COULOMB-BLOCKADE THRESHOLD IN INHOMOGENEOUS ONE-DIMENSIONAL ARRAYS OFTUNNEL-JUNCTIONS

A general expression is given for the change in free energy when a cha rge tunnels through a junction in a one-dimensional array of N metalli c islands with arbitrary capacitances and arbitrary background charges . This is used to obtain expressions for the (average) threshold volta ge of the Coulomb blockade for a few characteristic geometries. We fin d that including random background charges has a large effect on the N dependence of the threshold voltage: In an array with identical junct ion capacitances C and gate capacitances C-g, the threshold voltage, a veraged over the background charge, is proportional to N-G, where a cr osses over from 1/2 to 1 when N becomes larger than 2.5 root C/C-g.