Reliability of the minimal resistance path 1D approach for 2D and 3D nanometer-size disordered arrays

Two-dimensional (2D) or three-dimensional (3D) arrays of metallic dots on insulator have been considered for single-electron devices or floating gates. Up to now, only disordered lattices could be fabricated. Straight Monte Carlo (MC) techniques lead to cumbersome and time-consuming calculations once the array size increases, especially at high temperature. We show here that for disordered arrays, with a quasi-one-dimensional (1D) approach, a fair estimation can be obtained for Vth(T) and σ(Vth)/Vth for 2D arrays. Discrepancies are less than 10% in the pertinent temperature range. For 3D arrays, the estimations are rough, but main information can still be extracted. Such an approach yields a gain factor greater than one order of magnitude.