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 charge dynamics of electron tunneling in single electron devices consisting of long arrays with equal stray capacitances and equal junction capacitances. 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 traps, and single electron turnstiles, and the results are compared with that of the existing experiments. We point out the advantages of our method vis-à-vis other approaches used in the literature