Numerical study of inhomogeneity effects on Hall measurements of graphene films

• Hall mobility of inhomogeneous graphene was studied with 2-D numerical simulation.
• Fluctuation is controlled by location, size and amplitude of local inhomogeneity.
• Variations in mobility, Dirac point, device-to-device uniformity are demonstrated.
• Step edges are sources of inhomogeneity in epitaxial graphene on SiC.

This paper presents a two-dimensional model calculation of inhomogeneous graphene films which incorporates a random distribution of dopants (leading to electron and hole puddles) for analysis of Hall measurements. The model predicts significant effects of inhomogeneity on the Hall coefficient, which can lead to an underestimate of carrier mobility. We investigate the effect of parameters including size of puddles, local charge density deviation, and device sizes. The inhomogeneity of epitaxial graphene generated by steps and terraces of SiC substrates is also discussed. The simulation results quantify possible statistical errors in Hall mobility measurements, Dirac point estimation and non-uniformity of scaled devices over wafers.