Scaling of the single-electron tunnelling current through ultrasmall tunnel junctions

The effect of a tunnelling electron on the tunnel barrier shape is studied at the limit where a static image charge model is applicable. It is shown that the single-electron tunnelling current through an ultrasmall voltage-biased junction is not proportional to the junction area because of charging at the electrodes. Simple expressions are presented for the effective static barrier shape of a voltage-biased junction and of a junction in a circuit, the former of which accounts for the anomalous current scaling. A possible experimental arrangement for verifying the scaling relationship is suggested, with numerical results.