Carlo (DSMC) • Stochastic method • Particle motions and collisions are decoupled over small time intervals

  36. Multiscale Simulation – Thermal Sensing AFM Coupling Scheme: Alternating Schwarz Coupling

  37. Multiscale Simulation – Temperature Field Continuum solution Multiscale solution

  38. Multiscale Simulation – Heat Flux Total heat flux from the cantilever: 84.46 W/m 1-D decoupled model: 91.56 W/m

  39. Multiscale Simulation – Velocity Field Near the Cantilever

  40. Noncontinuum Phenomena • Thermally Induced Gas Flow • Knudsen Force TH TC F

  41. Crookes Radiometer Phenomena

  42. James Clerk Maxwell (1831–1879) A Einstein (1879- 1955) William Crookes (1832-1919) Radiometric Force

  43. Radiometric Force • Experimental data; • Numerical Studies by DSMC and ES-BGK Model equation. N Selden, et al., J Fluid Mech., 2009 N Selden, et al.,Phys. Rev. E, 2009

  44. Thermal Transpiration TH TC After Collision Before Collision Th Tc Tc Tw Th Tw zero tangential momentum nonzero net tangential momentum

  45. Thermal Transpiration - Velocity OSIP-DSMC

  46. Thermal Transpiration - Velocity

  47. Thermal Transpiration - Pressure

  48. Knudsen’s Pump 162 stages; 760 Torr 0.9 Torr Gianchandani: JMEMS 2005; JMM 2012; JMEMS in press. Gianchandani & Ye, Transducers 2009

  49. Knudsen Force Passian, et al. Journal of Applied Physics, 2002 Physical Review Letters, 2003 Lereu, et al Applied Physics Letters, 2004 Wall: 500K Argon Symmetric Wall: 300K

  50. Knudsen Force

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