A simple KPFM-based approach for electrostatic-free topographic measurements: the case of MoS$_2$ on SiO$_2$

A simple implementation of Kelvin probe force microscopy is reported that enables recording topographic images in the absence of any component of the electrostatic force. Our approach is based on a close loop z-spectroscopy operated in data cube mode. Curves of the tip-sample distance as a function of time are recorded onto a 2D grid. A dedicated circuit holds the KPFM compensation bias and subsequently cut off the modulation voltage during well-defined time-windows within the spectroscopic acquisition. Topographic images are recalculated from the matrix of spectroscopic curves. This approach is applied to the case of transition metal dichalcogenides (TMD) monolayers grown by chemical vapour deposition on silicon oxide substrates. In addition, we check to what extent a proper stacking height estimation can also be performed by recording series of images for decreasing values of the bias modulation amplitude. The outputs of both approaches are shown to be fully consistent. The results exemplify how in the operating conditions of non-contact AFM under ultra-high vacuum, the stacking height values can dramatically be overestimated due to variations in the tip-surface capacitive gradient, even though the KPFM controller nullifies the potential difference. We show that the number of atomic layers of a TMD can be safely assessed, only if the KPFM measurement is performed with a modulated bias amplitude reduced at its strict minimum or, even better, without any modulated bias. Last, the spectroscopic data reveal that defects at the TMD/oxide interface can have a counterintuitive impact on the electrostatic landscape, resulting in an apparent decrease of the measured stacking height by conventional nc-AFM/KPFM compared to non-defective sample areas. Hence, electrostatic free z-imaging proves to be a promising tool to assess the existence of defects in atomically thin TMD layers grown on oxides