Coulomb Charging in SWNTs

In the experiments discussed above, the finite-sized nanotubes remained in good contact with the underlying substrate after cutting, and the voltage drop was primarily over the vacuum tunnel junction. If the nanotubes are weakly coupled to the surface, a second barrier for electron tunneling is created and these nanotubes may behave as coulomb islands and exhibit coulomb blockade and staircase features in their I-V [55]. The investigation of finite-sized nanotubes in the presence of charging effects is interesting since both effects scale inversely with length and thus can be probed experimentally, in contrast to 3D metal quantum dots [56,57].

Odom et al. [29] recently reported the first detailed investigation of the interplay between these two effects in nanotubes at ultra-short length scales and compared the tunneling spectra with a modified semi-classical theory for single-electron tunneling. The tunneling current vs. voltage of the nanotube in Fig. 12a exhibits suppression of current at zero bias as well as relatively sharp, irregular step-like increases at larger | V| (Fig. 12b), reminiscent of the coulomb blockade and staircase [55]. Similar to [47], the irregularities in the conductance peak spacing and amplitude are attributed to contributions from the discrete level spacing of the finite-sized nanotube [29].

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Fig. 12. Charging effects in finite-sized SWNTs. (a) STM image of SWNTs shortened by voltage pulses. The scale bar is 1nm. (b) Measured I—V and dl/dV performed on the tube indicated by an arrow in (a). (c) Numerical derivative of the I-V curve calculated by a semi-classical calculation including the level spacing of a 1D box. (d) Same calculation as in (c) except the nanotube DOS is treated as continuous [29]

To compare directly the complex tunneling spectra with calculations, Odom and co-workers [29] modified a semi-classical double junction model [56] to include the level spacing of the nanotube quantum dot, A E ~ 1.67 eV/7 = 0.24 eV. The capacitance of a SWNT resting on a metal surface may be approximated by [58]

where d is the distance from the center of the nanotube to the surface, and e is 8.85 x 10~3 aF/nm. Estimating d ~ 1.9 nm, the geometric capacitance for the nanotube in Fig. 12a is 0.21 aF. The calculated dl/dV that best fits the tunneling conductance is shown in Fig. 12c, and yields a Au-tube capacitance Ci = 0.21 ± 0.01 aF, in good agreement with the capacitance estimated by the geometry of the nanotube. In contrast, if the calculation neglected the level spacing of the nanotube island, only the blockade region is reproduced well (Fig. 12d). These studies demonstrate that it is possible also to study the interplay of finite size effects and charging effects in SWNT quantum dots of ultra-short lengths.

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