Multiparametric analytical quantification of materials at nanoscale in tapping force microscopy

Atomic force microscopy (AFM) is a powerful technique for accurate, reliable and non-destructive imaging and characterization of materials at the nanoscale. Among the numerous AFM methods, amplitude modulation or tapping mode AFM (AM-AFM) is an established method for imaging and characterization for most commercial AFM systems. Despite its high spatial resolution and sensitivity, quantitative characterization by AM-AFM lag behind other advanced AFM methods as far as quantification of materials properties is concerned. In this paper a fully analytical multiparametric approach for AM-AFM is proposed which simultaneously quantifies the Hamaker constant and viscoelastic properties of materials. The main advantage of the proposed method lies in the inclusion of adhesion to calculate viscoelasticity, which makes it superior to the current equations used in the AFM community. The accuracy of the proposed method is validated by several simulations and experiments and comparison with nanoindentation results, which strongly support its candidacy as a method of choice for material properties quantification by dynamic AFM.