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Heterostructures from mechanically-assembled stacks of two-dimensional materials allow for versatile electronic device applications. Here, we demonstrate the intrinsic charge transport behaviors in graphene-black phosphorus heterojunction devices under different charge carrier densities and temperature regimes. At high carrier densities or in the ON state, tunneling through the Schottky barrier at the interface between graphene and black phosphorus dominates at low temperatures. With temperature increasing, the Schottky barrier at the interface is vanishing, and the channel current starts to decrease with increasing temperature, behaving like a metal. While at low carrier densities or in the OFF state, thermal emission over the Schottky barrier at the interface dominates the carriers transport process. A barrier height of ~ 67.3 meV can be extracted from the thermal emission-diffusion theory.

We report the direct measurements of conductivity and mobility in millimeter-sized single-crystalline graphene on SiO2/Si via van der Pauw geometry by using a home-designed four-probe scanning tunneling microscope (4P-STM). The gate-tunable conductivity and mobility are extracted from standard van der Pauw resistance measurements where the four STM probes contact the four peripheries of hexagonal graphene flakes, respectively. The high homogeneity of transport properties of the single-crystalline graphene flake is confirmed by comparing the extracted conductivities and mobilities from three setups with different geometry factors. Our studies provide a reliable solution for directly evaluating the entire electrical properties of graphene in a non-invasive way and could be extended to characterizing other two-dimensional materials.