Nonlinear Phase Imaging of Gold Nanoparticles Embedded in Organic Thin Films

The phase detection in the dynamic mode of the atomic force microscopes is a known technique for mapping nanoscale surface heterogeneities. We present here an additional functionality of this technique, which allows high-resolution imaging of embedded inorganic nanoparticles with diameter and interparticle distances of a few nanometers. The method is based on a highly nonlinear tip-sample interaction occurring markedly above the nanoparticles, giving thus a high phase contrast between zones with and without nanoparticles. A relationship between the tip-sample interaction strength and the phase signal is established in experiments and from calculations conducted with the model developed by Haviland et al. [ Soft Matter 2016 , 12 , 619 ], which is based on solving a combined equation of motion for both the cantilever and surface while taking into account the time-varying interaction forces. The nonlinear phase behavior at the origin of the subnanometer spatial resolution is found by numerical analyses to be the result of a local mechanical stiffening of the zone containing nanoparticles, which is enhanced by 2 orders of magnitude or more.