Quantification of atomic-scale elasticity on Ge(001)-c(4 × 2) surfaces via noncontact atomic force microscopy with a...

We investigated the bonding stiffness of individual atoms on substrate surfaces using noncontact atomic force microscopy with frequency modulation. We measured the frequency shift distribution of the (110) plane above buckling-up and buckling-down dimer atoms of the Ge(001)-c(4 × 2) surface using a tungsten-coated atomic force microscopy cantilever. The tip-surface chemical force distribution was reproduced from the frequency shift data using calculations based on Sader's formula. The total harmonic bonding stiffness between the dimer atoms and the substrate was first discovered by fitting the Morse force to the tip-surface chemical force distribution with consideration of the relaxation in the tip-surface gap. By excluding the contribution exerted by the probe tip, we observed that the harmonic bonding compliance of the buckling-up dimer atom was 4.8 × 10(-3) m/N stiffer than that of the buckling-down dimer atom. This technique for probing the elastic bonding states of individual surface atoms at the atomic scale is unique.