Mechanistic modeling of electric field-assisted atomic force microscopy-based nanopatterning of PEDOT: PSS

Electric field-assisted atomic force microscopy (E-AFM)-based nanopatterning is a versatile and cost-effective nanomanufacturing technique for fabricating nanoscale features with high spatial resolutions. Here, we investigate the E-AFM-based nanopatterning of poly(3,4-ethylenedioxythiophene): polystyrene sulfonate (PEDOT: PSS) thin films by combining systematic experimental measurements, finite-element simulations, and mechanistic modeling. A key finding of this study is the direct observation and mechanistic explanation of nanoscale protrusion formation under an applied electric field, arising from the coupled action of localized Joule heating and dielectrophoretic (DEP) forces at the AFM tip-film interface. Specifically, the localized Joule heating generates a confined softened zone beneath the biased tip, within which the DEP forces redistribute and attract PEDOT-rich domains toward the tip, leading to upward material transport and protrusion growth. Based on these coupled mechanisms, we developed a mathematical model that predicts protrusion formation as a function of applied bias and dwell time while incorporating relevant material parameters. The model captures feature-height evolution. The model captures the interaction between temperature-dependent viscosity and DEP-driven flow, yielding a scaling relation for feature-height evolution, while an empirical correction accounting for lateral microstructural reorientation improves the width prediction. Experiments over a range of voltage-dwell time combinations produced protrusion features with heights from approximately 8 to 37 nm and widths from approximately 232 to 378 nm, showing strong agreement with the model predictions. This framework achieves a coefficient of determination (R 2 value) of 94.5% for feature height and 93.9% for empirically adjusted feature width. Overall, this combined experimental and theoretical framework provides both predictive capability and mechanistic insight into E-AFM-based nanopatterning. The identification of protrusion formation as a coupled thermo-electromechanical process, where Joule-induced softening and DEP-driven polymer redistribution act synergistically, offers a new physical understanding of feature formation in electrically assisted nanofabrication. The findings support the advancement of E-AFM as a controllable technique for fabricating nanoscale structures for various applications, such as advanced nanoelectronics, optoelectronics, and sensing devices.