Modeling the Dynamics of Electric Field-Assisted Local Functionalization in Two-Dimensional Materials

Electric field-assisted local functionalization of materials is a resist-free technique generally applied at the nanoscale, which has been understood within the paradigm of the water meniscus. Using a home-made prototype the authors applied this technique at scales compatible with the biosensor industry (tens of microns). However, interpreting these results requires a different paradigm. The expansion of the oxidized region over time in two-dimensional materials under a localized electric field is modeled from first physical principles. Boltzmann statistics is applied to the oxyanion incorporation at the perimeter of the oxidized zone, and a new general relation between oxide radius and time is formulated. It includes the reduction in the energy barrier due to the field effect and its dependence on the oxide radius. To gain insight into this dependence whatever the layers structure, 2D material involved, or electrical operating conditions, simple structures based on multilayer stacks representing the main constituents are proposed, where the Poisson equation is solved using finite element calculations. This enables to derive energy barriers for oxyanion incorporation at varying spot radii which are consistent with those resulting from fitting experimental data. The reasonable agreement obtained provides researchers with a new tool to predict the evolution of local functionalization of 2D layers as a function of the following fabrication parameters: time, applied voltage, and relative humidity, solely based on materials properties.