Modelling slip flow in micro/nano gaps with moving boundary

• Exact solution models are constructed for slip flow in micro/nano gap.
• Models of slip flow are applied to the investigation of immersion lithography.
• Boundary slip on wafer improves the quality of immersion lithography.
• Desirable slip length is 0.02–0.05h for proper lens distortion and manufacturing cost.

The analytical solution models have been constructed to describe the slip flow in the micro/nano gaps with moving boundary, including the case of immersion lithography. The two-dimensional computational fluid dynamics models are established to validate them. The results show that the slip flow varies with time and tends to a steady state quickly. The transient and steady states are investigated respectively to overall describe the slip flow, and there are significant differences between the slip and non-slip flow. Moreover, the stationary liquid on moving wall may be generated when the direction of pressure-driven flow is opposite to the direction of shear flow. This phenomenon is important to prevent liquid leakage during wafer scanning, and the corresponding parameters are optimized to improve the quality of advanced immersion lithography.

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