ИСТИНА

Local electrodeposition (LED) is one of effective methods for formation of 3D micro- and nanostructures. It exhibits several important advantages: the absence of mechanical and heat impacts on the workpiece, no tool wear, wide possibilities for controlling the shape of microstructures by varying machining modes, low cost of electrochemical processes, and good reproducibility of results [1]. Electrodeposition is particularly unique in its ability to create deposit at sub-nanometer vertical resolutions [2]. Various schemes of maskless local electrodeposition are used: jet LED, scanning probe based LED and micro/nanopipette based LED (electrochemical micro/nanoprinting). At present, the schemes of LED using unipolar or bipolar electrodes [3, 4], are widely used, whereas the electrodeless LED remains almost unstudied. This work is devoted to the theoretical analysis of electrodeless electrochemical nanoprinting using a nanopipette filled with the electrolyte solution more concentrated than the bulk solution. No external potential is imposed onto the conductive substrate, and there are no other electrodes. As a result of different solution concentrations near the substrate, cathodic and anodic zones form on it. The local metal deposition from the solution occurs on the cathodic zone near the nanopipette, and anodic dissolution of substrate metal occurs on the large anodic zone on the periphery of electrochemical cell. The ionic transport equations, which take into account diffusion, migration, and convection, and the condition of electroneutrality, are used as the mathematical model. The boundary conditions on the substrate are set using the Butler-Volmer equation. The numerical solution of the problem is carried out by the finite element method on the deformable grid that takes into account the change of the substrate surface shape due to the local deposition and dissolution of metal. As a result of simulation, the distributions of ion concentrations and potential over the solution, and the distributions of current density, overpotential, and concentration of electroactive ions over the substrate surface are obtained for various time instants and under various conditions.