Sequential tunneling and inelastic cotunneling in nanoparticle arrays

Abstract

We investigate transport in weakly coupled metal nanoparticle arrays, focusing on the regime where tunneling is competing with strong single electron charging effects. This competition gives rise to an interplay between two types of charge transport. In sequential tunneling, transport is dominated by independent electron hops from a particle to its nearest neighbor along the current path. In inelastic cotunneling, transport is dominated by cooperative multielectron hops that each go to the nearest neighbor but are synchronized to move charge over distances of several particles. In order to test how the temperature-dependent cotunnel distance affects the current-voltage (I-V) characteristics, we perform a series of systematic experiments on highly ordered close-packed nanoparticle arrays. The arrays consist of ∼5.5 nm diameter gold nanocrystals with tight size dispersion, spaced ∼1.7 nm apart by interdigitating shells of dodecanethiol ligands. We present I-V data for monolayer, bilayer, trilayer, and tetralayer arrays. For stacks 2–4 layers thick we compare in-plane measurements with data for vertical transport perpendicular to the array plane. Our results support a picture whereby transport inside the Coulomb blockade regime occurs by inelastic cotunneling, while sequential tunneling takes over at large bias above the global Coulomb blockade threshold Vt(T) and at high temperatures. For the smallest measurable voltages, our data was fitted well by recent predictions for the temperature dependence zero-bias conductance due to multiple cotunneling. At finite but small bias, the cotunnel distance is predicted to set the curvature of the nonlinear I-V characteristics, in good agreement with our data. The absence of significant magnetic-field dependence up to 10 T in the measured I-V characteristics further supports the picture of inelastic cotunneling events where individual electrons hop no further than the nearest neighbor. At large bias, above the global Coulomb blockade threshold, the I-V characteristics follow power-law behavior with temperature-independent exponent close to two, predicted for sequential tunneling along branching paths that optimize the overall charging energy cost.

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