Screening of charged impurities as a possible mechanism for conductance change in graphene gas sensing

In carbon nanotube and graphene gas sensing, the measured conductance change after the sensor is exposed to target molecules has been traditionally attributed to carrier density change due to charge transfer between the sample and the adsorbed molecule. However, this explanation has many problems when it is applied to graphene: The increased amount of Coulomb impurities should lead to decrease in carrier mobility which was not observed in many experiments, carrier density is controlled by the gate voltage in the experimental setup, and there are inconsistencies in the energetics of the charge transfer. In this paper we explore an alternative mechanism. Charged functional groups and dipolar molecules on the surface of graphene may counteract the effect of charged impurities on the substrate. Because scattering of electrons with these charged impurities has been shown to be the limiting factor in graphene conductivity, this leads to significant changes in the transport behavior. A model for the conductivity is established using the random phase approximation dielectric function of graphene and the first-order Born approximation for scattering. The model predicts optimal magnitudes for the charge and dipole moment which maximally screen a given charged impurity. The dipole screening is shown to be generally weaker than the charge screening although the former becomes more effective with higher gate voltage away from the charge neutrality point. The model also predicts that with increasing amount of adsorbates, the charge impurities eventually become saturated and additional adsorption always lead to decreasing conductivity.

Figure 1

Comparison of gas sensing with NO, ${\mathrm{NO}}_2$, and ${\mathrm{NH}}_3$. Dashed lines are given as guides to the eye. The inset shows the enlarged response curve of NO detection. The detection limit (DL) estimation was explained in Ref. [1]. PPT: parts-per-trillion. PPQ: parts-per-quadrillion.

Figure 2

The electric potential created by the charged impurity and the screening charge in graphene in the space on the opposite side of the graphene sheet. As shown in the inset, $z$ is the coordinate for the direction perpendicular to the graphene plane. The screening reduces the potential but preserves the direction of the electric field. The screening is more effective when there is a higher carrier density in graphene. The electric field of each case is labeled at a typical distance of the adsorbates.

Figure 3

(a) Schematic illustration of the proposed structures: bare charge impurity, $\mathrm{CI}|$graphene$|$CFG structure ($i=Z\delta$), and $\mathrm{CI}|$graphene$|$dipole structure ($i=Zp$), from left to right. (b) The induced charge density in graphene of the same configuration before and after adsorption of the charged functional group and the dipolar molecule. The potential of the charged impurity is partially canceled by the adsorbates and the scattering is reduced.

Figure 4

Ratio of the conductivity of graphene before and after all charged impurities are covered by adorption of dipolar molecules (black) or charged functional groups (red) vs the dipole moment (bottom axis) or the charge (top axis). The dipole moment of a few common molecules are marked to show the theoretical prediction of their effect on the conductivity in this parameter regime. The dotted line separates increased conductivity (larger than one) and decreased conductivity (smaller than one). The parameters used in the calculations are: for the dipole screening, $k_{\mathrm{F}}=0.05{\AA }^{-1}$, $Z=0.01$; for the charge screening, $k_{\mathrm{F}}=0.01{\AA }^{-1}$, $Z=0.5$.

Figure 5

Calculated results of the carrier density dependence of the conductivity before and after all charge impurities are saturated with adsorbates and transformed into $\mathrm{CI}|$graphene$|$adsorbate scattering centers. The black line is the base conductivity before adsorption, parameters used are $Z=0.1$, $n_{\mathrm{imp}}^Z=2\times {10}^{14}{\mathrm{cm}}^{-2}$. The red, blue, and brown lines are conductivities after adsorption of charged functional groups ($\delta =0.15$), weakly dipolar molecules ($p=0.5\AA$), and strongly dipolar molecules ($p=2\AA$), respectively.

Figure 6

The coverage dependent conductivity normalized by the conductivity before adsorption. The dotted line shows the coverage of adsorbates that saturates the charged impurities. The parameters used are $k_{\mathrm{F}}=0.05{\AA }^{-1}$, $Z=0.1$, $\delta =0.15$, and $p=0.2\AA$. See text for more details.