Effect of a High-$\kappa$ Environment on Charge Carrier Mobility in Graphene

It is widely assumed that the dominant source of scattering in graphene is charged impurities in a substrate. We have tested this conjecture by studying graphene placed on various substrates and in high-$\kappa$ media. Unexpectedly, we have found no significant changes in carrier mobility either for different substrates or by using glycerol, ethanol, and water as a top dielectric layer. This suggests that Coulomb impurities are not the scattering mechanism that limits the mean free path attainable for graphene on a substrate.

Figure 1

Effect of the substrate on electron transport in graphene. (a) Electric field effect for graphene on top of ${\mathrm{SiO}}_2$, mica, and PMMA. In each case, the induced carrier concentrations $n$ were related to $V_g$ through the gate capacitance [2] found by using Hall measurements. Positive and negative $n$ correspond to electrons and holes, respectively. (b),(c) ${\rho }_{xx}$ and ${\rho }_{xy}$ for graphene on BSCCO and ${\mathrm{SiO}}_2$, respectively. These measurements were done at zero $V_g$ for the device made as shown schematically in (c): graphene extends over the edge of a thin BSCCO crystal to cover ${\mathrm{SiO}}_2$. Upper inset: Optical micrograph of a graphene-on-BSCCO device. The central area is a BSCCO crystal on top of an oxidized Si wafer. Graphene is etched in the Hall bar geometry as indicated by the black lines on the left (in order to see the weak contrast due to graphene, we do not show such lines on the right). The width of the Hall bar is $1\mu \mathrm{m}$.

Figure 2

Dielectric screening by high-$\kappa$ media. (a) Graphene in a helium atmosphere (red curve) and after covering it with a thin layer of glycerol at room $T$ (blue curve). The significant changes in the peak position and its width are not accompanied by the tenfold increase in $\mu$, which would be expected for Coulomb scatterers [4, 15]. The observed changes were even smaller for higher-$\mu$ devices. (b) Another graphene device in ethanol and helium (inset) at room temperature $T$. Simultaneous measurements of ${\rho }_{xx}$ and ${\rho }_{xy}$ (blue curve and red curve, respectively) allow us to find $n=B/{\rho }_{xy}e$ and ${\mu }_H={\rho }_{xy}/B{\rho }_{xx}$ (see Fig. 3). Note that the experiments in ethanol were done by using the liquid gate so that one can imagine additional scatterers induced in the double layer by gate voltage. First, it is rather unlikely that the number of these scatterers exactly compensates the effect of dielectric screening and does this for all $n$. Second, the experiments using glycerol and the standard gating make this explanation even less likely. Nevertheless, let us mention that this doping effect can exist and was observed when we used a polymer electrolyte containing ${\mathrm{LiClO}}_4$. In this case, $\mu$ did not stay constant but reduced very rapidly as $\propto 1/n$.

Figure 3

Changes in $\mu$ induced by ethanol. (a) Behavior of ${\mu }_H$ and ${\mu }_{\mathrm{FE}}$ for the device shown in Fig. 2b. Measurements of $\mu$ are generally reliable only if ${\mu }_H\approx {\mu }_{\mathrm{FE}}$. Inside the region around the NP, which is indicated by the gray area, apparent ${\mu }_{\mathrm{FE}}$ diverges because $V_g$ passes through zero whereas apparent ${\mu }_H$ goes to zero because ${\rho }_{xy}$ passes through zero. The small difference between ${\mu }_H$ and ${\mu }_{\mathrm{FE}}$ observed outside the gray area is attributed to a macroscopic inhomogeneity that leads to slightly different ${\rho }_{xy}$ for different pairs of Hall contacts. (b) Varying dielectric screening in situ. $\mu$ as a function of $T$ for two devices immersed in ethanol (symbols). Dielectric constant $\kappa$ of ethanol increases from $\approx 25$ to 55 with decreasing $T$. The solid curve is the $T$ dependence expected in the case of dominant Coulomb scatterers [4, 15]. The measurements are presented for $n=3\times {10}^{12}{\mathrm{cm}}^{-2}$, but there is little difference for other assessable $n>1\times {10}^{12}{\mathrm{cm}}^{-2}$. For the sample that shows a slight increase in ${\mu }_H$ at lower $T$, we have found [by fitting the curves such as shown in Fig. 3a] that this increase is related to changes in ${\mu }_L$ rather than ${\rho }_S$.