Prediction of Nanoscale Water Meniscus Shape between Deliquescent KDP Crystal Optics and AFM Probe for...

KDP (KH₂PO₄) crystal optics are the key elements for megajoule laser facilities. Nanoscale surface defects would cause laser-induced damage when the optics are irradiated by a high-fluence laser (over 10 J/cm²). Dip-pen nanolithography (DPN) could be used to repair the nanoscale surface defects in the KDP optics by the water meniscus. The high humidity required for high-efficiency and soft KDP surfaces penetrated by the AFM probe brings challenges for accurately predicting the water meniscus shape to evaluate the effectiveness of the DPN water-dissolution repairing. The multisolutions of the Young-Laplace and Kelvin equations also lead to the wrong water meniscus shape. A theoretical model that takes the high humidity and the penetration of the AFM probes into account is developed. The parametrization Young-Laplace equations are adopted for the zero contact angle of the water films, and the AFM probe is treated as the combination of the cone and sphere for the water meniscus whose size is larger than the AFM tip radius under high humidity. The penetration of the AFM probe is modeled by Hertz theory. Both the water films (3.3 nm thickness at 99% relative humidity) and indentations (1.46 nm depth at 300 nN contact force) are non-negligible for the nanoscale water meniscus between the KDP surface and the AFM probe. Moreover, the rough-fine two-step method is proposed to lock the correct solution of the Young-Laplace and Kelvin equations. The effectiveness of the proposed model is verified by comparison with reported ESEM images and pull-off forces. In addition, the overgrowth dots on the KDP surface are compared with the water meniscus. The linear growth of the water meniscus would cause the linear growth of the overgrowth dot, which proves the proposed model could be used to guide the DPN water-dissolution repairing for the nanoscale surface defects in the KDP optics.