Good practice guide on the electrical characterisation of graphene using contact methods

The electrical characterisation of graphene, either in plane sheets or in properly geometrised form can be approached using methods already employed for thin film materials. The extraordinary thinness (and, correspondingly, the volume) of graphene, however, makes the proper application of these methods difficult. The electrical properties of interest (sheet electrical resistivity/conductivity, concentration and mobility of charge carriers) must be indirectly derived from the measurement outcome by geometrical and electrical modelling; the assumptions behind such models (e.g., uniformity and isotropy, effective value of the applied fields, etc.) require careful consideration. The traceability of the measurement to the International System of units and a proper expression of measurement uncertainty is an issue. This guide focuses on contact methods, that is method where the graphene sample surface is physically contacted with metallic electrodes. A companion guide about non-contact and high-throughput methods is also available. The methods discussed are: the in-line four-point probe (4PP); the van der Pauw method (vdP) for sheet resistance measurement; the van der Pauw method for charge carrier mobility measurement; the electrical resistance tomography (ERT); the coplanar waveguide method (CPW). For each method, a corresponding measurement protocol is discussed, which describes: the measurement principle; sample requirements and preparation; a description of the measurement equipment / apparatus; calibration standards and ways to achieve a traceable measurement; environmental conditions to be considered; a detailed measurement procedure, with specific hints to achieve a reliable measurement; modeling and data analysis to determine the electrical property of interest; considerations about the expression of measurement uncertainty.