Influence of electron-electron scattering on transport characteristics in monolayer graphene

Abstract

The influence of electron-electron scattering on the distribution function and transport characteristics of intrinsic monolayer graphene is investigated via an ensemble Monte Carlo simulation. Due to the linear dispersion relation in the vicinity of the Dirac points, it is found that pair-wise collisions in graphene do not conserve the ensemble average velocity in contrast to conventional semiconductors with parabolic energy bands. Numerical results indicate that electron-electron scattering can lead to a decrease in the low field mobility by more than 80 % for moderate electron densities. At high densities, the impact gradually diminishes due to increased degeneracy.Since graphene was first realized experimentally in 2004, 1 it has attracted significant interest due to its unique electronic properties. At low electron energies near the inequivalent Dirac points, there is no gap between the valence and conduction bands and the dispersion of the energy bands is linear. 2 Extremely high electrical mobilities have been reported in suspended graphene, exceeding 10 5 cm 2 /Vs near room temperature, 3 suggesting potential applications to ultrahigh frequency electronic devices. 4 The carrier density, which is controlled by the gate voltage, can be expected to vary by orders of magnitude. An interesting consequence of the linear energy dispersion is that the ensemble average velocity is not necessarily conserved upon an electronelectron (e-e) scattering event. Accordingly, inter-carrier collisions deserve careful consideration in the determination of the transport properties.Das Sarma et al. 5 found the inelastic e-e scattering rate and mean free path in graphene through the analysis of the quasiparticle self-energies. The scattering rate, calculated for electron densities from 1−10×10 12 cm −2 , was found to be of the same order of magnitude for electronphonon scattering rates evaluated in the deformation potential approximation (DPA). 6 Several authors have considered the electronic transport properties of graphene based on approaches such as the Monte Carlo simulation (see, for example, Ref. 7); however, the effects of e-e scattering have yet to be addressed to the best of our knowledge. In the present study, we examine the influence of this interaction mechanism in intrinsic monolayer graphene at room temperature. A full-band ensemble Monte Carlo method is used for accurate analysis of the distribution function as well as its macroscopic manifestations, particularly, the electron low-field mobilities and drift velocities.In both bulk and two-dimensional (2D) conventional semiconducting systems, e-e scattering has been well studied as is documented in the literature. 8 During an e-e scattering event, both the energy and momentum are conserved. In a parabolic band structure, common in conventional semiconductors, momentum conservation directly leads to the conservation of velocity. This can be readily shown by multiplying the momentum conservation equation by /m, which givesIt is then clear that, in a material with a p...

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