Local surface potential variations and charge puddling in graphene on SiC(0001)*

We performed Kelvin probe microscopy in ultra-high vacuum on epitaxial graphene grown on SiC(0001). In agreement with previous work, we see discrete surface potentials corresponding to interface layer and monolayer regions separated by steps of $\sim $100 mV. We used the step width to determine the spatial resolution of the probe to be approximately 20 nm. Within a monolayer area we see smaller fluctuations in surface potential of only a few mV. The data set limits on the scale of possible electron/hole puddles in monolayer graphene on SiC(0001).