Strongly Correlated Charge Transport in Silicon Metal-Oxide-Semiconductor Field-Effect Transistor Quantum Dots

Quantum shot noise probes the dynamics of charge transfers through a quantum conductor, reflecting whether quasiparticles flow across the conductor in a steady stream, or in syncopated bursts. We have performed high-sensitivity shot noise measurements in a quantum dot obtained in a silicon metal-oxide-semiconductor field-effect transistor. The quality of our device allows us to precisely associate the different transport regimes and their statistics with the internal state of the quantum dot. In particular, we report on large current fluctuations in the inelastic cotunneling regime, corresponding to different highly correlated, non-Markovian charge transfer processes. We have also observed unusually large current fluctuations at low energy in the elastic cotunneling regime, the origin of which remains to be fully investigated.

Figure 1

Sketches of cotunneling processes giving rise to super-Poissonian noise, described in the text. The thin blue arrows correspond to usual inelastic cotunneling; the thick, dashed, red arrows to COSET. In ③, the dashed green arrows correspond to elastic cotunneling with different rates depending on the state of the dot.

Figure 2

Description of the experiment. The charge carriers in the silicon-on-insulator (SOI) channel are symbolized by the red clouds, showing the drain and source reservoirs on either side of the quantum dot. The spacers, realizing the tunnel barriers coupling the dot to the leads, are shown in light blue. The gate is shown in yellow and the gate insulator in dark gray. The electrical schematic is a simplified description of the measurement setup, including the pair of $RLC$ tanks used in the shot noise measurements.

Figure 3

(a) Differential conductance $dI/d{V}_{\mathrm{DS}}$ measured as a function of gate voltage $V_g$ and drain-source voltage $V_{\mathrm{DS}}$. The continuous yellow lines locate the edges of the Coulomb diamonds, and the dashed yellow lines the excited states. The thick dotted white lines show the onset of inelastic cotunneling, extracted from current measurements (see below). The regions labeled ①, ②, and ③, separated by the light blue dashed lines (see text for their construction), correspond to the processes depicted in Fig. 1. (b) Current $I$ (blue symbols, left axis) and Fano factor $F$ (red symbols, right axis) as a function of $V_{\mathrm{DS}}$ in, respectively, log-log and semi-log scale, for $V_g=-0.7975\mathrm{V}$ [black vertical arrow in (a)]. Continuous violet line: linear fit of $I(V_{\mathrm{DS}})$ at low $V_{\mathrm{DS}}$ [35]. The horizontal red dashed line indicates the Poisson value $F=1$. The red area shows the inelastic cotunneling range, delimited by the value of $V_{\mathrm{DS}}$ at which $I(V_{\mathrm{DS}})$ deviates from a linear behavior, and by the edge of the Coulomb diamond.

Figure 4

Top: Fano factor $F$ measured as a function of $V_g$ and $V_{\mathrm{DS}}$. The (full and dashed) yellow lines, the dashed blue lines, and the white dashed lines are the same as in Fig. 3. The blue, green, and red vertical arrows indicate the line cuts at constant $V_g$ shown in Fig. 5. The brown and dark brown horizontal arrows indicate the line cuts at constant $V_{\mathrm{DS}}$ shown in the bottom panel. Bottom: Line cuts of $F$ as a function of $V_g$, for $V_{\mathrm{DS}}$ between 2.7 (dark brown) and 4.8 mV (brown); the translucent lines correspond to intermediary values of $V_{\mathrm{DS}}$.

Figure 5

Current $I$ (top panel) and Fano factor $F$ (bottom panel) as a function of $V_{\mathrm{DS}}$ in, respectively, log-log and semi-log scale, for three different values of $V_g$, located by the vertical arrows in Fig. 4: $V_g=-0.7935\mathrm{V}$ (red), $V_g=-0.795\mathrm{V}$ (green), and $V_g=-0.8\mathrm{V}$ (blue). Continuous lines in the top panel: linear fits of the low-$V_{\mathrm{DS}}$ data. The sequential tunneling ($F=0.5$) and Poissonian ($F=1$) values of $F$ are indicated by, respectively, horizontal dotted and dashed lines in the bottom panel. In both panels, the red area indicates the inelastic cotunneling range defined for $V_g=-0.8\mathrm{V}$.