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

Abstract

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 NavierStokes 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.

Modeling capillary forces for large displacements

“…Note that for R 1 | 0<u<h the small displacement values F 1 = −2γL u h and k 1 = 2γ L h of linear elastic models are recovered 9,12,20,29 . Conversely, the absence of elastic work in R 3 is evidenced by the null constant value of k 3 .…”

“…Thereby the focus has mainly been on sub-millimetric components actuated by droplets of similar size, and correspondingly on displacements from equilibrium of relatively small magnitude. Elastic models accurately capture the response of the capillary system to such small lateral displacements 9,12,[20][21][22] . In this type of models the restoring capillary forces arise exclusively from the shear deformation of liquid interfaces pinned to bounding solid surfaces.…”

In-Plane Mode Dynamics of Capillary Self-Alignment

“…Theoretical descriptions of the dynamics of uniaxial shift described in section 3.1 have been proposed for instance by Lu and Bailey 44 and Lambert et al 36 to estimate the characteristic damping time of the component oscillations in the final harmonic regime. In both models, the dynamics of the component is driven by the coupled physics of component motion and fluid dynamics of the liquid bridge.…”

Dynamics of freely moving plates connected by a shallow liquid bridge

“…This problem is relevant to the adhesion 1 and to the manipulation of solid bodies by capillary forces (specifically to the release scheme of the manipulated particles 2-5 ), flip-chip applications 6 and to spreading of contamination on a freely moving solid in contact with a flat plane filled with contaminated droplets. The dynamics of the solid bodies affects the droplet topology and will thus change the surface area in contact with the droplet and the pressure distribution within the liquid, thus affecting the spreading of contamination.…”