Spectral analysis and experimental study of lateral capillary dynamics for flip-chip applications

This article presents a study on the dynamics of lateral motion of a liquid meniscus confined by a pad and a chip moving parallel to the pad. This problem is a typical flip-chip case study, whose use is widespread in industrial assembly. The proposed model describing this dynamics is built upon two coupled physics: the Navier-Stokes equation governing the liquid flow between the pad and the chip, and the Newton's law describing the motion of the chip. This coupled problem is solved with a spectral method based on Chebyshev polynomials, by assuming a linear analytical expression of the lateral stiffness of the meniscus in the cases of circular and square pads. The theoretical results are benchmarked with literature results and thoroughly experimentally validated. From these results, we propose a map giving the characteristic time of the chip dynamics according to only two non-dimensional parameters, constructed with the physical (density, surface tension, and viscosity), geometrical (pad area and gap), or dynamical (chip mass) parameters of the problem.