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-V͒ characteristics, we perform a series of systematic experiments on highly ordered close-packed nanoparticle arrays. The arrays consist of ϳ5.5 nm diameter gold nanocrystals with tight size dispersion, spaced ϳ1.7 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 V t ͑T͒ 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.

Transport mechanism in granular Ni deposited on carbon nanotubes fibers

“…The upward curvature drops as the temperature rises but their shape are reminiscent of that already observed in monolayer of granular systems showing inelastic cotunneling mechanism. 3 The curves are fit to the data at T = 1.5 K obtained by power law dependence I ∝ V β with β between 1.5 and 3.5. Following the cotunneling model, the exponent β should be equal to the number of junctions between the electrodes that, in our case, results to be of the order of 10 4 .…”

“…For low external fields, a tunneling process can be established and the electrical current flows through the granular system by sequential tunneling or cotunneling. 3 In sequential tunneling each electron hops between two adjacent grains as in a separate quantum event until the opposite electrode is reached; in cotunneling, the electrons tunnel between the two electrodes passing through all the grains in between as in a single tunnel event. Whichever the mechanism responsible for the conduction in the insulating regime, it is well established experimentally that the electrical resistance in granular systems diverges as T → 0 following the R = R N e (T 0 /T ) 1/2 law, where R N is the resistance at a given temperature and the value of the parameter T 0 depends on the theoretical model adopted.…”

“…Whichever the mechanism responsible for the conduction in the insulating regime, it is well established experimentally that the electrical resistance in granular systems diverges as T → 0 following the R = R N e (T 0 /T ) 1/2 law, where R N is the resistance at a given temperature and the value of the parameter T 0 depends on the theoretical model adopted. 1,4,5 In the case of cotunneling, 3 T 0 = 2.8E c d/k B ξ , where k B is the Boltzmann constant and ξ is the electron localization length. In the case of magnetic granular particles, the temperature dependence of the resistance remains unchanged but the parameter T 0 is enhanced by a factor (1 + ln 2).…”

Universality and quantization of the power-to-heat ratio in nanogranular systems

“…(1) is a result of inelastic cotunneling processes, which govern the electron transport. The essence of these processes is that an electron tunnels via virtual states in intermediate grains thus bypassing the huge Coulomb barrier [2,4,[6][7][8][9][10][11][12][13][14][15][16][17][18]. This can be visualized as coherent superposition of two events: tunneling of an electron into a granule and the simultaneous escape of another electron from the same granule.…”

Inelastic cotunneling with energy-dependent contact transmission

“…1 Specifically, in inelastic multiple cotunneling, the electrical current depends on the transmission probability of the interconnecting molecules raised to a power N 2, with N related to the typical number of hops in the multiple cotunneling process. 9,10 Thus far, the resulting cotunneling current has only been calculated for systems in which the transmission probability is independent of energy. This assumption does not generally apply to molecules bridging between neighboring nanoparticles, however, as molecular transmission functions can be strongly energy-dependent.…”