Figure 1

(a) Schematic diagram of a nanocrystalline silicon cross SET (b) Scanning electron micrographs of a cross SET.Reuse & Permissions

Figure 2

(a) 3D gray scale characteristics at $4.2\mathrm{K}$, of a cross transistor, of the currents $I_1$, $I_2$, $I_3$, and $I_4$ as a function of the gate voltages $V_{\mathrm{g}1,\mathrm{g}2}$ (applied simultaneously to gates 1 and 2) and $V_{\mathrm{g}3,\mathrm{g}4}$ (applied simultaneously to gates 1 and 2) where $I_1$, $I_2$, $I_3$, and $I_4$ are measured respectively at terminals 1, 2, 3, and 4 with a terminal bias of $3\mathrm{mV}$. The dark regions have low current (Min: $0\mathrm{A}$) and the white regions have high current (Max: $6\mathrm{pA}$). F1 (dashed black lines), F2 (dashed white lines), F3 (solid white lines), and F4 (solid black lines) are Coulomb oscillation features used as fingerprint patterns to locate the dominant charging Si grains in the cross transistor. The characteristics are arranged in a matrix layout where the columns are represented by the currents. The rows, $1\mathrm{g}$, $2\mathrm{g}$, $3\mathrm{g}$, and $4\mathrm{g}$, correspond to terminals 1, 2, 3, and 4 grounded, respectively. (b) Schematic of the matrix in (a). Here the 3D plots are replaced by their matrix indices, $(i_g,I_j)$, where $i\ne j$: 1, 2, 3, 4, and $I_j$ is the current at terminal $j$ while terminal $i$ is grounded. (c) A single line plot of $I_4$ vs $V_{\mathrm{g}2,\mathrm{g}3}$ at $V_{\mathrm{g}1,\mathrm{g}2}=-0.775\mathrm{V}$ across ($3\mathrm{g},I_4$) characteristics.Reuse & Permissions

Figure 3

(a) Measurement on a second cross transistor of the current $I_4$ at $4.2\mathrm{K}$ vs $V_{\mathrm{g}1,\mathrm{g}2}$ and $V_{\mathrm{g}3,\mathrm{g}4}$ [see Fig. 2a caption], with terminals 1, 3, and 4 biased at $3\mathrm{mV}$ and terminal 2 connected to ground (b) $I_4$ measured with only terminal 4 biased at $3\mathrm{mV}$ and terminals 1 and 3 floating.Reuse & Permissions

Figure 4

Gray scale plot, at $4.2\mathrm{K}$, of terminal 4 current, $I_4$, vs gate 1 and 2 voltages, $V_{\mathrm{g}1}$ and $V_{\mathrm{g}2}$. Terminal 2 and gate 4 are grounded. Terminal 4 voltage $V_4=5\mathrm{mV}$ and gate 3 voltage $V_{\mathrm{g}3}=1\mathrm{V}$. Terminals 1 and 3 are floating. Top left inset: Schematics of the conduction band across a grain and two grain boundaries, at gate 1 voltage $V_{\mathrm{g}1\mathrm{A}}$ and $V_{\mathrm{g}1\mathrm{B}}$, where $V_{\mathrm{g}1\mathrm{A}}>V_{\mathrm{g}1\mathrm{B}}$. E1 is the intergrain Fermi level.Reuse & Permissions

Figure 5

Schematic diagrams of the possible current paths (double headed arrows) between the terminals (Ter. 1, Ter. 2, Ter. 3, and Ter. 4) of a cross transistor. These paths are associated with the observed Coulomb oscillation features in Fig. 2.Reuse & Permissions

Figure 6

(a) A schematic diagram showing the approximate locations of the dominant charging grains (G1, G2, G3, and G4) in a cross transistor. These locations were estimated using the patterns of the Coulomb oscillation features, F1, F2, F3, and F4 (Fig. 2), as fingerprints. The dashed arrows are the possible current paths through these grains.Reuse & Permissions

Figure 7

(a) A plot of the position of the Coulomb oscillations (diagonal black lines) for a single charging grain in the configuration of (g), connected by tunnel junctions $T_1$ and $T_2$ to the source and drain, and coupled capacitively to two gate voltages $V_{\mathrm{g}1}$ and $V_{\mathrm{g}2}$. (b) A plot of the Coulomb oscillation positions for the configuration in (h) of two grains along series current paths, without any capacitive interaction between the grains. The dashed lines form the boundaries of regions of stable charge on the grains. Conduction occurs at the black dots. (c) Charge stability diagram for two grains tunnel coupled in series, as shown in (i). Conduction occurs at the triple points (black dots). (d) A plot of the Coulomb oscillation positions for two grains along parallel current paths, without interaction between the grains. (e) The Coulomb oscillation position (solid lines) for the configuration of (j), excluding tunnel junction $T_4$. (f) The Coulomb oscillation lines for the configuration of (j), including the tunnel junction $T_4$.Reuse & Permissions