Numerical simulations for a quantitative analysis of AFM electrostatic nanopatterning on PMMA by Kelvin force microscopy

Electrostatic nanopatterning of electret thin films by atomic force microscopy (AFM) has emerged as an alternative efficient tool for the directed assembly of nano-objects on surfaces. High-resolution charge imaging of such charge patterns can be performed by AFM-based Kelvin force microscopy (KFM). Nevertheless, quantitative analysis of KFM surface potential mappings is not trivial because of side-capacitance effects induced by the tip cone and the cantilever of the scanning probe. In this paper, we developed numerical simulations of KFM measurements taking into account these artifacts, so as to estimate the actual surface charge density of square charge patterns (nominal sizes ranging from 100 nm to 10 μm) written by AFM into polymethylmethacrylate (PMMA) thin films. This work revealed that, under our conditions, such charge patterns exhibit a surface charge density between 1.5 x 10-3 and 3.8 x 10-3 C m-2, depending on the assumed depth of injected charges. These results are crucial to quantify the actual electric field generated by such charge patterns and thus the electrostatic forces responsible for the directed assembly of nano-objects onto these electrostatic traps.