Current-voltage response for unipolar funnel-shaped nanochannel diodes

Permselective nanochannels can rectify the electric current transported through them similar to solid-state diodes. The rectification is due to symmetry breaking related to distribution of the nanochannels' surface charge as well as the geometry. Thus far, most of the works related to the asymmetric current response have been primarily experimental. Here, we theoretically model a funnel-shaped nanochannel with a nonhomogeneous surface charge from which we derive a current-voltage relation (I-V). If the effects of the adjacent microchannels are ignored, the I-V is shown to behave like a unipolar diodes. When the effects of the adjacent microchannels are accounted for, the channel behaves like a diode only in a small voltage domain, while at larger voltages, the response is determined by the microchannels. The theoretical results are confirmed by numerical simulations.