Finite sample thickness effects on elasticity determination using atomic force microscopy

Finite sample thickness effects on material elasticity measurements made us ing an atomic force microscope have been calculated. The model includes an elastic layer on an elastic foundation and simulates sample indentation und er an applied load. Rigid axisymmetric tips with conical, paraboloidal, and hyperboloidal profiles are considered. The results show that a common appr oach to estimating elastic moduli from force-displacement curves can lead t o a significant error that depends on the units of measurement. A method to unambiguously estimate and correct this error is proposed. In addition, it is shown that elasticity estimates for monolayer thick samples using the f orce-modulation technique can contain a substantial, sample thickness-depen dent error. Local thickness variations can result in misleading contrast in force-modulation images for samples that are several nanometers thick.