Scaling of van der Waals and Electrostatic Adhesion Interactions from the Micro- to the Nano-Scale

Abstract

Work performed to study the scalability of continuum force models to describe particle adhesion from the micro- to the nano-scale is described. This work employed silicon nitride particles with nominal diameters on the micrometer scale and silicon nitride atomic force microscope cantilevers with nanometer-scale radii of curvature to determine adhesion interaction forces to substrates relevant to advanced lithography applications in the semiconductor industry. The force required to dislodge the particles or cantilevers from the substrates was taken to be the adhesion force. For all systems studied, a distribution of adhesion forces was observed resulting from roughness on the particles and/or substrates and geometry variations on the particles. Previously developed adhesion models that included van der Waals (vdW) and electrostatic (ES) interactions, and that also included the geometry and morphology of the interacting surfaces, were used to describe the force distributions. In air, the ES forces were found to be insignificant compared to the vdW forces. In aqueous electrolytes, the ES forces may play an important role, even at the point of particle–substrate contact, due to the formation of electrical double layers under certain conditions. The predicted force distributions showed good agreement with the experimental data.