TRANSFERRING ELECTRONS ONE BY ONE IN SINGLE-ELECTRON DEVICES WITH LONG ARRAYS OF TUNNEL-JUNCTIONS

We review recent theoretical work on an analytical approach to the cha rge dynamics of electron tunneling in single electron devices consisti ng of long arrays with equal stray capacitances and equal junction cap acitances. Our approach to the problem has two basic steps. First, we find the exact solution for the potential profiles and the associated Gibbs free energy, based on a technique for diagonalizing a particular type of a tridiagonal matrix equation. Second, we study the change of the Gibbs free energy arising from single charge transfer. The method has been applied to one-dimensional long arrays, single electron trap s, and single electron turnstiles, and the results are compared with t hat of the existing experiments. We point out the advantages of our me thod vis-a-vis other approaches used in the literature.