Theory of phonon-drag thermopower of extrinsic semiconducting single-wall carbon nanotubes and comparison with previous experimental data

A theoretical model for the calculation of the phonon-drag thermopower, Sᵍ, in degenerately doped semiconducting single-wall carbon nanotubes (SWCNTs) is proposed. Detailed calculations of Sᵍ are performed as a function of temperature, tube radius, and position of the Fermi level. We derive a simple analytical expression for Sᵍ that can be utilized to determine the free carrier density in doped nanotubes. At low temperatures Sᵍ shows an activated behavior characteristic of the one-dimensional character of carriers. Screening effects are taken into account and it is found that they dramatically reduce the magnitude of Sᵍ. Our results are compared with previous published experimental data in bulk p-doped SWCNT materials. Excellent agreement is obtained in the temperature range 10--200 K for a consistent set of parameters. This is a striking result in view of the complexity of these systems.