Charged impurity scattering in top-gated graphene nanostructures

We study charged impurity scattering and static screening in a top-gated substrate-supported graphene nanostructure. Our model describes how boundary conditions can be incorporated into scattering, sheds light on the dielectric response of these nanostructures, provides insights into the effect of the top gate on impurity scattering, and predicts that the carrier mobility in such graphene heterostructures decreases with increasing top dielectric thickness and higher carrier density. An increase of up to almost 60$\%$ in carrier mobility in ultrathin top-gated graphene is predicted.

Figure 1

Basic model used in our calculation. The SLG is an infinitely thin layer suspended in the middle of the vacuum gap between a semi-infinite substrate and a top oxide layer of thickness $t_{ox}$. The dielectric is capped with metal, which we assume to be a perfect conductor. The charged impurity on the SLG has image charges under and above it in the substrate and top gate, respectively.

Figure 2

Dependence of the carrier mobility ($\mu$) on top gate dielectric thickness ($t_{ox}$) for ${\mathrm{SiO}}_2$, ${\mathrm{Al}}_2{\mathrm{O}}_3$, and ${\mathrm{HfO}}_2$. The mobility decreases with increasing $t_{ox}$. This decrease is greater at $n={10}^{12}{\mathrm{cm}}^{-2}$ than at $n=5\times {10}^{12}{\mathrm{cm}}^{-2}$.

Figure 3

Dependence of the mobility on carrier density. The mobility decreases with carrier density, and the extent of the decrease is greater with smaller top gate dielectric thickness.