High-Field Quasiballistic Transport in Short Carbon Nanotubes

Single walled carbon nanotubes with Pd Ohmic contacts and lengths ranging from several microns down to 10 nm are investigated by electron transport experiments and theory. The mean-free path (MFP) for acoustic phonon scattering is estimated to be $l_{\mathrm{ap}}\sim 300\mathrm{nm}$, and that for optical phonon scattering is $l_{\mathrm{op}}\sim 15\mathrm{nm}$. Transport through very short ($\sim 10\mathrm{nm}$) nanotubes is free of significant acoustic and optical phonon scattering and thus ballistic and quasiballistic at the low- and high-bias voltage limits, respectively. High currents of up to $70\mu \mathrm{A}$ can flow through a short nanotube. Possible mechanisms for the eventual electrical breakdown of short nanotubes at high fields are discussed. The results presented here have important implications to high performance nanotube transistors and interconnects.

Figure 1

Atomic force microscopy (AFM) images of five devices consisting of individual SWNTs with lengths in the range of $L=600$ to 10 nm between the edges of Pd contact electrodes.

Figure 2

Electrical properties of an $L\sim 60\mathrm{nm}$ long Ohmically contacted metallic SWNT (diameter $\sim 1.5\mathrm{nm}$). (a) $G$ vs $V_{\mathrm{GS}}$ recorded (under a low bias of $V_{\mathrm{DS}}=1\mathrm{mV}$) at 290, 150, and 40 K, respectively. A noteworthy technical point is that thin Pd contact electrode fingers were used ($250\mathrm{nm}\times 25\mathrm{nm}$) for contacts in order to form small ($<100\mathrm{nm}$) gaps between electrodes by lift-off. The resulting narrow Pd electrodes had a resistance of $\sim 0.6\mathrm{k}\Omega$ at 290 K and a negligibly $\sim 0.02\mathrm{k}\Omega$ at 40 K. The series resistance was estimated from the geometry of the contact electrodes and the resistivity of the Pd film at various temperatures. The data shown here were after the correction of the series resistance of the Pd electrodes. (b) Differential conductance vs $V_{\mathrm{DS}}$ and $V_{\mathrm{GS}}$ for the device recorded at 2 K. The arrow points to a resonance peak [2, 7] at $V_{\mathrm{DS}}=\pi \hslash v_F/eL=25\mathrm{mV}$, where $v_F=8.1\times {10}^5\mathrm{m}/\mathrm{s}$ is the Fermi velocity and $L\sim 60\mathrm{nm}$. The gate oxide thickness $t_{\mathrm{ox}}\sim 10\mathrm{nm}$ for the device in this figure.

Figure 3

Electrical properties of Ohmically contacted metallic SWNTs of various lengths (diameters $d\sim 2–2.5\mathrm{nm}$, oxide thickness $t_{\mathrm{ox}}\sim 10\mathrm{nm}$ for the samples in this figure). Solid lines are experimental $I_{\mathrm{DS}}\mathrm{\text{−}}{V}_{\mathrm{DS}}$ curves and the symbols are Monte Carlo calculation and fitting results. Note that the devices in Fig. 3 had a series resistance of $\sim 1\mathrm{k}\Omega$ arising from the thin Pd electrodes except for the 55 nm long tube which had an electrode resistance of $\sim 3\mathrm{k}\Omega$. The experimental curves are all after the correction of $V_{\mathrm{DS}}$. We also note that for short tubes ($<100\mathrm{nm}$) a permanent change in the electrical properties was observed after applying large fields ($V_{\mathrm{DS}}>1\mathrm{V}$). This could be due to the degradation of the contacts at such high drain biases, and requires further work to illuminate the exact cause.

Figure 4

$I_{\mathrm{DS}}\mathrm{\text{−}}{V}_{\mathrm{DS}}$ breakdown characteristics of SWNTs. The lengths of three sections of a metallic SWNT are (a) $\sim 10\mathrm{nm}$, (b) $\sim 300\mathrm{nm}$, and (c) $\sim 3\mu \mathrm{m}$, with the Si substrate being grounded. The gate oxide thickness $t_{\mathrm{ox}}\sim 67\mathrm{nm}$ for the samples. (d) $I_{\mathrm{DS}}\mathrm{\text{−}}{V}_{\mathrm{DS}}$ data recorded for a semiconducting SWNT (in the ON state under $V_{\mathrm{GS}}=0\mathrm{V}$) with $L\sim 50\mathrm{nm}$ and $t_{\mathrm{ox}}\sim 10\mathrm{nm}$ (inset shows $I_{\mathrm{DS}}$ vs $V_{\mathrm{GS}}$ under $V_{\mathrm{DS}}=10\mathrm{mV}$). AFM image insets in (a)–(c) show the devices after electrical breakdown, and arrows in (b) and (c) point to the breakdown points. The parasitic electrode resistance is high ($\sim 15\mathrm{k}\Omega$, due to the very thin and narrow electrode geometry) for devices in (a)–(c). For this reason, they were not used for the quantitative analysis of $l_{\mathrm{op}}$ in Fig. 3.