CROSSOVER FROM GLOBAL TO LOCAL RULE FOR THE COULOMB-BLOCKADE IN SMALLTUNNEL-JUNCTIONS

We have investigated several single and double aluminum tunnel junctio ns in the nonsuperconducting state. Current-voltage (I-V) characterist ics were measured up to voltages corresponding to several hundred time s e/C, where C is the capacitance of each junction. The individual jun ctions had capacitances in the order of 0.5 fF and resistances of 50-1 50 k Omega. The offset voltage, defined as V-off= V-I/(dI/dV), is resi stance independent for given junction capacitances, but depends on the bias voltage. For a single junction the offset voltage is very small for low voltages, but it approaches the local-rule value of e/2C at hi gh voltages. For a double junction the global rule applies at low volt ages and the offset voltage equals V-off=e/C-Sigma, where C-Sigma= 2C + C-0. At large voltages the local rule applies and each junction cont ributes with a voltage of e/2C to the offset voltage, so that V-off=e/ C. This paper shows that a careful analysis of the offset voltage has to be made to determine the values of the capacitances involved.