Atom-size gaps and contacts between electrodes fabricated with a self-terminated electrochemical method

We describe a method to fabricate atomic-scale gaps and contacts between two metal electrodes. The method uses a directional electrodeposition process and has a built-in self-termination mechanism. The final gap width and contact size are preset by an external resistor ${\mathrm{(R}}_{\mathrm{ext}})$ that is connected in series to one of the electrodes. If ${\text{1/R}}_{\mathrm{ext}}$ is chosen to be much smaller than the conductance quantum ${\mathrm{(G}}_0{\text{=2e}}^2\mathrm{/h),}$ a small gap with conductance determined by electron tunneling is formed. If ${\text{1/R}}_{\mathrm{ext}}$ is comparable or greater than $G_0,$ a contact with conductance near a multiple of $G_0$ is fabricated.