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(2011) Phonon Scattering in Intrinsic Graphene using Tight-binding Bloch Waves


probability density graph of bloch wave

Fig. 1 Probability density for a Bloch wave with wave vector k=(14.5, 7.9) nm-1, calculated using the nearest-neighbor tight-binding technique.

The overall interest in graphene as a material for devices has led to tremendous advances in the knowledge of transport in graphene. However, there are still questions about the intrinsic limit to electron mobility. Recent experiments have demonstrated mobility greater than 107 cm2/Vs at 50 K temperature, exceeding previous theoretical predictions of the intrinsic mobility limit. Here, we present a simple model of phonon scattering rates in intrinsic graphene using electronic tight-binding Bloch wave functions with carbon 2pz orbitals and nearest-neighbor coupling. The tight-binding approximation results in an accurate band structure near the Dirac points, in contrast to the nearly free electron model; therefore, it is reasonable to assume that the electron wave functions are localized near the atomic centers. The scattering matrix is anisotropic and the small overlap of the tight-binding Bloch functions results in phonon scattering rates lower than those calculated by assuming plane waves by several orders of magnitude. The calculated phonon scattering rates are, in fact, in very good agreement with the rates obtained from the significantly more complex first-principles calculations, whereas computed much more simply and transparently, and suitable for further employment in complex transport calculations on graphene nanostructures.

 

References

[1] N. Sule and I. Knezevic, "Phonon Scattering in Intrinsic Graphene using Tight-binding Bloch Waves," Phys. Rev. B, submitted.