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浙江大学学报(工学版)
浙江大学学报(工学版)  2026, Vol. 60 Issue (11): 2346-2354    DOI: 10.3785/j.issn.1008-973X.2026.11.004
机械工程     
缝隙流场低频振动下钉扎液膜挤压力传递特性
徐杭杭(),阮晓东,胡亮
浙江大学 流体动力基础件与机电系统全国重点实验室，浙江 杭州 310058
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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摘要：

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    
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
收稿日期: 2025-09-02 出版日期: 2026-10-16
CLC:  TB 126  
基金资助: 浙江省自然科学基金资助项目（LD24E050008）.
作者简介: 徐杭杭（1993—），女，博士，从事应用流体力学研究. orcid.org/0009-0003-8971-2548. E-mail：mihhang@zju.edu.cn
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引用本文:

徐杭杭,阮晓东,胡亮. 缝隙流场低频振动下钉扎液膜挤压力传递特性[J]. 浙江大学学报(工学版), 2026, 60(11): 2346-2354.

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.

链接本文:

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

图 1  浸没罩的结构示意图
图 2  钉扎液膜挤压实验的示意图
图 3  钉扎液膜挤压实验的装置
图 4  下平板的振动幅值随输入电压的变化曲线
图 5  钉扎液膜挤压实验的流程图
图 6  钉扎液膜示意图
图 7  静态钉扎液膜的气液界面
图 8  不同缝隙高度下钉扎液膜的初始气液边界
H/mmr1/mm$ {{\theta }}_{2} $/（°）$ {{F}}_{\text{c}} $/Nδ/%
计算量测
1.036.05105?0.14?0.1216
1.535.7078?0.18?0.153
2.035.1664?0.17?0.185
表 1  不同缝隙高度下钉扎液膜的边界条件
图 9  挤压钉扎液膜时弯液面变化的示意图
图 10  准静态条件下钉扎液膜弯液面形貌变化
t/s$ {\theta }_{1} $/（$ {^{\circ}}） $$ {\theta }_{2} $/（$ {^{\circ}}） $$ {F}_{\text{c}} $/NΔ$ {F}_{\text{c}} $/N
计算量测
040125?0.14?0.120.02
0.12547127?0.10?0.070.03
0.25051129?0.08?0.050.03
0.37547122?0.13?0.070.06
0.50040118?0.18?0.130.05
0.62536113?0.21?0.180.03
0.75031107?0.26?0.200.06
0.87537118?0.19?0.170.02
1.00042121?0.15?0.120.03
表 2  准静态条件下钉扎液膜的边界条件
图 11  准静态条件下上平板受力的时域曲线
图 12  质量-弹簧-阻尼系统的示意图
图 13  低频振动条件下液膜挤压力的时域曲线
图 14  不同振动条件下的液膜挤压力
图 15  不同振动频率和液膜厚度下的液膜挤压力
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