In summer 2005 our group at NPL was the first to publish evidence of ballistic phonon transport in carbon nanotubes (CNTs) at room temperature, confirming the CNTs potential in the study of thermal transport at the nanoscale (see Brown et al., Appl. Phys. Lett. 87, 023107 (2005)).

The CNTs used in this work were multiwalled (MWNTs), produced by arc-discharge; an SEM image of a bundle is shown in Fig. 1.

Figure 1: MWNT bundle
produced by arc-discharge.
Figure 2: Tube diameter distribution.

The tube diameter distribution was determined from AFM images of the nanotubes dispersed on a substrate, as shown in Fig. 2.

The experimental set-up used is shown in Fig. 3.

Figure 3: MWNT measurement apparatus setup.

An MWNT bundle was mounted on a Veeco thermal probe, installed inside an AFM.

Using the AFM piezo controls the MWNT bundle was brought repeatedly in and out of contact with a substrate while thermal and electrical conductance were recorded simultaneously. This required independent temperature and voltage measurement circuits: a dc resistance thermometer technique recorded the probe tip temperature, whereas lock-in detection of an ac voltage drop along the tube measured the electrical conductance. The force between bundle and substrate was also recorded. All measurements were done in high vacuum (~10^-5 mbar) to reduce extraneous heat flow.

In Fig. 4 is shown a typical example of electrical and thermal conductance measurements as a function of vertical tube displacement (the temperature difference across the MWNT bundle was 264 K).

Figure 4: MWNT conductance versus tip travel distance.

The electrical conductance step is ~1 G₀ (as expected for an individual CNT); G₀ is the quantum of electrical conductance ( PDF, 271 KB): G₀ = 2e²/h = 1/12.9 kΩ

The thermal conductance step is ~260 G_th (corresponding to a heat transfer of ~26 μW); G_th is the quantum of thermal conductance ( PDF, 296 KB): G_th = π²k_B²T/3h = 9.456×10^-13 (W/K²)×T

Two pieces of evidence of ballistic phonon transport can be noted in this example:

1. Both electrical and thermal conductance measurements show flat plateaus as the tube length is altered by compression or bending, suggesting ballistic transport for both electrons and phonons.
2. Assuming the contrary, our estimated diffusive thermal conductivity for a typical tube (a solid rod of diameter 1.9 nm and length ~700 nm) is 2.5×10⁴ W/mK, which is an unrealistically high value, 4 times greater than the room temperature thermal conductivity of diamond!

The quantum of thermal conductance provides an upper limit to the thermal conductance contribution of each phonon mode of the CNT ( PDF, 104 KB). Thus a step of 260 G_th indicates that up to 260 phonon modes are transported. In Fig. 5 the thermal conductance steps are plotted as a function of the corresponding electrical steps – obtained from many measurements (in the inset are the temperature differences across the MWNT bundle).

Figure 5: MWNT thermal versus
electrical conductance.

There is a linear trend with mean slope of ~250, which agrees well with the number of phonon modes expected for CNTs of our diameter range.

This work has lead to further studies of nanotube properties:

• We investigated the electric current carrying capability of single conducting MWNTs and found that they can withstand current densities greater than 10¹⁴ A/m²! We also studied the tube behaviour at breakdown and reported an observation of possible van Hove singularities, even at room temperature. These results were presented ( PDF, 2.45 MB) at the Nanotube2006 conference in Japan.
• We studied the electrical properties of Nitrogen doped Nanotubes and were the first to publish evidence of their high electrical conductance.

Finally, our CNT expertise is also exploited in the development of Nanomechanical Resonators.