POTENTIAL DISTRIBUTION IN A FINITE 1-D ARRAY OF ARBITRARY MESOSCOPIC TUNNEL-JUNCTIONS

A general expression for the distribution of the potential in a finite one-dimensional array of arbitrary mesoscopic tunnel junctions in ter ms of Green's function is deduced. It is shown that the so-called part ial ''solitary'' problem of mesoscopic tunnel junctions can be formula ted similarly to the problem of the behavior of a electron in an one-d imensional tight binding and in a set of random delta-function models. We calculate analytically the potential distribution of a finite chai n, taking into account the details of the geometry, particularly, the finite-size distribution of the metallic islands. It is shown that the knowledge of the potential distribution allows us, in principle, to c alculate the capacitance and by this the diameter of the islands as an isolated sphere. This reveals to have its significance for design str ategies of single electron devices particularly if chemically size tai lored metal nanoparticles are used as building units.