Effects of the structure of charged impurities and dielectric environment on conductivity of graphene

Abstract

We investigate the conductivity of doped single-layer graphene in the semiclassical Boltzmann limit, as well as the conductivity minimum in neutral graphene within the self-consistent transport theory, pointing up the effects due to both the structure of charged impurities near graphene and the structure of the surrounding dielectrics. Using the hard-disk model for a two-dimensional (2D) distribution of impurities allows us to investigate structures with large packing fractions, which are shown to give rise to both strong increase in the slope of conductivity at low charge carrier densities in graphene and a strongly sub-linear behavior of the conductivity at high charge carrier densities when the correlation distance between the impurities is large. On the other hand, we find that a super-linear dependence of the conductivity on charge carrier density in heavily doped graphene may arise from increasing the distance of impurities from graphene or allowing their clustering into disk-like islands, whereas the existence of an electric dipole polarizability of impurities may give rise to an electron-hole asymmetry in the conductivity. Using the electrostatic Green's function for a three-layer structure of dielectrics, we show that finite thickness of a dielectric layer in the top gating configuration, as well as the existence of non-zero air gap(s) between graphene and the nearby dielectric(s) exert strong influences on the conductivity and its minimum. While a decrease in the dielectric thickness is shown to increase the conductivity in doped graphene and even gives rise to finite conductivity in neutral graphene for a 2D distribution of impurities, we find that an increase in the dielectric thickness gives rise to a super-linear behavior of the conductivity when impurities are homogeneously distributed throughout the dielectric. Moreover, the dependence of graphene's mobility on its charge carrier density is surprisingly strongly affected, quantitatively and qualitatively, by the graphene-dielectric gap(s) when combined with the precise position of a 2D distribution of charged impurities. Finally, we show that the conductivity minimum in neutral graphene is increased by increasing the correlation distance between the impurities, reduced by increasing the graphene-dielectric gap, and increased by decreasing the dielectric thickness in a top-gated configuration, even though the corresponding residual charge carrier density is reduced by decreasing the dielectric thickness.

Capacitance of graphene in aqueous electrolytes: The effects of dielectric saturation of water and finite size of ions

“…A Stern layer (SL) is assumed to occupy region 2 defined by 0 x h, and is characterized by a relative dielectric constant 2 , whereas a semi-infinite diffuse layer (DL) fills region 3 defined by x h, which is characterized by a relative dielectric constant of the solvent 3 , with the potential in the bulk of the electrolyte chosen to be a zero reference potential. Furthermore, we allow for the existence of fixed charged impurities in region 1, which are ubiquitous in typical substrates used for graphene devices [45,46]. Thus, in region 1 we may have a charge densityρ imp (x) describing those impurities, which is obtained by averaging the full density of impurities over a large area parallel to graphene [24].…”

“…We note that both densities σ g and σ a are assumed to be functions of the averaged values of the potentials φ 0 and φ h , thereby neglecting the potential fluctuations in the graphene and Stern planes due to the discreteness of charge in the impurity layer in the oxide [45,46] and the discreteness of charge in the layer of specifically adsorbed ions [47]. While we shall not pursue here any further details related to the ion adsorption, it is remarkable that both the presence of graphene and the specifically adsorbed ions enter the model through the jump conditions, Eqs.…”

Probing the Plasmon-Phonon Hybridization in Supported Graphene by Externally Moving Charged Particles

“…Probing graphene in this regime with a charged particle that moves at a subthreshold speed may then give dramatic effects in the available mechanisms of energy loss. Particularly intriguing would be to explore in future work the effects on stopping and image forces arising from electron-hole puddles in the charge carrier density of a nominally neutral graphene, which are induced by the system of static charged impurities in the SiO 2 substrate [1,43].…”

Ab initio study of the electron energy loss function in a graphene-sapphire-graphene composite system

“…The screened Coulomb interaction W (Q,ω,z,z ) is equal (in atomic units) to the Green's function (GF) of the Poisson equation, which may be easily derived for a layered structure exhibiting translational invariance in directions parallel to graphene layers by using the standard electrostatic matching conditions at the interfaces between different dielectric regions [47,48]. Accordingly, this approach is quite efficient for rather complex layered structures, where inclusion of graphene layers at arbitrary positions may be described by the Dyson-Schwinger (DS) equation for W (Q,ω,z,z ) of the form…”