On a deterministic approach for the evaluation of gas damping in inertial MEMS in the free-molecule regime

Sensors and Actuators, A: Physical

Volumn 149, Issue 1, 2009, Pages 21-28

  Frangi, A ^a   Ghisi, A ^a   Coronato, L ^b  

^a POLITECNICO DI MILANO   (Italy)

^b STMICROELECTRONICS   (Italy)

Author keywords

Dissipation; Free molecule flow; MEMS

Indexed keywords

BOUNDARY INTEGRAL EQUATIONS; INDUSTRIAL APPLICATIONS; MATHEMATICAL MODELS; MEMS; MICROELECTROMECHANICAL DEVICES; MONTE CARLO METHODS; POLYSILICON;

DETERMINISTIC APPROACHES; DIFFUSION MODELS; DISSIPATION; FREE-MOLECULE FLOW; GAS DAMPING; MOLECULE INTERACTIONS; MOLECULE REGIMES; NUMERICAL TOOLS; SMALL PERTURBATIONS; STATIC RESPONSES;

MOLECULES;

EID: 58149202219     PISSN: 09244247     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sna.2008.09.018     Document Type: Article

References (46)

1. Frangi A., Spinola G., and Vigna B. On the evaluation of damping in MEMS in the slip-flow regime. Int. J. Numer. Methods Eng. 68 (2006) 1031-1051
2. Chapman S., and Cowling T.G. The Mathematical Theory of Non-uniform Gases (1960), Cambridge University Press, Cambridge
3. Cercignani C. The Boltzmann Equation and its Applications (1988), Springer, New York
4. Bird G.A. Molecular Gas Dynamics and the Direct Simulation of Gas Flows (1994), Clarendon Press
5. Gad-el-Hak M. The fluid mechanics of microdevices-the Freeman scholar lecture. J. Fluids Eng. 121 (1999) 5-33
6. Karniadakis G.E., and Beskok A. Micro Flows, Fundamentals and Simulation (2002), Springer, New York
7. Ye W., Wang X., Hemmert W., Freeman D., and White J. Air damping in lateral oscillating micro-resonators: a numerical and experimental study. J. MEMS 12 (2003) 557-566
8. Frangi A., and Di Gioia A. Multipole BEM for the evaluation of damping forces on MEMS. Comput. Mech. 37 (2005) 24-31
9. Frangi A., and Tausch J. A qualocation enhanced approach for the Dirichlet problem of exterior Stokes flow. Eng. Anal. Bound. Elem. 29 (2005) 886-893
10. Mukherjee S., Telukunta S., and Mukherjee Y.X. BEM modeling of damping forces on MEMS with thin plates. Eng. Anal. Bound. Elem. 29 (2005) 1000-1007
11. Frangi A. A fast multipole implementation of the qualocation mixed-velocity-traction approach for exterior Stokes flows. Eng. Anal. Bound. Elem. 29 (2005) 1039-1046
12. Yuhong S., Barber R.W., and Emerson D.R. Inverted velocity profiles in rarefied cylindrical Couette gas flow and the impact of the accommodation coefficient. Phys. Fluids 17 (2006) 047102-047107
13. Liu Y.J., and Shen L. A dual BIE approach for large-scale modelling of 3-D electrostatic problems with the fast multipole boundary element method. Int. J. Numer. Methods Eng. 71 (2007) 837-855
14. Sone Y. Flow induced by thermal stress in rarefied gases. Phys. Fluids 15 (1971) 1418-1423
15. Loyalka S.K., Petrellis N., and Storvick S.T. Some exact numerical results for the BGK model: Couette, Poiseuille and thermal creep flow between plates. Z. Angew. Math. Phys. 30 (1979) 514-521
16. Shizgal B. A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems. J. Comput. Phys. 41 (1981) 309-327
17. Fukui S., and Kaneko R. Analysis of ultra-thin gas film lubrication based on the linearized Boltzmann equation. JSME Int. J. 30 (1987) 1660-1666
18. Cho Y., Kwak B., Pisano A.P., and Howe R.T. Slide film damping in laterally driven microstructures. Sens. Actuators A 40 (1993) 31-39
19. Sharipov F. Rarefied gas flow through a slit. Influence of the boundary condition. Phys. Fluids 8 (1995) 262-268
20. Zhang X., and Tang W.C. Viscous air damping in laterally driven micro-resonators. Sens. Mater. 7 (1995) 415-430
21. Yang J.Y., and Huang J.C. Rarefied flow computation using nonlinear model Boltzmann equations. J. Comput. Phys. 120 (1995) 323-339
22. Beskok A., Karniadakis G.E., and Trimmer W. Rarefaction and compressibility effects in gas microflows. J. Fluids Eng. 118 (1996) 448-456
23. J. Fan, C. Shen, Statistical simulation of low speed unidirectional flows in transition regime, in: Rarefied Gas Dynamics, R. Brun et al. (Ed.), (Cepadus-Editions, Toulouse, 1999), vol. 2, 1999, pp. 245-253
24. Cai C., Boyd I., Fan J., and Candler G. Direct simulation methods for low-speed microchannel flows. J. Thermophys. Heat Transfer 14 (2000) 368-380
25. Williams M.M.R. A review of the rarefied gas dynamics theory associated with some classical problems in flow and heat transfer. Z. Angew. Math. Phys. 52 (2001) 500-516
26. Aoki K., Takata S., and Nakanishi T. Poiseuille-type flow of a rarefied gas between two parallel plates driven by a uniform external force. Phys. Rev. 65 (2002) 026315-1-02631522-02631522
27. Lim C.Y., Shu C., Niu X.D., and Chew Y.T. Application of lattice Boltzmann method to simulate microchannel flow. Phys. Fluids 14 (2002) 2299-2308
28. Li Z.-H., and Zhang H.-X. Numerical investigation from rarefied flow to continuum by solving the Boltzmann model equation. Int. J. Numer. Methods Fluids 42 (2003) 361-382
29. Niu X.D., Shu C., and Chew Y.T. A lattice Boltzmann BGK model for simulation of micro flows. Europhys. Lett. 67 (2004) 600-606
30. Naris S., and Valougeorgis D. The driven cavity flow over the whole range of the Knudsen number. Phys. Fluids 17 (2005) 097106-097112
31. Shan X., Yuan X., and Chen H. Kinetic theory representation of hydrodynamics: a way beyond the Navier-Stokes equation. J. Fluid Mech. 550 (2006) 413-441
32. Emerson D.R., Gu X.J., Stefanov S.K., Sun Y.H., and Barber R.W. Nonplanar oscillatory shear flow: from the continuum to the free-molecular regime. Phys. Fluids 19 (2007) 105-107
33. Homolle T.M., and Hadjiconstantinou N.G. A low-variance deviational simulation Monte Carlo for the Boltzmann equation. J. Comput. Phys. 226 (2007) 2341-2358
34. Mieussens L. Discrete velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries. J. Comput. Phys. 162 (2000) 429-466
35. Frangi A., Frezzotti A., and Lorenzani S. On the application of the BGK kinetic model to the analysis of gas-structure interactions in MEMS. Comput. Struct. 85 (2007) 810-817
36. Zook J.D., Burns D.W., Guckel H., Sniegowski J.J., Engelstad R.L., and Feng Z. Characteristics of polysilicon resonant microbeams. Sens. Actuators A 35 (1992) 51-59
37. Christian R.G. The theory of oscillating-vane vacuum gauges. Vacuum 16 (1966) 175-178
38. Kadar Z., Kindt W., Bossche A., and Mollinger J. Quality factor of torsional resonators in the low-pressure region. Sens. Actuators A 53 (1996) 299-303
39. Li B., Wu H., Zhu C., and Liu J. The theoretical analysis on damping characteristics of resonant microbeam in vacuum. Sens. Actuators A 77 (1999) 191-194
40. Bao M., Yang H., Yin H., and Sun Y. Energy transfer model for squeeze-film air damping in low vacuum. J. Micromech. Microeng. 12 (2002) 341-346
41. Hutcherson S., and Ye W. On the squeeze-film damping of micro-resonators in the free-molecule regime. J. Micromech. Microeng. 14 (2004) 1726-1733
42. Andries P., Bourgat J.F., le Tallec P., and Perthame B. Numerical comparisons between the Boltzmann and ES-BGK models for rarefied gases. Comput. Method Appl. Mech. Eng. 191 (2002) 3369-3390
43. Frangi A., and Guiggiani M. Boundary element analysis of Kirchhoff plates with direct evaluation of hypersingular integrals. Int. J. Numer. Methods Eng. 46 (1999) 1845-1863
44. Frangi A., and Guiggiani M. A direct approach for boundary integral equations with high-order singularities. Int. J. Numer. Methods Eng. 49 (2000) 871-898
45. Park J.H., Bahukudumbi P., and Beskok A. Rarefaction effects on shear driven oscillatory gas flows: a direct simulation Monte Carlo study in the entire Knudsen regime. Phys. Fluids 16 (2004) 317-330
46. Liu Y.J. A new fast multipole boundary element method for solving 2-D Stokes flow problems based on a dual BIE formulation. Eng. Anal. Bound. Elem. 32 (2008) 139-151