The average number of electrons on a small metallic island biased by an external voltage source via a tunnel junction is investigated. The jumps of the electron number as a function of the applied voltage are smeared by quantum fluctuations arising from the finite tunneling conductance of the junction. A systematic expansion of the partition function in terms of the tunneling conductance is given. The average island charge is determined for the realistic case where the electronic bandwidth is large compared to the single-electron charging energy. It is shown that finite-temperature effects remain important for the lowest temperatures presently attainable experimentally.

• Received 19 May 1994

DOI:https://doi.org/10.1103/PhysRevB.50.17364