Scanning Probe Microscopy beyond Imaging: A General Tool for Quantitative Analysis

A simple, fast and general approach for quantitative analysis of scanning probe microscopy (SPM) images is reported. As a proof of concept it is used to determine with a high degree of precision the value of observables such as 1) the height, 2) the flowing current and 3) the corresponding surface potential (SP) of flat nanostructures such as gold electrodes, organic semiconductor architectures and graphenic sheets. Despite histogram analysis, or frequency count (Fc), being the most common mathematical tool used to analyse SPM images, the analytical approach is still lacking. By using the mathematical relationship between Fc and the collected data, the proposed method allows quantitative information on observable values close to the noise level to be gained. For instance, the thickness of nanostructures deposited on very rough substrates can be quantified, and this makes it possible to distinguish the contribution of an adsorbed nanostructure from that of the underlying substrate. Being non-numerical, this versatile analytical approach is a useful and general tool for quantitative analysis of the Fc that enables all signals acquired and recorded by an SPM data array to be studied with high precision.