Squeezing force transmission characteristics in pinned liquid film under low-frequency vibration in gap flow field

doi:10.3785/j.issn.1008-973X.2026.11.004

Journal of ZheJiang University (Engineering Science)

2026, Vol. 60

Issue (11): 2346-2354 DOI: 10.3785/j.issn.1008-973X.2026.11.004

Squeezing force transmission characteristics in pinned liquid film under low-frequency vibration in gap flow field

Hanghang XU(

),Xiaodong RUAN,Liang HU

State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310058, China

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Abstract

The influence of gas-liquid pressure fluctuations in the recovery system on the wafer is investigated for immersion lithography systems. First, the complex structure of the immersion hood was simplified, and an experimental platform was established based on a model for a pinned liquid film squeezed by circular plates. Subsequently, the capillary forces exerted by pinned liquid films of different thicknesses on the upper plate were experimentally measured. The evolution of the liquid meniscus morphology and the variation characteristics of the transmitted force on the upper plate during the squeeze process were summarized. Furthermore, the experimentally measured squeezing forces transmitted by the pinned liquid film under quasi-static conditions were compared with theoretical calculations. Finally, the pinned liquid film was modeled as a mass-spring-damper system. Such an equivalent system helped to reveal how the pinned liquid film transmits squeezing force and generates accompanying radial flow under low-frequency vibration, thereby inducing variations in the forces acting on the plate. The squeezing force transmitted by the pinned liquid film increased linearly with vibration amplitude, nonlinearly with vibration frequency, and decreased nonlinearly with film thickness.

Key words： semiconductor devices bit density immersion lithography pinned liquid film vibration squeezing force

Received: 02 September 2025 Published: 16 October 2026

CLC:

TB 126

Fund: 浙江省自然科学基金资助项目（LD24E050008）.

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Cite this article:

Hanghang XU,Xiaodong RUAN,Liang HU. Squeezing force transmission characteristics in pinned liquid film under low-frequency vibration in gap flow field. Journal of ZheJiang University (Engineering Science), 2026, 60(11): 2346-2354.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2026.11.004 OR https://www.zjujournals.com/eng/Y2026/V60/I11/2346

缝隙流场低频振动下钉扎液膜挤压力传递特性

探究浸没式光刻系统中浸液控制单元回收系统的气液压力波动对硅片的影响. 对浸液控制单元的复杂结构进行简化，基于圆平板挤压钉扎液膜模型搭建基础研究实验平台. 通过实验测得不同厚度钉扎液膜对上平板作用的毛细力，总结挤压过程中弯液面形貌的演变规律，以及上平板所受传递力的变化规律. 对比准静态条件下钉扎液膜传递的挤压压力实测值与理论计算值，提出将钉扎液膜等效为质量-弹簧-阻尼系统. 该等效系统有利于分析钉扎液膜在低频振动下传递的挤压压力及其伴随的径向流动导致平板受力变化的动态机理. 钉扎液膜传递的挤压压力随振动幅值增大而线性增大，随振动频率增大而非线性增大，随液膜厚度增大而非线性减小.

关键词： 半导体器件, 位元密度, 浸没式光刻, 钉扎液膜, 振动, 挤压力

Fig.1 Structural diagram of immersion hood

Fig.2 Schematic of pinned liquid film squeezing experiment

Fig.3 Squeezing setup for pinned liquid film

Fig.4 Vibration amplitude of lower plate as function of input voltage

Fig.5 Flowchart of pinned liquid film squeezing experiment

Fig.6 Schematic of pinned liquid film

Fig.7 Gas-liquid interface of statically pinned liquid film

Fig.8 Initial gas-liquid interface of pinned liquid film at different gap heights

Tab.1 Boundary conditions of pinned liquid films at different gap heights

Fig.9 Schematic of meniscus evolution during squeezing of pinned liquid film

Fig.10 Meniscus morphology evolution in pinned liquid film under quasi-static conditions

Tab.2 Boundary conditions for pinned liquid film under quasi-static conditions

Fig.11 Time-domain curve of force on upper plate under quasi-static condition

Fig.12 Schematic of mass-spring-damper system

Fig.13 Time-domain curve of liquid film squeezing force under low-frequency vibration conditions

Fig.14 Liquid film squeezing force under different vibration conditions

Fig.15 Liquid film squeezing force under different vibration frequencies and film thicknesses


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