Evolution of entrained water film thickness and dynamics of Marangoni flow in Marangoni drying

As an ultra-clean wafer drying technique, Marangoni drying has been widely applied in the integrated circuits manufacturing process. When the wafer is vertically withdrawn from a deionization water bath, Marangoni stress along the meniscus, which is induced by the organic vapour, strips off the water film entrained on the wafer surface, and the wafer drying is thereby realized. In this work, a numerical model is presented that is comprised of the film, meniscus, and bulk regions for Marangoni drying. The model combines the transfer of organic vapour from air to water and the withdrawal of the wafer from the bath. The evolution of the entrained water film thickness, the tangential velocity, and the stress at the air-water interface are quantitatively investigated. The results reveal that the thickness of the entrained water film is reduced by more than one order of magnitude compared with the wafer withdrawn process without the Marangoni effect. In addition, owing to the receding of the contact line, it is found that the capillary pressure gradient dramatically increases, which contributes to the sudden increase in the tangential velocity in the dynamic meniscus. Moreover, the tangential velocity decreases in the static meniscus adjacent to the dynamic meniscus, which results from the redistribution of the interfacial concentration of the organic species driven by the Marangoni flow.