## Large Bias Transport and Phonon Scattering

Electron-phonon interactions at high electric fields were investigated by Yao et al. [10] using low-resistance contacts. In contrast to high-contact-resistance samples where tunneling across the contacts dominates the transport, a bias voltage applied between two low-resistance contacts establishes an electric field inside the nanotubes which accelerates the electrons, enabling studies of intrinsic transport properties of high-energy electrons. Shown in Fig. 1.3.1 are I-V curves measured up to 5 V at different temperatures. The curves essentially overlap with each other. Remarkably, the current at 5 V exceeds 20 |A, which corresponds to a current density of more than 109 A/cm2. The current seems to saturate at large bias. It turns out that the resistance, R = V/I, can be fit very well with a simple linear function of V (right inset): R = R0 + V/Io, where R0 and I0 are constants with I0 being the extrapolated saturation current.

The behavior can be explained by considering optical or zone-boundary phonons as the main scattering mechanism for high-energy electrons. As shown in the schematic in the left inset to Fig. 1.3.1, assuming that the electron-phonon coupling is strong enough, once an electron gains enough energy to emit an optical or zone-boundary phonon of energy hQ, it is immediately backscattered. A steady state is then established in which the right moving electrons are populated to an energy hQ higher than the left moving ones, leading to a saturation current I0 = (4e/h)hQ. Taking a typical phonon energy of hQ = 0.16eV [40], this leads to a saturation current of 25 |A which agrees favorably with experiments. In this picture, the mean free path ¿q for backscattering phonons is just the distance an electron must travel to reach the phonon threshold: ¿q = hQL/eV with L being the electrode spacing. This may be combined with a constant elastic scattering term with mean

acteristics in metallic nanotubes at different temperatures. The right inset plots V/I vs V. The left inset

acteristics in metallic nanotubes at different temperatures. The right inset plots V/I vs V. The left inset

phonon emission model free path £e to obtain a resistance R = (h/ 4e2)L(£-1 + which then has exactly the same form as the simple phenomenological function. Further work is expected to address the heat dissipation issue and the role of electron-correlation effects.

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