Direct Imaging of Charged Impurities in Substrates used for Graphene Devices

The use of hexagonal boron nitride (h-BN) as a substrate for graphene led to approximately an order of magnitude improvement in electron mobility compared to graphene on SiO$_{2}$. One hypothesis for the improvement is a reduction in trapped charge density on the surface of h-BN compared to SiO$_{2}$. We address this directly by mapping local potential fluctuations above the bare substrates h-BN and SiO$_{2}$ using Kelvin probe microscopy in ultra-high vacuum. We compare the results to a model of randomly distributed charges in a 2D plane at the surface of an insulating substrate. For SiO$_{2}$, the results are well modeled by a 2D charge density of $\sim$ 2.5x10$^{11}$ cm$^{-2}$. Previous measurements of charged impurity scattering in graphene indicates that this density of substrate charges would limit graphene mobility to 20,000 cm$^{2}$/Vs, in good agreement with the maximum values reported for graphene on SiO$_{2}$. h-BN displays potential fluctuations that are approximately an order of magnitude lower than SiO$_{2}$, consistent with an order of magnitude improvement in mobility in graphene/h-BN devices. This work was supported by the US ONR MURI program, and the U. of MD NSF-MRSEC under Grant No. DMR 05-20471.