Mapping the density of scattering centers limiting the electron mean free path in graphene

Recently, giant carrier mobility μ (>10(5) cm(2) V(-1) s(-1)) and micrometer electron mean free path (l) have been measured in suspended graphene or in graphene encapsulated between inert and ultraflat BN layers. Much lower μ values (10000-20000 cm(2) V(-1) s(-1)) are typically reported in graphene on common substrates (SiO(2), SiC) used for device fabrication. The debate on the factors limiting graphene electron mean free path is still open with charged impurities (CI) and resonant scatterers (RS) indicated as the most probable candidates. As a matter of fact, the inhomogeneous distribution of such scattering sources in graphene is responsible of nanoscale lateral inhomogeneities in the electronic properties, which could affect the behavior of graphene nanodevices. Hence, high resolution two-dimensional (2D) mapping of their density is very important. Here, we used scanning capacitance microscopy/spectroscopy to obtain 2D maps of l in graphene on substrates with different dielectric permittivities, that is, SiO(2) (κ(SiO2) = 3.9), 4H-SiC (0001) (κ(SiC) = 9.7) and the very-high-κ perovskite strontium titanate, SrTiO(3) (001), briefly STO (κ(STO) = 330). After measuring l versus the gate bias V(g) on an array of points on graphene, maps of the CI density (N(CI)) have been determined by the neutrality point shift from V(g) = 0 V in each curve, whereas maps of the RS density (N(RS)) have been extracted by fitting the dependence of l on the carrier density (n). Laterally inhomogeneous densities of CI and RS have been found. The RS distribution exhibits an average value ∼3 × 10(10) cm(-2) independently on the substrate. For the first time, a clear correlation between the minima in the l map and the maxima in the N(CI) map is obtained for graphene on SiO(2) and 4H-SiC, indicating that CI are the main source of the lateral inhomogeneity of l. On the contrary, the l and N(CI) maps are uncorrelated in graphene on STO, while a clear correlation is found between l and N(RS) maps. This demonstrates a very efficient dielectric screening of CI in graphene on STO and the role of RS as limiting factor for electron mean free path.