Investigation on the critical velocity for liquid loss in immersion lithography

Immersion lithography seeks to extend the resolution of optical lithography by filling the gap between the final optical element and the wafer with a liquid characterized by a high index of refraction. The semiconductor industry demands high throughput, leading to relatively large wafer scanning velocities and accelerations. For higher scanning velocities, an issue that has been identified is the deposition of the immersion liquid while confining a relatively small amount of liquid to the under-lens region. Liquid loss occurs at the receding contact line that forms when a substrate is withdrawn from a liquid, which potentially leads to defects on printed patterns. There has been substantial prior work relative to understanding and building semi-empirical correlations and numerical models to investigate this behavior of the receding three-phase contact line. In the current work, a new liquid injection and collection model with analytic solutions is presented and compared with experimental results, in which the critical velocity for liquid loss is mainly a function of the vacuum degree, the injection flow rate, the properties of the immersion liquid. This correlation allows the critical velocity to be predicted with a given gap height between wafer and lens using only a measurement of the injection speed and knowledge of the fluid properties. Experimentally, glycerin–water mixtures of varying viscosities and different injection flow rates were tested, with variable outlet vacuum degree and inlet speed, showing a mean average error within 12%. This correlation represents a useful tool that can serve to approximately guide the development of fluid control for immersion systems as well as to evaluate alternative immersion fluid candidates to minimize liquid deposition while maximizing throughput.