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substrates. We compare the layer thickness dependency of the measured surface potential with ab initio density functional theory calculations of the work function for substrate-doped graphene. The ab initio calculations show that the work function of single- and bilayer graphene is mainly given by a variation of the Fermi energy with respect to the Dirac point energy as a function of doping, and that electrostatic interlayer screening only becomes relevant for thicker multilayer graphene. From the Raman G-line shift and the comparison of the Kelvin probe data with the ab initio calculations, we independently find an interlayer screening length in the order of four to five layers. Furthermore, we describe in-plane variations of the work function, which can be attributed to partial screening of charge impurities in the substrate, and result in a nonuniform charge density in single-layer graphene.

Variations in the work function of doped single- and few-layer graphene assessed by Kelvin probe force microscopy and density functional theory