Quality assessment of graphene: Continuity,uniformity, and accuracy of mobility measurements

With the increasing availability of large-area graphene,the ability to rapidly and accurately assess the quality of the electrical properties has become critically important.For practical applications,spatial variability in carrier density and carrier mobility must be controlled and minimized.We present a simple framework for assessing the quality and homogeneity of large-area graphene devices.The field effect in both exfoliated graphene devices encapsulated in hexagonal boron nitride and chemical vapor-deposited (CVD) devices was measured in dual current-voltage configurations and used to derive a single,gate-dependent effective shape factor,β,for each device.β is a sensitive indicator of spatial homogeneity that can be obtained from samples of arbitrary shape.All 50 devices investigated in this study show a variation (up to tenfold) inβ as a function of the gate bias.Finite element simulations suggest that spatial doping inhomogeneity,rather than mobility inhomogeneity,is the primary cause of the gate dependence ofβ,and that measurable variations ofβ can be caused by doping variations as small as 1010 cm-2.Our results suggest that local variations in the position of the Dirac point alter the current flow and thus the effective sample shape as a function of the gate bias.We also found that such variations lead to systematic errors in carrier mobility calculations,which can be revealed by inspecting the correspondingβ factor.