Receding contact lines: From sliding drops to immersion lithography

Abstract

Abstract. Instabilities of receding contact lines often occur through the formation of a corner with a very sharp tip. These dewetting structures also appear in the technology of Immersion Lithography, where water is put between the lens and the silicon wafer to increase the optical resolution. In this paper we aim to compare corners appearing in Immersion Lithography to those at the tail of gravity driven-drops sliding down an incline. We use high speed recordings to measure the dynamic contact angle and the sharpness of the corner, for varying contact line velocity. It is found that these quantities behave very similarly for Immersion Lithography and drops on an incline. In addition, the results agree well with predictions by a lubrication model for cornered contact lines, hinting at a generic structure of dewetting corners.

Enhancement of contact line mobility by means of infrared laser illumination. I. Experiments

“…3, a smaller value of h r would be expected, contrary to the experimental results. Winkels 44 measured the shape of isothermal sliding droplets as a function of speed and found that the opening angle at the critical substrate speed equalled u ¼ 60…”

Dynamical wetting transition: liquid film deposition and air entrainment

“…The problem is that, when the substrate is moving too fast, droplets are emitted at the receding part of the liquid similar to what happens in the moving drop case, see Fig. 1.2b [4]. Similarly, at much higher speed, air bubbles are observed in the advancing part, suggesting entrainment of air at the advancing contact line.…”

“…An additional complexity is that the contact line can spontaneously develop sharp corner structures, or even zig-zags. This has been observed in dip-coating [2], splashing [39], immersion lithography [4,40] and for drops sliding down an inclined plane [1,41]. The conical structure of the interface near the contact line renders the problem truly three-dimensional, which affects the balance of the capillary forces [42].…”

“…One example is in Immersion Lithography [4,5], where light is directed through a lens on a substrate to construct circuit patterns. A portion of liquid of high refractive index (usually water) is injected between the lens and the substrate and maintained there [1].…”

“…water) have a relatively low viscosity and inertia can be important at scales away from the contact line. As an example we mention Immersion Lithography [4], where the fluid in between the lens and the substrate is water that has viscosity η around 10 −3 mPa·s and density ρ = 10 3 kg/m 3 at room temperature. If we take the typical speed of flow U as 0.1 − 1 m/s and the distance between the lens and the substrate L as 0.1 − 1 mm, then the Reynolds number based on the macroscopic dimension is of order Re ≡ ρUL/η ≃ 10, or larger.…”