Investigation of contact and friction at multiple length scales is necessary for the design of surfaces in sliding microelectromechanical system (MEMS). A method is developed to investigate the geometry of summits at different length scales. Analysis of density, height, and curvature of summits on atomic force microscopy (AFM) images of actual silicon MEMS surfaces shows that these properties have a power law relationship with the sampling size used to define a summit, and no welldefined value for any is found, even at the smallest experimentally accessible length scale. This behavior and its similarity to results for fractal Weierstrass-Mandelbrot (W-M) function approximations indicate that a multiscale model is required to properly describe these surfaces. A multiscale contact model is developed to describe the behavior of asperities at different discrete length scales using an elastic single asperity contact description. The contact behavior is shown to be independent of the scaling constant when asperity heights and radii are scaled correctly in the model.
We have measured pre-sliding tangential deflections (PSTD) between micromachined surfaces of up to 200 nanometers in length before the static friction event using a polysilicon nanotractor actuator [1,2]. The detailed PSTD structure is resolved by a one-nanometer-resolution in-plane optical metrology we have developed, and may be a manifestation of discrete asperity-asperity interactions leading to an effective spatial distribution of friction coefficients. Results indicate a dependence on surface treatment, with a perfluorinated eight-carbon chain monolayer coating showing substantially different PSTD than an eighteen-carbon chain hydrocrabon monolayer. This behavior may qualitatively be related to variations in dynamic versus static friction. We present a simple phenomenological model that captures some of the behavior of PSTD, and suggest some possible microscopic interpretations.
This report details results from our last year of work (FY2005) on friction in MEMS as funded by the Campaign 6 program for the Microscale Friction project . We have applied different monolayers to a sensitive MEMS friction tester called the nanotractor . The nanotractor is also a useful actuator that can travel +100 µm in 40 nm steps, and is being considered for several MEMS applications . With this tester, we can find static and dynamic coefficients of friction. We can also quantify deviations from Amontons' and Coulomb's friction laws . Because of the huge surface-to-volume ratio at the microscale, surface properties such as adhesion and friction can dominate device performance, and therefore such deviations are important to quantify and understand. We find that static and dynamic friction depend on the monolayer lubricant applied. The friction data can be modeled with a non-zero adhesion force, which represents a deviation from Amontons' Law . Further, we show preliminary data indicating that the adhesion force depends not only on the monolayer, but also on the normal load applied . Finally, we also observe slip deflections before the transition from static to dynamic friction, and find that they depend on the monolayer .
Investigation of contact and friction at multiple length scales is necessary for the design of surfaces in sliding microelectromechanical system (MEMS). A method is developed to investigate the geometry of asperities at different length scales. Analysis of density, height, and curvature of asperities on atomic force microscopy (AFM) images of actual silicon MEMS surfaces show these properties have a power law relationship with the sampling size used to define an asperity. This behavior and its similarity to results for fractal Weierstrass-Mandelbrot (W-M) function approximations indicate that a multiscale model is required to properly describe the surfaces.
The primary goals of the present study are to: 1) determine how and why MEMSscale friction differs from friction on the macro-scale, and 2) to begin to develop a capability to perform finite element simulations of MEMS materials and components that accurately predicts response in the presence of adhesion and friction.Regarding the first goal, a newly developed nanotractor actuator was used to measure friction between molecular monolayer-coated, polysilicon surfaces. Amontons' law does indeed apply over a wide range of forces. However, at low loads, which are of relevance to MEMS, there is an important adhesive contribution to the normal load that cannot be neglected. More importantly, we found that at short sliding distances, the concept of a coefficient of friction is not relevant; rather, one must invoke the notion of "pre-sliding tangential deflections" (PSTD). Results of a simple 2-D model suggests that PSTD is a cascade of small-scale slips with a roughly constant number of contacts equilibrating the applied normal load.Regarding the second goal, an Adhesion Model and a Junction Model have been implemented in PRESTO, Sandia's transient dynamics, finite element code to enable asperity-level simulations. The Junction Model includes a tangential shear traction that opposes the relative tangential motion of contacting surfaces. An atomic force microscope (AFM)-based method was used to measure nano-scale, single asperity friction forces as a function of normal force. This data is used to determine Junction Model parameters. An illustrative simulation demonstrates the use of the Junction Model in conjunction with a mesh generated directly from an atomic force microscope (AFM) image to directly predict frictional response of a sliding asperity.Also with regards to the second goal, grid-level, homogenized models were studied. One would like to perform a finite element analysis of a MEMS component assuming nominally flat surfaces and to include the effect of roughness in such an analysis by using a homogenized contact and friction models. AFM measurements were made to determine statistical information on polysilicon surfaces with different roughnesses, and this data was used as input to a homogenized, multi-asperity contact model (the classical Greenwood and Williamson model). Extensions of the Greenwood and Williamson model are also discussed: one incorporates the effect of adhesion while the other modifies the theory so that it applies to the case of relatively few contacting asperities.5
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