Fig. 2: Meniscus model.
a Schematic diagram depicting the model parameters: a is the meniscus radius. twet = 1 nm, is the native water layer existent in all surfaces for typical scanning conditions. tmeniscus is the meniscus thickness, measured from the water surface on the substrate to the water surface on the tip. Therefore, the distance between the tip to the surface is ttotal = 2twet + tmeniscus. b Capacitance and tip deflection force data during tip approach in solid black and dashed red lines. Analytical and FEM models describing the tip-surface capacitance (orange line with solid circles and dashed black lines). The blue dashed lines and solid circles represent FEM model results for the tip, surface, and water meniscus system, with meniscus thickness tmeniscus (upper x-axis) ranging from 1 to 6 nm, with radii a of 3 nm and 6 nm (light and dark blue). For the tip approach cycle, the lower x-axis represents the tip-surface distance (excluding the 2twet contribution of the surface water layers) up until tip pull by the water meniscus until around 8 nm after which tip deflection is dominated by capillary forces and water meniscus formation. For the remaining travel of tip approach, and for the tip retraction cycle, the x-axis represents piezo-displacement, until the tip snaps off, at about 60 nm. The shaded blue represents the locus of sMIM operation with the presence of a water meniscus during tip retraction, i.e., an attractive mode where we conducted all sMIM experiments.
