Three-terminal scanning tunneling spectroscopy of suspended carbon nanotubes

We have performed low-temperature scanning tunneling spectroscopy measurements on suspended single-wall carbon nanotubes with a gate electrode allowing three-terminal spectroscopy measurements. These measurements show well-defined Coulomb diamonds as well as side peaks from phonon-assisted tunneling. The side peaks have the same gate voltage dependence as the main Coulomb peaks, directly proving that they are excitations of these states.

Figure 1

(Color online) AFM images of SWCNTs crossing (a) 100 and (b) $200\mathrm{nm}$ wide trenches. The scale bars are $500\mathrm{nm}$. (c) Schematic diagram showing the setup used to perform spectroscopy on suspended SWCNTs. The STM tip acts as the source while the substrate is the drain. The gate electrode is either formed by Pt at the bottom of the trench or the Si substrate. (d) Differential conductance as a function of energy before (red circles) and after (blue squares) heat sinking the wires in the STM. The solid lines are fits of the derivative of the Fermi distribution.

Figure 2

(Color online) (a) Logarithm of differential conductance as a function of gate and sample voltage, showing Coulomb diamonds. The data are on a SWCNT, which is suspended over a $100\mathrm{nm}$ wide trench. The feedback current was set to $300\mathrm{pA}$ at $-0.2\mathrm{V}$. (b)–(d) Diagrams showing from where the edges of the diamonds arise. The strong lines, (d) and (e) come from the Fermi level in the substrate lining up with a state on the SWCNT. On the other hand, the fainter lines (b) and (c) come from a state in the SWCNT lining up with the Fermi level of the tip.

Figure 3

Logarithm of differential conductance as a function of gate and substrate voltage at two different setpoint currents, (a) $300\mathrm{pA}$ at $-0.5\mathrm{V}$ and (b) $500\mathrm{pA}$ at $-0.5\mathrm{V}$. Side peaks due to phonon-assisted tunneling are visible in the negative substrate voltage region. (c) and (d) Zoom in on the boxes in (a) and (b), respectively. The side peaks due to phonon-assisted tunneling are running parallel to the main Coulomb peaks, demonstrating that they are excitations of this state. This SWCNT is suspended across a $200\mathrm{nm}$ wide trench.

Figure 4

(Color online) (a) Differential conductance as a function of substrate voltage showing Coulomb peaks due to the addition of electrons to the SWCNT. The feedback current was stabilized at $100\mathrm{pA}$ at $-0.6\mathrm{V}$. (b) Same as (a) but the feedback current was set to $300\mathrm{pA}$. Now additional side peaks are visible due to phonon-assisted tunneling. The side peaks are labeled by blue and red numbers corresponding to emission and absorption. (c) Energy of side peaks as a function of peak number. Blue squares correspond to emission peaks while red circles are for absorption peaks. (d) Histogram of side peak energy for both emission and absorption showing that all of the side peaks have similar energy. The solid line is a Gaussian fit to the histogram.

Figure 5

Differential conductance as a function of gate and substrate voltage, showing peaks due to the addition of electrons. For negative substrate voltages, there are sets of peaks that show an avoided crossing behavior. Data is taken at the suspended portion of a metallic SWCNT. The tube is suspended over a distance of $100\mathrm{nm}$. Feedback current is set to $300\mathrm{pA}$ at $-0.5\mathrm{V}$.