Conditions for the production of a single conducting nanostructure by electroforming

The process of electroforming (the production of a carboniferous conducting medium when the current flows through an organic material under a high electric field) in open sandwichlike structures with an insulating gap several tens of nanometers in width is considered. It is shown experimentally that there are factors that both favor (external ballast resistor) and prevent (local spreading resistance and the presence of the initial conductivity in the insulating gap) the production of a single conducting element between the electrodes. A simple model of the process in terms of the equivalent electric circuit is proposed. The model helps to find the trade-off between these factors and to construct an I-V diagram, which exhibits a region within which a single conducting nanostructure can be electroformed. An expression that relates the minimum permissible resistance of the nanostructure to its geometric parameters is derived.