Edge scattering of electrons in graphene: Boltzmann equation approach to the transport in graphene nanoribbons and nanodisks

Abstract

We discuss the contribution of edge scattering to the conductance of graphene nanoribbons and nanoflakes. Using different possible types of the boundary conditions for the electron wave function at the edge, we found dependences of the momentum relaxation time and conductance on the geometric sizes and on the carrier density. We also consider the case of ballistic nanoribbon and nanodisk, for which the edge scattering is the main mechanism of momentum relaxation.

Hydrodynamical Model for Charge Transport in Graphene Nanoribbons

“…The physical parameters for electron-phonon scatterings are reported in Table 1. To include the edge scattering we suppose disordered edges and consider an additional term as proposed by [6] whose expression is…”

“…In idealized situations the edges have zigzag or armchair structure, however today it is very difficult the production of graphene ribbon with one well defined edge, but they are available with a high degree of edge disorder. This leads to the investigation of the behavior of the charge transport in graphene taking into account the bandgap [4] and the scattering with edge [5,6] as well as the well known scattering with the lattice [8].…”

Theoretical study of scattering in graphene ribbons in the presence of structural and atomistic edge roughness

“…It is important to note that a strong resistivity suppression has not been reported in earlier publications on edgeroughness scattering in graphene ribbons. 23,27,28,30,63 . Our simulation results indicate that this effect only shows up when we calculate the relaxation times selfconsistently, considering a subband-quantized ribbon spectrum and a finite edge-roughness correlation length.…”

“…18 Several publications have already addressed the (diffusive) transport properties of graphene ribbons for different scattering mechanisms, e.g., impurity, edge (roughness or disorder) or acoustic and optical phonon scattering. 17,[19][20][21][22][23][24][25][26][27][28][29][30][31] The approaches that were considered vary widely, ranging from a nearest-neighbor tight-binding description for the band structure of a graphene ribbon near the charge-neutrality (Dirac) point to fullfledged atomistic simulations, e.g., based on empirical pseudopotentials. 29 Similarly, the treatment for these scattering mechanisms ranges from phenomenological or (semi)classical estimates of the mean free path, entering the Landauer conductance formula, to numerically solving Green's functions and perturbative or atomistic scattering approaches in combination with the Boltzmann transport equation.…”

Validity criteria for Fermi’s golden rule scattering rates applied to metallic nanowires

“…Ample examples can be found in literature, covering a great variety of devices and applications such as (conventional) metal-oxide-semiconductor transistors [1][2][3][4][5], quantum cascade lasers [6] and nanowire transistors [7][8][9], metallic thin films or nanowires [10,11], quasi-1D or -2D materials and devices [12][13][14][15][16][17], as well as for other applications, e.g. the Hall effect [18], spin [19] or thermal [20] transport.…”