Percolating through networks of random thresholds: Finite temperature electron tunneling in metal nanocrystal arrays

We investigate how temperature affects transport through large networks of nonlinear conductances with distributed thresholds. In monolayers of weakly-coupled gold nanocrystals, quenched charge disorder produces a range of local thresholds for the onset of electron tunneling. Our measurements delineate two regimes separated by a cross-over temperature $T^{\ast }$. Up to $T^{\ast }$ the nonlinear zero-temperature shape of the current-voltage curves survives, but with a threshold voltage for conduction that decreases linearly with temperature. Above $T^{\ast }$ the threshold vanishes and the low-bias conductance increases rapidly with temperature. We develop a model that accounts for these findings and predicts $T^{\ast }$.