Phonon-limited transport coefficients in extrinsic graphene

TL;DR

This paper investigates how electron-phonon interactions influence thermoelectric properties in extrinsic graphene, providing analytical models that match experimental observations and suggest ways to tune these properties via carrier density.

Contribution

It presents analytical expressions for transport coefficients in extrinsic graphene considering electron-phonon scattering, extending understanding of thermoelectric behavior at various temperatures.

Findings

Electrical resistivity is linear at high temperatures.

Thermal resistivity approaches a constant at high temperatures.

Seebeck coefficient varies with temperature and carrier density.

Abstract

The effect of electron-phonon scattering processes over the thermoelectric properties of extrinsic graphene was studied. Electrical and thermal resistivity, as well as the thermopower, were calculated within the Bloch theory approximations. Analytical expressions for the different transport coefficients were obtained from a variational solution of the Boltzmann equation. The phonon-limited electrical resistivity \rho_{e-ph} shows a linear dependence at high temperatures, and follows {\rho}_{e-ph} \sim T^{4} at low temperatures, in agreement with experiments and theory previously reported in the literature. The phonon-limited thermal resistivity at low temperatures exhibits a \sim T dependence, and achieves a nearly constant value at high temperatures. The predicted Seebeck coefficient at verylow temperatures is Q(T) \sim -\pi 2 k_B T /(3 e E_F), which shows a n^{-1/2} dependence with the density of carriers, in agreement with experimental evidence. Our results suggest that thermoelectric properties can be controlled by adjusting the Bloch-Gruneisen temperature through its dependence on the extrinsic carrier density in graphene.