Multiple Cotunneling in Large Quantum Dot Arrays

We investigate the effects of inelastic cotunneling on the electronic transport properties of gold nanoparticle multilayers and thick films at low applied bias, inside the Coulomb-blockade regime. We find that the zero-bias conductance, $g_0(T)$, in all systems exhibits Efros-Shklovskii-type variable range hopping transport. The resulting typical hopping distance, corresponding to the number of tunnel junctions participating in cotunneling events, is shown to be directly related to the power-law exponent in the measured current-voltage characteristics. We discuss the implications of these findings in light of models on cotunneling and hopping transport in mesoscopic, granular conductors.

Figure 1

Transmission electron micrographs showing the region between the in-plane electrodes for (a) bilayers, (b) trilayers, (c) tetralayers, and (d) thick films. The darker regions on top and bottom of (a)–(c) are the electrodes. The insets on the right sides are diffraction patterns computed by fast Fourier transform. The insets on the left sides of panels (a) and (c) are the zoomed-in images. The scale bars correspond to 200 nm (a)–(c) and 40 nm [(d), all insets].

Figure 2

(a) Zero-bias conductance $g_0$ vs inverse temperature $T^{-1/2}$ for representative multilayer and thick-film data. The thick-film curve has been shifted upward for clarity by multiplying the data by 40. Inset: for the high-temperature range, where the multilayer data in the main panel deviate from the dotted lines, $g_0$ has been replotted as a function of $T^{-1}$, indicating Arrhenius behavior from 100–160 K. (b)–(e) Evolution of the $I\mathrm{\text{−}}V$ characteristics with temperature for bilayers (b), (c) and thick films (d), (e). Panels (c) and (e) are log-log plots of the data shown in the plots above them. The straight solid lines are guides to the eye, indicating power-law behavior. The noise limit in these measurements was about 25 fA. Insets to (b) and (d): temperature dependence of the hopping distance $N^{*}$ obtained from $g_0(T)$ and the $I\mathrm{\text{−}}V$ power-law exponents obtained from panels (c) and (e) in the range $2\mathrm{V}<V<7\mathrm{V}$.