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 scann ing 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 f rom the sample surface. The exact geometric shape of the meniscus is consid ered, 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 dista nce between tip and surface. The influence of the different parameters, nam ely, humidity, tip geometry, tip-sample starting distance, surface tension, and contact angles are studied. For each force curve also the geometric sh ape of the meniscus is calculated. The capillary forces are compared with v an der Waals forces to understand their relative importance in various oper ating conditions. In addition to application in SFM, this analysis is usefu l in the design of surface roughness in microdevices for low adhesion in op erating environments.