Landscape of Charge Puddles in Graphene Nanoribbons on Hexagonal Boron Nitride

Recently, graphene nanoribbons (GNRs) on hexagonal boron nitride (h-BN) substrates have been studied to develop high-mobility devices or devices based on a 1D Moiré superlattice. For this purpose, a device-level understanding of the charge-puddle landscape of a GNR/h-BN structure is needed when the charge puddles function as scattering sources for mobile charge carriers. Here, a puddle landscape is constructed on the basis of an analysis of the temperature dependencies of the conductance of GNR/h-BN devices at various gate-voltage values. For low-, intermediate-, and high-temperature regions near the charge-neutral point (CNP), the puddle size (50–200 nm), distance between neighboring puddles (40–170 nm), and potential depth of the puddles (in a range of 10 meV) in ∼100 nm wide GNR/h-BN devices are obtained on the basis of Coulomb blockade, 1D variable-range hopping, and thermally activated hopping, respectively. Based on the constructed puddle landscape, it is also concluded that the confinement-gap energy for an ∼100 nm wide GNR is similar to that of the thermal activation energy near the CNP in the GNRs. The constructed puddle landscape for GNR/h-BN devices is consistent with that obtained from scanning tunneling microscopy observations of graphene on an h-BN structure.