  ElectroChemical Scanning Tunneling Microscopy (ECSTM) is gaining popularity
as a tool to implement proof-of-concept single (bio)molecular transistors. 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. In this article, 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.
