The Mechanism of Electric Conduction in Carbon Nanotubes

The electrons in a conventional electric conductor move toward the positive pole under the influence of an external electric field. In doing so they experience a resistance due to scatter on lattice defects and phonons (lattice vibrations). Finally, a stationary state of constant current is established that is described by the Fermi function. The conductivity of the material decreases with rising temperature because the scatter on phonons becomes more efficient due to thermal excitation. It is true that the electrons scatter on lattice defects, too, but for being temperature-independent, these play just a minor role at elevated temperatures. However, the effect becomes important at low temperatures because phonon scatter ceases under these conditions, and the specific residual resistance almost exclusively arises from scatter on lattice defects. Hence, the residual resistance is a measure for material s purity it lessens with increasing purity and defect density of a sample. 

Ohm s law holds for macroscopic samples of an electric conductor. It states that voltage and current are proportional (with the ohmic resistance as proportionaUty factor). The electric resistance itself for a macroscopic wire depends on length and cross-sectional area of the object. Yet these conditions are no longer effective for a nanoscale conductor. The resistance of such a nanowire is independent of its length because charge transport is achieved by so-caUed conduction channels. 

There is a very large number of them, and each of these exhibits a resistance of 13k 2 (in consideration of spin degrees of freedom, otherwise 6.5kf2). Strictly speaking, however, this statement is true only if the respective one-dimensional wire is absolutely free of defects. In reality, this is not very likely to be the case, and so in actual nanowires there are, for example, interactions with the electrons of the atomic lattice. 

This kind of electron movement is also termed ballistic transport because the electrons do not experience any resistance on their free paths. In a particle model they might be considered as objects flying freely before interacting again with the material at the end of a free path. It is due to this mechanism that the conductor does not heat much as there is no interaction with phonons and consequently the lattice is not excited to perform stronger vibration. This is of special interest for the development of efficient electronic devices. Conventional materials are limited in their tolerance to current density because too much heat is developed above a certain current density. 

According to calculations, the free path A in a defect-free carbon nanotube is about Igm, while values of about 100 nm have been determined experimentally. This is an extremely large value in comparison to classical electric conductors (e.g., Uthium llOA, copper 430A, silver 560A). 

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