a–c (Top) Net ion density i+(x, z) − i−(x, z) on the ionic liquid for a Vds = 0.5 V, b Vds = 2.5 V, and c Vds = 4 V. The gate voltage is fixed to Vgs = 1.5 V. (Bottom) Band profile of WSe2 and the metal. The Fermi-energy of the source contact is set to φmetal = 0. The dotted lines indicate the bottom of the conduction band, Ec (blue), and top of the valence band, Ev (red). The solid lines are the quasi-Fermi energy for electron φn(x) (blue) and hole φp(x) (red). d–f The extension view of the potential profile around the contacts (x = 7–13 nm and x = 87–93 nm) for d Vds = 0.5 V, e Vds = 2.5 V, and f Vds = 4 V. Black lines are the Fermi-level at the metal contacts. The arrows shows the transport direction of electrons (blue) and holes (red). The open arrows indicate the tunnel transport and the solid arrows denote the thermionic transport. The thicker arrows indicate the dominant paths of the current.