Using scanning tunneling potentiometry, we have obtained spatial distribution of electrochemical potential on the $\mathrm{Si}\left(111\right)\text{−}7\times 7$ surface and estimated a ratio of conductance across surface steps and domain boundaries to that of the reconstructed terrace. Our measurements reveal significant resistance across the steps, indicating that the conductance on the $7\times 7$ surface measured in macroscopic methods is basically determined by the step density, which is uncontrolled in most of the macroscopic measurements. The domain boundaries also exhibit measurable resistance, implying underestimation (overestimation) of the $7\times 7$ terrace (step) conductance when these conductance values are estimated from the anisotropy in the conductance along and across the step directions without considering the resistance at the domain boundaries.

• Received 21 September 2018
• Revised 4 February 2019

DOI:https://doi.org/10.1103/PhysRevB.99.125402