Paper TR+NS-WeM6
Which Fractal Parameter Most Determines Adhesion?

Wednesday, November 11, 2009, 9:40 am, Room C4

The topography of a surface can be characterized by three fractal parameters: its surface roughness, its roughness exponent, and its lateral correlation length [1]. In 2001, T.S. Chow [2] predicted that a decrease in adhesion by orders of magnitude would follow from increasing the roughness exponent of a surface (i.e. by making it smoother), and that adhesion could also be lowered by decreasing its lateral correlation length (shorter wavelength). In 2007 [3], we published a simple analytical model, together with experimental data, that demonstrated the strong influence of surface roughness on adhesion. This year, using atomic force microscopy, experimental data were collected from MEMS sidewalls of varying topography but with the same chemical treatment in order to untangle which of the three fractal parameters is – or are – most important in determining adhesion. The data are inconsistent with Chow’s predictions; his assumption was that only the asperities on the surface contribute to the adhesion. In contrast, our numerical simulations of the tip-sample adhesion for surfaces with varying fractal parameters include both the asperities and the bulk of the sample.

Together with the simulations, the previous and current experimental data support the conclusion that surface roughness is a significant predictor of adhesion, with the adhesion dropping by more than an order of magnitude for a roughness change from 1 to 10 nm. For the roughness exponent, the simulations follow the same trend as Chow’s predictions, in that adhesion should decrease with increasing roughness exponent (smoother), but rather than predicting orders of magnitude change, the simulations reveal only a 20% decrease as the roughness exponent changes from 0 to 1. Here, the experimental data were more consistent with the simulation than Chow’s predictions, although they were not conclusive. The scatter in the data was large, and the range of the roughness exponent only varied from 0.85 to 0.99, for which the simulations predict a change in adhesion of approximately 10%. For the lateral correlation length, the experiment showed a wide range of adhesion values for smaller correlation lengths and low adhesion for larger correlation lengths (longer wavelengths); we are still investigating the theoretical basis of this observation. We hope to contribute to the understanding of adhesion so as to minimize stiction in MEMS.