Although the spreading behavior of liquid droplets impacting on solid surfaces has been extensively studied, the mechanism of recoiling which takes place after the droplet reaches its maximum spread diameter has not yet been fully understood. This paper reports the study of the recoiling behavior of different liquid droplets ͑water, ink, and silicone oil͒ on different solid surfaces ͑polycarbonate and silicon oxide͒. The droplet dynamics are experimentally studied using a high speed video system. Analytical methods using the variational principle, which were originated by Kendall and Rohsenow ͑MIT Technical Report 85694-100, 1978͒ and Bechtel et al. ͓IBM J. Res. Dev. 25, 963 ͑1981͔͒, are modified to account for wetting and viscous effects. In our model, an empirically determined dissipation factor is used to estimate the viscous friction. It is shown that the model closely predicts the experimental results obtained for the varying dynamic impact conditions and wetting characteristics. This study shows that droplets recoil fast and vigorously when the Ohnesorge number decreases or the Weber number increases. Droplets with a large equilibrium contact angle are also found to recoil faster. Here the Ohnesorge number scales the resisting force to the recoiling motion, and is shown to play the most important role in characterizing the recoiling motion.

A linear perturbation theory is developed to investigate the interface instabilities of a radially-expanding, liquid jet in cylindrical geometries. The theory is applied to rapidly spreading droplets upon collision with solid surfaces as the fundamental mechanism behind splashing. The analysis is based on the observation that the instability of the liquid sheet, i.e., the formation of the fingers at the spreading front, develops in the extremely early stages of droplet impact. The shape evolution of the interface in the very early stages of spreading is numerically simulated based on the axisymmetric solutions obtained by a theoretical model. The effects that factors such as the transient profile of an interface radius, the perturbation onset time, and the Weber number have on the analysis results are examined. This study shows that a large impact inertia, associated with a high Weber number, promotes interface instability, and prefers high wave number for maximum instability. The numbers of fingers at the spreading front of droplets predicted by the model agree well with those experimentally observed.

Nonplanarity arising from the chemical mechanical polishing of Cu-oxide damascene structures results in the exposure field ͑die-size͒ being partially out of focus in the subsequent lithography process. Thus the corresponding mechanisms of within-die polishing must be determined and the within-die nonplanarity due to polishing needs to be minimized to increase the process yield. In this paper, contact mechanics models were developed to explain the role of pattern geometry on the variation of material removal rate. The effects of Cu linewidth, area fraction, and the elastic properties of the polishing pad on pad displacement into low features were examined to focus on the mechanical aspects of the process. The pressure distribution on the high features was determined and the rate of pattern planarization was quantified. Experiments on patterned Cu wafers were conducted to verify the model. Based on these results, the planarization and polishing behavior and the within-die nonplanarity due to the variation of pattern geometry were discussed.

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