Adhesive contact of solid surfaces

Abstract

The rapid progress in micro-and nanofabrication techniques over the last several decades has led to the development of various miniature electromechanical systems, such as microvibromotors [1], MEMS RF switches [2, 3], MEMS optical tweezers [4, 5], and MEMS mirrors [6, 7]. These have attracted great interest in using movable micromechanical structures in various MEMS and NEMS devices. The performance and lifetime of MEMS and NEMS devices are limited by the material confinement in submicron structures with large surface area, high electric field, large stress gradient, and other factors normally nonexistent in macroscale structures. On the microscale, material behavior is more controlled by surface-driving effects than by bulk effects. For example, frictional effects play a much more important role than inertia in the control of rotary or linear micromotors; i.e., the start-up conditions strongly depend on static friction and moving/rotational speed on kinetic friction. If there exists electric field, field-assisted contact is present. One of major concerns for long-term applications of MEMS and NEMS structures is mechanical failure, including surface contact, fracture and fatigue. Surface contact of micromechanical structures can contribute to stiction (adhesive contact), damage, pitting, and surface hardening over local contact area. The presence of stiction is due to high compliance and large surface-to-volume ratio of micromechanical structures, which do not have enough restoring force to overcome the surface interaction after mechanical contact. Stiction can be classified into two categories: release-related stiction and in-service stiction [8]. Release-related stiction appears during the removal of sacrificial layers for the release of micromechanical structures, which basically is due to liquid bridges and is controlled by the Laplace pressure and the surface tension of liquid etchants. Practical solutions to the problem of release-related stiction include use of dimples and cavity to reduce the contact area [9-11], change of meniscus shape [12], avoidance of liquid-vapor interfaces through supercritical fluid [13], freeze-sublimation drying [14], and drying release methods. However, all of these methods could not prevent the stiction from occurring during the operation of microdevices. When the separation between two solid surfaces reaches interatomic equilibrium distance, chemical bonding (ionic, covalent, or metallic) occurs and attractive force increases profoundly [15]. As attractive force is larger than restoring force, solid surfaces permanently stick to each other causing failure of microdevices-in-service stiction. Several models have been developed on the adhesive contact between spherical particles or between a spherical particle and a semi-infinite substrate, including Bradley model [16], JKR (Johnson-Kendall-Roberts) theory [17], and DMT (Derjaguin-Müller- Toporov) theory [18]. In the analysis, Bradley [16] calculated the interaction force between two rigid particles using a simple integration of molecular interaction without justification of the force additivity. Assuming that the surface interaction creates a uniform displacement over the contact zone and there is no surface interaction outside the contact zone, Johnson et al. [17] used the Hertz contact theory [19] to obtain the pull-off force required to separate two elastic spheres in frictionless contact. Recently, Li [20] also obtained the same relation by using the Moutier theorem. Derjaguin et al. [18] considered the effect of surface interaction outside the contact zone on the contact deformation of two elastic spheres. They obtained the pull-off force the same as the interaction force given by Bradley [16]. The pull-off force F a to separate two elastic spherical particles in frictionless contact can be expressed as Fa =χπReffγ, (4.1) where χ =3/2 for the JKR theory and χ =2 for the DMT theory. Here, R eff =R1R2/(R1+R2) with R1 and R2 being, respectively, the radius of the two spheres. γ is the work of adhesion, which is determined by the difference between the energy per unit area of the contacting surfaces, γ1 and γ2, before contact and that of the interface, γ12, after contact (γ =γ1+γ 2-γ12). The difference between the JKR theory and the DMT theory was later addressed by Tabor [21], who introduced the Tabor number of μ: the ratio of the maximum neck height in contact zone to intermolecular spacing. The DMT theory provides a good description of adhesive contact for small μ, while the JKR theory prevails for large μ. Such a behavior was also revealed by Müller et al. [22] using numerical calculation and by Maugis [23] using the theory of the Dugdale crack [24]. The development of microfabrication techniques in the last several decades has made use of compliant structures and submicron surface coatings in MEMS and NEMS devices. As the ratio of the contact size to the film thickness increases, the assumption of semi-infinite space becomes invalid and the substrate effect needs to be taken into account. This has limited the use of the JKR theory and the DMT theory in probing the adhesive contact of micromechanical structures and has imposed a tremendous challenge in understanding submicron adhesive behavior and in improving the mechanical design with a least possibility of adhesion. This chapter covers some basic physics related to adhesive contact of thin films, MEMS structures, and adhesion of thin films to substrates. It summarizes the recent development in studying the mechanical and interfacial behavior of materials. © Springer Science+Business Media, LLC, 2008.