(c) 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works
[en] Stiction, which results from contact between surfaces, is a major failure mode in micro electro-mechanical systems (MEMS). Indeed microscopic structures tend to adhere to each other when their surfaces enter into contact and when the restoring forces are unable to overcome the interfacial forces. Since incidental contacts cannot be completely excluded and since contacts between moving parts can be part of the normal operation of some types of MEMS, stiction prediction is an important consideration when designing micro and nano-devices. In this paper a micro-macro multi-scale approach is developed in order to predict possible stiction. At the lower scale, the unloading adhesive contact-distance curves of two interacting rough surfaces are established based on a previously presented model [L. Wu et al., J. Appl. Phys. 106, 113502, 2009]. In this model, dry conditions are assumed and only the van der Waals forces as adhesion source are accounted for. The resulting unloading adhesive contact-distance curves are dependant on the material and on surface properties, such as, elastic modulus, surface energy and on the rough surfaces topography parameters; the standard deviation of asperity heights and the asperities density. At the higher scale, a finite element analysis is considered to determine the residual cantilever beam configuration due to the
adhesive forces once contact happened. Toward this end, the adhesive contact-distance curve computed previously is integrated on the surface of the finite elements as a contact law.
Effects of design parameters can then be studied for given material and surface properties.
A. Hariri, J. W. Zu, and R. Ben Mrad, "Modeling of dry stiction in micro electro-mechanical systems (MEMS)," J. Micromech. Microeng., vol. 16, no. 7, pp. 1195-1206, Jul. 2006. (Pubitemid 43884495)
W. Robert Ashurst, C. Yau, C. Carraro, R. Maboudian, and M. T. Dugger, "Dichlorodimethylsilane as an anti-stiction monolayer for MEMS: A comparison to the octadecyltrichlosilane self-assembled monolayer," J. Micromech. Syst., vol. 10, no. 1, pp. 41-49, Mar. 2001. (Pubitemid 32287839)
W.M. van Spengen, R. Puers, and I. DeWolf, "A physical model to predict stiction in MEMS," J. Micromech. Microeng., vol. 12, no. 5, pp. 702-713, Sep. 2002.
W. M. van Spengen, R. Puers, and I. De Wolf, "On the physics of stiction and its impact on the reliability of microstructures," J. Adhesion Sci. Technol., vol. 17, no. 4, pp. 563-582, 2003.
K. L. Johnson, K. Kendall, and A. D. Roberts, "Surface energy and the contact of elastic solids," Proc. R. Soc. Lond. A, vol. 324, no. 1558, pp. 301-313, Sep. 1971.
B. V. Derjaguin, V. M. Muller, and Y. P. Toporov, "Effect of contact deformation on the adhesion of elastic solids," J. Colloid Interface Sci., vol. 53, no. 2, pp. 314-326, Nov. 1975.
D. Tabor, "Surface forces and surface interactions," J. Colloid Interface Sci., vol. 58, no. 1, pp. 2-13, Jan. 1977.
D. Maugis, "Adhesion of spheres: The JKR-DMT transition using a Dugdale model," J. Colloid and Interface Sci., vol. 150, no. 1, pp. 243-269, Apr. 1992.
L. Kogut and I. Etsion, "Adhesion in elastic-plastic spherical microcontact," J. Colloid and Interface Sci., vol. 261, no. 2, pp. 372-378, May 2003. (Pubitemid 36535449)
Y. Kadin, Y. Kligerman, and I. Etsion, "Loading-unloading of an elastic-plastic adhesive spherical microcontact," J. Colloid Interface Sci., vol. 321, no. 1, pp. 242-250, May 2008.
L. Johnson and J. A. Greenwood, "An adhesion map for the contact of elastic spheres," J. Colloid Interface Sci., vol. 192, no. 2, pp. 326-333, Aug. 1997. (Pubitemid 27475411)
P. Attard and J. L. Parker, "Deformation and adhesion of elastic bodies in contact," Phys. Rev. A, vol. 46, no. 12, pp. 7959-7971, Dec. 1992.
V. M. Muller, V. S. Yushchenko, and B. V. Derjaguin, "On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane," Progr. Surf. Sci., vol. 45, no. 1-4, pp. 157-167, Jan.-Apr. 1994.
J. A. Greenwood, "Adhesion of elastic spheres," Proc. R. Soc. London A, vol. 453, no. 1961, pp. 1277-1297, Jun. 1997. (Pubitemid 127758619)
R. Gissi and P. Decuzzi, "The effect of shape and size in micro-/nanodimples adhesion," J. Appl. Phys., vol. 98, no. 1, pp. 014310-1-014310-9, Jul. 2005.
Y. Kadin, Y. Kligerman, and I. Etsion, "Jump-in induced plastic yield onset of approaching microcontacts in the presence of adhesion," J. Appl. Phys., vol. 103, no. 1, pp. 013513-1-013513-8, Jan. 2008.
Y. Kadin, Y. Kligerman, and I. Etsion, "Cyclic loading of an elasticplastic adhesive spherical microcontact," J. Appl. Phys., vol. 104, no. 7, pp. 073522-1-073522-8, Oct. 2008.
Y. Du, L. Chen, N. E. McGruer, G. G. Adams, and I. Etsion, "A finite element model of loading and unloading of an asperity contact with adhesion and plasticity," J. Colloid Interface Sci., vol. 312, no. 2, pp. 522-528, Aug. 2007. (Pubitemid 46935764)
J. A. Greenwood and J. B. P. Williamson, "Contact of nominally flat surfaces," Proc. R. Soc. Lond. A, vol. 295, no. 1442, pp. 300-19, Dec. 1966.
J. A. Greenwood and J. H. Tripp, "The contact of two nominally flat rough surfaces," Proc. Inst. Mech. Eng., vol. 185, pp. 625-633, 1971.
S. Patra, S. M. Ali, and P. Sahoo, "Elastic-plastic adhesive contact of rough surfaces with asymmetric distribution of asperity heights," Wear, vol. 265, no. 3/4, pp. 554-559, Jul. 2008.
L. Wu, V. Rochus, L. Noels, and J. C. Golinval, "Influence of adhesive rough surface contact on microswitches," J. Appl. Phys., vol. 106, no. 11, pp. 113502-1-113502-10, Dec. 2009.
B. B. Mandelbrot, The Fractal Geometry of Nature. New York: Freeman, 1983.
A. Majumdar and B. Bhushan, "Fractal model of elastic-plastic contact between rough surfaces," J. Tribol., vol. 113, no. 1, pp. 1-11, Jan. 1991.
N. Tas, T. Sonnenberg, H. Jansen, R. Legtenberg, and M. Elwenspoek, "Stiction in surface micromachining," J. Micromech. Microeng., vol. 6, no. 4, pp. 385-397, Dec. 1996. (Pubitemid 126547728)
M. P. de Boer and T. A. Michalske, "Accurate method for determining adhesion of cantilever beams," J. Appl. Phys., vol. 86, no. 2, pp. 817-827, Jul. 1999. (Pubitemid 129308264)
M. P. de Boer, J. A. Knapp, T. M. Mayer, and T. A. Michalske, "The role of interfacial properties on MEMS performance and reliability," in Proc. SPIE/EOS Conf. Microsyst. Metrol. Inspection, Munich, Germany, Jun. 15, 1999, pp. 2-15.
L. L. Mercado, S.-M. Koo, T.-Y. Tom Lee, and L. Liu, "A mechanical approach to overcome RF MEMS switch stiction problem," in Proc. 53rd Electron. Components Technol. Conf., 2003, pp. 377-384.
R. Ardito, A. Corigliano, and A. Frangi, "Finite element modelling of adhesion phenomena in MEMS," in Proc. 11th Int. Conf. Thermal, Mech. Multiphys. Simul. MEMS, EuroSimE, Bordeau, France, 2010.
M. O'Callaghan and M. A. Cameron, "Static contact under load between nominally flat surfaces in which deformation is purely elastic," Wear, vol. 36, no. 1, pp. 79-97, Jan. 1976.
K. S. Kim, R. M. McMeeking, and K. L. J. Johnson, "Adhesion, slip, cohesive zones and energy fluxes for elastic spheres in contact," Mech. Phys. Solids, vol. 46, no. 2, pp. 243-266, Feb. 1998. (Pubitemid 128393868)
R. J. Stokes and D. F. Evans, Fundamentals of Interfacial Engineering. New York: Wiley-VCH, 1997.
N. Yu and A. A. Polycarpou, "Adhesive contact based on the Lennard-Jones potential: A correction to the value of the equilibrium distance as used in the potential," J. Colloid Interface Sci., vol. 278, no. 2, pp. 428-435, Oct. 2004. (Pubitemid 39140721)
F. Cacchione, "Mechanical characterization and simulation of fracture processes in polysilicon micro electro mechanical systems (MEMS)," Ph.D. dissertation, Dipartimento di Ingegneria Srutturale, Politechnico di Milano, Milan, Italy, 2007.
X. Xue, L. M. Phinney, and A. A. Polycarpou, "Asymmetric surface roughness measurements and meniscus modeling of polysilicon surface micromachined flaps," Microsyst. Technol., vol. 14, no. 1, pp. 17-29, Aug. 2007. (Pubitemid 47245152)
K. C. Fang and C. I. Weng, "An investigation into the melting of silicon nanoclusters using molecular dynamics simulations," Nanotechnol., vol. 16, no. 2, pp. 250-256, Feb. 2005.
J. J. Gilman, "Direct measurements of the surface energies of crystals," J. Appl. Phys., vol. 31, no. 12, pp. 2208-2218, Dec. 1960.
C. Messmer and J. C. Bilello, "The surface energy of Si, GaAs, and GaP," J. Appl. Phys., vol. 52, no. 7, pp. 4623-4629, Jul. 1981.
U. Gösele, Y. Bluhm, G. Kästner, P. Kopperschmidt, G. Kräuter, R. Scholz, L.-J. Huang, Y.-L. Chao, and T. H. Lee, "Fundamental issues in wafer bonding," J. Vac. Sci. Technol. A, Vac. Surf. Films, vol. 17, no. 4, pp. 1145-1152, Jul. 1999. (Pubitemid 129649382)
A. Plößl and G. Kräuter, "Wafer direct bonding: Tailoring adhesion between brittle materials," Mater. Sci. Eng. R, Rep., vol. 25, no. 1/2, pp. 1-88, Mar. 1999. (Pubitemid 32262839)
B. Cappela and G. Dietler, "Force-distance curves by atomic force microscopy," Surf. Sci. Rep., vol. 34, no. 1, pp. 1-104, Jul. 1999.
C. Y. Poon and B. Bhushan, "Comparison of surface roughness measurements by stylus profile AFM and non-contact optical profiler," Wear, vol. 190, no. 1, pp. 76-88, Nov. 1995.
J. I. McCool, "Predicting microfracture in ceramics via a microcontact model," J. Tribol., vol. 108, no. 3, pp. 380-386, Jul. 1986. (Pubitemid 16605142)
R. W. Carpick, E. E. Flater, J. R. VanLangendon, and M. P. de Boer, "Friction in MEMS: From single to multiple asperity contact," in Proc. Int. Congr. Expo. Exp. Appl. Mech., 2002, pp. 282-287.
L. Kogut and R. L. Jackson, "A comparison of contact modeling utilizing statistical and fractal approaches," J. Tribol., vol. 128, no. 1, pp. 213-217, Jan. 2006.
F. W. Delrio, M. P. de Boer, J. A. Knapp, E. D. Reedt, Jr, P. J. Clews, and M. L. Dunn, "The role of van der Waals forces in adhesion of micromachined surfaces," Nat. Mater., vol. 4, no. 8, pp. 629-634, Aug. 2005. (Pubitemid 41092694)
R. Legtenberg, "Electrostatic actuators fabricated by surface micromachining techniques," Ph.D. dissertation, Univ. Twente, Enschede, The Netherlands, 1996.
A. Y. Suh and A. A. Polycarpou, "Adhesion and pull-off forces for polysilicon MEMS surfaces using the sub-boundary lubrication model," J. Tribol., vol. 125, no. 1, pp. 193-199, Jan. 2003. (Pubitemid 36610786)
M. P. de Boer, "Capillary adhesion between elastically hard rough surfaces," Exp. Mech., vol. 47, no. 1, pp. 171-183, Feb. 2007.
F.W. Del Rio,M. L. Dunnb, andM. P. de Boer, "Capillary adhesion model for contacting micromachined surfaces," Script. Mater., vol. 59, no. 9, pp. 916-920, Nov. 2008.
O. Rezvanian, M. A. Zikry, C. Brown, and J. Krim, "Surface roughness, asperity contact and gold RF MEMS switch behavior," J. Micromech. Microeng., vol. 17, no. 10, pp. 2006-2015, Oct. 2007. (Pubitemid 47469907)
J. H. Kim, D. J. Srolovitz, P.-R. Cha, and J.-K. Yoon, "Capillarity and electromigration effects on asperity contact evolution in microelectromechanical systems switches," J. Appl. Phys., vol. 100, no. 5, pp. 054502-1-054502-8, Sep. 2006, Paper .
J. N. Reddy, "On locking-free shear deformable beam finite elements," Comput. Methods Appl. Mech. Eng., vol. 149, no. 1-4, pp. 113-132, Oct. 1997. (Pubitemid 127405817)
A. Tayebi and A. Polycarpou, "Adhesion and contact modeling and experiments in microelectromechanical systems including roughness effects," Microsyst. Technol., vol. 12, no. 9, pp. 854-869, Aug. 2006.