Dynamic behaviors of capillary water menisci during lithography process for dip-pen nanolithography

The stable water menisci are the key to guarantee the stability of molecular self-assembly processes for Dip-pen Nanolithography (DPN). However, the mainstream quasi-static method ignores tip velocity, boundary slip, etc., posing challenges for analyzing dynamic behaviors of the meniscus. Besides, the influences of the DPN parameters (humidity, temperature, tip structure, etc.) on the dynamic menisci remain unclear. In this work, a simulation model is established based on the Computational Fluid Dynamics, Phase Field theory, and Navier slip boundary to break the limitations of the prevailing quasi-static method and track the dynamic meniscus profiles. Its effectiveness is proved by comparing dynamic relaxation results with static meniscus profile under thermodynamic equilibrium. The Weber similarity criterion and Tolman theory further demonstrate its validity for the meniscus of which volume is over 200 nm³. The dynamic menisci are laminar flow driven by surface tension. As the probe is lifted off, the stabilities of the menisci are determined by their volumes. The dynamic rupture distances exhibit a power relationship with the volumes, and they are much larger than the static rupture distances. The high-humidity, low-temperature, hydrophilic surface, blunted probe, and contact SPM mode contribute to improve the stability of the DPN processes by increasing the meniscus volumes. Besides, the volumes of residual droplets on the probe- and substrate- surfaces are determined by their equivalent wettability, and the dynamic rupture distances reach the maximum when their equivalent wettability is the same. It is also found that the dynamic behaviors of the menisci are closely related to tip velocity, proving that the mainstream quasi-static method is controversial. The rupture distances increase rapidly with tip velocity of < 10 mm/s. As the probe traverses laterally, the excessive velocity differences (> 6 mm/s) would overstretch and destroy the menisci. This work helps to provide theoretical references for studying micro-nano fluid flow and probe-based techniques.