A qualitative argument is to consider the energy uncertainty of an electron
The characteristic time for charge fluctuations is
the time constant for charging capacitance C through tunnel resistor RT, and the energy gap associated with a single electron is
Combining (2.26) and (2.27) gives the condition for the tunnel resistance
Another line of thought proceeds as follows. The condition
requires that the time t which an electron
resides on the island be much greater than ,
the quantum uncertainty
in this time.
The current I cannot exceed e/t since for moderate bias and temperature at most one extra electron resides on the island at any time. The energy uncertainty of the electron, , is no larger than the applied voltage Vb.
Inserting t=e/I and (2.30) into (2.29) results in
In fact, more rigorous theoretical studies of this issue have supported this conclusion . Experimental tests have also shown this to be a necessary condition for observing single-electron charging effects .