Electrochemical scanning tunneling microscopy (ECSTM) is gaining popularity as a tool to implement a proof-of-concept single (bio)molecular transistor. The understanding of such systems requires a discussion of the mechanism of the electrochemical current gating, which is intimately related to the electrostatic potential distribution in the tip-substrate gap where the redox active adsorbate is placed. We derive a relation that connects the local standard potential of the redox molecule in the tunneling junction with the applied electrode potentials, and we compare it with previously proposed relations. In particular, we show that a linear dependence of the local standard potential on the applied bias does not necessarily imply a monotonous potential drop between the electrodes. In addition, we calculate the electrostatic potential distribution and the parameters entering the derived relation for ECSTM on a redox metalloprotein (Azurin from P. Aeruginosa), for which experimental results exist. Finally, we give an estimate of the gating efficiency when the ECSTM setup including Azurin is interpreted as a single biomolecular wet transistor, confirming the effectiveness of the electrochemical gating for this system.
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