Optimization of the master equation set for a multidot tunnel structure

ERM/PHASE, CNRS, ENSPS, boulevard Sébastien Brant, 67400 Illkirch, France

Corresponding author: cordan@erm1.u-strasbg.fr

Received: 4 December 1998
Revised: 4 May 1999
Accepted: 14 May 1999
Published online: 15 August 1999

Abstract

In the present paper, we report a procedure to calculate tunnel currents as a function of the applied voltage, by an optimization of the master equation, for a highly disordered tunnel junction array. We take a very large scatter of the tunnel resistances of the individual junctions. In order to reduce the number of equations, several approaches have still been considered in the past. Here, we propose a procedure without any decoupling: we show that relevant results can be obtained inside and outside the Coulomb gap once the charge state range is automatically centered, already from a ±2 truncation of the equation set, for small offset charges or low applied voltage. This last step is achieved in a straightforward way, through the calculation of the total tunneling rate leaving a given configuration. This has been assessed there for the first time on a highly disordered array of five junctions.