Energy dissipation in the presence of sub-harmonic excitation in dynamic atomic force microscopy

Amplitude modulation atomic force microscopy allows quantifying energy dissipation in the nanoscale with great accuracy with the use of analytical expressions that account for the fundamental frequency and higher harmonics. Here, we focus on the effects of sub-harmonic excitation on energy dissipation and its quantification. While there might be several mechanisms inducing sub-harmonics, a general analytical expression to quantify energy dissipation whenever sub-harmonics are excited is provided. The expression is a generalization of previous findings. We validate the expression via numerical integration by considering capillary forces and provide experimental evidence of sub-harmonic excitation for a range of operational parameters.