2.6 Influence of the Electromagnetic Environment

    The electromagnetic environment plays a crucial role in the observation of charging effects. For instance in a single tunnel junction a  high impedance environment is mandatory in order for  current oscillations to appear [8] [23] [31] [42]. In the case of a high impedance environment tunnel rates have to be calculated according to the  local rule [53], where only the junction through which the electron tunnels is considered for the calculation of the Coulomb energy. The high impedance kind of shields the rest of the environment from the junction. It is difficult to provide a high impedance environment for a single junction, because  stray capacitances which are usually much bigger than the capacitance of the junction itself, cause the junction to be voltage biased. Thus the saw-tooth voltage across the junction, which is produced by a current bias, is absent. G. Ingold et al. [54] studied the effect of the electromagnetic environment on a SET transistor. They found that for the  low impedance environment the  global rule which considers the change in free energy of the whole circuit, (2.11) and (2.23), applies. For a high impedance environment stray capacitances lead to a modification of the local rule. For multijunction circuits the effective environmental impedance decreases roughly as one over the square of the number of junctions [46]. As a consequence, tunnel junctions in large arrays see only a very low impedance environment and the tunnel rates may be calculated using the global rule.