Fig. 3

Electrical performance of hBN-encapsulated graphene device with FG via contacts. a Schematic of a hBN-encapsulated graphene device with FG via contacts and false-color cross-sectional HRTEM image of the FG via contact region (the scale bar is 5 nm). b Four-probe resistivity as a function of carrier density at room temperature. The right inset shows a Hall bar graphene device used for carrier mobility measurement (the scale bar is 5 μm). Right inset shows the electron (red) and hole (blue) mobilities extrapolated by applying the Drude model to the measured conductivity (σ = neμ, where σ, n, e, and μ are the sheet conductivity, carrier density, electron charge, and carrier mobility, respectively). Black dashed line shows the predicted intrinsic phonon limited mobility of graphene at room temperature²⁸. c Plot of total resistances of the graphene TLM device as a function of channel length, at fixed electron and hole carrier densities. The inset shows optical micrograph of the TLM device (the scale bar is 10 μm). d Contact resistances of the device as a function of carrier density and temperature. The inset shows contact resistances as a function of temperature and indicates no significant change in contact resistance. e Isosurfaces of the total charge densities at the interfaces between G–Cr, FG–Cr, G–Pd, and FG–Pd, calculated with DFT. The shortened atomic distances of C–F–Cr and C–F–Pd at the interfaces of FG–metal contacts lead to small contact resistance. This results because orbital overlap through a bridge of F facilitates charge transfer from metals to FG