Intrinsic limits of thermometers based on Coulomb charging effect in arrays of tunnel junctions

Arrays of normal metal tunnel junctions have been found to be suitable for a thermometer in the regime where thermal energy is comparable to charging energy. Using a functional integral approach, we have calculated the quantum conductance of an array of asymmetric double junctions including the effect of background charges. Our theoretical results allow us to investigate the influence of asymmetry and background charge, as well as the nonlinear correction to the linear calibration formula for the Coulomb blockade thermometer. We have also analyzed the current noise spectra and discovered that the noise to conductance ratio is proportional to temperature. Hence, this ratio provides a new kind of Coulomb blockade thermometer.