Theoretical investigation of the distance dependence of capillary and van der Waals forces in scanning force microscopy

The capillary and van der Waals forces between a tip and a plane in a scanning force microscope (SFM) are calculated. The forces are calculated for a fixed distance of tip and sample, as well as during retracting of the tip from the sample surface. The exact geometric shape of the meniscus is considered, with the boundary condition of fixed liquid volume during retraction. The starting volume is given by the operating and environmental conditions (surface tension, humidity, and tip geometry) at the point of lowest distance between tip and surface. The influence of the different parameters, namely, humidity, tip geometry, tip-sample starting distance, surface tension, and contact angles are studied. For each force curve also the geometric shape of the meniscus is calculated. The capillary forces are compared with van der Waals forces to understand their relative importance in various operating conditions. In addition to application in SFM, this analysis is useful in the design of surface roughness in microdevices for low adhesion in operating environments.