Polarizability of quantum-dot states within a suspended carbon nanotube

We have fabricated single-electron-transistor devices made from an individual carbon nanotube suspended between two independent side gates (Fig.1). The nanotube acts as a clean quantum dot, isolated from the disordered substrate. By applying gate voltages, we can populate the dot controllably with any number of electrons, from zero to many tens. By applying different voltages to the two side gates, we measure for the first time the electric polarizabilty of individual few-electron quantum states in a nanotube, and we observe the effect of electron-electron interactions on this polarizability.

People Involved

Ferdinand Kuemmeth, Shahal Ilani, Paul McEuen, and Dan Ralph


In the past, a variety of transistor geometries have been developed to study electronic and optical properties of carbon nanotubes. In addition to top gates [1] and buried gates [2], suspended nanotube devices [3,4] have attracted interest because they eliminate artifacts arising from contact with a disordered substrate and because they enable studies of a nanotube’s mechanical degrees of freedom. Here, we describe the development of a new fabrication scheme which allows complex gating of a suspended nanotube, and its use to measure the electric polarizibility of few-electron quantum states.

Fabrication starts with a highly doped silicon-on-insulator substrate. Dry etching of the device layer is employed to pattern electrically isolated gate electrodes spaced 500 nm apart, which are later individually contacted using wire bonds. After isolating the gate electrodes with 100 nm of thermal oxide, all metal electrodes, including bonding pads, are deposited using liftoff techniques before growing the nanotubes. This avoids damage or contamination of the nanotubes by post-growth processing, but requires metals which are compatible with the high temperature chemical vapor deposition (CVD) process. For this reason we contact the gate electrodes using photolithography and titanium/platinum leads, and we pattern source and drain electrodes using electron-beam lithography and a tungsten/platinum bilayer. After applying wet catalyst and growing nanotubes in a CVD furnace, the devices are tested in a probe station and wire-bonded for cooldown in a 4 Kelvin vacuum can.

At 4 K, we measure the electric conductance G through the nanotube to study the few-electron quantum dot which forms on the suspended part of the nanotube. Starting with zero electrons on the dot, one electron after the other can be added to the dot by increasing the voltage on both gate electrodes simultaneously. This manifests itself as equally spaced Coulomb oscillations when measuring the conductance along the gate-voltage diagonal where Vright=Vleft for the two gate voltages. The gate voltages can then be varied separately, and each Coulomb peak can be traced as a function of the voltage difference between Vright and Vleft. This difference generates an electric field parallel to the nanotube which we use to intentionally push the quantum dot towards the left or right gate electrode (Fig. 2). As a consequence, the capacitive coupling of the quantum dot to the gate electrodes is not symmetric anymore, and hence Coulomb oscillations are observed to curve when increasing the electric field (Fig. 3). When measured at zero bias, the curvature of the nth Coulomb oscillation is a measure of the electric polarizability of the nth electron groundstate. Unlike single particle levels in a harmonic potential (which all shift in space by an equal amount when applying a constant electric field), we find that an energy level in our quantum dot is less polarizable if other electrons are present on the dot. This indicates the importance of electron-electron interactions in suspended carbon nanotubes, and that screening takes place despite the one-dimensional confinement.

Figure 1
Figure 1: Schematic of a carbon nanotube single electron transistor. The nanotube is suspended between two independent, isolated gate electrodes spaced 500 nm apart, and contacted by source and drain electrodes.

Figure 2
Figure 2: At low temperatures a quantum dot forms in between the right and left gate electrode, and electrons can be added by increasing Vright and Vleft. Increasing the difference between Vright and Vleft pushes the quantum dot towards the left or right gate electrode.

Figure 3

Figure 3: Conductance G through the dot as a function of Vleft shows Coulomb oscillations at 4 K. The curvature of each Coulomb oscillation is a measure of the polarizability of individual levels of the quantum dot.


  1. Ilani S. et al, Measurement of the quantum capacitance of interacting electrons in carbon nanotubes, Nature Physics 2, 687 (2006).
  2. Bosnick K. et al, Transport in carbon nanotube p-i-n diodes, Appl. Phys. Lett., 89, 163121 (2006).
  3. Sazonova V. et al, A tunable carbon nanotube electromechanical oscillator, Nature 431, 284 (2004).
  4. Minot E. D. et al, Determination of electron orbital magnetic moments in carbon nanotubes, Nature 428, 536 (2004).

Last updated: 11-July-2007

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